0s autopkgtest [01:32:00]: starting date and time: 2024-03-24 01:32:00+0000 0s autopkgtest [01:32:00]: git checkout: 4a1cd702 l/adt_testbed: don't blame the testbed for unsolvable build deps 0s autopkgtest [01:32:00]: host juju-7f2275-prod-proposed-migration-environment-2; command line: /home/ubuntu/autopkgtest/runner/autopkgtest --output-dir /tmp/autopkgtest-work.h9w5c0vg/out --timeout-copy=6000 -a i386 --setup-commands /home/ubuntu/autopkgtest-cloud/worker-config-production/setup-canonical.sh --setup-commands /home/ubuntu/autopkgtest/setup-commands/setup-testbed --apt-pocket=proposed=src:r-base --apt-upgrade r-cran-systemfit --timeout-short=300 --timeout-copy=20000 --timeout-build=20000 --env=ADT_TEST_TRIGGERS=r-base/4.3.3-2build1 -- ssh -s /home/ubuntu/autopkgtest/ssh-setup/nova -- --flavor autopkgtest --security-groups autopkgtest-juju-7f2275-prod-proposed-migration-environment-2@lcy02-87.secgroup --name adt-noble-i386-r-cran-systemfit-20240324-013200-juju-7f2275-prod-proposed-migration-environment-2 --image adt/ubuntu-noble-amd64-server --keyname testbed-juju-7f2275-prod-proposed-migration-environment-2 --net-id=net_prod-proposed-migration -e TERM=linux -e ''"'"'http_proxy=http://squid.internal:3128'"'"'' -e ''"'"'https_proxy=http://squid.internal:3128'"'"'' -e ''"'"'no_proxy=127.0.0.1,127.0.1.1,login.ubuntu.com,localhost,localdomain,novalocal,internal,archive.ubuntu.com,ports.ubuntu.com,security.ubuntu.com,ddebs.ubuntu.com,changelogs.ubuntu.com,launchpadlibrarian.net,launchpadcontent.net,launchpad.net,10.24.0.0/24,keystone.ps5.canonical.com,objectstorage.prodstack5.canonical.com'"'"'' --mirror=http://ftpmaster.internal/ubuntu/ 65s autopkgtest [01:33:05]: testbed dpkg architecture: amd64 65s autopkgtest [01:33:05]: testbed apt version: 2.7.12 65s autopkgtest [01:33:05]: test architecture: i386 65s autopkgtest [01:33:05]: @@@@@@@@@@@@@@@@@@@@ test bed setup 66s Get:1 http://ftpmaster.internal/ubuntu noble-proposed InRelease [117 kB] 66s Get:2 http://ftpmaster.internal/ubuntu noble-proposed/multiverse Sources [56.9 kB] 66s Get:3 http://ftpmaster.internal/ubuntu noble-proposed/restricted Sources [6540 B] 66s Get:4 http://ftpmaster.internal/ubuntu noble-proposed/universe Sources [3988 kB] 66s Get:5 http://ftpmaster.internal/ubuntu noble-proposed/main Sources [494 kB] 66s Get:6 http://ftpmaster.internal/ubuntu noble-proposed/main i386 Packages [483 kB] 66s Get:7 http://ftpmaster.internal/ubuntu noble-proposed/main amd64 Packages [725 kB] 66s Get:8 http://ftpmaster.internal/ubuntu noble-proposed/main amd64 c-n-f Metadata [3508 B] 66s Get:9 http://ftpmaster.internal/ubuntu noble-proposed/restricted i386 Packages [6700 B] 66s Get:10 http://ftpmaster.internal/ubuntu noble-proposed/restricted amd64 Packages [30.5 kB] 66s Get:11 http://ftpmaster.internal/ubuntu noble-proposed/restricted amd64 c-n-f Metadata [116 B] 66s Get:12 http://ftpmaster.internal/ubuntu noble-proposed/universe amd64 Packages [4424 kB] 66s Get:13 http://ftpmaster.internal/ubuntu noble-proposed/universe i386 Packages [1306 kB] 66s Get:14 http://ftpmaster.internal/ubuntu noble-proposed/universe amd64 c-n-f Metadata [9396 B] 66s Get:15 http://ftpmaster.internal/ubuntu noble-proposed/multiverse amd64 Packages [96.1 kB] 66s Get:16 http://ftpmaster.internal/ubuntu noble-proposed/multiverse i386 Packages [27.1 kB] 66s Get:17 http://ftpmaster.internal/ubuntu noble-proposed/multiverse amd64 c-n-f Metadata [196 B] 69s Fetched 11.8 MB in 2s (7605 kB/s) 70s Reading package lists... 71s Reading package lists... 72s Building dependency tree... 72s Reading state information... 72s Calculating upgrade... 72s The following packages will be upgraded: 72s libc-bin libc6 locales 72s 3 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 72s Need to get 8176 kB of archives. 72s After this operation, 2048 B of additional disk space will be used. 72s Get:1 http://ftpmaster.internal/ubuntu noble/main amd64 libc6 amd64 2.39-0ubuntu6 [3262 kB] 72s Get:2 http://ftpmaster.internal/ubuntu noble/main amd64 libc-bin amd64 2.39-0ubuntu6 [682 kB] 72s Get:3 http://ftpmaster.internal/ubuntu noble/main amd64 locales all 2.39-0ubuntu6 [4232 kB] 73s Preconfiguring packages ... 73s Fetched 8176 kB in 0s (70.4 MB/s) 73s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 71864 files and directories currently installed.) 73s Preparing to unpack .../libc6_2.39-0ubuntu6_amd64.deb ... 73s Unpacking libc6:amd64 (2.39-0ubuntu6) over (2.39-0ubuntu2) ... 73s Setting up libc6:amd64 (2.39-0ubuntu6) ... 74s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 71864 files and directories currently installed.) 74s Preparing to unpack .../libc-bin_2.39-0ubuntu6_amd64.deb ... 74s Unpacking libc-bin (2.39-0ubuntu6) over (2.39-0ubuntu2) ... 74s Setting up libc-bin (2.39-0ubuntu6) ... 74s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 71864 files and directories currently installed.) 74s Preparing to unpack .../locales_2.39-0ubuntu6_all.deb ... 74s Unpacking locales (2.39-0ubuntu6) over (2.39-0ubuntu2) ... 74s Setting up locales (2.39-0ubuntu6) ... 75s Generating locales (this might take a while)... 76s en_US.UTF-8... done 76s Generation complete. 76s Processing triggers for man-db (2.12.0-3) ... 78s Reading package lists... 78s Building dependency tree... 78s Reading state information... 78s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 79s sh: Attempting to set up Debian/Ubuntu apt sources automatically 79s sh: Distribution appears to be Ubuntu 79s Reading package lists... 80s Building dependency tree... 80s Reading state information... 80s eatmydata is already the newest version (131-1). 80s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 80s Reading package lists... 80s Building dependency tree... 80s Reading state information... 81s dbus is already the newest version (1.14.10-4ubuntu1). 81s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 81s Reading package lists... 81s Building dependency tree... 81s Reading state information... 81s rng-tools-debian is already the newest version (2.4). 81s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 81s Reading package lists... 82s Building dependency tree... 82s Reading state information... 82s The following packages will be REMOVED: 82s cloud-init* python3-configobj* python3-debconf* 82s 0 upgraded, 0 newly installed, 3 to remove and 0 not upgraded. 82s After this operation, 3256 kB disk space will be freed. 82s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 71864 files and directories currently installed.) 82s Removing cloud-init (24.1.2-0ubuntu1) ... 83s Removing python3-configobj (5.0.8-3) ... 83s Removing python3-debconf (1.5.86) ... 83s Processing triggers for man-db (2.12.0-3) ... 83s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 71475 files and directories currently installed.) 83s Purging configuration files for cloud-init (24.1.2-0ubuntu1) ... 84s dpkg: warning: while removing cloud-init, directory '/etc/cloud/cloud.cfg.d' not empty so not removed 84s Processing triggers for rsyslog (8.2312.0-3ubuntu3) ... 84s invoke-rc.d: policy-rc.d denied execution of try-restart. 84s Reading package lists... 84s Building dependency tree... 84s Reading state information... 85s linux-generic is already the newest version (6.8.0-11.11+1). 85s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 85s Hit:1 http://ftpmaster.internal/ubuntu noble InRelease 85s Hit:2 http://ftpmaster.internal/ubuntu noble-updates InRelease 85s Hit:3 http://ftpmaster.internal/ubuntu noble-security InRelease 87s Reading package lists... 87s Reading package lists... 87s Building dependency tree... 87s Reading state information... 87s Calculating upgrade... 87s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 87s Reading package lists... 88s Building dependency tree... 88s Reading state information... 88s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 88s autopkgtest [01:33:28]: rebooting testbed after setup commands that affected boot 269s autopkgtest [01:36:29]: testbed running kernel: Linux 6.8.0-11-generic #11-Ubuntu SMP PREEMPT_DYNAMIC Wed Feb 14 00:29:05 UTC 2024 270s autopkgtest [01:36:30]: @@@@@@@@@@@@@@@@@@@@ apt-source r-cran-systemfit 271s Get:1 http://ftpmaster.internal/ubuntu noble/universe r-cran-systemfit 1.1-30-1 (dsc) [2203 B] 271s Get:2 http://ftpmaster.internal/ubuntu noble/universe r-cran-systemfit 1.1-30-1 (tar) [1040 kB] 271s Get:3 http://ftpmaster.internal/ubuntu noble/universe r-cran-systemfit 1.1-30-1 (diff) [2516 B] 271s gpgv: Signature made Wed Jun 28 12:43:54 2023 UTC 271s gpgv: using RSA key F1F007320A035541F0A663CA578A0494D1C646D1 271s gpgv: issuer "tille@debian.org" 271s gpgv: Can't check signature: No public key 271s dpkg-source: warning: cannot verify inline signature for ./r-cran-systemfit_1.1-30-1.dsc: no acceptable signature found 271s autopkgtest [01:36:31]: testing package r-cran-systemfit version 1.1-30-1 271s autopkgtest [01:36:31]: build not needed 273s autopkgtest [01:36:33]: test run-unit-test: preparing testbed 277s Note, using file '/tmp/autopkgtest.isQjql/1-autopkgtest-satdep.dsc' to get the build dependencies 277s Reading package lists... 277s Building dependency tree... 277s Reading state information... 278s Starting pkgProblemResolver with broken count: 0 278s Starting 2 pkgProblemResolver with broken count: 0 278s Done 278s The following NEW packages will be installed: 278s build-essential cpp cpp-13 cpp-13-x86-64-linux-gnu cpp-x86-64-linux-gnu 278s fontconfig fontconfig-config fonts-dejavu-core fonts-dejavu-mono 278s fonts-glyphicons-halflings fonts-mathjax g++ g++-13 g++-13-x86-64-linux-gnu 278s g++-x86-64-linux-gnu gcc gcc-13 gcc-13-x86-64-linux-gnu gcc-x86-64-linux-gnu 278s libasan8 libatomic1 libblas3 libc-dev-bin libc6-dev libcairo2 libcc1-0 278s libcrypt-dev libdatrie1 libdeflate0 libfontconfig1 libgcc-13-dev 278s libgfortran5 libgomp1 libgraphite2-3 libharfbuzz0b libhwasan0 libice6 278s libisl23 libitm1 libjbig0 libjpeg-turbo8 libjpeg8 libjs-bootstrap 278s libjs-highlight.js libjs-jquery libjs-jquery-datatables libjs-mathjax 278s liblapack3 liblerc4 liblsan0 libmpc3 libnlopt0 libpango-1.0-0 278s libpangocairo-1.0-0 libpangoft2-1.0-0 libpaper-utils libpaper1 libpixman-1-0 278s libquadmath0 libsharpyuv0 libsm6 libstdc++-13-dev libtcl8.6 libthai-data 278s libthai0 libtiff6 libtk8.6 libtsan2 libubsan1 libwebp7 libxcb-render0 278s libxcb-shm0 libxft2 libxrender1 libxss1 libxt6 linux-libc-dev littler 278s node-normalize.css r-base-core r-cran-abind r-cran-backports 278s r-cran-bdsmatrix r-cran-bit r-cran-bit64 r-cran-boot r-cran-brio 278s r-cran-broom r-cran-callr r-cran-car r-cran-cardata r-cran-caret 278s r-cran-cellranger r-cran-class r-cran-cli r-cran-clipr r-cran-clock 278s r-cran-codetools r-cran-collapse r-cran-colorspace r-cran-conquer 278s r-cran-cpp11 r-cran-crayon r-cran-curl r-cran-data.table r-cran-desc 278s r-cran-diagram r-cran-diffobj r-cran-digest r-cran-dplyr r-cran-e1071 278s r-cran-ellipsis r-cran-evaluate r-cran-fansi r-cran-farver r-cran-forcats 278s r-cran-foreach r-cran-foreign r-cran-formula r-cran-fs r-cran-future 278s r-cran-future.apply r-cran-generics r-cran-ggplot2 r-cran-globals 278s r-cran-glue r-cran-gower r-cran-gtable r-cran-hardhat r-cran-haven 278s r-cran-highr r-cran-hms r-cran-ipred r-cran-isoband r-cran-iterators 278s r-cran-jsonlite r-cran-kernsmooth r-cran-knitr r-cran-labeling 278s r-cran-lattice r-cran-lava r-cran-lifecycle r-cran-listenv r-cran-littler 278s r-cran-lme4 r-cran-lmtest r-cran-lubridate r-cran-magrittr r-cran-maptools 278s r-cran-mass r-cran-matrix r-cran-matrixmodels r-cran-matrixstats 278s r-cran-maxlik r-cran-mgcv r-cran-minqa r-cran-misctools r-cran-modelmetrics 278s r-cran-munsell r-cran-nlme r-cran-nloptr r-cran-nnet r-cran-numderiv 278s r-cran-openxlsx r-cran-parallelly r-cran-pbkrtest r-cran-pillar 278s r-cran-pkgbuild r-cran-pkgconfig r-cran-pkgkitten r-cran-pkgload r-cran-plm 278s r-cran-plyr r-cran-praise r-cran-prettyunits r-cran-proc r-cran-processx 278s r-cran-prodlim r-cran-progress r-cran-progressr r-cran-proxy r-cran-ps 278s r-cran-purrr r-cran-quantreg r-cran-r.methodss3 r-cran-r.oo r-cran-r.utils 278s r-cran-r6 r-cran-rbibutils r-cran-rcolorbrewer r-cran-rcpp 278s r-cran-rcpparmadillo r-cran-rcppeigen r-cran-rdpack r-cran-readr 278s r-cran-readxl r-cran-recipes r-cran-rematch r-cran-rematch2 r-cran-reshape2 278s r-cran-rio r-cran-rlang r-cran-rpart r-cran-rprojroot r-cran-sandwich 278s r-cran-scales r-cran-shape r-cran-sp r-cran-sparsem r-cran-squarem 278s r-cran-statmod r-cran-stringi r-cran-stringr r-cran-survival 278s r-cran-systemfit r-cran-testthat r-cran-tibble r-cran-tidyr 278s r-cran-tidyselect r-cran-timechange r-cran-timedate r-cran-tzdb r-cran-utf8 278s r-cran-vctrs r-cran-viridislite r-cran-vroom r-cran-waldo r-cran-withr 278s r-cran-writexl r-cran-xfun r-cran-yaml r-cran-zip r-cran-zoo rpcsvc-proto 278s unzip x11-common xdg-utils zip 278s 0 upgraded, 238 newly installed, 0 to remove and 0 not upgraded. 278s Need to get 229 MB of archives. 278s After this operation, 577 MB of additional disk space will be used. 278s Get:1 http://ftpmaster.internal/ubuntu noble/main amd64 libc-dev-bin amd64 2.39-0ubuntu6 [20.4 kB] 278s Get:2 http://ftpmaster.internal/ubuntu noble/main amd64 linux-libc-dev amd64 6.8.0-11.11 [1595 kB] 278s Get:3 http://ftpmaster.internal/ubuntu noble/main amd64 libcrypt-dev amd64 1:4.4.36-4 [128 kB] 278s Get:4 http://ftpmaster.internal/ubuntu noble/main amd64 rpcsvc-proto amd64 1.4.2-0ubuntu6 [68.5 kB] 278s Get:5 http://ftpmaster.internal/ubuntu noble/main amd64 libc6-dev amd64 2.39-0ubuntu6 [2126 kB] 278s Get:6 http://ftpmaster.internal/ubuntu noble/main amd64 libisl23 amd64 0.26-3 [741 kB] 278s Get:7 http://ftpmaster.internal/ubuntu noble/main amd64 libmpc3 amd64 1.3.1-1 [54.1 kB] 278s Get:8 http://ftpmaster.internal/ubuntu noble/main amd64 cpp-13-x86-64-linux-gnu amd64 13.2.0-17ubuntu2 [11.2 MB] 278s Get:9 http://ftpmaster.internal/ubuntu noble/main amd64 cpp-13 amd64 13.2.0-17ubuntu2 [1030 B] 278s Get:10 http://ftpmaster.internal/ubuntu noble/main amd64 cpp-x86-64-linux-gnu amd64 4:13.2.0-7ubuntu1 [5326 B] 278s Get:11 http://ftpmaster.internal/ubuntu noble/main amd64 cpp amd64 4:13.2.0-7ubuntu1 [22.4 kB] 278s Get:12 http://ftpmaster.internal/ubuntu noble/main amd64 libcc1-0 amd64 14-20240303-1ubuntu1 [47.7 kB] 278s Get:13 http://ftpmaster.internal/ubuntu noble/main amd64 libgomp1 amd64 14-20240303-1ubuntu1 [147 kB] 278s Get:14 http://ftpmaster.internal/ubuntu noble/main amd64 libitm1 amd64 14-20240303-1ubuntu1 [29.1 kB] 278s Get:15 http://ftpmaster.internal/ubuntu noble/main amd64 libatomic1 amd64 14-20240303-1ubuntu1 [10.4 kB] 278s Get:16 http://ftpmaster.internal/ubuntu noble/main amd64 libasan8 amd64 14-20240303-1ubuntu1 [3026 kB] 278s Get:17 http://ftpmaster.internal/ubuntu noble/main amd64 liblsan0 amd64 14-20240303-1ubuntu1 [1310 kB] 278s Get:18 http://ftpmaster.internal/ubuntu noble/main amd64 libtsan2 amd64 14-20240303-1ubuntu1 [2732 kB] 278s Get:19 http://ftpmaster.internal/ubuntu noble/main amd64 libubsan1 amd64 14-20240303-1ubuntu1 [1172 kB] 278s Get:20 http://ftpmaster.internal/ubuntu noble/main amd64 libhwasan0 amd64 14-20240303-1ubuntu1 [1629 kB] 278s Get:21 http://ftpmaster.internal/ubuntu noble/main amd64 libquadmath0 amd64 14-20240303-1ubuntu1 [155 kB] 278s Get:22 http://ftpmaster.internal/ubuntu noble/main amd64 libgcc-13-dev amd64 13.2.0-17ubuntu2 [2687 kB] 278s Get:23 http://ftpmaster.internal/ubuntu noble/main amd64 gcc-13-x86-64-linux-gnu amd64 13.2.0-17ubuntu2 [21.9 MB] 279s Get:24 http://ftpmaster.internal/ubuntu noble/main amd64 gcc-13 amd64 13.2.0-17ubuntu2 [477 kB] 279s Get:25 http://ftpmaster.internal/ubuntu noble/main amd64 gcc-x86-64-linux-gnu amd64 4:13.2.0-7ubuntu1 [1212 B] 279s Get:26 http://ftpmaster.internal/ubuntu noble/main amd64 gcc amd64 4:13.2.0-7ubuntu1 [5018 B] 279s Get:27 http://ftpmaster.internal/ubuntu noble/main amd64 libstdc++-13-dev amd64 13.2.0-17ubuntu2 [2340 kB] 279s Get:28 http://ftpmaster.internal/ubuntu noble/main amd64 g++-13-x86-64-linux-gnu amd64 13.2.0-17ubuntu2 [12.5 MB] 279s Get:29 http://ftpmaster.internal/ubuntu noble/main amd64 g++-13 amd64 13.2.0-17ubuntu2 [14.5 kB] 279s Get:30 http://ftpmaster.internal/ubuntu noble/main amd64 g++-x86-64-linux-gnu amd64 4:13.2.0-7ubuntu1 [964 B] 279s Get:31 http://ftpmaster.internal/ubuntu noble/main amd64 g++ amd64 4:13.2.0-7ubuntu1 [1100 B] 279s Get:32 http://ftpmaster.internal/ubuntu noble/main amd64 build-essential amd64 12.10ubuntu1 [4928 B] 279s Get:33 http://ftpmaster.internal/ubuntu noble/main amd64 fonts-dejavu-mono all 2.37-8 [502 kB] 279s Get:34 http://ftpmaster.internal/ubuntu noble/main amd64 fonts-dejavu-core all 2.37-8 [835 kB] 279s Get:35 http://ftpmaster.internal/ubuntu noble/main amd64 fontconfig-config amd64 2.15.0-1ubuntu1 [36.9 kB] 279s Get:36 http://ftpmaster.internal/ubuntu noble/main amd64 libfontconfig1 amd64 2.15.0-1ubuntu1 [139 kB] 279s Get:37 http://ftpmaster.internal/ubuntu noble/main amd64 fontconfig amd64 2.15.0-1ubuntu1 [180 kB] 279s Get:38 http://ftpmaster.internal/ubuntu noble/universe amd64 fonts-glyphicons-halflings all 1.009~3.4.1+dfsg-3 [118 kB] 279s Get:39 http://ftpmaster.internal/ubuntu noble/main amd64 fonts-mathjax all 2.7.9+dfsg-1 [2208 kB] 279s Get:40 http://ftpmaster.internal/ubuntu noble/main amd64 libblas3 amd64 3.12.0-3 [238 kB] 279s Get:41 http://ftpmaster.internal/ubuntu noble/main amd64 libpixman-1-0 amd64 0.42.2-1 [268 kB] 279s Get:42 http://ftpmaster.internal/ubuntu noble/main amd64 libxcb-render0 amd64 1.15-1 [16.3 kB] 279s Get:43 http://ftpmaster.internal/ubuntu noble/main amd64 libxcb-shm0 amd64 1.15-1 [5740 B] 279s Get:44 http://ftpmaster.internal/ubuntu noble/main amd64 libxrender1 amd64 1:0.9.10-1.1 [20.0 kB] 279s Get:45 http://ftpmaster.internal/ubuntu noble/main amd64 libcairo2 amd64 1.18.0-1 [572 kB] 279s Get:46 http://ftpmaster.internal/ubuntu noble/main amd64 libdatrie1 amd64 0.2.13-3 [20.9 kB] 279s Get:47 http://ftpmaster.internal/ubuntu noble/main amd64 libdeflate0 amd64 1.19-1 [43.7 kB] 279s Get:48 http://ftpmaster.internal/ubuntu noble/main amd64 libgfortran5 amd64 14-20240303-1ubuntu1 [924 kB] 279s Get:49 http://ftpmaster.internal/ubuntu noble/main amd64 libgraphite2-3 amd64 1.3.14-2 [83.1 kB] 279s Get:50 http://ftpmaster.internal/ubuntu noble/main amd64 libharfbuzz0b amd64 8.3.0-2 [469 kB] 279s Get:51 http://ftpmaster.internal/ubuntu noble/main amd64 x11-common all 1:7.7+23ubuntu2 [23.4 kB] 279s Get:52 http://ftpmaster.internal/ubuntu noble/main amd64 libice6 amd64 2:1.0.10-1build2 [42.6 kB] 279s Get:53 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg-turbo8 amd64 2.1.5-2ubuntu1 [147 kB] 279s Get:54 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg8 amd64 8c-2ubuntu11 [2148 B] 279s Get:55 http://ftpmaster.internal/ubuntu noble/universe amd64 libjs-bootstrap all 3.4.1+dfsg-3 [129 kB] 279s Get:56 http://ftpmaster.internal/ubuntu noble/universe amd64 libjs-highlight.js all 9.18.5+dfsg1-2 [385 kB] 279s Get:57 http://ftpmaster.internal/ubuntu noble/main amd64 libjs-jquery all 3.6.1+dfsg+~3.5.14-1 [328 kB] 279s Get:58 http://ftpmaster.internal/ubuntu noble/universe amd64 libjs-jquery-datatables all 1.11.5+dfsg-2 [146 kB] 279s Get:59 http://ftpmaster.internal/ubuntu noble/main amd64 liblapack3 amd64 3.12.0-3 [2649 kB] 279s Get:60 http://ftpmaster.internal/ubuntu noble/main amd64 liblerc4 amd64 4.0.0+ds-4ubuntu1 [184 kB] 279s Get:61 http://ftpmaster.internal/ubuntu noble/main amd64 libthai-data all 0.1.29-2 [158 kB] 279s Get:62 http://ftpmaster.internal/ubuntu noble/main amd64 libthai0 amd64 0.1.29-2 [18.8 kB] 279s Get:63 http://ftpmaster.internal/ubuntu noble/main amd64 libpango-1.0-0 amd64 1.51.0+ds-4 [228 kB] 279s Get:64 http://ftpmaster.internal/ubuntu noble/main amd64 libpangoft2-1.0-0 amd64 1.51.0+ds-4 [42.1 kB] 279s Get:65 http://ftpmaster.internal/ubuntu noble/main amd64 libpangocairo-1.0-0 amd64 1.51.0+ds-4 [29.0 kB] 279s Get:66 http://ftpmaster.internal/ubuntu noble/main amd64 libpaper1 amd64 1.1.29 [13.4 kB] 279s Get:67 http://ftpmaster.internal/ubuntu noble/main amd64 libpaper-utils amd64 1.1.29 [8658 B] 279s Get:68 http://ftpmaster.internal/ubuntu noble/main amd64 libsharpyuv0 amd64 1.3.2-0.4 [15.6 kB] 279s Get:69 http://ftpmaster.internal/ubuntu noble/main amd64 libsm6 amd64 2:1.2.3-1build2 [16.7 kB] 279s Get:70 http://ftpmaster.internal/ubuntu noble/main amd64 libtcl8.6 amd64 8.6.13+dfsg-2 [984 kB] 279s Get:71 http://ftpmaster.internal/ubuntu noble/main amd64 libjbig0 amd64 2.1-6.1ubuntu1 [29.3 kB] 279s Get:72 http://ftpmaster.internal/ubuntu noble/main amd64 libwebp7 amd64 1.3.2-0.4 [230 kB] 279s Get:73 http://ftpmaster.internal/ubuntu noble/main amd64 libtiff6 amd64 4.5.1+git230720-3ubuntu1 [232 kB] 279s Get:74 http://ftpmaster.internal/ubuntu noble/main amd64 libxft2 amd64 2.3.6-1 [44.5 kB] 279s Get:75 http://ftpmaster.internal/ubuntu noble/main amd64 libxss1 amd64 1:1.2.3-1build2 [8476 B] 279s Get:76 http://ftpmaster.internal/ubuntu noble/main amd64 libtk8.6 amd64 8.6.14-1 [779 kB] 279s Get:77 http://ftpmaster.internal/ubuntu noble/main amd64 libxt6 amd64 1:1.2.1-1.1 [173 kB] 279s Get:78 http://ftpmaster.internal/ubuntu noble/main amd64 zip amd64 3.0-13 [176 kB] 279s Get:79 http://ftpmaster.internal/ubuntu noble/main amd64 unzip amd64 6.0-28ubuntu3 [174 kB] 279s Get:80 http://ftpmaster.internal/ubuntu noble/main amd64 xdg-utils all 1.1.3-4.1ubuntu3 [62.0 kB] 279s Get:81 http://ftpmaster.internal/ubuntu noble/universe amd64 r-base-core amd64 4.3.2-1build1 [27.0 MB] 279s Get:82 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-littler amd64 0.3.19-1 [94.1 kB] 279s Get:83 http://ftpmaster.internal/ubuntu noble/universe amd64 littler all 0.3.19-1 [2472 B] 279s Get:84 http://ftpmaster.internal/ubuntu noble/universe amd64 node-normalize.css all 8.0.1-5 [10.8 kB] 279s Get:85 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-abind all 1.4-5-2 [63.6 kB] 279s Get:86 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-backports amd64 1.4.1-1 [101 kB] 279s Get:87 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-bdsmatrix amd64 1.3-6-1 [293 kB] 279s Get:88 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-bit amd64 4.0.5-1 [1063 kB] 279s Get:89 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-bit64 amd64 4.0.5-1 [465 kB] 279s Get:90 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-boot all 1.3-30-1 [619 kB] 279s Get:91 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-brio amd64 1.1.4-1 [37.9 kB] 279s Get:92 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-cli amd64 3.6.2-1 [1380 kB] 279s Get:93 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-generics all 0.1.3-1 [81.3 kB] 279s Get:94 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-glue amd64 1.7.0-1 [154 kB] 279s Get:95 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rlang amd64 1.1.3-1 [1663 kB] 279s Get:96 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lifecycle all 1.0.4+dfsg-1 [110 kB] 279s Get:97 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-magrittr amd64 2.0.3-1 [154 kB] 279s Get:98 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-fansi amd64 1.0.5-1 [619 kB] 279s Get:99 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-utf8 amd64 1.2.4-1 [140 kB] 279s Get:100 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-vctrs amd64 0.6.5-1 [1335 kB] 279s Get:101 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pillar all 1.9.0+dfsg-1 [464 kB] 279s Get:102 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-r6 all 2.5.1-1 [99.0 kB] 279s Get:103 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pkgconfig all 2.0.3-2build1 [19.7 kB] 279s Get:104 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-tibble amd64 3.2.1+dfsg-2 [415 kB] 279s Get:105 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-withr all 2.5.0-1 [225 kB] 279s Get:106 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-tidyselect amd64 1.2.0+dfsg-1 [218 kB] 279s Get:107 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-dplyr amd64 1.1.4-1 [1515 kB] 279s Get:108 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-ellipsis amd64 0.3.2-2 [35.6 kB] 279s Get:109 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-purrr amd64 1.0.2-1 [502 kB] 279s Get:110 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-stringi amd64 1.8.3-1 [873 kB] 279s Get:111 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-stringr all 1.5.1-1 [290 kB] 279s Get:112 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-cpp11 all 0.4.7-1 [266 kB] 279s Get:113 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-tidyr amd64 1.3.1-1 [1156 kB] 279s Get:114 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-broom all 1.0.5+dfsg-1 [1729 kB] 279s Get:115 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-ps amd64 1.7.6-1 [313 kB] 279s Get:116 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-processx amd64 3.8.3-1 [346 kB] 279s Get:117 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-callr all 3.7.3-2 [425 kB] 279s Get:118 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-cardata all 3.0.5-1 [1819 kB] 279s Get:119 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-mass amd64 7.3-60.0.1-1 [1119 kB] 279s Get:120 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lattice amd64 0.22-5-1 [1342 kB] 279s Get:121 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-nlme amd64 3.1.164-1 [2260 kB] 279s Get:122 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-matrix amd64 1.6-5-1 [3830 kB] 279s Get:123 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-mgcv amd64 1.9-1-1 [3252 kB] 279s Get:124 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-nnet amd64 7.3-19-2 [112 kB] 279s Get:125 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pkgkitten all 0.2.3-1 [25.1 kB] 279s Get:126 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rcpp amd64 1.0.12-1 [1981 kB] 279s Get:127 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-minqa amd64 1.2.6-1 [116 kB] 279s Get:128 http://ftpmaster.internal/ubuntu noble/universe amd64 libnlopt0 amd64 2.7.1-5build2 [184 kB] 279s Get:129 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-desc all 1.4.3-1 [359 kB] 279s Get:130 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-digest amd64 0.6.34-1 [186 kB] 279s Get:131 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-evaluate all 0.23-1 [90.2 kB] 279s Get:132 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-jsonlite amd64 1.8.8+dfsg-1 [441 kB] 279s Get:133 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-crayon all 1.5.2-1 [164 kB] 279s Get:134 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-fs amd64 1.6.3+dfsg-1 [229 kB] 279s Get:135 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pkgbuild all 1.4.3-1 [209 kB] 279s Get:136 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rprojroot all 2.0.4-1 [124 kB] 279s Get:137 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pkgload all 1.3.4-1 [207 kB] 279s Get:138 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-praise all 1.0.0-4build1 [20.3 kB] 279s Get:139 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-diffobj amd64 0.3.5-1 [1117 kB] 279s Get:140 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rematch2 all 2.1.2-2build1 [46.5 kB] 279s Get:141 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-waldo all 0.5.2-1build1 [120 kB] 279s Get:142 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-testthat amd64 3.2.1-1 [1684 kB] 279s Get:143 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-nloptr amd64 2.0.3-1 [381 kB] 279s Get:144 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rcppeigen amd64 0.3.3.9.4-1 [1189 kB] 279s Get:145 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-statmod amd64 1.5.0-1 [295 kB] 279s Get:146 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lme4 amd64 1.1-35.1-4 [4138 kB] 279s Get:147 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-numderiv all 2016.8-1.1-3 [115 kB] 279s Get:148 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-xfun amd64 0.41+dfsg-1 [415 kB] 279s Get:149 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-highr all 0.10+dfsg-1 [38.3 kB] 279s Get:150 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-yaml amd64 2.3.8-1 [108 kB] 279s Get:151 http://ftpmaster.internal/ubuntu noble/main amd64 libjs-mathjax all 2.7.9+dfsg-1 [5665 kB] 279s Get:152 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-knitr all 1.45+dfsg-1 [917 kB] 279s Get:153 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pbkrtest all 0.5.2-2 [182 kB] 279s Get:154 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-sparsem amd64 1.81-1 [905 kB] 279s Get:155 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-matrixmodels all 0.5-3-1 [361 kB] 279s Get:156 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-survival amd64 3.5-8-1 [6120 kB] 279s Get:157 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-matrixstats amd64 1.2.0-1 [488 kB] 279s Get:158 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rcpparmadillo amd64 0.12.8.0.0-1 [862 kB] 279s Get:159 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-gtable all 0.3.4+dfsg-1 [191 kB] 279s Get:160 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-isoband amd64 0.2.7-1 [1481 kB] 279s Get:161 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-farver amd64 2.1.1-1 [1353 kB] 280s Get:162 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-labeling all 0.4.3-1 [62.1 kB] 280s Get:163 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-colorspace amd64 2.1-0+dfsg-1 [1541 kB] 280s Get:164 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-munsell all 0.5.0-2build1 [208 kB] 280s Get:165 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rcolorbrewer all 1.1-3-1build1 [55.4 kB] 280s Get:166 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-viridislite all 0.4.2-2 [1088 kB] 280s Get:167 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-scales all 1.3.0-1 [603 kB] 280s Get:168 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-ggplot2 all 3.4.4+dfsg-1 [3411 kB] 280s Get:169 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-class amd64 7.3-22-2 [88.3 kB] 280s Get:170 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-proxy amd64 0.4-27-1 [182 kB] 280s Get:171 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-e1071 amd64 1.7-14-1 [558 kB] 280s Get:172 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-codetools all 0.2-19-1 [90.5 kB] 280s Get:173 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-iterators all 1.0.14-1 [336 kB] 280s Get:174 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-foreach all 1.5.2-1 [124 kB] 281s Get:175 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-data.table amd64 1.14.10+dfsg-1 [1837 kB] 282s Get:176 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-modelmetrics amd64 1.2.2.2-1build1 [128 kB] 282s Get:177 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-plyr amd64 1.8.9-1 [832 kB] 282s Get:178 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-proc amd64 1.18.5-1 [966 kB] 282s Get:179 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-tzdb amd64 0.4.0-2 [521 kB] 282s Get:180 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-clock amd64 0.7.0-1.1 [1765 kB] 282s Get:181 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-gower amd64 1.0.1-1 [207 kB] 282s Get:182 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-hardhat all 1.3.1+dfsg-1 [554 kB] 282s Get:183 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rpart amd64 4.1.23-1 [661 kB] 282s Get:184 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-shape all 1.4.6-1 [770 kB] 282s Get:185 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-diagram all 1.6.5-2 [656 kB] 282s Get:186 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-kernsmooth amd64 2.23-22-1 [91.7 kB] 282s Get:187 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-globals all 0.16.2-1 [117 kB] 282s Get:188 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-listenv all 0.9.1+dfsg-1 [112 kB] 282s Get:189 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-parallelly amd64 1.37.1-1 [365 kB] 282s Get:190 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-future all 1.33.1+dfsg-1 [634 kB] 282s Get:191 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-future.apply all 1.11.1+dfsg-1 [171 kB] 282s Get:192 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-progressr all 0.14.0-1 [338 kB] 282s Get:193 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-squarem all 2021.1-1 [179 kB] 282s Get:194 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lava all 1.7.3+dfsg-1 [2166 kB] 282s Get:195 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-prodlim amd64 2023.08.28-1 [408 kB] 282s Get:196 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-ipred amd64 0.9-14-1 [383 kB] 282s Get:197 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-timechange amd64 0.3.0-1 [178 kB] 282s Get:198 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lubridate amd64 1.9.3+dfsg-1 [1010 kB] 282s Get:199 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-timedate amd64 4032.109-1 [1229 kB] 282s Get:200 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-recipes all 1.0.9+dfsg-1 [1964 kB] 282s Get:201 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-reshape2 amd64 1.4.4-2build1 [114 kB] 282s Get:202 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-caret amd64 6.0-94+dfsg-1 [3434 kB] 282s Get:203 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-conquer amd64 1.3.3-1 [499 kB] 282s Get:204 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-quantreg amd64 5.97-1 [1533 kB] 282s Get:205 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-sp amd64 1:2.1-2+dfsg-1 [1447 kB] 282s Get:206 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-foreign amd64 0.8.86-1 [242 kB] 282s Get:207 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-maptools amd64 1:1.1-8+dfsg-1 [1365 kB] 282s Get:208 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-forcats all 1.0.0-1 [369 kB] 282s Get:209 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-hms all 1.1.3-1 [96.5 kB] 282s Get:210 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-clipr all 0.8.0-1 [53.5 kB] 282s Get:211 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-prettyunits all 1.2.0-1 [162 kB] 282s Get:212 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-progress all 1.2.3-1 [91.9 kB] 282s Get:213 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-vroom amd64 1.6.5-1 [848 kB] 282s Get:214 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-readr amd64 2.1.5-1 [766 kB] 282s Get:215 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-haven amd64 2.5.4-1 [346 kB] 282s Get:216 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-curl amd64 5.2.0+dfsg-1 [188 kB] 282s Get:217 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rematch all 2.0.0-1 [18.3 kB] 282s Get:218 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-cellranger all 1.1.0-3 [102 kB] 282s Get:219 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-readxl amd64 1.4.3-1 [736 kB] 282s Get:220 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-writexl amd64 1.5.0-1 [157 kB] 282s Get:221 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-r.methodss3 all 1.8.2-1 [84.0 kB] 282s Get:222 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-r.oo all 1.26.0-1 [955 kB] 282s Get:223 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-r.utils all 2.12.3-1 [1386 kB] 282s Get:224 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-zip amd64 2.3.1-1 [123 kB] 282s Get:225 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-openxlsx amd64 4.2.5.2-1 [1943 kB] 282s Get:226 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rio all 1.0.1-1 [529 kB] 282s Get:227 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-car all 3.1-2-2 [1692 kB] 282s Get:228 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-collapse amd64 2.0.10-1 [3112 kB] 282s Get:229 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-formula all 1.2-5-1 [158 kB] 282s Get:230 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-zoo amd64 1.8-12-2 [984 kB] 282s Get:231 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lmtest amd64 0.9.40-1 [396 kB] 282s Get:232 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-misctools all 0.6-28-1 [99.9 kB] 282s Get:233 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-sandwich all 3.1-0-1 [1484 kB] 282s Get:234 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-maxlik all 1.5-2-1 [1550 kB] 282s Get:235 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rbibutils amd64 2.2.16-1 [754 kB] 282s Get:236 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rdpack all 2.6-1 [742 kB] 282s Get:237 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-plm all 2.6-3-1 [2141 kB] 282s Get:238 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-systemfit all 1.1-30-1 [1174 kB] 283s Preconfiguring packages ... 283s Fetched 229 MB in 4s (60.0 MB/s) 283s Selecting previously unselected package libc-dev-bin. 283s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 71420 files and directories currently installed.) 283s Preparing to unpack .../000-libc-dev-bin_2.39-0ubuntu6_amd64.deb ... 283s Unpacking libc-dev-bin (2.39-0ubuntu6) ... 283s Selecting previously unselected package linux-libc-dev:amd64. 283s Preparing to unpack .../001-linux-libc-dev_6.8.0-11.11_amd64.deb ... 283s Unpacking linux-libc-dev:amd64 (6.8.0-11.11) ... 283s Selecting previously unselected package libcrypt-dev:amd64. 283s Preparing to unpack .../002-libcrypt-dev_1%3a4.4.36-4_amd64.deb ... 283s Unpacking libcrypt-dev:amd64 (1:4.4.36-4) ... 283s Selecting previously unselected package rpcsvc-proto. 283s Preparing to unpack .../003-rpcsvc-proto_1.4.2-0ubuntu6_amd64.deb ... 283s Unpacking rpcsvc-proto (1.4.2-0ubuntu6) ... 283s Selecting previously unselected package libc6-dev:amd64. 283s Preparing to unpack .../004-libc6-dev_2.39-0ubuntu6_amd64.deb ... 283s Unpacking libc6-dev:amd64 (2.39-0ubuntu6) ... 283s Selecting previously unselected package libisl23:amd64. 283s Preparing to unpack .../005-libisl23_0.26-3_amd64.deb ... 283s Unpacking libisl23:amd64 (0.26-3) ... 283s Selecting previously unselected package libmpc3:amd64. 283s Preparing to unpack .../006-libmpc3_1.3.1-1_amd64.deb ... 283s Unpacking libmpc3:amd64 (1.3.1-1) ... 284s Selecting previously unselected package cpp-13-x86-64-linux-gnu. 284s Preparing to unpack .../007-cpp-13-x86-64-linux-gnu_13.2.0-17ubuntu2_amd64.deb ... 284s Unpacking cpp-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 284s Selecting previously unselected package cpp-13. 284s Preparing to unpack .../008-cpp-13_13.2.0-17ubuntu2_amd64.deb ... 284s Unpacking cpp-13 (13.2.0-17ubuntu2) ... 284s Selecting previously unselected package cpp-x86-64-linux-gnu. 284s Preparing to unpack .../009-cpp-x86-64-linux-gnu_4%3a13.2.0-7ubuntu1_amd64.deb ... 284s Unpacking cpp-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 284s Selecting previously unselected package cpp. 284s Preparing to unpack .../010-cpp_4%3a13.2.0-7ubuntu1_amd64.deb ... 284s Unpacking cpp (4:13.2.0-7ubuntu1) ... 284s Selecting previously unselected package libcc1-0:amd64. 284s Preparing to unpack .../011-libcc1-0_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking libcc1-0:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package libgomp1:amd64. 284s Preparing to unpack .../012-libgomp1_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking libgomp1:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package libitm1:amd64. 284s Preparing to unpack .../013-libitm1_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking libitm1:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package libatomic1:amd64. 284s Preparing to unpack .../014-libatomic1_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking libatomic1:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package libasan8:amd64. 284s Preparing to unpack .../015-libasan8_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking libasan8:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package liblsan0:amd64. 284s Preparing to unpack .../016-liblsan0_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking liblsan0:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package libtsan2:amd64. 284s Preparing to unpack .../017-libtsan2_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking libtsan2:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package libubsan1:amd64. 284s Preparing to unpack .../018-libubsan1_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking libubsan1:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package libhwasan0:amd64. 284s Preparing to unpack .../019-libhwasan0_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking libhwasan0:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package libquadmath0:amd64. 284s Preparing to unpack .../020-libquadmath0_14-20240303-1ubuntu1_amd64.deb ... 284s Unpacking libquadmath0:amd64 (14-20240303-1ubuntu1) ... 284s Selecting previously unselected package libgcc-13-dev:amd64. 284s Preparing to unpack .../021-libgcc-13-dev_13.2.0-17ubuntu2_amd64.deb ... 284s Unpacking libgcc-13-dev:amd64 (13.2.0-17ubuntu2) ... 285s Selecting previously unselected package gcc-13-x86-64-linux-gnu. 285s Preparing to unpack .../022-gcc-13-x86-64-linux-gnu_13.2.0-17ubuntu2_amd64.deb ... 285s Unpacking gcc-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 285s Selecting previously unselected package gcc-13. 285s Preparing to unpack .../023-gcc-13_13.2.0-17ubuntu2_amd64.deb ... 285s Unpacking gcc-13 (13.2.0-17ubuntu2) ... 285s Selecting previously unselected package gcc-x86-64-linux-gnu. 285s Preparing to unpack .../024-gcc-x86-64-linux-gnu_4%3a13.2.0-7ubuntu1_amd64.deb ... 285s Unpacking gcc-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 285s Selecting previously unselected package gcc. 285s Preparing to unpack .../025-gcc_4%3a13.2.0-7ubuntu1_amd64.deb ... 285s Unpacking gcc (4:13.2.0-7ubuntu1) ... 285s Selecting previously unselected package libstdc++-13-dev:amd64. 285s Preparing to unpack .../026-libstdc++-13-dev_13.2.0-17ubuntu2_amd64.deb ... 285s Unpacking libstdc++-13-dev:amd64 (13.2.0-17ubuntu2) ... 285s Selecting previously unselected package g++-13-x86-64-linux-gnu. 285s Preparing to unpack .../027-g++-13-x86-64-linux-gnu_13.2.0-17ubuntu2_amd64.deb ... 285s Unpacking g++-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 286s Selecting previously unselected package g++-13. 286s Preparing to unpack .../028-g++-13_13.2.0-17ubuntu2_amd64.deb ... 286s Unpacking g++-13 (13.2.0-17ubuntu2) ... 286s Selecting previously unselected package g++-x86-64-linux-gnu. 286s Preparing to unpack .../029-g++-x86-64-linux-gnu_4%3a13.2.0-7ubuntu1_amd64.deb ... 286s Unpacking g++-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 286s Selecting previously unselected package g++. 286s Preparing to unpack .../030-g++_4%3a13.2.0-7ubuntu1_amd64.deb ... 286s Unpacking g++ (4:13.2.0-7ubuntu1) ... 286s Selecting previously unselected package build-essential. 286s Preparing to unpack .../031-build-essential_12.10ubuntu1_amd64.deb ... 286s Unpacking build-essential (12.10ubuntu1) ... 286s Selecting previously unselected package fonts-dejavu-mono. 286s Preparing to unpack .../032-fonts-dejavu-mono_2.37-8_all.deb ... 286s Unpacking fonts-dejavu-mono (2.37-8) ... 286s Selecting previously unselected package fonts-dejavu-core. 286s Preparing to unpack .../033-fonts-dejavu-core_2.37-8_all.deb ... 286s Unpacking fonts-dejavu-core (2.37-8) ... 286s Selecting previously unselected package fontconfig-config. 286s Preparing to unpack .../034-fontconfig-config_2.15.0-1ubuntu1_amd64.deb ... 286s Unpacking fontconfig-config (2.15.0-1ubuntu1) ... 286s Selecting previously unselected package libfontconfig1:amd64. 286s Preparing to unpack .../035-libfontconfig1_2.15.0-1ubuntu1_amd64.deb ... 286s Unpacking libfontconfig1:amd64 (2.15.0-1ubuntu1) ... 286s Selecting previously unselected package fontconfig. 286s Preparing to unpack .../036-fontconfig_2.15.0-1ubuntu1_amd64.deb ... 286s Unpacking fontconfig (2.15.0-1ubuntu1) ... 286s Selecting previously unselected package fonts-glyphicons-halflings. 286s Preparing to unpack .../037-fonts-glyphicons-halflings_1.009~3.4.1+dfsg-3_all.deb ... 286s Unpacking fonts-glyphicons-halflings (1.009~3.4.1+dfsg-3) ... 286s Selecting previously unselected package fonts-mathjax. 286s Preparing to unpack .../038-fonts-mathjax_2.7.9+dfsg-1_all.deb ... 286s Unpacking fonts-mathjax (2.7.9+dfsg-1) ... 287s Selecting previously unselected package libblas3:amd64. 287s Preparing to unpack .../039-libblas3_3.12.0-3_amd64.deb ... 287s Unpacking libblas3:amd64 (3.12.0-3) ... 287s Selecting previously unselected package libpixman-1-0:amd64. 287s Preparing to unpack .../040-libpixman-1-0_0.42.2-1_amd64.deb ... 287s Unpacking libpixman-1-0:amd64 (0.42.2-1) ... 287s Selecting previously unselected package libxcb-render0:amd64. 287s Preparing to unpack .../041-libxcb-render0_1.15-1_amd64.deb ... 287s Unpacking libxcb-render0:amd64 (1.15-1) ... 287s Selecting previously unselected package libxcb-shm0:amd64. 287s Preparing to unpack .../042-libxcb-shm0_1.15-1_amd64.deb ... 287s Unpacking libxcb-shm0:amd64 (1.15-1) ... 287s Selecting previously unselected package libxrender1:amd64. 287s Preparing to unpack .../043-libxrender1_1%3a0.9.10-1.1_amd64.deb ... 287s Unpacking libxrender1:amd64 (1:0.9.10-1.1) ... 287s Selecting previously unselected package libcairo2:amd64. 287s Preparing to unpack .../044-libcairo2_1.18.0-1_amd64.deb ... 287s Unpacking libcairo2:amd64 (1.18.0-1) ... 287s Selecting previously unselected package libdatrie1:amd64. 287s Preparing to unpack .../045-libdatrie1_0.2.13-3_amd64.deb ... 287s Unpacking libdatrie1:amd64 (0.2.13-3) ... 287s Selecting previously unselected package libdeflate0:amd64. 287s Preparing to unpack .../046-libdeflate0_1.19-1_amd64.deb ... 287s Unpacking libdeflate0:amd64 (1.19-1) ... 287s Selecting previously unselected package libgfortran5:amd64. 287s Preparing to unpack .../047-libgfortran5_14-20240303-1ubuntu1_amd64.deb ... 287s Unpacking libgfortran5:amd64 (14-20240303-1ubuntu1) ... 287s Selecting previously unselected package libgraphite2-3:amd64. 287s Preparing to unpack .../048-libgraphite2-3_1.3.14-2_amd64.deb ... 287s Unpacking libgraphite2-3:amd64 (1.3.14-2) ... 287s Selecting previously unselected package libharfbuzz0b:amd64. 287s Preparing to unpack .../049-libharfbuzz0b_8.3.0-2_amd64.deb ... 287s Unpacking libharfbuzz0b:amd64 (8.3.0-2) ... 287s Selecting previously unselected package x11-common. 287s Preparing to unpack .../050-x11-common_1%3a7.7+23ubuntu2_all.deb ... 287s Unpacking x11-common (1:7.7+23ubuntu2) ... 287s Selecting previously unselected package libice6:amd64. 287s Preparing to unpack .../051-libice6_2%3a1.0.10-1build2_amd64.deb ... 287s Unpacking libice6:amd64 (2:1.0.10-1build2) ... 287s Selecting previously unselected package libjpeg-turbo8:amd64. 287s Preparing to unpack .../052-libjpeg-turbo8_2.1.5-2ubuntu1_amd64.deb ... 287s Unpacking libjpeg-turbo8:amd64 (2.1.5-2ubuntu1) ... 287s Selecting previously unselected package libjpeg8:amd64. 287s Preparing to unpack .../053-libjpeg8_8c-2ubuntu11_amd64.deb ... 287s Unpacking libjpeg8:amd64 (8c-2ubuntu11) ... 287s Selecting previously unselected package libjs-bootstrap. 287s Preparing to unpack .../054-libjs-bootstrap_3.4.1+dfsg-3_all.deb ... 287s Unpacking libjs-bootstrap (3.4.1+dfsg-3) ... 287s Selecting previously unselected package libjs-highlight.js. 287s Preparing to unpack .../055-libjs-highlight.js_9.18.5+dfsg1-2_all.deb ... 287s Unpacking libjs-highlight.js (9.18.5+dfsg1-2) ... 287s Selecting previously unselected package libjs-jquery. 287s Preparing to unpack .../056-libjs-jquery_3.6.1+dfsg+~3.5.14-1_all.deb ... 287s Unpacking libjs-jquery (3.6.1+dfsg+~3.5.14-1) ... 287s Selecting previously unselected package libjs-jquery-datatables. 287s Preparing to unpack .../057-libjs-jquery-datatables_1.11.5+dfsg-2_all.deb ... 287s Unpacking libjs-jquery-datatables (1.11.5+dfsg-2) ... 287s Selecting previously unselected package liblapack3:amd64. 287s Preparing to unpack .../058-liblapack3_3.12.0-3_amd64.deb ... 287s Unpacking liblapack3:amd64 (3.12.0-3) ... 287s Selecting previously unselected package liblerc4:amd64. 287s Preparing to unpack .../059-liblerc4_4.0.0+ds-4ubuntu1_amd64.deb ... 287s Unpacking liblerc4:amd64 (4.0.0+ds-4ubuntu1) ... 287s Selecting previously unselected package libthai-data. 287s Preparing to unpack .../060-libthai-data_0.1.29-2_all.deb ... 287s Unpacking libthai-data (0.1.29-2) ... 287s Selecting previously unselected package libthai0:amd64. 287s Preparing to unpack .../061-libthai0_0.1.29-2_amd64.deb ... 287s Unpacking libthai0:amd64 (0.1.29-2) ... 287s Selecting previously unselected package libpango-1.0-0:amd64. 287s Preparing to unpack .../062-libpango-1.0-0_1.51.0+ds-4_amd64.deb ... 287s Unpacking libpango-1.0-0:amd64 (1.51.0+ds-4) ... 287s Selecting previously unselected package libpangoft2-1.0-0:amd64. 287s Preparing to unpack .../063-libpangoft2-1.0-0_1.51.0+ds-4_amd64.deb ... 287s Unpacking libpangoft2-1.0-0:amd64 (1.51.0+ds-4) ... 287s Selecting previously unselected package libpangocairo-1.0-0:amd64. 287s Preparing to unpack .../064-libpangocairo-1.0-0_1.51.0+ds-4_amd64.deb ... 287s Unpacking libpangocairo-1.0-0:amd64 (1.51.0+ds-4) ... 287s Selecting previously unselected package libpaper1:amd64. 287s Preparing to unpack .../065-libpaper1_1.1.29_amd64.deb ... 287s Unpacking libpaper1:amd64 (1.1.29) ... 287s Selecting previously unselected package libpaper-utils. 287s Preparing to unpack .../066-libpaper-utils_1.1.29_amd64.deb ... 287s Unpacking libpaper-utils (1.1.29) ... 287s Selecting previously unselected package libsharpyuv0:amd64. 287s Preparing to unpack .../067-libsharpyuv0_1.3.2-0.4_amd64.deb ... 287s Unpacking libsharpyuv0:amd64 (1.3.2-0.4) ... 287s Selecting previously unselected package libsm6:amd64. 287s Preparing to unpack .../068-libsm6_2%3a1.2.3-1build2_amd64.deb ... 287s Unpacking libsm6:amd64 (2:1.2.3-1build2) ... 287s Selecting previously unselected package libtcl8.6:amd64. 287s Preparing to unpack .../069-libtcl8.6_8.6.13+dfsg-2_amd64.deb ... 287s Unpacking libtcl8.6:amd64 (8.6.13+dfsg-2) ... 287s Selecting previously unselected package libjbig0:amd64. 287s Preparing to unpack .../070-libjbig0_2.1-6.1ubuntu1_amd64.deb ... 287s Unpacking libjbig0:amd64 (2.1-6.1ubuntu1) ... 287s Selecting previously unselected package libwebp7:amd64. 287s Preparing to unpack .../071-libwebp7_1.3.2-0.4_amd64.deb ... 287s Unpacking libwebp7:amd64 (1.3.2-0.4) ... 287s Selecting previously unselected package libtiff6:amd64. 287s Preparing to unpack .../072-libtiff6_4.5.1+git230720-3ubuntu1_amd64.deb ... 287s Unpacking libtiff6:amd64 (4.5.1+git230720-3ubuntu1) ... 288s Selecting previously unselected package libxft2:amd64. 288s Preparing to unpack .../073-libxft2_2.3.6-1_amd64.deb ... 288s Unpacking libxft2:amd64 (2.3.6-1) ... 288s Selecting previously unselected package libxss1:amd64. 288s Preparing to unpack .../074-libxss1_1%3a1.2.3-1build2_amd64.deb ... 288s Unpacking libxss1:amd64 (1:1.2.3-1build2) ... 288s Selecting previously unselected package libtk8.6:amd64. 288s Preparing to unpack .../075-libtk8.6_8.6.14-1_amd64.deb ... 288s Unpacking libtk8.6:amd64 (8.6.14-1) ... 288s Selecting previously unselected package libxt6:amd64. 288s Preparing to unpack .../076-libxt6_1%3a1.2.1-1.1_amd64.deb ... 288s Unpacking libxt6:amd64 (1:1.2.1-1.1) ... 288s Selecting previously unselected package zip. 288s Preparing to unpack .../077-zip_3.0-13_amd64.deb ... 288s Unpacking zip (3.0-13) ... 288s Selecting previously unselected package unzip. 288s Preparing to unpack .../078-unzip_6.0-28ubuntu3_amd64.deb ... 288s Unpacking unzip (6.0-28ubuntu3) ... 288s Selecting previously unselected package xdg-utils. 288s Preparing to unpack .../079-xdg-utils_1.1.3-4.1ubuntu3_all.deb ... 288s Unpacking xdg-utils (1.1.3-4.1ubuntu3) ... 288s Selecting previously unselected package r-base-core. 288s Preparing to unpack .../080-r-base-core_4.3.2-1build1_amd64.deb ... 288s Unpacking r-base-core (4.3.2-1build1) ... 288s Selecting previously unselected package r-cran-littler. 288s Preparing to unpack .../081-r-cran-littler_0.3.19-1_amd64.deb ... 288s Unpacking r-cran-littler (0.3.19-1) ... 288s Selecting previously unselected package littler. 288s Preparing to unpack .../082-littler_0.3.19-1_all.deb ... 288s Unpacking littler (0.3.19-1) ... 288s Selecting previously unselected package node-normalize.css. 288s Preparing to unpack .../083-node-normalize.css_8.0.1-5_all.deb ... 288s Unpacking node-normalize.css (8.0.1-5) ... 288s Selecting previously unselected package r-cran-abind. 288s Preparing to unpack .../084-r-cran-abind_1.4-5-2_all.deb ... 288s Unpacking r-cran-abind (1.4-5-2) ... 288s Selecting previously unselected package r-cran-backports. 288s Preparing to unpack .../085-r-cran-backports_1.4.1-1_amd64.deb ... 288s Unpacking r-cran-backports (1.4.1-1) ... 288s Selecting previously unselected package r-cran-bdsmatrix. 288s Preparing to unpack .../086-r-cran-bdsmatrix_1.3-6-1_amd64.deb ... 288s Unpacking r-cran-bdsmatrix (1.3-6-1) ... 288s Selecting previously unselected package r-cran-bit. 288s Preparing to unpack .../087-r-cran-bit_4.0.5-1_amd64.deb ... 288s Unpacking r-cran-bit (4.0.5-1) ... 288s Selecting previously unselected package r-cran-bit64. 288s Preparing to unpack .../088-r-cran-bit64_4.0.5-1_amd64.deb ... 288s Unpacking r-cran-bit64 (4.0.5-1) ... 288s Selecting previously unselected package r-cran-boot. 288s Preparing to unpack .../089-r-cran-boot_1.3-30-1_all.deb ... 288s Unpacking r-cran-boot (1.3-30-1) ... 288s Selecting previously unselected package r-cran-brio. 288s Preparing to unpack .../090-r-cran-brio_1.1.4-1_amd64.deb ... 288s Unpacking r-cran-brio (1.1.4-1) ... 288s Selecting previously unselected package r-cran-cli. 288s Preparing to unpack .../091-r-cran-cli_3.6.2-1_amd64.deb ... 288s Unpacking r-cran-cli (3.6.2-1) ... 289s Selecting previously unselected package r-cran-generics. 289s Preparing to unpack .../092-r-cran-generics_0.1.3-1_all.deb ... 289s Unpacking r-cran-generics (0.1.3-1) ... 289s Selecting previously unselected package r-cran-glue. 289s Preparing to unpack .../093-r-cran-glue_1.7.0-1_amd64.deb ... 289s Unpacking r-cran-glue (1.7.0-1) ... 289s Selecting previously unselected package r-cran-rlang. 289s Preparing to unpack .../094-r-cran-rlang_1.1.3-1_amd64.deb ... 289s Unpacking r-cran-rlang (1.1.3-1) ... 289s Selecting previously unselected package r-cran-lifecycle. 289s Preparing to unpack .../095-r-cran-lifecycle_1.0.4+dfsg-1_all.deb ... 289s Unpacking r-cran-lifecycle (1.0.4+dfsg-1) ... 289s Selecting previously unselected package r-cran-magrittr. 289s Preparing to unpack .../096-r-cran-magrittr_2.0.3-1_amd64.deb ... 289s Unpacking r-cran-magrittr (2.0.3-1) ... 289s Selecting previously unselected package r-cran-fansi. 289s Preparing to unpack .../097-r-cran-fansi_1.0.5-1_amd64.deb ... 289s Unpacking r-cran-fansi (1.0.5-1) ... 289s Selecting previously unselected package r-cran-utf8. 289s Preparing to unpack .../098-r-cran-utf8_1.2.4-1_amd64.deb ... 289s Unpacking r-cran-utf8 (1.2.4-1) ... 289s Selecting previously unselected package r-cran-vctrs. 289s Preparing to unpack .../099-r-cran-vctrs_0.6.5-1_amd64.deb ... 289s Unpacking r-cran-vctrs (0.6.5-1) ... 289s Selecting previously unselected package r-cran-pillar. 289s Preparing to unpack .../100-r-cran-pillar_1.9.0+dfsg-1_all.deb ... 289s Unpacking r-cran-pillar (1.9.0+dfsg-1) ... 289s Selecting previously unselected package r-cran-r6. 289s Preparing to unpack .../101-r-cran-r6_2.5.1-1_all.deb ... 289s Unpacking r-cran-r6 (2.5.1-1) ... 289s Selecting previously unselected package r-cran-pkgconfig. 289s Preparing to unpack .../102-r-cran-pkgconfig_2.0.3-2build1_all.deb ... 289s Unpacking r-cran-pkgconfig (2.0.3-2build1) ... 289s Selecting previously unselected package r-cran-tibble. 289s Preparing to unpack .../103-r-cran-tibble_3.2.1+dfsg-2_amd64.deb ... 289s Unpacking r-cran-tibble (3.2.1+dfsg-2) ... 289s Selecting previously unselected package r-cran-withr. 289s Preparing to unpack .../104-r-cran-withr_2.5.0-1_all.deb ... 289s Unpacking r-cran-withr (2.5.0-1) ... 289s Selecting previously unselected package r-cran-tidyselect. 289s Preparing to unpack .../105-r-cran-tidyselect_1.2.0+dfsg-1_amd64.deb ... 289s Unpacking r-cran-tidyselect (1.2.0+dfsg-1) ... 289s Selecting previously unselected package r-cran-dplyr. 289s Preparing to unpack .../106-r-cran-dplyr_1.1.4-1_amd64.deb ... 289s Unpacking r-cran-dplyr (1.1.4-1) ... 289s Selecting previously unselected package r-cran-ellipsis. 289s Preparing to unpack .../107-r-cran-ellipsis_0.3.2-2_amd64.deb ... 289s Unpacking r-cran-ellipsis (0.3.2-2) ... 289s Selecting previously unselected package r-cran-purrr. 289s Preparing to unpack .../108-r-cran-purrr_1.0.2-1_amd64.deb ... 289s Unpacking r-cran-purrr (1.0.2-1) ... 289s Selecting previously unselected package r-cran-stringi. 289s Preparing to unpack .../109-r-cran-stringi_1.8.3-1_amd64.deb ... 289s Unpacking r-cran-stringi (1.8.3-1) ... 289s Selecting previously unselected package r-cran-stringr. 289s Preparing to unpack .../110-r-cran-stringr_1.5.1-1_all.deb ... 289s Unpacking r-cran-stringr (1.5.1-1) ... 289s Selecting previously unselected package r-cran-cpp11. 290s Preparing to unpack .../111-r-cran-cpp11_0.4.7-1_all.deb ... 290s Unpacking r-cran-cpp11 (0.4.7-1) ... 290s Selecting previously unselected package r-cran-tidyr. 290s Preparing to unpack .../112-r-cran-tidyr_1.3.1-1_amd64.deb ... 290s Unpacking r-cran-tidyr (1.3.1-1) ... 290s Selecting previously unselected package r-cran-broom. 290s Preparing to unpack .../113-r-cran-broom_1.0.5+dfsg-1_all.deb ... 290s Unpacking r-cran-broom (1.0.5+dfsg-1) ... 290s Selecting previously unselected package r-cran-ps. 290s Preparing to unpack .../114-r-cran-ps_1.7.6-1_amd64.deb ... 290s Unpacking r-cran-ps (1.7.6-1) ... 290s Selecting previously unselected package r-cran-processx. 290s Preparing to unpack .../115-r-cran-processx_3.8.3-1_amd64.deb ... 290s Unpacking r-cran-processx (3.8.3-1) ... 290s Selecting previously unselected package r-cran-callr. 290s Preparing to unpack .../116-r-cran-callr_3.7.3-2_all.deb ... 290s Unpacking r-cran-callr (3.7.3-2) ... 290s Selecting previously unselected package r-cran-cardata. 290s Preparing to unpack .../117-r-cran-cardata_3.0.5-1_all.deb ... 290s Unpacking r-cran-cardata (3.0.5-1) ... 290s Selecting previously unselected package r-cran-mass. 290s Preparing to unpack .../118-r-cran-mass_7.3-60.0.1-1_amd64.deb ... 290s Unpacking r-cran-mass (7.3-60.0.1-1) ... 290s Selecting previously unselected package r-cran-lattice. 290s Preparing to unpack .../119-r-cran-lattice_0.22-5-1_amd64.deb ... 290s Unpacking r-cran-lattice (0.22-5-1) ... 290s Selecting previously unselected package r-cran-nlme. 290s Preparing to unpack .../120-r-cran-nlme_3.1.164-1_amd64.deb ... 290s Unpacking r-cran-nlme (3.1.164-1) ... 290s Selecting previously unselected package r-cran-matrix. 290s Preparing to unpack .../121-r-cran-matrix_1.6-5-1_amd64.deb ... 290s Unpacking r-cran-matrix (1.6-5-1) ... 290s Selecting previously unselected package r-cran-mgcv. 290s Preparing to unpack .../122-r-cran-mgcv_1.9-1-1_amd64.deb ... 290s Unpacking r-cran-mgcv (1.9-1-1) ... 290s Selecting previously unselected package r-cran-nnet. 290s Preparing to unpack .../123-r-cran-nnet_7.3-19-2_amd64.deb ... 290s Unpacking r-cran-nnet (7.3-19-2) ... 290s Selecting previously unselected package r-cran-pkgkitten. 290s Preparing to unpack .../124-r-cran-pkgkitten_0.2.3-1_all.deb ... 290s Unpacking r-cran-pkgkitten (0.2.3-1) ... 290s Selecting previously unselected package r-cran-rcpp. 290s Preparing to unpack .../125-r-cran-rcpp_1.0.12-1_amd64.deb ... 290s Unpacking r-cran-rcpp (1.0.12-1) ... 290s Selecting previously unselected package r-cran-minqa. 290s Preparing to unpack .../126-r-cran-minqa_1.2.6-1_amd64.deb ... 290s Unpacking r-cran-minqa (1.2.6-1) ... 290s Selecting previously unselected package libnlopt0:amd64. 290s Preparing to unpack .../127-libnlopt0_2.7.1-5build2_amd64.deb ... 290s Unpacking libnlopt0:amd64 (2.7.1-5build2) ... 290s Selecting previously unselected package r-cran-desc. 290s Preparing to unpack .../128-r-cran-desc_1.4.3-1_all.deb ... 290s Unpacking r-cran-desc (1.4.3-1) ... 290s Selecting previously unselected package r-cran-digest. 290s Preparing to unpack .../129-r-cran-digest_0.6.34-1_amd64.deb ... 290s Unpacking r-cran-digest (0.6.34-1) ... 290s Selecting previously unselected package r-cran-evaluate. 290s Preparing to unpack .../130-r-cran-evaluate_0.23-1_all.deb ... 290s Unpacking r-cran-evaluate (0.23-1) ... 291s Selecting previously unselected package r-cran-jsonlite. 291s Preparing to unpack .../131-r-cran-jsonlite_1.8.8+dfsg-1_amd64.deb ... 291s Unpacking r-cran-jsonlite (1.8.8+dfsg-1) ... 291s Selecting previously unselected package r-cran-crayon. 291s Preparing to unpack .../132-r-cran-crayon_1.5.2-1_all.deb ... 291s Unpacking r-cran-crayon (1.5.2-1) ... 291s Selecting previously unselected package r-cran-fs. 291s Preparing to unpack .../133-r-cran-fs_1.6.3+dfsg-1_amd64.deb ... 291s Unpacking r-cran-fs (1.6.3+dfsg-1) ... 291s Selecting previously unselected package r-cran-pkgbuild. 291s Preparing to unpack .../134-r-cran-pkgbuild_1.4.3-1_all.deb ... 291s Unpacking r-cran-pkgbuild (1.4.3-1) ... 291s Selecting previously unselected package r-cran-rprojroot. 291s Preparing to unpack .../135-r-cran-rprojroot_2.0.4-1_all.deb ... 291s Unpacking r-cran-rprojroot (2.0.4-1) ... 291s Selecting previously unselected package r-cran-pkgload. 291s Preparing to unpack .../136-r-cran-pkgload_1.3.4-1_all.deb ... 291s Unpacking r-cran-pkgload (1.3.4-1) ... 291s Selecting previously unselected package r-cran-praise. 291s Preparing to unpack .../137-r-cran-praise_1.0.0-4build1_all.deb ... 291s Unpacking r-cran-praise (1.0.0-4build1) ... 291s Selecting previously unselected package r-cran-diffobj. 291s Preparing to unpack .../138-r-cran-diffobj_0.3.5-1_amd64.deb ... 291s Unpacking r-cran-diffobj (0.3.5-1) ... 291s Selecting previously unselected package r-cran-rematch2. 291s Preparing to unpack .../139-r-cran-rematch2_2.1.2-2build1_all.deb ... 291s Unpacking r-cran-rematch2 (2.1.2-2build1) ... 291s Selecting previously unselected package r-cran-waldo. 291s Preparing to unpack .../140-r-cran-waldo_0.5.2-1build1_all.deb ... 291s Unpacking r-cran-waldo (0.5.2-1build1) ... 291s Selecting previously unselected package r-cran-testthat. 291s Preparing to unpack .../141-r-cran-testthat_3.2.1-1_amd64.deb ... 291s Unpacking r-cran-testthat (3.2.1-1) ... 291s Selecting previously unselected package r-cran-nloptr. 291s Preparing to unpack .../142-r-cran-nloptr_2.0.3-1_amd64.deb ... 291s Unpacking r-cran-nloptr (2.0.3-1) ... 291s Selecting previously unselected package r-cran-rcppeigen. 291s Preparing to unpack .../143-r-cran-rcppeigen_0.3.3.9.4-1_amd64.deb ... 291s Unpacking r-cran-rcppeigen (0.3.3.9.4-1) ... 291s Selecting previously unselected package r-cran-statmod. 291s Preparing to unpack .../144-r-cran-statmod_1.5.0-1_amd64.deb ... 291s Unpacking r-cran-statmod (1.5.0-1) ... 291s Selecting previously unselected package r-cran-lme4. 291s Preparing to unpack .../145-r-cran-lme4_1.1-35.1-4_amd64.deb ... 291s Unpacking r-cran-lme4 (1.1-35.1-4) ... 291s Selecting previously unselected package r-cran-numderiv. 291s Preparing to unpack .../146-r-cran-numderiv_2016.8-1.1-3_all.deb ... 291s Unpacking r-cran-numderiv (2016.8-1.1-3) ... 291s Selecting previously unselected package r-cran-xfun. 291s Preparing to unpack .../147-r-cran-xfun_0.41+dfsg-1_amd64.deb ... 291s Unpacking r-cran-xfun (0.41+dfsg-1) ... 291s Selecting previously unselected package r-cran-highr. 291s Preparing to unpack .../148-r-cran-highr_0.10+dfsg-1_all.deb ... 291s Unpacking r-cran-highr (0.10+dfsg-1) ... 291s Selecting previously unselected package r-cran-yaml. 291s Preparing to unpack .../149-r-cran-yaml_2.3.8-1_amd64.deb ... 291s Unpacking r-cran-yaml (2.3.8-1) ... 292s Selecting previously unselected package libjs-mathjax. 292s Preparing to unpack .../150-libjs-mathjax_2.7.9+dfsg-1_all.deb ... 292s Unpacking libjs-mathjax (2.7.9+dfsg-1) ... 292s Selecting previously unselected package r-cran-knitr. 292s Preparing to unpack .../151-r-cran-knitr_1.45+dfsg-1_all.deb ... 292s Unpacking r-cran-knitr (1.45+dfsg-1) ... 292s Selecting previously unselected package r-cran-pbkrtest. 292s Preparing to unpack .../152-r-cran-pbkrtest_0.5.2-2_all.deb ... 292s Unpacking r-cran-pbkrtest (0.5.2-2) ... 292s Selecting previously unselected package r-cran-sparsem. 292s Preparing to unpack .../153-r-cran-sparsem_1.81-1_amd64.deb ... 292s Unpacking r-cran-sparsem (1.81-1) ... 293s Selecting previously unselected package r-cran-matrixmodels. 293s Preparing to unpack .../154-r-cran-matrixmodels_0.5-3-1_all.deb ... 293s Unpacking r-cran-matrixmodels (0.5-3-1) ... 293s Selecting previously unselected package r-cran-survival. 293s Preparing to unpack .../155-r-cran-survival_3.5-8-1_amd64.deb ... 293s Unpacking r-cran-survival (3.5-8-1) ... 293s Selecting previously unselected package r-cran-matrixstats. 293s Preparing to unpack .../156-r-cran-matrixstats_1.2.0-1_amd64.deb ... 293s Unpacking r-cran-matrixstats (1.2.0-1) ... 293s Selecting previously unselected package r-cran-rcpparmadillo. 293s Preparing to unpack .../157-r-cran-rcpparmadillo_0.12.8.0.0-1_amd64.deb ... 293s Unpacking r-cran-rcpparmadillo (0.12.8.0.0-1) ... 293s Selecting previously unselected package r-cran-gtable. 293s Preparing to unpack .../158-r-cran-gtable_0.3.4+dfsg-1_all.deb ... 293s Unpacking r-cran-gtable (0.3.4+dfsg-1) ... 293s Selecting previously unselected package r-cran-isoband. 293s Preparing to unpack .../159-r-cran-isoband_0.2.7-1_amd64.deb ... 293s Unpacking r-cran-isoband (0.2.7-1) ... 293s Selecting previously unselected package r-cran-farver. 293s Preparing to unpack .../160-r-cran-farver_2.1.1-1_amd64.deb ... 293s Unpacking r-cran-farver (2.1.1-1) ... 293s Selecting previously unselected package r-cran-labeling. 293s Preparing to unpack .../161-r-cran-labeling_0.4.3-1_all.deb ... 293s Unpacking r-cran-labeling (0.4.3-1) ... 293s Selecting previously unselected package r-cran-colorspace. 293s Preparing to unpack .../162-r-cran-colorspace_2.1-0+dfsg-1_amd64.deb ... 293s Unpacking r-cran-colorspace (2.1-0+dfsg-1) ... 293s Selecting previously unselected package r-cran-munsell. 293s Preparing to unpack .../163-r-cran-munsell_0.5.0-2build1_all.deb ... 293s Unpacking r-cran-munsell (0.5.0-2build1) ... 293s Selecting previously unselected package r-cran-rcolorbrewer. 293s Preparing to unpack .../164-r-cran-rcolorbrewer_1.1-3-1build1_all.deb ... 293s Unpacking r-cran-rcolorbrewer (1.1-3-1build1) ... 293s Selecting previously unselected package r-cran-viridislite. 293s Preparing to unpack .../165-r-cran-viridislite_0.4.2-2_all.deb ... 293s Unpacking r-cran-viridislite (0.4.2-2) ... 293s Selecting previously unselected package r-cran-scales. 293s Preparing to unpack .../166-r-cran-scales_1.3.0-1_all.deb ... 293s Unpacking r-cran-scales (1.3.0-1) ... 293s Selecting previously unselected package r-cran-ggplot2. 293s Preparing to unpack .../167-r-cran-ggplot2_3.4.4+dfsg-1_all.deb ... 293s Unpacking r-cran-ggplot2 (3.4.4+dfsg-1) ... 293s Selecting previously unselected package r-cran-class. 293s Preparing to unpack .../168-r-cran-class_7.3-22-2_amd64.deb ... 293s Unpacking r-cran-class (7.3-22-2) ... 294s Selecting previously unselected package r-cran-proxy. 294s Preparing to unpack .../169-r-cran-proxy_0.4-27-1_amd64.deb ... 294s Unpacking r-cran-proxy (0.4-27-1) ... 294s Selecting previously unselected package r-cran-e1071. 294s Preparing to unpack .../170-r-cran-e1071_1.7-14-1_amd64.deb ... 294s Unpacking r-cran-e1071 (1.7-14-1) ... 294s Selecting previously unselected package r-cran-codetools. 294s Preparing to unpack .../171-r-cran-codetools_0.2-19-1_all.deb ... 294s Unpacking r-cran-codetools (0.2-19-1) ... 294s Selecting previously unselected package r-cran-iterators. 294s Preparing to unpack .../172-r-cran-iterators_1.0.14-1_all.deb ... 294s Unpacking r-cran-iterators (1.0.14-1) ... 294s Selecting previously unselected package r-cran-foreach. 294s Preparing to unpack .../173-r-cran-foreach_1.5.2-1_all.deb ... 294s Unpacking r-cran-foreach (1.5.2-1) ... 294s Selecting previously unselected package r-cran-data.table. 294s Preparing to unpack .../174-r-cran-data.table_1.14.10+dfsg-1_amd64.deb ... 294s Unpacking r-cran-data.table (1.14.10+dfsg-1) ... 294s Selecting previously unselected package r-cran-modelmetrics. 294s Preparing to unpack .../175-r-cran-modelmetrics_1.2.2.2-1build1_amd64.deb ... 294s Unpacking r-cran-modelmetrics (1.2.2.2-1build1) ... 294s Selecting previously unselected package r-cran-plyr. 294s Preparing to unpack .../176-r-cran-plyr_1.8.9-1_amd64.deb ... 294s Unpacking r-cran-plyr (1.8.9-1) ... 294s Selecting previously unselected package r-cran-proc. 294s Preparing to unpack .../177-r-cran-proc_1.18.5-1_amd64.deb ... 294s Unpacking r-cran-proc (1.18.5-1) ... 294s Selecting previously unselected package r-cran-tzdb. 294s Preparing to unpack .../178-r-cran-tzdb_0.4.0-2_amd64.deb ... 294s Unpacking r-cran-tzdb (0.4.0-2) ... 294s Selecting previously unselected package r-cran-clock. 294s Preparing to unpack .../179-r-cran-clock_0.7.0-1.1_amd64.deb ... 294s Unpacking r-cran-clock (0.7.0-1.1) ... 294s Selecting previously unselected package r-cran-gower. 294s Preparing to unpack .../180-r-cran-gower_1.0.1-1_amd64.deb ... 294s Unpacking r-cran-gower (1.0.1-1) ... 294s Selecting previously unselected package r-cran-hardhat. 294s Preparing to unpack .../181-r-cran-hardhat_1.3.1+dfsg-1_all.deb ... 294s Unpacking r-cran-hardhat (1.3.1+dfsg-1) ... 294s Selecting previously unselected package r-cran-rpart. 294s Preparing to unpack .../182-r-cran-rpart_4.1.23-1_amd64.deb ... 294s Unpacking r-cran-rpart (4.1.23-1) ... 294s Selecting previously unselected package r-cran-shape. 294s Preparing to unpack .../183-r-cran-shape_1.4.6-1_all.deb ... 294s Unpacking r-cran-shape (1.4.6-1) ... 294s Selecting previously unselected package r-cran-diagram. 294s Preparing to unpack .../184-r-cran-diagram_1.6.5-2_all.deb ... 294s Unpacking r-cran-diagram (1.6.5-2) ... 294s Selecting previously unselected package r-cran-kernsmooth. 294s Preparing to unpack .../185-r-cran-kernsmooth_2.23-22-1_amd64.deb ... 294s Unpacking r-cran-kernsmooth (2.23-22-1) ... 294s Selecting previously unselected package r-cran-globals. 294s Preparing to unpack .../186-r-cran-globals_0.16.2-1_all.deb ... 294s Unpacking r-cran-globals (0.16.2-1) ... 294s Selecting previously unselected package r-cran-listenv. 294s Preparing to unpack .../187-r-cran-listenv_0.9.1+dfsg-1_all.deb ... 294s Unpacking r-cran-listenv (0.9.1+dfsg-1) ... 294s Selecting previously unselected package r-cran-parallelly. 294s Preparing to unpack .../188-r-cran-parallelly_1.37.1-1_amd64.deb ... 294s Unpacking r-cran-parallelly (1.37.1-1) ... 295s Selecting previously unselected package r-cran-future. 295s Preparing to unpack .../189-r-cran-future_1.33.1+dfsg-1_all.deb ... 295s Unpacking r-cran-future (1.33.1+dfsg-1) ... 295s Selecting previously unselected package r-cran-future.apply. 295s Preparing to unpack .../190-r-cran-future.apply_1.11.1+dfsg-1_all.deb ... 295s Unpacking r-cran-future.apply (1.11.1+dfsg-1) ... 295s Selecting previously unselected package r-cran-progressr. 295s Preparing to unpack .../191-r-cran-progressr_0.14.0-1_all.deb ... 295s Unpacking r-cran-progressr (0.14.0-1) ... 295s Selecting previously unselected package r-cran-squarem. 295s Preparing to unpack .../192-r-cran-squarem_2021.1-1_all.deb ... 295s Unpacking r-cran-squarem (2021.1-1) ... 295s Selecting previously unselected package r-cran-lava. 295s Preparing to unpack .../193-r-cran-lava_1.7.3+dfsg-1_all.deb ... 295s Unpacking r-cran-lava (1.7.3+dfsg-1) ... 295s Selecting previously unselected package r-cran-prodlim. 295s Preparing to unpack .../194-r-cran-prodlim_2023.08.28-1_amd64.deb ... 295s Unpacking r-cran-prodlim (2023.08.28-1) ... 295s Selecting previously unselected package r-cran-ipred. 295s Preparing to unpack .../195-r-cran-ipred_0.9-14-1_amd64.deb ... 295s Unpacking r-cran-ipred (0.9-14-1) ... 295s Selecting previously unselected package r-cran-timechange. 295s Preparing to unpack .../196-r-cran-timechange_0.3.0-1_amd64.deb ... 295s Unpacking r-cran-timechange (0.3.0-1) ... 295s Selecting previously unselected package r-cran-lubridate. 295s Preparing to unpack .../197-r-cran-lubridate_1.9.3+dfsg-1_amd64.deb ... 295s Unpacking r-cran-lubridate (1.9.3+dfsg-1) ... 295s Selecting previously unselected package r-cran-timedate. 295s Preparing to unpack .../198-r-cran-timedate_4032.109-1_amd64.deb ... 295s Unpacking r-cran-timedate (4032.109-1) ... 295s Selecting previously unselected package r-cran-recipes. 295s Preparing to unpack .../199-r-cran-recipes_1.0.9+dfsg-1_all.deb ... 295s Unpacking r-cran-recipes (1.0.9+dfsg-1) ... 295s Selecting previously unselected package r-cran-reshape2. 295s Preparing to unpack .../200-r-cran-reshape2_1.4.4-2build1_amd64.deb ... 295s Unpacking r-cran-reshape2 (1.4.4-2build1) ... 295s Selecting previously unselected package r-cran-caret. 295s Preparing to unpack .../201-r-cran-caret_6.0-94+dfsg-1_amd64.deb ... 295s Unpacking r-cran-caret (6.0-94+dfsg-1) ... 295s Selecting previously unselected package r-cran-conquer. 295s Preparing to unpack .../202-r-cran-conquer_1.3.3-1_amd64.deb ... 295s Unpacking r-cran-conquer (1.3.3-1) ... 295s Selecting previously unselected package r-cran-quantreg. 295s Preparing to unpack .../203-r-cran-quantreg_5.97-1_amd64.deb ... 295s Unpacking r-cran-quantreg (5.97-1) ... 295s Selecting previously unselected package r-cran-sp. 295s Preparing to unpack .../204-r-cran-sp_1%3a2.1-2+dfsg-1_amd64.deb ... 295s Unpacking r-cran-sp (1:2.1-2+dfsg-1) ... 295s Selecting previously unselected package r-cran-foreign. 295s Preparing to unpack .../205-r-cran-foreign_0.8.86-1_amd64.deb ... 295s Unpacking r-cran-foreign (0.8.86-1) ... 295s Selecting previously unselected package r-cran-maptools. 295s Preparing to unpack .../206-r-cran-maptools_1%3a1.1-8+dfsg-1_amd64.deb ... 295s Unpacking r-cran-maptools (1:1.1-8+dfsg-1) ... 295s Selecting previously unselected package r-cran-forcats. 295s Preparing to unpack .../207-r-cran-forcats_1.0.0-1_all.deb ... 295s Unpacking r-cran-forcats (1.0.0-1) ... 295s Selecting previously unselected package r-cran-hms. 295s Preparing to unpack .../208-r-cran-hms_1.1.3-1_all.deb ... 295s Unpacking r-cran-hms (1.1.3-1) ... 296s Selecting previously unselected package r-cran-clipr. 296s Preparing to unpack .../209-r-cran-clipr_0.8.0-1_all.deb ... 296s Unpacking r-cran-clipr (0.8.0-1) ... 296s Selecting previously unselected package r-cran-prettyunits. 296s Preparing to unpack .../210-r-cran-prettyunits_1.2.0-1_all.deb ... 296s Unpacking r-cran-prettyunits (1.2.0-1) ... 296s Selecting previously unselected package r-cran-progress. 296s Preparing to unpack .../211-r-cran-progress_1.2.3-1_all.deb ... 296s Unpacking r-cran-progress (1.2.3-1) ... 296s Selecting previously unselected package r-cran-vroom. 296s Preparing to unpack .../212-r-cran-vroom_1.6.5-1_amd64.deb ... 296s Unpacking r-cran-vroom (1.6.5-1) ... 296s Selecting previously unselected package r-cran-readr. 296s Preparing to unpack .../213-r-cran-readr_2.1.5-1_amd64.deb ... 296s Unpacking r-cran-readr (2.1.5-1) ... 296s Selecting previously unselected package r-cran-haven. 296s Preparing to unpack .../214-r-cran-haven_2.5.4-1_amd64.deb ... 296s Unpacking r-cran-haven (2.5.4-1) ... 296s Selecting previously unselected package r-cran-curl. 296s Preparing to unpack .../215-r-cran-curl_5.2.0+dfsg-1_amd64.deb ... 296s Unpacking r-cran-curl (5.2.0+dfsg-1) ... 296s Selecting previously unselected package r-cran-rematch. 296s Preparing to unpack .../216-r-cran-rematch_2.0.0-1_all.deb ... 296s Unpacking r-cran-rematch (2.0.0-1) ... 296s Selecting previously unselected package r-cran-cellranger. 296s Preparing to unpack .../217-r-cran-cellranger_1.1.0-3_all.deb ... 296s Unpacking r-cran-cellranger (1.1.0-3) ... 296s Selecting previously unselected package r-cran-readxl. 296s Preparing to unpack .../218-r-cran-readxl_1.4.3-1_amd64.deb ... 296s Unpacking r-cran-readxl (1.4.3-1) ... 296s Selecting previously unselected package r-cran-writexl. 296s Preparing to unpack .../219-r-cran-writexl_1.5.0-1_amd64.deb ... 296s Unpacking r-cran-writexl (1.5.0-1) ... 296s Selecting previously unselected package r-cran-r.methodss3. 296s Preparing to unpack .../220-r-cran-r.methodss3_1.8.2-1_all.deb ... 296s Unpacking r-cran-r.methodss3 (1.8.2-1) ... 296s Selecting previously unselected package r-cran-r.oo. 296s Preparing to unpack .../221-r-cran-r.oo_1.26.0-1_all.deb ... 296s Unpacking r-cran-r.oo (1.26.0-1) ... 296s Selecting previously unselected package r-cran-r.utils. 296s Preparing to unpack .../222-r-cran-r.utils_2.12.3-1_all.deb ... 296s Unpacking r-cran-r.utils (2.12.3-1) ... 296s Selecting previously unselected package r-cran-zip. 296s Preparing to unpack .../223-r-cran-zip_2.3.1-1_amd64.deb ... 296s Unpacking r-cran-zip (2.3.1-1) ... 296s Selecting previously unselected package r-cran-openxlsx. 296s Preparing to unpack .../224-r-cran-openxlsx_4.2.5.2-1_amd64.deb ... 296s Unpacking r-cran-openxlsx (4.2.5.2-1) ... 296s Selecting previously unselected package r-cran-rio. 296s Preparing to unpack .../225-r-cran-rio_1.0.1-1_all.deb ... 296s Unpacking r-cran-rio (1.0.1-1) ... 296s Selecting previously unselected package r-cran-car. 296s Preparing to unpack .../226-r-cran-car_3.1-2-2_all.deb ... 296s Unpacking r-cran-car (3.1-2-2) ... 296s Selecting previously unselected package r-cran-collapse. 296s Preparing to unpack .../227-r-cran-collapse_2.0.10-1_amd64.deb ... 296s Unpacking r-cran-collapse (2.0.10-1) ... 296s Selecting previously unselected package r-cran-formula. 296s Preparing to unpack .../228-r-cran-formula_1.2-5-1_all.deb ... 296s Unpacking r-cran-formula (1.2-5-1) ... 296s Selecting previously unselected package r-cran-zoo. 296s Preparing to unpack .../229-r-cran-zoo_1.8-12-2_amd64.deb ... 296s Unpacking r-cran-zoo (1.8-12-2) ... 296s Selecting previously unselected package r-cran-lmtest. 297s Preparing to unpack .../230-r-cran-lmtest_0.9.40-1_amd64.deb ... 297s Unpacking r-cran-lmtest (0.9.40-1) ... 297s Selecting previously unselected package r-cran-misctools. 297s Preparing to unpack .../231-r-cran-misctools_0.6-28-1_all.deb ... 297s Unpacking r-cran-misctools (0.6-28-1) ... 297s Selecting previously unselected package r-cran-sandwich. 297s Preparing to unpack .../232-r-cran-sandwich_3.1-0-1_all.deb ... 297s Unpacking r-cran-sandwich (3.1-0-1) ... 297s Selecting previously unselected package r-cran-maxlik. 297s Preparing to unpack .../233-r-cran-maxlik_1.5-2-1_all.deb ... 297s Unpacking r-cran-maxlik (1.5-2-1) ... 297s Selecting previously unselected package r-cran-rbibutils. 297s Preparing to unpack .../234-r-cran-rbibutils_2.2.16-1_amd64.deb ... 297s Unpacking r-cran-rbibutils (2.2.16-1) ... 297s Selecting previously unselected package r-cran-rdpack. 297s Preparing to unpack .../235-r-cran-rdpack_2.6-1_all.deb ... 297s Unpacking r-cran-rdpack (2.6-1) ... 297s Selecting previously unselected package r-cran-plm. 297s Preparing to unpack .../236-r-cran-plm_2.6-3-1_all.deb ... 297s Unpacking r-cran-plm (2.6-3-1) ... 297s Selecting previously unselected package r-cran-systemfit. 297s Preparing to unpack .../237-r-cran-systemfit_1.1-30-1_all.deb ... 297s Unpacking r-cran-systemfit (1.1-30-1) ... 297s Setting up libgraphite2-3:amd64 (1.3.14-2) ... 297s Setting up libpixman-1-0:amd64 (0.42.2-1) ... 297s Setting up libsharpyuv0:amd64 (1.3.2-0.4) ... 297s Setting up libpaper1:amd64 (1.1.29) ... 297s 297s Creating config file /etc/papersize with new version 297s Setting up fonts-mathjax (2.7.9+dfsg-1) ... 297s Setting up liblerc4:amd64 (4.0.0+ds-4ubuntu1) ... 297s Setting up libjs-mathjax (2.7.9+dfsg-1) ... 297s Setting up libxrender1:amd64 (1:0.9.10-1.1) ... 297s Setting up libdatrie1:amd64 (0.2.13-3) ... 297s Setting up libxcb-render0:amd64 (1.15-1) ... 297s Setting up fonts-glyphicons-halflings (1.009~3.4.1+dfsg-3) ... 297s Setting up unzip (6.0-28ubuntu3) ... 297s Setting up x11-common (1:7.7+23ubuntu2) ... 298s Setting up libdeflate0:amd64 (1.19-1) ... 298s Setting up linux-libc-dev:amd64 (6.8.0-11.11) ... 298s Setting up libnlopt0:amd64 (2.7.1-5build2) ... 298s Setting up libxcb-shm0:amd64 (1.15-1) ... 298s Setting up libpaper-utils (1.1.29) ... 298s Setting up libgomp1:amd64 (14-20240303-1ubuntu1) ... 298s Setting up libjbig0:amd64 (2.1-6.1ubuntu1) ... 298s Setting up zip (3.0-13) ... 298s Setting up libblas3:amd64 (3.12.0-3) ... 298s update-alternatives: using /usr/lib/x86_64-linux-gnu/blas/libblas.so.3 to provide /usr/lib/x86_64-linux-gnu/libblas.so.3 (libblas.so.3-x86_64-linux-gnu) in auto mode 298s Setting up rpcsvc-proto (1.4.2-0ubuntu6) ... 298s Setting up libquadmath0:amd64 (14-20240303-1ubuntu1) ... 298s Setting up fonts-dejavu-mono (2.37-8) ... 298s Setting up libmpc3:amd64 (1.3.1-1) ... 298s Setting up libatomic1:amd64 (14-20240303-1ubuntu1) ... 298s Setting up libtcl8.6:amd64 (8.6.13+dfsg-2) ... 298s Setting up fonts-dejavu-core (2.37-8) ... 298s Setting up libjpeg-turbo8:amd64 (2.1.5-2ubuntu1) ... 298s Setting up libgfortran5:amd64 (14-20240303-1ubuntu1) ... 298s Setting up libwebp7:amd64 (1.3.2-0.4) ... 298s Setting up libubsan1:amd64 (14-20240303-1ubuntu1) ... 298s Setting up libjs-highlight.js (9.18.5+dfsg1-2) ... 298s Setting up libhwasan0:amd64 (14-20240303-1ubuntu1) ... 298s Setting up libcrypt-dev:amd64 (1:4.4.36-4) ... 298s Setting up libasan8:amd64 (14-20240303-1ubuntu1) ... 298s Setting up libharfbuzz0b:amd64 (8.3.0-2) ... 298s Setting up libthai-data (0.1.29-2) ... 298s Setting up libxss1:amd64 (1:1.2.3-1build2) ... 298s Setting up libtsan2:amd64 (14-20240303-1ubuntu1) ... 298s Setting up libjs-jquery (3.6.1+dfsg+~3.5.14-1) ... 298s Setting up libisl23:amd64 (0.26-3) ... 298s Setting up libc-dev-bin (2.39-0ubuntu6) ... 298s Setting up node-normalize.css (8.0.1-5) ... 298s Setting up xdg-utils (1.1.3-4.1ubuntu3) ... 298s update-alternatives: using /usr/bin/xdg-open to provide /usr/bin/open (open) in auto mode 298s Setting up libcc1-0:amd64 (14-20240303-1ubuntu1) ... 298s Setting up liblsan0:amd64 (14-20240303-1ubuntu1) ... 298s Setting up libjs-bootstrap (3.4.1+dfsg-3) ... 298s Setting up libitm1:amd64 (14-20240303-1ubuntu1) ... 298s Setting up libjpeg8:amd64 (8c-2ubuntu11) ... 298s Setting up libice6:amd64 (2:1.0.10-1build2) ... 298s Setting up liblapack3:amd64 (3.12.0-3) ... 298s update-alternatives: using /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3 to provide /usr/lib/x86_64-linux-gnu/liblapack.so.3 (liblapack.so.3-x86_64-linux-gnu) in auto mode 298s Setting up cpp-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 298s Setting up fontconfig-config (2.15.0-1ubuntu1) ... 298s Setting up libjs-jquery-datatables (1.11.5+dfsg-2) ... 298s Setting up libthai0:amd64 (0.1.29-2) ... 298s Setting up libgcc-13-dev:amd64 (13.2.0-17ubuntu2) ... 298s Setting up libtiff6:amd64 (4.5.1+git230720-3ubuntu1) ... 298s Setting up libc6-dev:amd64 (2.39-0ubuntu6) ... 298s Setting up libfontconfig1:amd64 (2.15.0-1ubuntu1) ... 298s Setting up libsm6:amd64 (2:1.2.3-1build2) ... 298s Setting up libstdc++-13-dev:amd64 (13.2.0-17ubuntu2) ... 298s Setting up cpp-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 298s Setting up fontconfig (2.15.0-1ubuntu1) ... 302s Regenerating fonts cache... done. 302s Setting up libxft2:amd64 (2.3.6-1) ... 302s Setting up cpp-13 (13.2.0-17ubuntu2) ... 302s Setting up gcc-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 302s Setting up libtk8.6:amd64 (8.6.14-1) ... 302s Setting up libpango-1.0-0:amd64 (1.51.0+ds-4) ... 302s Setting up libcairo2:amd64 (1.18.0-1) ... 302s Setting up gcc-13 (13.2.0-17ubuntu2) ... 302s Setting up libxt6:amd64 (1:1.2.1-1.1) ... 302s Setting up cpp (4:13.2.0-7ubuntu1) ... 302s Setting up libpangoft2-1.0-0:amd64 (1.51.0+ds-4) ... 302s Setting up libpangocairo-1.0-0:amd64 (1.51.0+ds-4) ... 302s Setting up g++-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 302s Setting up gcc-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 302s Setting up gcc (4:13.2.0-7ubuntu1) ... 302s Setting up r-base-core (4.3.2-1build1) ... 302s 302s Creating config file /etc/R/Renviron with new version 302s Setting up r-cran-crayon (1.5.2-1) ... 302s Setting up r-cran-squarem (2021.1-1) ... 302s Setting up r-cran-labeling (0.4.3-1) ... 302s Setting up r-cran-lattice (0.22-5-1) ... 302s Setting up r-cran-ps (1.7.6-1) ... 302s Setting up r-cran-nlme (3.1.164-1) ... 302s Setting up r-cran-farver (2.1.1-1) ... 302s Setting up r-cran-formula (1.2-5-1) ... 302s Setting up r-cran-zip (2.3.1-1) ... 302s Setting up r-cran-viridislite (0.4.2-2) ... 302s Setting up r-cran-sparsem (1.81-1) ... 302s Setting up r-cran-statmod (1.5.0-1) ... 302s Setting up g++-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 302s Setting up r-cran-nnet (7.3-19-2) ... 302s Setting up r-cran-clipr (0.8.0-1) ... 302s Setting up r-cran-proxy (0.4-27-1) ... 302s Setting up r-cran-r6 (2.5.1-1) ... 302s Setting up r-cran-pkgkitten (0.2.3-1) ... 302s Setting up r-cran-numderiv (2016.8-1.1-3) ... 302s Setting up r-cran-magrittr (2.0.3-1) ... 302s Setting up r-cran-littler (0.3.19-1) ... 302s Setting up r-cran-fs (1.6.3+dfsg-1) ... 302s Setting up r-cran-rcpp (1.0.12-1) ... 302s Setting up r-cran-curl (5.2.0+dfsg-1) ... 302s Setting up r-cran-codetools (0.2-19-1) ... 302s Setting up g++-13 (13.2.0-17ubuntu2) ... 302s Setting up r-cran-brio (1.1.4-1) ... 302s Setting up r-cran-boot (1.3-30-1) ... 302s Setting up r-cran-diffobj (0.3.5-1) ... 302s Setting up r-cran-rematch (2.0.0-1) ... 302s Setting up r-cran-rlang (1.1.3-1) ... 302s Setting up r-cran-matrixstats (1.2.0-1) ... 302s Setting up r-cran-listenv (0.9.1+dfsg-1) ... 302s Setting up littler (0.3.19-1) ... 302s Setting up r-cran-xfun (0.41+dfsg-1) ... 302s Setting up r-cran-withr (2.5.0-1) ... 302s Setting up r-cran-backports (1.4.1-1) ... 302s Setting up r-cran-processx (3.8.3-1) ... 302s Setting up r-cran-praise (1.0.0-4build1) ... 302s Setting up r-cran-generics (0.1.3-1) ... 302s Setting up r-cran-iterators (1.0.14-1) ... 302s Setting up r-cran-abind (1.4-5-2) ... 302s Setting up r-cran-digest (0.6.34-1) ... 302s Setting up r-cran-yaml (2.3.8-1) ... 302s Setting up r-cran-gower (1.0.1-1) ... 302s Setting up r-cran-evaluate (0.23-1) ... 302s Setting up r-cran-timedate (4032.109-1) ... 302s Setting up r-cran-highr (0.10+dfsg-1) ... 302s Setting up r-cran-foreach (1.5.2-1) ... 302s Setting up r-cran-prettyunits (1.2.0-1) ... 302s Setting up r-cran-fansi (1.0.5-1) ... 302s Setting up r-cran-cardata (3.0.5-1) ... 302s Setting up r-cran-mass (7.3-60.0.1-1) ... 302s Setting up r-cran-collapse (2.0.10-1) ... 302s Setting up r-cran-bdsmatrix (1.3-6-1) ... 302s Setting up r-cran-data.table (1.14.10+dfsg-1) ... 302s Setting up r-cran-glue (1.7.0-1) ... 302s Setting up r-cran-foreign (0.8.86-1) ... 302s Setting up r-cran-writexl (1.5.0-1) ... 302s Setting up r-cran-bit (4.0.5-1) ... 302s Setting up r-cran-cli (3.6.2-1) ... 302s Setting up r-cran-rbibutils (2.2.16-1) ... 302s Setting up r-cran-lifecycle (1.0.4+dfsg-1) ... 302s Setting up r-cran-rprojroot (2.0.4-1) ... 302s Setting up r-cran-bit64 (4.0.5-1) ... 302s Setting up r-cran-progressr (0.14.0-1) ... 302s Setting up r-cran-shape (1.4.6-1) ... 302s Setting up r-cran-r.methodss3 (1.8.2-1) ... 302s Setting up r-cran-jsonlite (1.8.8+dfsg-1) ... 302s Setting up r-cran-pkgconfig (2.0.3-2build1) ... 302s Setting up r-cran-sp (1:2.1-2+dfsg-1) ... 302s Setting up r-cran-utf8 (1.2.4-1) ... 302s Setting up r-cran-colorspace (2.1-0+dfsg-1) ... 302s Setting up r-cran-parallelly (1.37.1-1) ... 302s Setting up r-cran-stringi (1.8.3-1) ... 302s Setting up r-cran-cpp11 (0.4.7-1) ... 302s Setting up r-cran-plyr (1.8.9-1) ... 302s Setting up r-cran-rcolorbrewer (1.1-3-1build1) ... 302s Setting up r-cran-isoband (0.2.7-1) ... 302s Setting up r-cran-diagram (1.6.5-2) ... 302s Setting up r-cran-gtable (0.3.4+dfsg-1) ... 302s Setting up r-cran-zoo (1.8-12-2) ... 302s Setting up r-cran-matrix (1.6-5-1) ... 302s Setting up r-cran-kernsmooth (2.23-22-1) ... 302s Setting up r-cran-knitr (1.45+dfsg-1) ... 302s Setting up r-cran-mgcv (1.9-1-1) ... 302s Setting up g++ (4:13.2.0-7ubuntu1) ... 302s update-alternatives: using /usr/bin/g++ to provide /usr/bin/c++ (c++) in auto mode 302s Setting up r-cran-lmtest (0.9.40-1) ... 302s Setting up build-essential (12.10ubuntu1) ... 302s Setting up r-cran-rcpparmadillo (0.12.8.0.0-1) ... 302s Setting up r-cran-tzdb (0.4.0-2) ... 302s Setting up r-cran-globals (0.16.2-1) ... 302s Setting up r-cran-maptools (1:1.1-8+dfsg-1) ... 302s Setting up r-cran-vctrs (0.6.5-1) ... 302s Setting up r-cran-rcppeigen (0.3.3.9.4-1) ... 302s Setting up r-cran-pillar (1.9.0+dfsg-1) ... 302s Setting up r-cran-ellipsis (0.3.2-2) ... 302s Setting up r-cran-minqa (1.2.6-1) ... 302s Setting up r-cran-misctools (0.6-28-1) ... 302s Setting up r-cran-stringr (1.5.1-1) ... 302s Setting up r-cran-class (7.3-22-2) ... 302s Setting up r-cran-modelmetrics (1.2.2.2-1build1) ... 302s Setting up r-cran-callr (3.7.3-2) ... 302s Setting up r-cran-openxlsx (4.2.5.2-1) ... 302s Setting up r-cran-matrixmodels (0.5-3-1) ... 302s Setting up r-cran-desc (1.4.3-1) ... 302s Setting up r-cran-munsell (0.5.0-2build1) ... 302s Setting up r-cran-tibble (3.2.1+dfsg-2) ... 302s Setting up r-cran-clock (0.7.0-1.1) ... 302s Setting up r-cran-sandwich (3.1-0-1) ... 302s Setting up r-cran-proc (1.18.5-1) ... 302s Setting up r-cran-survival (3.5-8-1) ... 302s Setting up r-cran-r.oo (1.26.0-1) ... 302s Setting up r-cran-rdpack (2.6-1) ... 302s Setting up r-cran-future (1.33.1+dfsg-1) ... 302s Setting up r-cran-forcats (1.0.0-1) ... 302s Setting up r-cran-tidyselect (1.2.0+dfsg-1) ... 302s Setting up r-cran-reshape2 (1.4.4-2build1) ... 302s Setting up r-cran-future.apply (1.11.1+dfsg-1) ... 302s Setting up r-cran-timechange (0.3.0-1) ... 302s Setting up r-cran-hms (1.1.3-1) ... 302s Setting up r-cran-scales (1.3.0-1) ... 302s Setting up r-cran-lava (1.7.3+dfsg-1) ... 302s Setting up r-cran-purrr (1.0.2-1) ... 302s Setting up r-cran-e1071 (1.7-14-1) ... 302s Setting up r-cran-maxlik (1.5-2-1) ... 302s Setting up r-cran-pkgbuild (1.4.3-1) ... 302s Setting up r-cran-hardhat (1.3.1+dfsg-1) ... 302s Setting up r-cran-dplyr (1.1.4-1) ... 302s Setting up r-cran-progress (1.2.3-1) ... 302s Setting up r-cran-lubridate (1.9.3+dfsg-1) ... 302s Setting up r-cran-pkgload (1.3.4-1) ... 302s Setting up r-cran-r.utils (2.12.3-1) ... 302s Setting up r-cran-vroom (1.6.5-1) ... 302s Setting up r-cran-prodlim (2023.08.28-1) ... 302s Setting up r-cran-ggplot2 (3.4.4+dfsg-1) ... 302s Setting up r-cran-cellranger (1.1.0-3) ... 302s Setting up r-cran-rematch2 (2.1.2-2build1) ... 302s Setting up r-cran-rpart (4.1.23-1) ... 302s Setting up r-cran-plm (2.6-3-1) ... 302s Setting up r-cran-ipred (0.9-14-1) ... 302s Setting up r-cran-readr (2.1.5-1) ... 302s Setting up r-cran-waldo (0.5.2-1build1) ... 302s Setting up r-cran-tidyr (1.3.1-1) ... 302s Setting up r-cran-recipes (1.0.9+dfsg-1) ... 302s Setting up r-cran-readxl (1.4.3-1) ... 302s Setting up r-cran-haven (2.5.4-1) ... 302s Setting up r-cran-caret (6.0-94+dfsg-1) ... 302s Setting up r-cran-testthat (3.2.1-1) ... 302s Setting up r-cran-broom (1.0.5+dfsg-1) ... 302s Setting up r-cran-conquer (1.3.3-1) ... 302s Setting up r-cran-rio (1.0.1-1) ... 302s Setting up r-cran-nloptr (2.0.3-1) ... 302s Setting up r-cran-quantreg (5.97-1) ... 302s Setting up r-cran-lme4 (1.1-35.1-4) ... 302s Setting up r-cran-pbkrtest (0.5.2-2) ... 302s Setting up r-cran-car (3.1-2-2) ... 302s Setting up r-cran-systemfit (1.1-30-1) ... 302s Processing triggers for man-db (2.12.0-3) ... 302s Processing triggers for install-info (7.1-3) ... 302s Processing triggers for libc-bin (2.39-0ubuntu6) ... 304s Reading package lists... 305s Building dependency tree... 305s Reading state information... 305s Starting pkgProblemResolver with broken count: 0 305s Starting 2 pkgProblemResolver with broken count: 0 305s Done 306s The following NEW packages will be installed: 306s autopkgtest-satdep 306s 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. 306s Need to get 0 B/696 B of archives. 306s After this operation, 0 B of additional disk space will be used. 306s Get:1 /tmp/autopkgtest.isQjql/2-autopkgtest-satdep.deb autopkgtest-satdep amd64 0 [696 B] 306s Selecting previously unselected package autopkgtest-satdep. 306s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 95548 files and directories currently installed.) 306s Preparing to unpack .../2-autopkgtest-satdep.deb ... 306s Unpacking autopkgtest-satdep (0) ... 306s Setting up autopkgtest-satdep (0) ... 308s (Reading database ... 95548 files and directories currently installed.) 308s Removing autopkgtest-satdep (0) ... 309s autopkgtest [01:37:09]: test run-unit-test: [----------------------- 309s BEGIN TEST KleinI.R 309s 309s R version 4.3.2 (2023-10-31) -- "Eye Holes" 309s Copyright (C) 2023 The R Foundation for Statistical Computing 309s Platform: x86_64-pc-linux-gnu (64-bit) 309s 309s R is free software and comes with ABSOLUTELY NO WARRANTY. 309s You are welcome to redistribute it under certain conditions. 309s Type 'license()' or 'licence()' for distribution details. 309s 309s R is a collaborative project with many contributors. 309s Type 'contributors()' for more information and 309s 'citation()' on how to cite R or R packages in publications. 309s 309s Type 'demo()' for some demos, 'help()' for on-line help, or 309s 'help.start()' for an HTML browser interface to help. 309s Type 'q()' to quit R. 309s 309s > library( "systemfit" ) 309s Loading required package: Matrix 310s Loading required package: car 310s Loading required package: carData 310s Loading required package: lmtest 310s Loading required package: zoo 310s 310s Attaching package: ‘zoo’ 310s 310s The following objects are masked from ‘package:base’: 310s 310s as.Date, as.Date.numeric 310s 310s 310s Please cite the 'systemfit' package as: 310s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 310s 310s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 310s https://r-forge.r-project.org/projects/systemfit/ 310s > library( "sandwich" ) 310s > options( warn = 1 ) 310s > options( digits = 3 ) 310s > 310s > data( "KleinI" ) 310s > eqConsump <- consump ~ corpProf + corpProfLag + wages 310s > eqInvest <- invest ~ corpProf + corpProfLag + capitalLag 310s > eqPrivWage <- privWage ~ gnp + gnpLag + trend 310s > inst <- ~ govExp + taxes + govWage + trend + capitalLag + corpProfLag + gnpLag 310s > system <- list( Consumption = eqConsump, Investment = eqInvest, 310s + PrivateWages = eqPrivWage ) 310s > restrict <- c( "Consumption_corpProf + Investment_capitalLag = 0" ) 310s > restrict2 <- c( restrict, "Consumption_corpProfLag - PrivateWages_trend = 0" ) 310s > 310s > for( dataNo in 1:5 ) { 310s + # set some values of some variables to NA 310s + if( dataNo == 2 ) { 310s + KleinI$gnpLag[ 7 ] <- NA 310s + } else if( dataNo == 3 ) { 310s + KleinI$wages[ 10 ] <- NA 310s + } else if( dataNo == 4 ) { 310s + KleinI$corpProf[ 13 ] <- NA 310s + } else if( dataNo == 5 ) { 310s + KleinI$invest[ 16 ] <- NA 310s + } 310s + 310s + # single-equation OLS 310s + lmConsump <- lm( eqConsump, data = KleinI ) 310s + lmInvest <- lm( eqInvest, data = KleinI ) 310s + lmPrivWage <- lm( eqPrivWage, data = KleinI ) 310s + 310s + for( methodNo in 1:5 ) { 310s + method <- c( "OLS", "2SLS", "SUR", "3SLS", "3SLS" )[ methodNo ] 310s + maxit <- ifelse( methodNo == 5, 500, 1 ) 310s + 310s + cat( "> \n> # ", ifelse( maxit == 1, "", "I" ), method, "\n", sep = "" ) 310s + if( method %in% c( "OLS", "WLS", "SUR" ) ) { 310s + kleinModel <- systemfit( system, method = method, data = KleinI, 310s + methodResidCov = ifelse( method == "OLS", "geomean", "noDfCor" ), 310s + maxit = maxit ) 310s + } else { 310s + kleinModel <- systemfit( system, method = method, data = KleinI, 310s + inst = inst, methodResidCov = "noDfCor", maxit = maxit ) 310s + } 310s + cat( "> summary\n" ) 310s + print( summary( kleinModel ) ) 310s + if( method == "OLS" ) { 310s + cat( "compare coef with single-equation OLS\n" ) 310s + print( all.equal( coef( kleinModel ), 310s + c( coef( lmConsump ), coef( lmInvest ), coef( lmPrivWage ) ), 310s + check.attributes = FALSE ) ) 310s + } 310s + cat( "> residuals\n" ) 310s + print( residuals( kleinModel ) ) 310s + cat( "> fitted\n" ) 310s + print( fitted( kleinModel ) ) 310s + cat( "> predict\n" ) 310s + print( predict( kleinModel, se.fit = TRUE, 310s + interval = ifelse( methodNo %in% c( 1, 4 ), "prediction", "confidence" ), 310s + useDfSys = methodNo %in% c( 1, 3, 5 ) ) ) 310s + cat( "> model.frame\n" ) 310s + if( methodNo == 1 ) { 310s + mfOls <- model.frame( kleinModel ) 310s + print( mfOls ) 310s + } else if( methodNo == 2 ) { 310s + mf2sls <- model.frame( kleinModel ) 310s + print( mf2sls ) 310s + cat( "> Frames of instrumental variables\n" ) 310s + for( i in 1:3 ){ 310s + print( kleinModel$eq[[ i ]]$modelInst ) 310s + } 310s + } else if( methodNo == 3 ) { 310s + print( all.equal( mfOls, model.frame( kleinModel ) ) ) 310s + } else { 310s + print( all.equal( mf2sls, model.frame( kleinModel ) ) ) 310s + } 310s + cat( "> model.matrix\n" ) 310s + if( methodNo == 1 ) { 310s + mmOls <- model.matrix( kleinModel ) 310s + print( mmOls ) 310s + } else { 310s + print( all.equal( mmOls, model.matrix( kleinModel ) ) ) 310s + } 310s + if( methodNo == 2 ) { 310s + cat( "> matrix of instrumental variables\n" ) 310s + print( model.matrix( kleinModel, which = "z" ) ) 310s + cat( "> matrix of fitted regressors\n" ) 310s + print( round( model.matrix( kleinModel, which = "xHat" ), digits = 7 ) ) 310s + } 310s + cat( "> nobs\n" ) 310s + print( nobs( kleinModel ) ) 310s + cat( "> linearHypothesis\n" ) 310s + print( linearHypothesis( kleinModel, restrict ) ) 310s + print( linearHypothesis( kleinModel, restrict, test = "F" ) ) 310s + print( linearHypothesis( kleinModel, restrict, test = "Chisq" ) ) 310s + print( linearHypothesis( kleinModel, restrict2 ) ) 310s + print( linearHypothesis( kleinModel, restrict2, test = "F" ) ) 310s + print( linearHypothesis( kleinModel, restrict2, test = "Chisq" ) ) 310s + cat( "> logLik\n" ) 310s + print( logLik( kleinModel ) ) 310s + print( logLik( kleinModel, residCovDiag = TRUE ) ) 310s + if( method == "OLS" ) { 310s + cat( "compare log likelihood value with single-equation OLS\n" ) 310s + print( all.equal( logLik( kleinModel, residCovDiag = TRUE ), 310s + logLik( lmConsump ) + logLik( lmInvest ) + logLik( lmPrivWage ), 310s + check.attributes = FALSE ) ) 310s + } 310s + 310s + cat( "Estimating function\n" ) 310s + print( round( estfun( kleinModel ), digits = 7 ) ) 310s + print( all.equal( colSums( estfun( kleinModel ) ), 310s + rep( 0, ncol( estfun( kleinModel ) ) ), check.attributes = FALSE ) ) 310s + 310s + cat( "> Bread\n" ) 310s + print( bread( kleinModel ) ) 310s + } 310s + } 310s > 310s > # OLS 310s > summary 310s 310s systemfit results 310s method: OLS 310s 310s N DF SSR detRCov OLS-R2 McElroy-R2 310s system 63 51 45.2 0.371 0.977 0.991 310s 310s N DF SSR MSE RMSE R2 Adj R2 310s Consumption 21 17 17.9 1.052 1.026 0.981 0.978 310s Investment 21 17 17.3 1.019 1.009 0.931 0.919 310s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 310s 310s The covariance matrix of the residuals 310s Consumption Investment PrivateWages 310s Consumption 1.0517 0.0611 -0.470 310s Investment 0.0611 1.0190 0.150 310s PrivateWages -0.4704 0.1497 0.589 310s 310s The correlations of the residuals 310s Consumption Investment PrivateWages 310s Consumption 1.0000 0.0591 -0.598 310s Investment 0.0591 1.0000 0.193 310s PrivateWages -0.5979 0.1933 1.000 310s 310s 310s OLS estimates for 'Consumption' (equation 1) 310s Model Formula: consump ~ corpProf + corpProfLag + wages 310s 310s Estimate Std. Error t value Pr(>|t|) 310s (Intercept) 16.2366 1.3027 12.46 5.6e-10 *** 310s corpProf 0.1929 0.0912 2.12 0.049 * 310s corpProfLag 0.0899 0.0906 0.99 0.335 310s wages 0.7962 0.0399 19.93 3.2e-13 *** 310s --- 310s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 310s 310s Residual standard error: 1.026 on 17 degrees of freedom 310s Number of observations: 21 Degrees of Freedom: 17 310s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 310s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 310s 310s 310s OLS estimates for 'Investment' (equation 2) 310s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 310s 310s Estimate Std. Error t value Pr(>|t|) 310s (Intercept) 10.1258 5.4655 1.85 0.08137 . 310s corpProf 0.4796 0.0971 4.94 0.00012 *** 310s corpProfLag 0.3330 0.1009 3.30 0.00421 ** 310s capitalLag -0.1118 0.0267 -4.18 0.00062 *** 310s --- 310s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 310s 310s Residual standard error: 1.009 on 17 degrees of freedom 310s Number of observations: 21 Degrees of Freedom: 17 310s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 310s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 310s 310s 310s OLS estimates for 'PrivateWages' (equation 3) 310s Model Formula: privWage ~ gnp + gnpLag + trend 310s 310s Estimate Std. Error t value Pr(>|t|) 310s (Intercept) 1.4970 1.2700 1.18 0.25474 310s gnp 0.4395 0.0324 13.56 1.5e-10 *** 310s gnpLag 0.1461 0.0374 3.90 0.00114 ** 310s trend 0.1302 0.0319 4.08 0.00078 *** 310s --- 310s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 310s 310s Residual standard error: 0.767 on 17 degrees of freedom 310s Number of observations: 21 Degrees of Freedom: 17 310s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 310s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 310s 310s compare coef with single-equation OLS 310s [1] TRUE 310s > residuals 310s Consumption Investment PrivateWages 310s 1 NA NA NA 310s 2 -0.32389 -0.0668 -1.2942 310s 3 -1.25001 -0.0476 0.2957 310s 4 -1.56574 1.2467 1.1877 310s 5 -0.49350 -1.3512 -0.1358 310s 6 0.00761 0.4154 -0.4654 310s 7 0.86910 1.4923 -0.4838 310s 8 1.33848 0.7889 -0.7281 310s 9 1.05498 -0.6317 0.3392 310s 10 -0.58856 1.0830 1.1957 310s 11 0.28231 0.2791 -0.1508 310s 12 -0.22965 0.0369 0.5942 310s 13 -0.32213 0.3659 0.1027 310s 14 0.32228 0.2237 0.4503 310s 15 -0.05801 -0.1728 0.2816 310s 16 -0.03466 0.0101 0.0138 310s 17 1.61650 0.9719 -0.8508 310s 18 -0.43597 0.0516 0.9956 310s 19 0.21005 -2.5656 -0.4688 310s 20 0.98920 -0.6866 -0.3795 310s 21 0.78508 -0.7807 -1.0909 310s 22 -2.17345 -0.6623 0.5917 310s > fitted 310s Consumption Investment PrivateWages 310s 1 NA NA NA 310s 2 42.2 -0.133 26.8 310s 3 46.3 1.948 29.0 310s 4 50.8 3.953 32.9 310s 5 51.1 4.351 34.0 310s 6 52.6 4.685 35.9 310s 7 54.2 4.108 37.9 310s 8 54.9 3.411 38.6 310s 9 56.2 3.632 38.9 310s 10 58.4 4.017 40.1 310s 11 54.7 0.721 38.1 310s 12 51.1 -3.437 33.9 310s 13 45.9 -6.566 28.9 310s 14 46.2 -5.324 28.0 310s 15 48.8 -2.827 30.3 310s 16 51.3 -1.310 33.2 310s 17 56.1 1.128 37.7 310s 18 59.1 1.948 40.0 310s 19 57.3 0.666 38.7 310s 20 60.6 1.987 42.0 310s 21 64.2 4.081 46.1 310s 22 71.9 5.562 52.7 310s > predict 310s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 310s 1 NA NA NA NA 310s 2 42.2 0.462 40.0 44.5 310s 3 46.3 0.518 43.9 48.6 310s 4 50.8 0.341 48.6 52.9 310s 5 51.1 0.396 48.9 53.3 310s 6 52.6 0.397 50.4 54.8 310s 7 54.2 0.359 52.0 56.4 310s 8 54.9 0.327 52.7 57.0 310s 9 56.2 0.350 54.1 58.4 310s 10 58.4 0.370 56.2 60.6 310s 11 54.7 0.606 52.3 57.1 310s 12 51.1 0.484 48.9 53.4 310s 13 45.9 0.629 43.5 48.3 310s 14 46.2 0.602 43.8 48.6 310s 15 48.8 0.374 46.6 50.9 310s 16 51.3 0.333 49.2 53.5 310s 17 56.1 0.366 53.9 58.3 310s 18 59.1 0.321 57.0 61.3 310s 19 57.3 0.371 55.1 59.5 310s 20 60.6 0.434 58.4 62.8 310s 21 64.2 0.425 62.0 66.4 310s 22 71.9 0.666 69.4 74.3 310s Investment.pred Investment.se.fit Investment.lwr Investment.upr 310s 1 NA NA NA NA 310s 2 -0.133 0.607 -2.498 2.231 310s 3 1.948 0.499 -0.313 4.208 310s 4 3.953 0.449 1.735 6.171 310s 5 4.351 0.371 2.192 6.510 310s 6 4.685 0.349 2.540 6.829 310s 7 4.108 0.329 1.976 6.239 310s 8 3.411 0.292 1.301 5.521 310s 9 3.632 0.389 1.460 5.804 310s 10 4.017 0.447 1.801 6.233 310s 11 0.721 0.601 -1.638 3.080 310s 12 -3.437 0.507 -5.704 -1.169 310s 13 -6.566 0.616 -8.940 -4.192 310s 14 -5.324 0.694 -7.783 -2.865 310s 15 -2.827 0.373 -4.988 -0.667 310s 16 -1.310 0.320 -3.436 0.816 310s 17 1.128 0.347 -1.015 3.271 310s 18 1.948 0.243 -0.136 4.033 310s 19 0.666 0.312 -1.456 2.787 310s 20 1.987 0.366 -0.169 4.143 310s 21 4.081 0.332 1.948 6.214 310s 22 5.562 0.461 3.334 7.790 310s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 310s 1 NA NA NA NA 310s 2 26.8 0.354 25.1 28.5 310s 3 29.0 0.355 27.3 30.7 310s 4 32.9 0.354 31.2 34.6 310s 5 34.0 0.269 32.4 35.7 310s 6 35.9 0.266 34.2 37.5 310s 7 37.9 0.266 36.3 39.5 310s 8 38.6 0.273 37.0 40.3 310s 9 38.9 0.261 37.2 40.5 310s 10 40.1 0.247 38.5 41.7 310s 11 38.1 0.354 36.4 39.7 310s 12 33.9 0.363 32.2 35.6 310s 13 28.9 0.429 27.1 30.7 310s 14 28.0 0.376 26.3 29.8 310s 15 30.3 0.371 28.6 32.0 310s 16 33.2 0.310 31.5 34.8 310s 17 37.7 0.305 36.0 39.3 310s 18 40.0 0.238 38.4 41.6 310s 19 38.7 0.357 37.0 40.4 310s 20 42.0 0.321 40.3 43.6 310s 21 46.1 0.335 44.4 47.8 310s 22 52.7 0.502 50.9 54.5 310s > model.frame 310s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 310s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 310s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 310s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 310s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 310s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 310s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 310s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 310s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 310s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 310s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 310s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 310s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 310s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 310s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 310s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 310s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 310s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 310s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 310s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 310s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 310s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 310s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 310s trend 310s 1 -11 310s 2 -10 310s 3 -9 310s 4 -8 310s 5 -7 310s 6 -6 310s 7 -5 310s 8 -4 310s 9 -3 310s 10 -2 310s 11 -1 310s 12 0 310s 13 1 310s 14 2 310s 15 3 310s 16 4 310s 17 5 310s 18 6 310s 19 7 310s 20 8 310s 21 9 310s 22 10 310s > model.matrix 310s Consumption_(Intercept) Consumption_corpProf 310s Consumption_2 1 12.4 310s Consumption_3 1 16.9 310s Consumption_4 1 18.4 310s Consumption_5 1 19.4 310s Consumption_6 1 20.1 310s Consumption_7 1 19.6 310s Consumption_8 1 19.8 310s Consumption_9 1 21.1 310s Consumption_10 1 21.7 310s Consumption_11 1 15.6 310s Consumption_12 1 11.4 310s Consumption_13 1 7.0 310s Consumption_14 1 11.2 310s Consumption_15 1 12.3 310s Consumption_16 1 14.0 310s Consumption_17 1 17.6 310s Consumption_18 1 17.3 310s Consumption_19 1 15.3 310s Consumption_20 1 19.0 310s Consumption_21 1 21.1 310s Consumption_22 1 23.5 310s Investment_2 0 0.0 310s Investment_3 0 0.0 310s Investment_4 0 0.0 310s Investment_5 0 0.0 310s Investment_6 0 0.0 310s Investment_7 0 0.0 310s Investment_8 0 0.0 310s Investment_9 0 0.0 310s Investment_10 0 0.0 310s Investment_11 0 0.0 310s Investment_12 0 0.0 310s Investment_13 0 0.0 310s Investment_14 0 0.0 310s Investment_15 0 0.0 310s Investment_16 0 0.0 310s Investment_17 0 0.0 310s Investment_18 0 0.0 310s Investment_19 0 0.0 310s Investment_20 0 0.0 310s Investment_21 0 0.0 310s Investment_22 0 0.0 310s PrivateWages_2 0 0.0 310s PrivateWages_3 0 0.0 310s PrivateWages_4 0 0.0 310s PrivateWages_5 0 0.0 310s PrivateWages_6 0 0.0 310s PrivateWages_7 0 0.0 310s PrivateWages_8 0 0.0 310s PrivateWages_9 0 0.0 310s PrivateWages_10 0 0.0 310s PrivateWages_11 0 0.0 310s PrivateWages_12 0 0.0 310s PrivateWages_13 0 0.0 310s PrivateWages_14 0 0.0 310s PrivateWages_15 0 0.0 310s PrivateWages_16 0 0.0 310s PrivateWages_17 0 0.0 310s PrivateWages_18 0 0.0 310s PrivateWages_19 0 0.0 310s PrivateWages_20 0 0.0 310s PrivateWages_21 0 0.0 310s PrivateWages_22 0 0.0 310s Consumption_corpProfLag Consumption_wages 310s Consumption_2 12.7 28.2 310s Consumption_3 12.4 32.2 310s Consumption_4 16.9 37.0 310s Consumption_5 18.4 37.0 310s Consumption_6 19.4 38.6 310s Consumption_7 20.1 40.7 310s Consumption_8 19.6 41.5 310s Consumption_9 19.8 42.9 310s Consumption_10 21.1 45.3 310s Consumption_11 21.7 42.1 310s Consumption_12 15.6 39.3 310s Consumption_13 11.4 34.3 310s Consumption_14 7.0 34.1 310s Consumption_15 11.2 36.6 310s Consumption_16 12.3 39.3 310s Consumption_17 14.0 44.2 310s Consumption_18 17.6 47.7 310s Consumption_19 17.3 45.9 310s Consumption_20 15.3 49.4 310s Consumption_21 19.0 53.0 310s Consumption_22 21.1 61.8 310s Investment_2 0.0 0.0 310s Investment_3 0.0 0.0 310s Investment_4 0.0 0.0 310s Investment_5 0.0 0.0 310s Investment_6 0.0 0.0 310s Investment_7 0.0 0.0 310s Investment_8 0.0 0.0 310s Investment_9 0.0 0.0 310s Investment_10 0.0 0.0 310s Investment_11 0.0 0.0 310s Investment_12 0.0 0.0 310s Investment_13 0.0 0.0 310s Investment_14 0.0 0.0 310s Investment_15 0.0 0.0 310s Investment_16 0.0 0.0 310s Investment_17 0.0 0.0 310s Investment_18 0.0 0.0 310s Investment_19 0.0 0.0 310s Investment_20 0.0 0.0 310s Investment_21 0.0 0.0 310s Investment_22 0.0 0.0 310s PrivateWages_2 0.0 0.0 310s PrivateWages_3 0.0 0.0 310s PrivateWages_4 0.0 0.0 310s PrivateWages_5 0.0 0.0 310s PrivateWages_6 0.0 0.0 310s PrivateWages_7 0.0 0.0 310s PrivateWages_8 0.0 0.0 310s PrivateWages_9 0.0 0.0 310s PrivateWages_10 0.0 0.0 310s PrivateWages_11 0.0 0.0 310s PrivateWages_12 0.0 0.0 310s PrivateWages_13 0.0 0.0 310s PrivateWages_14 0.0 0.0 310s PrivateWages_15 0.0 0.0 310s PrivateWages_16 0.0 0.0 310s PrivateWages_17 0.0 0.0 310s PrivateWages_18 0.0 0.0 310s PrivateWages_19 0.0 0.0 310s PrivateWages_20 0.0 0.0 310s PrivateWages_21 0.0 0.0 310s PrivateWages_22 0.0 0.0 310s Investment_(Intercept) Investment_corpProf 310s Consumption_2 0 0.0 310s Consumption_3 0 0.0 310s Consumption_4 0 0.0 310s Consumption_5 0 0.0 310s Consumption_6 0 0.0 310s Consumption_7 0 0.0 310s Consumption_8 0 0.0 310s Consumption_9 0 0.0 310s Consumption_10 0 0.0 310s Consumption_11 0 0.0 310s Consumption_12 0 0.0 310s Consumption_13 0 0.0 310s Consumption_14 0 0.0 310s Consumption_15 0 0.0 310s Consumption_16 0 0.0 310s Consumption_17 0 0.0 310s Consumption_18 0 0.0 310s Consumption_19 0 0.0 310s Consumption_20 0 0.0 310s Consumption_21 0 0.0 310s Consumption_22 0 0.0 310s Investment_2 1 12.4 310s Investment_3 1 16.9 310s Investment_4 1 18.4 310s Investment_5 1 19.4 310s Investment_6 1 20.1 310s Investment_7 1 19.6 310s Investment_8 1 19.8 310s Investment_9 1 21.1 310s Investment_10 1 21.7 310s Investment_11 1 15.6 310s Investment_12 1 11.4 310s Investment_13 1 7.0 310s Investment_14 1 11.2 310s Investment_15 1 12.3 310s Investment_16 1 14.0 310s Investment_17 1 17.6 310s Investment_18 1 17.3 310s Investment_19 1 15.3 310s Investment_20 1 19.0 310s Investment_21 1 21.1 310s Investment_22 1 23.5 310s PrivateWages_2 0 0.0 310s PrivateWages_3 0 0.0 310s PrivateWages_4 0 0.0 310s PrivateWages_5 0 0.0 310s PrivateWages_6 0 0.0 310s PrivateWages_7 0 0.0 310s PrivateWages_8 0 0.0 310s PrivateWages_9 0 0.0 310s PrivateWages_10 0 0.0 310s PrivateWages_11 0 0.0 310s PrivateWages_12 0 0.0 310s PrivateWages_13 0 0.0 310s PrivateWages_14 0 0.0 310s PrivateWages_15 0 0.0 310s PrivateWages_16 0 0.0 310s PrivateWages_17 0 0.0 310s PrivateWages_18 0 0.0 310s PrivateWages_19 0 0.0 310s PrivateWages_20 0 0.0 310s PrivateWages_21 0 0.0 310s PrivateWages_22 0 0.0 310s Investment_corpProfLag Investment_capitalLag 310s Consumption_2 0.0 0 310s Consumption_3 0.0 0 310s Consumption_4 0.0 0 310s Consumption_5 0.0 0 310s Consumption_6 0.0 0 310s Consumption_7 0.0 0 310s Consumption_8 0.0 0 310s Consumption_9 0.0 0 310s Consumption_10 0.0 0 310s Consumption_11 0.0 0 310s Consumption_12 0.0 0 310s Consumption_13 0.0 0 310s Consumption_14 0.0 0 310s Consumption_15 0.0 0 310s Consumption_16 0.0 0 310s Consumption_17 0.0 0 310s Consumption_18 0.0 0 310s Consumption_19 0.0 0 310s Consumption_20 0.0 0 310s Consumption_21 0.0 0 310s Consumption_22 0.0 0 310s Investment_2 12.7 183 310s Investment_3 12.4 183 310s Investment_4 16.9 184 310s Investment_5 18.4 190 310s Investment_6 19.4 193 310s Investment_7 20.1 198 310s Investment_8 19.6 203 310s Investment_9 19.8 208 310s Investment_10 21.1 211 310s Investment_11 21.7 216 310s Investment_12 15.6 217 310s Investment_13 11.4 213 310s Investment_14 7.0 207 310s Investment_15 11.2 202 310s Investment_16 12.3 199 310s Investment_17 14.0 198 310s Investment_18 17.6 200 310s Investment_19 17.3 202 310s Investment_20 15.3 200 310s Investment_21 19.0 201 310s Investment_22 21.1 204 310s PrivateWages_2 0.0 0 310s PrivateWages_3 0.0 0 310s PrivateWages_4 0.0 0 310s PrivateWages_5 0.0 0 310s PrivateWages_6 0.0 0 310s PrivateWages_7 0.0 0 310s PrivateWages_8 0.0 0 310s PrivateWages_9 0.0 0 310s PrivateWages_10 0.0 0 310s PrivateWages_11 0.0 0 310s PrivateWages_12 0.0 0 310s PrivateWages_13 0.0 0 310s PrivateWages_14 0.0 0 310s PrivateWages_15 0.0 0 310s PrivateWages_16 0.0 0 310s PrivateWages_17 0.0 0 310s PrivateWages_18 0.0 0 310s PrivateWages_19 0.0 0 310s PrivateWages_20 0.0 0 310s PrivateWages_21 0.0 0 310s PrivateWages_22 0.0 0 310s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 310s Consumption_2 0 0.0 0.0 310s Consumption_3 0 0.0 0.0 310s Consumption_4 0 0.0 0.0 310s Consumption_5 0 0.0 0.0 310s Consumption_6 0 0.0 0.0 310s Consumption_7 0 0.0 0.0 310s Consumption_8 0 0.0 0.0 310s Consumption_9 0 0.0 0.0 310s Consumption_10 0 0.0 0.0 310s Consumption_11 0 0.0 0.0 310s Consumption_12 0 0.0 0.0 310s Consumption_13 0 0.0 0.0 310s Consumption_14 0 0.0 0.0 310s Consumption_15 0 0.0 0.0 310s Consumption_16 0 0.0 0.0 310s Consumption_17 0 0.0 0.0 310s Consumption_18 0 0.0 0.0 310s Consumption_19 0 0.0 0.0 310s Consumption_20 0 0.0 0.0 310s Consumption_21 0 0.0 0.0 310s Consumption_22 0 0.0 0.0 310s Investment_2 0 0.0 0.0 310s Investment_3 0 0.0 0.0 310s Investment_4 0 0.0 0.0 310s Investment_5 0 0.0 0.0 310s Investment_6 0 0.0 0.0 310s Investment_7 0 0.0 0.0 310s Investment_8 0 0.0 0.0 310s Investment_9 0 0.0 0.0 310s Investment_10 0 0.0 0.0 310s Investment_11 0 0.0 0.0 310s Investment_12 0 0.0 0.0 310s Investment_13 0 0.0 0.0 310s Investment_14 0 0.0 0.0 310s Investment_15 0 0.0 0.0 310s Investment_16 0 0.0 0.0 310s Investment_17 0 0.0 0.0 310s Investment_18 0 0.0 0.0 310s Investment_19 0 0.0 0.0 310s Investment_20 0 0.0 0.0 310s Investment_21 0 0.0 0.0 310s Investment_22 0 0.0 0.0 310s PrivateWages_2 1 45.6 44.9 310s PrivateWages_3 1 50.1 45.6 310s PrivateWages_4 1 57.2 50.1 310s PrivateWages_5 1 57.1 57.2 310s PrivateWages_6 1 61.0 57.1 310s PrivateWages_7 1 64.0 61.0 310s PrivateWages_8 1 64.4 64.0 310s PrivateWages_9 1 64.5 64.4 310s PrivateWages_10 1 67.0 64.5 310s PrivateWages_11 1 61.2 67.0 310s PrivateWages_12 1 53.4 61.2 310s PrivateWages_13 1 44.3 53.4 310s PrivateWages_14 1 45.1 44.3 310s PrivateWages_15 1 49.7 45.1 310s PrivateWages_16 1 54.4 49.7 310s PrivateWages_17 1 62.7 54.4 310s PrivateWages_18 1 65.0 62.7 310s PrivateWages_19 1 60.9 65.0 310s PrivateWages_20 1 69.5 60.9 310s PrivateWages_21 1 75.7 69.5 310s PrivateWages_22 1 88.4 75.7 310s PrivateWages_trend 310s Consumption_2 0 310s Consumption_3 0 310s Consumption_4 0 310s Consumption_5 0 310s Consumption_6 0 310s Consumption_7 0 310s Consumption_8 0 310s Consumption_9 0 310s Consumption_10 0 310s Consumption_11 0 310s Consumption_12 0 310s Consumption_13 0 310s Consumption_14 0 310s Consumption_15 0 310s Consumption_16 0 310s Consumption_17 0 310s Consumption_18 0 310s Consumption_19 0 310s Consumption_20 0 310s Consumption_21 0 310s Consumption_22 0 310s Investment_2 0 310s Investment_3 0 310s Investment_4 0 310s Investment_5 0 310s Investment_6 0 310s Investment_7 0 310s Investment_8 0 310s Investment_9 0 310s Investment_10 0 310s Investment_11 0 310s Investment_12 0 310s Investment_13 0 310s Investment_14 0 310s Investment_15 0 310s Investment_16 0 310s Investment_17 0 310s Investment_18 0 310s Investment_19 0 310s Investment_20 0 310s Investment_21 0 310s Investment_22 0 310s PrivateWages_2 -10 310s PrivateWages_3 -9 310s PrivateWages_4 -8 310s PrivateWages_5 -7 310s PrivateWages_6 -6 310s PrivateWages_7 -5 310s PrivateWages_8 -4 310s PrivateWages_9 -3 310s PrivateWages_10 -2 310s PrivateWages_11 -1 310s PrivateWages_12 0 310s PrivateWages_13 1 310s PrivateWages_14 2 310s PrivateWages_15 3 310s PrivateWages_16 4 310s PrivateWages_17 5 310s PrivateWages_18 6 310s PrivateWages_19 7 310s PrivateWages_20 8 310s PrivateWages_21 9 310s PrivateWages_22 10 310s > nobs 310s [1] 63 310s > linearHypothesis 310s Linear hypothesis test (Theil's F test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df F Pr(>F) 310s 1 52 310s 2 51 1 0.82 0.37 310s Linear hypothesis test (F statistic of a Wald test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df F Pr(>F) 310s 1 52 310s 2 51 1 0.73 0.4 310s Linear hypothesis test (Chi^2 statistic of a Wald test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df Chisq Pr(>Chisq) 310s 1 52 310s 2 51 1 0.73 0.39 310s Linear hypothesis test (Theil's F test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s Consumption_corpProfLag - PrivateWages_trend = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df F Pr(>F) 310s 1 53 310s 2 51 2 0.42 0.66 310s Linear hypothesis test (F statistic of a Wald test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s Consumption_corpProfLag - PrivateWages_trend = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df F Pr(>F) 310s 1 53 310s 2 51 2 0.37 0.69 310s Linear hypothesis test (Chi^2 statistic of a Wald test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s Consumption_corpProfLag - PrivateWages_trend = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df Chisq Pr(>Chisq) 310s 1 53 310s 2 51 2 0.74 0.69 310s > logLik 310s 'log Lik.' -72.3 (df=13) 310s 'log Lik.' -77.9 (df=13) 310s compare log likelihood value with single-equation OLS 310s [1] TRUE 310s Estimating function 310s Consumption_(Intercept) Consumption_corpProf 310s Consumption_2 -0.32389 -4.016 310s Consumption_3 -1.25001 -21.125 310s Consumption_4 -1.56574 -28.810 310s Consumption_5 -0.49350 -9.574 310s Consumption_6 0.00761 0.153 310s Consumption_7 0.86910 17.034 310s Consumption_8 1.33848 26.502 310s Consumption_9 1.05498 22.260 310s Consumption_10 -0.58856 -12.772 310s Consumption_11 0.28231 4.404 310s Consumption_12 -0.22965 -2.618 310s Consumption_13 -0.32213 -2.255 310s Consumption_14 0.32228 3.610 310s Consumption_15 -0.05801 -0.714 310s Consumption_16 -0.03466 -0.485 310s Consumption_17 1.61650 28.450 310s Consumption_18 -0.43597 -7.542 310s Consumption_19 0.21005 3.214 310s Consumption_20 0.98920 18.795 310s Consumption_21 0.78508 16.565 310s Consumption_22 -2.17345 -51.076 310s Investment_2 0.00000 0.000 310s Investment_3 0.00000 0.000 310s Investment_4 0.00000 0.000 310s Investment_5 0.00000 0.000 310s Investment_6 0.00000 0.000 310s Investment_7 0.00000 0.000 310s Investment_8 0.00000 0.000 310s Investment_9 0.00000 0.000 310s Investment_10 0.00000 0.000 310s Investment_11 0.00000 0.000 310s Investment_12 0.00000 0.000 310s Investment_13 0.00000 0.000 310s Investment_14 0.00000 0.000 310s Investment_15 0.00000 0.000 310s Investment_16 0.00000 0.000 310s Investment_17 0.00000 0.000 310s Investment_18 0.00000 0.000 310s Investment_19 0.00000 0.000 310s Investment_20 0.00000 0.000 310s Investment_21 0.00000 0.000 310s Investment_22 0.00000 0.000 310s PrivateWages_2 0.00000 0.000 310s PrivateWages_3 0.00000 0.000 310s PrivateWages_4 0.00000 0.000 310s PrivateWages_5 0.00000 0.000 310s PrivateWages_6 0.00000 0.000 310s PrivateWages_7 0.00000 0.000 310s PrivateWages_8 0.00000 0.000 310s PrivateWages_9 0.00000 0.000 310s PrivateWages_10 0.00000 0.000 310s PrivateWages_11 0.00000 0.000 310s PrivateWages_12 0.00000 0.000 310s PrivateWages_13 0.00000 0.000 310s PrivateWages_14 0.00000 0.000 310s PrivateWages_15 0.00000 0.000 310s PrivateWages_16 0.00000 0.000 310s PrivateWages_17 0.00000 0.000 310s PrivateWages_18 0.00000 0.000 310s PrivateWages_19 0.00000 0.000 310s PrivateWages_20 0.00000 0.000 310s PrivateWages_21 0.00000 0.000 310s PrivateWages_22 0.00000 0.000 310s Consumption_corpProfLag Consumption_wages 310s Consumption_2 -4.113 -9.134 310s Consumption_3 -15.500 -40.250 310s Consumption_4 -26.461 -57.932 310s Consumption_5 -9.080 -18.260 310s Consumption_6 0.148 0.294 310s Consumption_7 17.469 35.372 310s Consumption_8 26.234 55.547 310s Consumption_9 20.889 45.259 310s Consumption_10 -12.419 -26.662 310s Consumption_11 6.126 11.885 310s Consumption_12 -3.583 -9.025 310s Consumption_13 -3.672 -11.049 310s Consumption_14 2.256 10.990 310s Consumption_15 -0.650 -2.123 310s Consumption_16 -0.426 -1.362 310s Consumption_17 22.631 71.449 310s Consumption_18 -7.673 -20.796 310s Consumption_19 3.634 9.641 310s Consumption_20 15.135 48.867 310s Consumption_21 14.916 41.609 310s Consumption_22 -45.860 -134.319 310s Investment_2 0.000 0.000 310s Investment_3 0.000 0.000 310s Investment_4 0.000 0.000 310s Investment_5 0.000 0.000 310s Investment_6 0.000 0.000 310s Investment_7 0.000 0.000 310s Investment_8 0.000 0.000 310s Investment_9 0.000 0.000 310s Investment_10 0.000 0.000 310s Investment_11 0.000 0.000 310s Investment_12 0.000 0.000 310s Investment_13 0.000 0.000 310s Investment_14 0.000 0.000 310s Investment_15 0.000 0.000 310s Investment_16 0.000 0.000 310s Investment_17 0.000 0.000 310s Investment_18 0.000 0.000 310s Investment_19 0.000 0.000 310s Investment_20 0.000 0.000 310s Investment_21 0.000 0.000 310s Investment_22 0.000 0.000 310s PrivateWages_2 0.000 0.000 310s PrivateWages_3 0.000 0.000 310s PrivateWages_4 0.000 0.000 310s PrivateWages_5 0.000 0.000 310s PrivateWages_6 0.000 0.000 310s PrivateWages_7 0.000 0.000 310s PrivateWages_8 0.000 0.000 310s PrivateWages_9 0.000 0.000 310s PrivateWages_10 0.000 0.000 310s PrivateWages_11 0.000 0.000 310s PrivateWages_12 0.000 0.000 310s PrivateWages_13 0.000 0.000 310s PrivateWages_14 0.000 0.000 310s PrivateWages_15 0.000 0.000 310s PrivateWages_16 0.000 0.000 310s PrivateWages_17 0.000 0.000 310s PrivateWages_18 0.000 0.000 310s PrivateWages_19 0.000 0.000 310s PrivateWages_20 0.000 0.000 310s PrivateWages_21 0.000 0.000 310s PrivateWages_22 0.000 0.000 310s Investment_(Intercept) Investment_corpProf 310s Consumption_2 0.0000 0.000 310s Consumption_3 0.0000 0.000 310s Consumption_4 0.0000 0.000 310s Consumption_5 0.0000 0.000 310s Consumption_6 0.0000 0.000 310s Consumption_7 0.0000 0.000 310s Consumption_8 0.0000 0.000 310s Consumption_9 0.0000 0.000 310s Consumption_10 0.0000 0.000 310s Consumption_11 0.0000 0.000 310s Consumption_12 0.0000 0.000 310s Consumption_13 0.0000 0.000 310s Consumption_14 0.0000 0.000 310s Consumption_15 0.0000 0.000 310s Consumption_16 0.0000 0.000 310s Consumption_17 0.0000 0.000 310s Consumption_18 0.0000 0.000 310s Consumption_19 0.0000 0.000 310s Consumption_20 0.0000 0.000 310s Consumption_21 0.0000 0.000 310s Consumption_22 0.0000 0.000 310s Investment_2 -0.0668 -0.828 310s Investment_3 -0.0476 -0.804 310s Investment_4 1.2467 22.939 310s Investment_5 -1.3512 -26.213 310s Investment_6 0.4154 8.350 310s Investment_7 1.4923 29.248 310s Investment_8 0.7889 15.620 310s Investment_9 -0.6317 -13.329 310s Investment_10 1.0830 23.500 310s Investment_11 0.2791 4.353 310s Investment_12 0.0369 0.420 310s Investment_13 0.3659 2.561 310s Investment_14 0.2237 2.505 310s Investment_15 -0.1728 -2.126 310s Investment_16 0.0101 0.141 310s Investment_17 0.9719 17.105 310s Investment_18 0.0516 0.893 310s Investment_19 -2.5656 -39.254 310s Investment_20 -0.6866 -13.045 310s Investment_21 -0.7807 -16.474 310s Investment_22 -0.6623 -15.565 310s PrivateWages_2 0.0000 0.000 310s PrivateWages_3 0.0000 0.000 310s PrivateWages_4 0.0000 0.000 310s PrivateWages_5 0.0000 0.000 310s PrivateWages_6 0.0000 0.000 310s PrivateWages_7 0.0000 0.000 310s PrivateWages_8 0.0000 0.000 310s PrivateWages_9 0.0000 0.000 310s PrivateWages_10 0.0000 0.000 310s PrivateWages_11 0.0000 0.000 310s PrivateWages_12 0.0000 0.000 310s PrivateWages_13 0.0000 0.000 310s PrivateWages_14 0.0000 0.000 310s PrivateWages_15 0.0000 0.000 310s PrivateWages_16 0.0000 0.000 310s PrivateWages_17 0.0000 0.000 310s PrivateWages_18 0.0000 0.000 310s PrivateWages_19 0.0000 0.000 310s PrivateWages_20 0.0000 0.000 310s PrivateWages_21 0.0000 0.000 310s PrivateWages_22 0.0000 0.000 310s Investment_corpProfLag Investment_capitalLag 310s Consumption_2 0.000 0.00 310s Consumption_3 0.000 0.00 310s Consumption_4 0.000 0.00 310s Consumption_5 0.000 0.00 310s Consumption_6 0.000 0.00 310s Consumption_7 0.000 0.00 310s Consumption_8 0.000 0.00 310s Consumption_9 0.000 0.00 310s Consumption_10 0.000 0.00 310s Consumption_11 0.000 0.00 310s Consumption_12 0.000 0.00 310s Consumption_13 0.000 0.00 310s Consumption_14 0.000 0.00 310s Consumption_15 0.000 0.00 310s Consumption_16 0.000 0.00 310s Consumption_17 0.000 0.00 310s Consumption_18 0.000 0.00 310s Consumption_19 0.000 0.00 310s Consumption_20 0.000 0.00 310s Consumption_21 0.000 0.00 310s Consumption_22 0.000 0.00 310s Investment_2 -0.848 -12.21 310s Investment_3 -0.590 -8.69 310s Investment_4 21.069 230.01 310s Investment_5 -24.862 -256.32 310s Investment_6 8.059 80.05 310s Investment_7 29.994 295.17 310s Investment_8 15.463 160.46 310s Investment_9 -12.507 -131.14 310s Investment_10 22.850 228.07 310s Investment_11 6.056 60.20 310s Investment_12 0.575 7.99 310s Investment_13 4.172 78.05 310s Investment_14 1.566 46.33 310s Investment_15 -1.936 -34.91 310s Investment_16 0.124 2.01 310s Investment_17 13.606 192.14 310s Investment_18 0.908 10.31 310s Investment_19 -44.385 -517.74 310s Investment_20 -10.505 -137.25 310s Investment_21 -14.834 -157.09 310s Investment_22 -13.975 -135.45 310s PrivateWages_2 0.000 0.00 310s PrivateWages_3 0.000 0.00 310s PrivateWages_4 0.000 0.00 310s PrivateWages_5 0.000 0.00 310s PrivateWages_6 0.000 0.00 310s PrivateWages_7 0.000 0.00 310s PrivateWages_8 0.000 0.00 310s PrivateWages_9 0.000 0.00 310s PrivateWages_10 0.000 0.00 310s PrivateWages_11 0.000 0.00 310s PrivateWages_12 0.000 0.00 310s PrivateWages_13 0.000 0.00 310s PrivateWages_14 0.000 0.00 310s PrivateWages_15 0.000 0.00 310s PrivateWages_16 0.000 0.00 310s PrivateWages_17 0.000 0.00 310s PrivateWages_18 0.000 0.00 310s PrivateWages_19 0.000 0.00 310s PrivateWages_20 0.000 0.00 310s PrivateWages_21 0.000 0.00 310s PrivateWages_22 0.000 0.00 310s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 310s Consumption_2 0.0000 0.000 0.000 310s Consumption_3 0.0000 0.000 0.000 310s Consumption_4 0.0000 0.000 0.000 310s Consumption_5 0.0000 0.000 0.000 310s Consumption_6 0.0000 0.000 0.000 310s Consumption_7 0.0000 0.000 0.000 310s Consumption_8 0.0000 0.000 0.000 310s Consumption_9 0.0000 0.000 0.000 310s Consumption_10 0.0000 0.000 0.000 310s Consumption_11 0.0000 0.000 0.000 310s Consumption_12 0.0000 0.000 0.000 310s Consumption_13 0.0000 0.000 0.000 310s Consumption_14 0.0000 0.000 0.000 310s Consumption_15 0.0000 0.000 0.000 310s Consumption_16 0.0000 0.000 0.000 310s Consumption_17 0.0000 0.000 0.000 310s Consumption_18 0.0000 0.000 0.000 310s Consumption_19 0.0000 0.000 0.000 310s Consumption_20 0.0000 0.000 0.000 310s Consumption_21 0.0000 0.000 0.000 310s Consumption_22 0.0000 0.000 0.000 310s Investment_2 0.0000 0.000 0.000 310s Investment_3 0.0000 0.000 0.000 310s Investment_4 0.0000 0.000 0.000 310s Investment_5 0.0000 0.000 0.000 310s Investment_6 0.0000 0.000 0.000 310s Investment_7 0.0000 0.000 0.000 310s Investment_8 0.0000 0.000 0.000 310s Investment_9 0.0000 0.000 0.000 310s Investment_10 0.0000 0.000 0.000 310s Investment_11 0.0000 0.000 0.000 310s Investment_12 0.0000 0.000 0.000 310s Investment_13 0.0000 0.000 0.000 310s Investment_14 0.0000 0.000 0.000 310s Investment_15 0.0000 0.000 0.000 310s Investment_16 0.0000 0.000 0.000 310s Investment_17 0.0000 0.000 0.000 310s Investment_18 0.0000 0.000 0.000 310s Investment_19 0.0000 0.000 0.000 310s Investment_20 0.0000 0.000 0.000 310s Investment_21 0.0000 0.000 0.000 310s Investment_22 0.0000 0.000 0.000 310s PrivateWages_2 -1.2942 -59.015 -58.109 310s PrivateWages_3 0.2957 14.813 13.482 310s PrivateWages_4 1.1877 67.938 59.505 310s PrivateWages_5 -0.1358 -7.755 -7.768 310s PrivateWages_6 -0.4654 -28.390 -26.575 310s PrivateWages_7 -0.4838 -30.965 -29.514 310s PrivateWages_8 -0.7281 -46.892 -46.601 310s PrivateWages_9 0.3392 21.881 21.847 310s PrivateWages_10 1.1957 80.111 77.122 310s PrivateWages_11 -0.1508 -9.230 -10.105 310s PrivateWages_12 0.5942 31.729 36.364 310s PrivateWages_13 0.1027 4.549 5.483 310s PrivateWages_14 0.4503 20.307 19.947 310s PrivateWages_15 0.2816 13.993 12.698 310s PrivateWages_16 0.0138 0.748 0.684 310s PrivateWages_17 -0.8508 -53.343 -46.282 310s PrivateWages_18 0.9956 64.717 62.427 310s PrivateWages_19 -0.4688 -28.547 -30.469 310s PrivateWages_20 -0.3795 -26.378 -23.114 310s PrivateWages_21 -1.0909 -82.582 -75.818 310s PrivateWages_22 0.5917 52.309 44.794 310s PrivateWages_trend 310s Consumption_2 0.000 310s Consumption_3 0.000 310s Consumption_4 0.000 310s Consumption_5 0.000 310s Consumption_6 0.000 310s Consumption_7 0.000 310s Consumption_8 0.000 310s Consumption_9 0.000 310s Consumption_10 0.000 310s Consumption_11 0.000 310s Consumption_12 0.000 310s Consumption_13 0.000 310s Consumption_14 0.000 310s Consumption_15 0.000 310s Consumption_16 0.000 310s Consumption_17 0.000 310s Consumption_18 0.000 310s Consumption_19 0.000 310s Consumption_20 0.000 310s Consumption_21 0.000 310s Consumption_22 0.000 310s Investment_2 0.000 310s Investment_3 0.000 310s Investment_4 0.000 310s Investment_5 0.000 310s Investment_6 0.000 310s Investment_7 0.000 310s Investment_8 0.000 310s Investment_9 0.000 310s Investment_10 0.000 310s Investment_11 0.000 310s Investment_12 0.000 310s Investment_13 0.000 310s Investment_14 0.000 310s Investment_15 0.000 310s Investment_16 0.000 310s Investment_17 0.000 310s Investment_18 0.000 310s Investment_19 0.000 310s Investment_20 0.000 310s Investment_21 0.000 310s Investment_22 0.000 310s PrivateWages_2 12.942 310s PrivateWages_3 -2.661 310s PrivateWages_4 -9.502 310s PrivateWages_5 0.951 310s PrivateWages_6 2.792 310s PrivateWages_7 2.419 310s PrivateWages_8 2.913 310s PrivateWages_9 -1.018 310s PrivateWages_10 -2.391 310s PrivateWages_11 0.151 310s PrivateWages_12 0.000 310s PrivateWages_13 0.103 310s PrivateWages_14 0.901 310s PrivateWages_15 0.845 310s PrivateWages_16 0.055 310s PrivateWages_17 -4.254 310s PrivateWages_18 5.974 310s PrivateWages_19 -3.281 310s PrivateWages_20 -3.036 310s PrivateWages_21 -9.818 310s PrivateWages_22 5.917 310s [1] TRUE 310s > Bread 310s Consumption_(Intercept) Consumption_corpProf 310s Consumption_(Intercept) 101.65 0.030 310s Consumption_corpProf 0.03 0.498 310s Consumption_corpProfLag -1.06 -0.316 310s Consumption_wages -1.97 -0.079 310s Investment_(Intercept) 0.00 0.000 310s Investment_corpProf 0.00 0.000 310s Investment_corpProfLag 0.00 0.000 310s Investment_capitalLag 0.00 0.000 310s PrivateWages_(Intercept) 0.00 0.000 310s PrivateWages_gnp 0.00 0.000 310s PrivateWages_gnpLag 0.00 0.000 310s PrivateWages_trend 0.00 0.000 310s Consumption_corpProfLag Consumption_wages 310s Consumption_(Intercept) -1.0607 -1.9718 310s Consumption_corpProf -0.3157 -0.0790 310s Consumption_corpProfLag 0.4922 -0.0402 310s Consumption_wages -0.0402 0.0956 310s Investment_(Intercept) 0.0000 0.0000 310s Investment_corpProf 0.0000 0.0000 310s Investment_corpProfLag 0.0000 0.0000 310s Investment_capitalLag 0.0000 0.0000 310s PrivateWages_(Intercept) 0.0000 0.0000 310s PrivateWages_gnp 0.0000 0.0000 310s PrivateWages_gnpLag 0.0000 0.0000 310s PrivateWages_trend 0.0000 0.0000 310s Investment_(Intercept) Investment_corpProf 310s Consumption_(Intercept) 0.00 0.0000 310s Consumption_corpProf 0.00 0.0000 310s Consumption_corpProfLag 0.00 0.0000 310s Consumption_wages 0.00 0.0000 310s Investment_(Intercept) 1846.89 -17.9709 310s Investment_corpProf -17.97 0.5831 310s Investment_corpProfLag 14.67 -0.5008 310s Investment_capitalLag -8.88 0.0814 310s PrivateWages_(Intercept) 0.00 0.0000 310s PrivateWages_gnp 0.00 0.0000 310s PrivateWages_gnpLag 0.00 0.0000 310s PrivateWages_trend 0.00 0.0000 310s Investment_corpProfLag Investment_capitalLag 310s Consumption_(Intercept) 0.0000 0.0000 310s Consumption_corpProf 0.0000 0.0000 310s Consumption_corpProfLag 0.0000 0.0000 310s Consumption_wages 0.0000 0.0000 310s Investment_(Intercept) 14.6742 -8.8813 310s Investment_corpProf -0.5008 0.0814 310s Investment_corpProfLag 0.6289 -0.0824 310s Investment_capitalLag -0.0824 0.0442 310s PrivateWages_(Intercept) 0.0000 0.0000 310s PrivateWages_gnp 0.0000 0.0000 310s PrivateWages_gnpLag 0.0000 0.0000 310s PrivateWages_trend 0.0000 0.0000 310s PrivateWages_(Intercept) PrivateWages_gnp 310s Consumption_(Intercept) 0.000 0.0000 310s Consumption_corpProf 0.000 0.0000 310s Consumption_corpProfLag 0.000 0.0000 310s Consumption_wages 0.000 0.0000 310s Investment_(Intercept) 0.000 0.0000 310s Investment_corpProf 0.000 0.0000 310s Investment_corpProfLag 0.000 0.0000 310s Investment_capitalLag 0.000 0.0000 310s PrivateWages_(Intercept) 172.668 -0.5919 310s PrivateWages_gnp -0.592 0.1124 310s PrivateWages_gnpLag -2.313 -0.1062 310s PrivateWages_trend 1.993 -0.0274 310s PrivateWages_gnpLag PrivateWages_trend 310s Consumption_(Intercept) 0.00000 0.00000 310s Consumption_corpProf 0.00000 0.00000 310s Consumption_corpProfLag 0.00000 0.00000 310s Consumption_wages 0.00000 0.00000 310s Investment_(Intercept) 0.00000 0.00000 310s Investment_corpProf 0.00000 0.00000 310s Investment_corpProfLag 0.00000 0.00000 310s Investment_capitalLag 0.00000 0.00000 310s PrivateWages_(Intercept) -2.31299 1.99284 310s PrivateWages_gnp -0.10624 -0.02738 310s PrivateWages_gnpLag 0.14992 -0.00601 310s PrivateWages_trend -0.00601 0.10900 310s > 310s > # 2SLS 310s > summary 310s 310s systemfit results 310s method: 2SLS 310s 310s N DF SSR detRCov OLS-R2 McElroy-R2 310s system 63 51 61 0.288 0.969 0.992 310s 310s N DF SSR MSE RMSE R2 Adj R2 310s Consumption 21 17 21.9 1.290 1.136 0.977 0.973 310s Investment 21 17 29.0 1.709 1.307 0.885 0.865 310s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 310s 310s The covariance matrix of the residuals 310s Consumption Investment PrivateWages 310s Consumption 1.044 0.438 -0.385 310s Investment 0.438 1.383 0.193 310s PrivateWages -0.385 0.193 0.476 310s 310s The correlations of the residuals 310s Consumption Investment PrivateWages 310s Consumption 1.000 0.364 -0.546 310s Investment 0.364 1.000 0.237 310s PrivateWages -0.546 0.237 1.000 310s 310s 310s 2SLS estimates for 'Consumption' (equation 1) 310s Model Formula: consump ~ corpProf + corpProfLag + wages 310s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 310s gnpLag 310s 310s Estimate Std. Error t value Pr(>|t|) 310s (Intercept) 16.5548 1.3208 12.53 5.2e-10 *** 310s corpProf 0.0173 0.1180 0.15 0.89 310s corpProfLag 0.2162 0.1073 2.02 0.06 . 310s wages 0.8102 0.0402 20.13 2.7e-13 *** 310s --- 310s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 310s 310s Residual standard error: 1.136 on 17 degrees of freedom 310s Number of observations: 21 Degrees of Freedom: 17 310s SSR: 21.925 MSE: 1.29 Root MSE: 1.136 310s Multiple R-Squared: 0.977 Adjusted R-Squared: 0.973 310s 310s 310s 2SLS estimates for 'Investment' (equation 2) 310s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 310s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 310s gnpLag 310s 310s Estimate Std. Error t value Pr(>|t|) 310s (Intercept) 20.2782 7.5427 2.69 0.01555 * 310s corpProf 0.1502 0.1732 0.87 0.39792 310s corpProfLag 0.6159 0.1628 3.78 0.00148 ** 310s capitalLag -0.1578 0.0361 -4.37 0.00042 *** 310s --- 310s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 310s 310s Residual standard error: 1.307 on 17 degrees of freedom 310s Number of observations: 21 Degrees of Freedom: 17 310s SSR: 29.047 MSE: 1.709 Root MSE: 1.307 310s Multiple R-Squared: 0.885 Adjusted R-Squared: 0.865 310s 310s 310s 2SLS estimates for 'PrivateWages' (equation 3) 310s Model Formula: privWage ~ gnp + gnpLag + trend 310s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 310s gnpLag 310s 310s Estimate Std. Error t value Pr(>|t|) 310s (Intercept) 1.5003 1.1478 1.31 0.20857 310s gnp 0.4389 0.0356 12.32 6.8e-10 *** 310s gnpLag 0.1467 0.0388 3.78 0.00150 ** 310s trend 0.1304 0.0291 4.47 0.00033 *** 310s --- 310s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 310s 310s Residual standard error: 0.767 on 17 degrees of freedom 310s Number of observations: 21 Degrees of Freedom: 17 310s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 310s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 310s 310s > residuals 310s Consumption Investment PrivateWages 310s 1 NA NA NA 310s 2 -0.46263 -1.320 -1.2940 310s 3 -0.61635 0.257 0.2981 310s 4 -1.30423 0.860 1.1918 310s 5 -0.24588 -1.594 -0.1361 310s 6 0.22948 0.259 -0.4634 310s 7 0.88538 1.207 -0.4824 310s 8 1.44189 0.969 -0.7284 310s 9 1.34190 0.113 0.3387 310s 10 -0.39403 1.796 1.1965 310s 11 -0.62564 -0.953 -0.1552 310s 12 -1.06543 -0.807 0.5882 310s 13 -1.33021 -0.895 0.0955 310s 14 0.61059 1.306 0.4487 310s 15 -0.14208 -0.151 0.2822 310s 16 0.00315 0.142 0.0145 310s 17 2.00337 1.749 -0.8478 310s 18 -0.60552 -0.192 0.9950 310s 19 -0.24771 -3.291 -0.4734 310s 20 1.38510 0.285 -0.3766 310s 21 1.03204 -0.104 -1.0893 310s 22 -1.89319 0.363 0.5974 310s > fitted 310s Consumption Investment PrivateWages 310s 1 NA NA NA 310s 2 42.4 1.120 26.8 310s 3 45.6 1.643 29.0 310s 4 50.5 4.340 32.9 310s 5 50.8 4.594 34.0 310s 6 52.4 4.841 35.9 310s 7 54.2 4.393 37.9 310s 8 54.8 3.231 38.6 310s 9 56.0 2.887 38.9 310s 10 58.2 3.304 40.1 310s 11 55.6 1.953 38.1 310s 12 52.0 -2.593 33.9 310s 13 46.9 -5.305 28.9 310s 14 45.9 -6.406 28.1 310s 15 48.8 -2.849 30.3 310s 16 51.3 -1.442 33.2 310s 17 55.7 0.351 37.6 310s 18 59.3 2.192 40.0 310s 19 57.7 1.391 38.7 310s 20 60.2 1.015 42.0 310s 21 64.0 3.404 46.1 310s 22 71.6 4.537 52.7 310s > predict 310s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 310s 1 NA NA NA NA 310s 2 42.4 0.471 41.4 43.4 310s 3 45.6 0.577 44.4 46.8 310s 4 50.5 0.354 49.8 51.3 310s 5 50.8 0.405 50.0 51.7 310s 6 52.4 0.404 51.5 53.2 310s 7 54.2 0.359 53.5 55.0 310s 8 54.8 0.328 54.1 55.4 310s 9 56.0 0.368 55.2 56.7 310s 10 58.2 0.377 57.4 59.0 310s 11 55.6 0.728 54.1 57.2 310s 12 52.0 0.604 50.7 53.2 310s 13 46.9 0.765 45.3 48.5 310s 14 45.9 0.615 44.6 47.2 310s 15 48.8 0.374 48.1 49.6 310s 16 51.3 0.333 50.6 52.0 310s 17 55.7 0.409 54.8 56.6 310s 18 59.3 0.326 58.6 60.0 310s 19 57.7 0.414 56.9 58.6 310s 20 60.2 0.478 59.2 61.2 310s 21 64.0 0.446 63.0 64.9 310s 22 71.6 0.689 70.1 73.0 310s Investment.pred Investment.se.fit Investment.lwr Investment.upr 310s 1 NA NA NA NA 310s 2 1.120 0.865 -0.706 2.946 310s 3 1.643 0.594 0.390 2.895 310s 4 4.340 0.545 3.190 5.490 310s 5 4.594 0.443 3.660 5.527 310s 6 4.841 0.411 3.973 5.709 310s 7 4.393 0.399 3.550 5.235 310s 8 3.231 0.348 2.497 3.965 310s 9 2.887 0.542 1.744 4.030 310s 10 3.304 0.593 2.054 4.555 310s 11 1.953 0.855 0.148 3.757 310s 12 -2.593 0.679 -4.026 -1.160 310s 13 -5.305 0.876 -7.152 -3.457 310s 14 -6.406 0.916 -8.338 -4.473 310s 15 -2.849 0.435 -3.765 -1.932 310s 16 -1.442 0.376 -2.236 -0.649 310s 17 0.351 0.510 -0.724 1.426 310s 18 2.192 0.299 1.560 2.823 310s 19 1.391 0.464 0.411 2.371 310s 20 1.015 0.576 -0.201 2.230 310s 21 3.404 0.471 2.410 4.398 310s 22 4.537 0.675 3.114 5.961 310s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 310s 1 NA NA NA NA 310s 2 26.8 0.318 26.1 27.5 310s 3 29.0 0.330 28.3 29.7 310s 4 32.9 0.346 32.2 33.6 310s 5 34.0 0.242 33.5 34.5 310s 6 35.9 0.248 35.3 36.4 310s 7 37.9 0.244 37.4 38.4 310s 8 38.6 0.246 38.1 39.1 310s 9 38.9 0.235 38.4 39.4 310s 10 40.1 0.224 39.6 40.6 310s 11 38.1 0.350 37.3 38.8 310s 12 33.9 0.382 33.1 34.7 310s 13 28.9 0.454 27.9 29.9 310s 14 28.1 0.342 27.3 28.8 310s 15 30.3 0.335 29.6 31.0 310s 16 33.2 0.280 32.6 33.8 310s 17 37.6 0.291 37.0 38.3 310s 18 40.0 0.215 39.6 40.5 310s 19 38.7 0.356 37.9 39.4 310s 20 42.0 0.304 41.3 42.6 310s 21 46.1 0.306 45.4 46.7 310s 22 52.7 0.489 51.7 53.7 310s > model.frame 310s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 310s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 310s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 310s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 310s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 310s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 310s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 310s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 310s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 310s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 310s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 310s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 310s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 310s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 310s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 310s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 310s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 310s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 310s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 310s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 310s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 310s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 310s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 310s trend 310s 1 -11 310s 2 -10 310s 3 -9 310s 4 -8 310s 5 -7 310s 6 -6 310s 7 -5 310s 8 -4 310s 9 -3 310s 10 -2 310s 11 -1 310s 12 0 310s 13 1 310s 14 2 310s 15 3 310s 16 4 310s 17 5 310s 18 6 310s 19 7 310s 20 8 310s 21 9 310s 22 10 310s > Frames of instrumental variables 310s govExp taxes govWage trend capitalLag corpProfLag gnpLag 310s 1 2.4 3.4 2.2 -11 180 NA NA 310s 2 3.9 7.7 2.7 -10 183 12.7 44.9 310s 3 3.2 3.9 2.9 -9 183 12.4 45.6 310s 4 2.8 4.7 2.9 -8 184 16.9 50.1 310s 5 3.5 3.8 3.1 -7 190 18.4 57.2 310s 6 3.3 5.5 3.2 -6 193 19.4 57.1 310s 7 3.3 7.0 3.3 -5 198 20.1 61.0 310s 8 4.0 6.7 3.6 -4 203 19.6 64.0 310s 9 4.2 4.2 3.7 -3 208 19.8 64.4 310s 10 4.1 4.0 4.0 -2 211 21.1 64.5 310s 11 5.2 7.7 4.2 -1 216 21.7 67.0 310s 12 5.9 7.5 4.8 0 217 15.6 61.2 310s 13 4.9 8.3 5.3 1 213 11.4 53.4 310s 14 3.7 5.4 5.6 2 207 7.0 44.3 310s 15 4.0 6.8 6.0 3 202 11.2 45.1 310s 16 4.4 7.2 6.1 4 199 12.3 49.7 310s 17 2.9 8.3 7.4 5 198 14.0 54.4 310s 18 4.3 6.7 6.7 6 200 17.6 62.7 310s 19 5.3 7.4 7.7 7 202 17.3 65.0 310s 20 6.6 8.9 7.8 8 200 15.3 60.9 310s 21 7.4 9.6 8.0 9 201 19.0 69.5 310s 22 13.8 11.6 8.5 10 204 21.1 75.7 310s govExp taxes govWage trend capitalLag corpProfLag gnpLag 310s 1 2.4 3.4 2.2 -11 180 NA NA 310s 2 3.9 7.7 2.7 -10 183 12.7 44.9 310s 3 3.2 3.9 2.9 -9 183 12.4 45.6 310s 4 2.8 4.7 2.9 -8 184 16.9 50.1 310s 5 3.5 3.8 3.1 -7 190 18.4 57.2 310s 6 3.3 5.5 3.2 -6 193 19.4 57.1 310s 7 3.3 7.0 3.3 -5 198 20.1 61.0 310s 8 4.0 6.7 3.6 -4 203 19.6 64.0 310s 9 4.2 4.2 3.7 -3 208 19.8 64.4 310s 10 4.1 4.0 4.0 -2 211 21.1 64.5 310s 11 5.2 7.7 4.2 -1 216 21.7 67.0 310s 12 5.9 7.5 4.8 0 217 15.6 61.2 310s 13 4.9 8.3 5.3 1 213 11.4 53.4 310s 14 3.7 5.4 5.6 2 207 7.0 44.3 310s 15 4.0 6.8 6.0 3 202 11.2 45.1 310s 16 4.4 7.2 6.1 4 199 12.3 49.7 310s 17 2.9 8.3 7.4 5 198 14.0 54.4 310s 18 4.3 6.7 6.7 6 200 17.6 62.7 310s 19 5.3 7.4 7.7 7 202 17.3 65.0 310s 20 6.6 8.9 7.8 8 200 15.3 60.9 310s 21 7.4 9.6 8.0 9 201 19.0 69.5 310s 22 13.8 11.6 8.5 10 204 21.1 75.7 310s govExp taxes govWage trend capitalLag corpProfLag gnpLag 310s 1 2.4 3.4 2.2 -11 180 NA NA 310s 2 3.9 7.7 2.7 -10 183 12.7 44.9 310s 3 3.2 3.9 2.9 -9 183 12.4 45.6 310s 4 2.8 4.7 2.9 -8 184 16.9 50.1 310s 5 3.5 3.8 3.1 -7 190 18.4 57.2 310s 6 3.3 5.5 3.2 -6 193 19.4 57.1 310s 7 3.3 7.0 3.3 -5 198 20.1 61.0 310s 8 4.0 6.7 3.6 -4 203 19.6 64.0 310s 9 4.2 4.2 3.7 -3 208 19.8 64.4 310s 10 4.1 4.0 4.0 -2 211 21.1 64.5 310s 11 5.2 7.7 4.2 -1 216 21.7 67.0 310s 12 5.9 7.5 4.8 0 217 15.6 61.2 310s 13 4.9 8.3 5.3 1 213 11.4 53.4 310s 14 3.7 5.4 5.6 2 207 7.0 44.3 310s 15 4.0 6.8 6.0 3 202 11.2 45.1 310s 16 4.4 7.2 6.1 4 199 12.3 49.7 310s 17 2.9 8.3 7.4 5 198 14.0 54.4 310s 18 4.3 6.7 6.7 6 200 17.6 62.7 310s 19 5.3 7.4 7.7 7 202 17.3 65.0 310s 20 6.6 8.9 7.8 8 200 15.3 60.9 310s 21 7.4 9.6 8.0 9 201 19.0 69.5 310s 22 13.8 11.6 8.5 10 204 21.1 75.7 310s > model.matrix 310s [1] TRUE 310s > matrix of instrumental variables 310s Consumption_(Intercept) Consumption_govExp Consumption_taxes 310s Consumption_2 1 3.9 7.7 310s Consumption_3 1 3.2 3.9 310s Consumption_4 1 2.8 4.7 310s Consumption_5 1 3.5 3.8 310s Consumption_6 1 3.3 5.5 310s Consumption_7 1 3.3 7.0 310s Consumption_8 1 4.0 6.7 310s Consumption_9 1 4.2 4.2 310s Consumption_10 1 4.1 4.0 310s Consumption_11 1 5.2 7.7 310s Consumption_12 1 5.9 7.5 310s Consumption_13 1 4.9 8.3 310s Consumption_14 1 3.7 5.4 310s Consumption_15 1 4.0 6.8 310s Consumption_16 1 4.4 7.2 310s Consumption_17 1 2.9 8.3 310s Consumption_18 1 4.3 6.7 310s Consumption_19 1 5.3 7.4 310s Consumption_20 1 6.6 8.9 310s Consumption_21 1 7.4 9.6 310s Consumption_22 1 13.8 11.6 310s Investment_2 0 0.0 0.0 310s Investment_3 0 0.0 0.0 310s Investment_4 0 0.0 0.0 310s Investment_5 0 0.0 0.0 310s Investment_6 0 0.0 0.0 310s Investment_7 0 0.0 0.0 310s Investment_8 0 0.0 0.0 310s Investment_9 0 0.0 0.0 310s Investment_10 0 0.0 0.0 310s Investment_11 0 0.0 0.0 310s Investment_12 0 0.0 0.0 310s Investment_13 0 0.0 0.0 310s Investment_14 0 0.0 0.0 310s Investment_15 0 0.0 0.0 310s Investment_16 0 0.0 0.0 310s Investment_17 0 0.0 0.0 310s Investment_18 0 0.0 0.0 310s Investment_19 0 0.0 0.0 310s Investment_20 0 0.0 0.0 310s Investment_21 0 0.0 0.0 310s Investment_22 0 0.0 0.0 310s PrivateWages_2 0 0.0 0.0 310s PrivateWages_3 0 0.0 0.0 310s PrivateWages_4 0 0.0 0.0 310s PrivateWages_5 0 0.0 0.0 310s PrivateWages_6 0 0.0 0.0 310s PrivateWages_7 0 0.0 0.0 310s PrivateWages_8 0 0.0 0.0 310s PrivateWages_9 0 0.0 0.0 310s PrivateWages_10 0 0.0 0.0 310s PrivateWages_11 0 0.0 0.0 310s PrivateWages_12 0 0.0 0.0 310s PrivateWages_13 0 0.0 0.0 310s PrivateWages_14 0 0.0 0.0 310s PrivateWages_15 0 0.0 0.0 310s PrivateWages_16 0 0.0 0.0 310s PrivateWages_17 0 0.0 0.0 310s PrivateWages_18 0 0.0 0.0 310s PrivateWages_19 0 0.0 0.0 310s PrivateWages_20 0 0.0 0.0 310s PrivateWages_21 0 0.0 0.0 310s PrivateWages_22 0 0.0 0.0 310s Consumption_govWage Consumption_trend Consumption_capitalLag 310s Consumption_2 2.7 -10 183 310s Consumption_3 2.9 -9 183 310s Consumption_4 2.9 -8 184 310s Consumption_5 3.1 -7 190 310s Consumption_6 3.2 -6 193 310s Consumption_7 3.3 -5 198 310s Consumption_8 3.6 -4 203 310s Consumption_9 3.7 -3 208 310s Consumption_10 4.0 -2 211 310s Consumption_11 4.2 -1 216 310s Consumption_12 4.8 0 217 310s Consumption_13 5.3 1 213 310s Consumption_14 5.6 2 207 310s Consumption_15 6.0 3 202 310s Consumption_16 6.1 4 199 310s Consumption_17 7.4 5 198 310s Consumption_18 6.7 6 200 310s Consumption_19 7.7 7 202 310s Consumption_20 7.8 8 200 310s Consumption_21 8.0 9 201 310s Consumption_22 8.5 10 204 310s Investment_2 0.0 0 0 310s Investment_3 0.0 0 0 310s Investment_4 0.0 0 0 310s Investment_5 0.0 0 0 310s Investment_6 0.0 0 0 310s Investment_7 0.0 0 0 310s Investment_8 0.0 0 0 310s Investment_9 0.0 0 0 310s Investment_10 0.0 0 0 310s Investment_11 0.0 0 0 310s Investment_12 0.0 0 0 310s Investment_13 0.0 0 0 310s Investment_14 0.0 0 0 310s Investment_15 0.0 0 0 310s Investment_16 0.0 0 0 310s Investment_17 0.0 0 0 310s Investment_18 0.0 0 0 310s Investment_19 0.0 0 0 310s Investment_20 0.0 0 0 310s Investment_21 0.0 0 0 310s Investment_22 0.0 0 0 310s PrivateWages_2 0.0 0 0 310s PrivateWages_3 0.0 0 0 310s PrivateWages_4 0.0 0 0 310s PrivateWages_5 0.0 0 0 310s PrivateWages_6 0.0 0 0 310s PrivateWages_7 0.0 0 0 310s PrivateWages_8 0.0 0 0 310s PrivateWages_9 0.0 0 0 310s PrivateWages_10 0.0 0 0 310s PrivateWages_11 0.0 0 0 310s PrivateWages_12 0.0 0 0 310s PrivateWages_13 0.0 0 0 310s PrivateWages_14 0.0 0 0 310s PrivateWages_15 0.0 0 0 310s PrivateWages_16 0.0 0 0 310s PrivateWages_17 0.0 0 0 310s PrivateWages_18 0.0 0 0 310s PrivateWages_19 0.0 0 0 310s PrivateWages_20 0.0 0 0 310s PrivateWages_21 0.0 0 0 310s PrivateWages_22 0.0 0 0 310s Consumption_corpProfLag Consumption_gnpLag 310s Consumption_2 12.7 44.9 310s Consumption_3 12.4 45.6 310s Consumption_4 16.9 50.1 310s Consumption_5 18.4 57.2 310s Consumption_6 19.4 57.1 310s Consumption_7 20.1 61.0 310s Consumption_8 19.6 64.0 310s Consumption_9 19.8 64.4 310s Consumption_10 21.1 64.5 310s Consumption_11 21.7 67.0 310s Consumption_12 15.6 61.2 310s Consumption_13 11.4 53.4 310s Consumption_14 7.0 44.3 310s Consumption_15 11.2 45.1 310s Consumption_16 12.3 49.7 310s Consumption_17 14.0 54.4 310s Consumption_18 17.6 62.7 310s Consumption_19 17.3 65.0 310s Consumption_20 15.3 60.9 310s Consumption_21 19.0 69.5 310s Consumption_22 21.1 75.7 310s Investment_2 0.0 0.0 310s Investment_3 0.0 0.0 310s Investment_4 0.0 0.0 310s Investment_5 0.0 0.0 310s Investment_6 0.0 0.0 310s Investment_7 0.0 0.0 310s Investment_8 0.0 0.0 310s Investment_9 0.0 0.0 310s Investment_10 0.0 0.0 310s Investment_11 0.0 0.0 310s Investment_12 0.0 0.0 310s Investment_13 0.0 0.0 310s Investment_14 0.0 0.0 310s Investment_15 0.0 0.0 310s Investment_16 0.0 0.0 310s Investment_17 0.0 0.0 310s Investment_18 0.0 0.0 310s Investment_19 0.0 0.0 310s Investment_20 0.0 0.0 310s Investment_21 0.0 0.0 310s Investment_22 0.0 0.0 310s PrivateWages_2 0.0 0.0 310s PrivateWages_3 0.0 0.0 310s PrivateWages_4 0.0 0.0 310s PrivateWages_5 0.0 0.0 310s PrivateWages_6 0.0 0.0 310s PrivateWages_7 0.0 0.0 310s PrivateWages_8 0.0 0.0 310s PrivateWages_9 0.0 0.0 310s PrivateWages_10 0.0 0.0 310s PrivateWages_11 0.0 0.0 310s PrivateWages_12 0.0 0.0 310s PrivateWages_13 0.0 0.0 310s PrivateWages_14 0.0 0.0 310s PrivateWages_15 0.0 0.0 310s PrivateWages_16 0.0 0.0 310s PrivateWages_17 0.0 0.0 310s PrivateWages_18 0.0 0.0 310s PrivateWages_19 0.0 0.0 310s PrivateWages_20 0.0 0.0 310s PrivateWages_21 0.0 0.0 310s PrivateWages_22 0.0 0.0 310s Investment_(Intercept) Investment_govExp Investment_taxes 310s Consumption_2 0 0.0 0.0 310s Consumption_3 0 0.0 0.0 310s Consumption_4 0 0.0 0.0 310s Consumption_5 0 0.0 0.0 310s Consumption_6 0 0.0 0.0 310s Consumption_7 0 0.0 0.0 310s Consumption_8 0 0.0 0.0 310s Consumption_9 0 0.0 0.0 310s Consumption_10 0 0.0 0.0 310s Consumption_11 0 0.0 0.0 310s Consumption_12 0 0.0 0.0 310s Consumption_13 0 0.0 0.0 310s Consumption_14 0 0.0 0.0 310s Consumption_15 0 0.0 0.0 310s Consumption_16 0 0.0 0.0 310s Consumption_17 0 0.0 0.0 310s Consumption_18 0 0.0 0.0 310s Consumption_19 0 0.0 0.0 310s Consumption_20 0 0.0 0.0 310s Consumption_21 0 0.0 0.0 310s Consumption_22 0 0.0 0.0 310s Investment_2 1 3.9 7.7 310s Investment_3 1 3.2 3.9 310s Investment_4 1 2.8 4.7 310s Investment_5 1 3.5 3.8 310s Investment_6 1 3.3 5.5 310s Investment_7 1 3.3 7.0 310s Investment_8 1 4.0 6.7 310s Investment_9 1 4.2 4.2 310s Investment_10 1 4.1 4.0 310s Investment_11 1 5.2 7.7 310s Investment_12 1 5.9 7.5 310s Investment_13 1 4.9 8.3 310s Investment_14 1 3.7 5.4 310s Investment_15 1 4.0 6.8 310s Investment_16 1 4.4 7.2 310s Investment_17 1 2.9 8.3 310s Investment_18 1 4.3 6.7 310s Investment_19 1 5.3 7.4 310s Investment_20 1 6.6 8.9 310s Investment_21 1 7.4 9.6 310s Investment_22 1 13.8 11.6 310s PrivateWages_2 0 0.0 0.0 310s PrivateWages_3 0 0.0 0.0 310s PrivateWages_4 0 0.0 0.0 310s PrivateWages_5 0 0.0 0.0 310s PrivateWages_6 0 0.0 0.0 310s PrivateWages_7 0 0.0 0.0 310s PrivateWages_8 0 0.0 0.0 310s PrivateWages_9 0 0.0 0.0 310s PrivateWages_10 0 0.0 0.0 310s PrivateWages_11 0 0.0 0.0 310s PrivateWages_12 0 0.0 0.0 310s PrivateWages_13 0 0.0 0.0 310s PrivateWages_14 0 0.0 0.0 310s PrivateWages_15 0 0.0 0.0 310s PrivateWages_16 0 0.0 0.0 310s PrivateWages_17 0 0.0 0.0 310s PrivateWages_18 0 0.0 0.0 310s PrivateWages_19 0 0.0 0.0 310s PrivateWages_20 0 0.0 0.0 310s PrivateWages_21 0 0.0 0.0 310s PrivateWages_22 0 0.0 0.0 310s Investment_govWage Investment_trend Investment_capitalLag 310s Consumption_2 0.0 0 0 310s Consumption_3 0.0 0 0 310s Consumption_4 0.0 0 0 310s Consumption_5 0.0 0 0 310s Consumption_6 0.0 0 0 310s Consumption_7 0.0 0 0 310s Consumption_8 0.0 0 0 310s Consumption_9 0.0 0 0 310s Consumption_10 0.0 0 0 310s Consumption_11 0.0 0 0 310s Consumption_12 0.0 0 0 310s Consumption_13 0.0 0 0 310s Consumption_14 0.0 0 0 310s Consumption_15 0.0 0 0 310s Consumption_16 0.0 0 0 310s Consumption_17 0.0 0 0 310s Consumption_18 0.0 0 0 310s Consumption_19 0.0 0 0 310s Consumption_20 0.0 0 0 310s Consumption_21 0.0 0 0 310s Consumption_22 0.0 0 0 310s Investment_2 2.7 -10 183 310s Investment_3 2.9 -9 183 310s Investment_4 2.9 -8 184 310s Investment_5 3.1 -7 190 310s Investment_6 3.2 -6 193 310s Investment_7 3.3 -5 198 310s Investment_8 3.6 -4 203 310s Investment_9 3.7 -3 208 310s Investment_10 4.0 -2 211 310s Investment_11 4.2 -1 216 310s Investment_12 4.8 0 217 310s Investment_13 5.3 1 213 310s Investment_14 5.6 2 207 310s Investment_15 6.0 3 202 310s Investment_16 6.1 4 199 310s Investment_17 7.4 5 198 310s Investment_18 6.7 6 200 310s Investment_19 7.7 7 202 310s Investment_20 7.8 8 200 310s Investment_21 8.0 9 201 310s Investment_22 8.5 10 204 310s PrivateWages_2 0.0 0 0 310s PrivateWages_3 0.0 0 0 310s PrivateWages_4 0.0 0 0 310s PrivateWages_5 0.0 0 0 310s PrivateWages_6 0.0 0 0 310s PrivateWages_7 0.0 0 0 310s PrivateWages_8 0.0 0 0 310s PrivateWages_9 0.0 0 0 310s PrivateWages_10 0.0 0 0 310s PrivateWages_11 0.0 0 0 310s PrivateWages_12 0.0 0 0 310s PrivateWages_13 0.0 0 0 310s PrivateWages_14 0.0 0 0 310s PrivateWages_15 0.0 0 0 310s PrivateWages_16 0.0 0 0 310s PrivateWages_17 0.0 0 0 310s PrivateWages_18 0.0 0 0 310s PrivateWages_19 0.0 0 0 310s PrivateWages_20 0.0 0 0 310s PrivateWages_21 0.0 0 0 310s PrivateWages_22 0.0 0 0 310s Investment_corpProfLag Investment_gnpLag 310s Consumption_2 0.0 0.0 310s Consumption_3 0.0 0.0 310s Consumption_4 0.0 0.0 310s Consumption_5 0.0 0.0 310s Consumption_6 0.0 0.0 310s Consumption_7 0.0 0.0 310s Consumption_8 0.0 0.0 310s Consumption_9 0.0 0.0 310s Consumption_10 0.0 0.0 310s Consumption_11 0.0 0.0 310s Consumption_12 0.0 0.0 310s Consumption_13 0.0 0.0 310s Consumption_14 0.0 0.0 310s Consumption_15 0.0 0.0 310s Consumption_16 0.0 0.0 310s Consumption_17 0.0 0.0 310s Consumption_18 0.0 0.0 310s Consumption_19 0.0 0.0 310s Consumption_20 0.0 0.0 310s Consumption_21 0.0 0.0 310s Consumption_22 0.0 0.0 310s Investment_2 12.7 44.9 310s Investment_3 12.4 45.6 310s Investment_4 16.9 50.1 310s Investment_5 18.4 57.2 310s Investment_6 19.4 57.1 310s Investment_7 20.1 61.0 310s Investment_8 19.6 64.0 310s Investment_9 19.8 64.4 310s Investment_10 21.1 64.5 310s Investment_11 21.7 67.0 310s Investment_12 15.6 61.2 310s Investment_13 11.4 53.4 310s Investment_14 7.0 44.3 310s Investment_15 11.2 45.1 310s Investment_16 12.3 49.7 310s Investment_17 14.0 54.4 310s Investment_18 17.6 62.7 310s Investment_19 17.3 65.0 310s Investment_20 15.3 60.9 310s Investment_21 19.0 69.5 310s Investment_22 21.1 75.7 310s PrivateWages_2 0.0 0.0 310s PrivateWages_3 0.0 0.0 310s PrivateWages_4 0.0 0.0 310s PrivateWages_5 0.0 0.0 310s PrivateWages_6 0.0 0.0 310s PrivateWages_7 0.0 0.0 310s PrivateWages_8 0.0 0.0 310s PrivateWages_9 0.0 0.0 310s PrivateWages_10 0.0 0.0 310s PrivateWages_11 0.0 0.0 310s PrivateWages_12 0.0 0.0 310s PrivateWages_13 0.0 0.0 310s PrivateWages_14 0.0 0.0 310s PrivateWages_15 0.0 0.0 310s PrivateWages_16 0.0 0.0 310s PrivateWages_17 0.0 0.0 310s PrivateWages_18 0.0 0.0 310s PrivateWages_19 0.0 0.0 310s PrivateWages_20 0.0 0.0 310s PrivateWages_21 0.0 0.0 310s PrivateWages_22 0.0 0.0 310s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 310s Consumption_2 0 0.0 0.0 310s Consumption_3 0 0.0 0.0 310s Consumption_4 0 0.0 0.0 310s Consumption_5 0 0.0 0.0 310s Consumption_6 0 0.0 0.0 310s Consumption_7 0 0.0 0.0 310s Consumption_8 0 0.0 0.0 310s Consumption_9 0 0.0 0.0 310s Consumption_10 0 0.0 0.0 310s Consumption_11 0 0.0 0.0 310s Consumption_12 0 0.0 0.0 310s Consumption_13 0 0.0 0.0 310s Consumption_14 0 0.0 0.0 310s Consumption_15 0 0.0 0.0 310s Consumption_16 0 0.0 0.0 310s Consumption_17 0 0.0 0.0 310s Consumption_18 0 0.0 0.0 310s Consumption_19 0 0.0 0.0 310s Consumption_20 0 0.0 0.0 310s Consumption_21 0 0.0 0.0 310s Consumption_22 0 0.0 0.0 310s Investment_2 0 0.0 0.0 310s Investment_3 0 0.0 0.0 310s Investment_4 0 0.0 0.0 310s Investment_5 0 0.0 0.0 310s Investment_6 0 0.0 0.0 310s Investment_7 0 0.0 0.0 310s Investment_8 0 0.0 0.0 310s Investment_9 0 0.0 0.0 310s Investment_10 0 0.0 0.0 310s Investment_11 0 0.0 0.0 310s Investment_12 0 0.0 0.0 310s Investment_13 0 0.0 0.0 310s Investment_14 0 0.0 0.0 310s Investment_15 0 0.0 0.0 310s Investment_16 0 0.0 0.0 310s Investment_17 0 0.0 0.0 310s Investment_18 0 0.0 0.0 310s Investment_19 0 0.0 0.0 310s Investment_20 0 0.0 0.0 310s Investment_21 0 0.0 0.0 310s Investment_22 0 0.0 0.0 310s PrivateWages_2 1 3.9 7.7 310s PrivateWages_3 1 3.2 3.9 310s PrivateWages_4 1 2.8 4.7 310s PrivateWages_5 1 3.5 3.8 310s PrivateWages_6 1 3.3 5.5 310s PrivateWages_7 1 3.3 7.0 310s PrivateWages_8 1 4.0 6.7 310s PrivateWages_9 1 4.2 4.2 310s PrivateWages_10 1 4.1 4.0 310s PrivateWages_11 1 5.2 7.7 310s PrivateWages_12 1 5.9 7.5 310s PrivateWages_13 1 4.9 8.3 310s PrivateWages_14 1 3.7 5.4 310s PrivateWages_15 1 4.0 6.8 310s PrivateWages_16 1 4.4 7.2 310s PrivateWages_17 1 2.9 8.3 310s PrivateWages_18 1 4.3 6.7 310s PrivateWages_19 1 5.3 7.4 310s PrivateWages_20 1 6.6 8.9 310s PrivateWages_21 1 7.4 9.6 310s PrivateWages_22 1 13.8 11.6 310s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 310s Consumption_2 0.0 0 0 310s Consumption_3 0.0 0 0 310s Consumption_4 0.0 0 0 310s Consumption_5 0.0 0 0 310s Consumption_6 0.0 0 0 310s Consumption_7 0.0 0 0 310s Consumption_8 0.0 0 0 310s Consumption_9 0.0 0 0 310s Consumption_10 0.0 0 0 310s Consumption_11 0.0 0 0 310s Consumption_12 0.0 0 0 310s Consumption_13 0.0 0 0 310s Consumption_14 0.0 0 0 310s Consumption_15 0.0 0 0 310s Consumption_16 0.0 0 0 310s Consumption_17 0.0 0 0 310s Consumption_18 0.0 0 0 310s Consumption_19 0.0 0 0 310s Consumption_20 0.0 0 0 310s Consumption_21 0.0 0 0 310s Consumption_22 0.0 0 0 310s Investment_2 0.0 0 0 310s Investment_3 0.0 0 0 310s Investment_4 0.0 0 0 310s Investment_5 0.0 0 0 310s Investment_6 0.0 0 0 310s Investment_7 0.0 0 0 310s Investment_8 0.0 0 0 310s Investment_9 0.0 0 0 310s Investment_10 0.0 0 0 310s Investment_11 0.0 0 0 310s Investment_12 0.0 0 0 310s Investment_13 0.0 0 0 310s Investment_14 0.0 0 0 310s Investment_15 0.0 0 0 310s Investment_16 0.0 0 0 310s Investment_17 0.0 0 0 310s Investment_18 0.0 0 0 310s Investment_19 0.0 0 0 310s Investment_20 0.0 0 0 310s Investment_21 0.0 0 0 310s Investment_22 0.0 0 0 310s PrivateWages_2 2.7 -10 183 310s PrivateWages_3 2.9 -9 183 310s PrivateWages_4 2.9 -8 184 310s PrivateWages_5 3.1 -7 190 310s PrivateWages_6 3.2 -6 193 310s PrivateWages_7 3.3 -5 198 310s PrivateWages_8 3.6 -4 203 310s PrivateWages_9 3.7 -3 208 310s PrivateWages_10 4.0 -2 211 310s PrivateWages_11 4.2 -1 216 310s PrivateWages_12 4.8 0 217 310s PrivateWages_13 5.3 1 213 310s PrivateWages_14 5.6 2 207 310s PrivateWages_15 6.0 3 202 310s PrivateWages_16 6.1 4 199 310s PrivateWages_17 7.4 5 198 310s PrivateWages_18 6.7 6 200 310s PrivateWages_19 7.7 7 202 310s PrivateWages_20 7.8 8 200 310s PrivateWages_21 8.0 9 201 310s PrivateWages_22 8.5 10 204 310s PrivateWages_corpProfLag PrivateWages_gnpLag 310s Consumption_2 0.0 0.0 310s Consumption_3 0.0 0.0 310s Consumption_4 0.0 0.0 310s Consumption_5 0.0 0.0 310s Consumption_6 0.0 0.0 310s Consumption_7 0.0 0.0 310s Consumption_8 0.0 0.0 310s Consumption_9 0.0 0.0 310s Consumption_10 0.0 0.0 310s Consumption_11 0.0 0.0 310s Consumption_12 0.0 0.0 310s Consumption_13 0.0 0.0 310s Consumption_14 0.0 0.0 310s Consumption_15 0.0 0.0 310s Consumption_16 0.0 0.0 310s Consumption_17 0.0 0.0 310s Consumption_18 0.0 0.0 310s Consumption_19 0.0 0.0 310s Consumption_20 0.0 0.0 310s Consumption_21 0.0 0.0 310s Consumption_22 0.0 0.0 310s Investment_2 0.0 0.0 310s Investment_3 0.0 0.0 310s Investment_4 0.0 0.0 310s Investment_5 0.0 0.0 310s Investment_6 0.0 0.0 310s Investment_7 0.0 0.0 310s Investment_8 0.0 0.0 310s Investment_9 0.0 0.0 310s Investment_10 0.0 0.0 310s Investment_11 0.0 0.0 310s Investment_12 0.0 0.0 310s Investment_13 0.0 0.0 310s Investment_14 0.0 0.0 310s Investment_15 0.0 0.0 310s Investment_16 0.0 0.0 310s Investment_17 0.0 0.0 310s Investment_18 0.0 0.0 310s Investment_19 0.0 0.0 310s Investment_20 0.0 0.0 310s Investment_21 0.0 0.0 310s Investment_22 0.0 0.0 310s PrivateWages_2 12.7 44.9 310s PrivateWages_3 12.4 45.6 310s PrivateWages_4 16.9 50.1 310s PrivateWages_5 18.4 57.2 310s PrivateWages_6 19.4 57.1 310s PrivateWages_7 20.1 61.0 310s PrivateWages_8 19.6 64.0 310s PrivateWages_9 19.8 64.4 310s PrivateWages_10 21.1 64.5 310s PrivateWages_11 21.7 67.0 310s PrivateWages_12 15.6 61.2 310s PrivateWages_13 11.4 53.4 310s PrivateWages_14 7.0 44.3 310s PrivateWages_15 11.2 45.1 310s PrivateWages_16 12.3 49.7 310s PrivateWages_17 14.0 54.4 310s PrivateWages_18 17.6 62.7 310s PrivateWages_19 17.3 65.0 310s PrivateWages_20 15.3 60.9 310s PrivateWages_21 19.0 69.5 310s PrivateWages_22 21.1 75.7 310s > matrix of fitted regressors 310s Consumption_(Intercept) Consumption_corpProf 310s Consumption_2 1 13.26 310s Consumption_3 1 16.58 310s Consumption_4 1 19.28 310s Consumption_5 1 20.96 310s Consumption_6 1 19.77 310s Consumption_7 1 18.24 310s Consumption_8 1 17.57 310s Consumption_9 1 19.54 310s Consumption_10 1 20.38 310s Consumption_11 1 17.18 310s Consumption_12 1 12.71 310s Consumption_13 1 9.00 310s Consumption_14 1 9.05 310s Consumption_15 1 12.67 310s Consumption_16 1 14.42 310s Consumption_17 1 14.71 310s Consumption_18 1 19.80 310s Consumption_19 1 19.21 310s Consumption_20 1 17.42 310s Consumption_21 1 20.31 310s Consumption_22 1 22.66 310s Investment_2 0 0.00 310s Investment_3 0 0.00 310s Investment_4 0 0.00 310s Investment_5 0 0.00 310s Investment_6 0 0.00 310s Investment_7 0 0.00 310s Investment_8 0 0.00 310s Investment_9 0 0.00 310s Investment_10 0 0.00 310s Investment_11 0 0.00 310s Investment_12 0 0.00 310s Investment_13 0 0.00 310s Investment_14 0 0.00 310s Investment_15 0 0.00 310s Investment_16 0 0.00 310s Investment_17 0 0.00 310s Investment_18 0 0.00 310s Investment_19 0 0.00 310s Investment_20 0 0.00 310s Investment_21 0 0.00 310s Investment_22 0 0.00 310s PrivateWages_2 0 0.00 310s PrivateWages_3 0 0.00 310s PrivateWages_4 0 0.00 310s PrivateWages_5 0 0.00 310s PrivateWages_6 0 0.00 310s PrivateWages_7 0 0.00 310s PrivateWages_8 0 0.00 310s PrivateWages_9 0 0.00 310s PrivateWages_10 0 0.00 310s PrivateWages_11 0 0.00 310s PrivateWages_12 0 0.00 310s PrivateWages_13 0 0.00 310s PrivateWages_14 0 0.00 310s PrivateWages_15 0 0.00 310s PrivateWages_16 0 0.00 310s PrivateWages_17 0 0.00 310s PrivateWages_18 0 0.00 310s PrivateWages_19 0 0.00 310s PrivateWages_20 0 0.00 310s PrivateWages_21 0 0.00 310s PrivateWages_22 0 0.00 310s Consumption_corpProfLag Consumption_wages 310s Consumption_2 12.7 29.4 310s Consumption_3 12.4 31.8 310s Consumption_4 16.9 35.8 310s Consumption_5 18.4 39.1 310s Consumption_6 19.4 39.1 310s Consumption_7 20.1 39.4 310s Consumption_8 19.6 40.2 310s Consumption_9 19.8 42.3 310s Consumption_10 21.1 44.0 310s Consumption_11 21.7 43.7 310s Consumption_12 15.6 39.5 310s Consumption_13 11.4 35.1 310s Consumption_14 7.0 32.8 310s Consumption_15 11.2 37.5 310s Consumption_16 12.3 40.1 310s Consumption_17 14.0 41.7 310s Consumption_18 17.6 47.9 310s Consumption_19 17.3 49.3 310s Consumption_20 15.3 48.4 310s Consumption_21 19.0 53.4 310s Consumption_22 21.1 60.7 310s Investment_2 0.0 0.0 310s Investment_3 0.0 0.0 310s Investment_4 0.0 0.0 310s Investment_5 0.0 0.0 310s Investment_6 0.0 0.0 310s Investment_7 0.0 0.0 310s Investment_8 0.0 0.0 310s Investment_9 0.0 0.0 310s Investment_10 0.0 0.0 310s Investment_11 0.0 0.0 310s Investment_12 0.0 0.0 310s Investment_13 0.0 0.0 310s Investment_14 0.0 0.0 310s Investment_15 0.0 0.0 310s Investment_16 0.0 0.0 310s Investment_17 0.0 0.0 310s Investment_18 0.0 0.0 310s Investment_19 0.0 0.0 310s Investment_20 0.0 0.0 310s Investment_21 0.0 0.0 310s Investment_22 0.0 0.0 310s PrivateWages_2 0.0 0.0 310s PrivateWages_3 0.0 0.0 310s PrivateWages_4 0.0 0.0 310s PrivateWages_5 0.0 0.0 310s PrivateWages_6 0.0 0.0 310s PrivateWages_7 0.0 0.0 310s PrivateWages_8 0.0 0.0 310s PrivateWages_9 0.0 0.0 310s PrivateWages_10 0.0 0.0 310s PrivateWages_11 0.0 0.0 310s PrivateWages_12 0.0 0.0 310s PrivateWages_13 0.0 0.0 310s PrivateWages_14 0.0 0.0 310s PrivateWages_15 0.0 0.0 310s PrivateWages_16 0.0 0.0 310s PrivateWages_17 0.0 0.0 310s PrivateWages_18 0.0 0.0 310s PrivateWages_19 0.0 0.0 310s PrivateWages_20 0.0 0.0 310s PrivateWages_21 0.0 0.0 310s PrivateWages_22 0.0 0.0 310s Investment_(Intercept) Investment_corpProf 310s Consumption_2 0 0.00 310s Consumption_3 0 0.00 310s Consumption_4 0 0.00 310s Consumption_5 0 0.00 310s Consumption_6 0 0.00 310s Consumption_7 0 0.00 310s Consumption_8 0 0.00 310s Consumption_9 0 0.00 310s Consumption_10 0 0.00 310s Consumption_11 0 0.00 310s Consumption_12 0 0.00 310s Consumption_13 0 0.00 310s Consumption_14 0 0.00 310s Consumption_15 0 0.00 310s Consumption_16 0 0.00 310s Consumption_17 0 0.00 310s Consumption_18 0 0.00 310s Consumption_19 0 0.00 310s Consumption_20 0 0.00 310s Consumption_21 0 0.00 310s Consumption_22 0 0.00 310s Investment_2 1 13.26 310s Investment_3 1 16.58 310s Investment_4 1 19.28 310s Investment_5 1 20.96 310s Investment_6 1 19.77 310s Investment_7 1 18.24 310s Investment_8 1 17.57 310s Investment_9 1 19.54 310s Investment_10 1 20.38 310s Investment_11 1 17.18 310s Investment_12 1 12.71 310s Investment_13 1 9.00 310s Investment_14 1 9.05 310s Investment_15 1 12.67 310s Investment_16 1 14.42 310s Investment_17 1 14.71 310s Investment_18 1 19.80 310s Investment_19 1 19.21 310s Investment_20 1 17.42 310s Investment_21 1 20.31 310s Investment_22 1 22.66 310s PrivateWages_2 0 0.00 310s PrivateWages_3 0 0.00 310s PrivateWages_4 0 0.00 310s PrivateWages_5 0 0.00 310s PrivateWages_6 0 0.00 310s PrivateWages_7 0 0.00 310s PrivateWages_8 0 0.00 310s PrivateWages_9 0 0.00 310s PrivateWages_10 0 0.00 310s PrivateWages_11 0 0.00 310s PrivateWages_12 0 0.00 310s PrivateWages_13 0 0.00 310s PrivateWages_14 0 0.00 310s PrivateWages_15 0 0.00 310s PrivateWages_16 0 0.00 310s PrivateWages_17 0 0.00 310s PrivateWages_18 0 0.00 310s PrivateWages_19 0 0.00 310s PrivateWages_20 0 0.00 310s PrivateWages_21 0 0.00 310s PrivateWages_22 0 0.00 310s Investment_corpProfLag Investment_capitalLag 310s Consumption_2 0.0 0 310s Consumption_3 0.0 0 310s Consumption_4 0.0 0 310s Consumption_5 0.0 0 310s Consumption_6 0.0 0 310s Consumption_7 0.0 0 310s Consumption_8 0.0 0 310s Consumption_9 0.0 0 310s Consumption_10 0.0 0 310s Consumption_11 0.0 0 310s Consumption_12 0.0 0 310s Consumption_13 0.0 0 310s Consumption_14 0.0 0 310s Consumption_15 0.0 0 310s Consumption_16 0.0 0 310s Consumption_17 0.0 0 310s Consumption_18 0.0 0 310s Consumption_19 0.0 0 310s Consumption_20 0.0 0 310s Consumption_21 0.0 0 310s Consumption_22 0.0 0 310s Investment_2 12.7 183 310s Investment_3 12.4 183 310s Investment_4 16.9 184 310s Investment_5 18.4 190 310s Investment_6 19.4 193 310s Investment_7 20.1 198 310s Investment_8 19.6 203 310s Investment_9 19.8 208 310s Investment_10 21.1 211 310s Investment_11 21.7 216 310s Investment_12 15.6 217 310s Investment_13 11.4 213 310s Investment_14 7.0 207 310s Investment_15 11.2 202 310s Investment_16 12.3 199 310s Investment_17 14.0 198 310s Investment_18 17.6 200 310s Investment_19 17.3 202 310s Investment_20 15.3 200 310s Investment_21 19.0 201 310s Investment_22 21.1 204 310s PrivateWages_2 0.0 0 310s PrivateWages_3 0.0 0 310s PrivateWages_4 0.0 0 310s PrivateWages_5 0.0 0 310s PrivateWages_6 0.0 0 310s PrivateWages_7 0.0 0 310s PrivateWages_8 0.0 0 310s PrivateWages_9 0.0 0 310s PrivateWages_10 0.0 0 310s PrivateWages_11 0.0 0 310s PrivateWages_12 0.0 0 310s PrivateWages_13 0.0 0 310s PrivateWages_14 0.0 0 310s PrivateWages_15 0.0 0 310s PrivateWages_16 0.0 0 310s PrivateWages_17 0.0 0 310s PrivateWages_18 0.0 0 310s PrivateWages_19 0.0 0 310s PrivateWages_20 0.0 0 310s PrivateWages_21 0.0 0 310s PrivateWages_22 0.0 0 310s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 310s Consumption_2 0 0.0 0.0 310s Consumption_3 0 0.0 0.0 310s Consumption_4 0 0.0 0.0 310s Consumption_5 0 0.0 0.0 310s Consumption_6 0 0.0 0.0 310s Consumption_7 0 0.0 0.0 310s Consumption_8 0 0.0 0.0 310s Consumption_9 0 0.0 0.0 310s Consumption_10 0 0.0 0.0 310s Consumption_11 0 0.0 0.0 310s Consumption_12 0 0.0 0.0 310s Consumption_13 0 0.0 0.0 310s Consumption_14 0 0.0 0.0 310s Consumption_15 0 0.0 0.0 310s Consumption_16 0 0.0 0.0 310s Consumption_17 0 0.0 0.0 310s Consumption_18 0 0.0 0.0 310s Consumption_19 0 0.0 0.0 310s Consumption_20 0 0.0 0.0 310s Consumption_21 0 0.0 0.0 310s Consumption_22 0 0.0 0.0 310s Investment_2 0 0.0 0.0 310s Investment_3 0 0.0 0.0 310s Investment_4 0 0.0 0.0 310s Investment_5 0 0.0 0.0 310s Investment_6 0 0.0 0.0 310s Investment_7 0 0.0 0.0 310s Investment_8 0 0.0 0.0 310s Investment_9 0 0.0 0.0 310s Investment_10 0 0.0 0.0 310s Investment_11 0 0.0 0.0 310s Investment_12 0 0.0 0.0 310s Investment_13 0 0.0 0.0 310s Investment_14 0 0.0 0.0 310s Investment_15 0 0.0 0.0 310s Investment_16 0 0.0 0.0 310s Investment_17 0 0.0 0.0 310s Investment_18 0 0.0 0.0 310s Investment_19 0 0.0 0.0 310s Investment_20 0 0.0 0.0 310s Investment_21 0 0.0 0.0 310s Investment_22 0 0.0 0.0 310s PrivateWages_2 1 47.7 44.9 310s PrivateWages_3 1 49.3 45.6 310s PrivateWages_4 1 56.8 50.1 310s PrivateWages_5 1 60.7 57.2 310s PrivateWages_6 1 61.2 57.1 310s PrivateWages_7 1 61.3 61.0 310s PrivateWages_8 1 60.9 64.0 310s PrivateWages_9 1 62.4 64.4 310s PrivateWages_10 1 64.4 64.5 310s PrivateWages_11 1 64.4 67.0 310s PrivateWages_12 1 54.9 61.2 310s PrivateWages_13 1 47.1 53.4 310s PrivateWages_14 1 41.6 44.3 310s PrivateWages_15 1 51.0 45.1 310s PrivateWages_16 1 55.7 49.7 310s PrivateWages_17 1 57.3 54.4 310s PrivateWages_18 1 67.7 62.7 310s PrivateWages_19 1 68.2 65.0 310s PrivateWages_20 1 66.9 60.9 310s PrivateWages_21 1 75.3 69.5 310s PrivateWages_22 1 86.5 75.7 310s PrivateWages_trend 310s Consumption_2 0 310s Consumption_3 0 310s Consumption_4 0 310s Consumption_5 0 310s Consumption_6 0 310s Consumption_7 0 310s Consumption_8 0 310s Consumption_9 0 310s Consumption_10 0 310s Consumption_11 0 310s Consumption_12 0 310s Consumption_13 0 310s Consumption_14 0 310s Consumption_15 0 310s Consumption_16 0 310s Consumption_17 0 310s Consumption_18 0 310s Consumption_19 0 310s Consumption_20 0 310s Consumption_21 0 310s Consumption_22 0 310s Investment_2 0 310s Investment_3 0 310s Investment_4 0 310s Investment_5 0 310s Investment_6 0 310s Investment_7 0 310s Investment_8 0 310s Investment_9 0 310s Investment_10 0 310s Investment_11 0 310s Investment_12 0 310s Investment_13 0 310s Investment_14 0 310s Investment_15 0 310s Investment_16 0 310s Investment_17 0 310s Investment_18 0 310s Investment_19 0 310s Investment_20 0 310s Investment_21 0 310s Investment_22 0 310s PrivateWages_2 -10 310s PrivateWages_3 -9 310s PrivateWages_4 -8 310s PrivateWages_5 -7 310s PrivateWages_6 -6 310s PrivateWages_7 -5 310s PrivateWages_8 -4 310s PrivateWages_9 -3 310s PrivateWages_10 -2 310s PrivateWages_11 -1 310s PrivateWages_12 0 310s PrivateWages_13 1 310s PrivateWages_14 2 310s PrivateWages_15 3 310s PrivateWages_16 4 310s PrivateWages_17 5 310s PrivateWages_18 6 310s PrivateWages_19 7 310s PrivateWages_20 8 310s PrivateWages_21 9 310s PrivateWages_22 10 310s > nobs 310s [1] 63 310s > linearHypothesis 310s Linear hypothesis test (Theil's F test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df F Pr(>F) 310s 1 52 310s 2 51 1 1.08 0.3 310s Linear hypothesis test (F statistic of a Wald test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df F Pr(>F) 310s 1 52 310s 2 51 1 1.29 0.26 310s Linear hypothesis test (Chi^2 statistic of a Wald test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df Chisq Pr(>Chisq) 310s 1 52 310s 2 51 1 1.29 0.26 310s Linear hypothesis test (Theil's F test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s Consumption_corpProfLag - PrivateWages_trend = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df F Pr(>F) 310s 1 53 310s 2 51 2 0.54 0.58 310s Linear hypothesis test (F statistic of a Wald test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s Consumption_corpProfLag - PrivateWages_trend = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df F Pr(>F) 310s 1 53 310s 2 51 2 0.65 0.53 310s Linear hypothesis test (Chi^2 statistic of a Wald test) 310s 310s Hypothesis: 310s Consumption_corpProf + Investment_capitalLag = 0 310s Consumption_corpProfLag - PrivateWages_trend = 0 310s 310s Model 1: restricted model 310s Model 2: kleinModel 310s 310s Res.Df Df Chisq Pr(>Chisq) 310s 1 53 310s 2 51 2 1.3 0.52 310s > logLik 310s 'log Lik.' -76.3 (df=13) 310s 'log Lik.' -85.5 (df=13) 310s Estimating function 310s Consumption_(Intercept) Consumption_corpProf 310s Consumption_2 -1.455 -19.28 310s Consumption_3 -0.246 -4.08 310s Consumption_4 -0.309 -5.96 310s Consumption_5 -1.952 -40.92 310s Consumption_6 -0.199 -3.93 310s Consumption_7 2.000 36.47 310s Consumption_8 2.547 44.76 310s Consumption_9 1.829 35.74 310s Consumption_10 0.665 13.55 310s Consumption_11 -1.947 -33.46 310s Consumption_12 -1.232 -15.65 310s Consumption_13 -2.039 -18.35 310s Consumption_14 1.714 15.52 310s Consumption_15 -0.877 -11.11 310s Consumption_16 -0.684 -9.87 310s Consumption_17 4.077 59.98 310s Consumption_18 -0.793 -15.70 310s Consumption_19 -3.072 -59.01 310s Consumption_20 2.230 38.84 310s Consumption_21 0.744 15.11 310s Consumption_22 -1.000 -22.66 310s Investment_2 0.000 0.00 310s Investment_3 0.000 0.00 310s Investment_4 0.000 0.00 310s Investment_5 0.000 0.00 310s Investment_6 0.000 0.00 310s Investment_7 0.000 0.00 310s Investment_8 0.000 0.00 310s Investment_9 0.000 0.00 310s Investment_10 0.000 0.00 310s Investment_11 0.000 0.00 310s Investment_12 0.000 0.00 310s Investment_13 0.000 0.00 310s Investment_14 0.000 0.00 310s Investment_15 0.000 0.00 310s Investment_16 0.000 0.00 310s Investment_17 0.000 0.00 310s Investment_18 0.000 0.00 310s Investment_19 0.000 0.00 310s Investment_20 0.000 0.00 310s Investment_21 0.000 0.00 310s Investment_22 0.000 0.00 310s PrivateWages_2 0.000 0.00 310s PrivateWages_3 0.000 0.00 310s PrivateWages_4 0.000 0.00 310s PrivateWages_5 0.000 0.00 310s PrivateWages_6 0.000 0.00 310s PrivateWages_7 0.000 0.00 310s PrivateWages_8 0.000 0.00 310s PrivateWages_9 0.000 0.00 310s PrivateWages_10 0.000 0.00 310s PrivateWages_11 0.000 0.00 310s PrivateWages_12 0.000 0.00 310s PrivateWages_13 0.000 0.00 310s PrivateWages_14 0.000 0.00 310s PrivateWages_15 0.000 0.00 310s PrivateWages_16 0.000 0.00 310s PrivateWages_17 0.000 0.00 310s PrivateWages_18 0.000 0.00 310s PrivateWages_19 0.000 0.00 310s PrivateWages_20 0.000 0.00 310s PrivateWages_21 0.000 0.00 310s PrivateWages_22 0.000 0.00 310s Consumption_corpProfLag Consumption_wages 310s Consumption_2 -18.47 -42.77 310s Consumption_3 -3.05 -7.82 310s Consumption_4 -5.22 -11.05 310s Consumption_5 -35.93 -76.29 310s Consumption_6 -3.85 -7.77 310s Consumption_7 40.20 78.70 310s Consumption_8 49.93 102.36 310s Consumption_9 36.21 77.42 310s Consumption_10 14.03 29.28 310s Consumption_11 -42.26 -85.10 310s Consumption_12 -19.22 -48.63 310s Consumption_13 -23.25 -71.64 310s Consumption_14 12.00 56.20 310s Consumption_15 -9.82 -32.89 310s Consumption_16 -8.42 -27.47 310s Consumption_17 57.07 170.01 310s Consumption_18 -13.96 -37.97 310s Consumption_19 -53.15 -151.48 310s Consumption_20 34.12 107.90 310s Consumption_21 14.14 39.73 310s Consumption_22 -21.10 -60.72 310s Investment_2 0.00 0.00 310s Investment_3 0.00 0.00 310s Investment_4 0.00 0.00 310s Investment_5 0.00 0.00 310s Investment_6 0.00 0.00 310s Investment_7 0.00 0.00 310s Investment_8 0.00 0.00 310s Investment_9 0.00 0.00 310s Investment_10 0.00 0.00 310s Investment_11 0.00 0.00 310s Investment_12 0.00 0.00 310s Investment_13 0.00 0.00 310s Investment_14 0.00 0.00 310s Investment_15 0.00 0.00 310s Investment_16 0.00 0.00 310s Investment_17 0.00 0.00 310s Investment_18 0.00 0.00 310s Investment_19 0.00 0.00 310s Investment_20 0.00 0.00 310s Investment_21 0.00 0.00 310s Investment_22 0.00 0.00 310s PrivateWages_2 0.00 0.00 310s PrivateWages_3 0.00 0.00 310s PrivateWages_4 0.00 0.00 310s PrivateWages_5 0.00 0.00 310s PrivateWages_6 0.00 0.00 310s PrivateWages_7 0.00 0.00 310s PrivateWages_8 0.00 0.00 310s PrivateWages_9 0.00 0.00 310s PrivateWages_10 0.00 0.00 310s PrivateWages_11 0.00 0.00 310s PrivateWages_12 0.00 0.00 310s PrivateWages_13 0.00 0.00 310s PrivateWages_14 0.00 0.00 310s PrivateWages_15 0.00 0.00 310s PrivateWages_16 0.00 0.00 310s PrivateWages_17 0.00 0.00 310s PrivateWages_18 0.00 0.00 310s PrivateWages_19 0.00 0.00 310s PrivateWages_20 0.00 0.00 310s PrivateWages_21 0.00 0.00 310s PrivateWages_22 0.00 0.00 310s Investment_(Intercept) Investment_corpProf 310s Consumption_2 0.0000 0.000 310s Consumption_3 0.0000 0.000 310s Consumption_4 0.0000 0.000 310s Consumption_5 0.0000 0.000 310s Consumption_6 0.0000 0.000 310s Consumption_7 0.0000 0.000 310s Consumption_8 0.0000 0.000 310s Consumption_9 0.0000 0.000 310s Consumption_10 0.0000 0.000 310s Consumption_11 0.0000 0.000 310s Consumption_12 0.0000 0.000 310s Consumption_13 0.0000 0.000 310s Consumption_14 0.0000 0.000 310s Consumption_15 0.0000 0.000 310s Consumption_16 0.0000 0.000 310s Consumption_17 0.0000 0.000 310s Consumption_18 0.0000 0.000 310s Consumption_19 0.0000 0.000 310s Consumption_20 0.0000 0.000 310s Consumption_21 0.0000 0.000 310s Consumption_22 0.0000 0.000 310s Investment_2 -1.4484 -19.199 310s Investment_3 0.3058 5.070 310s Investment_4 0.7275 14.029 310s Investment_5 -1.8279 -38.314 310s Investment_6 0.3088 6.104 310s Investment_7 1.4119 25.751 310s Investment_8 1.3034 22.906 310s Investment_9 0.3472 6.785 310s Investment_10 1.9947 40.642 310s Investment_11 -1.1903 -20.449 310s Investment_12 -1.0029 -12.742 310s Investment_13 -1.1958 -10.762 310s Investment_14 1.6279 14.739 310s Investment_15 -0.2072 -2.625 310s Investment_16 0.0790 1.140 310s Investment_17 2.1831 32.118 310s Investment_18 -0.5667 -11.219 310s Investment_19 -3.8778 -74.479 310s Investment_20 0.5228 9.107 310s Investment_21 0.0154 0.312 310s Investment_22 0.4893 11.087 310s PrivateWages_2 0.0000 0.000 310s PrivateWages_3 0.0000 0.000 310s PrivateWages_4 0.0000 0.000 310s PrivateWages_5 0.0000 0.000 310s PrivateWages_6 0.0000 0.000 310s PrivateWages_7 0.0000 0.000 310s PrivateWages_8 0.0000 0.000 310s PrivateWages_9 0.0000 0.000 310s PrivateWages_10 0.0000 0.000 310s PrivateWages_11 0.0000 0.000 310s PrivateWages_12 0.0000 0.000 310s PrivateWages_13 0.0000 0.000 310s PrivateWages_14 0.0000 0.000 310s PrivateWages_15 0.0000 0.000 310s PrivateWages_16 0.0000 0.000 310s PrivateWages_17 0.0000 0.000 310s PrivateWages_18 0.0000 0.000 310s PrivateWages_19 0.0000 0.000 310s PrivateWages_20 0.0000 0.000 310s PrivateWages_21 0.0000 0.000 310s PrivateWages_22 0.0000 0.000 310s Investment_corpProfLag Investment_capitalLag 310s Consumption_2 0.000 0.0 310s Consumption_3 0.000 0.0 310s Consumption_4 0.000 0.0 310s Consumption_5 0.000 0.0 310s Consumption_6 0.000 0.0 310s Consumption_7 0.000 0.0 310s Consumption_8 0.000 0.0 310s Consumption_9 0.000 0.0 310s Consumption_10 0.000 0.0 310s Consumption_11 0.000 0.0 310s Consumption_12 0.000 0.0 310s Consumption_13 0.000 0.0 310s Consumption_14 0.000 0.0 310s Consumption_15 0.000 0.0 310s Consumption_16 0.000 0.0 310s Consumption_17 0.000 0.0 310s Consumption_18 0.000 0.0 310s Consumption_19 0.000 0.0 310s Consumption_20 0.000 0.0 310s Consumption_21 0.000 0.0 310s Consumption_22 0.000 0.0 310s Investment_2 -18.395 -264.8 310s Investment_3 3.792 55.8 310s Investment_4 12.295 134.2 310s Investment_5 -33.634 -346.8 310s Investment_6 5.991 59.5 310s Investment_7 28.378 279.3 310s Investment_8 25.548 265.1 310s Investment_9 6.875 72.1 310s Investment_10 42.088 420.1 310s Investment_11 -25.829 -256.7 310s Investment_12 -15.646 -217.3 310s Investment_13 -13.632 -255.1 310s Investment_14 11.395 337.1 310s Investment_15 -2.320 -41.8 310s Investment_16 0.972 15.7 310s Investment_17 30.564 431.6 310s Investment_18 -9.974 -113.2 310s Investment_19 -67.085 -782.5 310s Investment_20 7.999 104.5 310s Investment_21 0.292 3.1 310s Investment_22 10.325 100.1 310s PrivateWages_2 0.000 0.0 310s PrivateWages_3 0.000 0.0 310s PrivateWages_4 0.000 0.0 310s PrivateWages_5 0.000 0.0 310s PrivateWages_6 0.000 0.0 310s PrivateWages_7 0.000 0.0 310s PrivateWages_8 0.000 0.0 310s PrivateWages_9 0.000 0.0 310s PrivateWages_10 0.000 0.0 310s PrivateWages_11 0.000 0.0 310s PrivateWages_12 0.000 0.0 310s PrivateWages_13 0.000 0.0 310s PrivateWages_14 0.000 0.0 310s PrivateWages_15 0.000 0.0 310s PrivateWages_16 0.000 0.0 310s PrivateWages_17 0.000 0.0 310s PrivateWages_18 0.000 0.0 310s PrivateWages_19 0.000 0.0 310s PrivateWages_20 0.000 0.0 310s PrivateWages_21 0.000 0.0 310s PrivateWages_22 0.000 0.0 310s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 310s Consumption_2 0.0000 0.00 0.00 310s Consumption_3 0.0000 0.00 0.00 310s Consumption_4 0.0000 0.00 0.00 310s Consumption_5 0.0000 0.00 0.00 310s Consumption_6 0.0000 0.00 0.00 310s Consumption_7 0.0000 0.00 0.00 310s Consumption_8 0.0000 0.00 0.00 310s Consumption_9 0.0000 0.00 0.00 310s Consumption_10 0.0000 0.00 0.00 310s Consumption_11 0.0000 0.00 0.00 310s Consumption_12 0.0000 0.00 0.00 310s Consumption_13 0.0000 0.00 0.00 310s Consumption_14 0.0000 0.00 0.00 310s Consumption_15 0.0000 0.00 0.00 310s Consumption_16 0.0000 0.00 0.00 310s Consumption_17 0.0000 0.00 0.00 310s Consumption_18 0.0000 0.00 0.00 310s Consumption_19 0.0000 0.00 0.00 310s Consumption_20 0.0000 0.00 0.00 310s Consumption_21 0.0000 0.00 0.00 310s Consumption_22 0.0000 0.00 0.00 310s Investment_2 0.0000 0.00 0.00 310s Investment_3 0.0000 0.00 0.00 310s Investment_4 0.0000 0.00 0.00 310s Investment_5 0.0000 0.00 0.00 310s Investment_6 0.0000 0.00 0.00 310s Investment_7 0.0000 0.00 0.00 310s Investment_8 0.0000 0.00 0.00 310s Investment_9 0.0000 0.00 0.00 310s Investment_10 0.0000 0.00 0.00 310s Investment_11 0.0000 0.00 0.00 310s Investment_12 0.0000 0.00 0.00 310s Investment_13 0.0000 0.00 0.00 310s Investment_14 0.0000 0.00 0.00 310s Investment_15 0.0000 0.00 0.00 310s Investment_16 0.0000 0.00 0.00 310s Investment_17 0.0000 0.00 0.00 310s Investment_18 0.0000 0.00 0.00 310s Investment_19 0.0000 0.00 0.00 310s Investment_20 0.0000 0.00 0.00 310s Investment_21 0.0000 0.00 0.00 310s Investment_22 0.0000 0.00 0.00 310s PrivateWages_2 -2.1987 -104.79 -98.72 310s PrivateWages_3 0.6372 31.43 29.06 310s PrivateWages_4 1.3519 76.84 67.73 310s PrivateWages_5 -1.7306 -105.10 -98.99 310s PrivateWages_6 -0.5521 -33.79 -31.52 310s PrivateWages_7 0.7059 43.27 43.06 310s PrivateWages_8 0.8269 50.32 52.92 310s PrivateWages_9 1.2718 79.33 81.90 310s PrivateWages_10 2.3392 150.64 150.88 310s PrivateWages_11 -1.5500 -99.78 -103.85 310s PrivateWages_12 -0.0625 -3.43 -3.82 310s PrivateWages_13 -1.1474 -54.08 -61.27 310s PrivateWages_14 1.9682 81.95 87.19 310s PrivateWages_15 -0.2753 -14.03 -12.42 310s PrivateWages_16 -0.5389 -30.00 -26.78 310s PrivateWages_17 1.5156 86.87 82.45 310s PrivateWages_18 -0.1787 -12.09 -11.21 310s PrivateWages_19 -3.6814 -251.10 -239.29 310s PrivateWages_20 0.7597 50.83 46.27 310s PrivateWages_21 -0.9040 -68.05 -62.83 310s PrivateWages_22 1.4431 124.79 109.24 310s PrivateWages_trend 310s Consumption_2 0.000 310s Consumption_3 0.000 310s Consumption_4 0.000 310s Consumption_5 0.000 310s Consumption_6 0.000 310s Consumption_7 0.000 310s Consumption_8 0.000 310s Consumption_9 0.000 310s Consumption_10 0.000 310s Consumption_11 0.000 310s Consumption_12 0.000 310s Consumption_13 0.000 310s Consumption_14 0.000 310s Consumption_15 0.000 310s Consumption_16 0.000 310s Consumption_17 0.000 310s Consumption_18 0.000 310s Consumption_19 0.000 310s Consumption_20 0.000 310s Consumption_21 0.000 310s Consumption_22 0.000 310s Investment_2 0.000 310s Investment_3 0.000 310s Investment_4 0.000 310s Investment_5 0.000 310s Investment_6 0.000 310s Investment_7 0.000 310s Investment_8 0.000 310s Investment_9 0.000 310s Investment_10 0.000 310s Investment_11 0.000 310s Investment_12 0.000 310s Investment_13 0.000 310s Investment_14 0.000 310s Investment_15 0.000 310s Investment_16 0.000 310s Investment_17 0.000 310s Investment_18 0.000 310s Investment_19 0.000 310s Investment_20 0.000 310s Investment_21 0.000 310s Investment_22 0.000 310s PrivateWages_2 21.987 310s PrivateWages_3 -5.735 310s PrivateWages_4 -10.815 310s PrivateWages_5 12.114 310s PrivateWages_6 3.312 310s PrivateWages_7 -3.529 310s PrivateWages_8 -3.307 310s PrivateWages_9 -3.815 310s PrivateWages_10 -4.678 310s PrivateWages_11 1.550 310s PrivateWages_12 0.000 310s PrivateWages_13 -1.147 310s PrivateWages_14 3.936 310s PrivateWages_15 -0.826 310s PrivateWages_16 -2.156 310s PrivateWages_17 7.578 310s PrivateWages_18 -1.072 310s PrivateWages_19 -25.769 310s PrivateWages_20 6.078 310s PrivateWages_21 -8.136 310s PrivateWages_22 14.431 310s [1] TRUE 310s > Bread 310s Consumption_(Intercept) Consumption_corpProf 310s Consumption_(Intercept) 105.265 -0.9259 310s Consumption_corpProf -0.926 0.8409 310s Consumption_corpProfLag -0.287 -0.5775 310s Consumption_wages -1.975 -0.0921 310s Investment_(Intercept) 0.000 0.0000 310s Investment_corpProf 0.000 0.0000 310s Investment_corpProfLag 0.000 0.0000 310s Investment_capitalLag 0.000 0.0000 310s PrivateWages_(Intercept) 0.000 0.0000 310s PrivateWages_gnp 0.000 0.0000 310s PrivateWages_gnpLag 0.000 0.0000 310s PrivateWages_trend 0.000 0.0000 310s Consumption_corpProfLag Consumption_wages 310s Consumption_(Intercept) -0.287 -1.9751 310s Consumption_corpProf -0.578 -0.0921 310s Consumption_corpProfLag 0.694 -0.0320 310s Consumption_wages -0.032 0.0978 310s Investment_(Intercept) 0.000 0.0000 310s Investment_corpProf 0.000 0.0000 310s Investment_corpProfLag 0.000 0.0000 310s Investment_capitalLag 0.000 0.0000 310s PrivateWages_(Intercept) 0.000 0.0000 310s PrivateWages_gnp 0.000 0.0000 310s PrivateWages_gnpLag 0.000 0.0000 310s PrivateWages_trend 0.000 0.0000 310s Investment_(Intercept) Investment_corpProf 310s Consumption_(Intercept) 0.0 0.000 310s Consumption_corpProf 0.0 0.000 310s Consumption_corpProfLag 0.0 0.000 310s Consumption_wages 0.0 0.000 310s Investment_(Intercept) 2591.3 -42.124 310s Investment_corpProf -42.1 1.367 310s Investment_corpProfLag 35.4 -1.174 310s Investment_capitalLag -12.3 0.191 310s PrivateWages_(Intercept) 0.0 0.000 310s PrivateWages_gnp 0.0 0.000 310s PrivateWages_gnpLag 0.0 0.000 310s PrivateWages_trend 0.0 0.000 310s Investment_corpProfLag Investment_capitalLag 310s Consumption_(Intercept) 0.000 0.0000 310s Consumption_corpProf 0.000 0.0000 310s Consumption_corpProfLag 0.000 0.0000 310s Consumption_wages 0.000 0.0000 310s Investment_(Intercept) 35.417 -12.2536 310s Investment_corpProf -1.174 0.1908 310s Investment_corpProfLag 1.207 -0.1763 310s Investment_capitalLag -0.176 0.0594 310s PrivateWages_(Intercept) 0.000 0.0000 310s PrivateWages_gnp 0.000 0.0000 310s PrivateWages_gnpLag 0.000 0.0000 310s PrivateWages_trend 0.000 0.0000 310s PrivateWages_(Intercept) PrivateWages_gnp 310s Consumption_(Intercept) 0.000 0.0000 310s Consumption_corpProf 0.000 0.0000 310s Consumption_corpProfLag 0.000 0.0000 310s Consumption_wages 0.000 0.0000 310s Investment_(Intercept) 0.000 0.0000 310s Investment_corpProf 0.000 0.0000 310s Investment_corpProfLag 0.000 0.0000 310s Investment_capitalLag 0.000 0.0000 310s PrivateWages_(Intercept) 174.205 -0.8839 310s PrivateWages_gnp -0.884 0.1679 310s PrivateWages_gnpLag -2.037 -0.1586 310s PrivateWages_trend 2.064 -0.0409 310s PrivateWages_gnpLag PrivateWages_trend 310s Consumption_(Intercept) 0.00000 0.00000 310s Consumption_corpProf 0.00000 0.00000 310s Consumption_corpProfLag 0.00000 0.00000 310s Consumption_wages 0.00000 0.00000 310s Investment_(Intercept) 0.00000 0.00000 310s Investment_corpProf 0.00000 0.00000 310s Investment_corpProfLag 0.00000 0.00000 310s Investment_capitalLag 0.00000 0.00000 310s PrivateWages_(Intercept) -2.03709 2.06394 310s PrivateWages_gnp -0.15864 -0.04088 310s PrivateWages_gnpLag 0.19944 0.00675 310s PrivateWages_trend 0.00675 0.11229 310s > 310s > # SUR 311s > summary 311s 311s systemfit results 311s method: SUR 311s 311s N DF SSR detRCov OLS-R2 McElroy-R2 311s system 63 51 46.5 0.158 0.977 0.993 311s 311s N DF SSR MSE RMSE R2 Adj R2 311s Consumption 21 17 18.1 1.065 1.032 0.981 0.977 311s Investment 21 17 17.6 1.036 1.018 0.930 0.918 311s PrivateWages 21 17 10.8 0.633 0.796 0.986 0.984 311s 311s The covariance matrix of the residuals used for estimation 311s Consumption Investment PrivateWages 311s Consumption 0.8514 0.0495 -0.381 311s Investment 0.0495 0.8249 0.121 311s PrivateWages -0.3808 0.1212 0.476 311s 311s The covariance matrix of the residuals 311s Consumption Investment PrivateWages 311s Consumption 0.8618 0.0766 -0.437 311s Investment 0.0766 0.8384 0.203 311s PrivateWages -0.4368 0.2027 0.513 311s 311s The correlations of the residuals 311s Consumption Investment PrivateWages 311s Consumption 1.0000 0.0901 -0.657 311s Investment 0.0901 1.0000 0.309 311s PrivateWages -0.6572 0.3092 1.000 311s 311s 311s SUR estimates for 'Consumption' (equation 1) 311s Model Formula: consump ~ corpProf + corpProfLag + wages 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 15.9805 1.1687 13.67 1.3e-10 *** 311s corpProf 0.2302 0.0767 3.00 0.008 ** 311s corpProfLag 0.0673 0.0769 0.87 0.394 311s wages 0.7962 0.0353 22.58 4.1e-14 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.032 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 18.098 MSE: 1.065 Root MSE: 1.032 311s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 311s 311s 311s SUR estimates for 'Investment' (equation 2) 311s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 12.9293 4.8014 2.69 0.01540 * 311s corpProf 0.4429 0.0861 5.15 8.1e-05 *** 311s corpProfLag 0.3655 0.0894 4.09 0.00077 *** 311s capitalLag -0.1253 0.0235 -5.34 5.4e-05 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.018 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 17.606 MSE: 1.036 Root MSE: 1.018 311s Multiple R-Squared: 0.93 Adjusted R-Squared: 0.918 311s 311s 311s SUR estimates for 'PrivateWages' (equation 3) 311s Model Formula: privWage ~ gnp + gnpLag + trend 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 1.6347 1.1173 1.46 0.16 311s gnp 0.4098 0.0273 15.04 3.0e-11 *** 311s gnpLag 0.1744 0.0312 5.59 3.2e-05 *** 311s trend 0.1558 0.0276 5.65 2.9e-05 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 0.796 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 10.763 MSE: 0.633 Root MSE: 0.796 311s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 311s 311s > residuals 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 -0.24064 -0.3522 -1.0960 311s 3 -1.34080 -0.1605 0.5818 311s 4 -1.61038 1.0687 1.5313 311s 5 -0.54147 -1.4707 -0.0220 311s 6 -0.04372 0.3299 -0.2587 311s 7 0.85234 1.4346 -0.3243 311s 8 1.30302 0.8306 -0.6674 311s 9 0.97574 -0.4918 0.3660 311s 10 -0.66060 1.2434 1.2682 311s 11 0.45069 0.2647 -0.3467 311s 12 -0.04295 0.0795 0.3057 311s 13 -0.06686 0.3369 -0.2602 311s 14 0.32177 0.4080 0.3434 311s 15 -0.00441 -0.1533 0.2628 311s 16 -0.01931 0.0158 -0.0216 311s 17 1.53656 1.0372 -0.7988 311s 18 -0.42317 0.0176 0.8550 311s 19 0.29041 -2.6364 -0.8217 311s 20 0.88685 -0.5822 -0.3869 311s 21 0.68839 -0.7015 -1.1838 311s 22 -2.31147 -0.5183 0.6742 311s > fitted 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 42.1 0.152 26.6 311s 3 46.3 2.060 28.7 311s 4 50.8 4.131 32.6 311s 5 51.1 4.471 33.9 311s 6 52.6 4.770 35.7 311s 7 54.2 4.165 37.7 311s 8 54.9 3.369 38.6 311s 9 56.3 3.492 38.8 311s 10 58.5 3.857 40.0 311s 11 54.5 0.735 38.2 311s 12 50.9 -3.479 34.2 311s 13 45.7 -6.537 29.3 311s 14 46.2 -5.508 28.2 311s 15 48.7 -2.847 30.3 311s 16 51.3 -1.316 33.2 311s 17 56.2 1.063 37.6 311s 18 59.1 1.982 40.1 311s 19 57.2 0.736 39.0 311s 20 60.7 1.882 42.0 311s 21 64.3 4.002 46.2 311s 22 72.0 5.418 52.6 311s > predict 311s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 311s 1 NA NA NA NA 311s 2 42.1 0.415 41.3 43.0 311s 3 46.3 0.449 45.4 47.2 311s 4 50.8 0.300 50.2 51.4 311s 5 51.1 0.348 50.4 51.8 311s 6 52.6 0.350 51.9 53.3 311s 7 54.2 0.317 53.6 54.9 311s 8 54.9 0.289 54.3 55.5 311s 9 56.3 0.309 55.7 56.9 311s 10 58.5 0.328 57.8 59.1 311s 11 54.5 0.516 53.5 55.6 311s 12 50.9 0.414 50.1 51.8 311s 13 45.7 0.544 44.6 46.8 311s 14 46.2 0.527 45.1 47.2 311s 15 48.7 0.332 48.0 49.4 311s 16 51.3 0.295 50.7 51.9 311s 17 56.2 0.319 55.5 56.8 311s 18 59.1 0.286 58.5 59.7 311s 19 57.2 0.323 56.6 57.9 311s 20 60.7 0.381 59.9 61.5 311s 21 64.3 0.381 63.5 65.1 311s 22 72.0 0.597 70.8 73.2 311s Investment.pred Investment.se.fit Investment.lwr Investment.upr 311s 1 NA NA NA NA 311s 2 0.152 0.536 -0.924 1.229 311s 3 2.060 0.446 1.166 2.955 311s 4 4.131 0.397 3.334 4.929 311s 5 4.471 0.329 3.809 5.132 311s 6 4.770 0.311 4.145 5.395 311s 7 4.165 0.294 3.575 4.756 311s 8 3.369 0.263 2.842 3.897 311s 9 3.492 0.347 2.796 4.188 311s 10 3.857 0.398 3.058 4.656 311s 11 0.735 0.539 -0.346 1.816 311s 12 -3.479 0.454 -4.390 -2.569 311s 13 -6.537 0.552 -7.646 -5.428 311s 14 -5.508 0.617 -6.747 -4.269 311s 15 -2.847 0.335 -3.519 -2.175 311s 16 -1.316 0.287 -1.892 -0.739 311s 17 1.063 0.311 0.439 1.686 311s 18 1.982 0.218 1.545 2.420 311s 19 0.736 0.279 0.176 1.296 311s 20 1.882 0.327 1.227 2.538 311s 21 4.002 0.297 3.405 4.598 311s 22 5.418 0.412 4.591 6.245 311s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 311s 1 NA NA NA NA 311s 2 26.6 0.313 26.0 27.2 311s 3 28.7 0.310 28.1 29.3 311s 4 32.6 0.305 32.0 33.2 311s 5 33.9 0.236 33.4 34.4 311s 6 35.7 0.233 35.2 36.1 311s 7 37.7 0.234 37.3 38.2 311s 8 38.6 0.239 38.1 39.0 311s 9 38.8 0.229 38.4 39.3 311s 10 40.0 0.219 39.6 40.5 311s 11 38.2 0.301 37.6 38.9 311s 12 34.2 0.308 33.6 34.8 311s 13 29.3 0.370 28.5 30.0 311s 14 28.2 0.332 27.5 28.8 311s 15 30.3 0.324 29.7 31.0 311s 16 33.2 0.271 32.7 33.8 311s 17 37.6 0.263 37.1 38.1 311s 18 40.1 0.211 39.7 40.6 311s 19 39.0 0.306 38.4 39.6 311s 20 42.0 0.280 41.4 42.5 311s 21 46.2 0.298 45.6 46.8 311s 22 52.6 0.445 51.7 53.5 311s > model.frame 311s [1] TRUE 311s > model.matrix 311s [1] TRUE 311s > nobs 311s [1] 63 311s > linearHypothesis 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 51 1 1.44 0.24 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 51 1 1.69 0.2 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 52 311s 2 51 1 1.69 0.19 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 53 311s 2 51 2 0.77 0.47 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 53 311s 2 51 2 0.91 0.41 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 53 311s 2 51 2 1.83 0.4 311s > logLik 311s 'log Lik.' -70 (df=18) 311s 'log Lik.' -79 (df=18) 311s Estimating function 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_2 -0.46275 -5.7381 311s Consumption_3 -2.57830 -43.5733 311s Consumption_4 -3.09670 -56.9792 311s Consumption_5 -1.04122 -20.1997 311s Consumption_6 -0.08406 -1.6897 311s Consumption_7 1.63901 32.1246 311s Consumption_8 2.50567 49.6122 311s Consumption_9 1.87631 39.5902 311s Consumption_10 -1.27032 -27.5659 311s Consumption_11 0.86667 13.5200 311s Consumption_12 -0.08259 -0.9415 311s Consumption_13 -0.12857 -0.9000 311s Consumption_14 0.61874 6.9299 311s Consumption_15 -0.00847 -0.1042 311s Consumption_16 -0.03714 -0.5200 311s Consumption_17 2.95475 52.0036 311s Consumption_18 -0.81375 -14.0778 311s Consumption_19 0.55845 8.5443 311s Consumption_20 1.70539 32.4023 311s Consumption_21 1.32376 27.9312 311s Consumption_22 -4.44487 -104.4543 311s Investment_2 0.12481 1.5477 311s Investment_3 0.05687 0.9611 311s Investment_4 -0.37877 -6.9693 311s Investment_5 0.52122 10.1116 311s Investment_6 -0.11690 -2.3498 311s Investment_7 -0.50845 -9.9656 311s Investment_8 -0.29439 -5.8289 311s Investment_9 0.17430 3.6777 311s Investment_10 -0.44066 -9.5623 311s Investment_11 -0.09381 -1.4634 311s Investment_12 -0.02816 -0.3210 311s Investment_13 -0.11941 -0.8359 311s Investment_14 -0.14460 -1.6195 311s Investment_15 0.05435 0.6685 311s Investment_16 -0.00559 -0.0783 311s Investment_17 -0.36761 -6.4700 311s Investment_18 -0.00622 -0.1077 311s Investment_19 0.93438 14.2960 311s Investment_20 0.20633 3.9202 311s Investment_21 0.24863 5.2460 311s Investment_22 0.18369 4.3168 311s PrivateWages_2 -1.78352 -22.1156 311s PrivateWages_3 0.94670 15.9992 311s PrivateWages_4 2.49170 45.8473 311s PrivateWages_5 -0.03583 -0.6950 311s PrivateWages_6 -0.42104 -8.4630 311s PrivateWages_7 -0.52776 -10.3441 311s PrivateWages_8 -1.08598 -21.5024 311s PrivateWages_9 0.59560 12.5672 311s PrivateWages_10 2.06359 44.7800 311s PrivateWages_11 -0.56422 -8.8019 311s PrivateWages_12 0.49749 5.6714 311s PrivateWages_13 -0.42337 -2.9636 311s PrivateWages_14 0.55874 6.2579 311s PrivateWages_15 0.42760 5.2595 311s PrivateWages_16 -0.03516 -0.4922 311s PrivateWages_17 -1.29986 -22.8775 311s PrivateWages_18 1.39131 24.0696 311s PrivateWages_19 -1.33711 -20.4578 311s PrivateWages_20 -0.62964 -11.9631 311s PrivateWages_21 -1.92625 -40.6439 311s PrivateWages_22 1.09700 25.7794 311s Consumption_corpProfLag Consumption_wages 311s Consumption_2 -5.8769 -13.049 311s Consumption_3 -31.9709 -83.021 311s Consumption_4 -52.3342 -114.578 311s Consumption_5 -19.1585 -38.525 311s Consumption_6 -1.6308 -3.245 311s Consumption_7 32.9441 66.708 311s Consumption_8 49.1110 103.985 311s Consumption_9 37.1510 80.494 311s Consumption_10 -26.8037 -57.545 311s Consumption_11 18.8066 36.487 311s Consumption_12 -1.2884 -3.246 311s Consumption_13 -1.4658 -4.410 311s Consumption_14 4.3312 21.099 311s Consumption_15 -0.0949 -0.310 311s Consumption_16 -0.4568 -1.460 311s Consumption_17 41.3665 130.600 311s Consumption_18 -14.3220 -38.816 311s Consumption_19 9.6612 25.633 311s Consumption_20 26.0924 84.246 311s Consumption_21 25.1514 70.159 311s Consumption_22 -93.7867 -274.693 311s Investment_2 1.5851 3.520 311s Investment_3 0.7052 1.831 311s Investment_4 -6.4012 -14.014 311s Investment_5 9.5904 19.285 311s Investment_6 -2.2679 -4.513 311s Investment_7 -10.2199 -20.694 311s Investment_8 -5.7700 -12.217 311s Investment_9 3.4511 7.477 311s Investment_10 -9.2979 -19.962 311s Investment_11 -2.0356 -3.949 311s Investment_12 -0.4393 -1.107 311s Investment_13 -1.3613 -4.096 311s Investment_14 -1.0122 -4.931 311s Investment_15 0.6087 1.989 311s Investment_16 -0.0688 -0.220 311s Investment_17 -5.1466 -16.248 311s Investment_18 -0.1095 -0.297 311s Investment_19 16.1648 42.888 311s Investment_20 3.1568 10.193 311s Investment_21 4.7239 13.177 311s Investment_22 3.8759 11.352 311s PrivateWages_2 -22.6507 -50.295 311s PrivateWages_3 11.7391 30.484 311s PrivateWages_4 42.1098 92.193 311s PrivateWages_5 -0.6592 -1.326 311s PrivateWages_6 -8.1683 -16.252 311s PrivateWages_7 -10.6080 -21.480 311s PrivateWages_8 -21.2852 -45.068 311s PrivateWages_9 11.7929 25.551 311s PrivateWages_10 43.5418 93.481 311s PrivateWages_11 -12.2437 -23.754 311s PrivateWages_12 7.7609 19.551 311s PrivateWages_13 -4.8264 -14.521 311s PrivateWages_14 3.9112 19.053 311s PrivateWages_15 4.7891 15.650 311s PrivateWages_16 -0.4325 -1.382 311s PrivateWages_17 -18.1980 -57.454 311s PrivateWages_18 24.4870 66.365 311s PrivateWages_19 -23.1320 -61.373 311s PrivateWages_20 -9.6335 -31.104 311s PrivateWages_21 -36.5988 -102.091 311s PrivateWages_22 23.1466 67.794 311s Investment_(Intercept) Investment_corpProf 311s Consumption_2 0.08529 1.0576 311s Consumption_3 0.47520 8.0308 311s Consumption_4 0.57074 10.5016 311s Consumption_5 0.19190 3.7229 311s Consumption_6 0.01549 0.3114 311s Consumption_7 -0.30208 -5.9207 311s Consumption_8 -0.46181 -9.1438 311s Consumption_9 -0.34582 -7.2967 311s Consumption_10 0.23413 5.0806 311s Consumption_11 -0.15973 -2.4918 311s Consumption_12 0.01522 0.1735 311s Consumption_13 0.02370 0.1659 311s Consumption_14 -0.11404 -1.2772 311s Consumption_15 0.00156 0.0192 311s Consumption_16 0.00685 0.0958 311s Consumption_17 -0.54458 -9.5846 311s Consumption_18 0.14998 2.5946 311s Consumption_19 -0.10293 -1.5748 311s Consumption_20 -0.31431 -5.9719 311s Consumption_21 -0.24398 -5.1479 311s Consumption_22 0.81921 19.2515 311s Investment_2 -0.46650 -5.7846 311s Investment_3 -0.21255 -3.5922 311s Investment_4 1.41568 26.0484 311s Investment_5 -1.94810 -37.7932 311s Investment_6 0.43694 8.7825 311s Investment_7 1.90038 37.2474 311s Investment_8 1.10030 21.7860 311s Investment_9 -0.65146 -13.7457 311s Investment_10 1.64701 35.7401 311s Investment_11 0.35062 5.4696 311s Investment_12 0.10525 1.1998 311s Investment_13 0.44632 3.1242 311s Investment_14 0.54045 6.0530 311s Investment_15 -0.20313 -2.4985 311s Investment_16 0.02090 0.2926 311s Investment_17 1.37398 24.1820 311s Investment_18 0.02326 0.4024 311s Investment_19 -3.49233 -53.4327 311s Investment_20 -0.77116 -14.6521 311s Investment_21 -0.92927 -19.6075 311s Investment_22 -0.68657 -16.1344 311s PrivateWages_2 0.67977 8.4291 311s PrivateWages_3 -0.36082 -6.0979 311s PrivateWages_4 -0.94969 -17.4742 311s PrivateWages_5 0.01365 0.2649 311s PrivateWages_6 0.16048 3.2256 311s PrivateWages_7 0.20115 3.9426 311s PrivateWages_8 0.41391 8.1954 311s PrivateWages_9 -0.22701 -4.7899 311s PrivateWages_10 -0.78652 -17.0674 311s PrivateWages_11 0.21505 3.3548 311s PrivateWages_12 -0.18961 -2.1616 311s PrivateWages_13 0.16136 1.1295 311s PrivateWages_14 -0.21296 -2.3851 311s PrivateWages_15 -0.16298 -2.0046 311s PrivateWages_16 0.01340 0.1876 311s PrivateWages_17 0.49543 8.7195 311s PrivateWages_18 -0.53028 -9.1739 311s PrivateWages_19 0.50963 7.7973 311s PrivateWages_20 0.23998 4.5596 311s PrivateWages_21 0.73417 15.4910 311s PrivateWages_22 -0.41811 -9.8256 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_2 1.0831 15.590 311s Consumption_3 5.8924 86.771 311s Consumption_4 9.6455 105.301 311s Consumption_5 3.5310 36.404 311s Consumption_6 0.3006 2.986 311s Consumption_7 -6.0718 -59.751 311s Consumption_8 -9.0514 -93.932 311s Consumption_9 -6.8471 -71.791 311s Consumption_10 4.9401 49.307 311s Consumption_11 -3.4662 -34.454 311s Consumption_12 0.2375 3.299 311s Consumption_13 0.2701 5.055 311s Consumption_14 -0.7983 -23.617 311s Consumption_15 0.0175 0.315 311s Consumption_16 0.0842 1.362 311s Consumption_17 -7.6241 -107.663 311s Consumption_18 2.6396 29.966 311s Consumption_19 -1.7806 -20.770 311s Consumption_20 -4.8090 -62.831 311s Consumption_21 -4.6355 -49.088 311s Consumption_22 17.2854 167.529 311s Investment_2 -5.9246 -85.277 311s Investment_3 -2.6357 -38.812 311s Investment_4 23.9249 261.192 311s Investment_5 -35.8451 -369.555 311s Investment_6 8.4767 84.199 311s Investment_7 38.1976 375.895 311s Investment_8 21.5660 223.802 311s Investment_9 -12.8988 -135.242 311s Investment_10 34.7519 346.860 311s Investment_11 7.6084 75.628 311s Investment_12 1.6419 22.807 311s Investment_13 5.0880 95.199 311s Investment_14 3.7831 111.927 311s Investment_15 -2.2751 -41.032 311s Investment_16 0.2571 4.159 311s Investment_17 19.2357 271.636 311s Investment_18 0.4094 4.648 311s Investment_19 -60.4174 -704.753 311s Investment_20 -11.7988 -154.156 311s Investment_21 -17.6560 -186.968 311s Investment_22 -14.4866 -140.403 311s PrivateWages_2 8.6331 124.262 311s PrivateWages_3 -4.4742 -65.887 311s PrivateWages_4 -16.0497 -175.217 311s PrivateWages_5 0.2512 2.590 311s PrivateWages_6 3.1132 30.924 311s PrivateWages_7 4.0431 39.788 311s PrivateWages_8 8.1126 84.189 311s PrivateWages_9 -4.4947 -47.127 311s PrivateWages_10 -16.5955 -165.640 311s PrivateWages_11 4.6666 46.386 311s PrivateWages_12 -2.9580 -41.089 311s PrivateWages_13 1.8395 34.418 311s PrivateWages_14 -1.4907 -44.104 311s PrivateWages_15 -1.8253 -32.921 311s PrivateWages_16 0.1648 2.667 311s PrivateWages_17 6.9360 97.946 311s PrivateWages_18 -9.3330 -105.950 311s PrivateWages_19 8.8165 102.843 311s PrivateWages_20 3.6717 47.972 311s PrivateWages_21 13.9492 147.715 311s PrivateWages_22 -8.8221 -85.503 311s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 311s Consumption_2 -0.39158 -17.856 -17.582 311s Consumption_3 -2.18178 -109.307 -99.489 311s Consumption_4 -2.62045 -149.890 -131.285 311s Consumption_5 -0.88109 -50.310 -50.398 311s Consumption_6 -0.07113 -4.339 -4.062 311s Consumption_7 1.38694 88.764 84.604 311s Consumption_8 2.12032 136.548 135.700 311s Consumption_9 1.58775 102.410 102.251 311s Consumption_10 -1.07495 -72.022 -69.335 311s Consumption_11 0.73338 44.883 49.136 311s Consumption_12 -0.06989 -3.732 -4.277 311s Consumption_13 -0.10880 -4.820 -5.810 311s Consumption_14 0.52359 23.614 23.195 311s Consumption_15 -0.00717 -0.356 -0.323 311s Consumption_16 -0.03143 -1.710 -1.562 311s Consumption_17 2.50033 156.771 136.018 311s Consumption_18 -0.68860 -44.759 -43.175 311s Consumption_19 0.47257 28.779 30.717 311s Consumption_20 1.44311 100.296 87.885 311s Consumption_21 1.12017 84.797 77.852 311s Consumption_22 -3.76128 -332.497 -284.729 311s Investment_2 0.21842 9.960 9.807 311s Investment_3 0.09952 4.986 4.538 311s Investment_4 -0.66282 -37.913 -33.207 311s Investment_5 0.91210 52.081 52.172 311s Investment_6 -0.20458 -12.479 -11.681 311s Investment_7 -0.88976 -56.944 -54.275 311s Investment_8 -0.51516 -33.176 -32.970 311s Investment_9 0.30501 19.673 19.643 311s Investment_10 -0.77113 -51.666 -49.738 311s Investment_11 -0.16416 -10.047 -10.999 311s Investment_12 -0.04928 -2.631 -3.016 311s Investment_13 -0.20897 -9.257 -11.159 311s Investment_14 -0.25304 -11.412 -11.210 311s Investment_15 0.09511 4.727 4.289 311s Investment_16 -0.00978 -0.532 -0.486 311s Investment_17 -0.64330 -40.335 -34.995 311s Investment_18 -0.01089 -0.708 -0.683 311s Investment_19 1.63511 99.578 106.282 311s Investment_20 0.36106 25.094 21.989 311s Investment_21 0.43508 32.936 30.238 311s Investment_22 0.32145 28.416 24.334 311s PrivateWages_2 -3.89912 -177.800 -175.070 311s PrivateWages_3 2.06967 103.690 94.377 311s PrivateWages_4 5.44735 311.588 272.912 311s PrivateWages_5 -0.07832 -4.472 -4.480 311s PrivateWages_6 -0.92048 -56.150 -52.560 311s PrivateWages_7 -1.15379 -73.843 -70.381 311s PrivateWages_8 -2.37416 -152.896 -151.946 311s PrivateWages_9 1.30210 83.986 83.855 311s PrivateWages_10 4.51142 302.265 290.986 311s PrivateWages_11 -1.23351 -75.491 -82.645 311s PrivateWages_12 1.08762 58.079 66.562 311s PrivateWages_13 -0.92556 -41.002 -49.425 311s PrivateWages_14 1.22152 55.091 54.114 311s PrivateWages_15 0.93482 46.461 42.160 311s PrivateWages_16 -0.07687 -4.182 -3.820 311s PrivateWages_17 -2.84174 -178.177 -154.591 311s PrivateWages_18 3.04167 197.708 190.713 311s PrivateWages_19 -2.92319 -178.022 -190.007 311s PrivateWages_20 -1.37651 -95.667 -83.829 311s PrivateWages_21 -4.21116 -318.785 -292.676 311s PrivateWages_22 2.39825 212.005 181.548 311s PrivateWages_trend 311s Consumption_2 3.9158 311s Consumption_3 19.6360 311s Consumption_4 20.9636 311s Consumption_5 6.1676 311s Consumption_6 0.4268 311s Consumption_7 -6.9347 311s Consumption_8 -8.4813 311s Consumption_9 -4.7633 311s Consumption_10 2.1499 311s Consumption_11 -0.7334 311s Consumption_12 0.0000 311s Consumption_13 -0.1088 311s Consumption_14 1.0472 311s Consumption_15 -0.0215 311s Consumption_16 -0.1257 311s Consumption_17 12.5017 311s Consumption_18 -4.1316 311s Consumption_19 3.3080 311s Consumption_20 11.5449 311s Consumption_21 10.0816 311s Consumption_22 -37.6128 311s Investment_2 -2.1842 311s Investment_3 -0.8957 311s Investment_4 5.3026 311s Investment_5 -6.3847 311s Investment_6 1.2275 311s Investment_7 4.4488 311s Investment_8 2.0606 311s Investment_9 -0.9150 311s Investment_10 1.5423 311s Investment_11 0.1642 311s Investment_12 0.0000 311s Investment_13 -0.2090 311s Investment_14 -0.5061 311s Investment_15 0.2853 311s Investment_16 -0.0391 311s Investment_17 -3.2165 311s Investment_18 -0.0653 311s Investment_19 11.4458 311s Investment_20 2.8885 311s Investment_21 3.9157 311s Investment_22 3.2145 311s PrivateWages_2 38.9912 311s PrivateWages_3 -18.6270 311s PrivateWages_4 -43.5788 311s PrivateWages_5 0.5483 311s PrivateWages_6 5.5229 311s PrivateWages_7 5.7689 311s PrivateWages_8 9.4967 311s PrivateWages_9 -3.9063 311s PrivateWages_10 -9.0228 311s PrivateWages_11 1.2335 311s PrivateWages_12 0.0000 311s PrivateWages_13 -0.9256 311s PrivateWages_14 2.4431 311s PrivateWages_15 2.8045 311s PrivateWages_16 -0.3075 311s PrivateWages_17 -14.2087 311s PrivateWages_18 18.2500 311s PrivateWages_19 -20.4623 311s PrivateWages_20 -11.0121 311s PrivateWages_21 -37.9005 311s PrivateWages_22 23.9825 311s [1] TRUE 311s > Bread 311s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 311s [1,] 86.0484 -0.02454 -0.83573 311s [2,] -0.0245 0.37055 -0.22831 311s [3,] -0.8357 -0.22831 0.37290 311s [4,] -1.6729 -0.06016 -0.03411 311s [5,] 10.1786 -0.46129 0.72764 311s [6,] -0.1293 0.03988 -0.03792 311s [7,] -0.0505 -0.03436 0.04602 311s [8,] -0.0350 0.00175 -0.00419 311s [9,] -37.4223 0.06800 1.80971 311s [10,] 0.4074 -0.06333 0.04058 311s [11,] 0.2037 0.06442 -0.07324 311s [12,] 0.2057 0.03217 0.03109 311s Consumption_wages Investment_(Intercept) Investment_corpProf 311s [1,] -1.67e+00 10.179 -0.12933 311s [2,] -6.02e-02 -0.461 0.03988 311s [3,] -3.41e-02 0.728 -0.03792 311s [4,] 7.83e-02 -0.341 0.00185 311s [5,] -3.41e-01 1452.346 -13.96098 311s [6,] 1.85e-03 -13.961 0.46676 311s [7,] -2.96e-03 11.230 -0.39879 311s [8,] 1.79e-03 -6.973 0.06288 311s [9,] 1.32e-01 19.427 -0.13338 311s [10,] -5.46e-05 0.416 0.01516 311s [11,] -2.23e-03 -0.760 -0.01340 311s [12,] -3.03e-02 -0.736 0.00571 311s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 311s [1,] -0.05046 -0.03501 -37.4223 311s [2,] -0.03436 0.00175 0.0680 311s [3,] 0.04602 -0.00419 1.8097 311s [4,] -0.00296 0.00179 0.1325 311s [5,] 11.22954 -6.97254 19.4266 311s [6,] -0.39879 0.06288 -0.1334 311s [7,] 0.50387 -0.06357 -0.5157 311s [8,] -0.06357 0.03467 -0.0417 311s [9,] -0.51574 -0.04172 78.6495 311s [10,] -0.00784 -0.00271 -0.3339 311s [11,] 0.01702 0.00353 -0.9859 311s [12,] -0.01390 0.00432 0.8712 311s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 311s [1,] 4.07e-01 0.20374 0.20573 311s [2,] -6.33e-02 0.06442 0.03217 311s [3,] 4.06e-02 -0.07324 0.03109 311s [4,] -5.46e-05 -0.00223 -0.03033 311s [5,] 4.16e-01 -0.75990 -0.73581 311s [6,] 1.52e-02 -0.01340 0.00571 311s [7,] -7.84e-03 0.01702 -0.01390 311s [8,] -2.71e-03 0.00353 0.00432 311s [9,] -3.34e-01 -0.98593 0.87119 311s [10,] 4.68e-02 -0.04271 -0.01162 311s [11,] -4.27e-02 0.06124 -0.00299 311s [12,] -1.16e-02 -0.00299 0.04791 311s > 311s > # 3SLS 311s > summary 311s 311s systemfit results 311s method: 3SLS 311s 311s N DF SSR detRCov OLS-R2 McElroy-R2 311s system 63 51 73.6 0.283 0.963 0.995 311s 311s N DF SSR MSE RMSE R2 Adj R2 311s Consumption 21 17 18.7 1.102 1.050 0.980 0.977 311s Investment 21 17 44.0 2.586 1.608 0.826 0.795 311s PrivateWages 21 17 10.9 0.642 0.801 0.986 0.984 311s 311s The covariance matrix of the residuals used for estimation 311s Consumption Investment PrivateWages 311s Consumption 1.044 0.438 -0.385 311s Investment 0.438 1.383 0.193 311s PrivateWages -0.385 0.193 0.476 311s 311s The covariance matrix of the residuals 311s Consumption Investment PrivateWages 311s Consumption 0.892 0.411 -0.394 311s Investment 0.411 2.093 0.403 311s PrivateWages -0.394 0.403 0.520 311s 311s The correlations of the residuals 311s Consumption Investment PrivateWages 311s Consumption 1.000 0.301 -0.578 311s Investment 0.301 1.000 0.386 311s PrivateWages -0.578 0.386 1.000 311s 311s 311s 3SLS estimates for 'Consumption' (equation 1) 311s Model Formula: consump ~ corpProf + corpProfLag + wages 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 16.4408 1.3045 12.60 4.7e-10 *** 311s corpProf 0.1249 0.1081 1.16 0.26 311s corpProfLag 0.1631 0.1004 1.62 0.12 311s wages 0.7901 0.0379 20.83 1.5e-13 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.05 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 18.727 MSE: 1.102 Root MSE: 1.05 311s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 311s 311s 311s 3SLS estimates for 'Investment' (equation 2) 311s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 28.1778 6.7938 4.15 0.00067 *** 311s corpProf -0.0131 0.1619 -0.08 0.93655 311s corpProfLag 0.7557 0.1529 4.94 0.00012 *** 311s capitalLag -0.1948 0.0325 -5.99 1.5e-05 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.608 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 43.954 MSE: 2.586 Root MSE: 1.608 311s Multiple R-Squared: 0.826 Adjusted R-Squared: 0.795 311s 311s 311s 3SLS estimates for 'PrivateWages' (equation 3) 311s Model Formula: privWage ~ gnp + gnpLag + trend 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 1.7972 1.1159 1.61 0.13 311s gnp 0.4005 0.0318 12.59 4.8e-10 *** 311s gnpLag 0.1813 0.0342 5.31 5.8e-05 *** 311s trend 0.1497 0.0279 5.36 5.2e-05 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 0.801 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 10.921 MSE: 0.642 Root MSE: 0.801 311s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 311s 311s > residuals 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 -0.4416 -2.1951 -1.20287 311s 3 -1.0150 0.1515 0.51834 311s 4 -1.5289 0.4406 1.50936 311s 5 -0.4985 -1.8667 -0.08743 311s 6 -0.0132 0.0713 -0.28089 311s 7 0.7759 1.0294 -0.33908 311s 8 1.3004 1.1011 -0.69282 311s 9 1.0993 0.5853 0.34494 311s 10 -0.5839 2.2952 1.27590 311s 11 -0.1917 -1.3443 -0.40414 311s 12 -0.5598 -0.9944 0.22151 311s 13 -0.6746 -1.3404 -0.36962 311s 14 0.5767 1.9316 0.31006 311s 15 -0.0211 -0.1217 0.27309 311s 16 0.0539 0.1847 0.00716 311s 17 1.8555 2.0937 -0.71866 311s 18 -0.4596 -0.3216 0.90582 311s 19 0.0613 -3.6314 -0.81881 311s 20 1.2602 0.7582 -0.26942 311s 21 0.9500 0.2428 -1.06125 311s 22 -1.9451 0.9302 0.87883 311s > fitted 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 42.3 1.99510 26.7 311s 3 46.0 1.74850 28.8 311s 4 50.7 4.75942 32.6 311s 5 51.1 4.86672 34.0 311s 6 52.6 5.02874 35.7 311s 7 54.3 4.57056 37.7 311s 8 54.9 3.09893 38.6 311s 9 56.2 2.41471 38.9 311s 10 58.4 2.80476 40.0 311s 11 55.2 2.34425 38.3 311s 12 51.5 -2.40558 34.3 311s 13 46.3 -4.85959 29.4 311s 14 45.9 -7.03164 28.2 311s 15 48.7 -2.87827 30.3 311s 16 51.2 -1.48466 33.2 311s 17 55.8 0.00629 37.5 311s 18 59.2 2.32164 40.1 311s 19 57.4 1.73138 39.0 311s 20 60.3 0.54175 41.9 311s 21 64.1 3.05716 46.1 311s 22 71.6 3.96979 52.4 311s > predict 311s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 311s 1 NA NA NA NA 311s 2 42.3 0.464 39.9 44.8 311s 3 46.0 0.541 43.5 48.5 311s 4 50.7 0.337 48.4 53.1 311s 5 51.1 0.385 48.7 53.5 311s 6 52.6 0.386 50.3 55.0 311s 7 54.3 0.349 52.0 56.7 311s 8 54.9 0.320 52.6 57.2 311s 9 56.2 0.355 53.9 58.5 311s 10 58.4 0.370 56.0 60.7 311s 11 55.2 0.682 52.6 57.8 311s 12 51.5 0.563 48.9 54.0 311s 13 46.3 0.719 43.6 49.0 311s 14 45.9 0.597 43.4 48.5 311s 15 48.7 0.370 46.4 51.1 311s 16 51.2 0.327 48.9 53.6 311s 17 55.8 0.391 53.5 58.2 311s 18 59.2 0.316 56.8 61.5 311s 19 57.4 0.389 55.1 59.8 311s 20 60.3 0.459 57.9 62.8 311s 21 64.1 0.438 61.7 66.4 311s 22 71.6 0.674 69.0 74.3 311s Investment.pred Investment.se.fit Investment.lwr Investment.upr 311s 1 NA NA NA NA 311s 2 1.99510 0.792 -1.787 5.777 311s 3 1.74850 0.585 -1.861 5.358 311s 4 4.75942 0.510 1.200 8.319 311s 5 4.86672 0.423 1.359 8.375 311s 6 5.02874 0.400 1.533 8.525 311s 7 4.57056 0.391 1.079 8.062 311s 8 3.09893 0.345 -0.371 6.568 311s 9 2.41471 0.511 -1.145 5.974 311s 10 2.80476 0.560 -0.788 6.397 311s 11 2.34425 0.839 -1.482 6.170 311s 12 -2.40558 0.673 -6.083 1.272 311s 13 -4.85959 0.862 -8.708 -1.011 311s 14 -7.03164 0.874 -10.893 -3.171 311s 15 -2.87827 0.433 -6.392 0.635 311s 16 -1.48466 0.375 -4.968 1.999 311s 17 0.00629 0.491 -3.541 3.554 311s 18 2.32164 0.294 -1.127 5.771 311s 19 1.73138 0.446 -1.789 5.252 311s 20 0.54175 0.547 -3.042 4.125 311s 21 3.05716 0.454 -0.468 6.582 311s 22 3.96979 0.642 0.317 7.623 311s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 311s 1 NA NA NA NA 311s 2 26.7 0.314 24.9 28.5 311s 3 28.8 0.318 27.0 30.6 311s 4 32.6 0.325 30.8 34.4 311s 5 34.0 0.235 32.2 35.7 311s 6 35.7 0.241 33.9 37.4 311s 7 37.7 0.238 36.0 39.5 311s 8 38.6 0.237 36.8 40.4 311s 9 38.9 0.227 37.1 40.6 311s 10 40.0 0.219 38.3 41.8 311s 11 38.3 0.317 36.5 40.1 311s 12 34.3 0.344 32.4 36.1 311s 13 29.4 0.419 27.5 31.3 311s 14 28.2 0.334 26.4 30.0 311s 15 30.3 0.320 28.5 32.1 311s 16 33.2 0.268 31.4 35.0 311s 17 37.5 0.269 35.7 39.3 311s 18 40.1 0.212 38.3 41.8 311s 19 39.0 0.331 37.2 40.8 311s 20 41.9 0.287 40.1 43.7 311s 21 46.1 0.301 44.3 47.9 311s 22 52.4 0.471 50.5 54.4 311s > model.frame 311s [1] TRUE 311s > model.matrix 311s [1] TRUE 311s > nobs 311s [1] 63 311s > linearHypothesis 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 51 1 0.29 0.59 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 51 1 0.39 0.54 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 52 311s 2 51 1 0.39 0.53 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 53 311s 2 51 2 0.3 0.74 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 53 311s 2 51 2 0.4 0.67 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 53 311s 2 51 2 0.8 0.67 311s > logLik 311s 'log Lik.' -76.1 (df=18) 311s 'log Lik.' -89.1 (df=18) 311s Estimating function 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_2 -3.2451 -43.02 311s Consumption_3 -1.3384 -22.19 311s Consumption_4 -1.4130 -27.25 311s Consumption_5 -5.0390 -105.62 311s Consumption_6 -0.8531 -16.86 311s Consumption_7 4.3438 79.23 311s Consumption_8 5.6608 99.48 311s Consumption_9 3.7666 73.61 311s Consumption_10 1.2798 26.08 311s Consumption_11 -3.5695 -61.32 311s Consumption_12 -1.8656 -23.70 311s Consumption_13 -3.4193 -30.77 311s Consumption_14 4.0738 36.88 311s Consumption_15 -1.6814 -21.31 311s Consumption_16 -1.4312 -20.64 311s Consumption_17 9.0552 133.22 311s Consumption_18 -1.9716 -39.03 311s Consumption_19 -6.7338 -129.33 311s Consumption_20 4.8735 84.89 311s Consumption_21 1.6324 33.15 311s Consumption_22 -2.1249 -48.14 311s Investment_2 2.1466 28.45 311s Investment_3 -0.1448 -2.40 311s Investment_4 -0.4444 -8.57 311s Investment_5 1.8148 38.04 311s Investment_6 -0.0658 -1.30 311s Investment_7 -0.9944 -18.14 311s Investment_8 -1.0536 -18.52 311s Investment_9 -0.5553 -10.85 311s Investment_10 -2.2390 -45.62 311s Investment_11 1.3010 22.35 311s Investment_12 0.9607 12.21 311s Investment_13 1.2918 11.63 311s Investment_14 -1.8711 -16.94 311s Investment_15 0.1149 1.46 311s Investment_16 -0.1869 -2.70 311s Investment_17 -2.0208 -29.73 311s Investment_18 0.2841 5.62 311s Investment_19 3.5191 67.59 311s Investment_20 -0.7250 -12.63 311s Investment_21 -0.2285 -4.64 311s Investment_22 -0.9035 -20.47 311s PrivateWages_2 -4.3513 -57.68 311s PrivateWages_3 1.7756 29.44 311s PrivateWages_4 3.5512 68.47 311s PrivateWages_5 -3.3088 -69.35 311s PrivateWages_6 -0.7761 -15.34 311s PrivateWages_7 1.5988 29.16 311s PrivateWages_8 1.5583 27.38 311s PrivateWages_9 2.5665 50.15 311s PrivateWages_10 4.9740 101.35 311s PrivateWages_11 -3.5972 -61.80 311s PrivateWages_12 -0.7986 -10.15 311s PrivateWages_13 -3.2258 -29.03 311s PrivateWages_14 3.6395 32.95 311s PrivateWages_15 -0.5056 -6.41 311s PrivateWages_16 -1.0680 -15.40 311s PrivateWages_17 3.0850 45.39 311s PrivateWages_18 -0.3546 -7.02 311s PrivateWages_19 -8.0362 -154.35 311s PrivateWages_20 1.6465 28.68 311s PrivateWages_21 -1.9137 -38.86 311s PrivateWages_22 3.5407 80.22 311s Consumption_corpProfLag Consumption_wages 311s Consumption_2 -41.21 -95.43 311s Consumption_3 -16.60 -42.49 311s Consumption_4 -23.88 -50.52 311s Consumption_5 -92.72 -196.89 311s Consumption_6 -16.55 -33.39 311s Consumption_7 87.31 170.95 311s Consumption_8 110.95 227.47 311s Consumption_9 74.58 159.45 311s Consumption_10 27.00 56.34 311s Consumption_11 -77.46 -155.98 311s Consumption_12 -29.10 -73.65 311s Consumption_13 -38.98 -120.13 311s Consumption_14 28.52 133.55 311s Consumption_15 -18.83 -63.05 311s Consumption_16 -17.60 -57.45 311s Consumption_17 126.77 377.63 311s Consumption_18 -34.70 -94.39 311s Consumption_19 -116.49 -332.00 311s Consumption_20 74.56 235.83 311s Consumption_21 31.02 87.12 311s Consumption_22 -44.84 -129.02 311s Investment_2 27.26 63.12 311s Investment_3 -1.80 -4.60 311s Investment_4 -7.51 -15.89 311s Investment_5 33.39 70.91 311s Investment_6 -1.28 -2.57 311s Investment_7 -19.99 -39.13 311s Investment_8 -20.65 -42.34 311s Investment_9 -10.99 -23.51 311s Investment_10 -47.24 -98.56 311s Investment_11 28.23 56.85 311s Investment_12 14.99 37.92 311s Investment_13 14.73 45.38 311s Investment_14 -13.10 -61.34 311s Investment_15 1.29 4.31 311s Investment_16 -2.30 -7.50 311s Investment_17 -28.29 -84.27 311s Investment_18 5.00 13.60 311s Investment_19 60.88 173.50 311s Investment_20 -11.09 -35.08 311s Investment_21 -4.34 -12.19 311s Investment_22 -19.06 -54.86 311s PrivateWages_2 -55.26 -127.96 311s PrivateWages_3 22.02 56.38 311s PrivateWages_4 60.01 126.96 311s PrivateWages_5 -60.88 -129.29 311s PrivateWages_6 -15.06 -30.37 311s PrivateWages_7 32.14 62.92 311s PrivateWages_8 30.54 62.62 311s PrivateWages_9 50.82 108.65 311s PrivateWages_10 104.95 218.96 311s PrivateWages_11 -78.06 -157.19 311s PrivateWages_12 -12.46 -31.53 311s PrivateWages_13 -36.77 -113.33 311s PrivateWages_14 25.48 119.32 311s PrivateWages_15 -5.66 -18.96 311s PrivateWages_16 -13.14 -42.87 311s PrivateWages_17 43.19 128.65 311s PrivateWages_18 -6.24 -16.98 311s PrivateWages_19 -139.03 -396.21 311s PrivateWages_20 25.19 79.68 311s PrivateWages_21 -36.36 -102.14 311s PrivateWages_22 74.71 214.98 311s Investment_(Intercept) Investment_corpProf 311s Consumption_2 1.4757 19.56 311s Consumption_3 0.6086 10.09 311s Consumption_4 0.6425 12.39 311s Consumption_5 2.2915 48.03 311s Consumption_6 0.3879 7.67 311s Consumption_7 -1.9753 -36.03 311s Consumption_8 -2.5742 -45.24 311s Consumption_9 -1.7128 -33.47 311s Consumption_10 -0.5820 -11.86 311s Consumption_11 1.6232 27.89 311s Consumption_12 0.8484 10.78 311s Consumption_13 1.5549 13.99 311s Consumption_14 -1.8525 -16.77 311s Consumption_15 0.7646 9.69 311s Consumption_16 0.6508 9.39 311s Consumption_17 -4.1178 -60.58 311s Consumption_18 0.8965 17.75 311s Consumption_19 3.0621 58.81 311s Consumption_20 -2.2162 -38.60 311s Consumption_21 -0.7423 -15.07 311s Consumption_22 0.9663 21.89 311s Investment_2 -2.6492 -35.12 311s Investment_3 0.1787 2.96 311s Investment_4 0.5485 10.58 311s Investment_5 -2.2397 -46.94 311s Investment_6 0.0811 1.60 311s Investment_7 1.2272 22.38 311s Investment_8 1.3003 22.85 311s Investment_9 0.6853 13.39 311s Investment_10 2.7633 56.30 311s Investment_11 -1.6056 -27.58 311s Investment_12 -1.1856 -15.06 311s Investment_13 -1.5943 -14.35 311s Investment_14 2.3092 20.91 311s Investment_15 -0.1418 -1.80 311s Investment_16 0.2307 3.33 311s Investment_17 2.4940 36.69 311s Investment_18 -0.3506 -6.94 311s Investment_19 -4.3431 -83.42 311s Investment_20 0.8947 15.59 311s Investment_21 0.2820 5.73 311s Investment_22 1.1150 25.26 311s PrivateWages_2 2.6070 34.56 311s PrivateWages_3 -1.0638 -17.64 311s PrivateWages_4 -2.1276 -41.02 311s PrivateWages_5 1.9824 41.55 311s PrivateWages_6 0.4650 9.19 311s PrivateWages_7 -0.9579 -17.47 311s PrivateWages_8 -0.9336 -16.41 311s PrivateWages_9 -1.5377 -30.05 311s PrivateWages_10 -2.9800 -60.72 311s PrivateWages_11 2.1552 37.03 311s PrivateWages_12 0.4785 6.08 311s PrivateWages_13 1.9327 17.39 311s PrivateWages_14 -2.1805 -19.74 311s PrivateWages_15 0.3029 3.84 311s PrivateWages_16 0.6398 9.23 311s PrivateWages_17 -1.8483 -27.19 311s PrivateWages_18 0.2125 4.21 311s PrivateWages_19 4.8147 92.47 311s PrivateWages_20 -0.9865 -17.18 311s PrivateWages_21 1.1466 23.28 311s PrivateWages_22 -2.1213 -48.06 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_2 18.74 269.8 311s Consumption_3 7.55 111.1 311s Consumption_4 10.86 118.5 311s Consumption_5 42.16 434.7 311s Consumption_6 7.53 74.8 311s Consumption_7 -39.70 -390.7 311s Consumption_8 -50.45 -523.6 311s Consumption_9 -33.91 -355.6 311s Consumption_10 -12.28 -122.6 311s Consumption_11 35.22 350.1 311s Consumption_12 13.23 183.8 311s Consumption_13 17.73 331.7 311s Consumption_14 -12.97 -383.7 311s Consumption_15 8.56 154.5 311s Consumption_16 8.01 129.5 311s Consumption_17 -57.65 -814.1 311s Consumption_18 15.78 179.1 311s Consumption_19 52.98 617.9 311s Consumption_20 -33.91 -443.0 311s Consumption_21 -14.10 -149.4 311s Consumption_22 20.39 197.6 311s Investment_2 -33.65 -484.3 311s Investment_3 2.22 32.6 311s Investment_4 9.27 101.2 311s Investment_5 -41.21 -424.9 311s Investment_6 1.57 15.6 311s Investment_7 24.67 242.7 311s Investment_8 25.49 264.5 311s Investment_9 13.57 142.3 311s Investment_10 58.30 581.9 311s Investment_11 -34.84 -346.3 311s Investment_12 -18.50 -256.9 311s Investment_13 -18.17 -340.1 311s Investment_14 16.16 478.2 311s Investment_15 -1.59 -28.6 311s Investment_16 2.84 45.9 311s Investment_17 34.92 493.1 311s Investment_18 -6.17 -70.0 311s Investment_19 -75.14 -876.4 311s Investment_20 13.69 178.9 311s Investment_21 5.36 56.7 311s Investment_22 23.53 228.0 311s PrivateWages_2 33.11 476.6 311s PrivateWages_3 -13.19 -194.3 311s PrivateWages_4 -35.96 -392.5 311s PrivateWages_5 36.48 376.1 311s PrivateWages_6 9.02 89.6 311s PrivateWages_7 -19.25 -189.5 311s PrivateWages_8 -18.30 -189.9 311s PrivateWages_9 -30.45 -319.2 311s PrivateWages_10 -62.88 -627.6 311s PrivateWages_11 46.77 464.9 311s PrivateWages_12 7.46 103.7 311s PrivateWages_13 22.03 412.2 311s PrivateWages_14 -15.26 -451.6 311s PrivateWages_15 3.39 61.2 311s PrivateWages_16 7.87 127.3 311s PrivateWages_17 -25.88 -365.4 311s PrivateWages_18 3.74 42.5 311s PrivateWages_19 83.29 971.6 311s PrivateWages_20 -15.09 -197.2 311s PrivateWages_21 21.78 230.7 311s PrivateWages_22 -44.76 -433.8 311s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 311s Consumption_2 -3.220 -153.49 -144.60 311s Consumption_3 -1.328 -65.52 -60.57 311s Consumption_4 -1.402 -79.70 -70.25 311s Consumption_5 -5.001 -303.71 -286.05 311s Consumption_6 -0.847 -51.81 -48.34 311s Consumption_7 4.311 264.22 262.96 311s Consumption_8 5.618 341.88 359.54 311s Consumption_9 3.738 233.16 240.73 311s Consumption_10 1.270 81.79 81.92 311s Consumption_11 -3.542 -228.05 -237.34 311s Consumption_12 -1.851 -101.61 -113.31 311s Consumption_13 -3.393 -159.94 -181.21 311s Consumption_14 4.043 168.34 179.10 311s Consumption_15 -1.669 -85.05 -75.26 311s Consumption_16 -1.420 -79.06 -70.59 311s Consumption_17 8.987 515.06 488.87 311s Consumption_18 -1.957 -132.41 -122.68 311s Consumption_19 -6.683 -455.83 -434.38 311s Consumption_20 4.837 323.61 294.54 311s Consumption_21 1.620 121.95 112.59 311s Consumption_22 -2.109 -182.35 -159.64 311s Investment_2 2.807 133.77 126.02 311s Investment_3 -0.189 -9.34 -8.63 311s Investment_4 -0.581 -33.02 -29.11 311s Investment_5 2.373 144.11 135.73 311s Investment_6 -0.086 -5.26 -4.91 311s Investment_7 -1.300 -79.69 -79.31 311s Investment_8 -1.378 -83.84 -88.17 311s Investment_9 -0.726 -45.28 -46.75 311s Investment_10 -2.928 -188.52 -188.82 311s Investment_11 1.701 109.51 113.97 311s Investment_12 1.256 68.94 76.87 311s Investment_13 1.689 79.61 90.20 311s Investment_14 -2.446 -101.86 -108.38 311s Investment_15 0.150 7.66 6.77 311s Investment_16 -0.244 -13.60 -12.15 311s Investment_17 -2.642 -151.44 -143.74 311s Investment_18 0.371 25.13 23.29 311s Investment_19 4.601 313.85 299.09 311s Investment_20 -0.948 -63.43 -57.73 311s Investment_21 -0.299 -22.49 -20.76 311s Investment_22 -1.181 -102.15 -89.43 311s PrivateWages_2 -8.830 -420.86 -396.47 311s PrivateWages_3 3.603 177.74 164.31 311s PrivateWages_4 7.206 409.57 361.04 311s PrivateWages_5 -6.715 -407.80 -384.07 311s PrivateWages_6 -1.575 -96.39 -89.93 311s PrivateWages_7 3.244 198.86 197.91 311s PrivateWages_8 3.162 192.44 202.38 311s PrivateWages_9 5.208 324.85 335.40 311s PrivateWages_10 10.094 649.99 651.03 311s PrivateWages_11 -7.300 -469.94 -489.08 311s PrivateWages_12 -1.621 -88.94 -99.18 311s PrivateWages_13 -6.546 -308.53 -349.56 311s PrivateWages_14 7.386 307.52 327.18 311s PrivateWages_15 -1.026 -52.30 -46.27 311s PrivateWages_16 -2.167 -120.63 -107.71 311s PrivateWages_17 6.260 358.81 340.56 311s PrivateWages_18 -0.720 -48.70 -45.12 311s PrivateWages_19 -16.308 -1112.35 -1060.00 311s PrivateWages_20 3.341 223.57 203.48 311s PrivateWages_21 -3.883 -292.34 -269.90 311s PrivateWages_22 7.185 621.32 543.91 311s PrivateWages_trend 311s Consumption_2 32.205 311s Consumption_3 11.954 311s Consumption_4 11.218 311s Consumption_5 35.006 311s Consumption_6 5.080 311s Consumption_7 -21.554 311s Consumption_8 -22.471 311s Consumption_9 -11.214 311s Consumption_10 -2.540 311s Consumption_11 3.542 311s Consumption_12 0.000 311s Consumption_13 -3.393 311s Consumption_14 8.086 311s Consumption_15 -5.006 311s Consumption_16 -5.681 311s Consumption_17 44.933 311s Consumption_18 -11.740 311s Consumption_19 -46.779 311s Consumption_20 38.692 311s Consumption_21 14.580 311s Consumption_22 -21.088 311s Investment_2 -28.067 311s Investment_3 1.704 311s Investment_4 4.648 311s Investment_5 -16.610 311s Investment_6 0.516 311s Investment_7 6.501 311s Investment_8 5.511 311s Investment_9 2.178 311s Investment_10 5.855 311s Investment_11 -1.701 311s Investment_12 0.000 311s Investment_13 1.689 311s Investment_14 -4.893 311s Investment_15 0.451 311s Investment_16 -0.978 311s Investment_17 -13.211 311s Investment_18 2.228 311s Investment_19 32.209 311s Investment_20 -7.583 311s Investment_21 -2.689 311s Investment_22 -11.813 311s PrivateWages_2 88.301 311s PrivateWages_3 -32.429 311s PrivateWages_4 -57.650 311s PrivateWages_5 47.002 311s PrivateWages_6 9.450 311s PrivateWages_7 -16.222 311s PrivateWages_8 -12.649 311s PrivateWages_9 -15.624 311s PrivateWages_10 -20.187 311s PrivateWages_11 7.300 311s PrivateWages_12 0.000 311s PrivateWages_13 -6.546 311s PrivateWages_14 14.771 311s PrivateWages_15 -3.078 311s PrivateWages_16 -8.669 311s PrivateWages_17 31.301 311s PrivateWages_18 -4.318 311s PrivateWages_19 -114.154 311s PrivateWages_20 26.730 311s PrivateWages_21 -34.951 311s PrivateWages_22 71.851 311s [1] TRUE 311s > Bread 311s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 311s [1,] 1.07e+02 -1.06982 -0.3515 311s [2,] -1.07e+00 0.73659 -0.5079 311s [3,] -3.51e-01 -0.50793 0.6355 311s [4,] -1.93e+00 -0.07361 -0.0356 311s [5,] 1.24e+02 -0.98618 3.4455 311s [6,] -2.71e+00 0.38390 -0.3719 311s [7,] 9.65e-01 -0.31139 0.3992 311s [8,] -4.61e-01 -0.00199 -0.0185 311s [9,] -3.88e+01 0.05351 1.8003 311s [10,] 6.27e-01 -0.08533 0.0556 311s [11,] -5.96e-04 0.08746 -0.0887 311s [12,] 2.14e-01 0.04029 0.0279 311s Consumption_wages Investment_(Intercept) Investment_corpProf 311s [1,] -1.934840 123.765 -2.71e+00 311s [2,] -0.073613 -0.986 3.84e-01 311s [3,] -0.035606 3.445 -3.72e-01 311s [4,] 0.090675 -3.911 5.58e-02 311s [5,] -3.910682 2907.785 -4.61e+01 311s [6,] 0.055805 -46.132 1.65e+00 311s [7,] -0.054072 38.083 -1.41e+00 311s [8,] 0.019220 -13.707 2.06e-01 311s [9,] 0.174112 17.422 -1.06e-01 311s [10,] -0.002325 2.389 2.04e-03 311s [11,] -0.000594 -2.765 -2.91e-04 311s [12,] -0.032572 -2.080 3.10e-02 311s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 311s [1,] 0.96474 -0.46130 -38.76422 311s [2,] -0.31139 -0.00199 0.05351 311s [3,] 0.39923 -0.01847 1.80032 311s [4,] -0.05407 0.01922 0.17411 311s [5,] 38.08346 -13.70662 17.42245 311s [6,] -1.40785 0.20597 -0.10564 311s [7,] 1.47348 -0.19170 -0.93153 311s [8,] -0.19170 0.06667 0.00097 311s [9,] -0.93153 0.00097 78.44334 311s [10,] 0.01112 -0.01300 -0.49810 311s [11,] 0.00455 0.01344 -0.81226 311s [12,] -0.04174 0.01117 0.88592 311s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 311s [1,] 0.62679 -0.000596 0.21374 311s [2,] -0.08533 0.087455 0.04029 311s [3,] 0.05563 -0.088660 0.02790 311s [4,] -0.00233 -0.000594 -0.03257 311s [5,] 2.38888 -2.764716 -2.07974 311s [6,] 0.00204 -0.000291 0.03105 311s [7,] 0.01112 0.004547 -0.04174 311s [8,] -0.01300 0.013443 0.01117 311s [9,] -0.49810 -0.812260 0.88592 311s [10,] 0.06376 -0.057450 -0.01781 311s [11,] -0.05745 0.073510 0.00317 311s [12,] -0.01781 0.003170 0.04916 311s > 311s > # I3SLS 311s > summary 311s 311s systemfit results 311s method: iterated 3SLS 311s 311s convergence achieved after 20 iterations 311s 311s N DF SSR detRCov OLS-R2 McElroy-R2 311s system 63 51 128 0.509 0.936 0.996 311s 311s N DF SSR MSE RMSE R2 Adj R2 311s Consumption 21 17 19.2 1.130 1.063 0.980 0.976 311s Investment 21 17 95.7 5.627 2.372 0.621 0.554 311s PrivateWages 21 17 12.7 0.748 0.865 0.984 0.981 311s 311s The covariance matrix of the residuals used for estimation 311s Consumption Investment PrivateWages 311s Consumption 0.915 0.642 -0.435 311s Investment 0.642 4.555 0.734 311s PrivateWages -0.435 0.734 0.606 311s 311s The covariance matrix of the residuals 311s Consumption Investment PrivateWages 311s Consumption 0.915 0.642 -0.435 311s Investment 0.642 4.555 0.734 311s PrivateWages -0.435 0.734 0.606 311s 311s The correlations of the residuals 311s Consumption Investment PrivateWages 311s Consumption 1.000 0.314 -0.584 311s Investment 0.314 1.000 0.442 311s PrivateWages -0.584 0.442 1.000 311s 311s 311s 3SLS estimates for 'Consumption' (equation 1) 311s Model Formula: consump ~ corpProf + corpProfLag + wages 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 16.5590 1.2244 13.52 1.6e-10 *** 311s corpProf 0.1645 0.0962 1.71 0.105 311s corpProfLag 0.1766 0.0901 1.96 0.067 . 311s wages 0.7658 0.0348 22.03 6.1e-14 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.063 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 19.213 MSE: 1.13 Root MSE: 1.063 311s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 311s 311s 311s 3SLS estimates for 'Investment' (equation 2) 311s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 42.8959 10.5937 4.05 0.00083 *** 311s corpProf -0.3565 0.2602 -1.37 0.18838 311s corpProfLag 1.0113 0.2488 4.07 0.00081 *** 311s capitalLag -0.2602 0.0509 -5.12 8.6e-05 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 2.372 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 95.661 MSE: 5.627 Root MSE: 2.372 311s Multiple R-Squared: 0.621 Adjusted R-Squared: 0.554 311s 311s 311s 3SLS estimates for 'PrivateWages' (equation 3) 311s Model Formula: privWage ~ gnp + gnpLag + trend 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 2.6247 1.1956 2.20 0.042 * 311s gnp 0.3748 0.0311 12.05 9.4e-10 *** 311s gnpLag 0.1937 0.0324 5.98 1.5e-05 *** 311s trend 0.1679 0.0289 5.80 2.1e-05 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 0.865 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 12.719 MSE: 0.748 Root MSE: 0.865 311s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.981 311s 311s > residuals 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 -0.537 -3.95419 -1.2303 311s 3 -1.187 0.00151 0.5797 311s 4 -1.705 -0.22015 1.6794 311s 5 -0.734 -2.22753 -0.0260 311s 6 -0.251 -0.10866 -0.1362 311s 7 0.600 0.83218 -0.1837 311s 8 1.142 1.46624 -0.5825 311s 9 0.921 1.62030 0.4347 311s 10 -0.745 3.40013 1.4104 311s 11 -0.197 -2.15443 -0.4679 311s 12 -0.385 -1.62274 0.0106 311s 13 -0.390 -2.62869 -0.7363 311s 14 0.749 2.80517 0.0581 311s 15 0.112 -0.27710 0.1113 311s 16 0.170 0.13598 -0.1089 311s 17 1.925 2.76200 -0.6976 311s 18 -0.341 -0.53919 0.8651 311s 19 0.219 -4.32845 -1.0116 311s 20 1.383 1.71889 -0.2087 311s 21 1.028 1.06406 -0.9656 311s 22 -1.777 2.25466 1.2061 311s > fitted 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 42.4 3.754 26.7 311s 3 46.2 1.898 28.7 311s 4 50.9 5.420 32.4 311s 5 51.3 5.228 33.9 311s 6 52.9 5.209 35.5 311s 7 54.5 4.768 37.6 311s 8 55.1 2.734 38.5 311s 9 56.4 1.380 38.8 311s 10 58.5 1.700 39.9 311s 11 55.2 3.154 38.4 311s 12 51.3 -1.777 34.5 311s 13 46.0 -3.571 29.7 311s 14 45.8 -7.905 28.4 311s 15 48.6 -2.723 30.5 311s 16 51.1 -1.436 33.3 311s 17 55.8 -0.662 37.5 311s 18 59.0 2.539 40.1 311s 19 57.3 2.428 39.2 311s 20 60.2 -0.419 41.8 311s 21 64.0 2.236 46.0 311s 22 71.5 2.645 52.1 311s > predict 311s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 311s 1 NA NA NA NA 311s 2 42.4 0.434 41.6 43.3 311s 3 46.2 0.491 45.2 47.2 311s 4 50.9 0.309 50.3 51.5 311s 5 51.3 0.351 50.6 52.0 311s 6 52.9 0.352 52.1 53.6 311s 7 54.5 0.320 53.9 55.1 311s 8 55.1 0.293 54.5 55.6 311s 9 56.4 0.324 55.7 57.0 311s 10 58.5 0.340 57.9 59.2 311s 11 55.2 0.613 54.0 56.4 311s 12 51.3 0.506 50.3 52.3 311s 13 46.0 0.649 44.7 47.3 311s 14 45.8 0.546 44.7 46.8 311s 15 48.6 0.341 47.9 49.3 311s 16 51.1 0.301 50.5 51.7 311s 17 55.8 0.357 55.1 56.5 311s 18 59.0 0.293 58.5 59.6 311s 19 57.3 0.353 56.6 58.0 311s 20 60.2 0.421 59.4 61.1 311s 21 64.0 0.409 63.2 64.8 311s 22 71.5 0.630 70.2 72.7 311s Investment.pred Investment.se.fit Investment.lwr Investment.upr 311s 1 NA NA NA NA 311s 2 3.754 1.263 1.218 6.2906 311s 3 1.898 1.022 -0.153 3.9503 311s 4 5.420 0.853 3.709 7.1317 311s 5 5.228 0.727 3.767 6.6877 311s 6 5.209 0.703 3.797 6.6200 311s 7 4.768 0.688 3.387 6.1487 311s 8 2.734 0.615 1.499 3.9683 311s 9 1.380 0.852 -0.330 3.0893 311s 10 1.700 0.938 -0.184 3.5836 311s 11 3.154 1.437 0.269 6.0398 311s 12 -1.777 1.173 -4.133 0.5780 311s 13 -3.571 1.494 -6.570 -0.5725 311s 14 -7.905 1.479 -10.875 -4.9350 311s 15 -2.723 0.778 -4.285 -1.1613 311s 16 -1.436 0.672 -2.784 -0.0875 311s 17 -0.662 0.832 -2.333 1.0088 311s 18 2.539 0.522 1.491 3.5875 311s 19 2.428 0.753 0.918 3.9392 311s 20 -0.419 0.907 -2.240 1.4019 311s 21 2.236 0.775 0.679 3.7928 311s 22 2.645 1.076 0.486 4.8047 311s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 311s 1 NA NA NA NA 311s 2 26.7 0.340 26.0 27.4 311s 3 28.7 0.339 28.0 29.4 311s 4 32.4 0.340 31.7 33.1 311s 5 33.9 0.250 33.4 34.4 311s 6 35.5 0.258 35.0 36.1 311s 7 37.6 0.256 37.1 38.1 311s 8 38.5 0.252 38.0 39.0 311s 9 38.8 0.241 38.3 39.2 311s 10 39.9 0.239 39.4 40.4 311s 11 38.4 0.314 37.7 39.0 311s 12 34.5 0.342 33.8 35.2 311s 13 29.7 0.430 28.9 30.6 311s 14 28.4 0.361 27.7 29.2 311s 15 30.5 0.336 29.8 31.2 311s 16 33.3 0.281 32.7 33.9 311s 17 37.5 0.270 37.0 38.0 311s 18 40.1 0.231 39.7 40.6 311s 19 39.2 0.343 38.5 39.9 311s 20 41.8 0.294 41.2 42.4 311s 21 46.0 0.326 45.3 46.6 311s 22 52.1 0.501 51.1 53.1 311s > model.frame 311s [1] TRUE 311s > model.matrix 311s [1] TRUE 311s > nobs 311s [1] 63 311s > linearHypothesis 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 51 1 0.59 0.45 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 51 1 0.73 0.4 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 52 311s 2 51 1 0.73 0.39 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 53 311s 2 51 2 0.72 0.49 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 53 311s 2 51 2 0.88 0.42 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 53 311s 2 51 2 1.77 0.41 311s > logLik 311s 'log Lik.' -82.3 (df=18) 311s 'log Lik.' -99.1 (df=18) 311s Estimating function 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_2 -6.979 -92.51 311s Consumption_3 -3.442 -57.06 311s Consumption_4 -3.899 -75.19 311s Consumption_5 -11.237 -235.54 311s Consumption_6 -2.642 -52.22 311s Consumption_7 8.084 147.44 311s Consumption_8 10.972 192.80 311s Consumption_9 7.028 137.33 311s Consumption_10 1.972 40.17 311s Consumption_11 -7.325 -125.85 311s Consumption_12 -3.206 -40.73 311s Consumption_13 -5.913 -53.22 311s Consumption_14 9.196 83.26 311s Consumption_15 -2.781 -35.23 311s Consumption_16 -2.363 -34.08 311s Consumption_17 18.799 276.57 311s Consumption_18 -3.872 -76.65 311s Consumption_19 -13.205 -253.63 311s Consumption_20 10.531 183.44 311s Consumption_21 3.807 77.30 311s Consumption_22 -3.522 -79.79 311s Investment_2 5.075 67.27 311s Investment_3 0.158 2.62 311s Investment_4 -0.131 -2.53 311s Investment_5 2.324 48.72 311s Investment_6 0.316 6.26 311s Investment_7 -0.482 -8.80 311s Investment_8 -0.935 -16.43 311s Investment_9 -1.481 -28.94 311s Investment_10 -4.072 -82.96 311s Investment_11 2.213 38.01 311s Investment_12 1.610 20.45 311s Investment_13 2.664 23.98 311s Investment_14 -2.837 -25.69 311s Investment_15 0.201 2.55 311s Investment_16 -0.398 -5.74 311s Investment_17 -2.409 -35.45 311s Investment_18 -0.488 -9.66 311s Investment_19 4.083 78.42 311s Investment_20 -1.607 -27.99 311s Investment_21 -1.086 -22.05 311s Investment_22 -2.718 -61.58 311s PrivateWages_2 -9.649 -127.90 311s PrivateWages_3 4.187 69.41 311s PrivateWages_4 8.749 168.69 311s PrivateWages_5 -6.685 -140.11 311s PrivateWages_6 -1.021 -20.18 311s PrivateWages_7 4.003 73.02 311s PrivateWages_8 3.592 63.12 311s PrivateWages_9 5.932 115.93 311s PrivateWages_10 11.495 234.22 311s PrivateWages_11 -7.992 -137.30 311s PrivateWages_12 -2.626 -33.36 311s PrivateWages_13 -8.660 -77.94 311s PrivateWages_14 6.531 59.13 311s PrivateWages_15 -1.757 -22.27 311s PrivateWages_16 -2.801 -40.40 311s PrivateWages_17 6.362 93.60 311s PrivateWages_18 -0.661 -13.09 311s PrivateWages_19 -18.070 -347.06 311s PrivateWages_20 3.670 63.92 311s PrivateWages_21 -3.889 -78.97 311s PrivateWages_22 9.289 210.47 311s Consumption_corpProfLag Consumption_wages 311s Consumption_2 -88.63 -205.23 311s Consumption_3 -42.68 -109.29 311s Consumption_4 -65.90 -139.41 311s Consumption_5 -206.77 -439.08 311s Consumption_6 -51.26 -103.40 311s Consumption_7 162.48 318.13 311s Consumption_8 215.04 440.87 311s Consumption_9 139.15 297.49 311s Consumption_10 41.60 86.79 311s Consumption_11 -158.95 -320.08 311s Consumption_12 -50.01 -126.56 311s Consumption_13 -67.41 -207.75 311s Consumption_14 64.37 301.49 311s Consumption_15 -31.14 -104.27 311s Consumption_16 -29.07 -94.86 311s Consumption_17 263.19 783.97 311s Consumption_18 -68.15 -185.39 311s Consumption_19 -228.45 -651.06 311s Consumption_20 161.12 509.58 311s Consumption_21 72.33 203.19 311s Consumption_22 -74.31 -213.82 311s Investment_2 64.45 149.24 311s Investment_3 1.96 5.01 311s Investment_4 -2.22 -4.70 311s Investment_5 42.77 90.82 311s Investment_6 6.14 12.39 311s Investment_7 -9.70 -18.98 311s Investment_8 -18.33 -37.57 311s Investment_9 -29.32 -62.69 311s Investment_10 -85.92 -179.25 311s Investment_11 48.02 96.69 311s Investment_12 25.11 63.55 311s Investment_13 30.37 93.60 311s Investment_14 -19.86 -93.02 311s Investment_15 2.25 7.55 311s Investment_16 -4.90 -15.98 311s Investment_17 -33.73 -100.47 311s Investment_18 -8.59 -23.36 311s Investment_19 70.63 201.29 311s Investment_20 -24.59 -77.76 311s Investment_21 -20.63 -57.96 311s Investment_22 -57.35 -165.02 311s PrivateWages_2 -122.54 -283.73 311s PrivateWages_3 51.92 132.94 311s PrivateWages_4 147.85 312.78 311s PrivateWages_5 -123.00 -261.19 311s PrivateWages_6 -19.80 -39.95 311s PrivateWages_7 80.47 157.55 311s PrivateWages_8 70.40 144.33 311s PrivateWages_9 117.46 251.13 311s PrivateWages_10 242.55 506.03 311s PrivateWages_11 -173.42 -349.22 311s PrivateWages_12 -40.96 -103.66 311s PrivateWages_13 -98.72 -304.24 311s PrivateWages_14 45.71 214.10 311s PrivateWages_15 -19.68 -65.90 311s PrivateWages_16 -34.45 -112.44 311s PrivateWages_17 89.07 265.31 311s PrivateWages_18 -11.64 -31.65 311s PrivateWages_19 -312.61 -890.90 311s PrivateWages_20 56.14 177.57 311s PrivateWages_21 -73.89 -207.57 311s PrivateWages_22 196.00 564.00 311s Investment_(Intercept) Investment_corpProf 311s Consumption_2 2.2268 29.52 311s Consumption_3 1.0983 18.21 311s Consumption_4 1.2442 23.99 311s Consumption_5 3.5856 75.15 311s Consumption_6 0.8430 16.66 311s Consumption_7 -2.5793 -47.04 311s Consumption_8 -3.5007 -61.52 311s Consumption_9 -2.2423 -43.82 311s Consumption_10 -0.6291 -12.82 311s Consumption_11 2.3372 40.15 311s Consumption_12 1.0229 13.00 311s Consumption_13 1.8868 16.98 311s Consumption_14 -2.9343 -26.57 311s Consumption_15 0.8872 11.24 311s Consumption_16 0.7541 10.87 311s Consumption_17 -5.9983 -88.25 311s Consumption_18 1.2355 24.46 311s Consumption_19 4.2135 80.93 311s Consumption_20 -3.3600 -58.53 311s Consumption_21 -1.2147 -24.67 311s Consumption_22 1.1237 25.46 311s Investment_2 -2.6152 -34.67 311s Investment_3 -0.0813 -1.35 311s Investment_4 0.0677 1.30 311s Investment_5 -1.1977 -25.10 311s Investment_6 -0.1631 -3.22 311s Investment_7 0.2486 4.53 311s Investment_8 0.4818 8.47 311s Investment_9 0.7630 14.91 311s Investment_10 2.0982 42.75 311s Investment_11 -1.1402 -19.59 311s Investment_12 -0.8295 -10.54 311s Investment_13 -1.3729 -12.36 311s Investment_14 1.4620 13.24 311s Investment_15 -0.1037 -1.31 311s Investment_16 0.2051 2.96 311s Investment_17 1.2415 18.26 311s Investment_18 0.2514 4.98 311s Investment_19 -2.1038 -40.41 311s Investment_20 0.8280 14.42 311s Investment_21 0.5596 11.36 311s Investment_22 1.4005 31.73 311s PrivateWages_2 3.7415 49.60 311s PrivateWages_3 -1.6237 -26.92 311s PrivateWages_4 -3.3924 -65.41 311s PrivateWages_5 2.5921 54.33 311s PrivateWages_6 0.3959 7.82 311s PrivateWages_7 -1.5524 -28.31 311s PrivateWages_8 -1.3929 -24.48 311s PrivateWages_9 -2.3004 -44.95 311s PrivateWages_10 -4.4576 -90.82 311s PrivateWages_11 3.0990 53.24 311s PrivateWages_12 1.0182 12.94 311s PrivateWages_13 3.3581 30.22 311s PrivateWages_14 -2.5324 -22.93 311s PrivateWages_15 0.6815 8.64 311s PrivateWages_16 1.0862 15.66 311s PrivateWages_17 -2.4670 -36.29 311s PrivateWages_18 0.2564 5.07 311s PrivateWages_19 7.0070 134.58 311s PrivateWages_20 -1.4230 -24.79 311s PrivateWages_21 1.5081 30.62 311s PrivateWages_22 -3.6021 -81.61 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_2 28.28 407.1 311s Consumption_3 13.62 200.5 311s Consumption_4 21.03 229.5 311s Consumption_5 65.97 680.2 311s Consumption_6 16.35 162.4 311s Consumption_7 -51.84 -510.2 311s Consumption_8 -68.61 -712.1 311s Consumption_9 -44.40 -465.5 311s Consumption_10 -13.27 -132.5 311s Consumption_11 50.72 504.1 311s Consumption_12 15.96 221.7 311s Consumption_13 21.51 402.5 311s Consumption_14 -20.54 -607.7 311s Consumption_15 9.94 179.2 311s Consumption_16 9.27 150.1 311s Consumption_17 -83.98 -1185.9 311s Consumption_18 21.74 246.9 311s Consumption_19 72.89 850.3 311s Consumption_20 -51.41 -671.7 311s Consumption_21 -23.08 -244.4 311s Consumption_22 23.71 229.8 311s Investment_2 -33.21 -478.1 311s Investment_3 -1.01 -14.9 311s Investment_4 1.14 12.5 311s Investment_5 -22.04 -227.2 311s Investment_6 -3.16 -31.4 311s Investment_7 5.00 49.2 311s Investment_8 9.44 98.0 311s Investment_9 15.11 158.4 311s Investment_10 44.27 441.9 311s Investment_11 -24.74 -245.9 311s Investment_12 -12.94 -179.8 311s Investment_13 -15.65 -292.8 311s Investment_14 10.23 302.8 311s Investment_15 -1.16 -21.0 311s Investment_16 2.52 40.8 311s Investment_17 17.38 245.4 311s Investment_18 4.43 50.2 311s Investment_19 -36.40 -424.5 311s Investment_20 12.67 165.5 311s Investment_21 10.63 112.6 311s Investment_22 29.55 286.4 311s PrivateWages_2 47.52 683.9 311s PrivateWages_3 -20.13 -296.5 311s PrivateWages_4 -57.33 -625.9 311s PrivateWages_5 47.69 491.7 311s PrivateWages_6 7.68 76.3 311s PrivateWages_7 -31.20 -307.1 311s PrivateWages_8 -27.30 -283.3 311s PrivateWages_9 -45.55 -477.6 311s PrivateWages_10 -94.05 -938.8 311s PrivateWages_11 67.25 668.4 311s PrivateWages_12 15.88 220.6 311s PrivateWages_13 38.28 716.3 311s PrivateWages_14 -17.73 -524.5 311s PrivateWages_15 7.63 137.7 311s PrivateWages_16 13.36 216.2 311s PrivateWages_17 -34.54 -487.7 311s PrivateWages_18 4.51 51.2 311s PrivateWages_19 121.22 1414.0 311s PrivateWages_20 -21.77 -284.4 311s PrivateWages_21 28.65 303.4 311s PrivateWages_22 -76.00 -736.6 311s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 311s Consumption_2 -7.713 -367.6 -346.32 311s Consumption_3 -3.804 -187.6 -173.47 311s Consumption_4 -4.309 -244.9 -215.90 311s Consumption_5 -12.419 -754.3 -710.38 311s Consumption_6 -2.920 -178.7 -166.72 311s Consumption_7 8.934 547.6 544.97 311s Consumption_8 12.125 737.9 776.02 311s Consumption_9 7.767 484.4 500.17 311s Consumption_10 2.179 140.3 140.54 311s Consumption_11 -8.095 -521.2 -542.38 311s Consumption_12 -3.543 -194.5 -216.84 311s Consumption_13 -6.535 -308.0 -348.98 311s Consumption_14 10.163 423.2 450.24 311s Consumption_15 -3.073 -156.6 -138.60 311s Consumption_16 -2.612 -145.4 -129.81 311s Consumption_17 20.776 1190.8 1130.21 311s Consumption_18 -4.279 -289.6 -268.32 311s Consumption_19 -14.594 -995.5 -948.61 311s Consumption_20 11.638 778.7 708.75 311s Consumption_21 4.207 316.7 292.41 311s Consumption_22 -3.892 -336.6 -294.62 311s Investment_2 6.817 324.9 306.06 311s Investment_3 0.212 10.5 9.67 311s Investment_4 -0.176 -10.0 -8.84 311s Investment_5 3.122 189.6 178.58 311s Investment_6 0.425 26.0 24.27 311s Investment_7 -0.648 -39.7 -39.52 311s Investment_8 -1.256 -76.4 -80.37 311s Investment_9 -1.989 -124.1 -128.08 311s Investment_10 -5.469 -352.2 -352.75 311s Investment_11 2.972 191.3 199.12 311s Investment_12 2.162 118.7 132.32 311s Investment_13 3.579 168.7 191.09 311s Investment_14 -3.811 -158.7 -168.82 311s Investment_15 0.270 13.8 12.19 311s Investment_16 -0.535 -29.8 -26.57 311s Investment_17 -3.236 -185.5 -176.04 311s Investment_18 -0.655 -44.4 -41.09 311s Investment_19 5.484 374.0 356.44 311s Investment_20 -2.158 -144.4 -131.44 311s Investment_21 -1.459 -109.8 -101.37 311s Investment_22 -3.650 -315.7 -276.34 311s PrivateWages_2 -14.774 -704.2 -663.37 311s PrivateWages_3 6.412 316.3 292.37 311s PrivateWages_4 13.396 761.4 671.14 311s PrivateWages_5 -10.236 -621.6 -585.48 311s PrivateWages_6 -1.563 -95.7 -89.26 311s PrivateWages_7 6.130 375.7 373.95 311s PrivateWages_8 5.500 334.7 352.01 311s PrivateWages_9 9.084 566.6 585.00 311s PrivateWages_10 17.602 1133.5 1135.33 311s PrivateWages_11 -12.237 -787.8 -819.89 311s PrivateWages_12 -4.021 -220.7 -246.06 311s PrivateWages_13 -13.260 -625.0 -708.11 311s PrivateWages_14 10.000 416.4 443.00 311s PrivateWages_15 -2.691 -137.2 -121.37 311s PrivateWages_16 -4.289 -238.7 -213.18 311s PrivateWages_17 9.742 558.3 529.95 311s PrivateWages_18 -1.012 -68.5 -63.47 311s PrivateWages_19 -27.669 -1887.3 -1798.51 311s PrivateWages_20 5.619 376.0 342.19 311s PrivateWages_21 -5.955 -448.3 -413.89 311s PrivateWages_22 14.224 1230.0 1076.76 311s PrivateWages_trend 311s Consumption_2 77.130 311s Consumption_3 34.237 311s Consumption_4 34.475 311s Consumption_5 86.935 311s Consumption_6 17.519 311s Consumption_7 -44.670 311s Consumption_8 -48.501 311s Consumption_9 -23.300 311s Consumption_10 -4.358 311s Consumption_11 8.095 311s Consumption_12 0.000 311s Consumption_13 -6.535 311s Consumption_14 20.327 311s Consumption_15 -9.219 311s Consumption_16 -10.447 311s Consumption_17 103.880 311s Consumption_18 -25.676 311s Consumption_19 -102.158 311s Consumption_20 93.104 311s Consumption_21 37.866 311s Consumption_22 -38.920 311s Investment_2 -68.165 311s Investment_3 -1.908 311s Investment_4 1.411 311s Investment_5 -21.854 311s Investment_6 -2.550 311s Investment_7 3.240 311s Investment_8 5.023 311s Investment_9 5.967 311s Investment_10 10.938 311s Investment_11 -2.972 311s Investment_12 0.000 311s Investment_13 3.579 311s Investment_14 -7.622 311s Investment_15 0.811 311s Investment_16 -2.138 311s Investment_17 -16.180 311s Investment_18 -3.932 311s Investment_19 38.386 311s Investment_20 -17.267 311s Investment_21 -13.128 311s Investment_22 -36.504 311s PrivateWages_2 147.744 311s PrivateWages_3 -57.704 311s PrivateWages_4 -107.168 311s PrivateWages_5 71.650 311s PrivateWages_6 9.379 311s PrivateWages_7 -30.651 311s PrivateWages_8 -22.000 311s PrivateWages_9 -27.251 311s PrivateWages_10 -35.204 311s PrivateWages_11 12.237 311s PrivateWages_12 0.000 311s PrivateWages_13 -13.260 311s PrivateWages_14 20.000 311s PrivateWages_15 -8.073 311s PrivateWages_16 -17.157 311s PrivateWages_17 48.709 311s PrivateWages_18 -6.074 311s PrivateWages_19 -193.685 311s PrivateWages_20 44.952 311s PrivateWages_21 -53.597 311s PrivateWages_22 142.240 311s [1] TRUE 311s > Bread 311s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 311s [1,] 94.44678 -0.9198 -0.3009 311s [2,] -0.91977 0.5830 -0.4036 311s [3,] -0.30085 -0.4036 0.5114 311s [4,] -1.71741 -0.0559 -0.0303 311s [5,] 169.11432 -7.0463 6.8731 311s [6,] -3.78719 0.8222 -0.7139 311s [7,] 1.24504 -0.6799 0.7545 311s [8,] -0.61653 0.0214 -0.0358 311s [9,] -43.93927 0.0941 1.6110 311s [10,] 0.70520 -0.0665 0.0417 311s [11,] 0.00487 0.0673 -0.0710 311s [12,] 0.27782 0.0450 0.0254 311s Consumption_wages Investment_(Intercept) Investment_corpProf 311s [1,] -1.71741 169.11 -3.79e+00 311s [2,] -0.05588 -7.05 8.22e-01 311s [3,] -0.03031 6.87 -7.14e-01 311s [4,] 0.07612 -3.87 3.83e-02 311s [5,] -3.87475 7070.32 -1.04e+02 311s [6,] 0.03834 -104.41 4.26e+00 311s [7,] -0.05106 83.93 -3.59e+00 311s [8,] 0.02027 -33.26 4.55e-01 311s [9,] 0.35346 48.43 -5.08e-01 311s [10,] -0.00637 6.61 4.29e-03 311s [11,] 0.00050 -7.65 4.31e-03 311s [12,] -0.03505 -5.67 7.94e-02 311s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 311s [1,] 1.24504 -0.6165 -43.9393 311s [2,] -0.67986 0.0214 0.0941 311s [3,] 0.75452 -0.0358 1.6110 311s [4,] -0.05106 0.0203 0.3535 311s [5,] 83.92612 -33.2552 48.4291 311s [6,] -3.59218 0.4550 -0.5077 311s [7,] 3.89889 -0.4344 -3.1131 311s [8,] -0.43443 0.1630 0.0665 311s [9,] -3.11309 0.0665 90.0495 311s [10,] 0.04234 -0.0368 -0.7131 311s [11,] 0.00984 0.0370 -0.7830 311s [12,] -0.11558 0.0310 0.9385 311s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 311s [1,] 0.70520 0.00487 0.27782 311s [2,] -0.06653 0.06728 0.04499 311s [3,] 0.04169 -0.07096 0.02543 311s [4,] -0.00637 0.00050 -0.03505 311s [5,] 6.61461 -7.64810 -5.66883 311s [6,] 0.00429 0.00431 0.07939 311s [7,] 0.04234 0.00984 -0.11558 311s [8,] -0.03681 0.03698 0.03103 311s [9,] -0.71315 -0.78300 0.93852 311s [10,] 0.06094 -0.05082 -0.02122 311s [11,] -0.05082 0.06614 0.00579 311s [12,] -0.02122 0.00579 0.05272 311s > 311s > # OLS 311s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 311s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 311s > summary 311s 311s systemfit results 311s method: OLS 311s 311s N DF SSR detRCov OLS-R2 McElroy-R2 311s system 62 50 44.9 0.372 0.977 0.991 311s 311s N DF SSR MSE RMSE R2 Adj R2 311s Consumption 21 17 17.88 1.052 1.03 0.981 0.978 311s Investment 21 17 17.32 1.019 1.01 0.931 0.919 311s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 311s 311s The covariance matrix of the residuals 311s Consumption Investment PrivateWages 311s Consumption 1.0703 -0.0161 -0.463 311s Investment -0.0161 0.9435 0.199 311s PrivateWages -0.4633 0.1993 0.609 311s 311s The correlations of the residuals 311s Consumption Investment PrivateWages 311s Consumption 1.0000 -0.0201 -0.575 311s Investment -0.0201 1.0000 0.264 311s PrivateWages -0.5747 0.2639 1.000 311s 311s 311s OLS estimates for 'Consumption' (equation 1) 311s Model Formula: consump ~ corpProf + corpProfLag + wages 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 16.2366 1.3141 12.36 6.4e-10 *** 311s corpProf 0.1929 0.0920 2.10 0.051 . 311s corpProfLag 0.0899 0.0914 0.98 0.339 311s wages 0.7962 0.0403 19.76 3.6e-13 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.026 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 311s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 311s 311s 311s OLS estimates for 'Investment' (equation 2) 311s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 10.1258 5.2592 1.93 0.07108 . 311s corpProf 0.4796 0.0934 5.13 8.3e-05 *** 311s corpProfLag 0.3330 0.0971 3.43 0.00318 ** 311s capitalLag -0.1118 0.0257 -4.35 0.00044 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.009 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 311s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 311s 311s 311s OLS estimates for 'PrivateWages' (equation 3) 311s Model Formula: privWage ~ gnp + gnpLag + trend 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 1.3550 1.3093 1.03 0.3161 311s gnp 0.4417 0.0331 13.33 4.4e-10 *** 311s gnpLag 0.1466 0.0381 3.85 0.0014 ** 311s trend 0.1244 0.0336 3.70 0.0020 ** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 0.78 on 16 degrees of freedom 311s Number of observations: 20 Degrees of Freedom: 16 311s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 311s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 311s 311s compare coef with single-equation OLS 311s [1] TRUE 311s > residuals 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 -0.32389 -0.0668 -1.3389 311s 3 -1.25001 -0.0476 0.2462 311s 4 -1.56574 1.2467 1.1255 311s 5 -0.49350 -1.3512 -0.1959 311s 6 0.00761 0.4154 -0.5284 311s 7 0.86910 1.4923 NA 311s 8 1.33848 0.7889 -0.7909 311s 9 1.05498 -0.6317 0.2819 311s 10 -0.58856 1.0830 1.1384 311s 11 0.28231 0.2791 -0.1904 311s 12 -0.22965 0.0369 0.5813 311s 13 -0.32213 0.3659 0.1206 311s 14 0.32228 0.2237 0.4773 311s 15 -0.05801 -0.1728 0.3035 311s 16 -0.03466 0.0101 0.0284 311s 17 1.61650 0.9719 -0.8517 311s 18 -0.43597 0.0516 0.9908 311s 19 0.21005 -2.5656 -0.4597 311s 20 0.98920 -0.6866 -0.3819 311s 21 0.78508 -0.7807 -1.1062 311s 22 -2.17345 -0.6623 0.5501 311s > fitted 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 42.2 -0.133 26.8 311s 3 46.3 1.948 29.1 311s 4 50.8 3.953 33.0 311s 5 51.1 4.351 34.1 311s 6 52.6 4.685 35.9 311s 7 54.2 4.108 NA 311s 8 54.9 3.411 38.7 311s 9 56.2 3.632 38.9 311s 10 58.4 4.017 40.2 311s 11 54.7 0.721 38.1 311s 12 51.1 -3.437 33.9 311s 13 45.9 -6.566 28.9 311s 14 46.2 -5.324 28.0 311s 15 48.8 -2.827 30.3 311s 16 51.3 -1.310 33.2 311s 17 56.1 1.128 37.7 311s 18 59.1 1.948 40.0 311s 19 57.3 0.666 38.7 311s 20 60.6 1.987 42.0 311s 21 64.2 4.081 46.1 311s 22 71.9 5.562 52.7 311s > predict 311s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 311s 1 NA NA NA NA 311s 2 42.2 0.466 40.0 44.5 311s 3 46.3 0.523 43.9 48.6 311s 4 50.8 0.344 48.6 52.9 311s 5 51.1 0.399 48.9 53.3 311s 6 52.6 0.401 50.4 54.8 311s 7 54.2 0.363 52.0 56.4 311s 8 54.9 0.330 52.7 57.0 311s 9 56.2 0.354 54.1 58.4 311s 10 58.4 0.373 56.2 60.6 311s 11 54.7 0.612 52.3 57.1 311s 12 51.1 0.489 48.8 53.4 311s 13 45.9 0.634 43.5 48.3 311s 14 46.2 0.608 43.8 48.6 311s 15 48.8 0.378 46.6 51.0 311s 16 51.3 0.336 49.2 53.5 311s 17 56.1 0.369 53.9 58.3 311s 18 59.1 0.324 57.0 61.3 311s 19 57.3 0.375 55.1 59.5 311s 20 60.6 0.437 58.4 62.9 311s 21 64.2 0.429 62.0 66.4 311s 22 71.9 0.672 69.4 74.3 311s Investment.pred Investment.se.fit Investment.lwr Investment.upr 311s 1 NA NA NA NA 311s 2 -0.133 0.584 -2.476 2.209 311s 3 1.948 0.480 -0.297 4.193 311s 4 3.953 0.432 1.748 6.159 311s 5 4.351 0.357 2.201 6.502 311s 6 4.685 0.336 2.548 6.821 311s 7 4.108 0.316 1.983 6.232 311s 8 3.411 0.281 1.306 5.516 311s 9 3.632 0.374 1.469 5.794 311s 10 4.017 0.430 1.813 6.221 311s 11 0.721 0.579 -1.616 3.058 311s 12 -3.437 0.488 -5.688 -1.185 311s 13 -6.566 0.592 -8.917 -4.215 311s 14 -5.324 0.667 -7.754 -2.893 311s 15 -2.827 0.359 -4.979 -0.675 311s 16 -1.310 0.308 -3.430 0.810 311s 17 1.128 0.334 -1.008 3.264 311s 18 1.948 0.234 -0.133 4.030 311s 19 0.666 0.300 -1.450 2.781 311s 20 1.987 0.353 -0.161 4.134 311s 21 4.081 0.319 1.954 6.207 311s 22 5.562 0.444 3.348 7.777 311s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 311s 1 NA NA NA NA 311s 2 26.8 0.366 25.1 28.6 311s 3 29.1 0.369 27.3 30.8 311s 4 33.0 0.372 31.2 34.7 311s 5 34.1 0.288 32.4 35.8 311s 6 35.9 0.287 34.3 37.6 311s 7 NA NA NA NA 311s 8 38.7 0.293 37.0 40.4 311s 9 38.9 0.279 37.3 40.6 311s 10 40.2 0.266 38.5 41.8 311s 11 38.1 0.365 36.4 39.8 311s 12 33.9 0.369 32.2 35.7 311s 13 28.9 0.438 27.1 30.7 311s 14 28.0 0.385 26.3 29.8 311s 15 30.3 0.379 28.6 32.0 311s 16 33.2 0.316 31.5 34.9 311s 17 37.7 0.310 36.0 39.3 311s 18 40.0 0.243 38.4 41.7 311s 19 38.7 0.363 36.9 40.4 311s 20 42.0 0.326 40.3 43.7 311s 21 46.1 0.341 44.4 47.8 311s 22 52.7 0.514 50.9 54.6 311s > model.frame 311s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 311s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 311s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 311s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 311s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 311s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 311s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 311s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 311s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 311s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 311s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 311s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 311s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 311s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 311s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 311s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 311s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 311s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 311s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 311s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 311s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 311s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 311s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 311s trend 311s 1 -11 311s 2 -10 311s 3 -9 311s 4 -8 311s 5 -7 311s 6 -6 311s 7 -5 311s 8 -4 311s 9 -3 311s 10 -2 311s 11 -1 311s 12 0 311s 13 1 311s 14 2 311s 15 3 311s 16 4 311s 17 5 311s 18 6 311s 19 7 311s 20 8 311s 21 9 311s 22 10 311s > model.matrix 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_2 1 12.4 311s Consumption_3 1 16.9 311s Consumption_4 1 18.4 311s Consumption_5 1 19.4 311s Consumption_6 1 20.1 311s Consumption_7 1 19.6 311s Consumption_8 1 19.8 311s Consumption_9 1 21.1 311s Consumption_10 1 21.7 311s Consumption_11 1 15.6 311s Consumption_12 1 11.4 311s Consumption_13 1 7.0 311s Consumption_14 1 11.2 311s Consumption_15 1 12.3 311s Consumption_16 1 14.0 311s Consumption_17 1 17.6 311s Consumption_18 1 17.3 311s Consumption_19 1 15.3 311s Consumption_20 1 19.0 311s Consumption_21 1 21.1 311s Consumption_22 1 23.5 311s Investment_2 0 0.0 311s Investment_3 0 0.0 311s Investment_4 0 0.0 311s Investment_5 0 0.0 311s Investment_6 0 0.0 311s Investment_7 0 0.0 311s Investment_8 0 0.0 311s Investment_9 0 0.0 311s Investment_10 0 0.0 311s Investment_11 0 0.0 311s Investment_12 0 0.0 311s Investment_13 0 0.0 311s Investment_14 0 0.0 311s Investment_15 0 0.0 311s Investment_16 0 0.0 311s Investment_17 0 0.0 311s Investment_18 0 0.0 311s Investment_19 0 0.0 311s Investment_20 0 0.0 311s Investment_21 0 0.0 311s Investment_22 0 0.0 311s PrivateWages_2 0 0.0 311s PrivateWages_3 0 0.0 311s PrivateWages_4 0 0.0 311s PrivateWages_5 0 0.0 311s PrivateWages_6 0 0.0 311s PrivateWages_8 0 0.0 311s PrivateWages_9 0 0.0 311s PrivateWages_10 0 0.0 311s PrivateWages_11 0 0.0 311s PrivateWages_12 0 0.0 311s PrivateWages_13 0 0.0 311s PrivateWages_14 0 0.0 311s PrivateWages_15 0 0.0 311s PrivateWages_16 0 0.0 311s PrivateWages_17 0 0.0 311s PrivateWages_18 0 0.0 311s PrivateWages_19 0 0.0 311s PrivateWages_20 0 0.0 311s PrivateWages_21 0 0.0 311s PrivateWages_22 0 0.0 311s Consumption_corpProfLag Consumption_wages 311s Consumption_2 12.7 28.2 311s Consumption_3 12.4 32.2 311s Consumption_4 16.9 37.0 311s Consumption_5 18.4 37.0 311s Consumption_6 19.4 38.6 311s Consumption_7 20.1 40.7 311s Consumption_8 19.6 41.5 311s Consumption_9 19.8 42.9 311s Consumption_10 21.1 45.3 311s Consumption_11 21.7 42.1 311s Consumption_12 15.6 39.3 311s Consumption_13 11.4 34.3 311s Consumption_14 7.0 34.1 311s Consumption_15 11.2 36.6 311s Consumption_16 12.3 39.3 311s Consumption_17 14.0 44.2 311s Consumption_18 17.6 47.7 311s Consumption_19 17.3 45.9 311s Consumption_20 15.3 49.4 311s Consumption_21 19.0 53.0 311s Consumption_22 21.1 61.8 311s Investment_2 0.0 0.0 311s Investment_3 0.0 0.0 311s Investment_4 0.0 0.0 311s Investment_5 0.0 0.0 311s Investment_6 0.0 0.0 311s Investment_7 0.0 0.0 311s Investment_8 0.0 0.0 311s Investment_9 0.0 0.0 311s Investment_10 0.0 0.0 311s Investment_11 0.0 0.0 311s Investment_12 0.0 0.0 311s Investment_13 0.0 0.0 311s Investment_14 0.0 0.0 311s Investment_15 0.0 0.0 311s Investment_16 0.0 0.0 311s Investment_17 0.0 0.0 311s Investment_18 0.0 0.0 311s Investment_19 0.0 0.0 311s Investment_20 0.0 0.0 311s Investment_21 0.0 0.0 311s Investment_22 0.0 0.0 311s PrivateWages_2 0.0 0.0 311s PrivateWages_3 0.0 0.0 311s PrivateWages_4 0.0 0.0 311s PrivateWages_5 0.0 0.0 311s PrivateWages_6 0.0 0.0 311s PrivateWages_8 0.0 0.0 311s PrivateWages_9 0.0 0.0 311s PrivateWages_10 0.0 0.0 311s PrivateWages_11 0.0 0.0 311s PrivateWages_12 0.0 0.0 311s PrivateWages_13 0.0 0.0 311s PrivateWages_14 0.0 0.0 311s PrivateWages_15 0.0 0.0 311s PrivateWages_16 0.0 0.0 311s PrivateWages_17 0.0 0.0 311s PrivateWages_18 0.0 0.0 311s PrivateWages_19 0.0 0.0 311s PrivateWages_20 0.0 0.0 311s PrivateWages_21 0.0 0.0 311s PrivateWages_22 0.0 0.0 311s Investment_(Intercept) Investment_corpProf 311s Consumption_2 0 0.0 311s Consumption_3 0 0.0 311s Consumption_4 0 0.0 311s Consumption_5 0 0.0 311s Consumption_6 0 0.0 311s Consumption_7 0 0.0 311s Consumption_8 0 0.0 311s Consumption_9 0 0.0 311s Consumption_10 0 0.0 311s Consumption_11 0 0.0 311s Consumption_12 0 0.0 311s Consumption_13 0 0.0 311s Consumption_14 0 0.0 311s Consumption_15 0 0.0 311s Consumption_16 0 0.0 311s Consumption_17 0 0.0 311s Consumption_18 0 0.0 311s Consumption_19 0 0.0 311s Consumption_20 0 0.0 311s Consumption_21 0 0.0 311s Consumption_22 0 0.0 311s Investment_2 1 12.4 311s Investment_3 1 16.9 311s Investment_4 1 18.4 311s Investment_5 1 19.4 311s Investment_6 1 20.1 311s Investment_7 1 19.6 311s Investment_8 1 19.8 311s Investment_9 1 21.1 311s Investment_10 1 21.7 311s Investment_11 1 15.6 311s Investment_12 1 11.4 311s Investment_13 1 7.0 311s Investment_14 1 11.2 311s Investment_15 1 12.3 311s Investment_16 1 14.0 311s Investment_17 1 17.6 311s Investment_18 1 17.3 311s Investment_19 1 15.3 311s Investment_20 1 19.0 311s Investment_21 1 21.1 311s Investment_22 1 23.5 311s PrivateWages_2 0 0.0 311s PrivateWages_3 0 0.0 311s PrivateWages_4 0 0.0 311s PrivateWages_5 0 0.0 311s PrivateWages_6 0 0.0 311s PrivateWages_8 0 0.0 311s PrivateWages_9 0 0.0 311s PrivateWages_10 0 0.0 311s PrivateWages_11 0 0.0 311s PrivateWages_12 0 0.0 311s PrivateWages_13 0 0.0 311s PrivateWages_14 0 0.0 311s PrivateWages_15 0 0.0 311s PrivateWages_16 0 0.0 311s PrivateWages_17 0 0.0 311s PrivateWages_18 0 0.0 311s PrivateWages_19 0 0.0 311s PrivateWages_20 0 0.0 311s PrivateWages_21 0 0.0 311s PrivateWages_22 0 0.0 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_2 0.0 0 311s Consumption_3 0.0 0 311s Consumption_4 0.0 0 311s Consumption_5 0.0 0 311s Consumption_6 0.0 0 311s Consumption_7 0.0 0 311s Consumption_8 0.0 0 311s Consumption_9 0.0 0 311s Consumption_10 0.0 0 311s Consumption_11 0.0 0 311s Consumption_12 0.0 0 311s Consumption_13 0.0 0 311s Consumption_14 0.0 0 311s Consumption_15 0.0 0 311s Consumption_16 0.0 0 311s Consumption_17 0.0 0 311s Consumption_18 0.0 0 311s Consumption_19 0.0 0 311s Consumption_20 0.0 0 311s Consumption_21 0.0 0 311s Consumption_22 0.0 0 311s Investment_2 12.7 183 311s Investment_3 12.4 183 311s Investment_4 16.9 184 311s Investment_5 18.4 190 311s Investment_6 19.4 193 311s Investment_7 20.1 198 311s Investment_8 19.6 203 311s Investment_9 19.8 208 311s Investment_10 21.1 211 311s Investment_11 21.7 216 311s Investment_12 15.6 217 311s Investment_13 11.4 213 311s Investment_14 7.0 207 311s Investment_15 11.2 202 311s Investment_16 12.3 199 311s Investment_17 14.0 198 311s Investment_18 17.6 200 311s Investment_19 17.3 202 311s Investment_20 15.3 200 311s Investment_21 19.0 201 311s Investment_22 21.1 204 311s PrivateWages_2 0.0 0 311s PrivateWages_3 0.0 0 311s PrivateWages_4 0.0 0 311s PrivateWages_5 0.0 0 311s PrivateWages_6 0.0 0 311s PrivateWages_8 0.0 0 311s PrivateWages_9 0.0 0 311s PrivateWages_10 0.0 0 311s PrivateWages_11 0.0 0 311s PrivateWages_12 0.0 0 311s PrivateWages_13 0.0 0 311s PrivateWages_14 0.0 0 311s PrivateWages_15 0.0 0 311s PrivateWages_16 0.0 0 311s PrivateWages_17 0.0 0 311s PrivateWages_18 0.0 0 311s PrivateWages_19 0.0 0 311s PrivateWages_20 0.0 0 311s PrivateWages_21 0.0 0 311s PrivateWages_22 0.0 0 311s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 311s Consumption_2 0 0.0 0.0 311s Consumption_3 0 0.0 0.0 311s Consumption_4 0 0.0 0.0 311s Consumption_5 0 0.0 0.0 311s Consumption_6 0 0.0 0.0 311s Consumption_7 0 0.0 0.0 311s Consumption_8 0 0.0 0.0 311s Consumption_9 0 0.0 0.0 311s Consumption_10 0 0.0 0.0 311s Consumption_11 0 0.0 0.0 311s Consumption_12 0 0.0 0.0 311s Consumption_13 0 0.0 0.0 311s Consumption_14 0 0.0 0.0 311s Consumption_15 0 0.0 0.0 311s Consumption_16 0 0.0 0.0 311s Consumption_17 0 0.0 0.0 311s Consumption_18 0 0.0 0.0 311s Consumption_19 0 0.0 0.0 311s Consumption_20 0 0.0 0.0 311s Consumption_21 0 0.0 0.0 311s Consumption_22 0 0.0 0.0 311s Investment_2 0 0.0 0.0 311s Investment_3 0 0.0 0.0 311s Investment_4 0 0.0 0.0 311s Investment_5 0 0.0 0.0 311s Investment_6 0 0.0 0.0 311s Investment_7 0 0.0 0.0 311s Investment_8 0 0.0 0.0 311s Investment_9 0 0.0 0.0 311s Investment_10 0 0.0 0.0 311s Investment_11 0 0.0 0.0 311s Investment_12 0 0.0 0.0 311s Investment_13 0 0.0 0.0 311s Investment_14 0 0.0 0.0 311s Investment_15 0 0.0 0.0 311s Investment_16 0 0.0 0.0 311s Investment_17 0 0.0 0.0 311s Investment_18 0 0.0 0.0 311s Investment_19 0 0.0 0.0 311s Investment_20 0 0.0 0.0 311s Investment_21 0 0.0 0.0 311s Investment_22 0 0.0 0.0 311s PrivateWages_2 1 45.6 44.9 311s PrivateWages_3 1 50.1 45.6 311s PrivateWages_4 1 57.2 50.1 311s PrivateWages_5 1 57.1 57.2 311s PrivateWages_6 1 61.0 57.1 311s PrivateWages_8 1 64.4 64.0 311s PrivateWages_9 1 64.5 64.4 311s PrivateWages_10 1 67.0 64.5 311s PrivateWages_11 1 61.2 67.0 311s PrivateWages_12 1 53.4 61.2 311s PrivateWages_13 1 44.3 53.4 311s PrivateWages_14 1 45.1 44.3 311s PrivateWages_15 1 49.7 45.1 311s PrivateWages_16 1 54.4 49.7 311s PrivateWages_17 1 62.7 54.4 311s PrivateWages_18 1 65.0 62.7 311s PrivateWages_19 1 60.9 65.0 311s PrivateWages_20 1 69.5 60.9 311s PrivateWages_21 1 75.7 69.5 311s PrivateWages_22 1 88.4 75.7 311s PrivateWages_trend 311s Consumption_2 0 311s Consumption_3 0 311s Consumption_4 0 311s Consumption_5 0 311s Consumption_6 0 311s Consumption_7 0 311s Consumption_8 0 311s Consumption_9 0 311s Consumption_10 0 311s Consumption_11 0 311s Consumption_12 0 311s Consumption_13 0 311s Consumption_14 0 311s Consumption_15 0 311s Consumption_16 0 311s Consumption_17 0 311s Consumption_18 0 311s Consumption_19 0 311s Consumption_20 0 311s Consumption_21 0 311s Consumption_22 0 311s Investment_2 0 311s Investment_3 0 311s Investment_4 0 311s Investment_5 0 311s Investment_6 0 311s Investment_7 0 311s Investment_8 0 311s Investment_9 0 311s Investment_10 0 311s Investment_11 0 311s Investment_12 0 311s Investment_13 0 311s Investment_14 0 311s Investment_15 0 311s Investment_16 0 311s Investment_17 0 311s Investment_18 0 311s Investment_19 0 311s Investment_20 0 311s Investment_21 0 311s Investment_22 0 311s PrivateWages_2 -10 311s PrivateWages_3 -9 311s PrivateWages_4 -8 311s PrivateWages_5 -7 311s PrivateWages_6 -6 311s PrivateWages_8 -4 311s PrivateWages_9 -3 311s PrivateWages_10 -2 311s PrivateWages_11 -1 311s PrivateWages_12 0 311s PrivateWages_13 1 311s PrivateWages_14 2 311s PrivateWages_15 3 311s PrivateWages_16 4 311s PrivateWages_17 5 311s PrivateWages_18 6 311s PrivateWages_19 7 311s PrivateWages_20 8 311s PrivateWages_21 9 311s PrivateWages_22 10 311s > nobs 311s [1] 62 311s > linearHypothesis 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 51 311s 2 50 1 0.8 0.37 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 51 311s 2 50 1 0.72 0.4 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 51 311s 2 50 1 0.72 0.4 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 50 2 0.42 0.66 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 50 2 0.37 0.69 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 52 311s 2 50 2 0.75 0.69 311s > logLik 311s 'log Lik.' -71.9 (df=13) 311s 'log Lik.' -77.1 (df=13) 311s compare log likelihood value with single-equation OLS 311s [1] "Mean relative difference: 0.000555" 311s Estimating function 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_2 -0.32389 -4.016 311s Consumption_3 -1.25001 -21.125 311s Consumption_4 -1.56574 -28.810 311s Consumption_5 -0.49350 -9.574 311s Consumption_6 0.00761 0.153 311s Consumption_7 0.86910 17.034 311s Consumption_8 1.33848 26.502 311s Consumption_9 1.05498 22.260 311s Consumption_10 -0.58856 -12.772 311s Consumption_11 0.28231 4.404 311s Consumption_12 -0.22965 -2.618 311s Consumption_13 -0.32213 -2.255 311s Consumption_14 0.32228 3.610 311s Consumption_15 -0.05801 -0.714 311s Consumption_16 -0.03466 -0.485 311s Consumption_17 1.61650 28.450 311s Consumption_18 -0.43597 -7.542 311s Consumption_19 0.21005 3.214 311s Consumption_20 0.98920 18.795 311s Consumption_21 0.78508 16.565 311s Consumption_22 -2.17345 -51.076 311s Investment_2 0.00000 0.000 311s Investment_3 0.00000 0.000 311s Investment_4 0.00000 0.000 311s Investment_5 0.00000 0.000 311s Investment_6 0.00000 0.000 311s Investment_7 0.00000 0.000 311s Investment_8 0.00000 0.000 311s Investment_9 0.00000 0.000 311s Investment_10 0.00000 0.000 311s Investment_11 0.00000 0.000 311s Investment_12 0.00000 0.000 311s Investment_13 0.00000 0.000 311s Investment_14 0.00000 0.000 311s Investment_15 0.00000 0.000 311s Investment_16 0.00000 0.000 311s Investment_17 0.00000 0.000 311s Investment_18 0.00000 0.000 311s Investment_19 0.00000 0.000 311s Investment_20 0.00000 0.000 311s Investment_21 0.00000 0.000 311s Investment_22 0.00000 0.000 311s PrivateWages_2 0.00000 0.000 311s PrivateWages_3 0.00000 0.000 311s PrivateWages_4 0.00000 0.000 311s PrivateWages_5 0.00000 0.000 311s PrivateWages_6 0.00000 0.000 311s PrivateWages_8 0.00000 0.000 311s PrivateWages_9 0.00000 0.000 311s PrivateWages_10 0.00000 0.000 311s PrivateWages_11 0.00000 0.000 311s PrivateWages_12 0.00000 0.000 311s PrivateWages_13 0.00000 0.000 311s PrivateWages_14 0.00000 0.000 311s PrivateWages_15 0.00000 0.000 311s PrivateWages_16 0.00000 0.000 311s PrivateWages_17 0.00000 0.000 311s PrivateWages_18 0.00000 0.000 311s PrivateWages_19 0.00000 0.000 311s PrivateWages_20 0.00000 0.000 311s PrivateWages_21 0.00000 0.000 311s PrivateWages_22 0.00000 0.000 311s Consumption_corpProfLag Consumption_wages 311s Consumption_2 -4.113 -9.134 311s Consumption_3 -15.500 -40.250 311s Consumption_4 -26.461 -57.932 311s Consumption_5 -9.080 -18.260 311s Consumption_6 0.148 0.294 311s Consumption_7 17.469 35.372 311s Consumption_8 26.234 55.547 311s Consumption_9 20.889 45.259 311s Consumption_10 -12.419 -26.662 311s Consumption_11 6.126 11.885 311s Consumption_12 -3.583 -9.025 311s Consumption_13 -3.672 -11.049 311s Consumption_14 2.256 10.990 311s Consumption_15 -0.650 -2.123 311s Consumption_16 -0.426 -1.362 311s Consumption_17 22.631 71.449 311s Consumption_18 -7.673 -20.796 311s Consumption_19 3.634 9.641 311s Consumption_20 15.135 48.867 311s Consumption_21 14.916 41.609 311s Consumption_22 -45.860 -134.319 311s Investment_2 0.000 0.000 311s Investment_3 0.000 0.000 311s Investment_4 0.000 0.000 311s Investment_5 0.000 0.000 311s Investment_6 0.000 0.000 311s Investment_7 0.000 0.000 311s Investment_8 0.000 0.000 311s Investment_9 0.000 0.000 311s Investment_10 0.000 0.000 311s Investment_11 0.000 0.000 311s Investment_12 0.000 0.000 311s Investment_13 0.000 0.000 311s Investment_14 0.000 0.000 311s Investment_15 0.000 0.000 311s Investment_16 0.000 0.000 311s Investment_17 0.000 0.000 311s Investment_18 0.000 0.000 311s Investment_19 0.000 0.000 311s Investment_20 0.000 0.000 311s Investment_21 0.000 0.000 311s Investment_22 0.000 0.000 311s PrivateWages_2 0.000 0.000 311s PrivateWages_3 0.000 0.000 311s PrivateWages_4 0.000 0.000 311s PrivateWages_5 0.000 0.000 311s PrivateWages_6 0.000 0.000 311s PrivateWages_8 0.000 0.000 311s PrivateWages_9 0.000 0.000 311s PrivateWages_10 0.000 0.000 311s PrivateWages_11 0.000 0.000 311s PrivateWages_12 0.000 0.000 311s PrivateWages_13 0.000 0.000 311s PrivateWages_14 0.000 0.000 311s PrivateWages_15 0.000 0.000 311s PrivateWages_16 0.000 0.000 311s PrivateWages_17 0.000 0.000 311s PrivateWages_18 0.000 0.000 311s PrivateWages_19 0.000 0.000 311s PrivateWages_20 0.000 0.000 311s PrivateWages_21 0.000 0.000 311s PrivateWages_22 0.000 0.000 311s Investment_(Intercept) Investment_corpProf 311s Consumption_2 0.0000 0.000 311s Consumption_3 0.0000 0.000 311s Consumption_4 0.0000 0.000 311s Consumption_5 0.0000 0.000 311s Consumption_6 0.0000 0.000 311s Consumption_7 0.0000 0.000 311s Consumption_8 0.0000 0.000 311s Consumption_9 0.0000 0.000 311s Consumption_10 0.0000 0.000 311s Consumption_11 0.0000 0.000 311s Consumption_12 0.0000 0.000 311s Consumption_13 0.0000 0.000 311s Consumption_14 0.0000 0.000 311s Consumption_15 0.0000 0.000 311s Consumption_16 0.0000 0.000 311s Consumption_17 0.0000 0.000 311s Consumption_18 0.0000 0.000 311s Consumption_19 0.0000 0.000 311s Consumption_20 0.0000 0.000 311s Consumption_21 0.0000 0.000 311s Consumption_22 0.0000 0.000 311s Investment_2 -0.0668 -0.828 311s Investment_3 -0.0476 -0.804 311s Investment_4 1.2467 22.939 311s Investment_5 -1.3512 -26.213 311s Investment_6 0.4154 8.350 311s Investment_7 1.4923 29.248 311s Investment_8 0.7889 15.620 311s Investment_9 -0.6317 -13.329 311s Investment_10 1.0830 23.500 311s Investment_11 0.2791 4.353 311s Investment_12 0.0369 0.420 311s Investment_13 0.3659 2.561 311s Investment_14 0.2237 2.505 311s Investment_15 -0.1728 -2.126 311s Investment_16 0.0101 0.141 311s Investment_17 0.9719 17.105 311s Investment_18 0.0516 0.893 311s Investment_19 -2.5656 -39.254 311s Investment_20 -0.6866 -13.045 311s Investment_21 -0.7807 -16.474 311s Investment_22 -0.6623 -15.565 311s PrivateWages_2 0.0000 0.000 311s PrivateWages_3 0.0000 0.000 311s PrivateWages_4 0.0000 0.000 311s PrivateWages_5 0.0000 0.000 311s PrivateWages_6 0.0000 0.000 311s PrivateWages_8 0.0000 0.000 311s PrivateWages_9 0.0000 0.000 311s PrivateWages_10 0.0000 0.000 311s PrivateWages_11 0.0000 0.000 311s PrivateWages_12 0.0000 0.000 311s PrivateWages_13 0.0000 0.000 311s PrivateWages_14 0.0000 0.000 311s PrivateWages_15 0.0000 0.000 311s PrivateWages_16 0.0000 0.000 311s PrivateWages_17 0.0000 0.000 311s PrivateWages_18 0.0000 0.000 311s PrivateWages_19 0.0000 0.000 311s PrivateWages_20 0.0000 0.000 311s PrivateWages_21 0.0000 0.000 311s PrivateWages_22 0.0000 0.000 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_2 0.000 0.00 311s Consumption_3 0.000 0.00 311s Consumption_4 0.000 0.00 311s Consumption_5 0.000 0.00 311s Consumption_6 0.000 0.00 311s Consumption_7 0.000 0.00 311s Consumption_8 0.000 0.00 311s Consumption_9 0.000 0.00 311s Consumption_10 0.000 0.00 311s Consumption_11 0.000 0.00 311s Consumption_12 0.000 0.00 311s Consumption_13 0.000 0.00 311s Consumption_14 0.000 0.00 311s Consumption_15 0.000 0.00 311s Consumption_16 0.000 0.00 311s Consumption_17 0.000 0.00 311s Consumption_18 0.000 0.00 311s Consumption_19 0.000 0.00 311s Consumption_20 0.000 0.00 311s Consumption_21 0.000 0.00 311s Consumption_22 0.000 0.00 311s Investment_2 -0.848 -12.21 311s Investment_3 -0.590 -8.69 311s Investment_4 21.069 230.01 311s Investment_5 -24.862 -256.32 311s Investment_6 8.059 80.05 311s Investment_7 29.994 295.17 311s Investment_8 15.463 160.46 311s Investment_9 -12.507 -131.14 311s Investment_10 22.850 228.07 311s Investment_11 6.056 60.20 311s Investment_12 0.575 7.99 311s Investment_13 4.172 78.05 311s Investment_14 1.566 46.33 311s Investment_15 -1.936 -34.91 311s Investment_16 0.124 2.01 311s Investment_17 13.606 192.14 311s Investment_18 0.908 10.31 311s Investment_19 -44.385 -517.74 311s Investment_20 -10.505 -137.25 311s Investment_21 -14.834 -157.09 311s Investment_22 -13.975 -135.45 311s PrivateWages_2 0.000 0.00 311s PrivateWages_3 0.000 0.00 311s PrivateWages_4 0.000 0.00 311s PrivateWages_5 0.000 0.00 311s PrivateWages_6 0.000 0.00 311s PrivateWages_8 0.000 0.00 311s PrivateWages_9 0.000 0.00 311s PrivateWages_10 0.000 0.00 311s PrivateWages_11 0.000 0.00 311s PrivateWages_12 0.000 0.00 311s PrivateWages_13 0.000 0.00 311s PrivateWages_14 0.000 0.00 311s PrivateWages_15 0.000 0.00 311s PrivateWages_16 0.000 0.00 311s PrivateWages_17 0.000 0.00 311s PrivateWages_18 0.000 0.00 311s PrivateWages_19 0.000 0.00 311s PrivateWages_20 0.000 0.00 311s PrivateWages_21 0.000 0.00 311s PrivateWages_22 0.000 0.00 311s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 311s Consumption_2 0.0000 0.00 0.00 311s Consumption_3 0.0000 0.00 0.00 311s Consumption_4 0.0000 0.00 0.00 311s Consumption_5 0.0000 0.00 0.00 311s Consumption_6 0.0000 0.00 0.00 311s Consumption_7 0.0000 0.00 0.00 311s Consumption_8 0.0000 0.00 0.00 311s Consumption_9 0.0000 0.00 0.00 311s Consumption_10 0.0000 0.00 0.00 311s Consumption_11 0.0000 0.00 0.00 311s Consumption_12 0.0000 0.00 0.00 311s Consumption_13 0.0000 0.00 0.00 311s Consumption_14 0.0000 0.00 0.00 311s Consumption_15 0.0000 0.00 0.00 311s Consumption_16 0.0000 0.00 0.00 311s Consumption_17 0.0000 0.00 0.00 311s Consumption_18 0.0000 0.00 0.00 311s Consumption_19 0.0000 0.00 0.00 311s Consumption_20 0.0000 0.00 0.00 311s Consumption_21 0.0000 0.00 0.00 311s Consumption_22 0.0000 0.00 0.00 311s Investment_2 0.0000 0.00 0.00 311s Investment_3 0.0000 0.00 0.00 311s Investment_4 0.0000 0.00 0.00 311s Investment_5 0.0000 0.00 0.00 311s Investment_6 0.0000 0.00 0.00 311s Investment_7 0.0000 0.00 0.00 311s Investment_8 0.0000 0.00 0.00 311s Investment_9 0.0000 0.00 0.00 311s Investment_10 0.0000 0.00 0.00 311s Investment_11 0.0000 0.00 0.00 311s Investment_12 0.0000 0.00 0.00 311s Investment_13 0.0000 0.00 0.00 311s Investment_14 0.0000 0.00 0.00 311s Investment_15 0.0000 0.00 0.00 311s Investment_16 0.0000 0.00 0.00 311s Investment_17 0.0000 0.00 0.00 311s Investment_18 0.0000 0.00 0.00 311s Investment_19 0.0000 0.00 0.00 311s Investment_20 0.0000 0.00 0.00 311s Investment_21 0.0000 0.00 0.00 311s Investment_22 0.0000 0.00 0.00 311s PrivateWages_2 -1.3389 -61.06 -60.12 311s PrivateWages_3 0.2462 12.33 11.23 311s PrivateWages_4 1.1255 64.38 56.39 311s PrivateWages_5 -0.1959 -11.18 -11.20 311s PrivateWages_6 -0.5284 -32.23 -30.17 311s PrivateWages_8 -0.7909 -50.94 -50.62 311s PrivateWages_9 0.2819 18.18 18.15 311s PrivateWages_10 1.1384 76.28 73.43 311s PrivateWages_11 -0.1904 -11.65 -12.76 311s PrivateWages_12 0.5813 31.04 35.58 311s PrivateWages_13 0.1206 5.34 6.44 311s PrivateWages_14 0.4773 21.53 21.14 311s PrivateWages_15 0.3035 15.09 13.69 311s PrivateWages_16 0.0284 1.55 1.41 311s PrivateWages_17 -0.8517 -53.40 -46.33 311s PrivateWages_18 0.9908 64.40 62.12 311s PrivateWages_19 -0.4597 -28.00 -29.88 311s PrivateWages_20 -0.3819 -26.54 -23.26 311s PrivateWages_21 -1.1062 -83.74 -76.88 311s PrivateWages_22 0.5501 48.63 41.64 311s PrivateWages_trend 311s Consumption_2 0.000 311s Consumption_3 0.000 311s Consumption_4 0.000 311s Consumption_5 0.000 311s Consumption_6 0.000 311s Consumption_7 0.000 311s Consumption_8 0.000 311s Consumption_9 0.000 311s Consumption_10 0.000 311s Consumption_11 0.000 311s Consumption_12 0.000 311s Consumption_13 0.000 311s Consumption_14 0.000 311s Consumption_15 0.000 311s Consumption_16 0.000 311s Consumption_17 0.000 311s Consumption_18 0.000 311s Consumption_19 0.000 311s Consumption_20 0.000 311s Consumption_21 0.000 311s Consumption_22 0.000 311s Investment_2 0.000 311s Investment_3 0.000 311s Investment_4 0.000 311s Investment_5 0.000 311s Investment_6 0.000 311s Investment_7 0.000 311s Investment_8 0.000 311s Investment_9 0.000 311s Investment_10 0.000 311s Investment_11 0.000 311s Investment_12 0.000 311s Investment_13 0.000 311s Investment_14 0.000 311s Investment_15 0.000 311s Investment_16 0.000 311s Investment_17 0.000 311s Investment_18 0.000 311s Investment_19 0.000 311s Investment_20 0.000 311s Investment_21 0.000 311s Investment_22 0.000 311s PrivateWages_2 13.389 311s PrivateWages_3 -2.216 311s PrivateWages_4 -9.004 311s PrivateWages_5 1.371 311s PrivateWages_6 3.170 311s PrivateWages_8 3.164 311s PrivateWages_9 -0.846 311s PrivateWages_10 -2.277 311s PrivateWages_11 0.190 311s PrivateWages_12 0.000 311s PrivateWages_13 0.121 311s PrivateWages_14 0.955 311s PrivateWages_15 0.911 311s PrivateWages_16 0.114 311s PrivateWages_17 -4.258 311s PrivateWages_18 5.945 311s PrivateWages_19 -3.218 311s PrivateWages_20 -3.055 311s PrivateWages_21 -9.956 311s PrivateWages_22 5.501 311s [1] TRUE 311s > Bread 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_(Intercept) 100.0401 0.0296 311s Consumption_corpProf 0.0296 0.4904 311s Consumption_corpProfLag -1.0438 -0.3107 311s Consumption_wages -1.9405 -0.0777 311s Investment_(Intercept) 0.0000 0.0000 311s Investment_corpProf 0.0000 0.0000 311s Investment_corpProfLag 0.0000 0.0000 311s Investment_capitalLag 0.0000 0.0000 311s PrivateWages_(Intercept) 0.0000 0.0000 311s PrivateWages_gnp 0.0000 0.0000 311s PrivateWages_gnpLag 0.0000 0.0000 311s PrivateWages_trend 0.0000 0.0000 311s Consumption_corpProfLag Consumption_wages 311s Consumption_(Intercept) -1.0438 -1.9405 311s Consumption_corpProf -0.3107 -0.0777 311s Consumption_corpProfLag 0.4844 -0.0396 311s Consumption_wages -0.0396 0.0941 311s Investment_(Intercept) 0.0000 0.0000 311s Investment_corpProf 0.0000 0.0000 311s Investment_corpProfLag 0.0000 0.0000 311s Investment_capitalLag 0.0000 0.0000 311s PrivateWages_(Intercept) 0.0000 0.0000 311s PrivateWages_gnp 0.0000 0.0000 311s PrivateWages_gnpLag 0.0000 0.0000 311s PrivateWages_trend 0.0000 0.0000 311s Investment_(Intercept) Investment_corpProf 311s Consumption_(Intercept) 0.00 0.0000 311s Consumption_corpProf 0.00 0.0000 311s Consumption_corpProfLag 0.00 0.0000 311s Consumption_wages 0.00 0.0000 311s Investment_(Intercept) 1817.57 -17.6857 311s Investment_corpProf -17.69 0.5738 311s Investment_corpProfLag 14.44 -0.4928 311s Investment_capitalLag -8.74 0.0801 311s PrivateWages_(Intercept) 0.00 0.0000 311s PrivateWages_gnp 0.00 0.0000 311s PrivateWages_gnpLag 0.00 0.0000 311s PrivateWages_trend 0.00 0.0000 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_(Intercept) 0.0000 0.0000 311s Consumption_corpProf 0.0000 0.0000 311s Consumption_corpProfLag 0.0000 0.0000 311s Consumption_wages 0.0000 0.0000 311s Investment_(Intercept) 14.4412 -8.7403 311s Investment_corpProf -0.4928 0.0801 311s Investment_corpProfLag 0.6190 -0.0811 311s Investment_capitalLag -0.0811 0.0435 311s PrivateWages_(Intercept) 0.0000 0.0000 311s PrivateWages_gnp 0.0000 0.0000 311s PrivateWages_gnpLag 0.0000 0.0000 311s PrivateWages_trend 0.0000 0.0000 311s PrivateWages_(Intercept) PrivateWages_gnp 311s Consumption_(Intercept) 0.000 0.000 311s Consumption_corpProf 0.000 0.000 311s Consumption_corpProfLag 0.000 0.000 311s Consumption_wages 0.000 0.000 311s Investment_(Intercept) 0.000 0.000 311s Investment_corpProf 0.000 0.000 311s Investment_corpProfLag 0.000 0.000 311s Investment_capitalLag 0.000 0.000 311s PrivateWages_(Intercept) 174.627 -0.658 311s PrivateWages_gnp -0.658 0.112 311s PrivateWages_gnpLag -2.295 -0.104 311s PrivateWages_trend 2.155 -0.030 311s PrivateWages_gnpLag PrivateWages_trend 311s Consumption_(Intercept) 0.00000 0.00000 311s Consumption_corpProf 0.00000 0.00000 311s Consumption_corpProfLag 0.00000 0.00000 311s Consumption_wages 0.00000 0.00000 311s Investment_(Intercept) 0.00000 0.00000 311s Investment_corpProf 0.00000 0.00000 311s Investment_corpProfLag 0.00000 0.00000 311s Investment_capitalLag 0.00000 0.00000 311s PrivateWages_(Intercept) -2.29451 2.15506 311s PrivateWages_gnp -0.10426 -0.03004 311s PrivateWages_gnpLag 0.14761 -0.00667 311s PrivateWages_trend -0.00667 0.11527 311s > 311s > # 2SLS 311s > summary 311s 311s systemfit results 311s method: 2SLS 311s 311s N DF SSR detRCov OLS-R2 McElroy-R2 311s system 60 48 53.4 0.274 0.973 0.992 311s 311s N DF SSR MSE RMSE R2 Adj R2 311s Consumption 20 16 20.67 1.292 1.14 0.978 0.974 311s Investment 20 16 23.02 1.438 1.20 0.901 0.883 311s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 311s 311s The covariance matrix of the residuals 311s Consumption Investment PrivateWages 311s Consumption 1.034 0.309 -0.383 311s Investment 0.309 1.151 0.202 311s PrivateWages -0.383 0.202 0.487 311s 311s The correlations of the residuals 311s Consumption Investment PrivateWages 311s Consumption 1.000 0.284 -0.540 311s Investment 0.284 1.000 0.269 311s PrivateWages -0.540 0.269 1.000 311s 311s 311s 2SLS estimates for 'Consumption' (equation 1) 311s Model Formula: consump ~ corpProf + corpProfLag + wages 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 16.5093 1.3121 12.58 1.0e-09 *** 311s corpProf 0.0219 0.1159 0.19 0.85 311s corpProfLag 0.1931 0.1071 1.80 0.09 . 311s wages 0.8174 0.0408 20.05 9.2e-13 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.137 on 16 degrees of freedom 311s Number of observations: 20 Degrees of Freedom: 16 311s SSR: 20.671 MSE: 1.292 Root MSE: 1.137 311s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.974 311s 311s 311s 2SLS estimates for 'Investment' (equation 2) 311s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 17.843 6.850 2.60 0.01915 * 311s corpProf 0.217 0.155 1.40 0.18106 311s corpProfLag 0.542 0.148 3.65 0.00216 ** 311s capitalLag -0.145 0.033 -4.41 0.00044 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.199 on 16 degrees of freedom 311s Number of observations: 20 Degrees of Freedom: 16 311s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 311s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 311s 311s 311s 2SLS estimates for 'PrivateWages' (equation 3) 311s Model Formula: privWage ~ gnp + gnpLag + trend 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 1.3431 1.1772 1.14 0.27070 311s gnp 0.4438 0.0358 12.39 1.3e-09 *** 311s gnpLag 0.1447 0.0389 3.72 0.00185 ** 311s trend 0.1238 0.0306 4.05 0.00093 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 0.78 on 16 degrees of freedom 311s Number of observations: 20 Degrees of Freedom: 16 311s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 311s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 311s 311s > residuals 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 -0.383 -1.0104 -1.3401 311s 3 -0.593 0.2478 0.2378 311s 4 -1.219 1.0621 1.1117 311s 5 -0.130 -1.4104 -0.1954 311s 6 0.354 0.4328 -0.5355 311s 7 NA NA NA 311s 8 1.551 1.0463 -0.7908 311s 9 1.440 0.0674 0.2831 311s 10 -0.286 1.7698 1.1353 311s 11 -0.453 -0.5912 -0.1765 311s 12 -0.994 -0.6318 0.6007 311s 13 -1.300 -0.6983 0.1443 311s 14 0.521 0.9724 0.4826 311s 15 -0.157 -0.1827 0.3016 311s 16 -0.014 0.1167 0.0261 311s 17 1.974 1.6266 -0.8614 311s 18 -0.576 -0.0525 0.9927 311s 19 -0.203 -3.0656 -0.4446 311s 20 1.342 0.1393 -0.3914 311s 21 1.039 -0.1305 -1.1115 311s 22 -1.912 0.2922 0.5312 311s > fitted 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 42.3 0.810 26.8 311s 3 45.6 1.652 29.1 311s 4 50.4 4.138 33.0 311s 5 50.7 4.410 34.1 311s 6 52.2 4.667 35.9 311s 7 NA NA NA 311s 8 54.6 3.154 38.7 311s 9 55.9 2.933 38.9 311s 10 58.1 3.330 40.2 311s 11 55.5 1.591 38.1 311s 12 51.9 -2.768 33.9 311s 13 46.9 -5.502 28.9 311s 14 46.0 -6.072 28.0 311s 15 48.9 -2.817 30.3 311s 16 51.3 -1.417 33.2 311s 17 55.7 0.473 37.7 311s 18 59.3 2.053 40.0 311s 19 57.7 1.166 38.6 311s 20 60.3 1.161 42.0 311s 21 64.0 3.431 46.1 311s 22 71.6 4.608 52.8 311s > predict 311s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 311s 1 NA NA NA NA 311s 2 42.3 0.473 41.3 43.3 311s 3 45.6 0.573 44.4 46.8 311s 4 50.4 0.366 49.6 51.2 311s 5 50.7 0.423 49.8 51.6 311s 6 52.2 0.426 51.3 53.1 311s 7 NA NA NA NA 311s 8 54.6 0.347 53.9 55.4 311s 9 55.9 0.384 55.0 56.7 311s 10 58.1 0.395 57.2 58.9 311s 11 55.5 0.729 53.9 57.0 311s 12 51.9 0.594 50.6 53.2 311s 13 46.9 0.752 45.3 48.5 311s 14 46.0 0.616 44.7 47.3 311s 15 48.9 0.373 48.1 49.6 311s 16 51.3 0.331 50.6 52.0 311s 17 55.7 0.403 54.9 56.6 311s 18 59.3 0.326 58.6 60.0 311s 19 57.7 0.411 56.8 58.6 311s 20 60.3 0.472 59.3 61.3 311s 21 64.0 0.443 63.0 64.9 311s 22 71.6 0.683 70.2 73.1 311s Investment.pred Investment.se.fit Investment.lwr Investment.upr 311s 1 NA NA NA NA 311s 2 0.810 0.786 -0.8569 2.48 311s 3 1.652 0.541 0.5056 2.80 311s 4 4.138 0.511 3.0552 5.22 311s 5 4.410 0.421 3.5172 5.30 311s 6 4.667 0.395 3.8294 5.51 311s 7 NA NA NA NA 311s 8 3.154 0.327 2.4602 3.85 311s 9 2.933 0.489 1.8967 3.97 311s 10 3.330 0.537 2.1915 4.47 311s 11 1.591 0.786 -0.0748 3.26 311s 12 -2.768 0.615 -4.0716 -1.46 311s 13 -5.502 0.787 -7.1696 -3.83 311s 14 -6.072 0.842 -7.8568 -4.29 311s 15 -2.817 0.397 -3.6591 -1.98 311s 16 -1.417 0.343 -2.1436 -0.69 311s 17 0.473 0.457 -0.4954 1.44 311s 18 2.053 0.286 1.4471 2.66 311s 19 1.166 0.430 0.2549 2.08 311s 20 1.161 0.515 0.0698 2.25 311s 21 3.431 0.426 2.5282 4.33 311s 22 4.608 0.606 3.3223 5.89 311s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 311s 1 NA NA NA NA 311s 2 26.8 0.328 26.1 27.5 311s 3 29.1 0.340 28.3 29.8 311s 4 33.0 0.360 32.2 33.8 311s 5 34.1 0.258 33.5 34.6 311s 6 35.9 0.266 35.4 36.5 311s 7 NA NA NA NA 311s 8 38.7 0.262 38.1 39.2 311s 9 38.9 0.250 38.4 39.4 311s 10 40.2 0.240 39.7 40.7 311s 11 38.1 0.355 37.3 38.8 311s 12 33.9 0.382 33.1 34.7 311s 13 28.9 0.456 27.9 29.8 311s 14 28.0 0.348 27.3 28.8 311s 15 30.3 0.339 29.6 31.0 311s 16 33.2 0.284 32.6 33.8 311s 17 37.7 0.293 37.0 38.3 311s 18 40.0 0.218 39.5 40.5 311s 19 38.6 0.358 37.9 39.4 311s 20 42.0 0.307 41.3 42.6 311s 21 46.1 0.310 45.5 46.8 311s 22 52.8 0.496 51.7 53.8 311s > model.frame 311s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 311s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 311s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 311s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 311s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 311s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 311s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 311s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 311s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 311s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 311s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 311s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 311s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 311s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 311s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 311s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 311s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 311s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 311s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 311s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 311s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 311s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 311s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 311s trend 311s 1 -11 311s 2 -10 311s 3 -9 311s 4 -8 311s 5 -7 311s 6 -6 311s 7 -5 311s 8 -4 311s 9 -3 311s 10 -2 311s 11 -1 311s 12 0 311s 13 1 311s 14 2 311s 15 3 311s 16 4 311s 17 5 311s 18 6 311s 19 7 311s 20 8 311s 21 9 311s 22 10 311s > Frames of instrumental variables 311s govExp taxes govWage trend capitalLag corpProfLag gnpLag 311s 1 2.4 3.4 2.2 -11 180 NA NA 311s 2 3.9 7.7 2.7 -10 183 12.7 44.9 311s 3 3.2 3.9 2.9 -9 183 12.4 45.6 311s 4 2.8 4.7 2.9 -8 184 16.9 50.1 311s 5 3.5 3.8 3.1 -7 190 18.4 57.2 311s 6 3.3 5.5 3.2 -6 193 19.4 57.1 311s 7 3.3 7.0 3.3 -5 198 20.1 NA 311s 8 4.0 6.7 3.6 -4 203 19.6 64.0 311s 9 4.2 4.2 3.7 -3 208 19.8 64.4 311s 10 4.1 4.0 4.0 -2 211 21.1 64.5 311s 11 5.2 7.7 4.2 -1 216 21.7 67.0 311s 12 5.9 7.5 4.8 0 217 15.6 61.2 311s 13 4.9 8.3 5.3 1 213 11.4 53.4 311s 14 3.7 5.4 5.6 2 207 7.0 44.3 311s 15 4.0 6.8 6.0 3 202 11.2 45.1 311s 16 4.4 7.2 6.1 4 199 12.3 49.7 311s 17 2.9 8.3 7.4 5 198 14.0 54.4 311s 18 4.3 6.7 6.7 6 200 17.6 62.7 311s 19 5.3 7.4 7.7 7 202 17.3 65.0 311s 20 6.6 8.9 7.8 8 200 15.3 60.9 311s 21 7.4 9.6 8.0 9 201 19.0 69.5 311s 22 13.8 11.6 8.5 10 204 21.1 75.7 311s govExp taxes govWage trend capitalLag corpProfLag gnpLag 311s 1 2.4 3.4 2.2 -11 180 NA NA 311s 2 3.9 7.7 2.7 -10 183 12.7 44.9 311s 3 3.2 3.9 2.9 -9 183 12.4 45.6 311s 4 2.8 4.7 2.9 -8 184 16.9 50.1 311s 5 3.5 3.8 3.1 -7 190 18.4 57.2 311s 6 3.3 5.5 3.2 -6 193 19.4 57.1 311s 7 3.3 7.0 3.3 -5 198 20.1 NA 311s 8 4.0 6.7 3.6 -4 203 19.6 64.0 311s 9 4.2 4.2 3.7 -3 208 19.8 64.4 311s 10 4.1 4.0 4.0 -2 211 21.1 64.5 311s 11 5.2 7.7 4.2 -1 216 21.7 67.0 311s 12 5.9 7.5 4.8 0 217 15.6 61.2 311s 13 4.9 8.3 5.3 1 213 11.4 53.4 311s 14 3.7 5.4 5.6 2 207 7.0 44.3 311s 15 4.0 6.8 6.0 3 202 11.2 45.1 311s 16 4.4 7.2 6.1 4 199 12.3 49.7 311s 17 2.9 8.3 7.4 5 198 14.0 54.4 311s 18 4.3 6.7 6.7 6 200 17.6 62.7 311s 19 5.3 7.4 7.7 7 202 17.3 65.0 311s 20 6.6 8.9 7.8 8 200 15.3 60.9 311s 21 7.4 9.6 8.0 9 201 19.0 69.5 311s 22 13.8 11.6 8.5 10 204 21.1 75.7 311s govExp taxes govWage trend capitalLag corpProfLag gnpLag 311s 1 2.4 3.4 2.2 -11 180 NA NA 311s 2 3.9 7.7 2.7 -10 183 12.7 44.9 311s 3 3.2 3.9 2.9 -9 183 12.4 45.6 311s 4 2.8 4.7 2.9 -8 184 16.9 50.1 311s 5 3.5 3.8 3.1 -7 190 18.4 57.2 311s 6 3.3 5.5 3.2 -6 193 19.4 57.1 311s 7 3.3 7.0 3.3 -5 198 20.1 NA 311s 8 4.0 6.7 3.6 -4 203 19.6 64.0 311s 9 4.2 4.2 3.7 -3 208 19.8 64.4 311s 10 4.1 4.0 4.0 -2 211 21.1 64.5 311s 11 5.2 7.7 4.2 -1 216 21.7 67.0 311s 12 5.9 7.5 4.8 0 217 15.6 61.2 311s 13 4.9 8.3 5.3 1 213 11.4 53.4 311s 14 3.7 5.4 5.6 2 207 7.0 44.3 311s 15 4.0 6.8 6.0 3 202 11.2 45.1 311s 16 4.4 7.2 6.1 4 199 12.3 49.7 311s 17 2.9 8.3 7.4 5 198 14.0 54.4 311s 18 4.3 6.7 6.7 6 200 17.6 62.7 311s 19 5.3 7.4 7.7 7 202 17.3 65.0 311s 20 6.6 8.9 7.8 8 200 15.3 60.9 311s 21 7.4 9.6 8.0 9 201 19.0 69.5 311s 22 13.8 11.6 8.5 10 204 21.1 75.7 311s > model.matrix 311s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 311s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 311s [3] "Numeric: lengths (744, 720) differ" 311s > matrix of instrumental variables 311s Consumption_(Intercept) Consumption_govExp Consumption_taxes 311s Consumption_2 1 3.9 7.7 311s Consumption_3 1 3.2 3.9 311s Consumption_4 1 2.8 4.7 311s Consumption_5 1 3.5 3.8 311s Consumption_6 1 3.3 5.5 311s Consumption_8 1 4.0 6.7 311s Consumption_9 1 4.2 4.2 311s Consumption_10 1 4.1 4.0 311s Consumption_11 1 5.2 7.7 311s Consumption_12 1 5.9 7.5 311s Consumption_13 1 4.9 8.3 311s Consumption_14 1 3.7 5.4 311s Consumption_15 1 4.0 6.8 311s Consumption_16 1 4.4 7.2 311s Consumption_17 1 2.9 8.3 311s Consumption_18 1 4.3 6.7 311s Consumption_19 1 5.3 7.4 311s Consumption_20 1 6.6 8.9 311s Consumption_21 1 7.4 9.6 311s Consumption_22 1 13.8 11.6 311s Investment_2 0 0.0 0.0 311s Investment_3 0 0.0 0.0 311s Investment_4 0 0.0 0.0 311s Investment_5 0 0.0 0.0 311s Investment_6 0 0.0 0.0 311s Investment_8 0 0.0 0.0 311s Investment_9 0 0.0 0.0 311s Investment_10 0 0.0 0.0 311s Investment_11 0 0.0 0.0 311s Investment_12 0 0.0 0.0 311s Investment_13 0 0.0 0.0 311s Investment_14 0 0.0 0.0 311s Investment_15 0 0.0 0.0 311s Investment_16 0 0.0 0.0 311s Investment_17 0 0.0 0.0 311s Investment_18 0 0.0 0.0 311s Investment_19 0 0.0 0.0 311s Investment_20 0 0.0 0.0 311s Investment_21 0 0.0 0.0 311s Investment_22 0 0.0 0.0 311s PrivateWages_2 0 0.0 0.0 311s PrivateWages_3 0 0.0 0.0 311s PrivateWages_4 0 0.0 0.0 311s PrivateWages_5 0 0.0 0.0 311s PrivateWages_6 0 0.0 0.0 311s PrivateWages_8 0 0.0 0.0 311s PrivateWages_9 0 0.0 0.0 311s PrivateWages_10 0 0.0 0.0 311s PrivateWages_11 0 0.0 0.0 311s PrivateWages_12 0 0.0 0.0 311s PrivateWages_13 0 0.0 0.0 311s PrivateWages_14 0 0.0 0.0 311s PrivateWages_15 0 0.0 0.0 311s PrivateWages_16 0 0.0 0.0 311s PrivateWages_17 0 0.0 0.0 311s PrivateWages_18 0 0.0 0.0 311s PrivateWages_19 0 0.0 0.0 311s PrivateWages_20 0 0.0 0.0 311s PrivateWages_21 0 0.0 0.0 311s PrivateWages_22 0 0.0 0.0 311s Consumption_govWage Consumption_trend Consumption_capitalLag 311s Consumption_2 2.7 -10 183 311s Consumption_3 2.9 -9 183 311s Consumption_4 2.9 -8 184 311s Consumption_5 3.1 -7 190 311s Consumption_6 3.2 -6 193 311s Consumption_8 3.6 -4 203 311s Consumption_9 3.7 -3 208 311s Consumption_10 4.0 -2 211 311s Consumption_11 4.2 -1 216 311s Consumption_12 4.8 0 217 311s Consumption_13 5.3 1 213 311s Consumption_14 5.6 2 207 311s Consumption_15 6.0 3 202 311s Consumption_16 6.1 4 199 311s Consumption_17 7.4 5 198 311s Consumption_18 6.7 6 200 311s Consumption_19 7.7 7 202 311s Consumption_20 7.8 8 200 311s Consumption_21 8.0 9 201 311s Consumption_22 8.5 10 204 311s Investment_2 0.0 0 0 311s Investment_3 0.0 0 0 311s Investment_4 0.0 0 0 311s Investment_5 0.0 0 0 311s Investment_6 0.0 0 0 311s Investment_8 0.0 0 0 311s Investment_9 0.0 0 0 311s Investment_10 0.0 0 0 311s Investment_11 0.0 0 0 311s Investment_12 0.0 0 0 311s Investment_13 0.0 0 0 311s Investment_14 0.0 0 0 311s Investment_15 0.0 0 0 311s Investment_16 0.0 0 0 311s Investment_17 0.0 0 0 311s Investment_18 0.0 0 0 311s Investment_19 0.0 0 0 311s Investment_20 0.0 0 0 311s Investment_21 0.0 0 0 311s Investment_22 0.0 0 0 311s PrivateWages_2 0.0 0 0 311s PrivateWages_3 0.0 0 0 311s PrivateWages_4 0.0 0 0 311s PrivateWages_5 0.0 0 0 311s PrivateWages_6 0.0 0 0 311s PrivateWages_8 0.0 0 0 311s PrivateWages_9 0.0 0 0 311s PrivateWages_10 0.0 0 0 311s PrivateWages_11 0.0 0 0 311s PrivateWages_12 0.0 0 0 311s PrivateWages_13 0.0 0 0 311s PrivateWages_14 0.0 0 0 311s PrivateWages_15 0.0 0 0 311s PrivateWages_16 0.0 0 0 311s PrivateWages_17 0.0 0 0 311s PrivateWages_18 0.0 0 0 311s PrivateWages_19 0.0 0 0 311s PrivateWages_20 0.0 0 0 311s PrivateWages_21 0.0 0 0 311s PrivateWages_22 0.0 0 0 311s Consumption_corpProfLag Consumption_gnpLag 311s Consumption_2 12.7 44.9 311s Consumption_3 12.4 45.6 311s Consumption_4 16.9 50.1 311s Consumption_5 18.4 57.2 311s Consumption_6 19.4 57.1 311s Consumption_8 19.6 64.0 311s Consumption_9 19.8 64.4 311s Consumption_10 21.1 64.5 311s Consumption_11 21.7 67.0 311s Consumption_12 15.6 61.2 311s Consumption_13 11.4 53.4 311s Consumption_14 7.0 44.3 311s Consumption_15 11.2 45.1 311s Consumption_16 12.3 49.7 311s Consumption_17 14.0 54.4 311s Consumption_18 17.6 62.7 311s Consumption_19 17.3 65.0 311s Consumption_20 15.3 60.9 311s Consumption_21 19.0 69.5 311s Consumption_22 21.1 75.7 311s Investment_2 0.0 0.0 311s Investment_3 0.0 0.0 311s Investment_4 0.0 0.0 311s Investment_5 0.0 0.0 311s Investment_6 0.0 0.0 311s Investment_8 0.0 0.0 311s Investment_9 0.0 0.0 311s Investment_10 0.0 0.0 311s Investment_11 0.0 0.0 311s Investment_12 0.0 0.0 311s Investment_13 0.0 0.0 311s Investment_14 0.0 0.0 311s Investment_15 0.0 0.0 311s Investment_16 0.0 0.0 311s Investment_17 0.0 0.0 311s Investment_18 0.0 0.0 311s Investment_19 0.0 0.0 311s Investment_20 0.0 0.0 311s Investment_21 0.0 0.0 311s Investment_22 0.0 0.0 311s PrivateWages_2 0.0 0.0 311s PrivateWages_3 0.0 0.0 311s PrivateWages_4 0.0 0.0 311s PrivateWages_5 0.0 0.0 311s PrivateWages_6 0.0 0.0 311s PrivateWages_8 0.0 0.0 311s PrivateWages_9 0.0 0.0 311s PrivateWages_10 0.0 0.0 311s PrivateWages_11 0.0 0.0 311s PrivateWages_12 0.0 0.0 311s PrivateWages_13 0.0 0.0 311s PrivateWages_14 0.0 0.0 311s PrivateWages_15 0.0 0.0 311s PrivateWages_16 0.0 0.0 311s PrivateWages_17 0.0 0.0 311s PrivateWages_18 0.0 0.0 311s PrivateWages_19 0.0 0.0 311s PrivateWages_20 0.0 0.0 311s PrivateWages_21 0.0 0.0 311s PrivateWages_22 0.0 0.0 311s Investment_(Intercept) Investment_govExp Investment_taxes 311s Consumption_2 0 0.0 0.0 311s Consumption_3 0 0.0 0.0 311s Consumption_4 0 0.0 0.0 311s Consumption_5 0 0.0 0.0 311s Consumption_6 0 0.0 0.0 311s Consumption_8 0 0.0 0.0 311s Consumption_9 0 0.0 0.0 311s Consumption_10 0 0.0 0.0 311s Consumption_11 0 0.0 0.0 311s Consumption_12 0 0.0 0.0 311s Consumption_13 0 0.0 0.0 311s Consumption_14 0 0.0 0.0 311s Consumption_15 0 0.0 0.0 311s Consumption_16 0 0.0 0.0 311s Consumption_17 0 0.0 0.0 311s Consumption_18 0 0.0 0.0 311s Consumption_19 0 0.0 0.0 311s Consumption_20 0 0.0 0.0 311s Consumption_21 0 0.0 0.0 311s Consumption_22 0 0.0 0.0 311s Investment_2 1 3.9 7.7 311s Investment_3 1 3.2 3.9 311s Investment_4 1 2.8 4.7 311s Investment_5 1 3.5 3.8 311s Investment_6 1 3.3 5.5 311s Investment_8 1 4.0 6.7 311s Investment_9 1 4.2 4.2 311s Investment_10 1 4.1 4.0 311s Investment_11 1 5.2 7.7 311s Investment_12 1 5.9 7.5 311s Investment_13 1 4.9 8.3 311s Investment_14 1 3.7 5.4 311s Investment_15 1 4.0 6.8 311s Investment_16 1 4.4 7.2 311s Investment_17 1 2.9 8.3 311s Investment_18 1 4.3 6.7 311s Investment_19 1 5.3 7.4 311s Investment_20 1 6.6 8.9 311s Investment_21 1 7.4 9.6 311s Investment_22 1 13.8 11.6 311s PrivateWages_2 0 0.0 0.0 311s PrivateWages_3 0 0.0 0.0 311s PrivateWages_4 0 0.0 0.0 311s PrivateWages_5 0 0.0 0.0 311s PrivateWages_6 0 0.0 0.0 311s PrivateWages_8 0 0.0 0.0 311s PrivateWages_9 0 0.0 0.0 311s PrivateWages_10 0 0.0 0.0 311s PrivateWages_11 0 0.0 0.0 311s PrivateWages_12 0 0.0 0.0 311s PrivateWages_13 0 0.0 0.0 311s PrivateWages_14 0 0.0 0.0 311s PrivateWages_15 0 0.0 0.0 311s PrivateWages_16 0 0.0 0.0 311s PrivateWages_17 0 0.0 0.0 311s PrivateWages_18 0 0.0 0.0 311s PrivateWages_19 0 0.0 0.0 311s PrivateWages_20 0 0.0 0.0 311s PrivateWages_21 0 0.0 0.0 311s PrivateWages_22 0 0.0 0.0 311s Investment_govWage Investment_trend Investment_capitalLag 311s Consumption_2 0.0 0 0 311s Consumption_3 0.0 0 0 311s Consumption_4 0.0 0 0 311s Consumption_5 0.0 0 0 311s Consumption_6 0.0 0 0 311s Consumption_8 0.0 0 0 311s Consumption_9 0.0 0 0 311s Consumption_10 0.0 0 0 311s Consumption_11 0.0 0 0 311s Consumption_12 0.0 0 0 311s Consumption_13 0.0 0 0 311s Consumption_14 0.0 0 0 311s Consumption_15 0.0 0 0 311s Consumption_16 0.0 0 0 311s Consumption_17 0.0 0 0 311s Consumption_18 0.0 0 0 311s Consumption_19 0.0 0 0 311s Consumption_20 0.0 0 0 311s Consumption_21 0.0 0 0 311s Consumption_22 0.0 0 0 311s Investment_2 2.7 -10 183 311s Investment_3 2.9 -9 183 311s Investment_4 2.9 -8 184 311s Investment_5 3.1 -7 190 311s Investment_6 3.2 -6 193 311s Investment_8 3.6 -4 203 311s Investment_9 3.7 -3 208 311s Investment_10 4.0 -2 211 311s Investment_11 4.2 -1 216 311s Investment_12 4.8 0 217 311s Investment_13 5.3 1 213 311s Investment_14 5.6 2 207 311s Investment_15 6.0 3 202 311s Investment_16 6.1 4 199 311s Investment_17 7.4 5 198 311s Investment_18 6.7 6 200 311s Investment_19 7.7 7 202 311s Investment_20 7.8 8 200 311s Investment_21 8.0 9 201 311s Investment_22 8.5 10 204 311s PrivateWages_2 0.0 0 0 311s PrivateWages_3 0.0 0 0 311s PrivateWages_4 0.0 0 0 311s PrivateWages_5 0.0 0 0 311s PrivateWages_6 0.0 0 0 311s PrivateWages_8 0.0 0 0 311s PrivateWages_9 0.0 0 0 311s PrivateWages_10 0.0 0 0 311s PrivateWages_11 0.0 0 0 311s PrivateWages_12 0.0 0 0 311s PrivateWages_13 0.0 0 0 311s PrivateWages_14 0.0 0 0 311s PrivateWages_15 0.0 0 0 311s PrivateWages_16 0.0 0 0 311s PrivateWages_17 0.0 0 0 311s PrivateWages_18 0.0 0 0 311s PrivateWages_19 0.0 0 0 311s PrivateWages_20 0.0 0 0 311s PrivateWages_21 0.0 0 0 311s PrivateWages_22 0.0 0 0 311s Investment_corpProfLag Investment_gnpLag 311s Consumption_2 0.0 0.0 311s Consumption_3 0.0 0.0 311s Consumption_4 0.0 0.0 311s Consumption_5 0.0 0.0 311s Consumption_6 0.0 0.0 311s Consumption_8 0.0 0.0 311s Consumption_9 0.0 0.0 311s Consumption_10 0.0 0.0 311s Consumption_11 0.0 0.0 311s Consumption_12 0.0 0.0 311s Consumption_13 0.0 0.0 311s Consumption_14 0.0 0.0 311s Consumption_15 0.0 0.0 311s Consumption_16 0.0 0.0 311s Consumption_17 0.0 0.0 311s Consumption_18 0.0 0.0 311s Consumption_19 0.0 0.0 311s Consumption_20 0.0 0.0 311s Consumption_21 0.0 0.0 311s Consumption_22 0.0 0.0 311s Investment_2 12.7 44.9 311s Investment_3 12.4 45.6 311s Investment_4 16.9 50.1 311s Investment_5 18.4 57.2 311s Investment_6 19.4 57.1 311s Investment_8 19.6 64.0 311s Investment_9 19.8 64.4 311s Investment_10 21.1 64.5 311s Investment_11 21.7 67.0 311s Investment_12 15.6 61.2 311s Investment_13 11.4 53.4 311s Investment_14 7.0 44.3 311s Investment_15 11.2 45.1 311s Investment_16 12.3 49.7 311s Investment_17 14.0 54.4 311s Investment_18 17.6 62.7 311s Investment_19 17.3 65.0 311s Investment_20 15.3 60.9 311s Investment_21 19.0 69.5 311s Investment_22 21.1 75.7 311s PrivateWages_2 0.0 0.0 311s PrivateWages_3 0.0 0.0 311s PrivateWages_4 0.0 0.0 311s PrivateWages_5 0.0 0.0 311s PrivateWages_6 0.0 0.0 311s PrivateWages_8 0.0 0.0 311s PrivateWages_9 0.0 0.0 311s PrivateWages_10 0.0 0.0 311s PrivateWages_11 0.0 0.0 311s PrivateWages_12 0.0 0.0 311s PrivateWages_13 0.0 0.0 311s PrivateWages_14 0.0 0.0 311s PrivateWages_15 0.0 0.0 311s PrivateWages_16 0.0 0.0 311s PrivateWages_17 0.0 0.0 311s PrivateWages_18 0.0 0.0 311s PrivateWages_19 0.0 0.0 311s PrivateWages_20 0.0 0.0 311s PrivateWages_21 0.0 0.0 311s PrivateWages_22 0.0 0.0 311s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 311s Consumption_2 0 0.0 0.0 311s Consumption_3 0 0.0 0.0 311s Consumption_4 0 0.0 0.0 311s Consumption_5 0 0.0 0.0 311s Consumption_6 0 0.0 0.0 311s Consumption_8 0 0.0 0.0 311s Consumption_9 0 0.0 0.0 311s Consumption_10 0 0.0 0.0 311s Consumption_11 0 0.0 0.0 311s Consumption_12 0 0.0 0.0 311s Consumption_13 0 0.0 0.0 311s Consumption_14 0 0.0 0.0 311s Consumption_15 0 0.0 0.0 311s Consumption_16 0 0.0 0.0 311s Consumption_17 0 0.0 0.0 311s Consumption_18 0 0.0 0.0 311s Consumption_19 0 0.0 0.0 311s Consumption_20 0 0.0 0.0 311s Consumption_21 0 0.0 0.0 311s Consumption_22 0 0.0 0.0 311s Investment_2 0 0.0 0.0 311s Investment_3 0 0.0 0.0 311s Investment_4 0 0.0 0.0 311s Investment_5 0 0.0 0.0 311s Investment_6 0 0.0 0.0 311s Investment_8 0 0.0 0.0 311s Investment_9 0 0.0 0.0 311s Investment_10 0 0.0 0.0 311s Investment_11 0 0.0 0.0 311s Investment_12 0 0.0 0.0 311s Investment_13 0 0.0 0.0 311s Investment_14 0 0.0 0.0 311s Investment_15 0 0.0 0.0 311s Investment_16 0 0.0 0.0 311s Investment_17 0 0.0 0.0 311s Investment_18 0 0.0 0.0 311s Investment_19 0 0.0 0.0 311s Investment_20 0 0.0 0.0 311s Investment_21 0 0.0 0.0 311s Investment_22 0 0.0 0.0 311s PrivateWages_2 1 3.9 7.7 311s PrivateWages_3 1 3.2 3.9 311s PrivateWages_4 1 2.8 4.7 311s PrivateWages_5 1 3.5 3.8 311s PrivateWages_6 1 3.3 5.5 311s PrivateWages_8 1 4.0 6.7 311s PrivateWages_9 1 4.2 4.2 311s PrivateWages_10 1 4.1 4.0 311s PrivateWages_11 1 5.2 7.7 311s PrivateWages_12 1 5.9 7.5 311s PrivateWages_13 1 4.9 8.3 311s PrivateWages_14 1 3.7 5.4 311s PrivateWages_15 1 4.0 6.8 311s PrivateWages_16 1 4.4 7.2 311s PrivateWages_17 1 2.9 8.3 311s PrivateWages_18 1 4.3 6.7 311s PrivateWages_19 1 5.3 7.4 311s PrivateWages_20 1 6.6 8.9 311s PrivateWages_21 1 7.4 9.6 311s PrivateWages_22 1 13.8 11.6 311s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 311s Consumption_2 0.0 0 0 311s Consumption_3 0.0 0 0 311s Consumption_4 0.0 0 0 311s Consumption_5 0.0 0 0 311s Consumption_6 0.0 0 0 311s Consumption_8 0.0 0 0 311s Consumption_9 0.0 0 0 311s Consumption_10 0.0 0 0 311s Consumption_11 0.0 0 0 311s Consumption_12 0.0 0 0 311s Consumption_13 0.0 0 0 311s Consumption_14 0.0 0 0 311s Consumption_15 0.0 0 0 311s Consumption_16 0.0 0 0 311s Consumption_17 0.0 0 0 311s Consumption_18 0.0 0 0 311s Consumption_19 0.0 0 0 311s Consumption_20 0.0 0 0 311s Consumption_21 0.0 0 0 311s Consumption_22 0.0 0 0 311s Investment_2 0.0 0 0 311s Investment_3 0.0 0 0 311s Investment_4 0.0 0 0 311s Investment_5 0.0 0 0 311s Investment_6 0.0 0 0 311s Investment_8 0.0 0 0 311s Investment_9 0.0 0 0 311s Investment_10 0.0 0 0 311s Investment_11 0.0 0 0 311s Investment_12 0.0 0 0 311s Investment_13 0.0 0 0 311s Investment_14 0.0 0 0 311s Investment_15 0.0 0 0 311s Investment_16 0.0 0 0 311s Investment_17 0.0 0 0 311s Investment_18 0.0 0 0 311s Investment_19 0.0 0 0 311s Investment_20 0.0 0 0 311s Investment_21 0.0 0 0 311s Investment_22 0.0 0 0 311s PrivateWages_2 2.7 -10 183 311s PrivateWages_3 2.9 -9 183 311s PrivateWages_4 2.9 -8 184 311s PrivateWages_5 3.1 -7 190 311s PrivateWages_6 3.2 -6 193 311s PrivateWages_8 3.6 -4 203 311s PrivateWages_9 3.7 -3 208 311s PrivateWages_10 4.0 -2 211 311s PrivateWages_11 4.2 -1 216 311s PrivateWages_12 4.8 0 217 311s PrivateWages_13 5.3 1 213 311s PrivateWages_14 5.6 2 207 311s PrivateWages_15 6.0 3 202 311s PrivateWages_16 6.1 4 199 311s PrivateWages_17 7.4 5 198 311s PrivateWages_18 6.7 6 200 311s PrivateWages_19 7.7 7 202 311s PrivateWages_20 7.8 8 200 311s PrivateWages_21 8.0 9 201 311s PrivateWages_22 8.5 10 204 311s PrivateWages_corpProfLag PrivateWages_gnpLag 311s Consumption_2 0.0 0.0 311s Consumption_3 0.0 0.0 311s Consumption_4 0.0 0.0 311s Consumption_5 0.0 0.0 311s Consumption_6 0.0 0.0 311s Consumption_8 0.0 0.0 311s Consumption_9 0.0 0.0 311s Consumption_10 0.0 0.0 311s Consumption_11 0.0 0.0 311s Consumption_12 0.0 0.0 311s Consumption_13 0.0 0.0 311s Consumption_14 0.0 0.0 311s Consumption_15 0.0 0.0 311s Consumption_16 0.0 0.0 311s Consumption_17 0.0 0.0 311s Consumption_18 0.0 0.0 311s Consumption_19 0.0 0.0 311s Consumption_20 0.0 0.0 311s Consumption_21 0.0 0.0 311s Consumption_22 0.0 0.0 311s Investment_2 0.0 0.0 311s Investment_3 0.0 0.0 311s Investment_4 0.0 0.0 311s Investment_5 0.0 0.0 311s Investment_6 0.0 0.0 311s Investment_8 0.0 0.0 311s Investment_9 0.0 0.0 311s Investment_10 0.0 0.0 311s Investment_11 0.0 0.0 311s Investment_12 0.0 0.0 311s Investment_13 0.0 0.0 311s Investment_14 0.0 0.0 311s Investment_15 0.0 0.0 311s Investment_16 0.0 0.0 311s Investment_17 0.0 0.0 311s Investment_18 0.0 0.0 311s Investment_19 0.0 0.0 311s Investment_20 0.0 0.0 311s Investment_21 0.0 0.0 311s Investment_22 0.0 0.0 311s PrivateWages_2 12.7 44.9 311s PrivateWages_3 12.4 45.6 311s PrivateWages_4 16.9 50.1 311s PrivateWages_5 18.4 57.2 311s PrivateWages_6 19.4 57.1 311s PrivateWages_8 19.6 64.0 311s PrivateWages_9 19.8 64.4 311s PrivateWages_10 21.1 64.5 311s PrivateWages_11 21.7 67.0 311s PrivateWages_12 15.6 61.2 311s PrivateWages_13 11.4 53.4 311s PrivateWages_14 7.0 44.3 311s PrivateWages_15 11.2 45.1 311s PrivateWages_16 12.3 49.7 311s PrivateWages_17 14.0 54.4 311s PrivateWages_18 17.6 62.7 311s PrivateWages_19 17.3 65.0 311s PrivateWages_20 15.3 60.9 311s PrivateWages_21 19.0 69.5 311s PrivateWages_22 21.1 75.7 311s > matrix of fitted regressors 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_2 1 12.96 311s Consumption_3 1 16.70 311s Consumption_4 1 19.14 311s Consumption_5 1 20.94 311s Consumption_6 1 19.47 311s Consumption_8 1 17.14 311s Consumption_9 1 19.49 311s Consumption_10 1 20.46 311s Consumption_11 1 16.85 311s Consumption_12 1 12.68 311s Consumption_13 1 8.92 311s Consumption_14 1 9.30 311s Consumption_15 1 12.79 311s Consumption_16 1 14.26 311s Consumption_17 1 14.75 311s Consumption_18 1 19.54 311s Consumption_19 1 19.36 311s Consumption_20 1 17.39 311s Consumption_21 1 20.10 311s Consumption_22 1 22.86 311s Investment_2 0 0.00 311s Investment_3 0 0.00 311s Investment_4 0 0.00 311s Investment_5 0 0.00 311s Investment_6 0 0.00 311s Investment_8 0 0.00 311s Investment_9 0 0.00 311s Investment_10 0 0.00 311s Investment_11 0 0.00 311s Investment_12 0 0.00 311s Investment_13 0 0.00 311s Investment_14 0 0.00 311s Investment_15 0 0.00 311s Investment_16 0 0.00 311s Investment_17 0 0.00 311s Investment_18 0 0.00 311s Investment_19 0 0.00 311s Investment_20 0 0.00 311s Investment_21 0 0.00 311s Investment_22 0 0.00 311s PrivateWages_2 0 0.00 311s PrivateWages_3 0 0.00 311s PrivateWages_4 0 0.00 311s PrivateWages_5 0 0.00 311s PrivateWages_6 0 0.00 311s PrivateWages_8 0 0.00 311s PrivateWages_9 0 0.00 311s PrivateWages_10 0 0.00 311s PrivateWages_11 0 0.00 311s PrivateWages_12 0 0.00 311s PrivateWages_13 0 0.00 311s PrivateWages_14 0 0.00 311s PrivateWages_15 0 0.00 311s PrivateWages_16 0 0.00 311s PrivateWages_17 0 0.00 311s PrivateWages_18 0 0.00 311s PrivateWages_19 0 0.00 311s PrivateWages_20 0 0.00 311s PrivateWages_21 0 0.00 311s PrivateWages_22 0 0.00 311s Consumption_corpProfLag Consumption_wages 311s Consumption_2 12.7 29.1 311s Consumption_3 12.4 31.9 311s Consumption_4 16.9 35.6 311s Consumption_5 18.4 39.0 311s Consumption_6 19.4 38.8 311s Consumption_8 19.6 39.8 311s Consumption_9 19.8 42.3 311s Consumption_10 21.1 44.1 311s Consumption_11 21.7 43.4 311s Consumption_12 15.6 39.5 311s Consumption_13 11.4 35.1 311s Consumption_14 7.0 33.0 311s Consumption_15 11.2 37.6 311s Consumption_16 12.3 40.0 311s Consumption_17 14.0 41.7 311s Consumption_18 17.6 47.6 311s Consumption_19 17.3 49.5 311s Consumption_20 15.3 48.4 311s Consumption_21 19.0 53.2 311s Consumption_22 21.1 60.9 311s Investment_2 0.0 0.0 311s Investment_3 0.0 0.0 311s Investment_4 0.0 0.0 311s Investment_5 0.0 0.0 311s Investment_6 0.0 0.0 311s Investment_8 0.0 0.0 311s Investment_9 0.0 0.0 311s Investment_10 0.0 0.0 311s Investment_11 0.0 0.0 311s Investment_12 0.0 0.0 311s Investment_13 0.0 0.0 311s Investment_14 0.0 0.0 311s Investment_15 0.0 0.0 311s Investment_16 0.0 0.0 311s Investment_17 0.0 0.0 311s Investment_18 0.0 0.0 311s Investment_19 0.0 0.0 311s Investment_20 0.0 0.0 311s Investment_21 0.0 0.0 311s Investment_22 0.0 0.0 311s PrivateWages_2 0.0 0.0 311s PrivateWages_3 0.0 0.0 311s PrivateWages_4 0.0 0.0 311s PrivateWages_5 0.0 0.0 311s PrivateWages_6 0.0 0.0 311s PrivateWages_8 0.0 0.0 311s PrivateWages_9 0.0 0.0 311s PrivateWages_10 0.0 0.0 311s PrivateWages_11 0.0 0.0 311s PrivateWages_12 0.0 0.0 311s PrivateWages_13 0.0 0.0 311s PrivateWages_14 0.0 0.0 311s PrivateWages_15 0.0 0.0 311s PrivateWages_16 0.0 0.0 311s PrivateWages_17 0.0 0.0 311s PrivateWages_18 0.0 0.0 311s PrivateWages_19 0.0 0.0 311s PrivateWages_20 0.0 0.0 311s PrivateWages_21 0.0 0.0 311s PrivateWages_22 0.0 0.0 311s Investment_(Intercept) Investment_corpProf 311s Consumption_2 0 0.00 311s Consumption_3 0 0.00 311s Consumption_4 0 0.00 311s Consumption_5 0 0.00 311s Consumption_6 0 0.00 311s Consumption_8 0 0.00 311s Consumption_9 0 0.00 311s Consumption_10 0 0.00 311s Consumption_11 0 0.00 311s Consumption_12 0 0.00 311s Consumption_13 0 0.00 311s Consumption_14 0 0.00 311s Consumption_15 0 0.00 311s Consumption_16 0 0.00 311s Consumption_17 0 0.00 311s Consumption_18 0 0.00 311s Consumption_19 0 0.00 311s Consumption_20 0 0.00 311s Consumption_21 0 0.00 311s Consumption_22 0 0.00 311s Investment_2 1 12.96 311s Investment_3 1 16.70 311s Investment_4 1 19.14 311s Investment_5 1 20.94 311s Investment_6 1 19.47 311s Investment_8 1 17.14 311s Investment_9 1 19.49 311s Investment_10 1 20.46 311s Investment_11 1 16.85 311s Investment_12 1 12.68 311s Investment_13 1 8.92 311s Investment_14 1 9.30 311s Investment_15 1 12.79 311s Investment_16 1 14.26 311s Investment_17 1 14.75 311s Investment_18 1 19.54 311s Investment_19 1 19.36 311s Investment_20 1 17.39 311s Investment_21 1 20.10 311s Investment_22 1 22.86 311s PrivateWages_2 0 0.00 311s PrivateWages_3 0 0.00 311s PrivateWages_4 0 0.00 311s PrivateWages_5 0 0.00 311s PrivateWages_6 0 0.00 311s PrivateWages_8 0 0.00 311s PrivateWages_9 0 0.00 311s PrivateWages_10 0 0.00 311s PrivateWages_11 0 0.00 311s PrivateWages_12 0 0.00 311s PrivateWages_13 0 0.00 311s PrivateWages_14 0 0.00 311s PrivateWages_15 0 0.00 311s PrivateWages_16 0 0.00 311s PrivateWages_17 0 0.00 311s PrivateWages_18 0 0.00 311s PrivateWages_19 0 0.00 311s PrivateWages_20 0 0.00 311s PrivateWages_21 0 0.00 311s PrivateWages_22 0 0.00 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_2 0.0 0 311s Consumption_3 0.0 0 311s Consumption_4 0.0 0 311s Consumption_5 0.0 0 311s Consumption_6 0.0 0 311s Consumption_8 0.0 0 311s Consumption_9 0.0 0 311s Consumption_10 0.0 0 311s Consumption_11 0.0 0 311s Consumption_12 0.0 0 311s Consumption_13 0.0 0 311s Consumption_14 0.0 0 311s Consumption_15 0.0 0 311s Consumption_16 0.0 0 311s Consumption_17 0.0 0 311s Consumption_18 0.0 0 311s Consumption_19 0.0 0 311s Consumption_20 0.0 0 311s Consumption_21 0.0 0 311s Consumption_22 0.0 0 311s Investment_2 12.7 183 311s Investment_3 12.4 183 311s Investment_4 16.9 184 311s Investment_5 18.4 190 311s Investment_6 19.4 193 311s Investment_8 19.6 203 311s Investment_9 19.8 208 311s Investment_10 21.1 211 311s Investment_11 21.7 216 311s Investment_12 15.6 217 311s Investment_13 11.4 213 311s Investment_14 7.0 207 311s Investment_15 11.2 202 311s Investment_16 12.3 199 311s Investment_17 14.0 198 311s Investment_18 17.6 200 311s Investment_19 17.3 202 311s Investment_20 15.3 200 311s Investment_21 19.0 201 311s Investment_22 21.1 204 311s PrivateWages_2 0.0 0 311s PrivateWages_3 0.0 0 311s PrivateWages_4 0.0 0 311s PrivateWages_5 0.0 0 311s PrivateWages_6 0.0 0 311s PrivateWages_8 0.0 0 311s PrivateWages_9 0.0 0 311s PrivateWages_10 0.0 0 311s PrivateWages_11 0.0 0 311s PrivateWages_12 0.0 0 311s PrivateWages_13 0.0 0 311s PrivateWages_14 0.0 0 311s PrivateWages_15 0.0 0 311s PrivateWages_16 0.0 0 311s PrivateWages_17 0.0 0 311s PrivateWages_18 0.0 0 311s PrivateWages_19 0.0 0 311s PrivateWages_20 0.0 0 311s PrivateWages_21 0.0 0 311s PrivateWages_22 0.0 0 311s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 311s Consumption_2 0 0.0 0.0 311s Consumption_3 0 0.0 0.0 311s Consumption_4 0 0.0 0.0 311s Consumption_5 0 0.0 0.0 311s Consumption_6 0 0.0 0.0 311s Consumption_8 0 0.0 0.0 311s Consumption_9 0 0.0 0.0 311s Consumption_10 0 0.0 0.0 311s Consumption_11 0 0.0 0.0 311s Consumption_12 0 0.0 0.0 311s Consumption_13 0 0.0 0.0 311s Consumption_14 0 0.0 0.0 311s Consumption_15 0 0.0 0.0 311s Consumption_16 0 0.0 0.0 311s Consumption_17 0 0.0 0.0 311s Consumption_18 0 0.0 0.0 311s Consumption_19 0 0.0 0.0 311s Consumption_20 0 0.0 0.0 311s Consumption_21 0 0.0 0.0 311s Consumption_22 0 0.0 0.0 311s Investment_2 0 0.0 0.0 311s Investment_3 0 0.0 0.0 311s Investment_4 0 0.0 0.0 311s Investment_5 0 0.0 0.0 311s Investment_6 0 0.0 0.0 311s Investment_8 0 0.0 0.0 311s Investment_9 0 0.0 0.0 311s Investment_10 0 0.0 0.0 311s Investment_11 0 0.0 0.0 311s Investment_12 0 0.0 0.0 311s Investment_13 0 0.0 0.0 311s Investment_14 0 0.0 0.0 311s Investment_15 0 0.0 0.0 311s Investment_16 0 0.0 0.0 311s Investment_17 0 0.0 0.0 311s Investment_18 0 0.0 0.0 311s Investment_19 0 0.0 0.0 311s Investment_20 0 0.0 0.0 311s Investment_21 0 0.0 0.0 311s Investment_22 0 0.0 0.0 311s PrivateWages_2 1 47.1 44.9 311s PrivateWages_3 1 49.6 45.6 311s PrivateWages_4 1 56.5 50.1 311s PrivateWages_5 1 60.7 57.2 311s PrivateWages_6 1 60.6 57.1 311s PrivateWages_8 1 60.0 64.0 311s PrivateWages_9 1 62.3 64.4 311s PrivateWages_10 1 64.6 64.5 311s PrivateWages_11 1 63.7 67.0 311s PrivateWages_12 1 54.8 61.2 311s PrivateWages_13 1 47.0 53.4 311s PrivateWages_14 1 42.1 44.3 311s PrivateWages_15 1 51.2 45.1 311s PrivateWages_16 1 55.3 49.7 311s PrivateWages_17 1 57.4 54.4 311s PrivateWages_18 1 67.2 62.7 311s PrivateWages_19 1 68.5 65.0 311s PrivateWages_20 1 66.8 60.9 311s PrivateWages_21 1 74.9 69.5 311s PrivateWages_22 1 86.9 75.7 311s PrivateWages_trend 311s Consumption_2 0 311s Consumption_3 0 311s Consumption_4 0 311s Consumption_5 0 311s Consumption_6 0 311s Consumption_8 0 311s Consumption_9 0 311s Consumption_10 0 311s Consumption_11 0 311s Consumption_12 0 311s Consumption_13 0 311s Consumption_14 0 311s Consumption_15 0 311s Consumption_16 0 311s Consumption_17 0 311s Consumption_18 0 311s Consumption_19 0 311s Consumption_20 0 311s Consumption_21 0 311s Consumption_22 0 311s Investment_2 0 311s Investment_3 0 311s Investment_4 0 311s Investment_5 0 311s Investment_6 0 311s Investment_8 0 311s Investment_9 0 311s Investment_10 0 311s Investment_11 0 311s Investment_12 0 311s Investment_13 0 311s Investment_14 0 311s Investment_15 0 311s Investment_16 0 311s Investment_17 0 311s Investment_18 0 311s Investment_19 0 311s Investment_20 0 311s Investment_21 0 311s Investment_22 0 311s PrivateWages_2 -10 311s PrivateWages_3 -9 311s PrivateWages_4 -8 311s PrivateWages_5 -7 311s PrivateWages_6 -6 311s PrivateWages_8 -4 311s PrivateWages_9 -3 311s PrivateWages_10 -2 311s PrivateWages_11 -1 311s PrivateWages_12 0 311s PrivateWages_13 1 311s PrivateWages_14 2 311s PrivateWages_15 3 311s PrivateWages_16 4 311s PrivateWages_17 5 311s PrivateWages_18 6 311s PrivateWages_19 7 311s PrivateWages_20 8 311s PrivateWages_21 9 311s PrivateWages_22 10 311s > nobs 311s [1] 60 311s > linearHypothesis 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 49 311s 2 48 1 0.95 0.34 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 49 311s 2 48 1 1.05 0.31 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 49 311s 2 48 1 1.05 0.3 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 50 311s 2 48 2 0.48 0.62 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 50 311s 2 48 2 0.53 0.59 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 50 311s 2 48 2 1.06 0.59 311s > logLik 311s 'log Lik.' -72.2 (df=13) 311s 'log Lik.' -79.7 (df=13) 311s Estimating function 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_2 -1.1407 -14.78 311s Consumption_3 -0.3242 -5.42 311s Consumption_4 -0.0963 -1.84 311s Consumption_5 -1.8392 -38.51 311s Consumption_6 0.1702 3.31 311s Consumption_8 3.0349 52.02 311s Consumption_9 1.9822 38.63 311s Consumption_10 0.7162 14.65 311s Consumption_11 -1.5151 -25.52 311s Consumption_12 -1.1471 -14.54 311s Consumption_13 -1.9595 -17.48 311s Consumption_14 1.4394 13.39 311s Consumption_15 -1.0033 -12.84 311s Consumption_16 -0.5750 -8.20 311s Consumption_17 4.0452 59.67 311s Consumption_18 -0.5669 -11.08 311s Consumption_19 -3.1962 -61.88 311s Consumption_20 2.2286 38.75 311s Consumption_21 0.9237 18.57 311s Consumption_22 -1.1770 -26.91 311s Investment_2 0.0000 0.00 311s Investment_3 0.0000 0.00 311s Investment_4 0.0000 0.00 311s Investment_5 0.0000 0.00 311s Investment_6 0.0000 0.00 311s Investment_8 0.0000 0.00 311s Investment_9 0.0000 0.00 311s Investment_10 0.0000 0.00 311s Investment_11 0.0000 0.00 311s Investment_12 0.0000 0.00 311s Investment_13 0.0000 0.00 311s Investment_14 0.0000 0.00 311s Investment_15 0.0000 0.00 311s Investment_16 0.0000 0.00 311s Investment_17 0.0000 0.00 311s Investment_18 0.0000 0.00 311s Investment_19 0.0000 0.00 311s Investment_20 0.0000 0.00 311s Investment_21 0.0000 0.00 311s Investment_22 0.0000 0.00 311s PrivateWages_2 0.0000 0.00 311s PrivateWages_3 0.0000 0.00 311s PrivateWages_4 0.0000 0.00 311s PrivateWages_5 0.0000 0.00 311s PrivateWages_6 0.0000 0.00 311s PrivateWages_8 0.0000 0.00 311s PrivateWages_9 0.0000 0.00 311s PrivateWages_10 0.0000 0.00 311s PrivateWages_11 0.0000 0.00 311s PrivateWages_12 0.0000 0.00 311s PrivateWages_13 0.0000 0.00 311s PrivateWages_14 0.0000 0.00 311s PrivateWages_15 0.0000 0.00 311s PrivateWages_16 0.0000 0.00 311s PrivateWages_17 0.0000 0.00 311s PrivateWages_18 0.0000 0.00 311s PrivateWages_19 0.0000 0.00 311s PrivateWages_20 0.0000 0.00 311s PrivateWages_21 0.0000 0.00 311s PrivateWages_22 0.0000 0.00 311s Consumption_corpProfLag Consumption_wages 311s Consumption_2 -14.49 -33.21 311s Consumption_3 -4.02 -10.33 311s Consumption_4 -1.63 -3.43 311s Consumption_5 -33.84 -71.82 311s Consumption_6 3.30 6.61 311s Consumption_8 59.48 120.65 311s Consumption_9 39.25 83.81 311s Consumption_10 15.11 31.59 311s Consumption_11 -32.88 -65.70 311s Consumption_12 -17.89 -45.25 311s Consumption_13 -22.34 -68.69 311s Consumption_14 10.08 47.54 311s Consumption_15 -11.24 -37.74 311s Consumption_16 -7.07 -22.99 311s Consumption_17 56.63 168.85 311s Consumption_18 -9.98 -27.00 311s Consumption_19 -55.29 -158.06 311s Consumption_20 34.10 107.77 311s Consumption_21 17.55 49.11 311s Consumption_22 -24.84 -71.70 311s Investment_2 0.00 0.00 311s Investment_3 0.00 0.00 311s Investment_4 0.00 0.00 311s Investment_5 0.00 0.00 311s Investment_6 0.00 0.00 311s Investment_8 0.00 0.00 311s Investment_9 0.00 0.00 311s Investment_10 0.00 0.00 311s Investment_11 0.00 0.00 311s Investment_12 0.00 0.00 311s Investment_13 0.00 0.00 311s Investment_14 0.00 0.00 311s Investment_15 0.00 0.00 311s Investment_16 0.00 0.00 311s Investment_17 0.00 0.00 311s Investment_18 0.00 0.00 311s Investment_19 0.00 0.00 311s Investment_20 0.00 0.00 311s Investment_21 0.00 0.00 311s Investment_22 0.00 0.00 311s PrivateWages_2 0.00 0.00 311s PrivateWages_3 0.00 0.00 311s PrivateWages_4 0.00 0.00 311s PrivateWages_5 0.00 0.00 311s PrivateWages_6 0.00 0.00 311s PrivateWages_8 0.00 0.00 311s PrivateWages_9 0.00 0.00 311s PrivateWages_10 0.00 0.00 311s PrivateWages_11 0.00 0.00 311s PrivateWages_12 0.00 0.00 311s PrivateWages_13 0.00 0.00 311s PrivateWages_14 0.00 0.00 311s PrivateWages_15 0.00 0.00 311s PrivateWages_16 0.00 0.00 311s PrivateWages_17 0.00 0.00 311s PrivateWages_18 0.00 0.00 311s PrivateWages_19 0.00 0.00 311s PrivateWages_20 0.00 0.00 311s PrivateWages_21 0.00 0.00 311s PrivateWages_22 0.00 0.00 311s Investment_(Intercept) Investment_corpProf 311s Consumption_2 0.0000 0.000 311s Consumption_3 0.0000 0.000 311s Consumption_4 0.0000 0.000 311s Consumption_5 0.0000 0.000 311s Consumption_6 0.0000 0.000 311s Consumption_8 0.0000 0.000 311s Consumption_9 0.0000 0.000 311s Consumption_10 0.0000 0.000 311s Consumption_11 0.0000 0.000 311s Consumption_12 0.0000 0.000 311s Consumption_13 0.0000 0.000 311s Consumption_14 0.0000 0.000 311s Consumption_15 0.0000 0.000 311s Consumption_16 0.0000 0.000 311s Consumption_17 0.0000 0.000 311s Consumption_18 0.0000 0.000 311s Consumption_19 0.0000 0.000 311s Consumption_20 0.0000 0.000 311s Consumption_21 0.0000 0.000 311s Consumption_22 0.0000 0.000 311s Investment_2 -1.1313 -14.660 311s Investment_3 0.2902 4.847 311s Investment_4 0.9027 17.274 311s Investment_5 -1.7434 -36.502 311s Investment_6 0.5695 11.088 311s Investment_8 1.6225 27.812 311s Investment_9 0.4166 8.119 311s Investment_10 2.0381 41.703 311s Investment_11 -0.8611 -14.505 311s Investment_12 -0.9091 -11.527 311s Investment_13 -1.1148 -9.946 311s Investment_14 1.3841 12.873 311s Investment_15 -0.2900 -3.710 311s Investment_16 0.0605 0.862 311s Investment_17 2.2439 33.101 311s Investment_18 -0.5390 -10.534 311s Investment_19 -3.9452 -76.375 311s Investment_20 0.4890 8.502 311s Investment_21 0.0864 1.737 311s Investment_22 0.4306 9.843 311s PrivateWages_2 0.0000 0.000 311s PrivateWages_3 0.0000 0.000 311s PrivateWages_4 0.0000 0.000 311s PrivateWages_5 0.0000 0.000 311s PrivateWages_6 0.0000 0.000 311s PrivateWages_8 0.0000 0.000 311s PrivateWages_9 0.0000 0.000 311s PrivateWages_10 0.0000 0.000 311s PrivateWages_11 0.0000 0.000 311s PrivateWages_12 0.0000 0.000 311s PrivateWages_13 0.0000 0.000 311s PrivateWages_14 0.0000 0.000 311s PrivateWages_15 0.0000 0.000 311s PrivateWages_16 0.0000 0.000 311s PrivateWages_17 0.0000 0.000 311s PrivateWages_18 0.0000 0.000 311s PrivateWages_19 0.0000 0.000 311s PrivateWages_20 0.0000 0.000 311s PrivateWages_21 0.0000 0.000 311s PrivateWages_22 0.0000 0.000 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_2 0.000 0.0 311s Consumption_3 0.000 0.0 311s Consumption_4 0.000 0.0 311s Consumption_5 0.000 0.0 311s Consumption_6 0.000 0.0 311s Consumption_8 0.000 0.0 311s Consumption_9 0.000 0.0 311s Consumption_10 0.000 0.0 311s Consumption_11 0.000 0.0 311s Consumption_12 0.000 0.0 311s Consumption_13 0.000 0.0 311s Consumption_14 0.000 0.0 311s Consumption_15 0.000 0.0 311s Consumption_16 0.000 0.0 311s Consumption_17 0.000 0.0 311s Consumption_18 0.000 0.0 311s Consumption_19 0.000 0.0 311s Consumption_20 0.000 0.0 311s Consumption_21 0.000 0.0 311s Consumption_22 0.000 0.0 311s Investment_2 -14.368 -206.8 311s Investment_3 3.598 53.0 311s Investment_4 15.256 166.5 311s Investment_5 -32.079 -330.7 311s Investment_6 11.048 109.7 311s Investment_8 31.801 330.0 311s Investment_9 8.248 86.5 311s Investment_10 43.003 429.2 311s Investment_11 -18.685 -185.7 311s Investment_12 -14.182 -197.0 311s Investment_13 -12.709 -237.8 311s Investment_14 9.689 286.6 311s Investment_15 -3.247 -58.6 311s Investment_16 0.744 12.0 311s Investment_17 31.414 443.6 311s Investment_18 -9.486 -107.7 311s Investment_19 -68.252 -796.1 311s Investment_20 7.482 97.7 311s Investment_21 1.642 17.4 311s Investment_22 9.085 88.0 311s PrivateWages_2 0.000 0.0 311s PrivateWages_3 0.000 0.0 311s PrivateWages_4 0.000 0.0 311s PrivateWages_5 0.000 0.0 311s PrivateWages_6 0.000 0.0 311s PrivateWages_8 0.000 0.0 311s PrivateWages_9 0.000 0.0 311s PrivateWages_10 0.000 0.0 311s PrivateWages_11 0.000 0.0 311s PrivateWages_12 0.000 0.0 311s PrivateWages_13 0.000 0.0 311s PrivateWages_14 0.000 0.0 311s PrivateWages_15 0.000 0.0 311s PrivateWages_16 0.000 0.0 311s PrivateWages_17 0.000 0.0 311s PrivateWages_18 0.000 0.0 311s PrivateWages_19 0.000 0.0 311s PrivateWages_20 0.000 0.0 311s PrivateWages_21 0.000 0.0 311s PrivateWages_22 0.000 0.0 311s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 311s Consumption_2 0.0000 0.00 0.00 311s Consumption_3 0.0000 0.00 0.00 311s Consumption_4 0.0000 0.00 0.00 311s Consumption_5 0.0000 0.00 0.00 311s Consumption_6 0.0000 0.00 0.00 311s Consumption_8 0.0000 0.00 0.00 311s Consumption_9 0.0000 0.00 0.00 311s Consumption_10 0.0000 0.00 0.00 311s Consumption_11 0.0000 0.00 0.00 311s Consumption_12 0.0000 0.00 0.00 311s Consumption_13 0.0000 0.00 0.00 311s Consumption_14 0.0000 0.00 0.00 311s Consumption_15 0.0000 0.00 0.00 311s Consumption_16 0.0000 0.00 0.00 311s Consumption_17 0.0000 0.00 0.00 311s Consumption_18 0.0000 0.00 0.00 311s Consumption_19 0.0000 0.00 0.00 311s Consumption_20 0.0000 0.00 0.00 311s Consumption_21 0.0000 0.00 0.00 311s Consumption_22 0.0000 0.00 0.00 311s Investment_2 0.0000 0.00 0.00 311s Investment_3 0.0000 0.00 0.00 311s Investment_4 0.0000 0.00 0.00 311s Investment_5 0.0000 0.00 0.00 311s Investment_6 0.0000 0.00 0.00 311s Investment_8 0.0000 0.00 0.00 311s Investment_9 0.0000 0.00 0.00 311s Investment_10 0.0000 0.00 0.00 311s Investment_11 0.0000 0.00 0.00 311s Investment_12 0.0000 0.00 0.00 311s Investment_13 0.0000 0.00 0.00 311s Investment_14 0.0000 0.00 0.00 311s Investment_15 0.0000 0.00 0.00 311s Investment_16 0.0000 0.00 0.00 311s Investment_17 0.0000 0.00 0.00 311s Investment_18 0.0000 0.00 0.00 311s Investment_19 0.0000 0.00 0.00 311s Investment_20 0.0000 0.00 0.00 311s Investment_21 0.0000 0.00 0.00 311s Investment_22 0.0000 0.00 0.00 311s PrivateWages_2 -1.9924 -93.78 -89.46 311s PrivateWages_3 0.4683 23.22 21.35 311s PrivateWages_4 1.4034 79.35 70.31 311s PrivateWages_5 -1.7870 -108.45 -102.22 311s PrivateWages_6 -0.3627 -21.98 -20.71 311s PrivateWages_8 1.1629 69.77 74.43 311s PrivateWages_9 1.2735 79.30 82.01 311s PrivateWages_10 2.2141 142.96 142.81 311s PrivateWages_11 -1.2912 -82.26 -86.51 311s PrivateWages_12 -0.0350 -1.92 -2.14 311s PrivateWages_13 -1.0438 -49.04 -55.74 311s PrivateWages_14 1.8016 75.90 79.81 311s PrivateWages_15 -0.3714 -19.02 -16.75 311s PrivateWages_16 -0.3904 -21.61 -19.40 311s PrivateWages_17 1.4934 85.71 81.24 311s PrivateWages_18 0.0279 1.88 1.75 311s PrivateWages_19 -3.8229 -261.91 -248.49 311s PrivateWages_20 0.7870 52.61 47.93 311s PrivateWages_21 -0.7415 -55.52 -51.54 311s PrivateWages_22 1.2062 104.79 91.31 311s PrivateWages_trend 311s Consumption_2 0.000 311s Consumption_3 0.000 311s Consumption_4 0.000 311s Consumption_5 0.000 311s Consumption_6 0.000 311s Consumption_8 0.000 311s Consumption_9 0.000 311s Consumption_10 0.000 311s Consumption_11 0.000 311s Consumption_12 0.000 311s Consumption_13 0.000 311s Consumption_14 0.000 311s Consumption_15 0.000 311s Consumption_16 0.000 311s Consumption_17 0.000 311s Consumption_18 0.000 311s Consumption_19 0.000 311s Consumption_20 0.000 311s Consumption_21 0.000 311s Consumption_22 0.000 311s Investment_2 0.000 311s Investment_3 0.000 311s Investment_4 0.000 311s Investment_5 0.000 311s Investment_6 0.000 311s Investment_8 0.000 311s Investment_9 0.000 311s Investment_10 0.000 311s Investment_11 0.000 311s Investment_12 0.000 311s Investment_13 0.000 311s Investment_14 0.000 311s Investment_15 0.000 311s Investment_16 0.000 311s Investment_17 0.000 311s Investment_18 0.000 311s Investment_19 0.000 311s Investment_20 0.000 311s Investment_21 0.000 311s Investment_22 0.000 311s PrivateWages_2 19.924 311s PrivateWages_3 -4.214 311s PrivateWages_4 -11.227 311s PrivateWages_5 12.509 311s PrivateWages_6 2.176 311s PrivateWages_8 -4.652 311s PrivateWages_9 -3.820 311s PrivateWages_10 -4.428 311s PrivateWages_11 1.291 311s PrivateWages_12 0.000 311s PrivateWages_13 -1.044 311s PrivateWages_14 3.603 311s PrivateWages_15 -1.114 311s PrivateWages_16 -1.562 311s PrivateWages_17 7.467 311s PrivateWages_18 0.168 311s PrivateWages_19 -26.760 311s PrivateWages_20 6.296 311s PrivateWages_21 -6.674 311s PrivateWages_22 12.062 311s [1] TRUE 311s > Bread 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_(Intercept) 99.945 -0.7943 311s Consumption_corpProf -0.794 0.7797 311s Consumption_corpProfLag -0.325 -0.5285 311s Consumption_wages -1.888 -0.0894 311s Investment_(Intercept) 0.000 0.0000 311s Investment_corpProf 0.000 0.0000 311s Investment_corpProfLag 0.000 0.0000 311s Investment_capitalLag 0.000 0.0000 311s PrivateWages_(Intercept) 0.000 0.0000 311s PrivateWages_gnp 0.000 0.0000 311s PrivateWages_gnpLag 0.000 0.0000 311s PrivateWages_trend 0.000 0.0000 311s Consumption_corpProfLag Consumption_wages 311s Consumption_(Intercept) -0.3246 -1.8878 311s Consumption_corpProf -0.5285 -0.0894 311s Consumption_corpProfLag 0.6654 -0.0384 311s Consumption_wages -0.0384 0.0965 311s Investment_(Intercept) 0.0000 0.0000 311s Investment_corpProf 0.0000 0.0000 311s Investment_corpProfLag 0.0000 0.0000 311s Investment_capitalLag 0.0000 0.0000 311s PrivateWages_(Intercept) 0.0000 0.0000 311s PrivateWages_gnp 0.0000 0.0000 311s PrivateWages_gnpLag 0.0000 0.0000 311s PrivateWages_trend 0.0000 0.0000 311s Investment_(Intercept) Investment_corpProf 311s Consumption_(Intercept) 0.0 0.000 311s Consumption_corpProf 0.0 0.000 311s Consumption_corpProfLag 0.0 0.000 311s Consumption_wages 0.0 0.000 311s Investment_(Intercept) 2446.2 -38.918 311s Investment_corpProf -38.9 1.252 311s Investment_corpProfLag 33.4 -1.090 311s Investment_capitalLag -11.6 0.177 311s PrivateWages_(Intercept) 0.0 0.000 311s PrivateWages_gnp 0.0 0.000 311s PrivateWages_gnpLag 0.0 0.000 311s PrivateWages_trend 0.0 0.000 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_(Intercept) 0.000 0.0000 311s Consumption_corpProf 0.000 0.0000 311s Consumption_corpProfLag 0.000 0.0000 311s Consumption_wages 0.000 0.0000 311s Investment_(Intercept) 33.384 -11.6216 311s Investment_corpProf -1.090 0.1774 311s Investment_corpProfLag 1.148 -0.1680 311s Investment_capitalLag -0.168 0.0567 311s PrivateWages_(Intercept) 0.000 0.0000 311s PrivateWages_gnp 0.000 0.0000 311s PrivateWages_gnpLag 0.000 0.0000 311s PrivateWages_trend 0.000 0.0000 311s PrivateWages_(Intercept) PrivateWages_gnp 311s Consumption_(Intercept) 0.000 0.0000 311s Consumption_corpProf 0.000 0.0000 311s Consumption_corpProfLag 0.000 0.0000 311s Consumption_wages 0.000 0.0000 311s Investment_(Intercept) 0.000 0.0000 311s Investment_corpProf 0.000 0.0000 311s Investment_corpProfLag 0.000 0.0000 311s Investment_capitalLag 0.000 0.0000 311s PrivateWages_(Intercept) 170.714 -0.9289 311s PrivateWages_gnp -0.929 0.1580 311s PrivateWages_gnpLag -1.948 -0.1473 311s PrivateWages_trend 2.164 -0.0424 311s PrivateWages_gnpLag PrivateWages_trend 311s Consumption_(Intercept) 0.000 0.0000 311s Consumption_corpProf 0.000 0.0000 311s Consumption_corpProfLag 0.000 0.0000 311s Consumption_wages 0.000 0.0000 311s Investment_(Intercept) 0.000 0.0000 311s Investment_corpProf 0.000 0.0000 311s Investment_corpProfLag 0.000 0.0000 311s Investment_capitalLag 0.000 0.0000 311s PrivateWages_(Intercept) -1.948 2.1641 311s PrivateWages_gnp -0.147 -0.0424 311s PrivateWages_gnpLag 0.186 0.0060 311s PrivateWages_trend 0.006 0.1151 311s > 311s > # SUR 311s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 311s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 311s > summary 311s 311s systemfit results 311s method: SUR 311s 311s N DF SSR detRCov OLS-R2 McElroy-R2 311s system 62 50 46.2 0.154 0.977 0.993 311s 311s N DF SSR MSE RMSE R2 Adj R2 311s Consumption 21 17 18.1 1.062 1.031 0.981 0.977 311s Investment 21 17 17.5 1.030 1.015 0.931 0.918 311s PrivateWages 20 16 10.6 0.663 0.814 0.987 0.984 311s 311s The covariance matrix of the residuals used for estimation 311s Consumption Investment PrivateWages 311s Consumption 0.8562 -0.0129 -0.371 311s Investment -0.0129 0.7548 0.159 311s PrivateWages -0.3706 0.1594 0.487 311s 311s The covariance matrix of the residuals 311s Consumption Investment PrivateWages 311s Consumption 0.8684 0.0078 -0.442 311s Investment 0.0078 0.7702 0.237 311s PrivateWages -0.4416 0.2366 0.531 311s 311s The correlations of the residuals 311s Consumption Investment PrivateWages 311s Consumption 1.00000 0.00562 -0.651 311s Investment 0.00562 1.00000 0.372 311s PrivateWages -0.65109 0.37198 1.000 311s 311s 311s SUR estimates for 'Consumption' (equation 1) 311s Model Formula: consump ~ corpProf + corpProfLag + wages 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 16.0647 1.1729 13.70 1.3e-10 *** 311s corpProf 0.2283 0.0775 2.94 0.0091 ** 311s corpProfLag 0.0723 0.0771 0.94 0.3615 311s wages 0.7930 0.0352 22.51 4.3e-14 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.031 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 18.06 MSE: 1.062 Root MSE: 1.031 311s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 311s 311s 311s SUR estimates for 'Investment' (equation 2) 311s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 12.3516 4.5762 2.70 0.01520 * 311s corpProf 0.4461 0.0818 5.45 4.3e-05 *** 311s corpProfLag 0.3609 0.0849 4.25 0.00054 *** 311s capitalLag -0.1224 0.0223 -5.47 4.1e-05 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.015 on 17 degrees of freedom 311s Number of observations: 21 Degrees of Freedom: 17 311s SSR: 17.514 MSE: 1.03 Root MSE: 1.015 311s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 311s 311s 311s SUR estimates for 'PrivateWages' (equation 3) 311s Model Formula: privWage ~ gnp + gnpLag + trend 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 1.5433 1.1371 1.36 0.19 311s gnp 0.4117 0.0279 14.77 9.6e-11 *** 311s gnpLag 0.1743 0.0317 5.50 4.8e-05 *** 311s trend 0.1550 0.0283 5.49 5.0e-05 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 0.814 on 16 degrees of freedom 311s Number of observations: 20 Degrees of Freedom: 16 311s SSR: 10.611 MSE: 0.663 Root MSE: 0.814 311s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 311s 311s > residuals 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 -0.27628 -0.3003 -1.0910 311s 3 -1.35400 -0.1239 0.5795 311s 4 -1.62816 1.1154 1.5172 311s 5 -0.56494 -1.4358 -0.0341 311s 6 -0.06584 0.3581 -0.2772 311s 7 0.83245 1.4526 NA 311s 8 1.28855 0.8290 -0.6896 311s 9 0.96709 -0.5092 0.3445 311s 10 -0.66705 1.2210 1.2429 311s 11 0.41992 0.2497 -0.3602 311s 12 -0.05971 0.0470 0.3068 311s 13 -0.08649 0.3096 -0.2426 311s 14 0.33124 0.3652 0.3591 311s 15 -0.00604 -0.1652 0.2710 311s 16 -0.01478 0.0124 -0.0207 311s 17 1.55472 1.0339 -0.8117 311s 18 -0.41250 0.0255 0.8398 311s 19 0.29322 -2.6293 -0.8283 311s 20 0.91756 -0.5906 -0.4091 311s 21 0.71583 -0.7036 -1.2154 311s 22 -2.26223 -0.5283 0.6207 311s > fitted 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 42.2 0.100 26.6 311s 3 46.4 2.024 28.7 311s 4 50.8 4.085 32.6 311s 5 51.2 4.436 33.9 311s 6 52.7 4.742 35.7 311s 7 54.3 4.147 NA 311s 8 54.9 3.371 38.6 311s 9 56.3 3.509 38.9 311s 10 58.5 3.879 40.1 311s 11 54.6 0.750 38.3 311s 12 51.0 -3.447 34.2 311s 13 45.7 -6.510 29.2 311s 14 46.2 -5.465 28.1 311s 15 48.7 -2.835 30.3 311s 16 51.3 -1.312 33.2 311s 17 56.1 1.066 37.6 311s 18 59.1 1.974 40.2 311s 19 57.2 0.729 39.0 311s 20 60.7 1.891 42.0 311s 21 64.3 4.004 46.2 311s 22 72.0 5.428 52.7 311s > predict 311s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 311s 1 NA NA NA NA 311s 2 42.2 0.414 41.3 43.0 311s 3 46.4 0.451 45.4 47.3 311s 4 50.8 0.296 50.2 51.4 311s 5 51.2 0.342 50.5 51.9 311s 6 52.7 0.342 52.0 53.4 311s 7 54.3 0.309 53.6 54.9 311s 8 54.9 0.282 54.3 55.5 311s 9 56.3 0.303 55.7 56.9 311s 10 58.5 0.321 57.8 59.1 311s 11 54.6 0.515 53.5 55.6 311s 12 51.0 0.418 50.1 51.8 311s 13 45.7 0.548 44.6 46.8 311s 14 46.2 0.528 45.1 47.2 311s 15 48.7 0.333 48.0 49.4 311s 16 51.3 0.296 50.7 51.9 311s 17 56.1 0.321 55.5 56.8 311s 18 59.1 0.287 58.5 59.7 311s 19 57.2 0.325 56.6 57.9 311s 20 60.7 0.383 59.9 61.5 311s 21 64.3 0.382 63.5 65.1 311s 22 72.0 0.599 70.8 73.2 311s Investment.pred Investment.se.fit Investment.lwr Investment.upr 311s 1 NA NA NA NA 311s 2 0.100 0.511 -0.926 1.127 311s 3 2.024 0.425 1.170 2.878 311s 4 4.085 0.378 3.325 4.845 311s 5 4.436 0.313 3.806 5.065 311s 6 4.742 0.296 4.147 5.336 311s 7 4.147 0.279 3.586 4.709 311s 8 3.371 0.250 2.868 3.874 311s 9 3.509 0.331 2.845 4.174 311s 10 3.879 0.380 3.116 4.642 311s 11 0.750 0.512 -0.279 1.779 311s 12 -3.447 0.433 -4.316 -2.578 311s 13 -6.510 0.527 -7.568 -5.451 311s 14 -5.465 0.587 -6.645 -4.285 311s 15 -2.835 0.320 -3.477 -2.193 311s 16 -1.312 0.274 -1.863 -0.761 311s 17 1.066 0.296 0.472 1.661 311s 18 1.974 0.208 1.558 2.391 311s 19 0.729 0.265 0.197 1.262 311s 20 1.891 0.311 1.266 2.515 311s 21 4.004 0.283 3.435 4.572 311s 22 5.428 0.393 4.640 6.217 311s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 311s 1 NA NA NA NA 311s 2 26.6 0.318 26.0 27.2 311s 3 28.7 0.317 28.1 29.4 311s 4 32.6 0.315 32.0 33.2 311s 5 33.9 0.243 33.4 34.4 311s 6 35.7 0.242 35.2 36.2 311s 7 NA NA NA NA 311s 8 38.6 0.247 38.1 39.1 311s 9 38.9 0.236 38.4 39.3 311s 10 40.1 0.227 39.6 40.5 311s 11 38.3 0.306 37.6 38.9 311s 12 34.2 0.312 33.6 34.8 311s 13 29.2 0.376 28.5 30.0 311s 14 28.1 0.337 27.5 28.8 311s 15 30.3 0.328 29.7 31.0 311s 16 33.2 0.274 32.7 33.8 311s 17 37.6 0.266 37.1 38.1 311s 18 40.2 0.213 39.7 40.6 311s 19 39.0 0.310 38.4 39.7 311s 20 42.0 0.282 41.4 42.6 311s 21 46.2 0.300 45.6 46.8 311s 22 52.7 0.451 51.8 53.6 311s > model.frame 311s [1] TRUE 311s > model.matrix 311s [1] TRUE 311s > nobs 311s [1] 62 311s > linearHypothesis 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 51 311s 2 50 1 1.39 0.24 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 51 311s 2 50 1 1.7 0.2 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 51 311s 2 50 1 1.7 0.19 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 50 2 0.72 0.49 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 52 311s 2 50 2 0.87 0.42 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 52 311s 2 50 2 1.75 0.42 311s > logLik 311s 'log Lik.' -69.4 (df=18) 311s 'log Lik.' -78.2 (df=18) 311s Estimating function 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_2 -0.49572 -6.1470 311s Consumption_3 -2.42943 -41.0573 311s Consumption_4 -2.92134 -53.7526 311s Consumption_5 -1.01365 -19.6648 311s Consumption_6 -0.11814 -2.3746 311s Consumption_7 1.49363 29.2752 311s Consumption_8 2.31199 45.7775 311s Consumption_9 1.73521 36.6129 311s Consumption_10 -1.19687 -25.9720 311s Consumption_11 0.75344 11.7537 311s Consumption_12 -0.10714 -1.2214 311s Consumption_13 -0.15519 -1.0863 311s Consumption_14 0.59434 6.6566 311s Consumption_15 -0.01083 -0.1332 311s Consumption_16 -0.02651 -0.3712 311s Consumption_17 2.78956 49.0963 311s Consumption_18 -0.74013 -12.8043 311s Consumption_19 0.52610 8.0494 311s Consumption_20 1.64635 31.2806 311s Consumption_21 1.28438 27.1004 311s Consumption_22 -4.05902 -95.3870 311s Investment_2 0.08318 1.0314 311s Investment_3 0.03433 0.5802 311s Investment_4 -0.30897 -5.6851 311s Investment_5 0.39771 7.7155 311s Investment_6 -0.09921 -1.9941 311s Investment_7 -0.40237 -7.8864 311s Investment_8 -0.22963 -4.5466 311s Investment_9 0.14106 2.9764 311s Investment_10 -0.33822 -7.3394 311s Investment_11 -0.06917 -1.0790 311s Investment_12 -0.01303 -0.1485 311s Investment_13 -0.08575 -0.6003 311s Investment_14 -0.10117 -1.1331 311s Investment_15 0.04575 0.5628 311s Investment_16 -0.00344 -0.0482 311s Investment_17 -0.28639 -5.0405 311s Investment_18 -0.00707 -0.1223 311s Investment_19 0.72832 11.1433 311s Investment_20 0.16360 3.1083 311s Investment_21 0.19490 4.1123 311s Investment_22 0.14635 3.4391 311s PrivateWages_2 -1.58896 -19.7031 311s PrivateWages_3 0.84394 14.2626 311s PrivateWages_4 2.20977 40.6598 311s PrivateWages_5 -0.04965 -0.9631 311s PrivateWages_6 -0.40373 -8.1150 311s PrivateWages_8 -1.00430 -19.8851 311s PrivateWages_9 0.50179 10.5878 311s PrivateWages_10 1.81021 39.2815 311s PrivateWages_11 -0.52455 -8.1830 311s PrivateWages_12 0.44676 5.0931 311s PrivateWages_13 -0.35330 -2.4731 311s PrivateWages_14 0.52303 5.8579 311s PrivateWages_15 0.39464 4.8541 311s PrivateWages_16 -0.03009 -0.4213 311s PrivateWages_17 -1.18225 -20.8075 311s PrivateWages_18 1.22307 21.1590 311s PrivateWages_19 -1.20633 -18.4569 311s PrivateWages_20 -0.59580 -11.3203 311s PrivateWages_21 -1.77014 -37.3499 311s PrivateWages_22 0.90407 21.2457 311s Consumption_corpProfLag Consumption_wages 311s Consumption_2 -6.2957 -13.979 311s Consumption_3 -30.1249 -78.228 311s Consumption_4 -49.3706 -108.090 311s Consumption_5 -18.6512 -37.505 311s Consumption_6 -2.2919 -4.560 311s Consumption_7 30.0220 60.791 311s Consumption_8 45.3151 95.948 311s Consumption_9 34.3571 74.440 311s Consumption_10 -25.2539 -54.218 311s Consumption_11 16.3496 31.720 311s Consumption_12 -1.6714 -4.211 311s Consumption_13 -1.7691 -5.323 311s Consumption_14 4.1604 20.267 311s Consumption_15 -0.1213 -0.396 311s Consumption_16 -0.3261 -1.042 311s Consumption_17 39.0539 123.299 311s Consumption_18 -13.0263 -35.304 311s Consumption_19 9.1016 24.148 311s Consumption_20 25.1891 81.330 311s Consumption_21 24.4032 68.072 311s Consumption_22 -85.6453 -250.847 311s Investment_2 1.0563 2.346 311s Investment_3 0.4257 1.105 311s Investment_4 -5.2216 -11.432 311s Investment_5 7.3178 14.715 311s Investment_6 -1.9246 -3.829 311s Investment_7 -8.0876 -16.376 311s Investment_8 -4.5007 -9.530 311s Investment_9 2.7930 6.052 311s Investment_10 -7.1364 -15.321 311s Investment_11 -1.5009 -2.912 311s Investment_12 -0.2033 -0.512 311s Investment_13 -0.9776 -2.941 311s Investment_14 -0.7082 -3.450 311s Investment_15 0.5124 1.675 311s Investment_16 -0.0423 -0.135 311s Investment_17 -4.0095 -12.659 311s Investment_18 -0.1244 -0.337 311s Investment_19 12.5999 33.430 311s Investment_20 2.5030 8.082 311s Investment_21 3.7031 10.330 311s Investment_22 3.0879 9.044 311s PrivateWages_2 -20.1798 -44.809 311s PrivateWages_3 10.4649 27.175 311s PrivateWages_4 37.3452 81.762 311s PrivateWages_5 -0.9135 -1.837 311s PrivateWages_6 -7.8324 -15.584 311s PrivateWages_8 -19.6842 -41.678 311s PrivateWages_9 9.9355 21.527 311s PrivateWages_10 38.1953 82.002 311s PrivateWages_11 -11.3827 -22.084 311s PrivateWages_12 6.9695 17.558 311s PrivateWages_13 -4.0277 -12.118 311s PrivateWages_14 3.6612 17.835 311s PrivateWages_15 4.4200 14.444 311s PrivateWages_16 -0.3701 -1.183 311s PrivateWages_17 -16.5515 -52.255 311s PrivateWages_18 21.5260 58.340 311s PrivateWages_19 -20.8696 -55.371 311s PrivateWages_20 -9.1158 -29.433 311s PrivateWages_21 -33.6326 -93.817 311s PrivateWages_22 19.0759 55.872 311s Investment_(Intercept) Investment_corpProf 311s Consumption_2 0.07653 0.9490 311s Consumption_3 0.37506 6.3385 311s Consumption_4 0.45100 8.2984 311s Consumption_5 0.15649 3.0359 311s Consumption_6 0.01824 0.3666 311s Consumption_7 -0.23059 -4.5195 311s Consumption_8 -0.35693 -7.0672 311s Consumption_9 -0.26788 -5.6523 311s Consumption_10 0.18477 4.0096 311s Consumption_11 -0.11632 -1.8145 311s Consumption_12 0.01654 0.1886 311s Consumption_13 0.02396 0.1677 311s Consumption_14 -0.09175 -1.0277 311s Consumption_15 0.00167 0.0206 311s Consumption_16 0.00409 0.0573 311s Consumption_17 -0.43066 -7.5796 311s Consumption_18 0.11426 1.9767 311s Consumption_19 -0.08122 -1.2427 311s Consumption_20 -0.25417 -4.8291 311s Consumption_21 -0.19828 -4.1838 311s Consumption_22 0.62664 14.7260 311s Investment_2 -0.44022 -5.4587 311s Investment_3 -0.18170 -3.0707 311s Investment_4 1.63526 30.0888 311s Investment_5 -2.10489 -40.8348 311s Investment_6 0.52506 10.5537 311s Investment_7 2.12955 41.7392 311s Investment_8 1.21532 24.0633 311s Investment_9 -0.74658 -15.7528 311s Investment_10 1.79005 38.8441 311s Investment_11 0.36607 5.7107 311s Investment_12 0.06896 0.7861 311s Investment_13 0.45385 3.1769 311s Investment_14 0.53544 5.9969 311s Investment_15 -0.24215 -2.9785 311s Investment_16 0.01822 0.2551 311s Investment_17 1.51576 26.6774 311s Investment_18 0.03741 0.6472 311s Investment_19 -3.85468 -58.9766 311s Investment_20 -0.86584 -16.4509 311s Investment_21 -1.03151 -21.7649 311s Investment_22 -0.77455 -18.2019 311s PrivateWages_2 0.75366 9.3454 311s PrivateWages_3 -0.40029 -6.7649 311s PrivateWages_4 -1.04812 -19.2855 311s PrivateWages_5 0.02355 0.4568 311s PrivateWages_6 0.19149 3.8490 311s PrivateWages_8 0.47635 9.4317 311s PrivateWages_9 -0.23801 -5.0219 311s PrivateWages_10 -0.85860 -18.6317 311s PrivateWages_11 0.24880 3.8813 311s PrivateWages_12 -0.21191 -2.4157 311s PrivateWages_13 0.16758 1.1730 311s PrivateWages_14 -0.24808 -2.7785 311s PrivateWages_15 -0.18718 -2.3024 311s PrivateWages_16 0.01427 0.1998 311s PrivateWages_17 0.56075 9.8693 311s PrivateWages_18 -0.58012 -10.0360 311s PrivateWages_19 0.57218 8.7543 311s PrivateWages_20 0.28260 5.3694 311s PrivateWages_21 0.83960 17.7155 311s PrivateWages_22 -0.42881 -10.0771 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_2 0.9719 13.990 311s Consumption_3 4.6507 68.486 311s Consumption_4 7.6219 83.210 311s Consumption_5 2.8794 29.686 311s Consumption_6 0.3538 3.515 311s Consumption_7 -4.6348 -45.611 311s Consumption_8 -6.9958 -72.599 311s Consumption_9 -5.3041 -55.613 311s Consumption_10 3.8987 38.913 311s Consumption_11 -2.5241 -25.090 311s Consumption_12 0.2580 3.584 311s Consumption_13 0.2731 5.110 311s Consumption_14 -0.6423 -19.002 311s Consumption_15 0.0187 0.338 311s Consumption_16 0.0503 0.815 311s Consumption_17 -6.0292 -85.141 311s Consumption_18 2.0110 22.830 311s Consumption_19 -1.4051 -16.390 311s Consumption_20 -3.8887 -50.808 311s Consumption_21 -3.7674 -39.895 311s Consumption_22 13.2221 128.147 311s Investment_2 -5.5908 -80.472 311s Investment_3 -2.2531 -33.179 311s Investment_4 27.6359 301.706 311s Investment_5 -38.7299 -399.297 311s Investment_6 10.1862 101.179 311s Investment_7 42.8040 421.225 311s Investment_8 23.8203 247.196 311s Investment_9 -14.7822 -154.989 311s Investment_10 37.7701 376.985 311s Investment_11 7.9437 78.961 311s Investment_12 1.0757 14.943 311s Investment_13 5.1739 96.806 311s Investment_14 3.7481 110.889 311s Investment_15 -2.7121 -48.915 311s Investment_16 0.2241 3.626 311s Investment_17 21.2206 299.666 311s Investment_18 0.6585 7.475 311s Investment_19 -66.6860 -777.874 311s Investment_20 -13.2473 -173.081 311s Investment_21 -19.5987 -207.540 311s Investment_22 -16.3429 -158.395 311s PrivateWages_2 9.5715 137.769 311s PrivateWages_3 -4.9636 -73.093 311s PrivateWages_4 -17.7133 -193.379 311s PrivateWages_5 0.4333 4.467 311s PrivateWages_6 3.7150 36.901 311s PrivateWages_8 9.3365 96.890 311s PrivateWages_9 -4.7125 -49.410 311s PrivateWages_10 -18.1165 -180.822 311s PrivateWages_11 5.3990 53.666 311s PrivateWages_12 -3.3057 -45.920 311s PrivateWages_13 1.9104 35.744 311s PrivateWages_14 -1.7366 -51.377 311s PrivateWages_15 -2.0965 -37.811 311s PrivateWages_16 0.1756 2.840 311s PrivateWages_17 7.8506 110.861 311s PrivateWages_18 -10.2100 -115.907 311s PrivateWages_19 9.8987 115.466 311s PrivateWages_20 4.3237 56.491 311s PrivateWages_21 15.9524 168.927 311s PrivateWages_22 -9.0479 -87.692 311s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 311s Consumption_2 -0.40239 -18.349 -18.067 311s Consumption_3 -1.97202 -98.798 -89.924 311s Consumption_4 -2.37131 -135.639 -118.803 311s Consumption_5 -0.82280 -46.982 -47.064 311s Consumption_6 -0.09590 -5.850 -5.476 311s Consumption_7 0.00000 0.000 0.000 311s Consumption_8 1.87670 120.859 120.108 311s Consumption_9 1.40851 90.849 90.708 311s Consumption_10 -0.97152 -65.092 -62.663 311s Consumption_11 0.61158 37.429 40.976 311s Consumption_12 -0.08697 -4.644 -5.322 311s Consumption_13 -0.12597 -5.580 -6.727 311s Consumption_14 0.48244 21.758 21.372 311s Consumption_15 -0.00879 -0.437 -0.396 311s Consumption_16 -0.02152 -1.171 -1.070 311s Consumption_17 2.26435 141.975 123.181 311s Consumption_18 -0.60078 -39.051 -37.669 311s Consumption_19 0.42705 26.007 27.758 311s Consumption_20 1.33638 92.878 81.385 311s Consumption_21 1.04256 78.922 72.458 311s Consumption_22 -3.29479 -291.260 -249.416 311s Investment_2 0.20743 9.459 9.314 311s Investment_3 0.08562 4.289 3.904 311s Investment_4 -0.77054 -44.075 -38.604 311s Investment_5 0.99183 56.634 56.733 311s Investment_6 -0.24741 -15.092 -14.127 311s Investment_7 0.00000 0.000 0.000 311s Investment_8 -0.57266 -36.880 -36.650 311s Investment_9 0.35179 22.690 22.655 311s Investment_10 -0.84348 -56.513 -54.405 311s Investment_11 -0.17249 -10.557 -11.557 311s Investment_12 -0.03249 -1.735 -1.989 311s Investment_13 -0.21385 -9.474 -11.420 311s Investment_14 -0.25230 -11.379 -11.177 311s Investment_15 0.11410 5.671 5.146 311s Investment_16 -0.00859 -0.467 -0.427 311s Investment_17 -0.71423 -44.782 -38.854 311s Investment_18 -0.01763 -1.146 -1.105 311s Investment_19 1.81634 110.615 118.062 311s Investment_20 0.40799 28.355 24.846 311s Investment_21 0.48605 36.794 33.781 311s Investment_22 0.36497 32.263 27.628 311s PrivateWages_2 -3.69675 -168.572 -165.984 311s PrivateWages_3 1.96345 98.369 89.533 311s PrivateWages_4 5.14109 294.070 257.568 311s PrivateWages_5 -0.11550 -6.595 -6.607 311s PrivateWages_6 -0.93929 -57.297 -53.633 311s PrivateWages_8 -2.33652 -150.472 -149.537 311s PrivateWages_9 1.16743 75.299 75.183 311s PrivateWages_10 4.21148 282.169 271.641 311s PrivateWages_11 -1.22037 -74.687 -81.765 311s PrivateWages_12 1.03941 55.504 63.612 311s PrivateWages_13 -0.82197 -36.413 -43.893 311s PrivateWages_14 1.21684 54.880 53.906 311s PrivateWages_15 0.91815 45.632 41.409 311s PrivateWages_16 -0.07001 -3.809 -3.480 311s PrivateWages_17 -2.75052 -172.458 -149.628 311s PrivateWages_18 2.84549 184.957 178.412 311s PrivateWages_19 -2.80656 -170.920 -182.427 311s PrivateWages_20 -1.38615 -96.338 -84.417 311s PrivateWages_21 -4.11826 -311.753 -286.219 311s PrivateWages_22 2.10334 185.935 159.223 311s PrivateWages_trend 311s Consumption_2 4.0239 311s Consumption_3 17.7482 311s Consumption_4 18.9705 311s Consumption_5 5.7596 311s Consumption_6 0.5754 311s Consumption_7 0.0000 311s Consumption_8 -7.5068 311s Consumption_9 -4.2255 311s Consumption_10 1.9430 311s Consumption_11 -0.6116 311s Consumption_12 0.0000 311s Consumption_13 -0.1260 311s Consumption_14 0.9649 311s Consumption_15 -0.0264 311s Consumption_16 -0.0861 311s Consumption_17 11.3217 311s Consumption_18 -3.6047 311s Consumption_19 2.9894 311s Consumption_20 10.6910 311s Consumption_21 9.3830 311s Consumption_22 -32.9479 311s Investment_2 -2.0743 311s Investment_3 -0.7706 311s Investment_4 6.1643 311s Investment_5 -6.9428 311s Investment_6 1.4845 311s Investment_7 0.0000 311s Investment_8 2.2907 311s Investment_9 -1.0554 311s Investment_10 1.6870 311s Investment_11 0.1725 311s Investment_12 0.0000 311s Investment_13 -0.2139 311s Investment_14 -0.5046 311s Investment_15 0.3423 311s Investment_16 -0.0343 311s Investment_17 -3.5712 311s Investment_18 -0.1058 311s Investment_19 12.7144 311s Investment_20 3.2639 311s Investment_21 4.3745 311s Investment_22 3.6497 311s PrivateWages_2 36.9675 311s PrivateWages_3 -17.6711 311s PrivateWages_4 -41.1287 311s PrivateWages_5 0.8085 311s PrivateWages_6 5.6357 311s PrivateWages_8 9.3461 311s PrivateWages_9 -3.5023 311s PrivateWages_10 -8.4230 311s PrivateWages_11 1.2204 311s PrivateWages_12 0.0000 311s PrivateWages_13 -0.8220 311s PrivateWages_14 2.4337 311s PrivateWages_15 2.7544 311s PrivateWages_16 -0.2801 311s PrivateWages_17 -13.7526 311s PrivateWages_18 17.0729 311s PrivateWages_19 -19.6459 311s PrivateWages_20 -11.0892 311s PrivateWages_21 -37.0644 311s PrivateWages_22 21.0334 311s [1] TRUE 311s > Bread 311s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 311s [1,] 85.2889 -0.01362 -0.83841 311s [2,] -0.0136 0.37283 -0.23220 311s [3,] -0.8384 -0.23220 0.36858 311s [4,] -1.6590 -0.05994 -0.03120 311s [5,] -3.1844 -0.68255 0.70355 311s [6,] 0.0595 0.01846 -0.01774 311s [7,] -0.0239 -0.01745 0.02009 311s [8,] 0.0127 0.00329 -0.00362 311s [9,] -36.0142 0.07978 1.66083 311s [10,] 0.3888 -0.06209 0.04032 311s [11,] 0.2001 0.06287 -0.07012 311s [12,] 0.1814 0.03185 0.02619 311s Consumption_wages Investment_(Intercept) Investment_corpProf 311s [1,] -1.66e+00 -3.184 0.05950 311s [2,] -5.99e-02 -0.683 0.01846 311s [3,] -3.12e-02 0.704 -0.01774 311s [4,] 7.69e-02 0.082 -0.00204 311s [5,] 8.20e-02 1298.386 -12.39923 311s [6,] -2.04e-03 -12.399 0.41486 311s [7,] -2.16e-05 9.908 -0.35328 311s [8,] -2.54e-04 -6.230 0.05576 311s [9,] 1.50e-01 24.451 -0.18195 311s [10,] 6.53e-06 0.391 0.02158 311s [11,] -2.68e-03 -0.821 -0.01913 311s [12,] -2.78e-02 -0.890 0.00590 311s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 311s [1,] -2.39e-02 0.012670 -36.0142 311s [2,] -1.75e-02 0.003286 0.0798 311s [3,] 2.01e-02 -0.003616 1.6608 311s [4,] -2.16e-05 -0.000254 0.1499 311s [5,] 9.91e+00 -6.230058 24.4513 311s [6,] -3.53e-01 0.055757 -0.1819 311s [7,] 4.47e-01 -0.056152 -0.6460 311s [8,] -5.62e-02 0.030966 -0.0512 311s [9,] -6.46e-01 -0.051180 80.1680 311s [10,] -1.22e-02 -0.002778 -0.3588 311s [11,] 2.36e-02 0.003775 -0.9890 311s [12,] -1.61e-02 0.005268 0.9201 311s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 311s [1,] 3.89e-01 0.20005 0.18143 311s [2,] -6.21e-02 0.06287 0.03185 311s [3,] 4.03e-02 -0.07012 0.02619 311s [4,] 6.53e-06 -0.00268 -0.02782 311s [5,] 3.91e-01 -0.82129 -0.89038 311s [6,] 2.16e-02 -0.01913 0.00590 311s [7,] -1.22e-02 0.02360 -0.01606 311s [8,] -2.78e-03 0.00377 0.00527 311s [9,] -3.59e-01 -0.98896 0.92007 311s [10,] 4.82e-02 -0.04360 -0.01308 311s [11,] -4.36e-02 0.06217 -0.00244 311s [12,] -1.31e-02 -0.00244 0.04948 311s > 311s > # 3SLS 311s > summary 311s 311s systemfit results 311s method: 3SLS 311s 311s N DF SSR detRCov OLS-R2 McElroy-R2 311s system 60 48 62.6 0.265 0.968 0.994 311s 311s N DF SSR MSE RMSE R2 Adj R2 311s Consumption 20 16 17.8 1.114 1.06 0.981 0.977 311s Investment 20 16 34.3 2.143 1.46 0.853 0.825 311s PrivateWages 20 16 10.5 0.656 0.81 0.987 0.984 311s 311s The covariance matrix of the residuals used for estimation 311s Consumption Investment PrivateWages 311s Consumption 1.034 0.309 -0.383 311s Investment 0.309 1.151 0.202 311s PrivateWages -0.383 0.202 0.487 311s 311s The covariance matrix of the residuals 311s Consumption Investment PrivateWages 311s Consumption 0.891 0.304 -0.391 311s Investment 0.304 1.715 0.388 311s PrivateWages -0.391 0.388 0.525 311s 311s The correlations of the residuals 311s Consumption Investment PrivateWages 311s Consumption 1.000 0.246 -0.571 311s Investment 0.246 1.000 0.409 311s PrivateWages -0.571 0.409 1.000 311s 311s 311s 3SLS estimates for 'Consumption' (equation 1) 311s Model Formula: consump ~ corpProf + corpProfLag + wages 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 16.3668 1.3024 12.57 1.1e-09 *** 311s corpProf 0.1186 0.1073 1.10 0.29 311s corpProfLag 0.1448 0.1008 1.44 0.17 311s wages 0.8006 0.0391 20.47 6.7e-13 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.056 on 16 degrees of freedom 311s Number of observations: 20 Degrees of Freedom: 16 311s SSR: 17.825 MSE: 1.114 Root MSE: 1.056 311s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 311s 311s 311s 3SLS estimates for 'Investment' (equation 2) 311s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 24.8872 6.2956 3.95 0.00114 ** 311s corpProf 0.0702 0.1458 0.48 0.63648 311s corpProfLag 0.6688 0.1402 4.77 0.00021 *** 311s capitalLag -0.1786 0.0303 -5.90 2.3e-05 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 1.464 on 16 degrees of freedom 311s Number of observations: 20 Degrees of Freedom: 16 311s SSR: 34.295 MSE: 2.143 Root MSE: 1.464 311s Multiple R-Squared: 0.853 Adjusted R-Squared: 0.825 311s 311s 311s 3SLS estimates for 'PrivateWages' (equation 3) 311s Model Formula: privWage ~ gnp + gnpLag + trend 311s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 311s gnpLag 311s 311s Estimate Std. Error t value Pr(>|t|) 311s (Intercept) 1.6387 1.1457 1.43 0.17188 311s gnp 0.4062 0.0324 12.52 1.1e-09 *** 311s gnpLag 0.1784 0.0347 5.14 1.0e-04 *** 311s trend 0.1435 0.0292 4.91 0.00016 *** 311s --- 311s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 311s 311s Residual standard error: 0.81 on 16 degrees of freedom 311s Number of observations: 20 Degrees of Freedom: 16 311s SSR: 10.497 MSE: 0.656 Root MSE: 0.81 311s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 311s 311s > residuals 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 -0.3538 -1.795 -1.2388 311s 3 -0.9465 0.154 0.4649 311s 4 -1.4189 0.678 1.4344 311s 5 -0.3546 -1.666 -0.1354 311s 6 0.1366 0.251 -0.3452 311s 7 NA NA NA 311s 8 1.4213 1.150 -0.7445 311s 9 1.2173 0.476 0.3001 311s 10 -0.4636 2.200 1.2232 311s 11 -0.0650 -0.962 -0.4104 311s 12 -0.5422 -0.808 0.2495 311s 13 -0.7092 -1.098 -0.3057 311s 14 0.4898 1.542 0.3497 311s 15 -0.0502 -0.155 0.2949 311s 16 0.0272 0.154 0.0214 311s 17 1.8311 1.932 -0.7322 311s 18 -0.4567 -0.180 0.9090 311s 19 0.0650 -3.381 -0.7795 311s 20 1.2135 0.557 -0.2847 311s 21 0.9466 0.167 -1.0812 311s 22 -1.9877 0.784 0.8102 311s > fitted 311s Consumption Investment PrivateWages 311s 1 NA NA NA 311s 2 42.3 1.595 26.7 311s 3 45.9 1.746 28.8 311s 4 50.6 4.522 32.7 311s 5 51.0 4.666 34.0 311s 6 52.5 4.849 35.7 311s 7 NA NA NA 311s 8 54.8 3.050 38.6 311s 9 56.1 2.524 38.9 311s 10 58.3 2.900 40.1 311s 11 55.1 1.962 38.3 311s 12 51.4 -2.592 34.3 311s 13 46.3 -5.102 29.3 311s 14 46.0 -6.642 28.2 311s 15 48.8 -2.845 30.3 311s 16 51.3 -1.454 33.2 311s 17 55.9 0.168 37.5 311s 18 59.2 2.180 40.1 311s 19 57.4 1.481 39.0 311s 20 60.4 0.743 41.9 311s 21 64.1 3.133 46.1 311s 22 71.7 4.116 52.5 311s > predict 311s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 311s 1 NA NA NA NA 311s 2 42.3 0.468 39.8 44.7 311s 3 45.9 0.543 43.4 48.5 311s 4 50.6 0.352 48.3 53.0 311s 5 51.0 0.407 48.6 53.4 311s 6 52.5 0.411 50.1 54.9 311s 7 NA NA NA NA 311s 8 54.8 0.340 52.4 57.1 311s 9 56.1 0.372 53.7 58.5 311s 10 58.3 0.387 55.9 60.6 311s 11 55.1 0.687 52.4 57.7 311s 12 51.4 0.558 48.9 54.0 311s 13 46.3 0.713 43.6 49.0 311s 14 46.0 0.599 43.4 48.6 311s 15 48.8 0.368 46.4 51.1 311s 16 51.3 0.326 48.9 53.6 311s 17 55.9 0.388 53.5 58.3 311s 18 59.2 0.319 56.8 61.5 311s 19 57.4 0.391 55.0 59.8 311s 20 60.4 0.457 57.9 62.8 311s 21 64.1 0.437 61.6 66.5 311s 22 71.7 0.674 69.0 74.3 311s Investment.pred Investment.se.fit Investment.lwr Investment.upr 311s 1 NA NA NA NA 311s 2 1.595 0.731 -1.8742 5.065 311s 3 1.746 0.533 -1.5566 5.050 311s 4 4.522 0.484 1.2530 7.791 311s 5 4.666 0.406 1.4458 7.887 311s 6 4.849 0.386 1.6390 8.058 311s 7 NA NA NA NA 311s 8 3.050 0.325 -0.1296 6.229 311s 9 2.524 0.467 -0.7334 5.782 311s 10 2.900 0.515 -0.3900 6.190 311s 11 1.962 0.769 -1.5438 5.467 311s 12 -2.592 0.608 -5.9519 0.769 311s 13 -5.102 0.774 -8.6129 -1.592 311s 14 -6.642 0.807 -10.1867 -3.098 311s 15 -2.845 0.395 -6.0599 0.370 311s 16 -1.454 0.341 -4.6409 1.733 311s 17 0.168 0.442 -3.0739 3.410 311s 18 2.180 0.281 -0.9807 5.340 311s 19 1.481 0.414 -1.7440 4.706 311s 20 0.743 0.492 -2.5310 4.017 311s 21 3.133 0.414 -0.0924 6.358 311s 22 4.116 0.583 0.7756 7.457 311s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 311s 1 NA NA NA NA 311s 2 26.7 0.322 24.9 28.6 311s 3 28.8 0.328 27.0 30.7 311s 4 32.7 0.340 30.8 34.5 311s 5 34.0 0.250 32.2 35.8 311s 6 35.7 0.257 33.9 37.5 311s 7 NA NA NA NA 311s 8 38.6 0.254 36.8 40.4 311s 9 38.9 0.241 37.1 40.7 311s 10 40.1 0.235 38.3 41.9 311s 11 38.3 0.325 36.5 40.2 311s 12 34.3 0.349 32.4 36.1 311s 13 29.3 0.425 27.4 31.2 311s 14 28.2 0.340 26.3 30.0 311s 15 30.3 0.326 28.5 32.2 311s 16 33.2 0.272 31.4 35.0 311s 17 37.5 0.273 35.7 39.3 311s 18 40.1 0.214 38.3 41.9 311s 19 39.0 0.336 37.1 40.8 311s 20 41.9 0.290 40.1 43.7 311s 21 46.1 0.305 44.2 47.9 311s 22 52.5 0.479 50.5 54.5 311s > model.frame 311s [1] TRUE 311s > model.matrix 311s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 311s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 311s [3] "Numeric: lengths (744, 720) differ" 311s > nobs 311s [1] 60 311s > linearHypothesis 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 49 311s 2 48 1 0.22 0.64 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 49 311s 2 48 1 0.29 0.59 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 49 311s 2 48 1 0.29 0.59 311s Linear hypothesis test (Theil's F test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 50 311s 2 48 2 0.29 0.75 311s Linear hypothesis test (F statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df F Pr(>F) 311s 1 50 311s 2 48 2 0.38 0.68 311s Linear hypothesis test (Chi^2 statistic of a Wald test) 311s 311s Hypothesis: 311s Consumption_corpProf + Investment_capitalLag = 0 311s Consumption_corpProfLag - PrivateWages_trend = 0 311s 311s Model 1: restricted model 311s Model 2: kleinModel 311s 311s Res.Df Df Chisq Pr(>Chisq) 311s 1 50 311s 2 48 2 0.77 0.68 311s > logLik 311s 'log Lik.' -71.9 (df=18) 311s 'log Lik.' -82.9 (df=18) 311s Estimating function 311s Consumption_(Intercept) Consumption_corpProf 311s Consumption_2 -2.1852 -28.316 311s Consumption_3 -1.2615 -21.074 311s Consumption_4 -0.7432 -14.221 311s Consumption_5 -4.1386 -86.649 311s Consumption_6 0.0344 0.669 311s Consumption_8 5.9528 102.039 311s Consumption_9 3.6199 70.548 311s Consumption_10 1.2130 24.820 311s Consumption_11 -2.3309 -39.266 311s Consumption_12 -1.5509 -19.665 311s Consumption_13 -2.9298 -26.139 311s Consumption_14 2.9907 27.815 311s Consumption_15 -1.7611 -22.533 311s Consumption_16 -1.0403 -14.834 311s Consumption_17 7.8605 115.957 311s Consumption_18 -1.2660 -24.744 311s Consumption_19 -6.1974 -119.976 311s Consumption_20 4.2546 73.971 311s Consumption_21 1.7695 35.564 311s Consumption_22 -2.2905 -52.365 311s Investment_2 1.5294 19.818 311s Investment_3 -0.1395 -2.330 311s Investment_4 -0.5222 -9.992 311s Investment_5 1.4794 30.973 311s Investment_6 -0.2466 -4.801 311s Investment_8 -1.1148 -19.108 311s Investment_9 -0.4909 -9.566 311s Investment_10 -1.9066 -39.013 311s Investment_11 0.8748 14.736 311s Investment_12 0.7489 9.496 311s Investment_13 1.0277 9.169 311s Investment_14 -1.3972 -12.995 311s Investment_15 0.1582 2.024 311s Investment_16 -0.1132 -1.614 311s Investment_17 -1.7775 -26.221 311s Investment_18 0.2812 5.496 311s Investment_19 3.0567 59.173 311s Investment_20 -0.5590 -9.719 311s Investment_21 -0.1981 -3.981 311s Investment_22 -0.6908 -15.792 311s PrivateWages_2 -3.3803 -43.802 311s PrivateWages_3 1.2445 20.789 311s PrivateWages_4 3.1328 59.947 311s PrivateWages_5 -2.9316 -61.378 311s PrivateWages_6 -0.3443 -6.703 311s PrivateWages_8 1.9219 32.944 311s PrivateWages_9 2.2216 43.296 311s PrivateWages_10 4.0703 83.288 311s PrivateWages_11 -2.6344 -44.377 311s PrivateWages_12 -0.6120 -7.760 311s PrivateWages_13 -2.5653 -22.887 311s PrivateWages_14 2.8669 26.663 311s PrivateWages_15 -0.5912 -7.565 311s PrivateWages_16 -0.6625 -9.447 311s PrivateWages_17 2.6204 38.656 311s PrivateWages_18 0.0477 0.933 311s PrivateWages_19 -7.1288 -138.006 311s PrivateWages_20 1.4620 25.419 311s PrivateWages_21 -1.3672 -27.479 311s PrivateWages_22 2.6294 60.113 311s Consumption_corpProfLag Consumption_wages 311s Consumption_2 -27.752 -63.61 311s Consumption_3 -15.643 -40.21 311s Consumption_4 -12.560 -26.46 311s Consumption_5 -76.150 -161.61 311s Consumption_6 0.667 1.34 311s Consumption_8 116.675 236.66 311s Consumption_9 71.675 153.05 311s Consumption_10 25.593 53.50 311s Consumption_11 -50.581 -101.08 311s Consumption_12 -24.194 -61.19 311s Consumption_13 -33.399 -102.70 311s Consumption_14 20.935 98.78 311s Consumption_15 -19.724 -66.25 311s Consumption_16 -12.795 -41.59 311s Consumption_17 110.047 328.11 311s Consumption_18 -22.282 -60.30 311s Consumption_19 -107.216 -306.49 311s Consumption_20 65.095 205.74 311s Consumption_21 33.620 94.08 311s Consumption_22 -48.330 -139.53 311s Investment_2 19.424 44.52 311s Investment_3 -1.729 -4.45 311s Investment_4 -8.825 -18.59 311s Investment_5 27.221 57.77 311s Investment_6 -4.784 -9.58 311s Investment_8 -21.849 -44.32 311s Investment_9 -9.719 -20.75 311s Investment_10 -40.229 -84.09 311s Investment_11 18.983 37.94 311s Investment_12 11.683 29.55 311s Investment_13 11.716 36.03 311s Investment_14 -9.780 -46.15 311s Investment_15 1.772 5.95 311s Investment_16 -1.392 -4.53 311s Investment_17 -24.885 -74.20 311s Investment_18 4.949 13.39 311s Investment_19 52.880 151.16 311s Investment_20 -8.553 -27.03 311s Investment_21 -3.764 -10.53 311s Investment_22 -14.576 -42.08 311s PrivateWages_2 -42.929 -98.41 311s PrivateWages_3 15.432 39.67 311s PrivateWages_4 52.944 111.55 311s PrivateWages_5 -53.942 -114.48 311s PrivateWages_6 -6.679 -13.37 311s PrivateWages_8 37.670 76.41 311s PrivateWages_9 43.987 93.93 311s PrivateWages_10 85.884 179.53 311s PrivateWages_11 -57.165 -114.24 311s PrivateWages_12 -9.547 -24.14 311s PrivateWages_13 -29.244 -89.93 311s PrivateWages_14 20.068 94.68 311s PrivateWages_15 -6.622 -22.24 311s PrivateWages_16 -8.149 -26.49 311s PrivateWages_17 36.686 109.38 311s PrivateWages_18 0.840 2.27 311s PrivateWages_19 -123.329 -352.55 311s PrivateWages_20 22.369 70.70 311s PrivateWages_21 -25.977 -72.69 311s PrivateWages_22 55.481 160.18 311s Investment_(Intercept) Investment_corpProf 311s Consumption_2 0.9588 12.424 311s Consumption_3 0.5535 9.246 311s Consumption_4 0.3261 6.240 311s Consumption_5 1.8159 38.018 311s Consumption_6 -0.0151 -0.294 311s Consumption_8 -2.6118 -44.771 311s Consumption_9 -1.5883 -30.954 311s Consumption_10 -0.5322 -10.890 311s Consumption_11 1.0227 17.228 311s Consumption_12 0.6805 8.628 311s Consumption_13 1.2855 11.469 311s Consumption_14 -1.3122 -12.204 311s Consumption_15 0.7727 9.887 311s Consumption_16 0.4564 6.508 311s Consumption_17 -3.4489 -50.877 311s Consumption_18 0.5555 10.857 311s Consumption_19 2.7192 52.640 311s Consumption_20 -1.8667 -32.456 311s Consumption_21 -0.7764 -15.604 311s Consumption_22 1.0050 22.976 311s Investment_2 -2.3899 -30.969 311s Investment_3 0.2179 3.641 311s Investment_4 0.8160 15.614 311s Investment_5 -2.3118 -48.401 311s Investment_6 0.3854 7.502 311s Investment_8 1.7420 29.860 311s Investment_9 0.7670 14.948 311s Investment_10 2.9794 60.964 311s Investment_11 -1.3670 -23.027 311s Investment_12 -1.1702 -14.838 311s Investment_13 -1.6060 -14.328 311s Investment_14 2.1833 20.306 311s Investment_15 -0.2472 -3.163 311s Investment_16 0.1769 2.522 311s Investment_17 2.7776 40.974 311s Investment_18 -0.4394 -8.588 311s Investment_19 -4.7765 -92.468 311s Investment_20 0.8735 15.187 311s Investment_21 0.3095 6.221 311s Investment_22 1.0795 24.678 311s PrivateWages_2 2.1957 28.452 311s PrivateWages_3 -0.8084 -13.504 311s PrivateWages_4 -2.0349 -38.939 311s PrivateWages_5 1.9043 39.869 311s PrivateWages_6 0.2236 4.354 311s PrivateWages_8 -1.2484 -21.399 311s PrivateWages_9 -1.4431 -28.123 311s PrivateWages_10 -2.6439 -54.100 311s PrivateWages_11 1.7112 28.826 311s PrivateWages_12 0.3975 5.041 311s PrivateWages_13 1.6663 14.867 311s PrivateWages_14 -1.8622 -17.319 311s PrivateWages_15 0.3840 4.914 311s PrivateWages_16 0.4304 6.137 311s PrivateWages_17 -1.7021 -25.110 311s PrivateWages_18 -0.0310 -0.606 311s PrivateWages_19 4.6306 89.644 311s PrivateWages_20 -0.9497 -16.511 311s PrivateWages_21 0.8881 17.849 311s PrivateWages_22 -1.7080 -39.047 311s Investment_corpProfLag Investment_capitalLag 311s Consumption_2 12.176 175.26 311s Consumption_3 6.864 101.07 311s Consumption_4 5.511 60.16 311s Consumption_5 33.412 344.47 311s Consumption_6 -0.293 -2.91 311s Consumption_8 -51.192 -531.25 311s Consumption_9 -31.448 -329.73 311s Consumption_10 -11.229 -112.08 311s Consumption_11 22.193 220.60 311s Consumption_12 10.615 147.46 311s Consumption_13 14.654 274.19 311s Consumption_14 -9.185 -271.76 311s Consumption_15 8.654 156.08 311s Consumption_16 5.614 90.83 311s Consumption_17 -48.284 -681.84 311s Consumption_18 9.776 110.98 311s Consumption_19 47.042 548.73 311s Consumption_20 -28.561 -373.16 311s Consumption_21 -14.751 -156.21 311s Consumption_22 21.205 205.52 311s Investment_2 -30.352 -436.88 311s Investment_3 2.702 39.79 311s Investment_4 13.790 150.55 311s Investment_5 -42.537 -438.54 311s Investment_6 7.476 74.26 311s Investment_8 34.143 354.32 311s Investment_9 15.187 159.24 311s Investment_10 62.865 627.45 311s Investment_11 -29.663 -294.86 311s Investment_12 -18.256 -253.59 311s Investment_13 -18.308 -342.55 311s Investment_14 15.283 452.17 311s Investment_15 -2.768 -49.93 311s Investment_16 2.176 35.20 311s Investment_17 38.886 549.13 311s Investment_18 -7.734 -87.79 311s Investment_19 -82.633 -963.90 311s Investment_20 13.365 174.61 311s Investment_21 5.881 62.28 311s Investment_22 22.777 220.75 311s PrivateWages_2 27.885 401.37 311s PrivateWages_3 -10.024 -147.61 311s PrivateWages_4 -34.390 -375.44 311s PrivateWages_5 35.039 361.24 311s PrivateWages_6 4.339 43.10 311s PrivateWages_8 -24.469 -253.93 311s PrivateWages_9 -28.572 -299.58 311s PrivateWages_10 -55.787 -556.81 311s PrivateWages_11 37.132 369.10 311s PrivateWages_12 6.201 86.14 311s PrivateWages_13 18.996 355.42 311s PrivateWages_14 -13.035 -385.66 311s PrivateWages_15 4.301 77.58 311s PrivateWages_16 5.293 85.64 311s PrivateWages_17 -23.830 -336.51 311s PrivateWages_18 -0.546 -6.19 311s PrivateWages_19 80.110 934.46 311s PrivateWages_20 -14.530 -189.84 311s PrivateWages_21 16.874 178.68 311s PrivateWages_22 -36.038 -349.28 311s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 311s Consumption_2 -2.1174 -99.67 -95.07 311s Consumption_3 -1.2224 -60.61 -55.74 311s Consumption_4 -0.7201 -40.72 -36.08 311s Consumption_5 -4.0103 -243.37 -229.39 311s Consumption_6 0.0333 2.02 1.90 311s Consumption_8 5.7682 346.08 369.17 311s Consumption_9 3.5077 218.42 225.90 311s Consumption_10 1.1754 75.89 75.81 311s Consumption_11 -2.2587 -143.90 -151.33 311s Consumption_12 -1.5028 -82.40 -91.97 311s Consumption_13 -2.8389 -133.36 -151.60 311s Consumption_14 2.8980 122.09 128.38 311s Consumption_15 -1.7065 -87.40 -76.96 311s Consumption_16 -1.0080 -55.78 -50.10 311s Consumption_17 7.6168 437.16 414.35 311s Consumption_18 -1.2268 -82.41 -76.92 311s Consumption_19 -6.0053 -411.44 -390.34 311s Consumption_20 4.1227 275.58 251.07 311s Consumption_21 1.7146 128.37 119.16 311s Consumption_22 -2.2195 -192.83 -168.02 311s Investment_2 2.1940 103.27 98.51 311s Investment_3 -0.2001 -9.92 -9.12 311s Investment_4 -0.7491 -42.36 -37.53 311s Investment_5 2.1223 128.79 121.39 311s Investment_6 -0.3538 -21.44 -20.20 311s Investment_8 -1.5992 -95.95 -102.35 311s Investment_9 -0.7042 -43.85 -45.35 311s Investment_10 -2.7351 -176.60 -176.41 311s Investment_11 1.2549 79.95 84.08 311s Investment_12 1.0743 58.91 65.75 311s Investment_13 1.4743 69.26 78.73 311s Investment_14 -2.0044 -84.44 -88.79 311s Investment_15 0.2269 11.62 10.23 311s Investment_16 -0.1624 -8.99 -8.07 311s Investment_17 -2.5499 -146.35 -138.71 311s Investment_18 0.4034 27.10 25.29 311s Investment_19 4.3849 300.42 285.02 311s Investment_20 -0.8019 -53.60 -48.84 311s Investment_21 -0.2842 -21.27 -19.75 311s Investment_22 -0.9910 -86.09 -75.02 311s PrivateWages_2 -7.3399 -345.49 -329.56 311s PrivateWages_3 2.7024 133.99 123.23 311s PrivateWages_4 6.8025 384.63 340.81 311s PrivateWages_5 -6.3658 -386.31 -364.12 311s PrivateWages_6 -0.7476 -45.31 -42.69 311s PrivateWages_8 4.1733 250.39 267.09 311s PrivateWages_9 4.8240 300.38 310.66 311s PrivateWages_10 8.8383 570.68 570.07 311s PrivateWages_11 -5.7203 -364.45 -383.26 311s PrivateWages_12 -1.3289 -72.87 -81.33 311s PrivateWages_13 -5.5702 -261.67 -297.45 311s PrivateWages_14 6.2251 262.25 275.77 311s PrivateWages_15 -1.2838 -65.75 -57.90 311s PrivateWages_16 -1.4387 -79.61 -71.50 311s PrivateWages_17 5.6900 326.57 309.54 311s PrivateWages_18 0.1036 6.96 6.50 311s PrivateWages_19 -15.4796 -1060.55 -1006.17 311s PrivateWages_20 3.1746 212.21 193.34 311s PrivateWages_21 -2.9688 -222.26 -206.33 311s PrivateWages_22 5.7096 496.04 432.21 311s PrivateWages_trend 311s Consumption_2 21.174 311s Consumption_3 11.002 311s Consumption_4 5.761 311s Consumption_5 28.072 311s Consumption_6 -0.200 311s Consumption_8 -23.073 311s Consumption_9 -10.523 311s Consumption_10 -2.351 311s Consumption_11 2.259 311s Consumption_12 0.000 311s Consumption_13 -2.839 311s Consumption_14 5.796 311s Consumption_15 -5.119 311s Consumption_16 -4.032 311s Consumption_17 38.084 311s Consumption_18 -7.361 311s Consumption_19 -42.037 311s Consumption_20 32.981 311s Consumption_21 15.431 311s Consumption_22 -22.195 311s Investment_2 -21.940 311s Investment_3 1.801 311s Investment_4 5.993 311s Investment_5 -14.856 311s Investment_6 2.123 311s Investment_8 6.397 311s Investment_9 2.112 311s Investment_10 5.470 311s Investment_11 -1.255 311s Investment_12 0.000 311s Investment_13 1.474 311s Investment_14 -4.009 311s Investment_15 0.681 311s Investment_16 -0.650 311s Investment_17 -12.749 311s Investment_18 2.420 311s Investment_19 30.694 311s Investment_20 -6.415 311s Investment_21 -2.557 311s Investment_22 -9.910 311s PrivateWages_2 73.399 311s PrivateWages_3 -24.321 311s PrivateWages_4 -54.420 311s PrivateWages_5 44.560 311s PrivateWages_6 4.486 311s PrivateWages_8 -16.693 311s PrivateWages_9 -14.472 311s PrivateWages_10 -17.677 311s PrivateWages_11 5.720 311s PrivateWages_12 0.000 311s PrivateWages_13 -5.570 311s PrivateWages_14 12.450 311s PrivateWages_15 -3.851 311s PrivateWages_16 -5.755 311s PrivateWages_17 28.450 311s PrivateWages_18 0.622 311s PrivateWages_19 -108.357 311s PrivateWages_20 25.397 311s PrivateWages_21 -26.719 311s PrivateWages_22 57.096 311s [1] TRUE 311s > Bread 311s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 311s [1,] 101.7742 -0.858360 -0.3736 311s [2,] -0.8584 0.690973 -0.4670 311s [3,] -0.3736 -0.466994 0.6099 311s [4,] -1.8845 -0.076066 -0.0404 311s [5,] 84.1239 -0.877202 2.8173 311s [6,] -1.7843 0.267204 -0.2636 311s [7,] 0.6061 -0.218819 0.2875 311s [8,] -0.3146 -0.000285 -0.0152 311s [9,] -36.6570 0.120759 1.7724 311s [10,] 0.5673 -0.083944 0.0542 311s [11,] 0.0259 0.084615 -0.0868 311s [12,] 0.2015 0.041756 0.0283 311s Consumption_wages Investment_(Intercept) Investment_corpProf 311s [1,] -1.884465 84.124 -1.7843 311s [2,] -0.076066 -0.877 0.2672 311s [3,] -0.040367 2.817 -0.2636 311s [4,] 0.091823 -2.748 0.0379 311s [5,] -2.748307 2378.068 -36.8158 311s [6,] 0.037919 -36.816 1.2756 311s [7,] -0.038383 31.099 -1.1022 311s [8,] 0.013629 -11.271 0.1659 311s [9,] 0.115318 17.951 -0.1175 311s [10,] -0.000915 1.841 0.0121 311s [11,] -0.000905 -2.197 -0.0106 311s [12,] -0.032751 -1.985 0.0278 311s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 311s [1,] 0.60609 -3.15e-01 -3.67e+01 311s [2,] -0.21882 -2.85e-04 1.21e-01 311s [3,] 0.28746 -1.52e-02 1.77e+00 311s [4,] -0.03838 1.36e-02 1.15e-01 311s [5,] 31.09923 -1.13e+01 1.80e+01 311s [6,] -1.10217 1.66e-01 -1.17e-01 311s [7,] 1.17984 -1.58e-01 -9.59e-01 311s [8,] -0.15817 5.51e-02 7.31e-04 311s [9,] -0.95890 7.31e-04 7.88e+01 311s [10,] 0.00248 -1.04e-02 -5.11e-01 311s [11,] 0.01419 1.07e-02 -8.12e-01 311s [12,] -0.04010 1.08e-02 9.53e-01 311s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 311s [1,] 0.567318 0.025878 0.20145 311s [2,] -0.083944 0.084615 0.04176 311s [3,] 0.054179 -0.086845 0.02834 311s [4,] -0.000915 -0.000905 -0.03275 311s [5,] 1.840734 -2.196531 -1.98486 311s [6,] 0.012109 -0.010622 0.02782 311s [7,] 0.002479 0.014187 -0.04010 311s [8,] -0.010386 0.010690 0.01081 311s [9,] -0.511083 -0.811688 0.95314 311s [10,] 0.063161 -0.056453 -0.01901 311s [11,] -0.056453 0.072451 0.00297 311s [12,] -0.019011 0.002975 0.05128 311s > 311s > # I3SLS 312s > summary 312s 312s systemfit results 312s method: iterated 3SLS 312s 312s convergence achieved after 22 iterations 312s 312s N DF SSR detRCov OLS-R2 McElroy-R2 312s system 60 48 107 0.47 0.946 0.996 312s 312s N DF SSR MSE RMSE R2 Adj R2 312s Consumption 20 16 18.1 1.13 1.063 0.981 0.977 312s Investment 20 16 76.4 4.77 2.185 0.672 0.610 312s PrivateWages 20 16 12.3 0.77 0.877 0.984 0.982 312s 312s The covariance matrix of the residuals used for estimation 312s Consumption Investment PrivateWages 312s Consumption 0.905 0.509 -0.437 312s Investment 0.509 3.819 0.709 312s PrivateWages -0.437 0.709 0.616 312s 312s The covariance matrix of the residuals 312s Consumption Investment PrivateWages 312s Consumption 0.905 0.509 -0.437 312s Investment 0.509 3.819 0.709 312s PrivateWages -0.437 0.709 0.616 312s 312s The correlations of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.000 0.274 -0.585 312s Investment 0.274 1.000 0.462 312s PrivateWages -0.585 0.462 1.000 312s 312s 312s 3SLS estimates for 'Consumption' (equation 1) 312s Model Formula: consump ~ corpProf + corpProfLag + wages 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 16.4728 1.2187 13.52 3.6e-10 *** 312s corpProf 0.1642 0.0952 1.73 0.10 312s corpProfLag 0.1552 0.0903 1.72 0.11 312s wages 0.7756 0.0356 21.82 2.5e-13 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.063 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 18.095 MSE: 1.131 Root MSE: 1.063 312s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 312s 312s 312s 3SLS estimates for 'Investment' (equation 2) 312s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 38.7938 9.7249 3.99 0.00106 ** 312s corpProf -0.2501 0.2337 -1.07 0.30036 312s corpProfLag 0.9129 0.2271 4.02 0.00099 *** 312s capitalLag -0.2409 0.0469 -5.14 9.9e-05 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 2.185 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 76.371 MSE: 4.773 Root MSE: 2.185 312s Multiple R-Squared: 0.672 Adjusted R-Squared: 0.61 312s 312s 312s 3SLS estimates for 'PrivateWages' (equation 3) 312s Model Formula: privWage ~ gnp + gnpLag + trend 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 2.4620 1.2228 2.01 0.061 . 312s gnp 0.3776 0.0318 11.88 2.4e-09 *** 312s gnpLag 0.1937 0.0331 5.85 2.5e-05 *** 312s trend 0.1619 0.0300 5.40 5.9e-05 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 0.877 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 12.318 MSE: 0.77 Root MSE: 0.877 312s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.982 312s 312s > residuals 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 -0.4522 -3.4485 -1.2596 312s 3 -1.1470 0.0027 0.5437 312s 4 -1.6147 0.0274 1.6290 312s 5 -0.6117 -2.0392 -0.0707 312s 6 -0.1229 0.0457 -0.1859 312s 7 NA NA NA 312s 8 1.2461 1.4658 -0.6304 312s 9 1.0158 1.4202 0.3924 312s 10 -0.6460 3.2062 1.3671 312s 11 -0.0554 -1.7386 -0.4891 312s 12 -0.3472 -1.3793 0.0179 312s 13 -0.3947 -2.2646 -0.6968 312s 14 0.6536 2.4092 0.1021 312s 15 0.0821 -0.2787 0.1482 312s 16 0.1381 0.1196 -0.0796 312s 17 1.8826 2.5548 -0.6862 312s 18 -0.3415 -0.4009 0.8755 312s 19 0.2296 -4.0454 -0.9839 312s 20 1.3178 1.4481 -0.1989 312s 21 1.0065 0.9087 -0.9681 312s 22 -1.8388 1.9868 1.1734 312s > fitted 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 42.4 3.249 26.8 312s 3 46.1 1.897 28.8 312s 4 50.8 5.173 32.5 312s 5 51.2 5.039 34.0 312s 6 52.7 5.054 35.6 312s 7 NA NA NA 312s 8 55.0 2.734 38.5 312s 9 56.3 1.580 38.8 312s 10 58.4 1.894 39.9 312s 11 55.1 2.739 38.4 312s 12 51.2 -2.021 34.5 312s 13 46.0 -3.935 29.7 312s 14 45.8 -7.509 28.4 312s 15 48.6 -2.721 30.5 312s 16 51.2 -1.420 33.3 312s 17 55.8 -0.455 37.5 312s 18 59.0 2.401 40.1 312s 19 57.3 2.145 39.2 312s 20 60.3 -0.148 41.8 312s 21 64.0 2.391 46.0 312s 22 71.5 2.913 52.1 312s > predict 312s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 312s 1 NA NA NA NA 312s 2 42.4 0.437 41.5 43.2 312s 3 46.1 0.492 45.2 47.1 312s 4 50.8 0.321 50.2 51.5 312s 5 51.2 0.369 50.5 52.0 312s 6 52.7 0.372 52.0 53.5 312s 7 NA NA NA NA 312s 8 55.0 0.310 54.3 55.6 312s 9 56.3 0.338 55.6 57.0 312s 10 58.4 0.355 57.7 59.2 312s 11 55.1 0.618 53.8 56.3 312s 12 51.2 0.501 50.2 52.3 312s 13 46.0 0.642 44.7 47.3 312s 14 45.8 0.547 44.7 46.9 312s 15 48.6 0.340 47.9 49.3 312s 16 51.2 0.300 50.6 51.8 312s 17 55.8 0.354 55.1 56.5 312s 18 59.0 0.294 58.4 59.6 312s 19 57.3 0.354 56.6 58.0 312s 20 60.3 0.418 59.4 61.1 312s 21 64.0 0.407 63.2 64.8 312s 22 71.5 0.628 70.3 72.8 312s Investment.pred Investment.se.fit Investment.lwr Investment.upr 312s 1 NA NA NA NA 312s 2 3.249 1.160 0.91672 5.580 312s 3 1.897 0.934 0.02009 3.775 312s 4 5.173 0.803 3.55865 6.787 312s 5 5.039 0.693 3.64486 6.433 312s 6 5.054 0.674 3.69840 6.410 312s 7 NA NA NA NA 312s 8 2.734 0.584 1.56002 3.908 312s 9 1.580 0.783 0.00466 3.155 312s 10 1.894 0.868 0.14846 3.639 312s 11 2.739 1.321 0.08241 5.395 312s 12 -2.021 1.064 -4.16036 0.119 312s 13 -3.935 1.349 -6.64712 -1.224 312s 14 -7.509 1.360 -10.24349 -4.775 312s 15 -2.721 0.712 -4.15288 -1.290 312s 16 -1.420 0.614 -2.65412 -0.185 312s 17 -0.455 0.751 -1.96433 1.055 312s 18 2.401 0.498 1.39939 3.402 312s 19 2.145 0.698 0.74152 3.549 312s 20 -0.148 0.816 -1.78957 1.493 312s 21 2.391 0.713 0.95855 3.824 312s 22 2.913 0.984 0.93419 4.892 312s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 312s 1 NA NA NA NA 312s 2 26.8 0.347 26.1 27.5 312s 3 28.8 0.348 28.1 29.5 312s 4 32.5 0.354 31.8 33.2 312s 5 34.0 0.263 33.4 34.5 312s 6 35.6 0.274 35.0 36.1 312s 7 NA NA NA NA 312s 8 38.5 0.268 38.0 39.1 312s 9 38.8 0.256 38.3 39.3 312s 10 39.9 0.254 39.4 40.4 312s 11 38.4 0.323 37.7 39.0 312s 12 34.5 0.347 33.8 35.2 312s 13 29.7 0.435 28.8 30.6 312s 14 28.4 0.366 27.7 29.1 312s 15 30.5 0.341 29.8 31.1 312s 16 33.3 0.285 32.7 33.9 312s 17 37.5 0.275 36.9 38.0 312s 18 40.1 0.233 39.7 40.6 312s 19 39.2 0.346 38.5 39.9 312s 20 41.8 0.298 41.2 42.4 312s 21 46.0 0.329 45.3 46.6 312s 22 52.1 0.510 51.1 53.2 312s > model.frame 312s [1] TRUE 312s > model.matrix 312s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 312s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 312s [3] "Numeric: lengths (744, 720) differ" 312s > nobs 312s [1] 60 312s > linearHypothesis 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 48 1 0.4 0.53 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 48 1 0.5 0.49 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 49 312s 2 48 1 0.5 0.48 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 50 312s 2 48 2 0.66 0.52 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 50 312s 2 48 2 0.83 0.44 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 50 312s 2 48 2 1.66 0.44 312s > logLik 312s 'log Lik.' -77.6 (df=18) 312s 'log Lik.' -92.7 (df=18) 312s Estimating function 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 -4.9216 -63.77 312s Consumption_3 -3.3974 -56.75 312s Consumption_4 -2.5781 -49.33 312s Consumption_5 -9.6538 -202.12 312s Consumption_6 -0.8124 -15.82 312s Consumption_8 11.9408 204.68 312s Consumption_9 6.9299 135.05 312s Consumption_10 1.8984 38.85 312s Consumption_11 -4.8868 -82.32 312s Consumption_12 -2.6585 -33.71 312s Consumption_13 -5.0990 -45.49 312s Consumption_14 7.0717 65.77 312s Consumption_15 -3.1138 -39.84 312s Consumption_16 -1.6973 -24.20 312s Consumption_17 16.7458 247.03 312s Consumption_18 -2.5779 -50.39 312s Consumption_19 -12.5621 -243.19 312s Consumption_20 9.4057 163.53 312s Consumption_21 4.0953 82.31 312s Consumption_22 -4.1289 -94.39 312s Investment_2 4.3863 56.84 312s Investment_3 0.0612 1.02 312s Investment_4 -0.2801 -5.36 312s Investment_5 2.1936 45.93 312s Investment_6 0.1486 2.89 312s Investment_8 -1.0616 -18.20 312s Investment_9 -1.3484 -26.28 312s Investment_10 -3.8396 -78.57 312s Investment_11 1.8918 31.87 312s Investment_12 1.4041 17.80 312s Investment_13 2.3647 21.10 312s Investment_14 -2.5638 -23.84 312s Investment_15 0.2053 2.63 312s Investment_16 -0.2445 -3.49 312s Investment_17 -2.4423 -36.03 312s Investment_18 -0.2128 -4.16 312s Investment_19 4.0168 77.76 312s Investment_20 -1.3846 -24.07 312s Investment_21 -0.8726 -17.54 312s Investment_22 -2.4220 -55.37 312s PrivateWages_2 -7.8312 -101.48 312s PrivateWages_3 3.1927 53.33 312s PrivateWages_4 8.1013 155.02 312s PrivateWages_5 -6.1495 -128.75 312s PrivateWages_6 -0.1677 -3.26 312s PrivateWages_8 4.4536 76.34 312s PrivateWages_9 5.3302 103.88 312s PrivateWages_10 9.8611 201.78 312s PrivateWages_11 -6.2042 -104.51 312s PrivateWages_12 -2.2572 -28.62 312s PrivateWages_13 -7.3701 -65.76 312s PrivateWages_14 5.2841 49.14 312s PrivateWages_15 -1.8316 -23.44 312s PrivateWages_16 -1.8732 -26.71 312s PrivateWages_17 5.6855 83.87 312s PrivateWages_18 0.2354 4.60 312s PrivateWages_19 -16.6516 -322.36 312s PrivateWages_20 3.4690 60.31 312s PrivateWages_21 -2.8192 -56.66 312s PrivateWages_22 7.5425 172.43 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 -62.504 -143.28 312s Consumption_3 -42.128 -108.30 312s Consumption_4 -43.571 -91.80 312s Consumption_5 -177.629 -376.98 312s Consumption_6 -15.760 -31.55 312s Consumption_8 234.039 474.72 312s Consumption_9 137.212 292.99 312s Consumption_10 40.056 83.73 312s Consumption_11 -106.045 -211.93 312s Consumption_12 -41.472 -104.88 312s Consumption_13 -58.128 -178.75 312s Consumption_14 49.502 233.56 312s Consumption_15 -34.874 -117.14 312s Consumption_16 -20.877 -67.86 312s Consumption_17 234.441 699.00 312s Consumption_18 -45.372 -122.79 312s Consumption_19 -217.325 -621.24 312s Consumption_20 143.908 454.84 312s Consumption_21 77.811 217.74 312s Consumption_22 -87.120 -251.52 312s Investment_2 55.705 127.69 312s Investment_3 0.759 1.95 312s Investment_4 -4.734 -9.97 312s Investment_5 40.363 85.66 312s Investment_6 2.882 5.77 312s Investment_8 -20.807 -42.21 312s Investment_9 -26.697 -57.01 312s Investment_10 -81.017 -169.36 312s Investment_11 41.052 82.04 312s Investment_12 21.904 55.40 312s Investment_13 26.957 82.89 312s Investment_14 -17.946 -84.67 312s Investment_15 2.299 7.72 312s Investment_16 -3.007 -9.77 312s Investment_17 -34.192 -101.95 312s Investment_18 -3.746 -10.14 312s Investment_19 69.491 198.65 312s Investment_20 -21.185 -66.96 312s Investment_21 -16.580 -46.40 312s Investment_22 -51.104 -147.54 312s PrivateWages_2 -99.457 -227.98 312s PrivateWages_3 39.589 101.77 312s PrivateWages_4 136.911 288.46 312s PrivateWages_5 -113.151 -240.14 312s PrivateWages_6 -3.252 -6.51 312s PrivateWages_8 87.291 177.06 312s PrivateWages_9 105.538 225.36 312s PrivateWages_10 208.070 434.95 312s PrivateWages_11 -134.631 -269.05 312s PrivateWages_12 -35.213 -89.05 312s PrivateWages_13 -84.019 -258.36 312s PrivateWages_14 36.989 174.52 312s PrivateWages_15 -20.514 -68.91 312s PrivateWages_16 -23.040 -74.89 312s PrivateWages_17 79.598 237.33 312s PrivateWages_18 4.143 11.21 312s PrivateWages_19 -288.073 -823.48 312s PrivateWages_20 53.076 167.75 312s PrivateWages_21 -53.565 -149.89 312s PrivateWages_22 159.147 459.47 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 1.6584 21.489 312s Consumption_3 1.1448 19.123 312s Consumption_4 0.8687 16.623 312s Consumption_5 3.2529 68.104 312s Consumption_6 0.2737 5.329 312s Consumption_8 -4.0235 -68.968 312s Consumption_9 -2.3351 -45.507 312s Consumption_10 -0.6397 -13.089 312s Consumption_11 1.6466 27.739 312s Consumption_12 0.8958 11.358 312s Consumption_13 1.7181 15.329 312s Consumption_14 -2.3828 -22.161 312s Consumption_15 1.0492 13.424 312s Consumption_16 0.5719 8.155 312s Consumption_17 -5.6426 -83.238 312s Consumption_18 0.8686 16.978 312s Consumption_19 4.2329 81.944 312s Consumption_20 -3.1693 -55.102 312s Consumption_21 -1.3799 -27.735 312s Consumption_22 1.3913 31.806 312s Investment_2 -2.5801 -33.433 312s Investment_3 -0.0360 -0.601 312s Investment_4 0.1648 3.153 312s Investment_5 -1.2904 -27.016 312s Investment_6 -0.0874 -1.701 312s Investment_8 0.6245 10.704 312s Investment_9 0.7931 15.457 312s Investment_10 2.2586 46.215 312s Investment_11 -1.1128 -18.746 312s Investment_12 -0.8259 -10.473 312s Investment_13 -1.3910 -12.410 312s Investment_14 1.5081 14.026 312s Investment_15 -0.1208 -1.545 312s Investment_16 0.1438 2.050 312s Investment_17 1.4366 21.193 312s Investment_18 0.1252 2.447 312s Investment_19 -2.3628 -45.741 312s Investment_20 0.8145 14.161 312s Investment_21 0.5133 10.317 312s Investment_22 1.4247 32.570 312s PrivateWages_2 3.3346 43.210 312s PrivateWages_3 -1.3594 -22.709 312s PrivateWages_4 -3.4495 -66.008 312s PrivateWages_5 2.6185 54.822 312s PrivateWages_6 0.0714 1.390 312s PrivateWages_8 -1.8964 -32.506 312s PrivateWages_9 -2.2696 -44.232 312s PrivateWages_10 -4.1989 -85.919 312s PrivateWages_11 2.6418 44.502 312s PrivateWages_12 0.9611 12.187 312s PrivateWages_13 3.1382 27.999 312s PrivateWages_14 -2.2500 -20.926 312s PrivateWages_15 0.7799 9.979 312s PrivateWages_16 0.7976 11.373 312s PrivateWages_17 -2.4209 -35.713 312s PrivateWages_18 -0.1002 -1.959 312s PrivateWages_19 7.0903 137.261 312s PrivateWages_20 -1.4771 -25.682 312s PrivateWages_21 1.2004 24.127 312s PrivateWages_22 -3.2116 -73.422 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 21.061 303.15 312s Consumption_3 14.195 209.04 312s Consumption_4 14.681 160.28 312s Consumption_5 59.853 617.07 312s Consumption_6 5.310 52.75 312s Consumption_8 -78.860 -818.38 312s Consumption_9 -46.234 -484.76 312s Consumption_10 -13.497 -134.72 312s Consumption_11 35.732 355.18 312s Consumption_12 13.974 194.12 312s Consumption_13 19.587 366.47 312s Consumption_14 -16.680 -493.49 312s Consumption_15 11.751 211.94 312s Consumption_16 7.034 113.81 312s Consumption_17 -78.996 -1115.54 312s Consumption_18 15.288 173.56 312s Consumption_19 73.229 854.19 312s Consumption_20 -48.490 -633.54 312s Consumption_21 -26.219 -277.64 312s Consumption_22 29.355 284.51 312s Investment_2 -32.767 -471.64 312s Investment_3 -0.446 -6.57 312s Investment_4 2.785 30.40 312s Investment_5 -23.742 -244.78 312s Investment_6 -1.695 -16.84 312s Investment_8 12.239 127.02 312s Investment_9 15.704 164.66 312s Investment_10 47.656 475.66 312s Investment_11 -24.148 -240.03 312s Investment_12 -12.884 -178.98 312s Investment_13 -15.857 -296.69 312s Investment_14 10.556 312.32 312s Investment_15 -1.352 -24.39 312s Investment_16 1.769 28.62 312s Investment_17 20.113 284.02 312s Investment_18 2.203 25.01 312s Investment_19 -40.876 -476.81 312s Investment_20 12.461 162.81 312s Investment_21 9.753 103.28 312s Investment_22 30.061 291.35 312s PrivateWages_2 42.349 609.56 312s PrivateWages_3 -16.857 -248.23 312s PrivateWages_4 -58.297 -636.44 312s PrivateWages_5 48.180 496.72 312s PrivateWages_6 1.385 13.76 312s PrivateWages_8 -37.169 -385.72 312s PrivateWages_9 -44.939 -471.17 312s PrivateWages_10 -88.597 -884.29 312s PrivateWages_11 57.326 569.83 312s PrivateWages_12 14.994 208.28 312s PrivateWages_13 35.776 669.38 312s PrivateWages_14 -15.750 -465.97 312s PrivateWages_15 8.735 157.54 312s PrivateWages_16 9.810 158.72 312s PrivateWages_17 -33.893 -478.62 312s PrivateWages_18 -1.764 -20.03 312s PrivateWages_19 122.662 1430.82 312s PrivateWages_20 -22.600 -295.28 312s PrivateWages_21 22.808 241.53 312s PrivateWages_22 -67.765 -656.78 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 -5.3990 -254.13 -242.42 312s Consumption_3 -3.7270 -184.79 -169.95 312s Consumption_4 -2.8282 -159.92 -141.69 312s Consumption_5 -10.5903 -642.68 -605.76 312s Consumption_6 -0.8912 -54.02 -50.89 312s Consumption_8 13.0991 785.91 838.34 312s Consumption_9 7.6022 473.37 489.58 312s Consumption_10 2.0826 134.47 134.33 312s Consumption_11 -5.3609 -341.55 -359.18 312s Consumption_12 -2.9163 -159.91 -178.48 312s Consumption_13 -5.5936 -262.77 -298.70 312s Consumption_14 7.7577 326.81 343.67 312s Consumption_15 -3.4158 -174.95 -154.05 312s Consumption_16 -1.8619 -103.04 -92.54 312s Consumption_17 18.3702 1054.34 999.34 312s Consumption_18 -2.8280 -189.97 -177.32 312s Consumption_19 -13.7808 -944.16 -895.75 312s Consumption_20 10.3182 689.71 628.38 312s Consumption_21 4.4926 336.34 312.24 312s Consumption_22 -4.5294 -393.51 -342.88 312s Investment_2 6.0805 286.21 273.02 312s Investment_3 0.0848 4.21 3.87 312s Investment_4 -0.3883 -21.96 -19.45 312s Investment_5 3.0410 184.55 173.94 312s Investment_6 0.2060 12.48 11.76 312s Investment_8 -1.4717 -88.30 -94.19 312s Investment_9 -1.8692 -116.39 -120.38 312s Investment_10 -5.3228 -343.69 -343.32 312s Investment_11 2.6225 167.09 175.71 312s Investment_12 1.9465 106.73 119.12 312s Investment_13 3.2781 154.00 175.05 312s Investment_14 -3.5541 -149.72 -157.44 312s Investment_15 0.2846 14.58 12.84 312s Investment_16 -0.3389 -18.75 -16.84 312s Investment_17 -3.3857 -194.32 -184.18 312s Investment_18 -0.2951 -19.82 -18.50 312s Investment_19 5.5684 381.50 361.95 312s Investment_20 -1.9195 -128.31 -116.90 312s Investment_21 -1.2097 -90.57 -84.07 312s Investment_22 -3.3575 -291.70 -254.16 312s PrivateWages_2 -12.3381 -580.75 -553.98 312s PrivateWages_3 5.0300 249.39 229.37 312s PrivateWages_4 12.7635 721.68 639.45 312s PrivateWages_5 -9.6885 -587.96 -554.18 312s PrivateWages_6 -0.2641 -16.01 -15.08 312s PrivateWages_8 7.0167 420.99 449.07 312s PrivateWages_9 8.3978 522.92 540.82 312s PrivateWages_10 15.5362 1003.16 1002.09 312s PrivateWages_11 -9.7747 -622.76 -654.90 312s PrivateWages_12 -3.5562 -195.00 -217.64 312s PrivateWages_13 -11.6116 -545.48 -620.06 312s PrivateWages_14 8.3251 350.72 368.80 312s PrivateWages_15 -2.8858 -147.80 -130.15 312s PrivateWages_16 -2.9512 -163.31 -146.67 312s PrivateWages_17 8.9576 514.11 487.29 312s PrivateWages_18 0.3709 24.92 23.26 312s PrivateWages_19 -26.2346 -1797.40 -1705.25 312s PrivateWages_20 5.4654 365.33 332.84 312s PrivateWages_21 -4.4417 -332.53 -308.70 312s PrivateWages_22 11.8832 1032.40 899.56 312s PrivateWages_trend 312s Consumption_2 53.990 312s Consumption_3 33.543 312s Consumption_4 22.626 312s Consumption_5 74.132 312s Consumption_6 5.347 312s Consumption_8 -52.396 312s Consumption_9 -22.806 312s Consumption_10 -4.165 312s Consumption_11 5.361 312s Consumption_12 0.000 312s Consumption_13 -5.594 312s Consumption_14 15.515 312s Consumption_15 -10.247 312s Consumption_16 -7.448 312s Consumption_17 91.851 312s Consumption_18 -16.968 312s Consumption_19 -96.465 312s Consumption_20 82.545 312s Consumption_21 40.433 312s Consumption_22 -45.294 312s Investment_2 -60.805 312s Investment_3 -0.763 312s Investment_4 3.106 312s Investment_5 -21.287 312s Investment_6 -1.236 312s Investment_8 5.887 312s Investment_9 5.608 312s Investment_10 10.646 312s Investment_11 -2.623 312s Investment_12 0.000 312s Investment_13 3.278 312s Investment_14 -7.108 312s Investment_15 0.854 312s Investment_16 -1.356 312s Investment_17 -16.928 312s Investment_18 -1.770 312s Investment_19 38.979 312s Investment_20 -15.356 312s Investment_21 -10.887 312s Investment_22 -33.575 312s PrivateWages_2 123.381 312s PrivateWages_3 -45.270 312s PrivateWages_4 -102.108 312s PrivateWages_5 67.820 312s PrivateWages_6 1.585 312s PrivateWages_8 -28.067 312s PrivateWages_9 -25.193 312s PrivateWages_10 -31.072 312s PrivateWages_11 9.775 312s PrivateWages_12 0.000 312s PrivateWages_13 -11.612 312s PrivateWages_14 16.650 312s PrivateWages_15 -8.657 312s PrivateWages_16 -11.805 312s PrivateWages_17 44.788 312s PrivateWages_18 2.225 312s PrivateWages_19 -183.642 312s PrivateWages_20 43.723 312s PrivateWages_21 -39.975 312s PrivateWages_22 118.832 312s [1] TRUE 312s > Bread 312s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 312s [1,] 89.117 -0.7628 -0.3161 312s [2,] -0.763 0.5437 -0.3702 312s [3,] -0.316 -0.3702 0.4897 312s [4,] -1.650 -0.0567 -0.0339 312s [5,] 127.149 -5.8142 6.0484 312s [6,] -2.757 0.6390 -0.5640 312s [7,] 0.822 -0.5332 0.6080 312s [8,] -0.462 0.0186 -0.0321 312s [9,] -41.723 0.1554 1.5996 312s [10,] 0.652 -0.0670 0.0422 312s [11,] 0.023 0.0665 -0.0715 312s [12,] 0.266 0.0460 0.0263 312s Consumption_wages Investment_(Intercept) Investment_corpProf 312s [1,] -1.649949 127.15 -2.7567 312s [2,] -0.056675 -5.81 0.6390 312s [3,] -0.033922 6.05 -0.5640 312s [4,] 0.075837 -3.04 0.0284 312s [5,] -3.037786 5674.46 -81.6232 312s [6,] 0.028439 -81.62 3.2764 312s [7,] -0.041721 66.55 -2.7837 312s [8,] 0.016133 -26.78 0.3579 312s [9,] 0.286845 49.74 -0.5482 312s [10,] -0.005120 5.39 0.0206 312s [11,] 0.000492 -6.38 -0.0122 312s [12,] -0.035219 -5.00 0.0650 312s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 312s [1,] 0.8223 -0.4623 -41.7225 312s [2,] -0.5332 0.0186 0.1554 312s [3,] 0.6080 -0.0321 1.5996 312s [4,] -0.0417 0.0161 0.2868 312s [5,] 66.5535 -26.7802 49.7422 312s [6,] -2.7837 0.3579 -0.5482 312s [7,] 3.0944 -0.3490 -2.9105 312s [8,] -0.3490 0.1318 0.0433 312s [9,] -2.9105 0.0433 89.7087 312s [10,] 0.0256 -0.0306 -0.7102 312s [11,] 0.0243 0.0308 -0.7883 312s [12,] -0.1021 0.0277 0.9946 312s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 312s [1,] 0.65175 0.023034 0.26557 312s [2,] -0.06703 0.066494 0.04602 312s [3,] 0.04225 -0.071498 0.02630 312s [4,] -0.00512 0.000492 -0.03522 312s [5,] 5.38683 -6.377135 -4.99571 312s [6,] 0.02064 -0.012164 0.06501 312s [7,] 0.02556 0.024313 -0.10213 312s [8,] -0.03064 0.030839 0.02771 312s [9,] -0.71025 -0.788347 0.99462 312s [10,] 0.06062 -0.050369 -0.02195 312s [11,] -0.05037 0.065741 0.00529 312s [12,] -0.02195 0.005286 0.05391 312s > 312s > # OLS 312s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 312s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 312s > summary 312s 312s systemfit results 312s method: OLS 312s 312s N DF SSR detRCov OLS-R2 McElroy-R2 312s system 61 49 44.5 0.382 0.977 0.99 312s 312s N DF SSR MSE RMSE R2 Adj R2 312s Consumption 20 16 17.48 1.093 1.04 0.981 0.978 312s Investment 21 17 17.32 1.019 1.01 0.931 0.919 312s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 312s 312s The covariance matrix of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.124 0.034 -0.442 312s Investment 0.034 0.928 0.130 312s PrivateWages -0.442 0.130 0.563 312s 312s The correlations of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.0000 0.0266 -0.563 312s Investment 0.0266 1.0000 0.169 312s PrivateWages -0.5630 0.1689 1.000 312s 312s 312s OLS estimates for 'Consumption' (equation 1) 312s Model Formula: consump ~ corpProf + corpProfLag + wages 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 16.1357 1.3571 11.89 2.4e-09 *** 312s corpProf 0.1994 0.0949 2.10 0.052 . 312s corpProfLag 0.0969 0.0944 1.03 0.320 312s wages 0.7940 0.0415 19.16 1.9e-12 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.045 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 17.481 MSE: 1.093 Root MSE: 1.045 312s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 312s 312s 312s OLS estimates for 'Investment' (equation 2) 312s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 10.1258 5.2164 1.94 0.06901 . 312s corpProf 0.4796 0.0927 5.17 7.6e-05 *** 312s corpProfLag 0.3330 0.0963 3.46 0.00299 ** 312s capitalLag -0.1118 0.0255 -4.38 0.00041 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.009 on 17 degrees of freedom 312s Number of observations: 21 Degrees of Freedom: 17 312s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 312s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 312s 312s 312s OLS estimates for 'PrivateWages' (equation 3) 312s Model Formula: privWage ~ gnp + gnpLag + trend 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 1.3550 1.2591 1.08 0.2978 312s gnp 0.4417 0.0319 13.86 2.5e-10 *** 312s gnpLag 0.1466 0.0366 4.01 0.0010 ** 312s trend 0.1244 0.0323 3.85 0.0014 ** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 0.78 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 312s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 312s 312s compare coef with single-equation OLS 312s [1] TRUE 312s > residuals 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 -0.3304 -0.0668 -1.3389 312s 3 -1.2748 -0.0476 0.2462 312s 4 -1.6213 1.2467 1.1255 312s 5 -0.5661 -1.3512 -0.1959 312s 6 -0.0730 0.4154 -0.5284 312s 7 0.7915 1.4923 NA 312s 8 1.2648 0.7889 -0.7909 312s 9 0.9746 -0.6317 0.2819 312s 10 NA 1.0830 1.1384 312s 11 0.2225 0.2791 -0.1904 312s 12 -0.2256 0.0369 0.5813 312s 13 -0.2711 0.3659 0.1206 312s 14 0.3765 0.2237 0.4773 312s 15 -0.0349 -0.1728 0.3035 312s 16 -0.0243 0.0101 0.0284 312s 17 1.6023 0.9719 -0.8517 312s 18 -0.4658 0.0516 0.9908 312s 19 0.1914 -2.5656 -0.4597 312s 20 0.9683 -0.6866 -0.3819 312s 21 0.7325 -0.7807 -1.1062 312s 22 -2.2370 -0.6623 0.5501 312s > fitted 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 42.2 -0.133 26.8 312s 3 46.3 1.948 29.1 312s 4 50.8 3.953 33.0 312s 5 51.2 4.351 34.1 312s 6 52.7 4.685 35.9 312s 7 54.3 4.108 NA 312s 8 54.9 3.411 38.7 312s 9 56.3 3.632 38.9 312s 10 NA 4.017 40.2 312s 11 54.8 0.721 38.1 312s 12 51.1 -3.437 33.9 312s 13 45.9 -6.566 28.9 312s 14 46.1 -5.324 28.0 312s 15 48.7 -2.827 30.3 312s 16 51.3 -1.310 33.2 312s 17 56.1 1.128 37.7 312s 18 59.2 1.948 40.0 312s 19 57.3 0.666 38.7 312s 20 60.6 1.987 42.0 312s 21 64.3 4.081 46.1 312s 22 71.9 5.562 52.7 312s > predict 312s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 312s 1 NA NA NA NA 312s 2 42.2 0.478 39.9 44.5 312s 3 46.3 0.537 43.9 48.6 312s 4 50.8 0.364 48.6 53.0 312s 5 51.2 0.427 48.9 53.4 312s 6 52.7 0.433 50.4 54.9 312s 7 54.3 0.394 52.1 56.6 312s 8 54.9 0.360 52.7 57.2 312s 9 56.3 0.387 54.1 58.6 312s 10 NA NA NA NA 312s 11 54.8 0.635 52.3 57.2 312s 12 51.1 0.501 48.8 53.5 312s 13 45.9 0.656 43.4 48.4 312s 14 46.1 0.629 43.7 48.6 312s 15 48.7 0.389 46.5 51.0 312s 16 51.3 0.345 49.1 53.5 312s 17 56.1 0.379 53.9 58.3 312s 18 59.2 0.336 57.0 61.4 312s 19 57.3 0.385 55.1 59.5 312s 20 60.6 0.450 58.3 62.9 312s 21 64.3 0.448 62.0 66.6 312s 22 71.9 0.697 69.4 74.5 312s Investment.pred Investment.se.fit Investment.lwr Investment.upr 312s 1 NA NA NA NA 312s 2 -0.133 0.579 -2.472 2.206 312s 3 1.948 0.476 -0.295 4.190 312s 4 3.953 0.428 1.750 6.157 312s 5 4.351 0.354 2.202 6.501 312s 6 4.685 0.333 2.548 6.821 312s 7 4.108 0.314 1.983 6.232 312s 8 3.411 0.279 1.306 5.516 312s 9 3.632 0.371 1.470 5.793 312s 10 4.017 0.426 1.815 6.219 312s 11 0.721 0.574 -1.613 3.054 312s 12 -3.437 0.484 -5.686 -1.188 312s 13 -6.566 0.588 -8.913 -4.219 312s 14 -5.324 0.662 -7.750 -2.898 312s 15 -2.827 0.356 -4.978 -0.676 312s 16 -1.310 0.305 -3.429 0.809 312s 17 1.128 0.332 -1.007 3.263 312s 18 1.948 0.232 -0.133 4.030 312s 19 0.666 0.298 -1.449 2.781 312s 20 1.987 0.350 -0.160 4.133 312s 21 4.081 0.317 1.955 6.207 312s 22 5.562 0.440 3.349 7.775 312s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 312s 1 NA NA NA NA 312s 2 26.8 0.352 25.1 28.6 312s 3 29.1 0.355 27.3 30.8 312s 4 33.0 0.358 31.2 34.7 312s 5 34.1 0.277 32.4 35.8 312s 6 35.9 0.276 34.3 37.6 312s 7 NA NA NA NA 312s 8 38.7 0.282 37.0 40.4 312s 9 38.9 0.268 37.3 40.6 312s 10 40.2 0.255 38.5 41.8 312s 11 38.1 0.351 36.4 39.8 312s 12 33.9 0.355 32.2 35.6 312s 13 28.9 0.421 27.1 30.7 312s 14 28.0 0.370 26.3 29.8 312s 15 30.3 0.364 28.6 32.0 312s 16 33.2 0.304 31.5 34.9 312s 17 37.7 0.298 36.0 39.3 312s 18 40.0 0.233 38.4 41.6 312s 19 38.7 0.349 36.9 40.4 312s 20 42.0 0.314 40.3 43.7 312s 21 46.1 0.328 44.4 47.8 312s 22 52.7 0.494 50.9 54.6 312s > model.frame 312s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 312s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 312s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 312s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 312s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 312s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 312s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 312s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 312s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 312s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 312s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 312s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 312s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 312s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 312s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 312s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 312s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 312s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 312s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 312s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 312s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 312s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 312s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 312s trend 312s 1 -11 312s 2 -10 312s 3 -9 312s 4 -8 312s 5 -7 312s 6 -6 312s 7 -5 312s 8 -4 312s 9 -3 312s 10 -2 312s 11 -1 312s 12 0 312s 13 1 312s 14 2 312s 15 3 312s 16 4 312s 17 5 312s 18 6 312s 19 7 312s 20 8 312s 21 9 312s 22 10 312s > model.matrix 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 1 12.4 312s Consumption_3 1 16.9 312s Consumption_4 1 18.4 312s Consumption_5 1 19.4 312s Consumption_6 1 20.1 312s Consumption_7 1 19.6 312s Consumption_8 1 19.8 312s Consumption_9 1 21.1 312s Consumption_11 1 15.6 312s Consumption_12 1 11.4 312s Consumption_13 1 7.0 312s Consumption_14 1 11.2 312s Consumption_15 1 12.3 312s Consumption_16 1 14.0 312s Consumption_17 1 17.6 312s Consumption_18 1 17.3 312s Consumption_19 1 15.3 312s Consumption_20 1 19.0 312s Consumption_21 1 21.1 312s Consumption_22 1 23.5 312s Investment_2 0 0.0 312s Investment_3 0 0.0 312s Investment_4 0 0.0 312s Investment_5 0 0.0 312s Investment_6 0 0.0 312s Investment_7 0 0.0 312s Investment_8 0 0.0 312s Investment_9 0 0.0 312s Investment_10 0 0.0 312s Investment_11 0 0.0 312s Investment_12 0 0.0 312s Investment_13 0 0.0 312s Investment_14 0 0.0 312s Investment_15 0 0.0 312s Investment_16 0 0.0 312s Investment_17 0 0.0 312s Investment_18 0 0.0 312s Investment_19 0 0.0 312s Investment_20 0 0.0 312s Investment_21 0 0.0 312s Investment_22 0 0.0 312s PrivateWages_2 0 0.0 312s PrivateWages_3 0 0.0 312s PrivateWages_4 0 0.0 312s PrivateWages_5 0 0.0 312s PrivateWages_6 0 0.0 312s PrivateWages_8 0 0.0 312s PrivateWages_9 0 0.0 312s PrivateWages_10 0 0.0 312s PrivateWages_11 0 0.0 312s PrivateWages_12 0 0.0 312s PrivateWages_13 0 0.0 312s PrivateWages_14 0 0.0 312s PrivateWages_15 0 0.0 312s PrivateWages_16 0 0.0 312s PrivateWages_17 0 0.0 312s PrivateWages_18 0 0.0 312s PrivateWages_19 0 0.0 312s PrivateWages_20 0 0.0 312s PrivateWages_21 0 0.0 312s PrivateWages_22 0 0.0 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 12.7 28.2 312s Consumption_3 12.4 32.2 312s Consumption_4 16.9 37.0 312s Consumption_5 18.4 37.0 312s Consumption_6 19.4 38.6 312s Consumption_7 20.1 40.7 312s Consumption_8 19.6 41.5 312s Consumption_9 19.8 42.9 312s Consumption_11 21.7 42.1 312s Consumption_12 15.6 39.3 312s Consumption_13 11.4 34.3 312s Consumption_14 7.0 34.1 312s Consumption_15 11.2 36.6 312s Consumption_16 12.3 39.3 312s Consumption_17 14.0 44.2 312s Consumption_18 17.6 47.7 312s Consumption_19 17.3 45.9 312s Consumption_20 15.3 49.4 312s Consumption_21 19.0 53.0 312s Consumption_22 21.1 61.8 312s Investment_2 0.0 0.0 312s Investment_3 0.0 0.0 312s Investment_4 0.0 0.0 312s Investment_5 0.0 0.0 312s Investment_6 0.0 0.0 312s Investment_7 0.0 0.0 312s Investment_8 0.0 0.0 312s Investment_9 0.0 0.0 312s Investment_10 0.0 0.0 312s Investment_11 0.0 0.0 312s Investment_12 0.0 0.0 312s Investment_13 0.0 0.0 312s Investment_14 0.0 0.0 312s Investment_15 0.0 0.0 312s Investment_16 0.0 0.0 312s Investment_17 0.0 0.0 312s Investment_18 0.0 0.0 312s Investment_19 0.0 0.0 312s Investment_20 0.0 0.0 312s Investment_21 0.0 0.0 312s Investment_22 0.0 0.0 312s PrivateWages_2 0.0 0.0 312s PrivateWages_3 0.0 0.0 312s PrivateWages_4 0.0 0.0 312s PrivateWages_5 0.0 0.0 312s PrivateWages_6 0.0 0.0 312s PrivateWages_8 0.0 0.0 312s PrivateWages_9 0.0 0.0 312s PrivateWages_10 0.0 0.0 312s PrivateWages_11 0.0 0.0 312s PrivateWages_12 0.0 0.0 312s PrivateWages_13 0.0 0.0 312s PrivateWages_14 0.0 0.0 312s PrivateWages_15 0.0 0.0 312s PrivateWages_16 0.0 0.0 312s PrivateWages_17 0.0 0.0 312s PrivateWages_18 0.0 0.0 312s PrivateWages_19 0.0 0.0 312s PrivateWages_20 0.0 0.0 312s PrivateWages_21 0.0 0.0 312s PrivateWages_22 0.0 0.0 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 0 0.0 312s Consumption_3 0 0.0 312s Consumption_4 0 0.0 312s Consumption_5 0 0.0 312s Consumption_6 0 0.0 312s Consumption_7 0 0.0 312s Consumption_8 0 0.0 312s Consumption_9 0 0.0 312s Consumption_11 0 0.0 312s Consumption_12 0 0.0 312s Consumption_13 0 0.0 312s Consumption_14 0 0.0 312s Consumption_15 0 0.0 312s Consumption_16 0 0.0 312s Consumption_17 0 0.0 312s Consumption_18 0 0.0 312s Consumption_19 0 0.0 312s Consumption_20 0 0.0 312s Consumption_21 0 0.0 312s Consumption_22 0 0.0 312s Investment_2 1 12.4 312s Investment_3 1 16.9 312s Investment_4 1 18.4 312s Investment_5 1 19.4 312s Investment_6 1 20.1 312s Investment_7 1 19.6 312s Investment_8 1 19.8 312s Investment_9 1 21.1 312s Investment_10 1 21.7 312s Investment_11 1 15.6 312s Investment_12 1 11.4 312s Investment_13 1 7.0 312s Investment_14 1 11.2 312s Investment_15 1 12.3 312s Investment_16 1 14.0 312s Investment_17 1 17.6 312s Investment_18 1 17.3 312s Investment_19 1 15.3 312s Investment_20 1 19.0 312s Investment_21 1 21.1 312s Investment_22 1 23.5 312s PrivateWages_2 0 0.0 312s PrivateWages_3 0 0.0 312s PrivateWages_4 0 0.0 312s PrivateWages_5 0 0.0 312s PrivateWages_6 0 0.0 312s PrivateWages_8 0 0.0 312s PrivateWages_9 0 0.0 312s PrivateWages_10 0 0.0 312s PrivateWages_11 0 0.0 312s PrivateWages_12 0 0.0 312s PrivateWages_13 0 0.0 312s PrivateWages_14 0 0.0 312s PrivateWages_15 0 0.0 312s PrivateWages_16 0 0.0 312s PrivateWages_17 0 0.0 312s PrivateWages_18 0 0.0 312s PrivateWages_19 0 0.0 312s PrivateWages_20 0 0.0 312s PrivateWages_21 0 0.0 312s PrivateWages_22 0 0.0 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 0.0 0 312s Consumption_3 0.0 0 312s Consumption_4 0.0 0 312s Consumption_5 0.0 0 312s Consumption_6 0.0 0 312s Consumption_7 0.0 0 312s Consumption_8 0.0 0 312s Consumption_9 0.0 0 312s Consumption_11 0.0 0 312s Consumption_12 0.0 0 312s Consumption_13 0.0 0 312s Consumption_14 0.0 0 312s Consumption_15 0.0 0 312s Consumption_16 0.0 0 312s Consumption_17 0.0 0 312s Consumption_18 0.0 0 312s Consumption_19 0.0 0 312s Consumption_20 0.0 0 312s Consumption_21 0.0 0 312s Consumption_22 0.0 0 312s Investment_2 12.7 183 312s Investment_3 12.4 183 312s Investment_4 16.9 184 312s Investment_5 18.4 190 312s Investment_6 19.4 193 312s Investment_7 20.1 198 312s Investment_8 19.6 203 312s Investment_9 19.8 208 312s Investment_10 21.1 211 312s Investment_11 21.7 216 312s Investment_12 15.6 217 312s Investment_13 11.4 213 312s Investment_14 7.0 207 312s Investment_15 11.2 202 312s Investment_16 12.3 199 312s Investment_17 14.0 198 312s Investment_18 17.6 200 312s Investment_19 17.3 202 312s Investment_20 15.3 200 312s Investment_21 19.0 201 312s Investment_22 21.1 204 312s PrivateWages_2 0.0 0 312s PrivateWages_3 0.0 0 312s PrivateWages_4 0.0 0 312s PrivateWages_5 0.0 0 312s PrivateWages_6 0.0 0 312s PrivateWages_8 0.0 0 312s PrivateWages_9 0.0 0 312s PrivateWages_10 0.0 0 312s PrivateWages_11 0.0 0 312s PrivateWages_12 0.0 0 312s PrivateWages_13 0.0 0 312s PrivateWages_14 0.0 0 312s PrivateWages_15 0.0 0 312s PrivateWages_16 0.0 0 312s PrivateWages_17 0.0 0 312s PrivateWages_18 0.0 0 312s PrivateWages_19 0.0 0 312s PrivateWages_20 0.0 0 312s PrivateWages_21 0.0 0 312s PrivateWages_22 0.0 0 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 0 0.0 0.0 312s Consumption_3 0 0.0 0.0 312s Consumption_4 0 0.0 0.0 312s Consumption_5 0 0.0 0.0 312s Consumption_6 0 0.0 0.0 312s Consumption_7 0 0.0 0.0 312s Consumption_8 0 0.0 0.0 312s Consumption_9 0 0.0 0.0 312s Consumption_11 0 0.0 0.0 312s Consumption_12 0 0.0 0.0 312s Consumption_13 0 0.0 0.0 312s Consumption_14 0 0.0 0.0 312s Consumption_15 0 0.0 0.0 312s Consumption_16 0 0.0 0.0 312s Consumption_17 0 0.0 0.0 312s Consumption_18 0 0.0 0.0 312s Consumption_19 0 0.0 0.0 312s Consumption_20 0 0.0 0.0 312s Consumption_21 0 0.0 0.0 312s Consumption_22 0 0.0 0.0 312s Investment_2 0 0.0 0.0 312s Investment_3 0 0.0 0.0 312s Investment_4 0 0.0 0.0 312s Investment_5 0 0.0 0.0 312s Investment_6 0 0.0 0.0 312s Investment_7 0 0.0 0.0 312s Investment_8 0 0.0 0.0 312s Investment_9 0 0.0 0.0 312s Investment_10 0 0.0 0.0 312s Investment_11 0 0.0 0.0 312s Investment_12 0 0.0 0.0 312s Investment_13 0 0.0 0.0 312s Investment_14 0 0.0 0.0 312s Investment_15 0 0.0 0.0 312s Investment_16 0 0.0 0.0 312s Investment_17 0 0.0 0.0 312s Investment_18 0 0.0 0.0 312s Investment_19 0 0.0 0.0 312s Investment_20 0 0.0 0.0 312s Investment_21 0 0.0 0.0 312s Investment_22 0 0.0 0.0 312s PrivateWages_2 1 45.6 44.9 312s PrivateWages_3 1 50.1 45.6 312s PrivateWages_4 1 57.2 50.1 312s PrivateWages_5 1 57.1 57.2 312s PrivateWages_6 1 61.0 57.1 312s PrivateWages_8 1 64.4 64.0 312s PrivateWages_9 1 64.5 64.4 312s PrivateWages_10 1 67.0 64.5 312s PrivateWages_11 1 61.2 67.0 312s PrivateWages_12 1 53.4 61.2 312s PrivateWages_13 1 44.3 53.4 312s PrivateWages_14 1 45.1 44.3 312s PrivateWages_15 1 49.7 45.1 312s PrivateWages_16 1 54.4 49.7 312s PrivateWages_17 1 62.7 54.4 312s PrivateWages_18 1 65.0 62.7 312s PrivateWages_19 1 60.9 65.0 312s PrivateWages_20 1 69.5 60.9 312s PrivateWages_21 1 75.7 69.5 312s PrivateWages_22 1 88.4 75.7 312s PrivateWages_trend 312s Consumption_2 0 312s Consumption_3 0 312s Consumption_4 0 312s Consumption_5 0 312s Consumption_6 0 312s Consumption_7 0 312s Consumption_8 0 312s Consumption_9 0 312s Consumption_11 0 312s Consumption_12 0 312s Consumption_13 0 312s Consumption_14 0 312s Consumption_15 0 312s Consumption_16 0 312s Consumption_17 0 312s Consumption_18 0 312s Consumption_19 0 312s Consumption_20 0 312s Consumption_21 0 312s Consumption_22 0 312s Investment_2 0 312s Investment_3 0 312s Investment_4 0 312s Investment_5 0 312s Investment_6 0 312s Investment_7 0 312s Investment_8 0 312s Investment_9 0 312s Investment_10 0 312s Investment_11 0 312s Investment_12 0 312s Investment_13 0 312s Investment_14 0 312s Investment_15 0 312s Investment_16 0 312s Investment_17 0 312s Investment_18 0 312s Investment_19 0 312s Investment_20 0 312s Investment_21 0 312s Investment_22 0 312s PrivateWages_2 -10 312s PrivateWages_3 -9 312s PrivateWages_4 -8 312s PrivateWages_5 -7 312s PrivateWages_6 -6 312s PrivateWages_8 -4 312s PrivateWages_9 -3 312s PrivateWages_10 -2 312s PrivateWages_11 -1 312s PrivateWages_12 0 312s PrivateWages_13 1 312s PrivateWages_14 2 312s PrivateWages_15 3 312s PrivateWages_16 4 312s PrivateWages_17 5 312s PrivateWages_18 6 312s PrivateWages_19 7 312s PrivateWages_20 8 312s PrivateWages_21 9 312s PrivateWages_22 10 312s > nobs 312s [1] 61 312s > linearHypothesis 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 50 312s 2 49 1 0.87 0.35 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 50 312s 2 49 1 0.8 0.38 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 50 312s 2 49 1 0.8 0.37 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 51 312s 2 49 2 0.48 0.62 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 51 312s 2 49 2 0.43 0.65 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 51 312s 2 49 2 0.87 0.65 312s > logLik 312s 'log Lik.' -71.7 (df=13) 312s 'log Lik.' -76.1 (df=13) 312s compare log likelihood value with single-equation OLS 312s [1] "Mean relative difference: 0.00159" 312s Estimating function 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 -0.3304 -4.097 312s Consumption_3 -1.2748 -21.544 312s Consumption_4 -1.6213 -29.832 312s Consumption_5 -0.5661 -10.982 312s Consumption_6 -0.0730 -1.467 312s Consumption_7 0.7915 15.513 312s Consumption_8 1.2648 25.043 312s Consumption_9 0.9746 20.563 312s Consumption_11 0.2225 3.470 312s Consumption_12 -0.2256 -2.572 312s Consumption_13 -0.2711 -1.898 312s Consumption_14 0.3765 4.217 312s Consumption_15 -0.0349 -0.429 312s Consumption_16 -0.0243 -0.341 312s Consumption_17 1.6023 28.201 312s Consumption_18 -0.4658 -8.058 312s Consumption_19 0.1914 2.928 312s Consumption_20 0.9683 18.397 312s Consumption_21 0.7325 15.456 312s Consumption_22 -2.2370 -52.569 312s Investment_2 0.0000 0.000 312s Investment_3 0.0000 0.000 312s Investment_4 0.0000 0.000 312s Investment_5 0.0000 0.000 312s Investment_6 0.0000 0.000 312s Investment_7 0.0000 0.000 312s Investment_8 0.0000 0.000 312s Investment_9 0.0000 0.000 312s Investment_10 0.0000 0.000 312s Investment_11 0.0000 0.000 312s Investment_12 0.0000 0.000 312s Investment_13 0.0000 0.000 312s Investment_14 0.0000 0.000 312s Investment_15 0.0000 0.000 312s Investment_16 0.0000 0.000 312s Investment_17 0.0000 0.000 312s Investment_18 0.0000 0.000 312s Investment_19 0.0000 0.000 312s Investment_20 0.0000 0.000 312s Investment_21 0.0000 0.000 312s Investment_22 0.0000 0.000 312s PrivateWages_2 0.0000 0.000 312s PrivateWages_3 0.0000 0.000 312s PrivateWages_4 0.0000 0.000 312s PrivateWages_5 0.0000 0.000 312s PrivateWages_6 0.0000 0.000 312s PrivateWages_8 0.0000 0.000 312s PrivateWages_9 0.0000 0.000 312s PrivateWages_10 0.0000 0.000 312s PrivateWages_11 0.0000 0.000 312s PrivateWages_12 0.0000 0.000 312s PrivateWages_13 0.0000 0.000 312s PrivateWages_14 0.0000 0.000 312s PrivateWages_15 0.0000 0.000 312s PrivateWages_16 0.0000 0.000 312s PrivateWages_17 0.0000 0.000 312s PrivateWages_18 0.0000 0.000 312s PrivateWages_19 0.0000 0.000 312s PrivateWages_20 0.0000 0.000 312s PrivateWages_21 0.0000 0.000 312s PrivateWages_22 0.0000 0.000 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 -4.196 -9.318 312s Consumption_3 -15.808 -41.049 312s Consumption_4 -27.400 -59.988 312s Consumption_5 -10.416 -20.944 312s Consumption_6 -1.416 -2.817 312s Consumption_7 15.908 32.212 312s Consumption_8 24.790 52.490 312s Consumption_9 19.296 41.809 312s Consumption_11 4.827 9.366 312s Consumption_12 -3.520 -8.867 312s Consumption_13 -3.091 -9.299 312s Consumption_14 2.636 12.839 312s Consumption_15 -0.391 -1.277 312s Consumption_16 -0.299 -0.957 312s Consumption_17 22.433 70.823 312s Consumption_18 -8.197 -22.217 312s Consumption_19 3.311 8.785 312s Consumption_20 14.815 47.833 312s Consumption_21 13.917 38.822 312s Consumption_22 -47.200 -138.245 312s Investment_2 0.000 0.000 312s Investment_3 0.000 0.000 312s Investment_4 0.000 0.000 312s Investment_5 0.000 0.000 312s Investment_6 0.000 0.000 312s Investment_7 0.000 0.000 312s Investment_8 0.000 0.000 312s Investment_9 0.000 0.000 312s Investment_10 0.000 0.000 312s Investment_11 0.000 0.000 312s Investment_12 0.000 0.000 312s Investment_13 0.000 0.000 312s Investment_14 0.000 0.000 312s Investment_15 0.000 0.000 312s Investment_16 0.000 0.000 312s Investment_17 0.000 0.000 312s Investment_18 0.000 0.000 312s Investment_19 0.000 0.000 312s Investment_20 0.000 0.000 312s Investment_21 0.000 0.000 312s Investment_22 0.000 0.000 312s PrivateWages_2 0.000 0.000 312s PrivateWages_3 0.000 0.000 312s PrivateWages_4 0.000 0.000 312s PrivateWages_5 0.000 0.000 312s PrivateWages_6 0.000 0.000 312s PrivateWages_8 0.000 0.000 312s PrivateWages_9 0.000 0.000 312s PrivateWages_10 0.000 0.000 312s PrivateWages_11 0.000 0.000 312s PrivateWages_12 0.000 0.000 312s PrivateWages_13 0.000 0.000 312s PrivateWages_14 0.000 0.000 312s PrivateWages_15 0.000 0.000 312s PrivateWages_16 0.000 0.000 312s PrivateWages_17 0.000 0.000 312s PrivateWages_18 0.000 0.000 312s PrivateWages_19 0.000 0.000 312s PrivateWages_20 0.000 0.000 312s PrivateWages_21 0.000 0.000 312s PrivateWages_22 0.000 0.000 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 0.0000 0.000 312s Consumption_3 0.0000 0.000 312s Consumption_4 0.0000 0.000 312s Consumption_5 0.0000 0.000 312s Consumption_6 0.0000 0.000 312s Consumption_7 0.0000 0.000 312s Consumption_8 0.0000 0.000 312s Consumption_9 0.0000 0.000 312s Consumption_11 0.0000 0.000 312s Consumption_12 0.0000 0.000 312s Consumption_13 0.0000 0.000 312s Consumption_14 0.0000 0.000 312s Consumption_15 0.0000 0.000 312s Consumption_16 0.0000 0.000 312s Consumption_17 0.0000 0.000 312s Consumption_18 0.0000 0.000 312s Consumption_19 0.0000 0.000 312s Consumption_20 0.0000 0.000 312s Consumption_21 0.0000 0.000 312s Consumption_22 0.0000 0.000 312s Investment_2 -0.0668 -0.828 312s Investment_3 -0.0476 -0.804 312s Investment_4 1.2467 22.939 312s Investment_5 -1.3512 -26.213 312s Investment_6 0.4154 8.350 312s Investment_7 1.4923 29.248 312s Investment_8 0.7889 15.620 312s Investment_9 -0.6317 -13.329 312s Investment_10 1.0830 23.500 312s Investment_11 0.2791 4.353 312s Investment_12 0.0369 0.420 312s Investment_13 0.3659 2.561 312s Investment_14 0.2237 2.505 312s Investment_15 -0.1728 -2.126 312s Investment_16 0.0101 0.141 312s Investment_17 0.9719 17.105 312s Investment_18 0.0516 0.893 312s Investment_19 -2.5656 -39.254 312s Investment_20 -0.6866 -13.045 312s Investment_21 -0.7807 -16.474 312s Investment_22 -0.6623 -15.565 312s PrivateWages_2 0.0000 0.000 312s PrivateWages_3 0.0000 0.000 312s PrivateWages_4 0.0000 0.000 312s PrivateWages_5 0.0000 0.000 312s PrivateWages_6 0.0000 0.000 312s PrivateWages_8 0.0000 0.000 312s PrivateWages_9 0.0000 0.000 312s PrivateWages_10 0.0000 0.000 312s PrivateWages_11 0.0000 0.000 312s PrivateWages_12 0.0000 0.000 312s PrivateWages_13 0.0000 0.000 312s PrivateWages_14 0.0000 0.000 312s PrivateWages_15 0.0000 0.000 312s PrivateWages_16 0.0000 0.000 312s PrivateWages_17 0.0000 0.000 312s PrivateWages_18 0.0000 0.000 312s PrivateWages_19 0.0000 0.000 312s PrivateWages_20 0.0000 0.000 312s PrivateWages_21 0.0000 0.000 312s PrivateWages_22 0.0000 0.000 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 0.000 0.00 312s Consumption_3 0.000 0.00 312s Consumption_4 0.000 0.00 312s Consumption_5 0.000 0.00 312s Consumption_6 0.000 0.00 312s Consumption_7 0.000 0.00 312s Consumption_8 0.000 0.00 312s Consumption_9 0.000 0.00 312s Consumption_11 0.000 0.00 312s Consumption_12 0.000 0.00 312s Consumption_13 0.000 0.00 312s Consumption_14 0.000 0.00 312s Consumption_15 0.000 0.00 312s Consumption_16 0.000 0.00 312s Consumption_17 0.000 0.00 312s Consumption_18 0.000 0.00 312s Consumption_19 0.000 0.00 312s Consumption_20 0.000 0.00 312s Consumption_21 0.000 0.00 312s Consumption_22 0.000 0.00 312s Investment_2 -0.848 -12.21 312s Investment_3 -0.590 -8.69 312s Investment_4 21.069 230.01 312s Investment_5 -24.862 -256.32 312s Investment_6 8.059 80.05 312s Investment_7 29.994 295.17 312s Investment_8 15.463 160.46 312s Investment_9 -12.507 -131.14 312s Investment_10 22.850 228.07 312s Investment_11 6.056 60.20 312s Investment_12 0.575 7.99 312s Investment_13 4.172 78.05 312s Investment_14 1.566 46.33 312s Investment_15 -1.936 -34.91 312s Investment_16 0.124 2.01 312s Investment_17 13.606 192.14 312s Investment_18 0.908 10.31 312s Investment_19 -44.385 -517.74 312s Investment_20 -10.505 -137.25 312s Investment_21 -14.834 -157.09 312s Investment_22 -13.975 -135.45 312s PrivateWages_2 0.000 0.00 312s PrivateWages_3 0.000 0.00 312s PrivateWages_4 0.000 0.00 312s PrivateWages_5 0.000 0.00 312s PrivateWages_6 0.000 0.00 312s PrivateWages_8 0.000 0.00 312s PrivateWages_9 0.000 0.00 312s PrivateWages_10 0.000 0.00 312s PrivateWages_11 0.000 0.00 312s PrivateWages_12 0.000 0.00 312s PrivateWages_13 0.000 0.00 312s PrivateWages_14 0.000 0.00 312s PrivateWages_15 0.000 0.00 312s PrivateWages_16 0.000 0.00 312s PrivateWages_17 0.000 0.00 312s PrivateWages_18 0.000 0.00 312s PrivateWages_19 0.000 0.00 312s PrivateWages_20 0.000 0.00 312s PrivateWages_21 0.000 0.00 312s PrivateWages_22 0.000 0.00 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 0.0000 0.00 0.00 312s Consumption_3 0.0000 0.00 0.00 312s Consumption_4 0.0000 0.00 0.00 312s Consumption_5 0.0000 0.00 0.00 312s Consumption_6 0.0000 0.00 0.00 312s Consumption_7 0.0000 0.00 0.00 312s Consumption_8 0.0000 0.00 0.00 312s Consumption_9 0.0000 0.00 0.00 312s Consumption_11 0.0000 0.00 0.00 312s Consumption_12 0.0000 0.00 0.00 312s Consumption_13 0.0000 0.00 0.00 312s Consumption_14 0.0000 0.00 0.00 312s Consumption_15 0.0000 0.00 0.00 312s Consumption_16 0.0000 0.00 0.00 312s Consumption_17 0.0000 0.00 0.00 312s Consumption_18 0.0000 0.00 0.00 312s Consumption_19 0.0000 0.00 0.00 312s Consumption_20 0.0000 0.00 0.00 312s Consumption_21 0.0000 0.00 0.00 312s Consumption_22 0.0000 0.00 0.00 312s Investment_2 0.0000 0.00 0.00 312s Investment_3 0.0000 0.00 0.00 312s Investment_4 0.0000 0.00 0.00 312s Investment_5 0.0000 0.00 0.00 312s Investment_6 0.0000 0.00 0.00 312s Investment_7 0.0000 0.00 0.00 312s Investment_8 0.0000 0.00 0.00 312s Investment_9 0.0000 0.00 0.00 312s Investment_10 0.0000 0.00 0.00 312s Investment_11 0.0000 0.00 0.00 312s Investment_12 0.0000 0.00 0.00 312s Investment_13 0.0000 0.00 0.00 312s Investment_14 0.0000 0.00 0.00 312s Investment_15 0.0000 0.00 0.00 312s Investment_16 0.0000 0.00 0.00 312s Investment_17 0.0000 0.00 0.00 312s Investment_18 0.0000 0.00 0.00 312s Investment_19 0.0000 0.00 0.00 312s Investment_20 0.0000 0.00 0.00 312s Investment_21 0.0000 0.00 0.00 312s Investment_22 0.0000 0.00 0.00 312s PrivateWages_2 -1.3389 -61.06 -60.12 312s PrivateWages_3 0.2462 12.33 11.23 312s PrivateWages_4 1.1255 64.38 56.39 312s PrivateWages_5 -0.1959 -11.18 -11.20 312s PrivateWages_6 -0.5284 -32.23 -30.17 312s PrivateWages_8 -0.7909 -50.94 -50.62 312s PrivateWages_9 0.2819 18.18 18.15 312s PrivateWages_10 1.1384 76.28 73.43 312s PrivateWages_11 -0.1904 -11.65 -12.76 312s PrivateWages_12 0.5813 31.04 35.58 312s PrivateWages_13 0.1206 5.34 6.44 312s PrivateWages_14 0.4773 21.53 21.14 312s PrivateWages_15 0.3035 15.09 13.69 312s PrivateWages_16 0.0284 1.55 1.41 312s PrivateWages_17 -0.8517 -53.40 -46.33 312s PrivateWages_18 0.9908 64.40 62.12 312s PrivateWages_19 -0.4597 -28.00 -29.88 312s PrivateWages_20 -0.3819 -26.54 -23.26 312s PrivateWages_21 -1.1062 -83.74 -76.88 312s PrivateWages_22 0.5501 48.63 41.64 312s PrivateWages_trend 312s Consumption_2 0.000 312s Consumption_3 0.000 312s Consumption_4 0.000 312s Consumption_5 0.000 312s Consumption_6 0.000 312s Consumption_7 0.000 312s Consumption_8 0.000 312s Consumption_9 0.000 312s Consumption_11 0.000 312s Consumption_12 0.000 312s Consumption_13 0.000 312s Consumption_14 0.000 312s Consumption_15 0.000 312s Consumption_16 0.000 312s Consumption_17 0.000 312s Consumption_18 0.000 312s Consumption_19 0.000 312s Consumption_20 0.000 312s Consumption_21 0.000 312s Consumption_22 0.000 312s Investment_2 0.000 312s Investment_3 0.000 312s Investment_4 0.000 312s Investment_5 0.000 312s Investment_6 0.000 312s Investment_7 0.000 312s Investment_8 0.000 312s Investment_9 0.000 312s Investment_10 0.000 312s Investment_11 0.000 312s Investment_12 0.000 312s Investment_13 0.000 312s Investment_14 0.000 312s Investment_15 0.000 312s Investment_16 0.000 312s Investment_17 0.000 312s Investment_18 0.000 312s Investment_19 0.000 312s Investment_20 0.000 312s Investment_21 0.000 312s Investment_22 0.000 312s PrivateWages_2 13.389 312s PrivateWages_3 -2.216 312s PrivateWages_4 -9.004 312s PrivateWages_5 1.371 312s PrivateWages_6 3.170 312s PrivateWages_8 3.164 312s PrivateWages_9 -0.846 312s PrivateWages_10 -2.277 312s PrivateWages_11 0.190 312s PrivateWages_12 0.000 312s PrivateWages_13 0.121 312s PrivateWages_14 0.955 312s PrivateWages_15 0.911 312s PrivateWages_16 0.114 312s PrivateWages_17 -4.258 312s PrivateWages_18 5.945 312s PrivateWages_19 -3.218 312s PrivateWages_20 -3.055 312s PrivateWages_21 -9.956 312s PrivateWages_22 5.501 312s [1] TRUE 312s > Bread 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_(Intercept) 99.9867 -0.0712 312s Consumption_corpProf -0.0712 0.4890 312s Consumption_corpProfLag -1.1355 -0.2987 312s Consumption_wages -1.8752 -0.0787 312s Investment_(Intercept) 0.0000 0.0000 312s Investment_corpProf 0.0000 0.0000 312s Investment_corpProfLag 0.0000 0.0000 312s Investment_capitalLag 0.0000 0.0000 312s PrivateWages_(Intercept) 0.0000 0.0000 312s PrivateWages_gnp 0.0000 0.0000 312s PrivateWages_gnpLag 0.0000 0.0000 312s PrivateWages_trend 0.0000 0.0000 312s Consumption_corpProfLag Consumption_wages 312s Consumption_(Intercept) -1.1355 -1.8752 312s Consumption_corpProf -0.2987 -0.0787 312s Consumption_corpProfLag 0.4841 -0.0413 312s Consumption_wages -0.0413 0.0933 312s Investment_(Intercept) 0.0000 0.0000 312s Investment_corpProf 0.0000 0.0000 312s Investment_corpProfLag 0.0000 0.0000 312s Investment_capitalLag 0.0000 0.0000 312s PrivateWages_(Intercept) 0.0000 0.0000 312s PrivateWages_gnp 0.0000 0.0000 312s PrivateWages_gnpLag 0.0000 0.0000 312s PrivateWages_trend 0.0000 0.0000 312s Investment_(Intercept) Investment_corpProf 312s Consumption_(Intercept) 0.0 0.0000 312s Consumption_corpProf 0.0 0.0000 312s Consumption_corpProfLag 0.0 0.0000 312s Consumption_wages 0.0 0.0000 312s Investment_(Intercept) 1788.3 -17.4004 312s Investment_corpProf -17.4 0.5646 312s Investment_corpProfLag 14.2 -0.4849 312s Investment_capitalLag -8.6 0.0788 312s PrivateWages_(Intercept) 0.0 0.0000 312s PrivateWages_gnp 0.0 0.0000 312s PrivateWages_gnpLag 0.0 0.0000 312s PrivateWages_trend 0.0 0.0000 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_(Intercept) 0.0000 0.0000 312s Consumption_corpProf 0.0000 0.0000 312s Consumption_corpProfLag 0.0000 0.0000 312s Consumption_wages 0.0000 0.0000 312s Investment_(Intercept) 14.2083 -8.5994 312s Investment_corpProf -0.4849 0.0788 312s Investment_corpProfLag 0.6090 -0.0798 312s Investment_capitalLag -0.0798 0.0428 312s PrivateWages_(Intercept) 0.0000 0.0000 312s PrivateWages_gnp 0.0000 0.0000 312s PrivateWages_gnpLag 0.0000 0.0000 312s PrivateWages_trend 0.0000 0.0000 312s PrivateWages_(Intercept) PrivateWages_gnp 312s Consumption_(Intercept) 0.000 0.0000 312s Consumption_corpProf 0.000 0.0000 312s Consumption_corpProfLag 0.000 0.0000 312s Consumption_wages 0.000 0.0000 312s Investment_(Intercept) 0.000 0.0000 312s Investment_corpProf 0.000 0.0000 312s Investment_corpProfLag 0.000 0.0000 312s Investment_capitalLag 0.000 0.0000 312s PrivateWages_(Intercept) 171.811 -0.6470 312s PrivateWages_gnp -0.647 0.1100 312s PrivateWages_gnpLag -2.257 -0.1026 312s PrivateWages_trend 2.120 -0.0296 312s PrivateWages_gnpLag PrivateWages_trend 312s Consumption_(Intercept) 0.00000 0.00000 312s Consumption_corpProf 0.00000 0.00000 312s Consumption_corpProfLag 0.00000 0.00000 312s Consumption_wages 0.00000 0.00000 312s Investment_(Intercept) 0.00000 0.00000 312s Investment_corpProf 0.00000 0.00000 312s Investment_corpProfLag 0.00000 0.00000 312s Investment_capitalLag 0.00000 0.00000 312s PrivateWages_(Intercept) -2.25750 2.12030 312s PrivateWages_gnp -0.10258 -0.02955 312s PrivateWages_gnpLag 0.14523 -0.00656 312s PrivateWages_trend -0.00656 0.11341 312s > 312s > # 2SLS 312s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 312s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 312s > summary 312s 312s systemfit results 312s method: 2SLS 312s 312s N DF SSR detRCov OLS-R2 McElroy-R2 312s system 59 47 53.2 0.251 0.973 0.991 312s 312s N DF SSR MSE RMSE R2 Adj R2 312s Consumption 19 15 20.49 1.366 1.17 0.978 0.973 312s Investment 20 16 23.02 1.438 1.20 0.901 0.883 312s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 312s 312s The covariance matrix of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.079 0.354 -0.383 312s Investment 0.354 1.047 0.107 312s PrivateWages -0.383 0.107 0.445 312s 312s The correlations of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.000 0.335 -0.556 312s Investment 0.335 1.000 0.149 312s PrivateWages -0.556 0.149 1.000 312s 312s 312s 2SLS estimates for 'Consumption' (equation 1) 312s Model Formula: consump ~ corpProf + corpProfLag + wages 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 16.4657 1.3505 12.19 3.5e-09 *** 312s corpProf 0.0243 0.1180 0.21 0.839 312s corpProfLag 0.1981 0.1087 1.82 0.088 . 312s wages 0.8159 0.0420 19.45 4.7e-12 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.169 on 15 degrees of freedom 312s Number of observations: 19 Degrees of Freedom: 15 312s SSR: 20.493 MSE: 1.366 Root MSE: 1.169 312s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.973 312s 312s 312s 2SLS estimates for 'Investment' (equation 2) 312s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 17.8425 6.5319 2.73 0.01478 * 312s corpProf 0.2167 0.1478 1.47 0.16189 312s corpProfLag 0.5416 0.1415 3.83 0.00149 ** 312s capitalLag -0.1455 0.0314 -4.63 0.00028 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.199 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 312s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 312s 312s 312s 2SLS estimates for 'PrivateWages' (equation 3) 312s Model Formula: privWage ~ gnp + gnpLag + trend 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 1.3431 1.1250 1.19 0.24995 312s gnp 0.4438 0.0342 12.97 6.6e-10 *** 312s gnpLag 0.1447 0.0371 3.90 0.00128 ** 312s trend 0.1238 0.0292 4.24 0.00063 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 0.78 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 312s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 312s 312s > residuals 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 -0.39161 -1.0104 -1.3401 312s 3 -0.60524 0.2478 0.2378 312s 4 -1.24952 1.0621 1.1117 312s 5 -0.17101 -1.4104 -0.1954 312s 6 0.30841 0.4328 -0.5355 312s 7 NA NA NA 312s 8 1.50999 1.0463 -0.7908 312s 9 1.39649 0.0674 0.2831 312s 10 NA 1.7698 1.1353 312s 11 -0.49339 -0.5912 -0.1765 312s 12 -0.99824 -0.6318 0.6007 312s 13 -1.27965 -0.6983 0.1443 312s 14 0.55302 0.9724 0.4826 312s 15 -0.14553 -0.1827 0.3016 312s 16 -0.00773 0.1167 0.0261 312s 17 1.97001 1.6266 -0.8614 312s 18 -0.59152 -0.0525 0.9927 312s 19 -0.21481 -3.0656 -0.4446 312s 20 1.33575 0.1393 -0.3914 312s 21 1.01443 -0.1305 -1.1115 312s 22 -1.93986 0.2922 0.5312 312s > fitted 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 42.3 0.810 26.8 312s 3 45.6 1.652 29.1 312s 4 50.4 4.138 33.0 312s 5 50.8 4.410 34.1 312s 6 52.3 4.667 35.9 312s 7 NA NA NA 312s 8 54.7 3.154 38.7 312s 9 55.9 2.933 38.9 312s 10 NA 3.330 40.2 312s 11 55.5 1.591 38.1 312s 12 51.9 -2.768 33.9 312s 13 46.9 -5.502 28.9 312s 14 45.9 -6.072 28.0 312s 15 48.8 -2.817 30.3 312s 16 51.3 -1.417 33.2 312s 17 55.7 0.473 37.7 312s 18 59.3 2.053 40.0 312s 19 57.7 1.166 38.6 312s 20 60.3 1.161 42.0 312s 21 64.0 3.431 46.1 312s 22 71.6 4.608 52.8 312s > predict 312s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 312s 1 NA NA NA NA 312s 2 42.3 0.483 41.3 43.3 312s 3 45.6 0.586 44.4 46.9 312s 4 50.4 0.390 49.6 51.3 312s 5 50.8 0.456 49.8 51.7 312s 6 52.3 0.463 51.3 53.3 312s 7 NA NA NA NA 312s 8 54.7 0.382 53.9 55.5 312s 9 55.9 0.422 55.0 56.8 312s 10 NA NA NA NA 312s 11 55.5 0.742 53.9 57.1 312s 12 51.9 0.600 50.6 53.2 312s 13 46.9 0.770 45.2 48.5 312s 14 45.9 0.635 44.6 47.3 312s 15 48.8 0.383 48.0 49.7 312s 16 51.3 0.339 50.6 52.0 312s 17 55.7 0.410 54.9 56.6 312s 18 59.3 0.336 58.6 60.0 312s 19 57.7 0.418 56.8 58.6 312s 20 60.3 0.481 59.2 61.3 312s 21 64.0 0.462 63.0 65.0 312s 22 71.6 0.706 70.1 73.1 312s Investment.pred Investment.se.fit Investment.lwr Investment.upr 312s 1 NA NA NA NA 312s 2 0.810 0.750 -0.77956 2.400 312s 3 1.652 0.516 0.55883 2.746 312s 4 4.138 0.487 3.10541 5.170 312s 5 4.410 0.402 3.55860 5.262 312s 6 4.667 0.377 3.86830 5.466 312s 7 NA NA NA NA 312s 8 3.154 0.312 2.49238 3.815 312s 9 2.933 0.466 1.94478 3.920 312s 10 3.330 0.512 2.24435 4.416 312s 11 1.591 0.749 0.00249 3.180 312s 12 -2.768 0.586 -4.01111 -1.525 312s 13 -5.502 0.750 -7.09222 -3.911 312s 14 -6.072 0.803 -7.77404 -4.371 312s 15 -2.817 0.379 -3.62002 -2.015 312s 16 -1.417 0.327 -2.10985 -0.723 312s 17 0.473 0.436 -0.45046 1.397 312s 18 2.053 0.272 1.47523 2.630 312s 19 1.166 0.410 0.29710 2.034 312s 20 1.161 0.491 0.12044 2.201 312s 21 3.431 0.406 2.57004 4.291 312s 22 4.608 0.578 3.38197 5.834 312s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 312s 1 NA NA NA NA 312s 2 26.8 0.313 26.2 27.5 312s 3 29.1 0.325 28.4 29.8 312s 4 33.0 0.344 32.3 33.7 312s 5 34.1 0.246 33.6 34.6 312s 6 35.9 0.254 35.4 36.5 312s 7 NA NA NA NA 312s 8 38.7 0.251 38.2 39.2 312s 9 38.9 0.239 38.4 39.4 312s 10 40.2 0.229 39.7 40.7 312s 11 38.1 0.339 37.4 38.8 312s 12 33.9 0.365 33.1 34.7 312s 13 28.9 0.436 27.9 29.8 312s 14 28.0 0.333 27.3 28.7 312s 15 30.3 0.324 29.6 31.0 312s 16 33.2 0.271 32.6 33.7 312s 17 37.7 0.280 37.1 38.3 312s 18 40.0 0.208 39.6 40.4 312s 19 38.6 0.342 37.9 39.4 312s 20 42.0 0.293 41.4 42.6 312s 21 46.1 0.296 45.5 46.7 312s 22 52.8 0.474 51.8 53.8 312s > model.frame 312s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 312s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 312s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 312s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 312s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 312s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 312s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 312s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 312s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 312s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 312s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 312s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 312s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 312s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 312s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 312s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 312s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 312s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 312s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 312s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 312s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 312s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 312s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 312s trend 312s 1 -11 312s 2 -10 312s 3 -9 312s 4 -8 312s 5 -7 312s 6 -6 312s 7 -5 312s 8 -4 312s 9 -3 312s 10 -2 312s 11 -1 312s 12 0 312s 13 1 312s 14 2 312s 15 3 312s 16 4 312s 17 5 312s 18 6 312s 19 7 312s 20 8 312s 21 9 312s 22 10 312s > Frames of instrumental variables 312s govExp taxes govWage trend capitalLag corpProfLag gnpLag 312s 1 2.4 3.4 2.2 -11 180 NA NA 312s 2 3.9 7.7 2.7 -10 183 12.7 44.9 312s 3 3.2 3.9 2.9 -9 183 12.4 45.6 312s 4 2.8 4.7 2.9 -8 184 16.9 50.1 312s 5 3.5 3.8 3.1 -7 190 18.4 57.2 312s 6 3.3 5.5 3.2 -6 193 19.4 57.1 312s 7 3.3 7.0 3.3 -5 198 20.1 NA 312s 8 4.0 6.7 3.6 -4 203 19.6 64.0 312s 9 4.2 4.2 3.7 -3 208 19.8 64.4 312s 10 4.1 4.0 4.0 -2 211 21.1 64.5 312s 11 5.2 7.7 4.2 -1 216 21.7 67.0 312s 12 5.9 7.5 4.8 0 217 15.6 61.2 312s 13 4.9 8.3 5.3 1 213 11.4 53.4 312s 14 3.7 5.4 5.6 2 207 7.0 44.3 312s 15 4.0 6.8 6.0 3 202 11.2 45.1 312s 16 4.4 7.2 6.1 4 199 12.3 49.7 312s 17 2.9 8.3 7.4 5 198 14.0 54.4 312s 18 4.3 6.7 6.7 6 200 17.6 62.7 312s 19 5.3 7.4 7.7 7 202 17.3 65.0 312s 20 6.6 8.9 7.8 8 200 15.3 60.9 312s 21 7.4 9.6 8.0 9 201 19.0 69.5 312s 22 13.8 11.6 8.5 10 204 21.1 75.7 312s govExp taxes govWage trend capitalLag corpProfLag gnpLag 312s 1 2.4 3.4 2.2 -11 180 NA NA 312s 2 3.9 7.7 2.7 -10 183 12.7 44.9 312s 3 3.2 3.9 2.9 -9 183 12.4 45.6 312s 4 2.8 4.7 2.9 -8 184 16.9 50.1 312s 5 3.5 3.8 3.1 -7 190 18.4 57.2 312s 6 3.3 5.5 3.2 -6 193 19.4 57.1 312s 7 3.3 7.0 3.3 -5 198 20.1 NA 312s 8 4.0 6.7 3.6 -4 203 19.6 64.0 312s 9 4.2 4.2 3.7 -3 208 19.8 64.4 312s 10 4.1 4.0 4.0 -2 211 21.1 64.5 312s 11 5.2 7.7 4.2 -1 216 21.7 67.0 312s 12 5.9 7.5 4.8 0 217 15.6 61.2 312s 13 4.9 8.3 5.3 1 213 11.4 53.4 312s 14 3.7 5.4 5.6 2 207 7.0 44.3 312s 15 4.0 6.8 6.0 3 202 11.2 45.1 312s 16 4.4 7.2 6.1 4 199 12.3 49.7 312s 17 2.9 8.3 7.4 5 198 14.0 54.4 312s 18 4.3 6.7 6.7 6 200 17.6 62.7 312s 19 5.3 7.4 7.7 7 202 17.3 65.0 312s 20 6.6 8.9 7.8 8 200 15.3 60.9 312s 21 7.4 9.6 8.0 9 201 19.0 69.5 312s 22 13.8 11.6 8.5 10 204 21.1 75.7 312s govExp taxes govWage trend capitalLag corpProfLag gnpLag 312s 1 2.4 3.4 2.2 -11 180 NA NA 312s 2 3.9 7.7 2.7 -10 183 12.7 44.9 312s 3 3.2 3.9 2.9 -9 183 12.4 45.6 312s 4 2.8 4.7 2.9 -8 184 16.9 50.1 312s 5 3.5 3.8 3.1 -7 190 18.4 57.2 312s 6 3.3 5.5 3.2 -6 193 19.4 57.1 312s 7 3.3 7.0 3.3 -5 198 20.1 NA 312s 8 4.0 6.7 3.6 -4 203 19.6 64.0 312s 9 4.2 4.2 3.7 -3 208 19.8 64.4 312s 10 4.1 4.0 4.0 -2 211 21.1 64.5 312s 11 5.2 7.7 4.2 -1 216 21.7 67.0 312s 12 5.9 7.5 4.8 0 217 15.6 61.2 312s 13 4.9 8.3 5.3 1 213 11.4 53.4 312s 14 3.7 5.4 5.6 2 207 7.0 44.3 312s 15 4.0 6.8 6.0 3 202 11.2 45.1 312s 16 4.4 7.2 6.1 4 199 12.3 49.7 312s 17 2.9 8.3 7.4 5 198 14.0 54.4 312s 18 4.3 6.7 6.7 6 200 17.6 62.7 312s 19 5.3 7.4 7.7 7 202 17.3 65.0 312s 20 6.6 8.9 7.8 8 200 15.3 60.9 312s 21 7.4 9.6 8.0 9 201 19.0 69.5 312s 22 13.8 11.6 8.5 10 204 21.1 75.7 312s > model.matrix 312s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 312s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 312s [3] "Numeric: lengths (732, 708) differ" 312s > matrix of instrumental variables 312s Consumption_(Intercept) Consumption_govExp Consumption_taxes 312s Consumption_2 1 3.9 7.7 312s Consumption_3 1 3.2 3.9 312s Consumption_4 1 2.8 4.7 312s Consumption_5 1 3.5 3.8 312s Consumption_6 1 3.3 5.5 312s Consumption_8 1 4.0 6.7 312s Consumption_9 1 4.2 4.2 312s Consumption_11 1 5.2 7.7 312s Consumption_12 1 5.9 7.5 312s Consumption_13 1 4.9 8.3 312s Consumption_14 1 3.7 5.4 312s Consumption_15 1 4.0 6.8 312s Consumption_16 1 4.4 7.2 312s Consumption_17 1 2.9 8.3 312s Consumption_18 1 4.3 6.7 312s Consumption_19 1 5.3 7.4 312s Consumption_20 1 6.6 8.9 312s Consumption_21 1 7.4 9.6 312s Consumption_22 1 13.8 11.6 312s Investment_2 0 0.0 0.0 312s Investment_3 0 0.0 0.0 312s Investment_4 0 0.0 0.0 312s Investment_5 0 0.0 0.0 312s Investment_6 0 0.0 0.0 312s Investment_8 0 0.0 0.0 312s Investment_9 0 0.0 0.0 312s Investment_10 0 0.0 0.0 312s Investment_11 0 0.0 0.0 312s Investment_12 0 0.0 0.0 312s Investment_13 0 0.0 0.0 312s Investment_14 0 0.0 0.0 312s Investment_15 0 0.0 0.0 312s Investment_16 0 0.0 0.0 312s Investment_17 0 0.0 0.0 312s Investment_18 0 0.0 0.0 312s Investment_19 0 0.0 0.0 312s Investment_20 0 0.0 0.0 312s Investment_21 0 0.0 0.0 312s Investment_22 0 0.0 0.0 312s PrivateWages_2 0 0.0 0.0 312s PrivateWages_3 0 0.0 0.0 312s PrivateWages_4 0 0.0 0.0 312s PrivateWages_5 0 0.0 0.0 312s PrivateWages_6 0 0.0 0.0 312s PrivateWages_8 0 0.0 0.0 312s PrivateWages_9 0 0.0 0.0 312s PrivateWages_10 0 0.0 0.0 312s PrivateWages_11 0 0.0 0.0 312s PrivateWages_12 0 0.0 0.0 312s PrivateWages_13 0 0.0 0.0 312s PrivateWages_14 0 0.0 0.0 312s PrivateWages_15 0 0.0 0.0 312s PrivateWages_16 0 0.0 0.0 312s PrivateWages_17 0 0.0 0.0 312s PrivateWages_18 0 0.0 0.0 312s PrivateWages_19 0 0.0 0.0 312s PrivateWages_20 0 0.0 0.0 312s PrivateWages_21 0 0.0 0.0 312s PrivateWages_22 0 0.0 0.0 312s Consumption_govWage Consumption_trend Consumption_capitalLag 312s Consumption_2 2.7 -10 183 312s Consumption_3 2.9 -9 183 312s Consumption_4 2.9 -8 184 312s Consumption_5 3.1 -7 190 312s Consumption_6 3.2 -6 193 312s Consumption_8 3.6 -4 203 312s Consumption_9 3.7 -3 208 312s Consumption_11 4.2 -1 216 312s Consumption_12 4.8 0 217 312s Consumption_13 5.3 1 213 312s Consumption_14 5.6 2 207 312s Consumption_15 6.0 3 202 312s Consumption_16 6.1 4 199 312s Consumption_17 7.4 5 198 312s Consumption_18 6.7 6 200 312s Consumption_19 7.7 7 202 312s Consumption_20 7.8 8 200 312s Consumption_21 8.0 9 201 312s Consumption_22 8.5 10 204 312s Investment_2 0.0 0 0 312s Investment_3 0.0 0 0 312s Investment_4 0.0 0 0 312s Investment_5 0.0 0 0 312s Investment_6 0.0 0 0 312s Investment_8 0.0 0 0 312s Investment_9 0.0 0 0 312s Investment_10 0.0 0 0 312s Investment_11 0.0 0 0 312s Investment_12 0.0 0 0 312s Investment_13 0.0 0 0 312s Investment_14 0.0 0 0 312s Investment_15 0.0 0 0 312s Investment_16 0.0 0 0 312s Investment_17 0.0 0 0 312s Investment_18 0.0 0 0 312s Investment_19 0.0 0 0 312s Investment_20 0.0 0 0 312s Investment_21 0.0 0 0 312s Investment_22 0.0 0 0 312s PrivateWages_2 0.0 0 0 312s PrivateWages_3 0.0 0 0 312s PrivateWages_4 0.0 0 0 312s PrivateWages_5 0.0 0 0 312s PrivateWages_6 0.0 0 0 312s PrivateWages_8 0.0 0 0 312s PrivateWages_9 0.0 0 0 312s PrivateWages_10 0.0 0 0 312s PrivateWages_11 0.0 0 0 312s PrivateWages_12 0.0 0 0 312s PrivateWages_13 0.0 0 0 312s PrivateWages_14 0.0 0 0 312s PrivateWages_15 0.0 0 0 312s PrivateWages_16 0.0 0 0 312s PrivateWages_17 0.0 0 0 312s PrivateWages_18 0.0 0 0 312s PrivateWages_19 0.0 0 0 312s PrivateWages_20 0.0 0 0 312s PrivateWages_21 0.0 0 0 312s PrivateWages_22 0.0 0 0 312s Consumption_corpProfLag Consumption_gnpLag 312s Consumption_2 12.7 44.9 312s Consumption_3 12.4 45.6 312s Consumption_4 16.9 50.1 312s Consumption_5 18.4 57.2 312s Consumption_6 19.4 57.1 312s Consumption_8 19.6 64.0 312s Consumption_9 19.8 64.4 312s Consumption_11 21.7 67.0 312s Consumption_12 15.6 61.2 312s Consumption_13 11.4 53.4 312s Consumption_14 7.0 44.3 312s Consumption_15 11.2 45.1 312s Consumption_16 12.3 49.7 312s Consumption_17 14.0 54.4 312s Consumption_18 17.6 62.7 312s Consumption_19 17.3 65.0 312s Consumption_20 15.3 60.9 312s Consumption_21 19.0 69.5 312s Consumption_22 21.1 75.7 312s Investment_2 0.0 0.0 312s Investment_3 0.0 0.0 312s Investment_4 0.0 0.0 312s Investment_5 0.0 0.0 312s Investment_6 0.0 0.0 312s Investment_8 0.0 0.0 312s Investment_9 0.0 0.0 312s Investment_10 0.0 0.0 312s Investment_11 0.0 0.0 312s Investment_12 0.0 0.0 312s Investment_13 0.0 0.0 312s Investment_14 0.0 0.0 312s Investment_15 0.0 0.0 312s Investment_16 0.0 0.0 312s Investment_17 0.0 0.0 312s Investment_18 0.0 0.0 312s Investment_19 0.0 0.0 312s Investment_20 0.0 0.0 312s Investment_21 0.0 0.0 312s Investment_22 0.0 0.0 312s PrivateWages_2 0.0 0.0 312s PrivateWages_3 0.0 0.0 312s PrivateWages_4 0.0 0.0 312s PrivateWages_5 0.0 0.0 312s PrivateWages_6 0.0 0.0 312s PrivateWages_8 0.0 0.0 312s PrivateWages_9 0.0 0.0 312s PrivateWages_10 0.0 0.0 312s PrivateWages_11 0.0 0.0 312s PrivateWages_12 0.0 0.0 312s PrivateWages_13 0.0 0.0 312s PrivateWages_14 0.0 0.0 312s PrivateWages_15 0.0 0.0 312s PrivateWages_16 0.0 0.0 312s PrivateWages_17 0.0 0.0 312s PrivateWages_18 0.0 0.0 312s PrivateWages_19 0.0 0.0 312s PrivateWages_20 0.0 0.0 312s PrivateWages_21 0.0 0.0 312s PrivateWages_22 0.0 0.0 312s Investment_(Intercept) Investment_govExp Investment_taxes 312s Consumption_2 0 0.0 0.0 312s Consumption_3 0 0.0 0.0 312s Consumption_4 0 0.0 0.0 312s Consumption_5 0 0.0 0.0 312s Consumption_6 0 0.0 0.0 312s Consumption_8 0 0.0 0.0 312s Consumption_9 0 0.0 0.0 312s Consumption_11 0 0.0 0.0 312s Consumption_12 0 0.0 0.0 312s Consumption_13 0 0.0 0.0 312s Consumption_14 0 0.0 0.0 312s Consumption_15 0 0.0 0.0 312s Consumption_16 0 0.0 0.0 312s Consumption_17 0 0.0 0.0 312s Consumption_18 0 0.0 0.0 312s Consumption_19 0 0.0 0.0 312s Consumption_20 0 0.0 0.0 312s Consumption_21 0 0.0 0.0 312s Consumption_22 0 0.0 0.0 312s Investment_2 1 3.9 7.7 312s Investment_3 1 3.2 3.9 312s Investment_4 1 2.8 4.7 312s Investment_5 1 3.5 3.8 312s Investment_6 1 3.3 5.5 312s Investment_8 1 4.0 6.7 312s Investment_9 1 4.2 4.2 312s Investment_10 1 4.1 4.0 312s Investment_11 1 5.2 7.7 312s Investment_12 1 5.9 7.5 312s Investment_13 1 4.9 8.3 312s Investment_14 1 3.7 5.4 312s Investment_15 1 4.0 6.8 312s Investment_16 1 4.4 7.2 312s Investment_17 1 2.9 8.3 312s Investment_18 1 4.3 6.7 312s Investment_19 1 5.3 7.4 312s Investment_20 1 6.6 8.9 312s Investment_21 1 7.4 9.6 312s Investment_22 1 13.8 11.6 312s PrivateWages_2 0 0.0 0.0 312s PrivateWages_3 0 0.0 0.0 312s PrivateWages_4 0 0.0 0.0 312s PrivateWages_5 0 0.0 0.0 312s PrivateWages_6 0 0.0 0.0 312s PrivateWages_8 0 0.0 0.0 312s PrivateWages_9 0 0.0 0.0 312s PrivateWages_10 0 0.0 0.0 312s PrivateWages_11 0 0.0 0.0 312s PrivateWages_12 0 0.0 0.0 312s PrivateWages_13 0 0.0 0.0 312s PrivateWages_14 0 0.0 0.0 312s PrivateWages_15 0 0.0 0.0 312s PrivateWages_16 0 0.0 0.0 312s PrivateWages_17 0 0.0 0.0 312s PrivateWages_18 0 0.0 0.0 312s PrivateWages_19 0 0.0 0.0 312s PrivateWages_20 0 0.0 0.0 312s PrivateWages_21 0 0.0 0.0 312s PrivateWages_22 0 0.0 0.0 312s Investment_govWage Investment_trend Investment_capitalLag 312s Consumption_2 0.0 0 0 312s Consumption_3 0.0 0 0 312s Consumption_4 0.0 0 0 312s Consumption_5 0.0 0 0 312s Consumption_6 0.0 0 0 312s Consumption_8 0.0 0 0 312s Consumption_9 0.0 0 0 312s Consumption_11 0.0 0 0 312s Consumption_12 0.0 0 0 312s Consumption_13 0.0 0 0 312s Consumption_14 0.0 0 0 312s Consumption_15 0.0 0 0 312s Consumption_16 0.0 0 0 312s Consumption_17 0.0 0 0 312s Consumption_18 0.0 0 0 312s Consumption_19 0.0 0 0 312s Consumption_20 0.0 0 0 312s Consumption_21 0.0 0 0 312s Consumption_22 0.0 0 0 312s Investment_2 2.7 -10 183 312s Investment_3 2.9 -9 183 312s Investment_4 2.9 -8 184 312s Investment_5 3.1 -7 190 312s Investment_6 3.2 -6 193 312s Investment_8 3.6 -4 203 312s Investment_9 3.7 -3 208 312s Investment_10 4.0 -2 211 312s Investment_11 4.2 -1 216 312s Investment_12 4.8 0 217 312s Investment_13 5.3 1 213 312s Investment_14 5.6 2 207 312s Investment_15 6.0 3 202 312s Investment_16 6.1 4 199 312s Investment_17 7.4 5 198 312s Investment_18 6.7 6 200 312s Investment_19 7.7 7 202 312s Investment_20 7.8 8 200 312s Investment_21 8.0 9 201 312s Investment_22 8.5 10 204 312s PrivateWages_2 0.0 0 0 312s PrivateWages_3 0.0 0 0 312s PrivateWages_4 0.0 0 0 312s PrivateWages_5 0.0 0 0 312s PrivateWages_6 0.0 0 0 312s PrivateWages_8 0.0 0 0 312s PrivateWages_9 0.0 0 0 312s PrivateWages_10 0.0 0 0 312s PrivateWages_11 0.0 0 0 312s PrivateWages_12 0.0 0 0 312s PrivateWages_13 0.0 0 0 312s PrivateWages_14 0.0 0 0 312s PrivateWages_15 0.0 0 0 312s PrivateWages_16 0.0 0 0 312s PrivateWages_17 0.0 0 0 312s PrivateWages_18 0.0 0 0 312s PrivateWages_19 0.0 0 0 312s PrivateWages_20 0.0 0 0 312s PrivateWages_21 0.0 0 0 312s PrivateWages_22 0.0 0 0 312s Investment_corpProfLag Investment_gnpLag 312s Consumption_2 0.0 0.0 312s Consumption_3 0.0 0.0 312s Consumption_4 0.0 0.0 312s Consumption_5 0.0 0.0 312s Consumption_6 0.0 0.0 312s Consumption_8 0.0 0.0 312s Consumption_9 0.0 0.0 312s Consumption_11 0.0 0.0 312s Consumption_12 0.0 0.0 312s Consumption_13 0.0 0.0 312s Consumption_14 0.0 0.0 312s Consumption_15 0.0 0.0 312s Consumption_16 0.0 0.0 312s Consumption_17 0.0 0.0 312s Consumption_18 0.0 0.0 312s Consumption_19 0.0 0.0 312s Consumption_20 0.0 0.0 312s Consumption_21 0.0 0.0 312s Consumption_22 0.0 0.0 312s Investment_2 12.7 44.9 312s Investment_3 12.4 45.6 312s Investment_4 16.9 50.1 312s Investment_5 18.4 57.2 312s Investment_6 19.4 57.1 312s Investment_8 19.6 64.0 312s Investment_9 19.8 64.4 312s Investment_10 21.1 64.5 312s Investment_11 21.7 67.0 312s Investment_12 15.6 61.2 312s Investment_13 11.4 53.4 312s Investment_14 7.0 44.3 312s Investment_15 11.2 45.1 312s Investment_16 12.3 49.7 312s Investment_17 14.0 54.4 312s Investment_18 17.6 62.7 312s Investment_19 17.3 65.0 312s Investment_20 15.3 60.9 312s Investment_21 19.0 69.5 312s Investment_22 21.1 75.7 312s PrivateWages_2 0.0 0.0 312s PrivateWages_3 0.0 0.0 312s PrivateWages_4 0.0 0.0 312s PrivateWages_5 0.0 0.0 312s PrivateWages_6 0.0 0.0 312s PrivateWages_8 0.0 0.0 312s PrivateWages_9 0.0 0.0 312s PrivateWages_10 0.0 0.0 312s PrivateWages_11 0.0 0.0 312s PrivateWages_12 0.0 0.0 312s PrivateWages_13 0.0 0.0 312s PrivateWages_14 0.0 0.0 312s PrivateWages_15 0.0 0.0 312s PrivateWages_16 0.0 0.0 312s PrivateWages_17 0.0 0.0 312s PrivateWages_18 0.0 0.0 312s PrivateWages_19 0.0 0.0 312s PrivateWages_20 0.0 0.0 312s PrivateWages_21 0.0 0.0 312s PrivateWages_22 0.0 0.0 312s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 312s Consumption_2 0 0.0 0.0 312s Consumption_3 0 0.0 0.0 312s Consumption_4 0 0.0 0.0 312s Consumption_5 0 0.0 0.0 312s Consumption_6 0 0.0 0.0 312s Consumption_8 0 0.0 0.0 312s Consumption_9 0 0.0 0.0 312s Consumption_11 0 0.0 0.0 312s Consumption_12 0 0.0 0.0 312s Consumption_13 0 0.0 0.0 312s Consumption_14 0 0.0 0.0 312s Consumption_15 0 0.0 0.0 312s Consumption_16 0 0.0 0.0 312s Consumption_17 0 0.0 0.0 312s Consumption_18 0 0.0 0.0 312s Consumption_19 0 0.0 0.0 312s Consumption_20 0 0.0 0.0 312s Consumption_21 0 0.0 0.0 312s Consumption_22 0 0.0 0.0 312s Investment_2 0 0.0 0.0 312s Investment_3 0 0.0 0.0 312s Investment_4 0 0.0 0.0 312s Investment_5 0 0.0 0.0 312s Investment_6 0 0.0 0.0 312s Investment_8 0 0.0 0.0 312s Investment_9 0 0.0 0.0 312s Investment_10 0 0.0 0.0 312s Investment_11 0 0.0 0.0 312s Investment_12 0 0.0 0.0 312s Investment_13 0 0.0 0.0 312s Investment_14 0 0.0 0.0 312s Investment_15 0 0.0 0.0 312s Investment_16 0 0.0 0.0 312s Investment_17 0 0.0 0.0 312s Investment_18 0 0.0 0.0 312s Investment_19 0 0.0 0.0 312s Investment_20 0 0.0 0.0 312s Investment_21 0 0.0 0.0 312s Investment_22 0 0.0 0.0 312s PrivateWages_2 1 3.9 7.7 312s PrivateWages_3 1 3.2 3.9 312s PrivateWages_4 1 2.8 4.7 312s PrivateWages_5 1 3.5 3.8 312s PrivateWages_6 1 3.3 5.5 312s PrivateWages_8 1 4.0 6.7 312s PrivateWages_9 1 4.2 4.2 312s PrivateWages_10 1 4.1 4.0 312s PrivateWages_11 1 5.2 7.7 312s PrivateWages_12 1 5.9 7.5 312s PrivateWages_13 1 4.9 8.3 312s PrivateWages_14 1 3.7 5.4 312s PrivateWages_15 1 4.0 6.8 312s PrivateWages_16 1 4.4 7.2 312s PrivateWages_17 1 2.9 8.3 312s PrivateWages_18 1 4.3 6.7 312s PrivateWages_19 1 5.3 7.4 312s PrivateWages_20 1 6.6 8.9 312s PrivateWages_21 1 7.4 9.6 312s PrivateWages_22 1 13.8 11.6 312s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 312s Consumption_2 0.0 0 0 312s Consumption_3 0.0 0 0 312s Consumption_4 0.0 0 0 312s Consumption_5 0.0 0 0 312s Consumption_6 0.0 0 0 312s Consumption_8 0.0 0 0 312s Consumption_9 0.0 0 0 312s Consumption_11 0.0 0 0 312s Consumption_12 0.0 0 0 312s Consumption_13 0.0 0 0 312s Consumption_14 0.0 0 0 312s Consumption_15 0.0 0 0 312s Consumption_16 0.0 0 0 312s Consumption_17 0.0 0 0 312s Consumption_18 0.0 0 0 312s Consumption_19 0.0 0 0 312s Consumption_20 0.0 0 0 312s Consumption_21 0.0 0 0 312s Consumption_22 0.0 0 0 312s Investment_2 0.0 0 0 312s Investment_3 0.0 0 0 312s Investment_4 0.0 0 0 312s Investment_5 0.0 0 0 312s Investment_6 0.0 0 0 312s Investment_8 0.0 0 0 312s Investment_9 0.0 0 0 312s Investment_10 0.0 0 0 312s Investment_11 0.0 0 0 312s Investment_12 0.0 0 0 312s Investment_13 0.0 0 0 312s Investment_14 0.0 0 0 312s Investment_15 0.0 0 0 312s Investment_16 0.0 0 0 312s Investment_17 0.0 0 0 312s Investment_18 0.0 0 0 312s Investment_19 0.0 0 0 312s Investment_20 0.0 0 0 312s Investment_21 0.0 0 0 312s Investment_22 0.0 0 0 312s PrivateWages_2 2.7 -10 183 312s PrivateWages_3 2.9 -9 183 312s PrivateWages_4 2.9 -8 184 312s PrivateWages_5 3.1 -7 190 312s PrivateWages_6 3.2 -6 193 312s PrivateWages_8 3.6 -4 203 312s PrivateWages_9 3.7 -3 208 312s PrivateWages_10 4.0 -2 211 312s PrivateWages_11 4.2 -1 216 312s PrivateWages_12 4.8 0 217 312s PrivateWages_13 5.3 1 213 312s PrivateWages_14 5.6 2 207 312s PrivateWages_15 6.0 3 202 312s PrivateWages_16 6.1 4 199 312s PrivateWages_17 7.4 5 198 312s PrivateWages_18 6.7 6 200 312s PrivateWages_19 7.7 7 202 312s PrivateWages_20 7.8 8 200 312s PrivateWages_21 8.0 9 201 312s PrivateWages_22 8.5 10 204 312s PrivateWages_corpProfLag PrivateWages_gnpLag 312s Consumption_2 0.0 0.0 312s Consumption_3 0.0 0.0 312s Consumption_4 0.0 0.0 312s Consumption_5 0.0 0.0 312s Consumption_6 0.0 0.0 312s Consumption_8 0.0 0.0 312s Consumption_9 0.0 0.0 312s Consumption_11 0.0 0.0 312s Consumption_12 0.0 0.0 312s Consumption_13 0.0 0.0 312s Consumption_14 0.0 0.0 312s Consumption_15 0.0 0.0 312s Consumption_16 0.0 0.0 312s Consumption_17 0.0 0.0 312s Consumption_18 0.0 0.0 312s Consumption_19 0.0 0.0 312s Consumption_20 0.0 0.0 312s Consumption_21 0.0 0.0 312s Consumption_22 0.0 0.0 312s Investment_2 0.0 0.0 312s Investment_3 0.0 0.0 312s Investment_4 0.0 0.0 312s Investment_5 0.0 0.0 312s Investment_6 0.0 0.0 312s Investment_8 0.0 0.0 312s Investment_9 0.0 0.0 312s Investment_10 0.0 0.0 312s Investment_11 0.0 0.0 312s Investment_12 0.0 0.0 312s Investment_13 0.0 0.0 312s Investment_14 0.0 0.0 312s Investment_15 0.0 0.0 312s Investment_16 0.0 0.0 312s Investment_17 0.0 0.0 312s Investment_18 0.0 0.0 312s Investment_19 0.0 0.0 312s Investment_20 0.0 0.0 312s Investment_21 0.0 0.0 312s Investment_22 0.0 0.0 312s PrivateWages_2 12.7 44.9 312s PrivateWages_3 12.4 45.6 312s PrivateWages_4 16.9 50.1 312s PrivateWages_5 18.4 57.2 312s PrivateWages_6 19.4 57.1 312s PrivateWages_8 19.6 64.0 312s PrivateWages_9 19.8 64.4 312s PrivateWages_10 21.1 64.5 312s PrivateWages_11 21.7 67.0 312s PrivateWages_12 15.6 61.2 312s PrivateWages_13 11.4 53.4 312s PrivateWages_14 7.0 44.3 312s PrivateWages_15 11.2 45.1 312s PrivateWages_16 12.3 49.7 312s PrivateWages_17 14.0 54.4 312s PrivateWages_18 17.6 62.7 312s PrivateWages_19 17.3 65.0 312s PrivateWages_20 15.3 60.9 312s PrivateWages_21 19.0 69.5 312s PrivateWages_22 21.1 75.7 312s > matrix of fitted regressors 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 1 13.44 312s Consumption_3 1 16.68 312s Consumption_4 1 18.95 312s Consumption_5 1 20.63 312s Consumption_6 1 19.28 312s Consumption_8 1 17.21 312s Consumption_9 1 18.99 312s Consumption_11 1 16.43 312s Consumption_12 1 12.49 312s Consumption_13 1 9.06 312s Consumption_14 1 9.28 312s Consumption_15 1 12.49 312s Consumption_16 1 14.39 312s Consumption_17 1 14.69 312s Consumption_18 1 19.60 312s Consumption_19 1 19.15 312s Consumption_20 1 17.54 312s Consumption_21 1 20.33 312s Consumption_22 1 22.78 312s Investment_2 0 0.00 312s Investment_3 0 0.00 312s Investment_4 0 0.00 312s Investment_5 0 0.00 312s Investment_6 0 0.00 312s Investment_8 0 0.00 312s Investment_9 0 0.00 312s Investment_10 0 0.00 312s Investment_11 0 0.00 312s Investment_12 0 0.00 312s Investment_13 0 0.00 312s Investment_14 0 0.00 312s Investment_15 0 0.00 312s Investment_16 0 0.00 312s Investment_17 0 0.00 312s Investment_18 0 0.00 312s Investment_19 0 0.00 312s Investment_20 0 0.00 312s Investment_21 0 0.00 312s Investment_22 0 0.00 312s PrivateWages_2 0 0.00 312s PrivateWages_3 0 0.00 312s PrivateWages_4 0 0.00 312s PrivateWages_5 0 0.00 312s PrivateWages_6 0 0.00 312s PrivateWages_8 0 0.00 312s PrivateWages_9 0 0.00 312s PrivateWages_10 0 0.00 312s PrivateWages_11 0 0.00 312s PrivateWages_12 0 0.00 312s PrivateWages_13 0 0.00 312s PrivateWages_14 0 0.00 312s PrivateWages_15 0 0.00 312s PrivateWages_16 0 0.00 312s PrivateWages_17 0 0.00 312s PrivateWages_18 0 0.00 312s PrivateWages_19 0 0.00 312s PrivateWages_20 0 0.00 312s PrivateWages_21 0 0.00 312s PrivateWages_22 0 0.00 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 12.7 29.6 312s Consumption_3 12.4 31.9 312s Consumption_4 16.9 35.4 312s Consumption_5 18.4 38.8 312s Consumption_6 19.4 38.7 312s Consumption_8 19.6 39.8 312s Consumption_9 19.8 41.8 312s Consumption_11 21.7 43.0 312s Consumption_12 15.6 39.3 312s Consumption_13 11.4 35.2 312s Consumption_14 7.0 33.0 312s Consumption_15 11.2 37.3 312s Consumption_16 12.3 40.1 312s Consumption_17 14.0 41.7 312s Consumption_18 17.6 47.7 312s Consumption_19 17.3 49.2 312s Consumption_20 15.3 48.5 312s Consumption_21 19.0 53.4 312s Consumption_22 21.1 60.8 312s Investment_2 0.0 0.0 312s Investment_3 0.0 0.0 312s Investment_4 0.0 0.0 312s Investment_5 0.0 0.0 312s Investment_6 0.0 0.0 312s Investment_8 0.0 0.0 312s Investment_9 0.0 0.0 312s Investment_10 0.0 0.0 312s Investment_11 0.0 0.0 312s Investment_12 0.0 0.0 312s Investment_13 0.0 0.0 312s Investment_14 0.0 0.0 312s Investment_15 0.0 0.0 312s Investment_16 0.0 0.0 312s Investment_17 0.0 0.0 312s Investment_18 0.0 0.0 312s Investment_19 0.0 0.0 312s Investment_20 0.0 0.0 312s Investment_21 0.0 0.0 312s Investment_22 0.0 0.0 312s PrivateWages_2 0.0 0.0 312s PrivateWages_3 0.0 0.0 312s PrivateWages_4 0.0 0.0 312s PrivateWages_5 0.0 0.0 312s PrivateWages_6 0.0 0.0 312s PrivateWages_8 0.0 0.0 312s PrivateWages_9 0.0 0.0 312s PrivateWages_10 0.0 0.0 312s PrivateWages_11 0.0 0.0 312s PrivateWages_12 0.0 0.0 312s PrivateWages_13 0.0 0.0 312s PrivateWages_14 0.0 0.0 312s PrivateWages_15 0.0 0.0 312s PrivateWages_16 0.0 0.0 312s PrivateWages_17 0.0 0.0 312s PrivateWages_18 0.0 0.0 312s PrivateWages_19 0.0 0.0 312s PrivateWages_20 0.0 0.0 312s PrivateWages_21 0.0 0.0 312s PrivateWages_22 0.0 0.0 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 0 0.00 312s Consumption_3 0 0.00 312s Consumption_4 0 0.00 312s Consumption_5 0 0.00 312s Consumption_6 0 0.00 312s Consumption_8 0 0.00 312s Consumption_9 0 0.00 312s Consumption_11 0 0.00 312s Consumption_12 0 0.00 312s Consumption_13 0 0.00 312s Consumption_14 0 0.00 312s Consumption_15 0 0.00 312s Consumption_16 0 0.00 312s Consumption_17 0 0.00 312s Consumption_18 0 0.00 312s Consumption_19 0 0.00 312s Consumption_20 0 0.00 312s Consumption_21 0 0.00 312s Consumption_22 0 0.00 312s Investment_2 1 12.96 312s Investment_3 1 16.70 312s Investment_4 1 19.14 312s Investment_5 1 20.94 312s Investment_6 1 19.47 312s Investment_8 1 17.14 312s Investment_9 1 19.49 312s Investment_10 1 20.46 312s Investment_11 1 16.85 312s Investment_12 1 12.68 312s Investment_13 1 8.92 312s Investment_14 1 9.30 312s Investment_15 1 12.79 312s Investment_16 1 14.26 312s Investment_17 1 14.75 312s Investment_18 1 19.54 312s Investment_19 1 19.36 312s Investment_20 1 17.39 312s Investment_21 1 20.10 312s Investment_22 1 22.86 312s PrivateWages_2 0 0.00 312s PrivateWages_3 0 0.00 312s PrivateWages_4 0 0.00 312s PrivateWages_5 0 0.00 312s PrivateWages_6 0 0.00 312s PrivateWages_8 0 0.00 312s PrivateWages_9 0 0.00 312s PrivateWages_10 0 0.00 312s PrivateWages_11 0 0.00 312s PrivateWages_12 0 0.00 312s PrivateWages_13 0 0.00 312s PrivateWages_14 0 0.00 312s PrivateWages_15 0 0.00 312s PrivateWages_16 0 0.00 312s PrivateWages_17 0 0.00 312s PrivateWages_18 0 0.00 312s PrivateWages_19 0 0.00 312s PrivateWages_20 0 0.00 312s PrivateWages_21 0 0.00 312s PrivateWages_22 0 0.00 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 0.0 0 312s Consumption_3 0.0 0 312s Consumption_4 0.0 0 312s Consumption_5 0.0 0 312s Consumption_6 0.0 0 312s Consumption_8 0.0 0 312s Consumption_9 0.0 0 312s Consumption_11 0.0 0 312s Consumption_12 0.0 0 312s Consumption_13 0.0 0 312s Consumption_14 0.0 0 312s Consumption_15 0.0 0 312s Consumption_16 0.0 0 312s Consumption_17 0.0 0 312s Consumption_18 0.0 0 312s Consumption_19 0.0 0 312s Consumption_20 0.0 0 312s Consumption_21 0.0 0 312s Consumption_22 0.0 0 312s Investment_2 12.7 183 312s Investment_3 12.4 183 312s Investment_4 16.9 184 312s Investment_5 18.4 190 312s Investment_6 19.4 193 312s Investment_8 19.6 203 312s Investment_9 19.8 208 312s Investment_10 21.1 211 312s Investment_11 21.7 216 312s Investment_12 15.6 217 312s Investment_13 11.4 213 312s Investment_14 7.0 207 312s Investment_15 11.2 202 312s Investment_16 12.3 199 312s Investment_17 14.0 198 312s Investment_18 17.6 200 312s Investment_19 17.3 202 312s Investment_20 15.3 200 312s Investment_21 19.0 201 312s Investment_22 21.1 204 312s PrivateWages_2 0.0 0 312s PrivateWages_3 0.0 0 312s PrivateWages_4 0.0 0 312s PrivateWages_5 0.0 0 312s PrivateWages_6 0.0 0 312s PrivateWages_8 0.0 0 312s PrivateWages_9 0.0 0 312s PrivateWages_10 0.0 0 312s PrivateWages_11 0.0 0 312s PrivateWages_12 0.0 0 312s PrivateWages_13 0.0 0 312s PrivateWages_14 0.0 0 312s PrivateWages_15 0.0 0 312s PrivateWages_16 0.0 0 312s PrivateWages_17 0.0 0 312s PrivateWages_18 0.0 0 312s PrivateWages_19 0.0 0 312s PrivateWages_20 0.0 0 312s PrivateWages_21 0.0 0 312s PrivateWages_22 0.0 0 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 0 0.0 0.0 312s Consumption_3 0 0.0 0.0 312s Consumption_4 0 0.0 0.0 312s Consumption_5 0 0.0 0.0 312s Consumption_6 0 0.0 0.0 312s Consumption_8 0 0.0 0.0 312s Consumption_9 0 0.0 0.0 312s Consumption_11 0 0.0 0.0 312s Consumption_12 0 0.0 0.0 312s Consumption_13 0 0.0 0.0 312s Consumption_14 0 0.0 0.0 312s Consumption_15 0 0.0 0.0 312s Consumption_16 0 0.0 0.0 312s Consumption_17 0 0.0 0.0 312s Consumption_18 0 0.0 0.0 312s Consumption_19 0 0.0 0.0 312s Consumption_20 0 0.0 0.0 312s Consumption_21 0 0.0 0.0 312s Consumption_22 0 0.0 0.0 312s Investment_2 0 0.0 0.0 312s Investment_3 0 0.0 0.0 312s Investment_4 0 0.0 0.0 312s Investment_5 0 0.0 0.0 312s Investment_6 0 0.0 0.0 312s Investment_8 0 0.0 0.0 312s Investment_9 0 0.0 0.0 312s Investment_10 0 0.0 0.0 312s Investment_11 0 0.0 0.0 312s Investment_12 0 0.0 0.0 312s Investment_13 0 0.0 0.0 312s Investment_14 0 0.0 0.0 312s Investment_15 0 0.0 0.0 312s Investment_16 0 0.0 0.0 312s Investment_17 0 0.0 0.0 312s Investment_18 0 0.0 0.0 312s Investment_19 0 0.0 0.0 312s Investment_20 0 0.0 0.0 312s Investment_21 0 0.0 0.0 312s Investment_22 0 0.0 0.0 312s PrivateWages_2 1 47.1 44.9 312s PrivateWages_3 1 49.6 45.6 312s PrivateWages_4 1 56.5 50.1 312s PrivateWages_5 1 60.7 57.2 312s PrivateWages_6 1 60.6 57.1 312s PrivateWages_8 1 60.0 64.0 312s PrivateWages_9 1 62.3 64.4 312s PrivateWages_10 1 64.6 64.5 312s PrivateWages_11 1 63.7 67.0 312s PrivateWages_12 1 54.8 61.2 312s PrivateWages_13 1 47.0 53.4 312s PrivateWages_14 1 42.1 44.3 312s PrivateWages_15 1 51.2 45.1 312s PrivateWages_16 1 55.3 49.7 312s PrivateWages_17 1 57.4 54.4 312s PrivateWages_18 1 67.2 62.7 312s PrivateWages_19 1 68.5 65.0 312s PrivateWages_20 1 66.8 60.9 312s PrivateWages_21 1 74.9 69.5 312s PrivateWages_22 1 86.9 75.7 312s PrivateWages_trend 312s Consumption_2 0 312s Consumption_3 0 312s Consumption_4 0 312s Consumption_5 0 312s Consumption_6 0 312s Consumption_8 0 312s Consumption_9 0 312s Consumption_11 0 312s Consumption_12 0 312s Consumption_13 0 312s Consumption_14 0 312s Consumption_15 0 312s Consumption_16 0 312s Consumption_17 0 312s Consumption_18 0 312s Consumption_19 0 312s Consumption_20 0 312s Consumption_21 0 312s Consumption_22 0 312s Investment_2 0 312s Investment_3 0 312s Investment_4 0 312s Investment_5 0 312s Investment_6 0 312s Investment_8 0 312s Investment_9 0 312s Investment_10 0 312s Investment_11 0 312s Investment_12 0 312s Investment_13 0 312s Investment_14 0 312s Investment_15 0 312s Investment_16 0 312s Investment_17 0 312s Investment_18 0 312s Investment_19 0 312s Investment_20 0 312s Investment_21 0 312s Investment_22 0 312s PrivateWages_2 -10 312s PrivateWages_3 -9 312s PrivateWages_4 -8 312s PrivateWages_5 -7 312s PrivateWages_6 -6 312s PrivateWages_8 -4 312s PrivateWages_9 -3 312s PrivateWages_10 -2 312s PrivateWages_11 -1 312s PrivateWages_12 0 312s PrivateWages_13 1 312s PrivateWages_14 2 312s PrivateWages_15 3 312s PrivateWages_16 4 312s PrivateWages_17 5 312s PrivateWages_18 6 312s PrivateWages_19 7 312s PrivateWages_20 8 312s PrivateWages_21 9 312s PrivateWages_22 10 312s > nobs 312s [1] 59 312s > linearHypothesis 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 48 312s 2 47 1 0.87 0.36 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 48 312s 2 47 1 0.98 0.33 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 48 312s 2 47 1 0.98 0.32 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 47 2 0.43 0.65 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 47 2 0.49 0.61 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 49 312s 2 47 2 0.98 0.61 312s > logLik 312s 'log Lik.' -71.5 (df=13) 312s 'log Lik.' -78.7 (df=13) 312s Estimating function 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 -1.5371 -20.65 312s Consumption_3 -0.3191 -5.32 312s Consumption_4 0.0169 0.32 312s Consumption_5 -1.6346 -33.73 312s Consumption_6 0.2820 5.44 312s Consumption_8 2.9429 50.64 312s Consumption_9 2.3495 44.61 312s Consumption_11 -1.2221 -20.08 312s Consumption_12 -1.0034 -12.54 312s Consumption_13 -2.0551 -18.62 312s Consumption_14 1.4937 13.86 312s Consumption_15 -0.7418 -9.26 312s Consumption_16 -0.6703 -9.64 312s Consumption_17 4.0943 60.15 312s Consumption_18 -0.6347 -12.44 312s Consumption_19 -3.0409 -58.22 312s Consumption_20 2.1019 36.86 312s Consumption_21 0.7142 14.52 312s Consumption_22 -1.1363 -25.88 312s Investment_2 0.0000 0.00 312s Investment_3 0.0000 0.00 312s Investment_4 0.0000 0.00 312s Investment_5 0.0000 0.00 312s Investment_6 0.0000 0.00 312s Investment_8 0.0000 0.00 312s Investment_9 0.0000 0.00 312s Investment_10 0.0000 0.00 312s Investment_11 0.0000 0.00 312s Investment_12 0.0000 0.00 312s Investment_13 0.0000 0.00 312s Investment_14 0.0000 0.00 312s Investment_15 0.0000 0.00 312s Investment_16 0.0000 0.00 312s Investment_17 0.0000 0.00 312s Investment_18 0.0000 0.00 312s Investment_19 0.0000 0.00 312s Investment_20 0.0000 0.00 312s Investment_21 0.0000 0.00 312s Investment_22 0.0000 0.00 312s PrivateWages_2 0.0000 0.00 312s PrivateWages_3 0.0000 0.00 312s PrivateWages_4 0.0000 0.00 312s PrivateWages_5 0.0000 0.00 312s PrivateWages_6 0.0000 0.00 312s PrivateWages_8 0.0000 0.00 312s PrivateWages_9 0.0000 0.00 312s PrivateWages_10 0.0000 0.00 312s PrivateWages_11 0.0000 0.00 312s PrivateWages_12 0.0000 0.00 312s PrivateWages_13 0.0000 0.00 312s PrivateWages_14 0.0000 0.00 312s PrivateWages_15 0.0000 0.00 312s PrivateWages_16 0.0000 0.00 312s PrivateWages_17 0.0000 0.00 312s PrivateWages_18 0.0000 0.00 312s PrivateWages_19 0.0000 0.00 312s PrivateWages_20 0.0000 0.00 312s PrivateWages_21 0.0000 0.00 312s PrivateWages_22 0.0000 0.00 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 -19.521 -45.456 312s Consumption_3 -3.957 -10.167 312s Consumption_4 0.286 0.599 312s Consumption_5 -30.078 -63.354 312s Consumption_6 5.471 10.901 312s Consumption_8 57.681 117.190 312s Consumption_9 46.520 98.197 312s Consumption_11 -26.520 -52.512 312s Consumption_12 -15.653 -39.407 312s Consumption_13 -23.428 -72.317 312s Consumption_14 10.456 49.297 312s Consumption_15 -8.308 -27.687 312s Consumption_16 -8.244 -26.878 312s Consumption_17 57.321 170.665 312s Consumption_18 -11.170 -30.264 312s Consumption_19 -52.608 -149.761 312s Consumption_20 32.159 101.952 312s Consumption_21 13.570 38.131 312s Consumption_22 -23.976 -69.128 312s Investment_2 0.000 0.000 312s Investment_3 0.000 0.000 312s Investment_4 0.000 0.000 312s Investment_5 0.000 0.000 312s Investment_6 0.000 0.000 312s Investment_8 0.000 0.000 312s Investment_9 0.000 0.000 312s Investment_10 0.000 0.000 312s Investment_11 0.000 0.000 312s Investment_12 0.000 0.000 312s Investment_13 0.000 0.000 312s Investment_14 0.000 0.000 312s Investment_15 0.000 0.000 312s Investment_16 0.000 0.000 312s Investment_17 0.000 0.000 312s Investment_18 0.000 0.000 312s Investment_19 0.000 0.000 312s Investment_20 0.000 0.000 312s Investment_21 0.000 0.000 312s Investment_22 0.000 0.000 312s PrivateWages_2 0.000 0.000 312s PrivateWages_3 0.000 0.000 312s PrivateWages_4 0.000 0.000 312s PrivateWages_5 0.000 0.000 312s PrivateWages_6 0.000 0.000 312s PrivateWages_8 0.000 0.000 312s PrivateWages_9 0.000 0.000 312s PrivateWages_10 0.000 0.000 312s PrivateWages_11 0.000 0.000 312s PrivateWages_12 0.000 0.000 312s PrivateWages_13 0.000 0.000 312s PrivateWages_14 0.000 0.000 312s PrivateWages_15 0.000 0.000 312s PrivateWages_16 0.000 0.000 312s PrivateWages_17 0.000 0.000 312s PrivateWages_18 0.000 0.000 312s PrivateWages_19 0.000 0.000 312s PrivateWages_20 0.000 0.000 312s PrivateWages_21 0.000 0.000 312s PrivateWages_22 0.000 0.000 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 0.0000 0.000 312s Consumption_3 0.0000 0.000 312s Consumption_4 0.0000 0.000 312s Consumption_5 0.0000 0.000 312s Consumption_6 0.0000 0.000 312s Consumption_8 0.0000 0.000 312s Consumption_9 0.0000 0.000 312s Consumption_11 0.0000 0.000 312s Consumption_12 0.0000 0.000 312s Consumption_13 0.0000 0.000 312s Consumption_14 0.0000 0.000 312s Consumption_15 0.0000 0.000 312s Consumption_16 0.0000 0.000 312s Consumption_17 0.0000 0.000 312s Consumption_18 0.0000 0.000 312s Consumption_19 0.0000 0.000 312s Consumption_20 0.0000 0.000 312s Consumption_21 0.0000 0.000 312s Consumption_22 0.0000 0.000 312s Investment_2 -1.1313 -14.660 312s Investment_3 0.2902 4.847 312s Investment_4 0.9027 17.274 312s Investment_5 -1.7434 -36.502 312s Investment_6 0.5695 11.088 312s Investment_8 1.6225 27.812 312s Investment_9 0.4166 8.119 312s Investment_10 2.0381 41.703 312s Investment_11 -0.8611 -14.505 312s Investment_12 -0.9091 -11.527 312s Investment_13 -1.1148 -9.946 312s Investment_14 1.3841 12.873 312s Investment_15 -0.2900 -3.710 312s Investment_16 0.0605 0.862 312s Investment_17 2.2439 33.101 312s Investment_18 -0.5390 -10.534 312s Investment_19 -3.9452 -76.375 312s Investment_20 0.4890 8.502 312s Investment_21 0.0864 1.737 312s Investment_22 0.4306 9.843 312s PrivateWages_2 0.0000 0.000 312s PrivateWages_3 0.0000 0.000 312s PrivateWages_4 0.0000 0.000 312s PrivateWages_5 0.0000 0.000 312s PrivateWages_6 0.0000 0.000 312s PrivateWages_8 0.0000 0.000 312s PrivateWages_9 0.0000 0.000 312s PrivateWages_10 0.0000 0.000 312s PrivateWages_11 0.0000 0.000 312s PrivateWages_12 0.0000 0.000 312s PrivateWages_13 0.0000 0.000 312s PrivateWages_14 0.0000 0.000 312s PrivateWages_15 0.0000 0.000 312s PrivateWages_16 0.0000 0.000 312s PrivateWages_17 0.0000 0.000 312s PrivateWages_18 0.0000 0.000 312s PrivateWages_19 0.0000 0.000 312s PrivateWages_20 0.0000 0.000 312s PrivateWages_21 0.0000 0.000 312s PrivateWages_22 0.0000 0.000 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 0.000 0.0 312s Consumption_3 0.000 0.0 312s Consumption_4 0.000 0.0 312s Consumption_5 0.000 0.0 312s Consumption_6 0.000 0.0 312s Consumption_8 0.000 0.0 312s Consumption_9 0.000 0.0 312s Consumption_11 0.000 0.0 312s Consumption_12 0.000 0.0 312s Consumption_13 0.000 0.0 312s Consumption_14 0.000 0.0 312s Consumption_15 0.000 0.0 312s Consumption_16 0.000 0.0 312s Consumption_17 0.000 0.0 312s Consumption_18 0.000 0.0 312s Consumption_19 0.000 0.0 312s Consumption_20 0.000 0.0 312s Consumption_21 0.000 0.0 312s Consumption_22 0.000 0.0 312s Investment_2 -14.368 -206.8 312s Investment_3 3.598 53.0 312s Investment_4 15.256 166.5 312s Investment_5 -32.079 -330.7 312s Investment_6 11.048 109.7 312s Investment_8 31.801 330.0 312s Investment_9 8.248 86.5 312s Investment_10 43.003 429.2 312s Investment_11 -18.685 -185.7 312s Investment_12 -14.182 -197.0 312s Investment_13 -12.709 -237.8 312s Investment_14 9.689 286.6 312s Investment_15 -3.247 -58.6 312s Investment_16 0.744 12.0 312s Investment_17 31.414 443.6 312s Investment_18 -9.486 -107.7 312s Investment_19 -68.252 -796.1 312s Investment_20 7.482 97.7 312s Investment_21 1.642 17.4 312s Investment_22 9.085 88.0 312s PrivateWages_2 0.000 0.0 312s PrivateWages_3 0.000 0.0 312s PrivateWages_4 0.000 0.0 312s PrivateWages_5 0.000 0.0 312s PrivateWages_6 0.000 0.0 312s PrivateWages_8 0.000 0.0 312s PrivateWages_9 0.000 0.0 312s PrivateWages_10 0.000 0.0 312s PrivateWages_11 0.000 0.0 312s PrivateWages_12 0.000 0.0 312s PrivateWages_13 0.000 0.0 312s PrivateWages_14 0.000 0.0 312s PrivateWages_15 0.000 0.0 312s PrivateWages_16 0.000 0.0 312s PrivateWages_17 0.000 0.0 312s PrivateWages_18 0.000 0.0 312s PrivateWages_19 0.000 0.0 312s PrivateWages_20 0.000 0.0 312s PrivateWages_21 0.000 0.0 312s PrivateWages_22 0.000 0.0 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 0.0000 0.00 0.00 312s Consumption_3 0.0000 0.00 0.00 312s Consumption_4 0.0000 0.00 0.00 312s Consumption_5 0.0000 0.00 0.00 312s Consumption_6 0.0000 0.00 0.00 312s Consumption_8 0.0000 0.00 0.00 312s Consumption_9 0.0000 0.00 0.00 312s Consumption_11 0.0000 0.00 0.00 312s Consumption_12 0.0000 0.00 0.00 312s Consumption_13 0.0000 0.00 0.00 312s Consumption_14 0.0000 0.00 0.00 312s Consumption_15 0.0000 0.00 0.00 312s Consumption_16 0.0000 0.00 0.00 312s Consumption_17 0.0000 0.00 0.00 312s Consumption_18 0.0000 0.00 0.00 312s Consumption_19 0.0000 0.00 0.00 312s Consumption_20 0.0000 0.00 0.00 312s Consumption_21 0.0000 0.00 0.00 312s Consumption_22 0.0000 0.00 0.00 312s Investment_2 0.0000 0.00 0.00 312s Investment_3 0.0000 0.00 0.00 312s Investment_4 0.0000 0.00 0.00 312s Investment_5 0.0000 0.00 0.00 312s Investment_6 0.0000 0.00 0.00 312s Investment_8 0.0000 0.00 0.00 312s Investment_9 0.0000 0.00 0.00 312s Investment_10 0.0000 0.00 0.00 312s Investment_11 0.0000 0.00 0.00 312s Investment_12 0.0000 0.00 0.00 312s Investment_13 0.0000 0.00 0.00 312s Investment_14 0.0000 0.00 0.00 312s Investment_15 0.0000 0.00 0.00 312s Investment_16 0.0000 0.00 0.00 312s Investment_17 0.0000 0.00 0.00 312s Investment_18 0.0000 0.00 0.00 312s Investment_19 0.0000 0.00 0.00 312s Investment_20 0.0000 0.00 0.00 312s Investment_21 0.0000 0.00 0.00 312s Investment_22 0.0000 0.00 0.00 312s PrivateWages_2 -1.9924 -93.78 -89.46 312s PrivateWages_3 0.4683 23.22 21.35 312s PrivateWages_4 1.4034 79.35 70.31 312s PrivateWages_5 -1.7870 -108.45 -102.22 312s PrivateWages_6 -0.3627 -21.98 -20.71 312s PrivateWages_8 1.1629 69.77 74.43 312s PrivateWages_9 1.2735 79.30 82.01 312s PrivateWages_10 2.2141 142.96 142.81 312s PrivateWages_11 -1.2912 -82.26 -86.51 312s PrivateWages_12 -0.0350 -1.92 -2.14 312s PrivateWages_13 -1.0438 -49.04 -55.74 312s PrivateWages_14 1.8016 75.90 79.81 312s PrivateWages_15 -0.3714 -19.02 -16.75 312s PrivateWages_16 -0.3904 -21.61 -19.40 312s PrivateWages_17 1.4934 85.71 81.24 312s PrivateWages_18 0.0279 1.88 1.75 312s PrivateWages_19 -3.8229 -261.91 -248.49 312s PrivateWages_20 0.7870 52.61 47.93 312s PrivateWages_21 -0.7415 -55.52 -51.54 312s PrivateWages_22 1.2062 104.79 91.31 312s PrivateWages_trend 312s Consumption_2 0.000 312s Consumption_3 0.000 312s Consumption_4 0.000 312s Consumption_5 0.000 312s Consumption_6 0.000 312s Consumption_8 0.000 312s Consumption_9 0.000 312s Consumption_11 0.000 312s Consumption_12 0.000 312s Consumption_13 0.000 312s Consumption_14 0.000 312s Consumption_15 0.000 312s Consumption_16 0.000 312s Consumption_17 0.000 312s Consumption_18 0.000 312s Consumption_19 0.000 312s Consumption_20 0.000 312s Consumption_21 0.000 312s Consumption_22 0.000 312s Investment_2 0.000 312s Investment_3 0.000 312s Investment_4 0.000 312s Investment_5 0.000 312s Investment_6 0.000 312s Investment_8 0.000 312s Investment_9 0.000 312s Investment_10 0.000 312s Investment_11 0.000 312s Investment_12 0.000 312s Investment_13 0.000 312s Investment_14 0.000 312s Investment_15 0.000 312s Investment_16 0.000 312s Investment_17 0.000 312s Investment_18 0.000 312s Investment_19 0.000 312s Investment_20 0.000 312s Investment_21 0.000 312s Investment_22 0.000 312s PrivateWages_2 19.924 312s PrivateWages_3 -4.214 312s PrivateWages_4 -11.227 312s PrivateWages_5 12.509 312s PrivateWages_6 2.176 312s PrivateWages_8 -4.652 312s PrivateWages_9 -3.820 312s PrivateWages_10 -4.428 312s PrivateWages_11 1.291 312s PrivateWages_12 0.000 312s PrivateWages_13 -1.044 312s PrivateWages_14 3.603 312s PrivateWages_15 -1.114 312s PrivateWages_16 -1.562 312s PrivateWages_17 7.467 312s PrivateWages_18 0.168 312s PrivateWages_19 -26.760 312s PrivateWages_20 6.296 312s PrivateWages_21 -6.674 312s PrivateWages_22 12.062 312s [1] TRUE 312s > Bread 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_(Intercept) 99.763 -0.8715 312s Consumption_corpProf -0.872 0.7621 312s Consumption_corpProfLag -0.479 -0.4940 312s Consumption_wages -1.807 -0.0927 312s Investment_(Intercept) 0.000 0.0000 312s Investment_corpProf 0.000 0.0000 312s Investment_corpProfLag 0.000 0.0000 312s Investment_capitalLag 0.000 0.0000 312s PrivateWages_(Intercept) 0.000 0.0000 312s PrivateWages_gnp 0.000 0.0000 312s PrivateWages_gnpLag 0.000 0.0000 312s PrivateWages_trend 0.000 0.0000 312s Consumption_corpProfLag Consumption_wages 312s Consumption_(Intercept) -0.4786 -1.8068 312s Consumption_corpProf -0.4940 -0.0927 312s Consumption_corpProfLag 0.6462 -0.0403 312s Consumption_wages -0.0403 0.0963 312s Investment_(Intercept) 0.0000 0.0000 312s Investment_corpProf 0.0000 0.0000 312s Investment_corpProfLag 0.0000 0.0000 312s Investment_capitalLag 0.0000 0.0000 312s PrivateWages_(Intercept) 0.0000 0.0000 312s PrivateWages_gnp 0.0000 0.0000 312s PrivateWages_gnpLag 0.0000 0.0000 312s PrivateWages_trend 0.0000 0.0000 312s Investment_(Intercept) Investment_corpProf 312s Consumption_(Intercept) 0.0 0.000 312s Consumption_corpProf 0.0 0.000 312s Consumption_corpProfLag 0.0 0.000 312s Consumption_wages 0.0 0.000 312s Investment_(Intercept) 2405.5 -38.269 312s Investment_corpProf -38.3 1.231 312s Investment_corpProfLag 32.8 -1.072 312s Investment_capitalLag -11.4 0.174 312s PrivateWages_(Intercept) 0.0 0.000 312s PrivateWages_gnp 0.0 0.000 312s PrivateWages_gnpLag 0.0 0.000 312s PrivateWages_trend 0.0 0.000 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_(Intercept) 0.000 0.0000 312s Consumption_corpProf 0.000 0.0000 312s Consumption_corpProfLag 0.000 0.0000 312s Consumption_wages 0.000 0.0000 312s Investment_(Intercept) 32.828 -11.4279 312s Investment_corpProf -1.072 0.1744 312s Investment_corpProfLag 1.129 -0.1652 312s Investment_capitalLag -0.165 0.0557 312s PrivateWages_(Intercept) 0.000 0.0000 312s PrivateWages_gnp 0.000 0.0000 312s PrivateWages_gnpLag 0.000 0.0000 312s PrivateWages_trend 0.000 0.0000 312s PrivateWages_(Intercept) PrivateWages_gnp 312s Consumption_(Intercept) 0.000 0.0000 312s Consumption_corpProf 0.000 0.0000 312s Consumption_corpProfLag 0.000 0.0000 312s Consumption_wages 0.000 0.0000 312s Investment_(Intercept) 0.000 0.0000 312s Investment_corpProf 0.000 0.0000 312s Investment_corpProfLag 0.000 0.0000 312s Investment_capitalLag 0.000 0.0000 312s PrivateWages_(Intercept) 167.869 -0.9135 312s PrivateWages_gnp -0.913 0.1554 312s PrivateWages_gnpLag -1.915 -0.1448 312s PrivateWages_trend 2.128 -0.0417 312s PrivateWages_gnpLag PrivateWages_trend 312s Consumption_(Intercept) 0.0000 0.0000 312s Consumption_corpProf 0.0000 0.0000 312s Consumption_corpProfLag 0.0000 0.0000 312s Consumption_wages 0.0000 0.0000 312s Investment_(Intercept) 0.0000 0.0000 312s Investment_corpProf 0.0000 0.0000 312s Investment_corpProfLag 0.0000 0.0000 312s Investment_capitalLag 0.0000 0.0000 312s PrivateWages_(Intercept) -1.9153 2.1280 312s PrivateWages_gnp -0.1448 -0.0417 312s PrivateWages_gnpLag 0.1830 0.0059 312s PrivateWages_trend 0.0059 0.1132 312s > 312s > # SUR 312s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 312s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 312s > summary 312s 312s systemfit results 312s method: SUR 312s 312s N DF SSR detRCov OLS-R2 McElroy-R2 312s system 61 49 45.4 0.151 0.977 0.992 312s 312s N DF SSR MSE RMSE R2 Adj R2 312s Consumption 20 16 17.6 1.102 1.050 0.981 0.977 312s Investment 21 17 17.5 1.029 1.015 0.931 0.918 312s PrivateWages 20 16 10.3 0.643 0.802 0.987 0.985 312s 312s The covariance matrix of the residuals used for estimation 312s Consumption Investment PrivateWages 312s Consumption 0.8871 0.0268 -0.349 312s Investment 0.0268 0.7328 0.103 312s PrivateWages -0.3492 0.1029 0.444 312s 312s The covariance matrix of the residuals 312s Consumption Investment PrivateWages 312s Consumption 0.8852 0.0508 -0.406 312s Investment 0.0508 0.7313 0.161 312s PrivateWages -0.4063 0.1609 0.467 312s 312s The correlations of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.000 0.065 -0.635 312s Investment 0.065 1.000 0.262 312s PrivateWages -0.635 0.262 1.000 312s 312s 312s SUR estimates for 'Consumption' (equation 1) 312s Model Formula: consump ~ corpProf + corpProfLag + wages 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 16.0876 1.2010 13.39 4.1e-10 *** 312s corpProf 0.2173 0.0799 2.72 0.015 * 312s corpProfLag 0.0694 0.0793 0.88 0.394 312s wages 0.7975 0.0360 22.15 2.0e-13 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.05 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 17.63 MSE: 1.102 Root MSE: 1.05 312s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 312s 312s 312s SUR estimates for 'Investment' (equation 2) 312s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 12.3518 4.5615 2.71 0.01493 * 312s corpProf 0.4511 0.0814 5.54 3.6e-05 *** 312s corpProfLag 0.3570 0.0846 4.22 0.00058 *** 312s capitalLag -0.1225 0.0223 -5.49 4.0e-05 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.015 on 17 degrees of freedom 312s Number of observations: 21 Degrees of Freedom: 17 312s SSR: 17.5 MSE: 1.029 Root MSE: 1.015 312s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 312s 312s 312s SUR estimates for 'PrivateWages' (equation 3) 312s Model Formula: privWage ~ gnp + gnpLag + trend 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 1.3964 1.0825 1.29 0.22 312s gnp 0.4177 0.0269 15.55 4.4e-11 *** 312s gnpLag 0.1709 0.0306 5.59 4.0e-05 *** 312s trend 0.1467 0.0272 5.40 5.9e-05 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 0.802 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 10.284 MSE: 0.643 Root MSE: 0.802 312s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 312s 312s > residuals 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 -0.2529 -0.2920 -1.15193 312s 3 -1.2998 -0.1392 0.50193 312s 4 -1.5662 1.1106 1.42026 312s 5 -0.4876 -1.4391 -0.09801 312s 6 0.0149 0.3556 -0.35678 312s 7 0.9002 1.4558 NA 312s 8 1.3535 0.8299 -0.74964 312s 9 1.0406 -0.5136 0.29355 312s 10 NA 1.2191 1.18544 312s 11 0.4417 0.2810 -0.36558 312s 12 -0.0892 0.0754 0.33733 312s 13 -0.1541 0.3429 -0.17490 312s 14 0.2984 0.3597 0.39941 312s 15 -0.0260 -0.1602 0.29441 312s 16 -0.0250 0.0130 -0.00177 312s 17 1.5671 1.0231 -0.81891 312s 18 -0.4089 0.0306 0.85516 312s 19 0.2819 -2.6153 -0.77184 312s 20 0.9257 -0.6030 -0.41040 312s 21 0.7415 -0.7118 -1.21679 312s 22 -2.2437 -0.5398 0.57166 312s > fitted 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 42.2 0.092 26.7 312s 3 46.3 2.039 28.8 312s 4 50.8 4.089 32.7 312s 5 51.1 4.439 34.0 312s 6 52.6 4.744 35.8 312s 7 54.2 4.144 NA 312s 8 54.8 3.370 38.6 312s 9 56.3 3.514 38.9 312s 10 NA 3.881 40.1 312s 11 54.6 0.719 38.3 312s 12 51.0 -3.475 34.2 312s 13 45.8 -6.543 29.2 312s 14 46.2 -5.460 28.1 312s 15 48.7 -2.840 30.3 312s 16 51.3 -1.313 33.2 312s 17 56.1 1.077 37.6 312s 18 59.1 1.969 40.1 312s 19 57.2 0.715 39.0 312s 20 60.7 1.903 42.0 312s 21 64.3 4.012 46.2 312s 22 71.9 5.440 52.7 312s > predict 312s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 312s 1 NA NA NA NA 312s 2 42.2 0.422 41.3 43.0 312s 3 46.3 0.462 45.4 47.2 312s 4 50.8 0.309 50.1 51.4 312s 5 51.1 0.359 50.4 51.8 312s 6 52.6 0.362 51.9 53.3 312s 7 54.2 0.328 53.5 54.9 312s 8 54.8 0.300 54.2 55.4 312s 9 56.3 0.323 55.6 56.9 312s 10 NA NA NA NA 312s 11 54.6 0.531 53.5 55.6 312s 12 51.0 0.427 50.1 51.8 312s 13 45.8 0.564 44.6 46.9 312s 14 46.2 0.543 45.1 47.3 312s 15 48.7 0.341 48.0 49.4 312s 16 51.3 0.302 50.7 51.9 312s 17 56.1 0.328 55.5 56.8 312s 18 59.1 0.294 58.5 59.7 312s 19 57.2 0.332 56.6 57.9 312s 20 60.7 0.392 59.9 61.5 312s 21 64.3 0.394 63.5 65.0 312s 22 71.9 0.615 70.7 73.2 312s Investment.pred Investment.se.fit Investment.lwr Investment.upr 312s 1 NA NA NA NA 312s 2 0.092 0.508 -0.929 1.113 312s 3 2.039 0.421 1.193 2.885 312s 4 4.089 0.376 3.333 4.846 312s 5 4.439 0.311 3.813 5.065 312s 6 4.744 0.294 4.154 5.335 312s 7 4.144 0.277 3.587 4.701 312s 8 3.370 0.247 2.873 3.867 312s 9 3.514 0.328 2.855 4.172 312s 10 3.881 0.376 3.126 4.636 312s 11 0.719 0.508 -0.301 1.739 312s 12 -3.475 0.428 -4.336 -2.615 312s 13 -6.543 0.521 -7.590 -5.496 312s 14 -5.460 0.583 -6.632 -4.288 312s 15 -2.840 0.316 -3.474 -2.205 312s 16 -1.313 0.271 -1.857 -0.769 312s 17 1.077 0.293 0.488 1.666 312s 18 1.969 0.205 1.557 2.382 312s 19 0.715 0.263 0.187 1.244 312s 20 1.903 0.309 1.283 2.523 312s 21 4.012 0.280 3.449 4.574 312s 22 5.440 0.389 4.659 6.221 312s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 312s 1 NA NA NA NA 312s 2 26.7 0.306 26.0 27.3 312s 3 28.8 0.305 28.2 29.4 312s 4 32.7 0.302 32.1 33.3 312s 5 34.0 0.231 33.5 34.5 312s 6 35.8 0.230 35.3 36.2 312s 7 NA NA NA NA 312s 8 38.6 0.233 38.2 39.1 312s 9 38.9 0.222 38.5 39.4 312s 10 40.1 0.213 39.7 40.5 312s 11 38.3 0.292 37.7 38.9 312s 12 34.2 0.300 33.6 34.8 312s 13 29.2 0.361 28.4 29.9 312s 14 28.1 0.322 27.5 28.7 312s 15 30.3 0.314 29.7 30.9 312s 16 33.2 0.263 32.7 33.7 312s 17 37.6 0.256 37.1 38.1 312s 18 40.1 0.204 39.7 40.6 312s 19 39.0 0.298 38.4 39.6 312s 20 42.0 0.272 41.5 42.6 312s 21 46.2 0.288 45.6 46.8 312s 22 52.7 0.431 51.9 53.6 312s > model.frame 312s [1] TRUE 312s > model.matrix 312s [1] TRUE 312s > nobs 312s [1] 61 312s > linearHypothesis 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 50 312s 2 49 1 1.01 0.32 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 50 312s 2 49 1 1.3 0.26 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 50 312s 2 49 1 1.3 0.25 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 51 312s 2 49 2 0.53 0.59 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 51 312s 2 49 2 0.69 0.51 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 51 312s 2 49 2 1.38 0.5 312s > logLik 312s 'log Lik.' -69.6 (df=18) 312s 'log Lik.' -76.9 (df=18) 312s Estimating function 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 -0.42417 -5.2597 312s Consumption_3 -2.17982 -36.8390 312s Consumption_4 -2.62648 -48.3271 312s Consumption_5 -0.81768 -15.8630 312s Consumption_6 0.02500 0.5025 312s Consumption_7 1.50966 29.5894 312s Consumption_8 2.26980 44.9421 312s Consumption_9 1.74517 36.8231 312s Consumption_11 0.74077 11.5559 312s Consumption_12 -0.14959 -1.7053 312s Consumption_13 -0.25842 -1.8090 312s Consumption_14 0.50036 5.6040 312s Consumption_15 -0.04361 -0.5363 312s Consumption_16 -0.04189 -0.5865 312s Consumption_17 2.62802 46.2532 312s Consumption_18 -0.68580 -11.8643 312s Consumption_19 0.47280 7.2339 312s Consumption_20 1.55235 29.4946 312s Consumption_21 1.24350 26.2379 312s Consumption_22 -3.76279 -88.4255 312s Investment_2 0.07441 0.9227 312s Investment_3 0.03547 0.5995 312s Investment_4 -0.28298 -5.2069 312s Investment_5 0.36669 7.1139 312s Investment_6 -0.09061 -1.8212 312s Investment_7 -0.37095 -7.2706 312s Investment_8 -0.21146 -4.1868 312s Investment_9 0.13086 2.7611 312s Investment_10 0.00000 0.0000 312s Investment_11 -0.07161 -1.1172 312s Investment_12 -0.01921 -0.2190 312s Investment_13 -0.08737 -0.6116 312s Investment_14 -0.09166 -1.0266 312s Investment_15 0.04082 0.5021 312s Investment_16 -0.00330 -0.0462 312s Investment_17 -0.26069 -4.5882 312s Investment_18 -0.00779 -0.1348 312s Investment_19 0.66639 10.1958 312s Investment_20 0.15365 2.9194 312s Investment_21 0.18136 3.8268 312s Investment_22 0.13754 3.2323 312s PrivateWages_2 -1.58616 -19.6684 312s PrivateWages_3 0.69114 11.6803 312s PrivateWages_4 1.95564 35.9837 312s PrivateWages_5 -0.13496 -2.6181 312s PrivateWages_6 -0.49127 -9.8746 312s PrivateWages_8 -1.03222 -20.4380 312s PrivateWages_9 0.40421 8.5288 312s PrivateWages_10 0.00000 0.0000 312s PrivateWages_11 -0.50339 -7.8529 312s PrivateWages_12 0.46449 5.2952 312s PrivateWages_13 -0.24083 -1.6858 312s PrivateWages_14 0.54997 6.1596 312s PrivateWages_15 0.40539 4.9863 312s PrivateWages_16 -0.00244 -0.0342 312s PrivateWages_17 -1.12761 -19.8459 312s PrivateWages_18 1.17751 20.3710 312s PrivateWages_19 -1.06279 -16.2607 312s PrivateWages_20 -0.56511 -10.7371 312s PrivateWages_21 -1.67547 -35.3524 312s PrivateWages_22 0.78715 18.4981 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 -5.3870 -11.962 312s Consumption_3 -27.0298 -70.190 312s Consumption_4 -44.3874 -97.180 312s Consumption_5 -15.0453 -30.254 312s Consumption_6 0.4850 0.965 312s Consumption_7 30.3442 61.443 312s Consumption_8 44.4881 94.197 312s Consumption_9 34.5544 74.868 312s Consumption_11 16.0746 31.186 312s Consumption_12 -2.3336 -5.879 312s Consumption_13 -2.9460 -8.864 312s Consumption_14 3.5025 17.062 312s Consumption_15 -0.4884 -1.596 312s Consumption_16 -0.5153 -1.646 312s Consumption_17 36.7923 116.159 312s Consumption_18 -12.0701 -32.713 312s Consumption_19 8.1795 21.702 312s Consumption_20 23.7509 76.686 312s Consumption_21 23.6265 65.906 312s Consumption_22 -79.3948 -232.540 312s Investment_2 0.9450 2.098 312s Investment_3 0.4399 1.142 312s Investment_4 -4.7824 -10.470 312s Investment_5 6.7472 13.568 312s Investment_6 -1.7577 -3.497 312s Investment_7 -7.4561 -15.098 312s Investment_8 -4.1445 -8.775 312s Investment_9 2.5910 5.614 312s Investment_10 0.0000 0.000 312s Investment_11 -1.5540 -3.015 312s Investment_12 -0.2997 -0.755 312s Investment_13 -0.9961 -2.997 312s Investment_14 -0.6416 -3.126 312s Investment_15 0.4572 1.494 312s Investment_16 -0.0406 -0.130 312s Investment_17 -3.6497 -11.523 312s Investment_18 -0.1371 -0.372 312s Investment_19 11.5286 30.587 312s Investment_20 2.3509 7.590 312s Investment_21 3.4459 9.612 312s Investment_22 2.9022 8.500 312s PrivateWages_2 -20.1442 -44.730 312s PrivateWages_3 8.5702 22.255 312s PrivateWages_4 33.0503 72.359 312s PrivateWages_5 -2.4832 -4.993 312s PrivateWages_6 -9.5307 -18.963 312s PrivateWages_8 -20.2315 -42.837 312s PrivateWages_9 8.0034 17.341 312s PrivateWages_10 0.0000 0.000 312s PrivateWages_11 -10.9235 -21.193 312s PrivateWages_12 7.2461 18.254 312s PrivateWages_13 -2.7454 -8.260 312s PrivateWages_14 3.8498 18.754 312s PrivateWages_15 4.5404 14.837 312s PrivateWages_16 -0.0300 -0.096 312s PrivateWages_17 -15.7865 -49.840 312s PrivateWages_18 20.7242 56.167 312s PrivateWages_19 -18.3863 -48.782 312s PrivateWages_20 -8.6462 -27.916 312s PrivateWages_21 -31.8339 -88.800 312s PrivateWages_22 16.6089 48.646 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 0.064449 0.7992 312s Consumption_3 0.331201 5.5973 312s Consumption_4 0.399066 7.3428 312s Consumption_5 0.124238 2.4102 312s Consumption_6 -0.003798 -0.0763 312s Consumption_7 -0.229378 -4.4958 312s Consumption_8 -0.344873 -6.8285 312s Consumption_9 -0.265161 -5.5949 312s Consumption_11 -0.112552 -1.7558 312s Consumption_12 0.022729 0.2591 312s Consumption_13 0.039265 0.2749 312s Consumption_14 -0.076024 -0.8515 312s Consumption_15 0.006625 0.0815 312s Consumption_16 0.006365 0.0891 312s Consumption_17 -0.399301 -7.0277 312s Consumption_18 0.104200 1.8027 312s Consumption_19 -0.071838 -1.0991 312s Consumption_20 -0.235863 -4.4814 312s Consumption_21 -0.188937 -3.9866 312s Consumption_22 0.571717 13.4353 312s Investment_2 -0.423201 -5.2477 312s Investment_3 -0.201766 -3.4098 312s Investment_4 1.609495 29.6147 312s Investment_5 -2.085613 -40.4609 312s Investment_6 0.515327 10.3581 312s Investment_7 2.109824 41.3526 312s Investment_8 1.202679 23.8131 312s Investment_9 -0.744277 -15.7042 312s Investment_10 1.766841 38.3405 312s Investment_11 0.407303 6.3539 312s Investment_12 0.109258 1.2455 312s Investment_13 0.496948 3.4786 312s Investment_14 0.521347 5.8391 312s Investment_15 -0.232156 -2.8555 312s Investment_16 0.018782 0.2630 312s Investment_17 1.482721 26.0959 312s Investment_18 0.044303 0.7664 312s Investment_19 -3.790179 -57.9897 312s Investment_20 -0.873905 -16.6042 312s Investment_21 -1.031520 -21.7651 312s Investment_22 -0.782292 -18.3839 312s PrivateWages_2 0.617327 7.6549 312s PrivateWages_3 -0.268990 -4.5459 312s PrivateWages_4 -0.761128 -14.0048 312s PrivateWages_5 0.052525 1.0190 312s PrivateWages_6 0.191202 3.8432 312s PrivateWages_8 0.401737 7.9544 312s PrivateWages_9 -0.157317 -3.3194 312s PrivateWages_10 -0.635285 -13.7857 312s PrivateWages_11 0.195917 3.0563 312s PrivateWages_12 -0.180778 -2.0609 312s PrivateWages_13 0.093729 0.6561 312s PrivateWages_14 -0.214045 -2.3973 312s PrivateWages_15 -0.157776 -1.9406 312s PrivateWages_16 0.000951 0.0133 312s PrivateWages_17 0.438862 7.7240 312s PrivateWages_18 -0.458284 -7.9283 312s PrivateWages_19 0.413636 6.3286 312s PrivateWages_20 0.219939 4.1788 312s PrivateWages_21 0.652086 13.7590 312s PrivateWages_22 -0.306358 -7.1994 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 0.8185 11.781 312s Consumption_3 4.1069 60.477 312s Consumption_4 6.7442 73.628 312s Consumption_5 2.2860 23.568 312s Consumption_6 -0.0737 -0.732 312s Consumption_7 -4.6105 -45.371 312s Consumption_8 -6.7595 -70.147 312s Consumption_9 -5.2502 -55.047 312s Consumption_11 -2.4424 -24.277 312s Consumption_12 0.3546 4.925 312s Consumption_13 0.4476 8.375 312s Consumption_14 -0.5322 -15.745 312s Consumption_15 0.0742 1.338 312s Consumption_16 0.0783 1.267 312s Consumption_17 -5.5902 -78.942 312s Consumption_18 1.8339 20.819 312s Consumption_19 -1.2428 -14.497 312s Consumption_20 -3.6087 -47.149 312s Consumption_21 -3.5898 -38.014 312s Consumption_22 12.0632 116.916 312s Investment_2 -5.3746 -77.361 312s Investment_3 -2.5019 -36.842 312s Investment_4 27.2005 296.952 312s Investment_5 -38.3753 -395.641 312s Investment_6 9.9974 99.304 312s Investment_7 42.4075 417.323 312s Investment_8 23.5725 244.625 312s Investment_9 -14.7367 -154.512 312s Investment_10 37.2803 372.097 312s Investment_11 8.8385 87.855 312s Investment_12 1.7044 23.676 312s Investment_13 5.6652 105.999 312s Investment_14 3.6494 107.971 312s Investment_15 -2.6002 -46.896 312s Investment_16 0.2310 3.738 312s Investment_17 20.7581 293.134 312s Investment_18 0.7797 8.852 312s Investment_19 -65.5701 -764.858 312s Investment_20 -13.3707 -174.694 312s Investment_21 -19.5989 -207.542 312s Investment_22 -16.5064 -159.979 312s PrivateWages_2 7.8401 112.847 312s PrivateWages_3 -3.3355 -49.118 312s PrivateWages_4 -12.8631 -140.428 312s PrivateWages_5 0.9665 9.964 312s PrivateWages_6 3.7093 36.845 312s PrivateWages_8 7.8740 81.713 312s PrivateWages_9 -3.1149 -32.659 312s PrivateWages_10 -13.4045 -133.791 312s PrivateWages_11 4.2514 42.259 312s PrivateWages_12 -2.8201 -39.175 312s PrivateWages_13 1.0685 19.992 312s PrivateWages_14 -1.4983 -44.329 312s PrivateWages_15 -1.7671 -31.871 312s PrivateWages_16 0.0117 0.189 312s PrivateWages_17 6.1441 86.763 312s PrivateWages_18 -8.0658 -91.565 312s PrivateWages_19 7.1559 83.472 312s PrivateWages_20 3.3651 43.966 312s PrivateWages_21 12.3896 131.200 312s PrivateWages_22 -6.4641 -62.650 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 -0.34828 -15.881 -15.638 312s Consumption_3 -1.78978 -89.668 -81.614 312s Consumption_4 -2.15652 -123.353 -108.042 312s Consumption_5 -0.67137 -38.335 -38.402 312s Consumption_6 0.02052 1.252 1.172 312s Consumption_7 0.00000 0.000 0.000 312s Consumption_8 1.86367 120.020 119.275 312s Consumption_9 1.43291 92.422 92.279 312s Consumption_11 0.60822 37.223 40.751 312s Consumption_12 -0.12282 -6.559 -7.517 312s Consumption_13 -0.21218 -9.400 -11.331 312s Consumption_14 0.41083 18.528 18.200 312s Consumption_15 -0.03580 -1.779 -1.615 312s Consumption_16 -0.03440 -1.871 -1.710 312s Consumption_17 2.15779 135.293 117.384 312s Consumption_18 -0.56309 -36.601 -35.306 312s Consumption_19 0.38821 23.642 25.233 312s Consumption_20 1.27458 88.584 77.622 312s Consumption_21 1.02100 77.290 70.960 312s Consumption_22 -3.08951 -273.113 -233.876 312s Investment_2 0.15649 7.136 7.027 312s Investment_3 0.07461 3.738 3.402 312s Investment_4 -0.59517 -34.043 -29.818 312s Investment_5 0.77123 44.037 44.114 312s Investment_6 -0.19056 -11.624 -10.881 312s Investment_7 0.00000 0.000 0.000 312s Investment_8 -0.44473 -28.641 -28.463 312s Investment_9 0.27522 17.752 17.724 312s Investment_10 -0.65335 -43.774 -42.141 312s Investment_11 -0.15061 -9.218 -10.091 312s Investment_12 -0.04040 -2.157 -2.473 312s Investment_13 -0.18376 -8.141 -9.813 312s Investment_14 -0.19279 -8.695 -8.540 312s Investment_15 0.08585 4.267 3.872 312s Investment_16 -0.00695 -0.378 -0.345 312s Investment_17 -0.54829 -34.378 -29.827 312s Investment_18 -0.01638 -1.065 -1.027 312s Investment_19 1.40155 85.354 91.101 312s Investment_20 0.32316 22.459 19.680 312s Investment_21 0.38144 28.875 26.510 312s Investment_22 0.28928 25.572 21.898 312s PrivateWages_2 -3.98191 -181.575 -178.788 312s PrivateWages_3 1.73505 86.926 79.118 312s PrivateWages_4 4.90946 280.821 245.964 312s PrivateWages_5 -0.33880 -19.345 -19.379 312s PrivateWages_6 -1.23330 -75.231 -70.421 312s PrivateWages_8 -2.59130 -166.880 -165.843 312s PrivateWages_9 1.01473 65.450 65.349 312s PrivateWages_10 4.09774 274.549 264.304 312s PrivateWages_11 -1.26371 -77.339 -84.669 312s PrivateWages_12 1.16606 62.268 71.363 312s PrivateWages_13 -0.60457 -26.783 -32.284 312s PrivateWages_14 1.38064 62.267 61.163 312s PrivateWages_15 1.01769 50.579 45.898 312s PrivateWages_16 -0.00613 -0.334 -0.305 312s PrivateWages_17 -2.83076 -177.489 -153.993 312s PrivateWages_18 2.95604 192.143 185.344 312s PrivateWages_19 -2.66805 -162.484 -173.423 312s PrivateWages_20 -1.41866 -98.597 -86.396 312s PrivateWages_21 -4.20611 -318.403 -292.325 312s PrivateWages_22 1.97608 174.686 149.589 312s PrivateWages_trend 312s Consumption_2 3.4828 312s Consumption_3 16.1081 312s Consumption_4 17.2522 312s Consumption_5 4.6996 312s Consumption_6 -0.1231 312s Consumption_7 0.0000 312s Consumption_8 -7.4547 312s Consumption_9 -4.2987 312s Consumption_11 -0.6082 312s Consumption_12 0.0000 312s Consumption_13 -0.2122 312s Consumption_14 0.8217 312s Consumption_15 -0.1074 312s Consumption_16 -0.1376 312s Consumption_17 10.7889 312s Consumption_18 -3.3785 312s Consumption_19 2.7174 312s Consumption_20 10.1967 312s Consumption_21 9.1890 312s Consumption_22 -30.8951 312s Investment_2 -1.5649 312s Investment_3 -0.6715 312s Investment_4 4.7613 312s Investment_5 -5.3986 312s Investment_6 1.1434 312s Investment_7 0.0000 312s Investment_8 1.7789 312s Investment_9 -0.8257 312s Investment_10 1.3067 312s Investment_11 0.1506 312s Investment_12 0.0000 312s Investment_13 -0.1838 312s Investment_14 -0.3856 312s Investment_15 0.2575 312s Investment_16 -0.0278 312s Investment_17 -2.7414 312s Investment_18 -0.0983 312s Investment_19 9.8108 312s Investment_20 2.5853 312s Investment_21 3.4330 312s Investment_22 2.8928 312s PrivateWages_2 39.8191 312s PrivateWages_3 -15.6154 312s PrivateWages_4 -39.2757 312s PrivateWages_5 2.3716 312s PrivateWages_6 7.3998 312s PrivateWages_8 10.3652 312s PrivateWages_9 -3.0442 312s PrivateWages_10 -8.1955 312s PrivateWages_11 1.2637 312s PrivateWages_12 0.0000 312s PrivateWages_13 -0.6046 312s PrivateWages_14 2.7613 312s PrivateWages_15 3.0531 312s PrivateWages_16 -0.0245 312s PrivateWages_17 -14.1538 312s PrivateWages_18 17.7363 312s PrivateWages_19 -18.6764 312s PrivateWages_20 -11.3493 312s PrivateWages_21 -37.8550 312s PrivateWages_22 19.7608 312s [1] TRUE 312s > Bread 312s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 312s [1,] 87.9904 -0.088084 -0.91416 312s [2,] -0.0881 0.389639 -0.23612 312s [3,] -0.9142 -0.236125 0.38341 312s [4,] -1.6692 -0.062952 -0.03326 312s [5,] 2.6851 -0.188961 0.72342 312s [6,] -0.0355 0.023370 -0.02643 312s [7,] -0.0563 -0.020038 0.03196 312s [8,] -0.0054 0.000618 -0.00397 312s [9,] -33.1687 0.063156 1.54217 312s [10,] 0.3665 -0.059172 0.03813 312s [11,] 0.1741 0.060188 -0.06574 312s [12,] 0.1831 0.029476 0.02425 312s Consumption_wages Investment_(Intercept) Investment_corpProf 312s [1,] -1.669236 2.685 -0.03549 312s [2,] -0.062952 -0.189 0.02337 312s [3,] -0.033257 0.723 -0.02643 312s [4,] 0.079061 -0.248 0.00151 312s [5,] -0.248317 1269.247 -12.23080 312s [6,] 0.001506 -12.231 0.40462 312s [7,] -0.002778 9.884 -0.34614 312s [8,] 0.001327 -6.097 0.05519 312s [9,] 0.134743 17.903 -0.13872 312s [10,] 0.000196 0.262 0.01397 312s [11,] -0.002616 -0.581 -0.01197 312s [12,] -0.026193 -0.551 0.00355 312s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 312s [1,] -0.05628 -0.005396 -33.1687 312s [2,] -0.02004 0.000618 0.0632 312s [3,] 0.03196 -0.003967 1.5422 312s [4,] -0.00278 0.001327 0.1347 312s [5,] 9.88435 -6.096982 17.9032 312s [6,] -0.34614 0.055190 -0.1387 312s [7,] 0.43632 -0.055785 -0.4000 312s [8,] -0.05578 0.030317 -0.0433 312s [9,] -0.40000 -0.043343 71.4840 312s [10,] -0.00786 -0.001844 -0.3085 312s [11,] 0.01493 0.002686 -0.8909 312s [12,] -0.01033 0.003295 0.8146 312s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 312s [1,] 0.366465 0.17405 0.18311 312s [2,] -0.059172 0.06019 0.02948 312s [3,] 0.038129 -0.06574 0.02425 312s [4,] 0.000196 -0.00262 -0.02619 312s [5,] 0.262390 -0.58123 -0.55064 312s [6,] 0.013966 -0.01197 0.00355 312s [7,] -0.007857 0.01493 -0.01033 312s [8,] -0.001844 0.00269 0.00330 312s [9,] -0.308484 -0.89087 0.81461 312s [10,] 0.044017 -0.04022 -0.01158 312s [11,] -0.040216 0.05696 -0.00212 312s [12,] -0.011575 -0.00212 0.04506 312s > 312s > # 3SLS 312s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 312s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 312s > summary 312s 312s systemfit results 312s method: 3SLS 312s 312s N DF SSR detRCov OLS-R2 McElroy-R2 312s system 59 47 59.5 0.241 0.97 0.994 312s 312s N DF SSR MSE RMSE R2 Adj R2 312s Consumption 19 15 18.1 1.203 1.097 0.980 0.977 312s Investment 20 16 31.1 1.945 1.395 0.866 0.841 312s PrivateWages 20 16 10.3 0.645 0.803 0.987 0.985 312s 312s The covariance matrix of the residuals used for estimation 312s Consumption Investment PrivateWages 312s Consumption 1.079 0.354 -0.383 312s Investment 0.354 1.047 0.107 312s PrivateWages -0.383 0.107 0.445 312s 312s The covariance matrix of the residuals 312s Consumption Investment PrivateWages 312s Consumption 0.950 0.324 -0.395 312s Investment 0.324 1.385 0.242 312s PrivateWages -0.395 0.242 0.475 312s 312s The correlations of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.000 0.293 -0.582 312s Investment 0.293 1.000 0.292 312s PrivateWages -0.582 0.292 1.000 312s 312s 312s 3SLS estimates for 'Consumption' (equation 1) 312s Model Formula: consump ~ corpProf + corpProfLag + wages 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 16.5606 1.3295 12.46 2.6e-09 *** 312s corpProf 0.1100 0.1098 1.00 0.33 312s corpProfLag 0.1155 0.1007 1.15 0.27 312s wages 0.8086 0.0401 20.18 2.8e-12 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.097 on 15 degrees of freedom 312s Number of observations: 19 Degrees of Freedom: 15 312s SSR: 18.051 MSE: 1.203 Root MSE: 1.097 312s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 312s 312s 312s 3SLS estimates for 'Investment' (equation 2) 312s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 23.6871 6.1159 3.87 0.00135 ** 312s corpProf 0.1072 0.1414 0.76 0.45918 312s corpProfLag 0.6278 0.1361 4.61 0.00029 *** 312s capitalLag -0.1726 0.0295 -5.85 2.5e-05 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.395 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 31.126 MSE: 1.945 Root MSE: 1.395 312s Multiple R-Squared: 0.866 Adjusted R-Squared: 0.841 312s 312s 312s 3SLS estimates for 'PrivateWages' (equation 3) 312s Model Formula: privWage ~ gnp + gnpLag + trend 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 1.3603 1.0927 1.24 0.23109 312s gnp 0.4117 0.0315 13.06 6.0e-10 *** 312s gnpLag 0.1782 0.0336 5.31 7.1e-05 *** 312s trend 0.1370 0.0280 4.89 0.00016 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 0.803 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 10.318 MSE: 0.645 Root MSE: 0.803 312s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 312s 312s > residuals 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 -0.29542 -1.636 -1.2658 312s 3 -0.89033 0.135 0.4198 312s 4 -1.25669 0.777 1.3578 312s 5 -0.14000 -1.574 -0.2036 312s 6 0.37365 0.341 -0.4283 312s 7 NA NA NA 312s 8 1.63850 1.194 -0.8319 312s 9 1.44030 0.454 0.2186 312s 10 NA 2.192 1.1346 312s 11 0.17274 -0.750 -0.4603 312s 12 -0.49629 -0.698 0.2476 312s 13 -0.78384 -0.976 -0.2528 312s 14 0.32420 1.365 0.4028 312s 15 -0.10364 -0.170 0.3295 312s 16 -0.00105 0.140 0.0377 312s 17 1.84421 1.862 -0.7540 312s 18 -0.36893 -0.103 0.8827 312s 19 0.14129 -3.255 -0.7764 312s 20 1.23511 0.475 -0.3230 312s 21 1.06553 0.152 -1.1453 312s 22 -1.85709 0.746 0.6843 312s > fitted 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 42.2 1.436 26.8 312s 3 45.9 1.765 28.9 312s 4 50.5 4.423 32.7 312s 5 50.7 4.574 34.1 312s 6 52.2 4.759 35.8 312s 7 NA NA NA 312s 8 54.6 3.006 38.7 312s 9 55.9 2.546 39.0 312s 10 NA 2.908 40.2 312s 11 54.8 1.750 38.4 312s 12 51.4 -2.702 34.3 312s 13 46.4 -5.224 29.3 312s 14 46.2 -6.465 28.1 312s 15 48.8 -2.830 30.3 312s 16 51.3 -1.440 33.2 312s 17 55.9 0.238 37.6 312s 18 59.1 2.103 40.1 312s 19 57.4 1.355 39.0 312s 20 60.4 0.825 41.9 312s 21 63.9 3.148 46.1 312s 22 71.6 4.154 52.6 312s > predict 312s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 312s 1 NA NA NA NA 312s 2 42.2 0.475 39.6 44.7 312s 3 45.9 0.557 43.3 48.5 312s 4 50.5 0.372 48.0 52.9 312s 5 50.7 0.433 48.2 53.3 312s 6 52.2 0.438 49.7 54.7 312s 7 NA NA NA NA 312s 8 54.6 0.362 52.1 57.0 312s 9 55.9 0.401 53.4 58.3 312s 10 NA NA NA NA 312s 11 54.8 0.684 52.1 57.6 312s 12 51.4 0.563 48.8 54.0 312s 13 46.4 0.733 43.6 49.2 312s 14 46.2 0.612 43.5 48.9 312s 15 48.8 0.379 46.3 51.3 312s 16 51.3 0.334 48.9 53.7 312s 17 55.9 0.394 53.4 58.3 312s 18 59.1 0.322 56.6 61.5 312s 19 57.4 0.392 54.9 59.8 312s 20 60.4 0.462 57.8 62.9 312s 21 63.9 0.448 61.4 66.5 312s 22 71.6 0.686 68.8 74.3 312s Investment.pred Investment.se.fit Investment.lwr Investment.upr 312s 1 NA NA NA NA 312s 2 1.436 0.709 -1.8811 4.754 312s 3 1.765 0.512 -1.3848 4.915 312s 4 4.423 0.470 1.3027 7.543 312s 5 4.574 0.392 1.5029 7.645 312s 6 4.759 0.370 1.7000 7.818 312s 7 NA NA NA NA 312s 8 3.006 0.306 -0.0214 6.033 312s 9 2.546 0.444 -0.5575 5.649 312s 10 2.908 0.488 -0.2245 6.041 312s 11 1.750 0.738 -1.5953 5.096 312s 12 -2.702 0.583 -5.9068 0.503 312s 13 -5.224 0.743 -8.5738 -1.874 312s 14 -6.465 0.780 -9.8530 -3.077 312s 15 -2.830 0.378 -5.8936 0.233 312s 16 -1.440 0.326 -4.4762 1.597 312s 17 0.238 0.426 -2.8533 3.329 312s 18 2.103 0.268 -0.9077 5.114 312s 19 1.355 0.399 -1.7201 4.431 312s 20 0.825 0.474 -2.2981 3.947 312s 21 3.148 0.393 0.0761 6.220 312s 22 4.154 0.555 0.9719 7.336 312s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 312s 1 NA NA NA NA 312s 2 26.8 0.309 24.9 28.6 312s 3 28.9 0.315 27.1 30.7 312s 4 32.7 0.326 30.9 34.6 312s 5 34.1 0.236 32.3 35.9 312s 6 35.8 0.244 34.0 37.6 312s 7 NA NA NA NA 312s 8 38.7 0.237 37.0 40.5 312s 9 39.0 0.225 37.2 40.7 312s 10 40.2 0.219 38.4 41.9 312s 11 38.4 0.309 36.5 40.2 312s 12 34.3 0.336 32.4 36.1 312s 13 29.3 0.411 27.3 31.2 312s 14 28.1 0.326 26.3 29.9 312s 15 30.3 0.313 28.4 32.1 312s 16 33.2 0.262 31.4 35.0 312s 17 37.6 0.265 35.8 39.3 312s 18 40.1 0.205 38.4 41.9 312s 19 39.0 0.323 37.1 40.8 312s 20 41.9 0.282 40.1 43.7 312s 21 46.1 0.293 44.3 48.0 312s 22 52.6 0.463 50.7 54.6 312s > model.frame 312s [1] TRUE 312s > model.matrix 312s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 312s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 312s [3] "Numeric: lengths (732, 708) differ" 312s > nobs 312s [1] 59 312s > linearHypothesis 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 48 312s 2 47 1 0.23 0.64 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 48 312s 2 47 1 0.31 0.58 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 48 312s 2 47 1 0.31 0.58 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 47 2 0.5 0.61 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 47 2 0.68 0.51 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 49 312s 2 47 2 1.37 0.5 312s > logLik 312s 'log Lik.' -71 (df=18) 312s 'log Lik.' -81.1 (df=18) 312s Estimating function 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 -2.7455 -36.891 312s Consumption_3 -1.0626 -17.729 312s Consumption_4 -0.0885 -1.678 312s Consumption_5 -3.0649 -63.238 312s Consumption_6 0.7553 14.561 312s Consumption_8 5.9278 102.010 312s Consumption_9 4.6365 88.027 312s Consumption_11 -1.1219 -18.435 312s Consumption_12 -1.0756 -13.439 312s Consumption_13 -3.1243 -28.309 312s Consumption_14 2.5683 23.826 312s Consumption_15 -1.2839 -16.033 312s Consumption_16 -1.2479 -17.951 312s Consumption_17 7.5868 111.454 312s Consumption_18 -1.1010 -21.581 312s Consumption_19 -5.4018 -103.426 312s Consumption_20 3.8300 67.171 312s Consumption_21 1.5068 30.633 312s Consumption_22 -1.8041 -41.092 312s Investment_2 1.3384 17.984 312s Investment_3 -0.1231 -2.053 312s Investment_4 -0.5511 -10.444 312s Investment_5 1.3722 28.313 312s Investment_6 -0.3224 -6.215 312s Investment_8 -1.1676 -20.092 312s Investment_9 -0.4950 -9.397 312s Investment_10 0.0000 0.000 312s Investment_11 0.6975 11.462 312s Investment_12 0.6591 8.235 312s Investment_13 0.9331 8.455 312s Investment_14 -1.2380 -11.485 312s Investment_15 0.1758 2.195 312s Investment_16 -0.0882 -1.269 312s Investment_17 -1.7103 -25.126 312s Investment_18 0.2715 5.322 312s Investment_19 2.9123 55.761 312s Investment_20 -0.5118 -8.975 312s Investment_21 -0.2046 -4.160 312s Investment_22 -0.6426 -14.637 312s PrivateWages_2 -3.2663 -43.888 312s PrivateWages_3 1.1062 18.456 312s PrivateWages_4 2.8429 53.880 312s PrivateWages_5 -2.9330 -60.515 312s PrivateWages_6 -0.4678 -9.018 312s PrivateWages_8 1.7117 29.456 312s PrivateWages_9 1.9856 37.698 312s PrivateWages_10 0.0000 0.000 312s PrivateWages_11 -2.6089 -42.870 312s PrivateWages_12 -0.5972 -7.462 312s PrivateWages_13 -2.3655 -21.434 312s PrivateWages_14 2.8394 26.341 312s PrivateWages_15 -0.5146 -6.427 312s PrivateWages_16 -0.6088 -8.757 312s PrivateWages_17 2.4972 36.686 312s PrivateWages_18 -0.0214 -0.419 312s PrivateWages_19 -6.8265 -130.705 312s PrivateWages_20 1.3447 23.584 312s PrivateWages_21 -1.4002 -28.468 312s PrivateWages_22 2.2878 52.110 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 -34.868 -81.19 312s Consumption_3 -13.177 -33.85 312s Consumption_4 -1.496 -3.14 312s Consumption_5 -56.394 -118.79 312s Consumption_6 14.654 29.20 312s Consumption_8 116.186 236.05 312s Consumption_9 91.802 193.78 312s Consumption_11 -24.345 -48.21 312s Consumption_12 -16.779 -42.24 312s Consumption_13 -35.617 -109.94 312s Consumption_14 17.978 84.77 312s Consumption_15 -14.380 -47.92 312s Consumption_16 -15.349 -50.04 312s Consumption_17 106.215 316.24 312s Consumption_18 -19.377 -52.50 312s Consumption_19 -93.451 -266.03 312s Consumption_20 58.598 185.77 312s Consumption_21 28.629 80.45 312s Consumption_22 -38.066 -109.75 312s Investment_2 16.998 39.58 312s Investment_3 -1.526 -3.92 312s Investment_4 -9.313 -19.52 312s Investment_5 25.249 53.18 312s Investment_6 -6.254 -12.46 312s Investment_8 -22.884 -46.49 312s Investment_9 -9.800 -20.69 312s Investment_10 0.000 0.00 312s Investment_11 15.136 29.97 312s Investment_12 10.282 25.88 312s Investment_13 10.638 32.84 312s Investment_14 -8.666 -40.86 312s Investment_15 1.969 6.56 312s Investment_16 -1.085 -3.54 312s Investment_17 -23.945 -71.29 312s Investment_18 4.779 12.95 312s Investment_19 50.383 143.43 312s Investment_20 -7.830 -24.82 312s Investment_21 -3.888 -10.92 312s Investment_22 -13.559 -39.09 312s PrivateWages_2 -41.482 -96.59 312s PrivateWages_3 13.717 35.24 312s PrivateWages_4 48.044 100.73 312s PrivateWages_5 -53.966 -113.67 312s PrivateWages_6 -9.075 -18.08 312s PrivateWages_8 33.550 68.16 312s PrivateWages_9 39.314 82.99 312s PrivateWages_10 0.000 0.00 312s PrivateWages_11 -56.613 -112.10 312s PrivateWages_12 -9.317 -23.46 312s PrivateWages_13 -26.967 -83.24 312s PrivateWages_14 19.876 93.71 312s PrivateWages_15 -5.764 -19.21 312s PrivateWages_16 -7.488 -24.41 312s PrivateWages_17 34.961 104.09 312s PrivateWages_18 -0.376 -1.02 312s PrivateWages_19 -118.099 -336.20 312s PrivateWages_20 20.574 65.22 312s PrivateWages_21 -26.605 -74.76 312s PrivateWages_22 48.272 139.18 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 1.1993 15.540 312s Consumption_3 0.4642 7.754 312s Consumption_4 0.0387 0.740 312s Consumption_5 1.3388 28.029 312s Consumption_6 -0.3299 -6.424 312s Consumption_8 -2.5893 -44.384 312s Consumption_9 -2.0252 -39.469 312s Consumption_11 0.4900 8.255 312s Consumption_12 0.4698 5.957 312s Consumption_13 1.3647 12.176 312s Consumption_14 -1.1219 -10.434 312s Consumption_15 0.5608 7.176 312s Consumption_16 0.5451 7.773 312s Consumption_17 -3.3140 -48.887 312s Consumption_18 0.4809 9.399 312s Consumption_19 2.3595 45.678 312s Consumption_20 -1.6729 -29.086 312s Consumption_21 -0.6582 -13.228 312s Consumption_22 0.7880 18.015 312s Investment_2 -2.2459 -29.102 312s Investment_3 0.2065 3.450 312s Investment_4 0.9247 17.694 312s Investment_5 -2.3026 -48.209 312s Investment_6 0.5410 10.532 312s Investment_8 1.9592 33.583 312s Investment_9 0.8306 16.187 312s Investment_10 3.0781 62.986 312s Investment_11 -1.1704 -19.716 312s Investment_12 -1.1059 -14.023 312s Investment_13 -1.5658 -13.970 312s Investment_14 2.0775 19.321 312s Investment_15 -0.2950 -3.775 312s Investment_16 0.1480 2.111 312s Investment_17 2.8700 42.338 312s Investment_18 -0.4556 -8.905 312s Investment_19 -4.8870 -94.607 312s Investment_20 0.8587 14.930 312s Investment_21 0.3434 6.901 312s Investment_22 1.0783 24.652 312s PrivateWages_2 1.8660 24.179 312s PrivateWages_3 -0.6320 -10.557 312s PrivateWages_4 -1.6241 -31.077 312s PrivateWages_5 1.6755 35.080 312s PrivateWages_6 0.2672 5.203 312s PrivateWages_8 -0.9779 -16.762 312s PrivateWages_9 -1.1343 -22.106 312s PrivateWages_10 -2.1296 -43.576 312s PrivateWages_11 1.4904 25.106 312s PrivateWages_12 0.3412 4.326 312s PrivateWages_13 1.3514 12.057 312s PrivateWages_14 -1.6221 -15.086 312s PrivateWages_15 0.2940 3.762 312s PrivateWages_16 0.3478 4.959 312s PrivateWages_17 -1.4266 -21.045 312s PrivateWages_18 0.0122 0.239 312s PrivateWages_19 3.8998 75.496 312s PrivateWages_20 -0.7682 -13.356 312s PrivateWages_21 0.7999 16.078 312s PrivateWages_22 -1.3070 -29.879 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 15.231 219.22 312s Consumption_3 5.756 84.76 312s Consumption_4 0.654 7.13 312s Consumption_5 24.633 253.96 312s Consumption_6 -6.401 -63.58 312s Consumption_8 -50.751 -526.67 312s Consumption_9 -40.100 -420.44 312s Consumption_11 10.634 105.70 312s Consumption_12 7.329 101.81 312s Consumption_13 15.558 291.09 312s Consumption_14 -7.853 -232.34 312s Consumption_15 6.281 113.29 312s Consumption_16 6.705 108.47 312s Consumption_17 -46.395 -655.17 312s Consumption_18 8.464 96.09 312s Consumption_19 40.820 476.15 312s Consumption_20 -25.596 -334.42 312s Consumption_21 -12.505 -132.42 312s Consumption_22 16.627 161.15 312s Investment_2 -28.522 -410.54 312s Investment_3 2.561 37.71 312s Investment_4 15.627 170.61 312s Investment_5 -42.368 -436.81 312s Investment_6 10.495 104.25 312s Investment_8 38.400 398.50 312s Investment_9 16.445 172.43 312s Investment_10 64.949 648.26 312s Investment_11 -25.398 -252.46 312s Investment_12 -17.253 -239.66 312s Investment_13 -17.850 -333.99 312s Investment_14 14.542 430.24 312s Investment_15 -3.304 -59.59 312s Investment_16 1.821 29.46 312s Investment_17 40.180 567.40 312s Investment_18 -8.019 -91.03 312s Investment_19 -84.545 -986.19 312s Investment_20 13.139 171.66 312s Investment_21 6.524 69.08 312s Investment_22 22.753 220.52 312s PrivateWages_2 23.698 341.10 312s PrivateWages_3 -7.836 -115.39 312s PrivateWages_4 -27.446 -299.64 312s PrivateWages_5 30.830 317.85 312s PrivateWages_6 5.185 51.50 312s PrivateWages_8 -19.166 -198.90 312s PrivateWages_9 -22.459 -235.48 312s PrivateWages_10 -44.934 -448.49 312s PrivateWages_11 32.341 321.48 312s PrivateWages_12 5.323 73.94 312s PrivateWages_13 15.406 288.25 312s PrivateWages_14 -11.355 -335.93 312s PrivateWages_15 3.293 59.39 312s PrivateWages_16 4.278 69.21 312s PrivateWages_17 -19.973 -282.04 312s PrivateWages_18 0.215 2.44 312s PrivateWages_19 67.467 786.98 312s PrivateWages_20 -11.753 -153.56 312s PrivateWages_21 15.199 160.94 312s PrivateWages_22 -27.577 -267.27 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 -2.6531 -124.88 -119.13 312s Consumption_3 -1.0269 -50.91 -46.83 312s Consumption_4 -0.0856 -4.84 -4.29 312s Consumption_5 -2.9618 -179.74 -169.41 312s Consumption_6 0.7299 44.24 41.68 312s Consumption_8 5.7284 343.69 366.62 312s Consumption_9 4.4804 278.99 288.54 312s Consumption_11 -1.0841 -69.07 -72.64 312s Consumption_12 -1.0394 -56.99 -63.61 312s Consumption_13 -3.0192 -141.83 -161.22 312s Consumption_14 2.4819 104.56 109.95 312s Consumption_15 -1.2407 -63.55 -55.96 312s Consumption_16 -1.2059 -66.73 -59.93 312s Consumption_17 7.3315 420.78 398.83 312s Consumption_18 -1.0639 -71.47 -66.71 312s Consumption_19 -5.2200 -357.64 -339.30 312s Consumption_20 3.7011 247.40 225.40 312s Consumption_21 1.4561 109.01 101.20 312s Consumption_22 -1.7434 -151.46 -131.97 312s Investment_2 1.6915 79.62 75.95 312s Investment_3 -0.1555 -7.71 -7.09 312s Investment_4 -0.6965 -39.38 -34.89 312s Investment_5 1.7343 105.25 99.20 312s Investment_6 -0.4074 -24.70 -23.26 312s Investment_8 -1.4756 -88.53 -94.44 312s Investment_9 -0.6256 -38.95 -40.29 312s Investment_10 -2.3184 -149.69 -149.53 312s Investment_11 0.8815 56.16 59.06 312s Investment_12 0.8330 45.67 50.98 312s Investment_13 1.1793 55.40 62.98 312s Investment_14 -1.5647 -65.92 -69.32 312s Investment_15 0.2222 11.38 10.02 312s Investment_16 -0.1115 -6.17 -5.54 312s Investment_17 -2.1616 -124.06 -117.59 312s Investment_18 0.3432 23.05 21.52 312s Investment_19 3.6807 252.18 239.25 312s Investment_20 -0.6468 -43.23 -39.39 312s Investment_21 -0.2586 -19.36 -17.97 312s Investment_22 -0.8122 -70.56 -61.48 312s PrivateWages_2 -7.4676 -351.50 -335.29 312s PrivateWages_3 2.5291 125.39 115.33 312s PrivateWages_4 6.4995 367.50 325.62 312s PrivateWages_5 -6.7054 -406.93 -383.55 312s PrivateWages_6 -1.0695 -64.82 -61.07 312s PrivateWages_8 3.9134 234.79 250.46 312s PrivateWages_9 4.5395 282.67 292.34 312s PrivateWages_10 8.5226 550.30 549.71 312s PrivateWages_11 -5.9646 -380.01 -399.63 312s PrivateWages_12 -1.3654 -74.87 -83.57 312s PrivateWages_13 -5.4082 -254.06 -288.80 312s PrivateWages_14 6.4916 273.48 287.58 312s PrivateWages_15 -1.1766 -60.26 -53.06 312s PrivateWages_16 -1.3918 -77.02 -69.17 312s PrivateWages_17 5.7093 327.68 310.59 312s PrivateWages_18 -0.0489 -3.28 -3.07 312s PrivateWages_19 -15.6071 -1069.28 -1014.46 312s PrivateWages_20 3.0743 205.50 187.22 312s PrivateWages_21 -3.2013 -239.67 -222.49 312s PrivateWages_22 5.2304 454.42 395.94 312s PrivateWages_trend 312s Consumption_2 26.531 312s Consumption_3 9.242 312s Consumption_4 0.684 312s Consumption_5 20.732 312s Consumption_6 -4.380 312s Consumption_8 -22.913 312s Consumption_9 -13.441 312s Consumption_11 1.084 312s Consumption_12 0.000 312s Consumption_13 -3.019 312s Consumption_14 4.964 312s Consumption_15 -3.722 312s Consumption_16 -4.824 312s Consumption_17 36.658 312s Consumption_18 -6.384 312s Consumption_19 -36.540 312s Consumption_20 29.609 312s Consumption_21 13.105 312s Consumption_22 -17.434 312s Investment_2 -16.915 312s Investment_3 1.400 312s Investment_4 5.572 312s Investment_5 -12.140 312s Investment_6 2.445 312s Investment_8 5.902 312s Investment_9 1.877 312s Investment_10 4.637 312s Investment_11 -0.882 312s Investment_12 0.000 312s Investment_13 1.179 312s Investment_14 -3.129 312s Investment_15 0.667 312s Investment_16 -0.446 312s Investment_17 -10.808 312s Investment_18 2.059 312s Investment_19 25.765 312s Investment_20 -5.174 312s Investment_21 -2.327 312s Investment_22 -8.122 312s PrivateWages_2 74.676 312s PrivateWages_3 -22.762 312s PrivateWages_4 -51.996 312s PrivateWages_5 46.938 312s PrivateWages_6 6.417 312s PrivateWages_8 -15.654 312s PrivateWages_9 -13.618 312s PrivateWages_10 -17.045 312s PrivateWages_11 5.965 312s PrivateWages_12 0.000 312s PrivateWages_13 -5.408 312s PrivateWages_14 12.983 312s PrivateWages_15 -3.530 312s PrivateWages_16 -5.567 312s PrivateWages_17 28.547 312s PrivateWages_18 -0.293 312s PrivateWages_19 -109.250 312s PrivateWages_20 24.594 312s PrivateWages_21 -28.812 312s PrivateWages_22 52.304 312s [1] TRUE 312s > Bread 312s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 312s [1,] 104.28657 -1.0082 -0.4696 312s [2,] -1.00824 0.7107 -0.4494 312s [3,] -0.46959 -0.4494 0.5979 312s [4,] -1.85053 -0.0857 -0.0409 312s [5,] 80.53000 1.3241 3.0428 312s [6,] -1.81359 0.2334 -0.2583 312s [7,] 0.54047 -0.1847 0.2826 312s [8,] -0.28778 -0.0112 -0.0165 312s [9,] -35.77159 0.2050 1.7044 312s [10,] 0.58031 -0.0870 0.0510 312s [11,] -0.00461 0.0862 -0.0821 312s [12,] 0.19369 0.0416 0.0268 312s Consumption_wages Investment_(Intercept) Investment_corpProf 312s [1,] -1.850529 80.530 -1.81359 312s [2,] -0.085701 1.324 0.23344 312s [3,] -0.040883 3.043 -0.25828 312s [4,] 0.094773 -3.542 0.04931 312s [5,] -3.542001 2206.842 -34.41529 312s [6,] 0.049311 -34.415 1.17951 312s [7,] -0.048133 29.517 -1.02562 312s [8,] 0.017421 -10.487 0.15573 312s [9,] 0.083728 18.025 -0.14810 312s [10,] 0.000958 1.156 0.00386 312s [11,] -0.002304 -1.519 -0.00126 312s [12,] -0.031989 -0.955 0.01443 312s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 312s [1,] 0.54047 -0.28778 -35.7716 312s [2,] -0.18475 -0.01117 0.2050 312s [3,] 0.28258 -0.01647 1.7044 312s [4,] -0.04813 0.01742 0.0837 312s [5,] 29.51706 -10.48672 18.0248 312s [6,] -1.02562 0.15573 -0.1481 312s [7,] 1.09362 -0.14971 -0.4803 312s [8,] -0.14971 0.05132 -0.0381 312s [9,] -0.48030 -0.03806 70.4425 312s [10,] 0.00353 -0.00637 -0.4681 312s [11,] 0.00471 0.00732 -0.7110 312s [12,] -0.02247 0.00534 0.8424 312s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 312s [1,] 0.580315 -0.00461 0.19369 312s [2,] -0.086985 0.08623 0.04160 312s [3,] 0.051027 -0.08213 0.02678 312s [4,] 0.000958 -0.00230 -0.03199 312s [5,] 1.156385 -1.51874 -0.95497 312s [6,] 0.003856 -0.00126 0.01443 312s [7,] 0.003528 0.00471 -0.02247 312s [8,] -0.006374 0.00732 0.00534 312s [9,] -0.468096 -0.71104 0.84245 312s [10,] 0.058634 -0.05251 -0.01709 312s [11,] -0.052508 0.06655 0.00301 312s [12,] -0.017087 0.00301 0.04635 312s > 312s > # I3SLS 312s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 312s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 312s > summary 312s 312s systemfit results 312s method: iterated 3SLS 312s 312s convergence achieved after 15 iterations 312s 312s N DF SSR detRCov OLS-R2 McElroy-R2 312s system 59 47 81.3 0.349 0.958 0.995 312s 312s N DF SSR MSE RMSE R2 Adj R2 312s Consumption 19 15 18.1 1.209 1.100 0.980 0.976 312s Investment 20 16 52.0 3.250 1.803 0.776 0.735 312s PrivateWages 20 16 11.2 0.699 0.836 0.986 0.983 312s 312s The covariance matrix of the residuals used for estimation 312s Consumption Investment PrivateWages 312s Consumption 0.955 0.456 -0.421 312s Investment 0.456 2.294 0.375 312s PrivateWages -0.421 0.375 0.522 312s 312s The covariance matrix of the residuals 312s Consumption Investment PrivateWages 312s Consumption 0.955 0.456 -0.421 312s Investment 0.456 2.294 0.375 312s PrivateWages -0.421 0.375 0.522 312s 312s The correlations of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.000 0.322 -0.582 312s Investment 0.322 1.000 0.341 312s PrivateWages -0.582 0.341 1.000 312s 312s 312s 3SLS estimates for 'Consumption' (equation 1) 312s Model Formula: consump ~ corpProf + corpProfLag + wages 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 16.8311 1.2489 13.48 8.7e-10 *** 312s corpProf 0.1468 0.0991 1.48 0.16 312s corpProfLag 0.0924 0.0906 1.02 0.32 312s wages 0.7945 0.0371 21.43 1.2e-12 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.1 on 15 degrees of freedom 312s Number of observations: 19 Degrees of Freedom: 15 312s SSR: 18.14 MSE: 1.209 Root MSE: 1.1 312s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 312s 312s 312s 3SLS estimates for 'Investment' (equation 2) 312s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 32.4128 8.2695 3.92 0.00122 ** 312s corpProf -0.0799 0.1934 -0.41 0.68498 312s corpProfLag 0.7607 0.1878 4.05 0.00093 *** 312s capitalLag -0.2114 0.0400 -5.29 7.4e-05 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.803 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 51.999 MSE: 3.25 Root MSE: 1.803 312s Multiple R-Squared: 0.776 Adjusted R-Squared: 0.735 312s 312s 312s 3SLS estimates for 'PrivateWages' (equation 3) 312s Model Formula: privWage ~ gnp + gnpLag + trend 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 1.5421 1.1496 1.34 0.19852 312s gnp 0.3936 0.0313 12.57 1.0e-09 *** 312s gnpLag 0.1945 0.0328 5.93 2.1e-05 *** 312s trend 0.1416 0.0286 4.95 0.00014 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 0.836 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 11.181 MSE: 0.699 Root MSE: 0.836 312s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.983 312s 312s > residuals 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 -0.3309 -2.6308 -1.3061 312s 3 -1.0419 0.0146 0.4450 312s 4 -1.2918 0.4128 1.4338 312s 5 -0.1772 -1.7488 -0.2494 312s 6 0.3563 0.2807 -0.4066 312s 7 NA NA NA 312s 8 1.6778 1.4671 -0.8700 312s 9 1.4561 1.1068 0.1712 312s 10 NA 2.9002 1.1262 312s 11 0.4237 -1.0652 -0.6189 312s 12 -0.2711 -0.9488 0.0375 312s 13 -0.5643 -1.6241 -0.5055 312s 14 0.2845 1.8477 0.3080 312s 15 -0.0514 -0.2379 0.3003 312s 16 0.0521 0.1268 0.0141 312s 17 1.8733 2.2462 -0.7083 312s 18 -0.1962 -0.1724 0.8305 312s 19 0.3553 -3.5810 -0.9448 312s 20 1.3161 1.0343 -0.2738 312s 21 1.2055 0.6622 -1.1283 312s 22 -1.6327 1.5541 0.8257 312s > fitted 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 42.2 2.431 26.8 312s 3 46.0 1.885 28.9 312s 4 50.5 4.787 32.7 312s 5 50.8 4.749 34.1 312s 6 52.2 4.819 35.8 312s 7 NA NA NA 312s 8 54.5 2.733 38.8 312s 9 55.8 1.893 39.0 312s 10 NA 2.200 40.2 312s 11 54.6 2.065 38.5 312s 12 51.2 -2.451 34.5 312s 13 46.2 -4.576 29.5 312s 14 46.2 -6.948 28.2 312s 15 48.8 -2.762 30.3 312s 16 51.2 -1.427 33.2 312s 17 55.8 -0.146 37.5 312s 18 58.9 2.172 40.2 312s 19 57.1 1.681 39.1 312s 20 60.3 0.266 41.9 312s 21 63.8 2.638 46.1 312s 22 71.3 3.346 52.5 312s > predict 312s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 312s 1 NA NA NA NA 312s 2 42.2 0.446 41.3 43.1 312s 3 46.0 0.511 45.0 47.1 312s 4 50.5 0.340 49.8 51.2 312s 5 50.8 0.393 50.0 51.6 312s 6 52.2 0.396 51.4 53.0 312s 7 NA NA NA NA 312s 8 54.5 0.326 53.9 55.2 312s 9 55.8 0.362 55.1 56.6 312s 10 NA NA NA NA 312s 11 54.6 0.612 53.3 55.8 312s 12 51.2 0.511 50.1 52.2 312s 13 46.2 0.671 44.8 47.5 312s 14 46.2 0.563 45.1 47.3 312s 15 48.8 0.354 48.0 49.5 312s 16 51.2 0.311 50.6 51.9 312s 17 55.8 0.362 55.1 56.6 312s 18 58.9 0.297 58.3 59.5 312s 19 57.1 0.357 56.4 57.9 312s 20 60.3 0.427 59.4 61.1 312s 21 63.8 0.416 63.0 64.6 312s 22 71.3 0.640 70.0 72.6 312s Investment.pred Investment.se.fit Investment.lwr Investment.upr 312s 1 NA NA NA NA 312s 2 2.431 0.970 0.4798 4.382 312s 3 1.885 0.745 0.3859 3.385 312s 4 4.787 0.664 3.4506 6.124 312s 5 4.749 0.562 3.6174 5.880 312s 6 4.819 0.537 3.7391 5.900 312s 7 NA NA NA NA 312s 8 2.733 0.446 1.8351 3.631 312s 9 1.893 0.620 0.6455 3.141 312s 10 2.200 0.684 0.8232 3.576 312s 11 2.065 1.055 -0.0569 4.187 312s 12 -2.451 0.845 -4.1517 -0.751 312s 13 -4.576 1.070 -6.7293 -2.423 312s 14 -6.948 1.103 -9.1676 -4.728 312s 15 -2.762 0.556 -3.8806 -1.644 312s 16 -1.427 0.480 -2.3919 -0.462 312s 17 -0.146 0.603 -1.3588 1.066 312s 18 2.172 0.390 1.3869 2.958 312s 19 1.681 0.563 0.5476 2.815 312s 20 0.266 0.661 -1.0634 1.595 312s 21 2.638 0.558 1.5144 3.761 312s 22 3.346 0.778 1.7808 4.911 312s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 312s 1 NA NA NA NA 312s 2 26.8 0.326 26.2 27.5 312s 3 28.9 0.328 28.2 29.5 312s 4 32.7 0.334 32.0 33.3 312s 5 34.1 0.242 33.7 34.6 312s 6 35.8 0.252 35.3 36.3 312s 7 NA NA NA NA 312s 8 38.8 0.244 38.3 39.3 312s 9 39.0 0.232 38.6 39.5 312s 10 40.2 0.230 39.7 40.6 312s 11 38.5 0.308 37.9 39.1 312s 12 34.5 0.336 33.8 35.1 312s 13 29.5 0.420 28.7 30.4 312s 14 28.2 0.345 27.5 28.9 312s 15 30.3 0.325 29.6 31.0 312s 16 33.2 0.271 32.6 33.7 312s 17 37.5 0.267 37.0 38.0 312s 18 40.2 0.218 39.7 40.6 312s 19 39.1 0.331 38.5 39.8 312s 20 41.9 0.289 41.3 42.5 312s 21 46.1 0.311 45.5 46.8 312s 22 52.5 0.485 51.5 53.5 312s > model.frame 312s [1] TRUE 312s > model.matrix 312s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 312s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 312s [3] "Numeric: lengths (732, 708) differ" 312s > nobs 312s [1] 59 312s > linearHypothesis 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 48 312s 2 47 1 0.28 0.6 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 48 312s 2 47 1 0.37 0.55 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 48 312s 2 47 1 0.37 0.54 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 47 2 1.25 0.3 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 47 2 1.64 0.21 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 49 312s 2 47 2 3.28 0.19 312s > logLik 312s 'log Lik.' -74.5 (df=18) 312s 'log Lik.' -87.1 (df=18) 312s Estimating function 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 -4.75944 -63.951 312s Consumption_3 -2.22772 -37.167 312s Consumption_4 -0.38275 -7.254 312s Consumption_5 -5.30482 -109.454 312s Consumption_6 1.30597 25.176 312s Consumption_8 10.25777 176.523 312s Consumption_9 7.99665 151.823 312s Consumption_11 -1.17443 -19.299 312s Consumption_12 -1.24242 -15.523 312s Consumption_13 -4.75716 -43.103 312s Consumption_14 4.34635 40.320 312s Consumption_15 -1.98107 -24.739 312s Consumption_16 -1.93670 -27.859 312s Consumption_17 13.00314 191.023 312s Consumption_18 -1.57749 -30.922 312s Consumption_19 -8.67959 -166.185 312s Consumption_20 6.77999 118.909 312s Consumption_21 3.04771 61.962 312s Consumption_22 -2.30170 -52.427 312s Investment_2 2.92832 39.347 312s Investment_3 0.00114 0.019 312s Investment_4 -0.53396 -10.120 312s Investment_5 1.84118 37.989 312s Investment_6 -0.26074 -5.026 312s Investment_8 -1.42063 -24.447 312s Investment_9 -1.10750 -21.027 312s Investment_10 0.00000 0.000 312s Investment_11 1.09344 17.968 312s Investment_12 0.95848 11.975 312s Investment_13 1.66503 15.086 312s Investment_14 -1.92032 -17.814 312s Investment_15 0.22458 2.804 312s Investment_16 -0.16698 -2.402 312s Investment_17 -2.28568 -33.578 312s Investment_18 -0.00785 -0.154 312s Investment_19 3.68757 70.604 312s Investment_20 -1.02511 -17.979 312s Investment_21 -0.65919 -13.402 312s Investment_22 -1.70192 -38.765 312s PrivateWages_2 -6.13297 -82.407 312s PrivateWages_3 2.11354 35.262 312s PrivateWages_4 5.50774 104.386 312s PrivateWages_5 -5.40526 -111.526 312s PrivateWages_6 -0.82424 -15.889 312s PrivateWages_8 2.80754 48.314 312s PrivateWages_9 3.41557 64.847 312s PrivateWages_10 0.00000 0.000 312s PrivateWages_11 -5.23135 -85.964 312s PrivateWages_12 -1.71264 -21.398 312s PrivateWages_13 -5.07393 -45.974 312s PrivateWages_14 4.80915 44.613 312s PrivateWages_15 -0.96519 -12.053 312s PrivateWages_16 -1.15621 -16.632 312s PrivateWages_17 4.49108 65.976 312s PrivateWages_18 -0.08188 -1.605 312s PrivateWages_19 -12.82495 -245.555 312s PrivateWages_20 2.51036 44.027 312s PrivateWages_21 -2.60385 -52.938 312s PrivateWages_22 4.63537 105.582 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 -60.4449 -140.7509 312s Consumption_3 -27.6237 -70.9657 312s Consumption_4 -6.4685 -13.5614 312s Consumption_5 -97.6087 -205.5997 312s Consumption_6 25.3358 50.4846 312s Consumption_8 201.0522 408.4748 312s Consumption_9 158.3336 334.2197 312s Consumption_11 -25.4852 -50.4634 312s Consumption_12 -19.3817 -48.7944 312s Consumption_13 -54.2317 -167.3998 312s Consumption_14 30.4244 143.4489 312s Consumption_15 -22.1880 -73.9440 312s Consumption_16 -23.8214 -77.6627 312s Consumption_17 182.0440 542.0110 312s Consumption_18 -27.7639 -75.2217 312s Consumption_19 -150.1568 -427.4616 312s Consumption_20 103.7339 328.8605 312s Consumption_21 57.9064 162.7199 312s Consumption_22 -48.5659 -140.0278 312s Investment_2 37.1896 86.5991 312s Investment_3 0.0141 0.0362 312s Investment_4 -9.0240 -18.9190 312s Investment_5 33.8777 71.3589 312s Investment_6 -5.0583 -10.0793 312s Investment_8 -27.8443 -56.5709 312s Investment_9 -21.9285 -46.2880 312s Investment_10 0.0000 0.0000 312s Investment_11 23.7276 46.9832 312s Investment_12 14.9524 37.6432 312s Investment_13 18.9813 58.5907 312s Investment_14 -13.4423 -63.3793 312s Investment_15 2.5153 8.3824 312s Investment_16 -2.0538 -6.6959 312s Investment_17 -31.9996 -95.2743 312s Investment_18 -0.1382 -0.3745 312s Investment_19 63.7949 181.6093 312s Investment_20 -15.6841 -49.7224 312s Investment_21 -12.5246 -35.1949 312s Investment_22 -35.9105 -103.5390 312s PrivateWages_2 -77.8887 -181.3703 312s PrivateWages_3 26.2079 67.3285 312s PrivateWages_4 93.0807 195.1464 312s PrivateWages_5 -99.4568 -209.4924 312s PrivateWages_6 -15.9902 -31.8624 312s PrivateWages_8 55.0278 111.7991 312s PrivateWages_9 67.6282 142.7536 312s PrivateWages_10 0.0000 0.0000 312s PrivateWages_11 -113.5202 -224.7822 312s PrivateWages_12 -26.7172 -67.2617 312s PrivateWages_13 -57.8428 -178.5466 312s PrivateWages_14 33.6641 158.7235 312s PrivateWages_15 -10.8101 -36.0260 312s PrivateWages_16 -14.2214 -46.3646 312s PrivateWages_17 62.8751 187.2021 312s PrivateWages_18 -1.4410 -3.9043 312s PrivateWages_19 -221.8716 -631.6170 312s PrivateWages_20 38.4085 121.7638 312s PrivateWages_21 -49.4732 -139.0222 312s PrivateWages_22 97.8064 282.0006 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 1.782157 23.0934 312s Consumption_3 0.834162 13.9344 312s Consumption_4 0.143320 2.7425 312s Consumption_5 1.986375 41.5880 312s Consumption_6 -0.489016 -9.5207 312s Consumption_8 -3.840991 -65.8399 312s Consumption_9 -2.994321 -58.3554 312s Consumption_11 0.439763 7.4080 312s Consumption_12 0.465220 5.8989 312s Consumption_13 1.781306 15.8927 312s Consumption_14 -1.627477 -15.1363 312s Consumption_15 0.741807 9.4914 312s Consumption_16 0.725191 10.3407 312s Consumption_17 -4.868989 -71.8262 312s Consumption_18 0.590688 11.5449 312s Consumption_19 3.250046 62.9174 312s Consumption_20 -2.538748 -44.1394 312s Consumption_21 -1.141204 -22.9368 312s Consumption_22 0.861865 19.7035 312s Investment_2 -2.373514 -30.7562 312s Investment_3 -0.000921 -0.0154 312s Investment_4 0.432798 8.2817 312s Investment_5 -1.492349 -31.2447 312s Investment_6 0.211337 4.1146 312s Investment_8 1.151475 19.7379 312s Investment_9 0.897673 17.4945 312s Investment_10 2.570865 52.6054 312s Investment_11 -0.886274 -14.9297 312s Investment_12 -0.776889 -9.8508 312s Investment_13 -1.349570 -12.0408 312s Investment_14 1.556498 14.4761 312s Investment_15 -0.182029 -2.3291 312s Investment_16 0.135342 1.9299 312s Investment_17 1.852635 27.3297 312s Investment_18 0.006366 0.1244 312s Investment_19 -2.988917 -57.8622 312s Investment_20 0.830890 14.4461 312s Investment_21 0.534301 10.7388 312s Investment_22 1.379471 31.5367 312s PrivateWages_2 2.964495 38.4142 312s PrivateWages_3 -1.021623 -17.0659 312s PrivateWages_4 -2.662277 -50.9436 312s PrivateWages_5 2.612743 54.7020 312s PrivateWages_6 0.398411 7.7567 312s PrivateWages_8 -1.357082 -23.2623 312s PrivateWages_9 -1.650985 -32.1755 312s PrivateWages_10 -3.276467 -67.0436 312s PrivateWages_11 2.528678 42.5968 312s PrivateWages_12 0.827840 10.4968 312s PrivateWages_13 2.452590 21.8819 312s PrivateWages_14 -2.324602 -21.6199 312s PrivateWages_15 0.466545 5.9694 312s PrivateWages_16 0.558877 7.9692 312s PrivateWages_17 -2.170857 -32.0240 312s PrivateWages_18 0.039577 0.7735 312s PrivateWages_19 6.199203 120.0098 312s PrivateWages_20 -1.213433 -21.0971 312s PrivateWages_21 1.258626 25.2969 312s PrivateWages_22 -2.240603 -51.2233 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 22.6334 325.778 312s Consumption_3 10.3436 152.318 312s Consumption_4 2.4221 26.443 312s Consumption_5 36.5493 376.815 312s Consumption_6 -9.4869 -94.233 312s Consumption_8 -75.2834 -781.258 312s Consumption_9 -59.2876 -621.621 312s Consumption_11 9.5429 94.857 312s Consumption_12 7.2574 100.813 312s Consumption_13 20.3069 379.952 312s Consumption_14 -11.3923 -337.050 312s Consumption_15 8.3082 149.845 312s Consumption_16 8.9199 144.313 312s Consumption_17 -68.1658 -962.599 312s Consumption_18 10.3961 118.019 312s Consumption_19 56.2258 655.859 312s Consumption_20 -38.8428 -507.496 312s Consumption_21 -21.6829 -229.610 312s Consumption_22 18.1854 176.251 312s Investment_2 -30.1436 -433.878 312s Investment_3 -0.0114 -0.168 312s Investment_4 7.3143 79.851 312s Investment_5 -27.4592 -283.099 312s Investment_6 4.0999 40.725 312s Investment_8 22.5689 234.210 312s Investment_9 17.7739 186.357 312s Investment_10 54.2453 541.424 312s Investment_11 -19.2321 -191.169 312s Investment_12 -12.1195 -168.352 312s Investment_13 -15.3851 -287.863 312s Investment_14 10.8955 322.351 312s Investment_15 -2.0387 -36.770 312s Investment_16 1.6647 26.933 312s Investment_17 25.9369 366.266 312s Investment_18 0.1120 1.272 312s Investment_19 -51.7083 -603.163 312s Investment_20 12.7126 166.095 312s Investment_21 10.1517 107.501 312s Investment_22 29.1068 282.102 312s PrivateWages_2 37.6491 541.910 312s PrivateWages_3 -12.6681 -186.548 312s PrivateWages_4 -44.9925 -491.190 312s PrivateWages_5 48.0745 495.637 312s PrivateWages_6 7.7292 76.774 312s PrivateWages_8 -26.5988 -276.031 312s PrivateWages_9 -32.6895 -342.744 312s PrivateWages_10 -69.1335 -690.024 312s PrivateWages_11 54.8723 545.436 312s PrivateWages_12 12.9143 179.393 312s PrivateWages_13 27.9595 523.137 312s PrivateWages_14 -16.2722 -481.425 312s PrivateWages_15 5.2253 94.242 312s PrivateWages_16 6.8742 111.217 312s PrivateWages_17 -30.3920 -429.178 312s PrivateWages_18 0.6966 7.908 312s PrivateWages_19 107.2462 1250.999 312s PrivateWages_20 -18.5655 -242.565 312s PrivateWages_21 23.9139 253.236 312s PrivateWages_22 -47.2767 -458.203 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 -5.12212 -2.41e+02 -229.983 312s Consumption_3 -2.39748 -1.19e+02 -109.325 312s Consumption_4 -0.41192 -2.33e+01 -20.637 312s Consumption_5 -5.70906 -3.46e+02 -326.558 312s Consumption_6 1.40549 8.52e+01 80.253 312s Consumption_8 11.03944 6.62e+02 706.524 312s Consumption_9 8.60601 5.36e+02 554.227 312s Consumption_11 -1.26393 -8.05e+01 -84.683 312s Consumption_12 -1.33709 -7.33e+01 -81.830 312s Consumption_13 -5.11967 -2.41e+02 -273.390 312s Consumption_14 4.67755 1.97e+02 207.216 312s Consumption_15 -2.13204 -1.09e+02 -96.155 312s Consumption_16 -2.08428 -1.15e+02 -103.589 312s Consumption_17 13.99402 8.03e+02 761.275 312s Consumption_18 -1.69770 -1.14e+02 -106.446 312s Consumption_19 -9.34099 -6.40e+02 -607.165 312s Consumption_20 7.29665 4.88e+02 444.366 312s Consumption_21 3.27995 2.46e+02 227.957 312s Consumption_22 -2.47710 -2.15e+02 -187.516 312s Investment_2 4.06820 1.91e+02 182.662 312s Investment_3 0.00158 7.83e-02 0.072 312s Investment_4 -0.74181 -4.19e+01 -37.165 312s Investment_5 2.55788 1.55e+02 146.311 312s Investment_6 -0.36223 -2.20e+01 -20.683 312s Investment_8 -1.97362 -1.18e+02 -126.312 312s Investment_9 -1.53861 -9.58e+01 -99.086 312s Investment_10 -4.40645 -2.85e+02 -284.216 312s Investment_11 1.51907 9.68e+01 101.778 312s Investment_12 1.33159 7.30e+01 81.493 312s Investment_13 2.31316 1.09e+02 123.523 312s Investment_14 -2.66783 -1.12e+02 -118.185 312s Investment_15 0.31200 1.60e+01 14.071 312s Investment_16 -0.23198 -1.28e+01 -11.529 312s Investment_17 -3.17541 -1.82e+02 -172.742 312s Investment_18 -0.01091 -7.33e-01 -0.684 312s Investment_19 5.12299 3.51e+02 332.995 312s Investment_20 -1.42414 -9.52e+01 -86.730 312s Investment_21 -0.91579 -6.86e+01 -63.647 312s Investment_22 -2.36441 -2.05e+02 -178.986 312s PrivateWages_2 -10.69229 -5.03e+02 -480.084 312s PrivateWages_3 3.68477 1.83e+02 168.026 312s PrivateWages_4 9.60226 5.43e+02 481.073 312s PrivateWages_5 -9.42360 -5.72e+02 -539.030 312s PrivateWages_6 -1.43698 -8.71e+01 -82.052 312s PrivateWages_8 4.89470 2.94e+02 313.261 312s PrivateWages_9 5.95474 3.71e+02 383.486 312s PrivateWages_10 11.81751 7.63e+02 762.229 312s PrivateWages_11 -9.12040 -5.81e+02 -611.067 312s PrivateWages_12 -2.98584 -1.64e+02 -182.733 312s PrivateWages_13 -8.84596 -4.16e+02 -472.374 312s PrivateWages_14 8.38434 3.53e+02 371.426 312s PrivateWages_15 -1.68273 -8.62e+01 -75.891 312s PrivateWages_16 -2.01575 -1.12e+02 -100.183 312s PrivateWages_17 7.82981 4.49e+02 425.942 312s PrivateWages_18 -0.14275 -9.59e+00 -8.950 312s PrivateWages_19 -22.35918 -1.53e+03 -1453.347 312s PrivateWages_20 4.37659 2.93e+02 266.534 312s PrivateWages_21 -4.53959 -3.40e+02 -315.502 312s PrivateWages_22 8.08137 7.02e+02 611.760 312s PrivateWages_trend 312s Consumption_2 51.2212 312s Consumption_3 21.5773 312s Consumption_4 3.2953 312s Consumption_5 39.9635 312s Consumption_6 -8.4329 312s Consumption_8 -44.1578 312s Consumption_9 -25.8180 312s Consumption_11 1.2639 312s Consumption_12 0.0000 312s Consumption_13 -5.1197 312s Consumption_14 9.3551 312s Consumption_15 -6.3961 312s Consumption_16 -8.3371 312s Consumption_17 69.9701 312s Consumption_18 -10.1862 312s Consumption_19 -65.3870 312s Consumption_20 58.3732 312s Consumption_21 29.5195 312s Consumption_22 -24.7710 312s Investment_2 -40.6819 312s Investment_3 -0.0142 312s Investment_4 5.9345 312s Investment_5 -17.9052 312s Investment_6 2.1734 312s Investment_8 7.8945 312s Investment_9 4.6158 312s Investment_10 8.8129 312s Investment_11 -1.5191 312s Investment_12 0.0000 312s Investment_13 2.3132 312s Investment_14 -5.3357 312s Investment_15 0.9360 312s Investment_16 -0.9279 312s Investment_17 -15.8771 312s Investment_18 -0.0655 312s Investment_19 35.8610 312s Investment_20 -11.3931 312s Investment_21 -8.2421 312s Investment_22 -23.6441 312s PrivateWages_2 106.9229 312s PrivateWages_3 -33.1629 312s PrivateWages_4 -76.8181 312s PrivateWages_5 65.9652 312s PrivateWages_6 8.6219 312s PrivateWages_8 -19.5788 312s PrivateWages_9 -17.8642 312s PrivateWages_10 -23.6350 312s PrivateWages_11 9.1204 312s PrivateWages_12 0.0000 312s PrivateWages_13 -8.8460 312s PrivateWages_14 16.7687 312s PrivateWages_15 -5.0482 312s PrivateWages_16 -8.0630 312s PrivateWages_17 39.1491 312s PrivateWages_18 -0.8565 312s PrivateWages_19 -156.5143 312s PrivateWages_20 35.0127 312s PrivateWages_21 -40.8563 312s PrivateWages_22 80.8137 312s [1] TRUE 312s > Bread 312s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 312s [1,] 92.02523 -0.8883 -0.3567 312s [2,] -0.88834 0.5799 -0.3635 312s [3,] -0.35667 -0.3635 0.4840 312s [4,] -1.65059 -0.0695 -0.0345 312s [5,] 87.30345 -0.4940 5.6093 312s [6,] -2.09669 0.4100 -0.4129 312s [7,] 0.52353 -0.3352 0.4397 312s [8,] -0.29441 -0.0047 -0.0291 312s [9,] -39.25694 0.2930 1.5879 312s [10,] 0.63395 -0.0766 0.0444 312s [11,] -0.00377 0.0739 -0.0730 312s [12,] 0.26412 0.0450 0.0239 312s Consumption_wages Investment_(Intercept) Investment_corpProf 312s [1,] -1.650593 87.303 -2.09669 312s [2,] -0.069509 -0.494 0.41001 312s [3,] -0.034488 5.609 -0.41285 312s [4,] 0.081060 -3.868 0.04419 312s [5,] -3.867758 4034.682 -59.45928 312s [6,] 0.044186 -59.459 2.20583 312s [7,] -0.048017 50.679 -1.90719 312s [8,] 0.019469 -19.184 0.26586 312s [9,] 0.172081 52.203 -0.49762 312s [10,] -0.001839 2.943 0.01728 312s [11,] -0.000946 -3.971 -0.00883 312s [12,] -0.034168 -2.641 0.03741 312s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 312s [1,] 0.52353 -0.2944 -39.2569 312s [2,] -0.33517 -0.0047 0.2930 312s [3,] 0.43972 -0.0291 1.5879 312s [4,] -0.04802 0.0195 0.1721 312s [5,] 50.67914 -19.1839 52.2027 312s [6,] -1.90719 0.2659 -0.4976 312s [7,] 2.08136 -0.2612 -1.5286 312s [8,] -0.26125 0.0944 -0.0914 312s [9,] -1.52864 -0.0914 77.9751 312s [10,] 0.00872 -0.0168 -0.5909 312s [11,] 0.01756 0.0191 -0.7086 312s [12,] -0.06267 0.0150 0.8675 312s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 312s [1,] 0.63395 -0.003771 0.26412 312s [2,] -0.07661 0.073937 0.04500 312s [3,] 0.04435 -0.072979 0.02395 312s [4,] -0.00184 -0.000946 -0.03417 312s [5,] 2.94321 -3.971150 -2.64074 312s [6,] 0.01728 -0.008829 0.03741 312s [7,] 0.00872 0.017559 -0.06267 312s [8,] -0.01682 0.019146 0.01504 312s [9,] -0.59094 -0.708614 0.86750 312s [10,] 0.05781 -0.049542 -0.01891 312s [11,] -0.04954 0.063408 0.00453 312s [12,] -0.01891 0.004534 0.04825 312s > 312s > # OLS 312s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 312s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 312s > summary 312s 312s systemfit results 312s method: OLS 312s 312s N DF SSR detRCov OLS-R2 McElroy-R2 312s system 59 47 44.2 0.453 0.976 0.99 312s 312s N DF SSR MSE RMSE R2 Adj R2 312s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 312s Investment 20 16 17.11 1.069 1.03 0.912 0.895 312s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 312s 312s The covariance matrix of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.1939 0.0559 -0.474 312s Investment 0.0559 0.9839 0.140 312s PrivateWages -0.4745 0.1403 0.602 312s 312s The correlations of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.0000 0.0447 -0.568 312s Investment 0.0447 1.0000 0.169 312s PrivateWages -0.5680 0.1689 1.000 312s 312s 312s OLS estimates for 'Consumption' (equation 1) 312s Model Formula: consump ~ corpProf + corpProfLag + wages 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 16.2957 1.4879 10.95 1.5e-08 *** 312s corpProf 0.1796 0.1162 1.55 0.14 312s corpProfLag 0.1032 0.0994 1.04 0.32 312s wages 0.7962 0.0433 18.39 1.1e-11 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.076 on 15 degrees of freedom 312s Number of observations: 19 Degrees of Freedom: 15 312s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 312s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 312s 312s 312s OLS estimates for 'Investment' (equation 2) 312s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 10.1813 5.3720 1.90 0.07627 . 312s corpProf 0.5003 0.1052 4.75 0.00022 *** 312s corpProfLag 0.3259 0.1003 3.25 0.00502 ** 312s capitalLag -0.1134 0.0265 -4.28 0.00057 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.034 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 17.109 MSE: 1.069 Root MSE: 1.034 312s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.895 312s 312s 312s OLS estimates for 'PrivateWages' (equation 3) 312s Model Formula: privWage ~ gnp + gnpLag + trend 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 1.3550 1.3021 1.04 0.3135 312s gnp 0.4417 0.0330 13.40 4.1e-10 *** 312s gnpLag 0.1466 0.0379 3.87 0.0013 ** 312s trend 0.1244 0.0335 3.72 0.0019 ** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 0.78 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 312s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 312s 312s compare coef with single-equation OLS 312s [1] TRUE 312s > residuals 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 -0.3863 -0.000301 -1.3389 312s 3 -1.2484 -0.076489 0.2462 312s 4 -1.6040 1.221792 1.1255 312s 5 -0.5384 -1.377872 -0.1959 312s 6 -0.0413 0.386104 -0.5284 312s 7 0.8043 1.486279 NA 312s 8 1.2830 0.784055 -0.7909 312s 9 1.0142 -0.655354 0.2819 312s 10 NA 1.060871 1.1384 312s 11 0.1429 0.395249 -0.1904 312s 12 -0.3439 0.198005 0.5813 312s 13 NA NA 0.1206 312s 14 0.3199 0.312725 0.4773 312s 15 -0.1016 -0.084685 0.3035 312s 16 -0.0702 0.066194 0.0284 312s 17 1.6064 0.963697 -0.8517 312s 18 -0.4980 0.078506 0.9908 312s 19 0.1253 -2.496401 -0.4597 312s 20 0.9805 -0.711004 -0.3819 312s 21 0.7551 -0.820172 -1.1062 312s 22 -2.1992 -0.731199 0.5501 312s > fitted 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 42.3 -0.200 26.8 312s 3 46.2 1.976 29.1 312s 4 50.8 3.978 33.0 312s 5 51.1 4.378 34.1 312s 6 52.6 4.714 35.9 312s 7 54.3 4.114 NA 312s 8 54.9 3.416 38.7 312s 9 56.3 3.655 38.9 312s 10 NA 4.039 40.2 312s 11 54.9 0.605 38.1 312s 12 51.2 -3.598 33.9 312s 13 NA NA 28.9 312s 14 46.2 -5.413 28.0 312s 15 48.8 -2.915 30.3 312s 16 51.4 -1.366 33.2 312s 17 56.1 1.136 37.7 312s 18 59.2 1.921 40.0 312s 19 57.4 0.596 38.7 312s 20 60.6 2.011 42.0 312s 21 64.2 4.120 46.1 312s 22 71.9 5.631 52.7 312s > predict 312s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 312s 1 NA NA NA NA 312s 2 42.3 0.523 39.9 44.7 312s 3 46.2 0.560 43.8 48.7 312s 4 50.8 0.379 48.5 53.1 312s 5 51.1 0.448 48.8 53.5 312s 6 52.6 0.457 50.3 55.0 312s 7 54.3 0.408 52.0 56.6 312s 8 54.9 0.375 52.6 57.2 312s 9 56.3 0.418 54.0 58.6 312s 10 NA NA NA NA 312s 11 54.9 0.701 52.3 57.4 312s 12 51.2 0.638 48.7 53.8 312s 13 NA NA NA NA 312s 14 46.2 0.673 43.6 48.7 312s 15 48.8 0.453 46.5 51.2 312s 16 51.4 0.384 49.1 53.7 312s 17 56.1 0.391 53.8 58.4 312s 18 59.2 0.361 56.9 61.5 312s 19 57.4 0.449 55.0 59.7 312s 20 60.6 0.465 58.3 63.0 312s 21 64.2 0.468 61.9 66.6 312s 22 71.9 0.728 69.3 74.5 312s Investment.pred Investment.se.fit Investment.lwr Investment.upr 312s 1 NA NA NA NA 312s 2 -0.200 0.613 -2.618 2.219 312s 3 1.976 0.494 -0.329 4.282 312s 4 3.978 0.444 1.714 6.242 312s 5 4.378 0.369 2.169 6.587 312s 6 4.714 0.349 2.519 6.909 312s 7 4.114 0.323 1.934 6.293 312s 8 3.416 0.287 1.257 5.575 312s 9 3.655 0.386 1.435 5.876 312s 10 4.039 0.441 1.777 6.301 312s 11 0.605 0.641 -1.843 3.053 312s 12 -3.598 0.606 -6.010 -1.186 312s 13 NA NA NA NA 312s 14 -5.413 0.708 -7.934 -2.892 312s 15 -2.915 0.412 -5.155 -0.676 312s 16 -1.366 0.336 -3.554 0.821 312s 17 1.136 0.342 -1.055 3.327 312s 18 1.921 0.246 -0.217 4.060 312s 19 0.596 0.341 -1.594 2.787 312s 20 2.011 0.364 -0.194 4.216 312s 21 4.120 0.337 1.932 6.308 312s 22 5.631 0.477 3.341 7.922 312s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 312s 1 NA NA NA NA 312s 2 26.8 0.364 25.1 28.6 312s 3 29.1 0.367 27.3 30.8 312s 4 33.0 0.370 31.2 34.7 312s 5 34.1 0.286 32.4 35.8 312s 6 35.9 0.285 34.3 37.6 312s 7 NA NA NA NA 312s 8 38.7 0.292 37.0 40.4 312s 9 38.9 0.277 37.3 40.6 312s 10 40.2 0.264 38.5 41.8 312s 11 38.1 0.363 36.4 39.8 312s 12 33.9 0.367 32.2 35.7 312s 13 28.9 0.435 27.1 30.7 312s 14 28.0 0.383 26.3 29.8 312s 15 30.3 0.377 28.6 32.0 312s 16 33.2 0.315 31.5 34.9 312s 17 37.7 0.308 36.0 39.3 312s 18 40.0 0.241 38.4 41.7 312s 19 38.7 0.361 36.9 40.4 312s 20 42.0 0.324 40.3 43.7 312s 21 46.1 0.339 44.4 47.8 312s 22 52.7 0.511 50.9 54.6 312s > model.frame 312s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 312s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 312s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 312s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 312s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 312s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 312s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 312s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 312s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 312s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 312s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 312s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 312s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 312s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 312s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 312s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 312s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 312s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 312s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 312s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 312s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 312s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 312s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 312s trend 312s 1 -11 312s 2 -10 312s 3 -9 312s 4 -8 312s 5 -7 312s 6 -6 312s 7 -5 312s 8 -4 312s 9 -3 312s 10 -2 312s 11 -1 312s 12 0 312s 13 1 312s 14 2 312s 15 3 312s 16 4 312s 17 5 312s 18 6 312s 19 7 312s 20 8 312s 21 9 312s 22 10 312s > model.matrix 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 1 12.4 312s Consumption_3 1 16.9 312s Consumption_4 1 18.4 312s Consumption_5 1 19.4 312s Consumption_6 1 20.1 312s Consumption_7 1 19.6 312s Consumption_8 1 19.8 312s Consumption_9 1 21.1 312s Consumption_11 1 15.6 312s Consumption_12 1 11.4 312s Consumption_14 1 11.2 312s Consumption_15 1 12.3 312s Consumption_16 1 14.0 312s Consumption_17 1 17.6 312s Consumption_18 1 17.3 312s Consumption_19 1 15.3 312s Consumption_20 1 19.0 312s Consumption_21 1 21.1 312s Consumption_22 1 23.5 312s Investment_2 0 0.0 312s Investment_3 0 0.0 312s Investment_4 0 0.0 312s Investment_5 0 0.0 312s Investment_6 0 0.0 312s Investment_7 0 0.0 312s Investment_8 0 0.0 312s Investment_9 0 0.0 312s Investment_10 0 0.0 312s Investment_11 0 0.0 312s Investment_12 0 0.0 312s Investment_14 0 0.0 312s Investment_15 0 0.0 312s Investment_16 0 0.0 312s Investment_17 0 0.0 312s Investment_18 0 0.0 312s Investment_19 0 0.0 312s Investment_20 0 0.0 312s Investment_21 0 0.0 312s Investment_22 0 0.0 312s PrivateWages_2 0 0.0 312s PrivateWages_3 0 0.0 312s PrivateWages_4 0 0.0 312s PrivateWages_5 0 0.0 312s PrivateWages_6 0 0.0 312s PrivateWages_8 0 0.0 312s PrivateWages_9 0 0.0 312s PrivateWages_10 0 0.0 312s PrivateWages_11 0 0.0 312s PrivateWages_12 0 0.0 312s PrivateWages_13 0 0.0 312s PrivateWages_14 0 0.0 312s PrivateWages_15 0 0.0 312s PrivateWages_16 0 0.0 312s PrivateWages_17 0 0.0 312s PrivateWages_18 0 0.0 312s PrivateWages_19 0 0.0 312s PrivateWages_20 0 0.0 312s PrivateWages_21 0 0.0 312s PrivateWages_22 0 0.0 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 12.7 28.2 312s Consumption_3 12.4 32.2 312s Consumption_4 16.9 37.0 312s Consumption_5 18.4 37.0 312s Consumption_6 19.4 38.6 312s Consumption_7 20.1 40.7 312s Consumption_8 19.6 41.5 312s Consumption_9 19.8 42.9 312s Consumption_11 21.7 42.1 312s Consumption_12 15.6 39.3 312s Consumption_14 7.0 34.1 312s Consumption_15 11.2 36.6 312s Consumption_16 12.3 39.3 312s Consumption_17 14.0 44.2 312s Consumption_18 17.6 47.7 312s Consumption_19 17.3 45.9 312s Consumption_20 15.3 49.4 312s Consumption_21 19.0 53.0 312s Consumption_22 21.1 61.8 312s Investment_2 0.0 0.0 312s Investment_3 0.0 0.0 312s Investment_4 0.0 0.0 312s Investment_5 0.0 0.0 312s Investment_6 0.0 0.0 312s Investment_7 0.0 0.0 312s Investment_8 0.0 0.0 312s Investment_9 0.0 0.0 312s Investment_10 0.0 0.0 312s Investment_11 0.0 0.0 312s Investment_12 0.0 0.0 312s Investment_14 0.0 0.0 312s Investment_15 0.0 0.0 312s Investment_16 0.0 0.0 312s Investment_17 0.0 0.0 312s Investment_18 0.0 0.0 312s Investment_19 0.0 0.0 312s Investment_20 0.0 0.0 312s Investment_21 0.0 0.0 312s Investment_22 0.0 0.0 312s PrivateWages_2 0.0 0.0 312s PrivateWages_3 0.0 0.0 312s PrivateWages_4 0.0 0.0 312s PrivateWages_5 0.0 0.0 312s PrivateWages_6 0.0 0.0 312s PrivateWages_8 0.0 0.0 312s PrivateWages_9 0.0 0.0 312s PrivateWages_10 0.0 0.0 312s PrivateWages_11 0.0 0.0 312s PrivateWages_12 0.0 0.0 312s PrivateWages_13 0.0 0.0 312s PrivateWages_14 0.0 0.0 312s PrivateWages_15 0.0 0.0 312s PrivateWages_16 0.0 0.0 312s PrivateWages_17 0.0 0.0 312s PrivateWages_18 0.0 0.0 312s PrivateWages_19 0.0 0.0 312s PrivateWages_20 0.0 0.0 312s PrivateWages_21 0.0 0.0 312s PrivateWages_22 0.0 0.0 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 0 0.0 312s Consumption_3 0 0.0 312s Consumption_4 0 0.0 312s Consumption_5 0 0.0 312s Consumption_6 0 0.0 312s Consumption_7 0 0.0 312s Consumption_8 0 0.0 312s Consumption_9 0 0.0 312s Consumption_11 0 0.0 312s Consumption_12 0 0.0 312s Consumption_14 0 0.0 312s Consumption_15 0 0.0 312s Consumption_16 0 0.0 312s Consumption_17 0 0.0 312s Consumption_18 0 0.0 312s Consumption_19 0 0.0 312s Consumption_20 0 0.0 312s Consumption_21 0 0.0 312s Consumption_22 0 0.0 312s Investment_2 1 12.4 312s Investment_3 1 16.9 312s Investment_4 1 18.4 312s Investment_5 1 19.4 312s Investment_6 1 20.1 312s Investment_7 1 19.6 312s Investment_8 1 19.8 312s Investment_9 1 21.1 312s Investment_10 1 21.7 312s Investment_11 1 15.6 312s Investment_12 1 11.4 312s Investment_14 1 11.2 312s Investment_15 1 12.3 312s Investment_16 1 14.0 312s Investment_17 1 17.6 312s Investment_18 1 17.3 312s Investment_19 1 15.3 312s Investment_20 1 19.0 312s Investment_21 1 21.1 312s Investment_22 1 23.5 312s PrivateWages_2 0 0.0 312s PrivateWages_3 0 0.0 312s PrivateWages_4 0 0.0 312s PrivateWages_5 0 0.0 312s PrivateWages_6 0 0.0 312s PrivateWages_8 0 0.0 312s PrivateWages_9 0 0.0 312s PrivateWages_10 0 0.0 312s PrivateWages_11 0 0.0 312s PrivateWages_12 0 0.0 312s PrivateWages_13 0 0.0 312s PrivateWages_14 0 0.0 312s PrivateWages_15 0 0.0 312s PrivateWages_16 0 0.0 312s PrivateWages_17 0 0.0 312s PrivateWages_18 0 0.0 312s PrivateWages_19 0 0.0 312s PrivateWages_20 0 0.0 312s PrivateWages_21 0 0.0 312s PrivateWages_22 0 0.0 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 0.0 0 312s Consumption_3 0.0 0 312s Consumption_4 0.0 0 312s Consumption_5 0.0 0 312s Consumption_6 0.0 0 312s Consumption_7 0.0 0 312s Consumption_8 0.0 0 312s Consumption_9 0.0 0 312s Consumption_11 0.0 0 312s Consumption_12 0.0 0 312s Consumption_14 0.0 0 312s Consumption_15 0.0 0 312s Consumption_16 0.0 0 312s Consumption_17 0.0 0 312s Consumption_18 0.0 0 312s Consumption_19 0.0 0 312s Consumption_20 0.0 0 312s Consumption_21 0.0 0 312s Consumption_22 0.0 0 312s Investment_2 12.7 183 312s Investment_3 12.4 183 312s Investment_4 16.9 184 312s Investment_5 18.4 190 312s Investment_6 19.4 193 312s Investment_7 20.1 198 312s Investment_8 19.6 203 312s Investment_9 19.8 208 312s Investment_10 21.1 211 312s Investment_11 21.7 216 312s Investment_12 15.6 217 312s Investment_14 7.0 207 312s Investment_15 11.2 202 312s Investment_16 12.3 199 312s Investment_17 14.0 198 312s Investment_18 17.6 200 312s Investment_19 17.3 202 312s Investment_20 15.3 200 312s Investment_21 19.0 201 312s Investment_22 21.1 204 312s PrivateWages_2 0.0 0 312s PrivateWages_3 0.0 0 312s PrivateWages_4 0.0 0 312s PrivateWages_5 0.0 0 312s PrivateWages_6 0.0 0 312s PrivateWages_8 0.0 0 312s PrivateWages_9 0.0 0 312s PrivateWages_10 0.0 0 312s PrivateWages_11 0.0 0 312s PrivateWages_12 0.0 0 312s PrivateWages_13 0.0 0 312s PrivateWages_14 0.0 0 312s PrivateWages_15 0.0 0 312s PrivateWages_16 0.0 0 312s PrivateWages_17 0.0 0 312s PrivateWages_18 0.0 0 312s PrivateWages_19 0.0 0 312s PrivateWages_20 0.0 0 312s PrivateWages_21 0.0 0 312s PrivateWages_22 0.0 0 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 0 0.0 0.0 312s Consumption_3 0 0.0 0.0 312s Consumption_4 0 0.0 0.0 312s Consumption_5 0 0.0 0.0 312s Consumption_6 0 0.0 0.0 312s Consumption_7 0 0.0 0.0 312s Consumption_8 0 0.0 0.0 312s Consumption_9 0 0.0 0.0 312s Consumption_11 0 0.0 0.0 312s Consumption_12 0 0.0 0.0 312s Consumption_14 0 0.0 0.0 312s Consumption_15 0 0.0 0.0 312s Consumption_16 0 0.0 0.0 312s Consumption_17 0 0.0 0.0 312s Consumption_18 0 0.0 0.0 312s Consumption_19 0 0.0 0.0 312s Consumption_20 0 0.0 0.0 312s Consumption_21 0 0.0 0.0 312s Consumption_22 0 0.0 0.0 312s Investment_2 0 0.0 0.0 312s Investment_3 0 0.0 0.0 312s Investment_4 0 0.0 0.0 312s Investment_5 0 0.0 0.0 312s Investment_6 0 0.0 0.0 312s Investment_7 0 0.0 0.0 312s Investment_8 0 0.0 0.0 312s Investment_9 0 0.0 0.0 312s Investment_10 0 0.0 0.0 312s Investment_11 0 0.0 0.0 312s Investment_12 0 0.0 0.0 312s Investment_14 0 0.0 0.0 312s Investment_15 0 0.0 0.0 312s Investment_16 0 0.0 0.0 312s Investment_17 0 0.0 0.0 312s Investment_18 0 0.0 0.0 312s Investment_19 0 0.0 0.0 312s Investment_20 0 0.0 0.0 312s Investment_21 0 0.0 0.0 312s Investment_22 0 0.0 0.0 312s PrivateWages_2 1 45.6 44.9 312s PrivateWages_3 1 50.1 45.6 312s PrivateWages_4 1 57.2 50.1 312s PrivateWages_5 1 57.1 57.2 312s PrivateWages_6 1 61.0 57.1 312s PrivateWages_8 1 64.4 64.0 312s PrivateWages_9 1 64.5 64.4 312s PrivateWages_10 1 67.0 64.5 312s PrivateWages_11 1 61.2 67.0 312s PrivateWages_12 1 53.4 61.2 312s PrivateWages_13 1 44.3 53.4 312s PrivateWages_14 1 45.1 44.3 312s PrivateWages_15 1 49.7 45.1 312s PrivateWages_16 1 54.4 49.7 312s PrivateWages_17 1 62.7 54.4 312s PrivateWages_18 1 65.0 62.7 312s PrivateWages_19 1 60.9 65.0 312s PrivateWages_20 1 69.5 60.9 312s PrivateWages_21 1 75.7 69.5 312s PrivateWages_22 1 88.4 75.7 312s PrivateWages_trend 312s Consumption_2 0 312s Consumption_3 0 312s Consumption_4 0 312s Consumption_5 0 312s Consumption_6 0 312s Consumption_7 0 312s Consumption_8 0 312s Consumption_9 0 312s Consumption_11 0 312s Consumption_12 0 312s Consumption_14 0 312s Consumption_15 0 312s Consumption_16 0 312s Consumption_17 0 312s Consumption_18 0 312s Consumption_19 0 312s Consumption_20 0 312s Consumption_21 0 312s Consumption_22 0 312s Investment_2 0 312s Investment_3 0 312s Investment_4 0 312s Investment_5 0 312s Investment_6 0 312s Investment_7 0 312s Investment_8 0 312s Investment_9 0 312s Investment_10 0 312s Investment_11 0 312s Investment_12 0 312s Investment_14 0 312s Investment_15 0 312s Investment_16 0 312s Investment_17 0 312s Investment_18 0 312s Investment_19 0 312s Investment_20 0 312s Investment_21 0 312s Investment_22 0 312s PrivateWages_2 -10 312s PrivateWages_3 -9 312s PrivateWages_4 -8 312s PrivateWages_5 -7 312s PrivateWages_6 -6 312s PrivateWages_8 -4 312s PrivateWages_9 -3 312s PrivateWages_10 -2 312s PrivateWages_11 -1 312s PrivateWages_12 0 312s PrivateWages_13 1 312s PrivateWages_14 2 312s PrivateWages_15 3 312s PrivateWages_16 4 312s PrivateWages_17 5 312s PrivateWages_18 6 312s PrivateWages_19 7 312s PrivateWages_20 8 312s PrivateWages_21 9 312s PrivateWages_22 10 312s > nobs 312s [1] 59 312s > linearHypothesis 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 48 312s 2 47 1 0.33 0.57 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 48 312s 2 47 1 0.31 0.58 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 48 312s 2 47 1 0.31 0.58 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 47 2 0.17 0.84 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 49 312s 2 47 2 0.16 0.85 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 49 312s 2 47 2 0.33 0.85 312s > logLik 312s 'log Lik.' -69.6 (df=13) 312s 'log Lik.' -74.2 (df=13) 312s compare log likelihood value with single-equation OLS 312s [1] "Mean relative difference: 0.00099" 312s Estimating function 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 -0.3863 -4.791 312s Consumption_3 -1.2484 -21.098 312s Consumption_4 -1.6040 -29.514 312s Consumption_5 -0.5384 -10.446 312s Consumption_6 -0.0413 -0.830 312s Consumption_7 0.8043 15.763 312s Consumption_8 1.2830 25.403 312s Consumption_9 1.0142 21.399 312s Consumption_11 0.1429 2.229 312s Consumption_12 -0.3439 -3.920 312s Consumption_14 0.3199 3.583 312s Consumption_15 -0.1016 -1.250 312s Consumption_16 -0.0702 -0.983 312s Consumption_17 1.6064 28.272 312s Consumption_18 -0.4980 -8.616 312s Consumption_19 0.1253 1.917 312s Consumption_20 0.9805 18.629 312s Consumption_21 0.7551 15.933 312s Consumption_22 -2.1992 -51.681 312s Investment_2 0.0000 0.000 312s Investment_3 0.0000 0.000 312s Investment_4 0.0000 0.000 312s Investment_5 0.0000 0.000 312s Investment_6 0.0000 0.000 312s Investment_7 0.0000 0.000 312s Investment_8 0.0000 0.000 312s Investment_9 0.0000 0.000 312s Investment_10 0.0000 0.000 312s Investment_11 0.0000 0.000 312s Investment_12 0.0000 0.000 312s Investment_14 0.0000 0.000 312s Investment_15 0.0000 0.000 312s Investment_16 0.0000 0.000 312s Investment_17 0.0000 0.000 312s Investment_18 0.0000 0.000 312s Investment_19 0.0000 0.000 312s Investment_20 0.0000 0.000 312s Investment_21 0.0000 0.000 312s Investment_22 0.0000 0.000 312s PrivateWages_2 0.0000 0.000 312s PrivateWages_3 0.0000 0.000 312s PrivateWages_4 0.0000 0.000 312s PrivateWages_5 0.0000 0.000 312s PrivateWages_6 0.0000 0.000 312s PrivateWages_8 0.0000 0.000 312s PrivateWages_9 0.0000 0.000 312s PrivateWages_10 0.0000 0.000 312s PrivateWages_11 0.0000 0.000 312s PrivateWages_12 0.0000 0.000 312s PrivateWages_13 0.0000 0.000 312s PrivateWages_14 0.0000 0.000 312s PrivateWages_15 0.0000 0.000 312s PrivateWages_16 0.0000 0.000 312s PrivateWages_17 0.0000 0.000 312s PrivateWages_18 0.0000 0.000 312s PrivateWages_19 0.0000 0.000 312s PrivateWages_20 0.0000 0.000 312s PrivateWages_21 0.0000 0.000 312s PrivateWages_22 0.0000 0.000 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 -4.907 -10.90 312s Consumption_3 -15.480 -40.20 312s Consumption_4 -27.108 -59.35 312s Consumption_5 -9.907 -19.92 312s Consumption_6 -0.801 -1.59 312s Consumption_7 16.166 32.73 312s Consumption_8 25.146 53.24 312s Consumption_9 20.081 43.51 312s Consumption_11 3.100 6.01 312s Consumption_12 -5.364 -13.51 312s Consumption_14 2.239 10.91 312s Consumption_15 -1.138 -3.72 312s Consumption_16 -0.864 -2.76 312s Consumption_17 22.489 71.00 312s Consumption_18 -8.765 -23.76 312s Consumption_19 2.168 5.75 312s Consumption_20 15.002 48.44 312s Consumption_21 14.348 40.02 312s Consumption_22 -46.403 -135.91 312s Investment_2 0.000 0.00 312s Investment_3 0.000 0.00 312s Investment_4 0.000 0.00 312s Investment_5 0.000 0.00 312s Investment_6 0.000 0.00 312s Investment_7 0.000 0.00 312s Investment_8 0.000 0.00 312s Investment_9 0.000 0.00 312s Investment_10 0.000 0.00 312s Investment_11 0.000 0.00 312s Investment_12 0.000 0.00 312s Investment_14 0.000 0.00 312s Investment_15 0.000 0.00 312s Investment_16 0.000 0.00 312s Investment_17 0.000 0.00 312s Investment_18 0.000 0.00 312s Investment_19 0.000 0.00 312s Investment_20 0.000 0.00 312s Investment_21 0.000 0.00 312s Investment_22 0.000 0.00 312s PrivateWages_2 0.000 0.00 312s PrivateWages_3 0.000 0.00 312s PrivateWages_4 0.000 0.00 312s PrivateWages_5 0.000 0.00 312s PrivateWages_6 0.000 0.00 312s PrivateWages_8 0.000 0.00 312s PrivateWages_9 0.000 0.00 312s PrivateWages_10 0.000 0.00 312s PrivateWages_11 0.000 0.00 312s PrivateWages_12 0.000 0.00 312s PrivateWages_13 0.000 0.00 312s PrivateWages_14 0.000 0.00 312s PrivateWages_15 0.000 0.00 312s PrivateWages_16 0.000 0.00 312s PrivateWages_17 0.000 0.00 312s PrivateWages_18 0.000 0.00 312s PrivateWages_19 0.000 0.00 312s PrivateWages_20 0.000 0.00 312s PrivateWages_21 0.000 0.00 312s PrivateWages_22 0.000 0.00 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 0.000000 0.00000 312s Consumption_3 0.000000 0.00000 312s Consumption_4 0.000000 0.00000 312s Consumption_5 0.000000 0.00000 312s Consumption_6 0.000000 0.00000 312s Consumption_7 0.000000 0.00000 312s Consumption_8 0.000000 0.00000 312s Consumption_9 0.000000 0.00000 312s Consumption_11 0.000000 0.00000 312s Consumption_12 0.000000 0.00000 312s Consumption_14 0.000000 0.00000 312s Consumption_15 0.000000 0.00000 312s Consumption_16 0.000000 0.00000 312s Consumption_17 0.000000 0.00000 312s Consumption_18 0.000000 0.00000 312s Consumption_19 0.000000 0.00000 312s Consumption_20 0.000000 0.00000 312s Consumption_21 0.000000 0.00000 312s Consumption_22 0.000000 0.00000 312s Investment_2 -0.000301 -0.00373 312s Investment_3 -0.076489 -1.29266 312s Investment_4 1.221792 22.48097 312s Investment_5 -1.377872 -26.73071 312s Investment_6 0.386104 7.76068 312s Investment_7 1.486279 29.13107 312s Investment_8 0.784055 15.52429 312s Investment_9 -0.655354 -13.82796 312s Investment_10 1.060871 23.02091 312s Investment_11 0.395249 6.16588 312s Investment_12 0.198005 2.25726 312s Investment_14 0.312725 3.50252 312s Investment_15 -0.084685 -1.04163 312s Investment_16 0.066194 0.92672 312s Investment_17 0.963697 16.96106 312s Investment_18 0.078506 1.35816 312s Investment_19 -2.496401 -38.19494 312s Investment_20 -0.711004 -13.50907 312s Investment_21 -0.820172 -17.30564 312s Investment_22 -0.731199 -17.18317 312s PrivateWages_2 0.000000 0.00000 312s PrivateWages_3 0.000000 0.00000 312s PrivateWages_4 0.000000 0.00000 312s PrivateWages_5 0.000000 0.00000 312s PrivateWages_6 0.000000 0.00000 312s PrivateWages_8 0.000000 0.00000 312s PrivateWages_9 0.000000 0.00000 312s PrivateWages_10 0.000000 0.00000 312s PrivateWages_11 0.000000 0.00000 312s PrivateWages_12 0.000000 0.00000 312s PrivateWages_13 0.000000 0.00000 312s PrivateWages_14 0.000000 0.00000 312s PrivateWages_15 0.000000 0.00000 312s PrivateWages_16 0.000000 0.00000 312s PrivateWages_17 0.000000 0.00000 312s PrivateWages_18 0.000000 0.00000 312s PrivateWages_19 0.000000 0.00000 312s PrivateWages_20 0.000000 0.00000 312s PrivateWages_21 0.000000 0.00000 312s PrivateWages_22 0.000000 0.00000 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 0.00000 0.000 312s Consumption_3 0.00000 0.000 312s Consumption_4 0.00000 0.000 312s Consumption_5 0.00000 0.000 312s Consumption_6 0.00000 0.000 312s Consumption_7 0.00000 0.000 312s Consumption_8 0.00000 0.000 312s Consumption_9 0.00000 0.000 312s Consumption_11 0.00000 0.000 312s Consumption_12 0.00000 0.000 312s Consumption_14 0.00000 0.000 312s Consumption_15 0.00000 0.000 312s Consumption_16 0.00000 0.000 312s Consumption_17 0.00000 0.000 312s Consumption_18 0.00000 0.000 312s Consumption_19 0.00000 0.000 312s Consumption_20 0.00000 0.000 312s Consumption_21 0.00000 0.000 312s Consumption_22 0.00000 0.000 312s Investment_2 -0.00382 -0.055 312s Investment_3 -0.94846 -13.967 312s Investment_4 20.64828 225.421 312s Investment_5 -25.35284 -261.382 312s Investment_6 7.49041 74.402 312s Investment_7 29.87421 293.986 312s Investment_8 15.36748 159.477 312s Investment_9 -12.97600 -136.051 312s Investment_10 22.38438 223.419 312s Investment_11 8.57690 85.255 312s Investment_12 3.08888 42.908 312s Investment_14 2.18907 64.765 312s Investment_15 -0.94848 -17.106 312s Investment_16 0.81419 13.173 312s Investment_17 13.49175 190.523 312s Investment_18 1.38171 15.686 312s Investment_19 -43.18774 -503.774 312s Investment_20 -10.87836 -142.130 312s Investment_21 -15.58327 -165.019 312s Investment_22 -15.42829 -149.530 312s PrivateWages_2 0.00000 0.000 312s PrivateWages_3 0.00000 0.000 312s PrivateWages_4 0.00000 0.000 312s PrivateWages_5 0.00000 0.000 312s PrivateWages_6 0.00000 0.000 312s PrivateWages_8 0.00000 0.000 312s PrivateWages_9 0.00000 0.000 312s PrivateWages_10 0.00000 0.000 312s PrivateWages_11 0.00000 0.000 312s PrivateWages_12 0.00000 0.000 312s PrivateWages_13 0.00000 0.000 312s PrivateWages_14 0.00000 0.000 312s PrivateWages_15 0.00000 0.000 312s PrivateWages_16 0.00000 0.000 312s PrivateWages_17 0.00000 0.000 312s PrivateWages_18 0.00000 0.000 312s PrivateWages_19 0.00000 0.000 312s PrivateWages_20 0.00000 0.000 312s PrivateWages_21 0.00000 0.000 312s PrivateWages_22 0.00000 0.000 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 0.0000 0.00 0.00 312s Consumption_3 0.0000 0.00 0.00 312s Consumption_4 0.0000 0.00 0.00 312s Consumption_5 0.0000 0.00 0.00 312s Consumption_6 0.0000 0.00 0.00 312s Consumption_7 0.0000 0.00 0.00 312s Consumption_8 0.0000 0.00 0.00 312s Consumption_9 0.0000 0.00 0.00 312s Consumption_11 0.0000 0.00 0.00 312s Consumption_12 0.0000 0.00 0.00 312s Consumption_14 0.0000 0.00 0.00 312s Consumption_15 0.0000 0.00 0.00 312s Consumption_16 0.0000 0.00 0.00 312s Consumption_17 0.0000 0.00 0.00 312s Consumption_18 0.0000 0.00 0.00 312s Consumption_19 0.0000 0.00 0.00 312s Consumption_20 0.0000 0.00 0.00 312s Consumption_21 0.0000 0.00 0.00 312s Consumption_22 0.0000 0.00 0.00 312s Investment_2 0.0000 0.00 0.00 312s Investment_3 0.0000 0.00 0.00 312s Investment_4 0.0000 0.00 0.00 312s Investment_5 0.0000 0.00 0.00 312s Investment_6 0.0000 0.00 0.00 312s Investment_7 0.0000 0.00 0.00 312s Investment_8 0.0000 0.00 0.00 312s Investment_9 0.0000 0.00 0.00 312s Investment_10 0.0000 0.00 0.00 312s Investment_11 0.0000 0.00 0.00 312s Investment_12 0.0000 0.00 0.00 312s Investment_14 0.0000 0.00 0.00 312s Investment_15 0.0000 0.00 0.00 312s Investment_16 0.0000 0.00 0.00 312s Investment_17 0.0000 0.00 0.00 312s Investment_18 0.0000 0.00 0.00 312s Investment_19 0.0000 0.00 0.00 312s Investment_20 0.0000 0.00 0.00 312s Investment_21 0.0000 0.00 0.00 312s Investment_22 0.0000 0.00 0.00 312s PrivateWages_2 -1.3389 -61.06 -60.12 312s PrivateWages_3 0.2462 12.33 11.23 312s PrivateWages_4 1.1255 64.38 56.39 312s PrivateWages_5 -0.1959 -11.18 -11.20 312s PrivateWages_6 -0.5284 -32.23 -30.17 312s PrivateWages_8 -0.7909 -50.94 -50.62 312s PrivateWages_9 0.2819 18.18 18.15 312s PrivateWages_10 1.1384 76.28 73.43 312s PrivateWages_11 -0.1904 -11.65 -12.76 312s PrivateWages_12 0.5813 31.04 35.58 312s PrivateWages_13 0.1206 5.34 6.44 312s PrivateWages_14 0.4773 21.53 21.14 312s PrivateWages_15 0.3035 15.09 13.69 312s PrivateWages_16 0.0284 1.55 1.41 312s PrivateWages_17 -0.8517 -53.40 -46.33 312s PrivateWages_18 0.9908 64.40 62.12 312s PrivateWages_19 -0.4597 -28.00 -29.88 312s PrivateWages_20 -0.3819 -26.54 -23.26 312s PrivateWages_21 -1.1062 -83.74 -76.88 312s PrivateWages_22 0.5501 48.63 41.64 312s PrivateWages_trend 312s Consumption_2 0.000 312s Consumption_3 0.000 312s Consumption_4 0.000 312s Consumption_5 0.000 312s Consumption_6 0.000 312s Consumption_7 0.000 312s Consumption_8 0.000 312s Consumption_9 0.000 312s Consumption_11 0.000 312s Consumption_12 0.000 312s Consumption_14 0.000 312s Consumption_15 0.000 312s Consumption_16 0.000 312s Consumption_17 0.000 312s Consumption_18 0.000 312s Consumption_19 0.000 312s Consumption_20 0.000 312s Consumption_21 0.000 312s Consumption_22 0.000 312s Investment_2 0.000 312s Investment_3 0.000 312s Investment_4 0.000 312s Investment_5 0.000 312s Investment_6 0.000 312s Investment_7 0.000 312s Investment_8 0.000 312s Investment_9 0.000 312s Investment_10 0.000 312s Investment_11 0.000 312s Investment_12 0.000 312s Investment_14 0.000 312s Investment_15 0.000 312s Investment_16 0.000 312s Investment_17 0.000 312s Investment_18 0.000 312s Investment_19 0.000 312s Investment_20 0.000 312s Investment_21 0.000 312s Investment_22 0.000 312s PrivateWages_2 13.389 312s PrivateWages_3 -2.216 312s PrivateWages_4 -9.004 312s PrivateWages_5 1.371 312s PrivateWages_6 3.170 312s PrivateWages_8 3.164 312s PrivateWages_9 -0.846 312s PrivateWages_10 -2.277 312s PrivateWages_11 0.190 312s PrivateWages_12 0.000 312s PrivateWages_13 0.121 312s PrivateWages_14 0.955 312s PrivateWages_15 0.911 312s PrivateWages_16 0.114 312s PrivateWages_17 -4.258 312s PrivateWages_18 5.945 312s PrivateWages_19 -3.218 312s PrivateWages_20 -3.055 312s PrivateWages_21 -9.956 312s PrivateWages_22 5.501 312s [1] TRUE 312s > Bread 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_(Intercept) 109.396 -1.6401 312s Consumption_corpProf -1.640 0.6675 312s Consumption_corpProfLag -0.598 -0.3509 312s Consumption_wages -1.641 -0.0975 312s Investment_(Intercept) 0.000 0.0000 312s Investment_corpProf 0.000 0.0000 312s Investment_corpProfLag 0.000 0.0000 312s Investment_capitalLag 0.000 0.0000 312s PrivateWages_(Intercept) 0.000 0.0000 312s PrivateWages_gnp 0.000 0.0000 312s PrivateWages_gnpLag 0.000 0.0000 312s PrivateWages_trend 0.000 0.0000 312s Consumption_corpProfLag Consumption_wages 312s Consumption_(Intercept) -0.5979 -1.6408 312s Consumption_corpProf -0.3509 -0.0975 312s Consumption_corpProfLag 0.4880 -0.0331 312s Consumption_wages -0.0331 0.0926 312s Investment_(Intercept) 0.0000 0.0000 312s Investment_corpProf 0.0000 0.0000 312s Investment_corpProfLag 0.0000 0.0000 312s Investment_capitalLag 0.0000 0.0000 312s PrivateWages_(Intercept) 0.0000 0.0000 312s PrivateWages_gnp 0.0000 0.0000 312s PrivateWages_gnpLag 0.0000 0.0000 312s PrivateWages_trend 0.0000 0.0000 312s Investment_(Intercept) Investment_corpProf 312s Consumption_(Intercept) 0.00 0.0000 312s Consumption_corpProf 0.00 0.0000 312s Consumption_corpProfLag 0.00 0.0000 312s Consumption_wages 0.00 0.0000 312s Investment_(Intercept) 1730.48 -16.5126 312s Investment_corpProf -16.51 0.6641 312s Investment_corpProfLag 13.63 -0.5096 312s Investment_capitalLag -8.34 0.0672 312s PrivateWages_(Intercept) 0.00 0.0000 312s PrivateWages_gnp 0.00 0.0000 312s PrivateWages_gnpLag 0.00 0.0000 312s PrivateWages_trend 0.00 0.0000 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_(Intercept) 0.000 0.0000 312s Consumption_corpProf 0.000 0.0000 312s Consumption_corpProfLag 0.000 0.0000 312s Consumption_wages 0.000 0.0000 312s Investment_(Intercept) 13.633 -8.3416 312s Investment_corpProf -0.510 0.0672 312s Investment_corpProfLag 0.603 -0.0740 312s Investment_capitalLag -0.074 0.0420 312s PrivateWages_(Intercept) 0.000 0.0000 312s PrivateWages_gnp 0.000 0.0000 312s PrivateWages_gnpLag 0.000 0.0000 312s PrivateWages_trend 0.000 0.0000 312s PrivateWages_(Intercept) PrivateWages_gnp 312s Consumption_(Intercept) 0.000 0.0000 312s Consumption_corpProf 0.000 0.0000 312s Consumption_corpProfLag 0.000 0.0000 312s Consumption_wages 0.000 0.0000 312s Investment_(Intercept) 0.000 0.0000 312s Investment_corpProf 0.000 0.0000 312s Investment_corpProfLag 0.000 0.0000 312s Investment_capitalLag 0.000 0.0000 312s PrivateWages_(Intercept) 166.178 -0.6258 312s PrivateWages_gnp -0.626 0.1064 312s PrivateWages_gnpLag -2.183 -0.0992 312s PrivateWages_trend 2.051 -0.0286 312s PrivateWages_gnpLag PrivateWages_trend 312s Consumption_(Intercept) 0.00000 0.00000 312s Consumption_corpProf 0.00000 0.00000 312s Consumption_corpProfLag 0.00000 0.00000 312s Consumption_wages 0.00000 0.00000 312s Investment_(Intercept) 0.00000 0.00000 312s Investment_corpProf 0.00000 0.00000 312s Investment_corpProfLag 0.00000 0.00000 312s Investment_capitalLag 0.00000 0.00000 312s PrivateWages_(Intercept) -2.18348 2.05079 312s PrivateWages_gnp -0.09921 -0.02859 312s PrivateWages_gnpLag 0.14047 -0.00635 312s PrivateWages_trend -0.00635 0.10969 312s > 312s > # 2SLS 312s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 312s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 312s > summary 312s 312s systemfit results 312s method: 2SLS 312s 312s N DF SSR detRCov OLS-R2 McElroy-R2 312s system 57 45 58.2 0.333 0.968 0.991 312s 312s N DF SSR MSE RMSE R2 Adj R2 312s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 312s Investment 19 15 26.21 1.748 1.32 0.852 0.823 312s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 312s 312s The covariance matrix of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.237 0.518 -0.408 312s Investment 0.518 1.263 0.113 312s PrivateWages -0.408 0.113 0.468 312s 312s The correlations of the residuals 312s Consumption Investment PrivateWages 312s Consumption 1.000 0.416 -0.538 312s Investment 0.416 1.000 0.139 312s PrivateWages -0.538 0.139 1.000 312s 312s 312s 2SLS estimates for 'Consumption' (equation 1) 312s Model Formula: consump ~ corpProf + corpProfLag + wages 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 17.2849 1.6018 10.79 3.6e-08 *** 312s corpProf -0.0770 0.1637 -0.47 0.645 312s corpProfLag 0.2327 0.1242 1.87 0.082 . 312s wages 0.8259 0.0459 17.98 4.5e-11 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.261 on 14 degrees of freedom 312s Number of observations: 18 Degrees of Freedom: 14 312s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 312s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 312s 312s 312s 2SLS estimates for 'Investment' (equation 2) 312s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 18.4005 7.1627 2.57 0.02138 * 312s corpProf 0.1507 0.1905 0.79 0.44118 312s corpProfLag 0.5757 0.1634 3.52 0.00307 ** 312s capitalLag -0.1452 0.0339 -4.28 0.00065 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 1.322 on 15 degrees of freedom 312s Number of observations: 19 Degrees of Freedom: 15 312s SSR: 26.213 MSE: 1.748 Root MSE: 1.322 312s Multiple R-Squared: 0.852 Adjusted R-Squared: 0.823 312s 312s 312s 2SLS estimates for 'PrivateWages' (equation 3) 312s Model Formula: privWage ~ gnp + gnpLag + trend 312s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 312s gnpLag 312s 312s Estimate Std. Error t value Pr(>|t|) 312s (Intercept) 1.3431 1.1544 1.16 0.26172 312s gnp 0.4438 0.0351 12.64 9.7e-10 *** 312s gnpLag 0.1447 0.0381 3.80 0.00158 ** 312s trend 0.1238 0.0300 4.13 0.00078 *** 312s --- 312s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 312s 312s Residual standard error: 0.78 on 16 degrees of freedom 312s Number of observations: 20 Degrees of Freedom: 16 312s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 312s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 312s 312s > residuals 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 -0.6754 -1.23599 -1.3401 312s 3 -0.4627 0.32957 0.2378 312s 4 -1.1585 1.08894 1.1117 312s 5 -0.0305 -1.37017 -0.1954 312s 6 0.4693 0.48431 -0.5355 312s 7 NA NA NA 312s 8 1.6045 1.06811 -0.7908 312s 9 1.6018 0.16695 0.2831 312s 10 NA 1.86380 1.1353 312s 11 -0.9031 -0.92183 -0.1765 312s 12 -1.5948 -1.03217 0.6007 312s 13 NA NA 0.1443 312s 14 0.2854 0.85468 0.4826 312s 15 -0.4718 -0.36943 0.3016 312s 16 -0.2268 0.00554 0.0261 312s 17 2.0079 1.69566 -0.8614 312s 18 -0.7434 -0.12659 0.9927 312s 19 -0.5410 -3.26209 -0.4446 312s 20 1.4186 0.25579 -0.3914 312s 21 1.1462 -0.00185 -1.1115 312s 22 -1.7256 0.50679 0.5312 312s > fitted 312s Consumption Investment PrivateWages 312s 1 NA NA NA 312s 2 42.6 1.036 26.8 312s 3 45.5 1.570 29.1 312s 4 50.4 4.111 33.0 312s 5 50.6 4.370 34.1 312s 6 52.1 4.616 35.9 312s 7 NA NA NA 312s 8 54.6 3.132 38.7 312s 9 55.7 2.833 38.9 312s 10 NA 3.236 40.2 312s 11 55.9 1.922 38.1 312s 12 52.5 -2.368 33.9 312s 13 NA NA 28.9 312s 14 46.2 -5.955 28.0 312s 15 49.2 -2.631 30.3 312s 16 51.5 -1.306 33.2 312s 17 55.7 0.404 37.7 312s 18 59.4 2.127 40.0 312s 19 58.0 1.362 38.6 312s 20 60.2 1.044 42.0 312s 21 63.9 3.302 46.1 312s 22 71.4 4.393 52.8 312s > predict 312s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 312s 1 NA NA NA NA 312s 2 42.6 0.571 41.4 43.8 312s 3 45.5 0.656 44.1 46.9 312s 4 50.4 0.431 49.4 51.3 312s 5 50.6 0.510 49.5 51.7 312s 6 52.1 0.521 51.0 53.2 312s 7 NA NA NA NA 312s 8 54.6 0.419 53.7 55.5 312s 9 55.7 0.496 54.6 56.8 312s 10 NA NA NA NA 312s 11 55.9 0.910 54.0 57.9 312s 12 52.5 0.869 50.6 54.4 312s 13 NA NA NA NA 312s 14 46.2 0.694 44.7 47.7 312s 15 49.2 0.487 48.1 50.2 312s 16 51.5 0.396 50.7 52.4 312s 17 55.7 0.445 54.7 56.6 312s 18 59.4 0.386 58.6 60.3 312s 19 58.0 0.548 56.9 59.2 312s 20 60.2 0.528 59.0 61.3 312s 21 63.9 0.515 62.8 65.0 312s 22 71.4 0.786 69.7 73.1 312s Investment.pred Investment.se.fit Investment.lwr Investment.upr 312s 1 NA NA NA NA 312s 2 1.036 0.892 -0.865 2.937 312s 3 1.570 0.579 0.335 2.805 312s 4 4.111 0.531 2.979 5.243 312s 5 4.370 0.440 3.432 5.308 312s 6 4.616 0.416 3.729 5.502 312s 7 NA NA NA NA 312s 8 3.132 0.344 2.398 3.866 312s 9 2.833 0.533 1.696 3.970 312s 10 3.236 0.580 2.000 4.473 312s 11 1.922 0.959 -0.122 3.966 312s 12 -2.368 0.860 -4.201 -0.534 312s 13 NA NA NA NA 312s 14 -5.955 0.865 -7.799 -4.110 312s 15 -2.631 0.479 -3.652 -1.610 312s 16 -1.306 0.382 -2.120 -0.491 312s 17 0.404 0.487 -0.635 1.443 312s 18 2.127 0.319 1.447 2.806 312s 19 1.362 0.537 0.218 2.506 312s 20 1.044 0.566 -0.162 2.250 312s 21 3.302 0.486 2.265 4.339 312s 22 4.393 0.713 2.874 5.912 312s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 312s 1 NA NA NA NA 312s 2 26.8 0.321 26.2 27.5 312s 3 29.1 0.334 28.4 29.8 312s 4 33.0 0.353 32.2 33.7 312s 5 34.1 0.253 33.6 34.6 312s 6 35.9 0.261 35.4 36.5 312s 7 NA NA NA NA 312s 8 38.7 0.257 38.1 39.2 312s 9 38.9 0.245 38.4 39.4 312s 10 40.2 0.235 39.7 40.7 312s 11 38.1 0.348 37.3 38.8 312s 12 33.9 0.374 33.1 34.7 312s 13 28.9 0.447 27.9 29.8 312s 14 28.0 0.341 27.3 28.7 312s 15 30.3 0.333 29.6 31.0 312s 16 33.2 0.278 32.6 33.8 312s 17 37.7 0.288 37.1 38.3 312s 18 40.0 0.214 39.6 40.5 312s 19 38.6 0.351 37.9 39.4 312s 20 42.0 0.301 41.4 42.6 312s 21 46.1 0.304 45.5 46.8 312s 22 52.8 0.486 51.7 53.8 312s > model.frame 312s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 312s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 312s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 312s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 312s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 312s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 312s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 312s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 312s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 312s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 312s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 312s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 312s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 312s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 312s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 312s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 312s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 312s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 312s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 312s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 312s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 312s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 312s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 312s trend 312s 1 -11 312s 2 -10 312s 3 -9 312s 4 -8 312s 5 -7 312s 6 -6 312s 7 -5 312s 8 -4 312s 9 -3 312s 10 -2 312s 11 -1 312s 12 0 312s 13 1 312s 14 2 312s 15 3 312s 16 4 312s 17 5 312s 18 6 312s 19 7 312s 20 8 312s 21 9 312s 22 10 312s > Frames of instrumental variables 312s govExp taxes govWage trend capitalLag corpProfLag gnpLag 312s 1 2.4 3.4 2.2 -11 180 NA NA 312s 2 3.9 7.7 2.7 -10 183 12.7 44.9 312s 3 3.2 3.9 2.9 -9 183 12.4 45.6 312s 4 2.8 4.7 2.9 -8 184 16.9 50.1 312s 5 3.5 3.8 3.1 -7 190 18.4 57.2 312s 6 3.3 5.5 3.2 -6 193 19.4 57.1 312s 7 3.3 7.0 3.3 -5 198 20.1 NA 312s 8 4.0 6.7 3.6 -4 203 19.6 64.0 312s 9 4.2 4.2 3.7 -3 208 19.8 64.4 312s 10 4.1 4.0 4.0 -2 211 21.1 64.5 312s 11 5.2 7.7 4.2 -1 216 21.7 67.0 312s 12 5.9 7.5 4.8 0 217 15.6 61.2 312s 13 4.9 8.3 5.3 1 213 11.4 53.4 312s 14 3.7 5.4 5.6 2 207 7.0 44.3 312s 15 4.0 6.8 6.0 3 202 11.2 45.1 312s 16 4.4 7.2 6.1 4 199 12.3 49.7 312s 17 2.9 8.3 7.4 5 198 14.0 54.4 312s 18 4.3 6.7 6.7 6 200 17.6 62.7 312s 19 5.3 7.4 7.7 7 202 17.3 65.0 312s 20 6.6 8.9 7.8 8 200 15.3 60.9 312s 21 7.4 9.6 8.0 9 201 19.0 69.5 312s 22 13.8 11.6 8.5 10 204 21.1 75.7 312s govExp taxes govWage trend capitalLag corpProfLag gnpLag 312s 1 2.4 3.4 2.2 -11 180 NA NA 312s 2 3.9 7.7 2.7 -10 183 12.7 44.9 312s 3 3.2 3.9 2.9 -9 183 12.4 45.6 312s 4 2.8 4.7 2.9 -8 184 16.9 50.1 312s 5 3.5 3.8 3.1 -7 190 18.4 57.2 312s 6 3.3 5.5 3.2 -6 193 19.4 57.1 312s 7 3.3 7.0 3.3 -5 198 20.1 NA 312s 8 4.0 6.7 3.6 -4 203 19.6 64.0 312s 9 4.2 4.2 3.7 -3 208 19.8 64.4 312s 10 4.1 4.0 4.0 -2 211 21.1 64.5 312s 11 5.2 7.7 4.2 -1 216 21.7 67.0 312s 12 5.9 7.5 4.8 0 217 15.6 61.2 312s 13 4.9 8.3 5.3 1 213 11.4 53.4 312s 14 3.7 5.4 5.6 2 207 7.0 44.3 312s 15 4.0 6.8 6.0 3 202 11.2 45.1 312s 16 4.4 7.2 6.1 4 199 12.3 49.7 312s 17 2.9 8.3 7.4 5 198 14.0 54.4 312s 18 4.3 6.7 6.7 6 200 17.6 62.7 312s 19 5.3 7.4 7.7 7 202 17.3 65.0 312s 20 6.6 8.9 7.8 8 200 15.3 60.9 312s 21 7.4 9.6 8.0 9 201 19.0 69.5 312s 22 13.8 11.6 8.5 10 204 21.1 75.7 312s govExp taxes govWage trend capitalLag corpProfLag gnpLag 312s 1 2.4 3.4 2.2 -11 180 NA NA 312s 2 3.9 7.7 2.7 -10 183 12.7 44.9 312s 3 3.2 3.9 2.9 -9 183 12.4 45.6 312s 4 2.8 4.7 2.9 -8 184 16.9 50.1 312s 5 3.5 3.8 3.1 -7 190 18.4 57.2 312s 6 3.3 5.5 3.2 -6 193 19.4 57.1 312s 7 3.3 7.0 3.3 -5 198 20.1 NA 312s 8 4.0 6.7 3.6 -4 203 19.6 64.0 312s 9 4.2 4.2 3.7 -3 208 19.8 64.4 312s 10 4.1 4.0 4.0 -2 211 21.1 64.5 312s 11 5.2 7.7 4.2 -1 216 21.7 67.0 312s 12 5.9 7.5 4.8 0 217 15.6 61.2 312s 13 4.9 8.3 5.3 1 213 11.4 53.4 312s 14 3.7 5.4 5.6 2 207 7.0 44.3 312s 15 4.0 6.8 6.0 3 202 11.2 45.1 312s 16 4.4 7.2 6.1 4 199 12.3 49.7 312s 17 2.9 8.3 7.4 5 198 14.0 54.4 312s 18 4.3 6.7 6.7 6 200 17.6 62.7 312s 19 5.3 7.4 7.7 7 202 17.3 65.0 312s 20 6.6 8.9 7.8 8 200 15.3 60.9 312s 21 7.4 9.6 8.0 9 201 19.0 69.5 312s 22 13.8 11.6 8.5 10 204 21.1 75.7 312s > model.matrix 312s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 312s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 312s [3] "Numeric: lengths (708, 684) differ" 312s > matrix of instrumental variables 312s Consumption_(Intercept) Consumption_govExp Consumption_taxes 312s Consumption_2 1 3.9 7.7 312s Consumption_3 1 3.2 3.9 312s Consumption_4 1 2.8 4.7 312s Consumption_5 1 3.5 3.8 312s Consumption_6 1 3.3 5.5 312s Consumption_8 1 4.0 6.7 312s Consumption_9 1 4.2 4.2 312s Consumption_11 1 5.2 7.7 312s Consumption_12 1 5.9 7.5 312s Consumption_14 1 3.7 5.4 312s Consumption_15 1 4.0 6.8 312s Consumption_16 1 4.4 7.2 312s Consumption_17 1 2.9 8.3 312s Consumption_18 1 4.3 6.7 312s Consumption_19 1 5.3 7.4 312s Consumption_20 1 6.6 8.9 312s Consumption_21 1 7.4 9.6 312s Consumption_22 1 13.8 11.6 312s Investment_2 0 0.0 0.0 312s Investment_3 0 0.0 0.0 312s Investment_4 0 0.0 0.0 312s Investment_5 0 0.0 0.0 312s Investment_6 0 0.0 0.0 312s Investment_8 0 0.0 0.0 312s Investment_9 0 0.0 0.0 312s Investment_10 0 0.0 0.0 312s Investment_11 0 0.0 0.0 312s Investment_12 0 0.0 0.0 312s Investment_14 0 0.0 0.0 312s Investment_15 0 0.0 0.0 312s Investment_16 0 0.0 0.0 312s Investment_17 0 0.0 0.0 312s Investment_18 0 0.0 0.0 312s Investment_19 0 0.0 0.0 312s Investment_20 0 0.0 0.0 312s Investment_21 0 0.0 0.0 312s Investment_22 0 0.0 0.0 312s PrivateWages_2 0 0.0 0.0 312s PrivateWages_3 0 0.0 0.0 312s PrivateWages_4 0 0.0 0.0 312s PrivateWages_5 0 0.0 0.0 312s PrivateWages_6 0 0.0 0.0 312s PrivateWages_8 0 0.0 0.0 312s PrivateWages_9 0 0.0 0.0 312s PrivateWages_10 0 0.0 0.0 312s PrivateWages_11 0 0.0 0.0 312s PrivateWages_12 0 0.0 0.0 312s PrivateWages_13 0 0.0 0.0 312s PrivateWages_14 0 0.0 0.0 312s PrivateWages_15 0 0.0 0.0 312s PrivateWages_16 0 0.0 0.0 312s PrivateWages_17 0 0.0 0.0 312s PrivateWages_18 0 0.0 0.0 312s PrivateWages_19 0 0.0 0.0 312s PrivateWages_20 0 0.0 0.0 312s PrivateWages_21 0 0.0 0.0 312s PrivateWages_22 0 0.0 0.0 312s Consumption_govWage Consumption_trend Consumption_capitalLag 312s Consumption_2 2.7 -10 183 312s Consumption_3 2.9 -9 183 312s Consumption_4 2.9 -8 184 312s Consumption_5 3.1 -7 190 312s Consumption_6 3.2 -6 193 312s Consumption_8 3.6 -4 203 312s Consumption_9 3.7 -3 208 312s Consumption_11 4.2 -1 216 312s Consumption_12 4.8 0 217 312s Consumption_14 5.6 2 207 312s Consumption_15 6.0 3 202 312s Consumption_16 6.1 4 199 312s Consumption_17 7.4 5 198 312s Consumption_18 6.7 6 200 312s Consumption_19 7.7 7 202 312s Consumption_20 7.8 8 200 312s Consumption_21 8.0 9 201 312s Consumption_22 8.5 10 204 312s Investment_2 0.0 0 0 312s Investment_3 0.0 0 0 312s Investment_4 0.0 0 0 312s Investment_5 0.0 0 0 312s Investment_6 0.0 0 0 312s Investment_8 0.0 0 0 312s Investment_9 0.0 0 0 312s Investment_10 0.0 0 0 312s Investment_11 0.0 0 0 312s Investment_12 0.0 0 0 312s Investment_14 0.0 0 0 312s Investment_15 0.0 0 0 312s Investment_16 0.0 0 0 312s Investment_17 0.0 0 0 312s Investment_18 0.0 0 0 312s Investment_19 0.0 0 0 312s Investment_20 0.0 0 0 312s Investment_21 0.0 0 0 312s Investment_22 0.0 0 0 312s PrivateWages_2 0.0 0 0 312s PrivateWages_3 0.0 0 0 312s PrivateWages_4 0.0 0 0 312s PrivateWages_5 0.0 0 0 312s PrivateWages_6 0.0 0 0 312s PrivateWages_8 0.0 0 0 312s PrivateWages_9 0.0 0 0 312s PrivateWages_10 0.0 0 0 312s PrivateWages_11 0.0 0 0 312s PrivateWages_12 0.0 0 0 312s PrivateWages_13 0.0 0 0 312s PrivateWages_14 0.0 0 0 312s PrivateWages_15 0.0 0 0 312s PrivateWages_16 0.0 0 0 312s PrivateWages_17 0.0 0 0 312s PrivateWages_18 0.0 0 0 312s PrivateWages_19 0.0 0 0 312s PrivateWages_20 0.0 0 0 312s PrivateWages_21 0.0 0 0 312s PrivateWages_22 0.0 0 0 312s Consumption_corpProfLag Consumption_gnpLag 312s Consumption_2 12.7 44.9 312s Consumption_3 12.4 45.6 312s Consumption_4 16.9 50.1 312s Consumption_5 18.4 57.2 312s Consumption_6 19.4 57.1 312s Consumption_8 19.6 64.0 312s Consumption_9 19.8 64.4 312s Consumption_11 21.7 67.0 312s Consumption_12 15.6 61.2 312s Consumption_14 7.0 44.3 312s Consumption_15 11.2 45.1 312s Consumption_16 12.3 49.7 312s Consumption_17 14.0 54.4 312s Consumption_18 17.6 62.7 312s Consumption_19 17.3 65.0 312s Consumption_20 15.3 60.9 312s Consumption_21 19.0 69.5 312s Consumption_22 21.1 75.7 312s Investment_2 0.0 0.0 312s Investment_3 0.0 0.0 312s Investment_4 0.0 0.0 312s Investment_5 0.0 0.0 312s Investment_6 0.0 0.0 312s Investment_8 0.0 0.0 312s Investment_9 0.0 0.0 312s Investment_10 0.0 0.0 312s Investment_11 0.0 0.0 312s Investment_12 0.0 0.0 312s Investment_14 0.0 0.0 312s Investment_15 0.0 0.0 312s Investment_16 0.0 0.0 312s Investment_17 0.0 0.0 312s Investment_18 0.0 0.0 312s Investment_19 0.0 0.0 312s Investment_20 0.0 0.0 312s Investment_21 0.0 0.0 312s Investment_22 0.0 0.0 312s PrivateWages_2 0.0 0.0 312s PrivateWages_3 0.0 0.0 312s PrivateWages_4 0.0 0.0 312s PrivateWages_5 0.0 0.0 312s PrivateWages_6 0.0 0.0 312s PrivateWages_8 0.0 0.0 312s PrivateWages_9 0.0 0.0 312s PrivateWages_10 0.0 0.0 312s PrivateWages_11 0.0 0.0 312s PrivateWages_12 0.0 0.0 312s PrivateWages_13 0.0 0.0 312s PrivateWages_14 0.0 0.0 312s PrivateWages_15 0.0 0.0 312s PrivateWages_16 0.0 0.0 312s PrivateWages_17 0.0 0.0 312s PrivateWages_18 0.0 0.0 312s PrivateWages_19 0.0 0.0 312s PrivateWages_20 0.0 0.0 312s PrivateWages_21 0.0 0.0 312s PrivateWages_22 0.0 0.0 312s Investment_(Intercept) Investment_govExp Investment_taxes 312s Consumption_2 0 0.0 0.0 312s Consumption_3 0 0.0 0.0 312s Consumption_4 0 0.0 0.0 312s Consumption_5 0 0.0 0.0 312s Consumption_6 0 0.0 0.0 312s Consumption_8 0 0.0 0.0 312s Consumption_9 0 0.0 0.0 312s Consumption_11 0 0.0 0.0 312s Consumption_12 0 0.0 0.0 312s Consumption_14 0 0.0 0.0 312s Consumption_15 0 0.0 0.0 312s Consumption_16 0 0.0 0.0 312s Consumption_17 0 0.0 0.0 312s Consumption_18 0 0.0 0.0 312s Consumption_19 0 0.0 0.0 312s Consumption_20 0 0.0 0.0 312s Consumption_21 0 0.0 0.0 312s Consumption_22 0 0.0 0.0 312s Investment_2 1 3.9 7.7 312s Investment_3 1 3.2 3.9 312s Investment_4 1 2.8 4.7 312s Investment_5 1 3.5 3.8 312s Investment_6 1 3.3 5.5 312s Investment_8 1 4.0 6.7 312s Investment_9 1 4.2 4.2 312s Investment_10 1 4.1 4.0 312s Investment_11 1 5.2 7.7 312s Investment_12 1 5.9 7.5 312s Investment_14 1 3.7 5.4 312s Investment_15 1 4.0 6.8 312s Investment_16 1 4.4 7.2 312s Investment_17 1 2.9 8.3 312s Investment_18 1 4.3 6.7 312s Investment_19 1 5.3 7.4 312s Investment_20 1 6.6 8.9 312s Investment_21 1 7.4 9.6 312s Investment_22 1 13.8 11.6 312s PrivateWages_2 0 0.0 0.0 312s PrivateWages_3 0 0.0 0.0 312s PrivateWages_4 0 0.0 0.0 312s PrivateWages_5 0 0.0 0.0 312s PrivateWages_6 0 0.0 0.0 312s PrivateWages_8 0 0.0 0.0 312s PrivateWages_9 0 0.0 0.0 312s PrivateWages_10 0 0.0 0.0 312s PrivateWages_11 0 0.0 0.0 312s PrivateWages_12 0 0.0 0.0 312s PrivateWages_13 0 0.0 0.0 312s PrivateWages_14 0 0.0 0.0 312s PrivateWages_15 0 0.0 0.0 312s PrivateWages_16 0 0.0 0.0 312s PrivateWages_17 0 0.0 0.0 312s PrivateWages_18 0 0.0 0.0 312s PrivateWages_19 0 0.0 0.0 312s PrivateWages_20 0 0.0 0.0 312s PrivateWages_21 0 0.0 0.0 312s PrivateWages_22 0 0.0 0.0 312s Investment_govWage Investment_trend Investment_capitalLag 312s Consumption_2 0.0 0 0 312s Consumption_3 0.0 0 0 312s Consumption_4 0.0 0 0 312s Consumption_5 0.0 0 0 312s Consumption_6 0.0 0 0 312s Consumption_8 0.0 0 0 312s Consumption_9 0.0 0 0 312s Consumption_11 0.0 0 0 312s Consumption_12 0.0 0 0 312s Consumption_14 0.0 0 0 312s Consumption_15 0.0 0 0 312s Consumption_16 0.0 0 0 312s Consumption_17 0.0 0 0 312s Consumption_18 0.0 0 0 312s Consumption_19 0.0 0 0 312s Consumption_20 0.0 0 0 312s Consumption_21 0.0 0 0 312s Consumption_22 0.0 0 0 312s Investment_2 2.7 -10 183 312s Investment_3 2.9 -9 183 312s Investment_4 2.9 -8 184 312s Investment_5 3.1 -7 190 312s Investment_6 3.2 -6 193 312s Investment_8 3.6 -4 203 312s Investment_9 3.7 -3 208 312s Investment_10 4.0 -2 211 312s Investment_11 4.2 -1 216 312s Investment_12 4.8 0 217 312s Investment_14 5.6 2 207 312s Investment_15 6.0 3 202 312s Investment_16 6.1 4 199 312s Investment_17 7.4 5 198 312s Investment_18 6.7 6 200 312s Investment_19 7.7 7 202 312s Investment_20 7.8 8 200 312s Investment_21 8.0 9 201 312s Investment_22 8.5 10 204 312s PrivateWages_2 0.0 0 0 312s PrivateWages_3 0.0 0 0 312s PrivateWages_4 0.0 0 0 312s PrivateWages_5 0.0 0 0 312s PrivateWages_6 0.0 0 0 312s PrivateWages_8 0.0 0 0 312s PrivateWages_9 0.0 0 0 312s PrivateWages_10 0.0 0 0 312s PrivateWages_11 0.0 0 0 312s PrivateWages_12 0.0 0 0 312s PrivateWages_13 0.0 0 0 312s PrivateWages_14 0.0 0 0 312s PrivateWages_15 0.0 0 0 312s PrivateWages_16 0.0 0 0 312s PrivateWages_17 0.0 0 0 312s PrivateWages_18 0.0 0 0 312s PrivateWages_19 0.0 0 0 312s PrivateWages_20 0.0 0 0 312s PrivateWages_21 0.0 0 0 312s PrivateWages_22 0.0 0 0 312s Investment_corpProfLag Investment_gnpLag 312s Consumption_2 0.0 0.0 312s Consumption_3 0.0 0.0 312s Consumption_4 0.0 0.0 312s Consumption_5 0.0 0.0 312s Consumption_6 0.0 0.0 312s Consumption_8 0.0 0.0 312s Consumption_9 0.0 0.0 312s Consumption_11 0.0 0.0 312s Consumption_12 0.0 0.0 312s Consumption_14 0.0 0.0 312s Consumption_15 0.0 0.0 312s Consumption_16 0.0 0.0 312s Consumption_17 0.0 0.0 312s Consumption_18 0.0 0.0 312s Consumption_19 0.0 0.0 312s Consumption_20 0.0 0.0 312s Consumption_21 0.0 0.0 312s Consumption_22 0.0 0.0 312s Investment_2 12.7 44.9 312s Investment_3 12.4 45.6 312s Investment_4 16.9 50.1 312s Investment_5 18.4 57.2 312s Investment_6 19.4 57.1 312s Investment_8 19.6 64.0 312s Investment_9 19.8 64.4 312s Investment_10 21.1 64.5 312s Investment_11 21.7 67.0 312s Investment_12 15.6 61.2 312s Investment_14 7.0 44.3 312s Investment_15 11.2 45.1 312s Investment_16 12.3 49.7 312s Investment_17 14.0 54.4 312s Investment_18 17.6 62.7 312s Investment_19 17.3 65.0 312s Investment_20 15.3 60.9 312s Investment_21 19.0 69.5 312s Investment_22 21.1 75.7 312s PrivateWages_2 0.0 0.0 312s PrivateWages_3 0.0 0.0 312s PrivateWages_4 0.0 0.0 312s PrivateWages_5 0.0 0.0 312s PrivateWages_6 0.0 0.0 312s PrivateWages_8 0.0 0.0 312s PrivateWages_9 0.0 0.0 312s PrivateWages_10 0.0 0.0 312s PrivateWages_11 0.0 0.0 312s PrivateWages_12 0.0 0.0 312s PrivateWages_13 0.0 0.0 312s PrivateWages_14 0.0 0.0 312s PrivateWages_15 0.0 0.0 312s PrivateWages_16 0.0 0.0 312s PrivateWages_17 0.0 0.0 312s PrivateWages_18 0.0 0.0 312s PrivateWages_19 0.0 0.0 312s PrivateWages_20 0.0 0.0 312s PrivateWages_21 0.0 0.0 312s PrivateWages_22 0.0 0.0 312s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 312s Consumption_2 0 0.0 0.0 312s Consumption_3 0 0.0 0.0 312s Consumption_4 0 0.0 0.0 312s Consumption_5 0 0.0 0.0 312s Consumption_6 0 0.0 0.0 312s Consumption_8 0 0.0 0.0 312s Consumption_9 0 0.0 0.0 312s Consumption_11 0 0.0 0.0 312s Consumption_12 0 0.0 0.0 312s Consumption_14 0 0.0 0.0 312s Consumption_15 0 0.0 0.0 312s Consumption_16 0 0.0 0.0 312s Consumption_17 0 0.0 0.0 312s Consumption_18 0 0.0 0.0 312s Consumption_19 0 0.0 0.0 312s Consumption_20 0 0.0 0.0 312s Consumption_21 0 0.0 0.0 312s Consumption_22 0 0.0 0.0 312s Investment_2 0 0.0 0.0 312s Investment_3 0 0.0 0.0 312s Investment_4 0 0.0 0.0 312s Investment_5 0 0.0 0.0 312s Investment_6 0 0.0 0.0 312s Investment_8 0 0.0 0.0 312s Investment_9 0 0.0 0.0 312s Investment_10 0 0.0 0.0 312s Investment_11 0 0.0 0.0 312s Investment_12 0 0.0 0.0 312s Investment_14 0 0.0 0.0 312s Investment_15 0 0.0 0.0 312s Investment_16 0 0.0 0.0 312s Investment_17 0 0.0 0.0 312s Investment_18 0 0.0 0.0 312s Investment_19 0 0.0 0.0 312s Investment_20 0 0.0 0.0 312s Investment_21 0 0.0 0.0 312s Investment_22 0 0.0 0.0 312s PrivateWages_2 1 3.9 7.7 312s PrivateWages_3 1 3.2 3.9 312s PrivateWages_4 1 2.8 4.7 312s PrivateWages_5 1 3.5 3.8 312s PrivateWages_6 1 3.3 5.5 312s PrivateWages_8 1 4.0 6.7 312s PrivateWages_9 1 4.2 4.2 312s PrivateWages_10 1 4.1 4.0 312s PrivateWages_11 1 5.2 7.7 312s PrivateWages_12 1 5.9 7.5 312s PrivateWages_13 1 4.9 8.3 312s PrivateWages_14 1 3.7 5.4 312s PrivateWages_15 1 4.0 6.8 312s PrivateWages_16 1 4.4 7.2 312s PrivateWages_17 1 2.9 8.3 312s PrivateWages_18 1 4.3 6.7 312s PrivateWages_19 1 5.3 7.4 312s PrivateWages_20 1 6.6 8.9 312s PrivateWages_21 1 7.4 9.6 312s PrivateWages_22 1 13.8 11.6 312s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 312s Consumption_2 0.0 0 0 312s Consumption_3 0.0 0 0 312s Consumption_4 0.0 0 0 312s Consumption_5 0.0 0 0 312s Consumption_6 0.0 0 0 312s Consumption_8 0.0 0 0 312s Consumption_9 0.0 0 0 312s Consumption_11 0.0 0 0 312s Consumption_12 0.0 0 0 312s Consumption_14 0.0 0 0 312s Consumption_15 0.0 0 0 312s Consumption_16 0.0 0 0 312s Consumption_17 0.0 0 0 312s Consumption_18 0.0 0 0 312s Consumption_19 0.0 0 0 312s Consumption_20 0.0 0 0 312s Consumption_21 0.0 0 0 312s Consumption_22 0.0 0 0 312s Investment_2 0.0 0 0 312s Investment_3 0.0 0 0 312s Investment_4 0.0 0 0 312s Investment_5 0.0 0 0 312s Investment_6 0.0 0 0 312s Investment_8 0.0 0 0 312s Investment_9 0.0 0 0 312s Investment_10 0.0 0 0 312s Investment_11 0.0 0 0 312s Investment_12 0.0 0 0 312s Investment_14 0.0 0 0 312s Investment_15 0.0 0 0 312s Investment_16 0.0 0 0 312s Investment_17 0.0 0 0 312s Investment_18 0.0 0 0 312s Investment_19 0.0 0 0 312s Investment_20 0.0 0 0 312s Investment_21 0.0 0 0 312s Investment_22 0.0 0 0 312s PrivateWages_2 2.7 -10 183 312s PrivateWages_3 2.9 -9 183 312s PrivateWages_4 2.9 -8 184 312s PrivateWages_5 3.1 -7 190 312s PrivateWages_6 3.2 -6 193 312s PrivateWages_8 3.6 -4 203 312s PrivateWages_9 3.7 -3 208 312s PrivateWages_10 4.0 -2 211 312s PrivateWages_11 4.2 -1 216 312s PrivateWages_12 4.8 0 217 312s PrivateWages_13 5.3 1 213 312s PrivateWages_14 5.6 2 207 312s PrivateWages_15 6.0 3 202 312s PrivateWages_16 6.1 4 199 312s PrivateWages_17 7.4 5 198 312s PrivateWages_18 6.7 6 200 312s PrivateWages_19 7.7 7 202 312s PrivateWages_20 7.8 8 200 312s PrivateWages_21 8.0 9 201 312s PrivateWages_22 8.5 10 204 312s PrivateWages_corpProfLag PrivateWages_gnpLag 312s Consumption_2 0.0 0.0 312s Consumption_3 0.0 0.0 312s Consumption_4 0.0 0.0 312s Consumption_5 0.0 0.0 312s Consumption_6 0.0 0.0 312s Consumption_8 0.0 0.0 312s Consumption_9 0.0 0.0 312s Consumption_11 0.0 0.0 312s Consumption_12 0.0 0.0 312s Consumption_14 0.0 0.0 312s Consumption_15 0.0 0.0 312s Consumption_16 0.0 0.0 312s Consumption_17 0.0 0.0 312s Consumption_18 0.0 0.0 312s Consumption_19 0.0 0.0 312s Consumption_20 0.0 0.0 312s Consumption_21 0.0 0.0 312s Consumption_22 0.0 0.0 312s Investment_2 0.0 0.0 312s Investment_3 0.0 0.0 312s Investment_4 0.0 0.0 312s Investment_5 0.0 0.0 312s Investment_6 0.0 0.0 312s Investment_8 0.0 0.0 312s Investment_9 0.0 0.0 312s Investment_10 0.0 0.0 312s Investment_11 0.0 0.0 312s Investment_12 0.0 0.0 312s Investment_14 0.0 0.0 312s Investment_15 0.0 0.0 312s Investment_16 0.0 0.0 312s Investment_17 0.0 0.0 312s Investment_18 0.0 0.0 312s Investment_19 0.0 0.0 312s Investment_20 0.0 0.0 312s Investment_21 0.0 0.0 312s Investment_22 0.0 0.0 312s PrivateWages_2 12.7 44.9 312s PrivateWages_3 12.4 45.6 312s PrivateWages_4 16.9 50.1 312s PrivateWages_5 18.4 57.2 312s PrivateWages_6 19.4 57.1 312s PrivateWages_8 19.6 64.0 312s PrivateWages_9 19.8 64.4 312s PrivateWages_10 21.1 64.5 312s PrivateWages_11 21.7 67.0 312s PrivateWages_12 15.6 61.2 312s PrivateWages_13 11.4 53.4 312s PrivateWages_14 7.0 44.3 312s PrivateWages_15 11.2 45.1 312s PrivateWages_16 12.3 49.7 312s PrivateWages_17 14.0 54.4 312s PrivateWages_18 17.6 62.7 312s PrivateWages_19 17.3 65.0 312s PrivateWages_20 15.3 60.9 312s PrivateWages_21 19.0 69.5 312s PrivateWages_22 21.1 75.7 312s > matrix of fitted regressors 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 1 14.0 312s Consumption_3 1 16.7 312s Consumption_4 1 18.5 312s Consumption_5 1 20.3 312s Consumption_6 1 19.0 312s Consumption_8 1 17.6 312s Consumption_9 1 18.9 312s Consumption_11 1 16.7 312s Consumption_12 1 13.4 312s Consumption_14 1 10.0 312s Consumption_15 1 12.5 312s Consumption_16 1 14.5 312s Consumption_17 1 14.9 312s Consumption_18 1 19.4 312s Consumption_19 1 19.1 312s Consumption_20 1 17.7 312s Consumption_21 1 20.4 312s Consumption_22 1 22.7 312s Investment_2 0 0.0 312s Investment_3 0 0.0 312s Investment_4 0 0.0 312s Investment_5 0 0.0 312s Investment_6 0 0.0 312s Investment_8 0 0.0 312s Investment_9 0 0.0 312s Investment_10 0 0.0 312s Investment_11 0 0.0 312s Investment_12 0 0.0 312s Investment_14 0 0.0 312s Investment_15 0 0.0 312s Investment_16 0 0.0 312s Investment_17 0 0.0 312s Investment_18 0 0.0 312s Investment_19 0 0.0 312s Investment_20 0 0.0 312s Investment_21 0 0.0 312s Investment_22 0 0.0 312s PrivateWages_2 0 0.0 312s PrivateWages_3 0 0.0 312s PrivateWages_4 0 0.0 312s PrivateWages_5 0 0.0 312s PrivateWages_6 0 0.0 312s PrivateWages_8 0 0.0 312s PrivateWages_9 0 0.0 312s PrivateWages_10 0 0.0 312s PrivateWages_11 0 0.0 312s PrivateWages_12 0 0.0 312s PrivateWages_13 0 0.0 312s PrivateWages_14 0 0.0 312s PrivateWages_15 0 0.0 312s PrivateWages_16 0 0.0 312s PrivateWages_17 0 0.0 312s PrivateWages_18 0 0.0 312s PrivateWages_19 0 0.0 312s PrivateWages_20 0 0.0 312s PrivateWages_21 0 0.0 312s PrivateWages_22 0 0.0 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 12.7 29.8 312s Consumption_3 12.4 31.8 312s Consumption_4 16.9 35.3 312s Consumption_5 18.4 38.6 312s Consumption_6 19.4 38.5 312s Consumption_8 19.6 40.0 312s Consumption_9 19.8 41.8 312s Consumption_11 21.7 43.1 312s Consumption_12 15.6 39.7 312s Consumption_14 7.0 33.3 312s Consumption_15 11.2 37.3 312s Consumption_16 12.3 40.1 312s Consumption_17 14.0 41.8 312s Consumption_18 17.6 47.6 312s Consumption_19 17.3 49.2 312s Consumption_20 15.3 48.6 312s Consumption_21 19.0 53.4 312s Consumption_22 21.1 60.8 312s Investment_2 0.0 0.0 312s Investment_3 0.0 0.0 312s Investment_4 0.0 0.0 312s Investment_5 0.0 0.0 312s Investment_6 0.0 0.0 312s Investment_8 0.0 0.0 312s Investment_9 0.0 0.0 312s Investment_10 0.0 0.0 312s Investment_11 0.0 0.0 312s Investment_12 0.0 0.0 312s Investment_14 0.0 0.0 312s Investment_15 0.0 0.0 312s Investment_16 0.0 0.0 312s Investment_17 0.0 0.0 312s Investment_18 0.0 0.0 312s Investment_19 0.0 0.0 312s Investment_20 0.0 0.0 312s Investment_21 0.0 0.0 312s Investment_22 0.0 0.0 312s PrivateWages_2 0.0 0.0 312s PrivateWages_3 0.0 0.0 312s PrivateWages_4 0.0 0.0 312s PrivateWages_5 0.0 0.0 312s PrivateWages_6 0.0 0.0 312s PrivateWages_8 0.0 0.0 312s PrivateWages_9 0.0 0.0 312s PrivateWages_10 0.0 0.0 312s PrivateWages_11 0.0 0.0 312s PrivateWages_12 0.0 0.0 312s PrivateWages_13 0.0 0.0 312s PrivateWages_14 0.0 0.0 312s PrivateWages_15 0.0 0.0 312s PrivateWages_16 0.0 0.0 312s PrivateWages_17 0.0 0.0 312s PrivateWages_18 0.0 0.0 312s PrivateWages_19 0.0 0.0 312s PrivateWages_20 0.0 0.0 312s PrivateWages_21 0.0 0.0 312s PrivateWages_22 0.0 0.0 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 0 0.00 312s Consumption_3 0 0.00 312s Consumption_4 0 0.00 312s Consumption_5 0 0.00 312s Consumption_6 0 0.00 312s Consumption_8 0 0.00 312s Consumption_9 0 0.00 312s Consumption_11 0 0.00 312s Consumption_12 0 0.00 312s Consumption_14 0 0.00 312s Consumption_15 0 0.00 312s Consumption_16 0 0.00 312s Consumption_17 0 0.00 312s Consumption_18 0 0.00 312s Consumption_19 0 0.00 312s Consumption_20 0 0.00 312s Consumption_21 0 0.00 312s Consumption_22 0 0.00 312s Investment_2 1 13.41 312s Investment_3 1 16.69 312s Investment_4 1 18.79 312s Investment_5 1 20.65 312s Investment_6 1 19.26 312s Investment_8 1 17.53 312s Investment_9 1 19.53 312s Investment_10 1 20.27 312s Investment_11 1 17.19 312s Investment_12 1 13.52 312s Investment_14 1 9.99 312s Investment_15 1 12.86 312s Investment_16 1 14.33 312s Investment_17 1 14.97 312s Investment_18 1 19.37 312s Investment_19 1 19.36 312s Investment_20 1 17.47 312s Investment_21 1 20.12 312s Investment_22 1 22.78 312s PrivateWages_2 0 0.00 312s PrivateWages_3 0 0.00 312s PrivateWages_4 0 0.00 312s PrivateWages_5 0 0.00 312s PrivateWages_6 0 0.00 312s PrivateWages_8 0 0.00 312s PrivateWages_9 0 0.00 312s PrivateWages_10 0 0.00 312s PrivateWages_11 0 0.00 312s PrivateWages_12 0 0.00 312s PrivateWages_13 0 0.00 312s PrivateWages_14 0 0.00 312s PrivateWages_15 0 0.00 312s PrivateWages_16 0 0.00 312s PrivateWages_17 0 0.00 312s PrivateWages_18 0 0.00 312s PrivateWages_19 0 0.00 312s PrivateWages_20 0 0.00 312s PrivateWages_21 0 0.00 312s PrivateWages_22 0 0.00 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 0.0 0 312s Consumption_3 0.0 0 312s Consumption_4 0.0 0 312s Consumption_5 0.0 0 312s Consumption_6 0.0 0 312s Consumption_8 0.0 0 312s Consumption_9 0.0 0 312s Consumption_11 0.0 0 312s Consumption_12 0.0 0 312s Consumption_14 0.0 0 312s Consumption_15 0.0 0 312s Consumption_16 0.0 0 312s Consumption_17 0.0 0 312s Consumption_18 0.0 0 312s Consumption_19 0.0 0 312s Consumption_20 0.0 0 312s Consumption_21 0.0 0 312s Consumption_22 0.0 0 312s Investment_2 12.7 183 312s Investment_3 12.4 183 312s Investment_4 16.9 184 312s Investment_5 18.4 190 312s Investment_6 19.4 193 312s Investment_8 19.6 203 312s Investment_9 19.8 208 312s Investment_10 21.1 211 312s Investment_11 21.7 216 312s Investment_12 15.6 217 312s Investment_14 7.0 207 312s Investment_15 11.2 202 312s Investment_16 12.3 199 312s Investment_17 14.0 198 312s Investment_18 17.6 200 312s Investment_19 17.3 202 312s Investment_20 15.3 200 312s Investment_21 19.0 201 312s Investment_22 21.1 204 312s PrivateWages_2 0.0 0 312s PrivateWages_3 0.0 0 312s PrivateWages_4 0.0 0 312s PrivateWages_5 0.0 0 312s PrivateWages_6 0.0 0 312s PrivateWages_8 0.0 0 312s PrivateWages_9 0.0 0 312s PrivateWages_10 0.0 0 312s PrivateWages_11 0.0 0 312s PrivateWages_12 0.0 0 312s PrivateWages_13 0.0 0 312s PrivateWages_14 0.0 0 312s PrivateWages_15 0.0 0 312s PrivateWages_16 0.0 0 312s PrivateWages_17 0.0 0 312s PrivateWages_18 0.0 0 312s PrivateWages_19 0.0 0 312s PrivateWages_20 0.0 0 312s PrivateWages_21 0.0 0 312s PrivateWages_22 0.0 0 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 0 0.0 0.0 312s Consumption_3 0 0.0 0.0 312s Consumption_4 0 0.0 0.0 312s Consumption_5 0 0.0 0.0 312s Consumption_6 0 0.0 0.0 312s Consumption_8 0 0.0 0.0 312s Consumption_9 0 0.0 0.0 312s Consumption_11 0 0.0 0.0 312s Consumption_12 0 0.0 0.0 312s Consumption_14 0 0.0 0.0 312s Consumption_15 0 0.0 0.0 312s Consumption_16 0 0.0 0.0 312s Consumption_17 0 0.0 0.0 312s Consumption_18 0 0.0 0.0 312s Consumption_19 0 0.0 0.0 312s Consumption_20 0 0.0 0.0 312s Consumption_21 0 0.0 0.0 312s Consumption_22 0 0.0 0.0 312s Investment_2 0 0.0 0.0 312s Investment_3 0 0.0 0.0 312s Investment_4 0 0.0 0.0 312s Investment_5 0 0.0 0.0 312s Investment_6 0 0.0 0.0 312s Investment_8 0 0.0 0.0 312s Investment_9 0 0.0 0.0 312s Investment_10 0 0.0 0.0 312s Investment_11 0 0.0 0.0 312s Investment_12 0 0.0 0.0 312s Investment_14 0 0.0 0.0 312s Investment_15 0 0.0 0.0 312s Investment_16 0 0.0 0.0 312s Investment_17 0 0.0 0.0 312s Investment_18 0 0.0 0.0 312s Investment_19 0 0.0 0.0 312s Investment_20 0 0.0 0.0 312s Investment_21 0 0.0 0.0 312s Investment_22 0 0.0 0.0 312s PrivateWages_2 1 47.1 44.9 312s PrivateWages_3 1 49.6 45.6 312s PrivateWages_4 1 56.5 50.1 312s PrivateWages_5 1 60.7 57.2 312s PrivateWages_6 1 60.6 57.1 312s PrivateWages_8 1 60.0 64.0 312s PrivateWages_9 1 62.3 64.4 312s PrivateWages_10 1 64.6 64.5 312s PrivateWages_11 1 63.7 67.0 312s PrivateWages_12 1 54.8 61.2 312s PrivateWages_13 1 47.0 53.4 312s PrivateWages_14 1 42.1 44.3 312s PrivateWages_15 1 51.2 45.1 312s PrivateWages_16 1 55.3 49.7 312s PrivateWages_17 1 57.4 54.4 312s PrivateWages_18 1 67.2 62.7 312s PrivateWages_19 1 68.5 65.0 312s PrivateWages_20 1 66.8 60.9 312s PrivateWages_21 1 74.9 69.5 312s PrivateWages_22 1 86.9 75.7 312s PrivateWages_trend 312s Consumption_2 0 312s Consumption_3 0 312s Consumption_4 0 312s Consumption_5 0 312s Consumption_6 0 312s Consumption_8 0 312s Consumption_9 0 312s Consumption_11 0 312s Consumption_12 0 312s Consumption_14 0 312s Consumption_15 0 312s Consumption_16 0 312s Consumption_17 0 312s Consumption_18 0 312s Consumption_19 0 312s Consumption_20 0 312s Consumption_21 0 312s Consumption_22 0 312s Investment_2 0 312s Investment_3 0 312s Investment_4 0 312s Investment_5 0 312s Investment_6 0 312s Investment_8 0 312s Investment_9 0 312s Investment_10 0 312s Investment_11 0 312s Investment_12 0 312s Investment_14 0 312s Investment_15 0 312s Investment_16 0 312s Investment_17 0 312s Investment_18 0 312s Investment_19 0 312s Investment_20 0 312s Investment_21 0 312s Investment_22 0 312s PrivateWages_2 -10 312s PrivateWages_3 -9 312s PrivateWages_4 -8 312s PrivateWages_5 -7 312s PrivateWages_6 -6 312s PrivateWages_8 -4 312s PrivateWages_9 -3 312s PrivateWages_10 -2 312s PrivateWages_11 -1 312s PrivateWages_12 0 312s PrivateWages_13 1 312s PrivateWages_14 2 312s PrivateWages_15 3 312s PrivateWages_16 4 312s PrivateWages_17 5 312s PrivateWages_18 6 312s PrivateWages_19 7 312s PrivateWages_20 8 312s PrivateWages_21 9 312s PrivateWages_22 10 312s > nobs 312s [1] 57 312s > linearHypothesis 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 46 312s 2 45 1 1.37 0.25 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 46 312s 2 45 1 1.77 0.19 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 46 312s 2 45 1 1.77 0.18 312s Linear hypothesis test (Theil's F test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 47 312s 2 45 2 0.69 0.51 312s Linear hypothesis test (F statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df F Pr(>F) 312s 1 47 312s 2 45 2 0.89 0.42 312s Linear hypothesis test (Chi^2 statistic of a Wald test) 312s 312s Hypothesis: 312s Consumption_corpProf + Investment_capitalLag = 0 312s Consumption_corpProfLag - PrivateWages_trend = 0 312s 312s Model 1: restricted model 312s Model 2: kleinModel 312s 312s Res.Df Df Chisq Pr(>Chisq) 312s 1 47 312s 2 45 2 1.78 0.41 312s > logLik 312s 'log Lik.' -70.6 (df=13) 312s 'log Lik.' -78.7 (df=13) 312s Estimating function 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_2 -1.891 -26.49 312s Consumption_3 -0.190 -3.16 312s Consumption_4 0.294 5.45 312s Consumption_5 -1.285 -26.05 312s Consumption_6 0.431 8.19 312s Consumption_8 2.670 47.11 312s Consumption_9 2.363 44.77 312s Consumption_11 -1.642 -27.49 312s Consumption_12 -1.735 -23.21 312s Consumption_14 0.834 8.35 312s Consumption_15 -1.061 -13.27 312s Consumption_16 -0.885 -12.82 312s Consumption_17 3.801 56.68 312s Consumption_18 -0.502 -9.76 312s Consumption_19 -3.000 -57.33 312s Consumption_20 2.012 35.52 312s Consumption_21 0.746 15.21 312s Consumption_22 -0.957 -21.70 312s Investment_2 0.000 0.00 312s Investment_3 0.000 0.00 312s Investment_4 0.000 0.00 312s Investment_5 0.000 0.00 312s Investment_6 0.000 0.00 312s Investment_8 0.000 0.00 312s Investment_9 0.000 0.00 312s Investment_10 0.000 0.00 312s Investment_11 0.000 0.00 312s Investment_12 0.000 0.00 312s Investment_14 0.000 0.00 312s Investment_15 0.000 0.00 312s Investment_16 0.000 0.00 312s Investment_17 0.000 0.00 312s Investment_18 0.000 0.00 312s Investment_19 0.000 0.00 312s Investment_20 0.000 0.00 312s Investment_21 0.000 0.00 312s Investment_22 0.000 0.00 312s PrivateWages_2 0.000 0.00 312s PrivateWages_3 0.000 0.00 312s PrivateWages_4 0.000 0.00 312s PrivateWages_5 0.000 0.00 312s PrivateWages_6 0.000 0.00 312s PrivateWages_8 0.000 0.00 312s PrivateWages_9 0.000 0.00 312s PrivateWages_10 0.000 0.00 312s PrivateWages_11 0.000 0.00 312s PrivateWages_12 0.000 0.00 312s PrivateWages_13 0.000 0.00 312s PrivateWages_14 0.000 0.00 312s PrivateWages_15 0.000 0.00 312s PrivateWages_16 0.000 0.00 312s PrivateWages_17 0.000 0.00 312s PrivateWages_18 0.000 0.00 312s PrivateWages_19 0.000 0.00 312s PrivateWages_20 0.000 0.00 312s PrivateWages_21 0.000 0.00 312s PrivateWages_22 0.000 0.00 312s Consumption_corpProfLag Consumption_wages 312s Consumption_2 -24.01 -56.38 312s Consumption_3 -2.35 -6.04 312s Consumption_4 4.96 10.35 312s Consumption_5 -23.65 -49.61 312s Consumption_6 8.35 16.60 312s Consumption_8 52.33 106.81 312s Consumption_9 46.80 98.74 312s Consumption_11 -35.64 -70.78 312s Consumption_12 -27.07 -68.81 312s Consumption_14 5.83 27.78 312s Consumption_15 -11.88 -39.61 312s Consumption_16 -10.89 -35.54 312s Consumption_17 53.21 158.79 312s Consumption_18 -8.84 -23.92 312s Consumption_19 -51.90 -147.70 312s Consumption_20 30.78 97.67 312s Consumption_21 14.17 39.83 312s Consumption_22 -20.20 -58.19 312s Investment_2 0.00 0.00 312s Investment_3 0.00 0.00 312s Investment_4 0.00 0.00 312s Investment_5 0.00 0.00 312s Investment_6 0.00 0.00 312s Investment_8 0.00 0.00 312s Investment_9 0.00 0.00 312s Investment_10 0.00 0.00 312s Investment_11 0.00 0.00 312s Investment_12 0.00 0.00 312s Investment_14 0.00 0.00 312s Investment_15 0.00 0.00 312s Investment_16 0.00 0.00 312s Investment_17 0.00 0.00 312s Investment_18 0.00 0.00 312s Investment_19 0.00 0.00 312s Investment_20 0.00 0.00 312s Investment_21 0.00 0.00 312s Investment_22 0.00 0.00 312s PrivateWages_2 0.00 0.00 312s PrivateWages_3 0.00 0.00 312s PrivateWages_4 0.00 0.00 312s PrivateWages_5 0.00 0.00 312s PrivateWages_6 0.00 0.00 312s PrivateWages_8 0.00 0.00 312s PrivateWages_9 0.00 0.00 312s PrivateWages_10 0.00 0.00 312s PrivateWages_11 0.00 0.00 312s PrivateWages_12 0.00 0.00 312s PrivateWages_13 0.00 0.00 312s PrivateWages_14 0.00 0.00 312s PrivateWages_15 0.00 0.00 312s PrivateWages_16 0.00 0.00 312s PrivateWages_17 0.00 0.00 312s PrivateWages_18 0.00 0.00 312s PrivateWages_19 0.00 0.00 312s PrivateWages_20 0.00 0.00 312s PrivateWages_21 0.00 0.00 312s PrivateWages_22 0.00 0.00 312s Investment_(Intercept) Investment_corpProf 312s Consumption_2 0.000 0.000 312s Consumption_3 0.000 0.000 312s Consumption_4 0.000 0.000 312s Consumption_5 0.000 0.000 312s Consumption_6 0.000 0.000 312s Consumption_8 0.000 0.000 312s Consumption_9 0.000 0.000 312s Consumption_11 0.000 0.000 312s Consumption_12 0.000 0.000 312s Consumption_14 0.000 0.000 312s Consumption_15 0.000 0.000 312s Consumption_16 0.000 0.000 312s Consumption_17 0.000 0.000 312s Consumption_18 0.000 0.000 312s Consumption_19 0.000 0.000 312s Consumption_20 0.000 0.000 312s Consumption_21 0.000 0.000 312s Consumption_22 0.000 0.000 312s Investment_2 -1.389 -18.632 312s Investment_3 0.361 6.028 312s Investment_4 1.031 19.362 312s Investment_5 -1.558 -32.177 312s Investment_6 0.610 11.759 312s Investment_8 1.410 24.716 312s Investment_9 0.404 7.885 312s Investment_10 2.080 42.149 312s Investment_11 -1.162 -19.982 312s Investment_12 -1.352 -18.282 312s Investment_14 1.037 10.359 312s Investment_15 -0.454 -5.832 312s Investment_16 -0.044 -0.631 312s Investment_17 2.093 31.318 312s Investment_18 -0.438 -8.488 312s Investment_19 -3.873 -74.977 312s Investment_20 0.486 8.486 312s Investment_21 0.145 2.925 312s Investment_22 0.615 14.015 312s PrivateWages_2 0.000 0.000 312s PrivateWages_3 0.000 0.000 312s PrivateWages_4 0.000 0.000 312s PrivateWages_5 0.000 0.000 312s PrivateWages_6 0.000 0.000 312s PrivateWages_8 0.000 0.000 312s PrivateWages_9 0.000 0.000 312s PrivateWages_10 0.000 0.000 312s PrivateWages_11 0.000 0.000 312s PrivateWages_12 0.000 0.000 312s PrivateWages_13 0.000 0.000 312s PrivateWages_14 0.000 0.000 312s PrivateWages_15 0.000 0.000 312s PrivateWages_16 0.000 0.000 312s PrivateWages_17 0.000 0.000 312s PrivateWages_18 0.000 0.000 312s PrivateWages_19 0.000 0.000 312s PrivateWages_20 0.000 0.000 312s PrivateWages_21 0.000 0.000 312s PrivateWages_22 0.000 0.000 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_2 0.000 0.00 312s Consumption_3 0.000 0.00 312s Consumption_4 0.000 0.00 312s Consumption_5 0.000 0.00 312s Consumption_6 0.000 0.00 312s Consumption_8 0.000 0.00 312s Consumption_9 0.000 0.00 312s Consumption_11 0.000 0.00 312s Consumption_12 0.000 0.00 312s Consumption_14 0.000 0.00 312s Consumption_15 0.000 0.00 312s Consumption_16 0.000 0.00 312s Consumption_17 0.000 0.00 312s Consumption_18 0.000 0.00 312s Consumption_19 0.000 0.00 312s Consumption_20 0.000 0.00 312s Consumption_21 0.000 0.00 312s Consumption_22 0.000 0.00 312s Investment_2 -17.639 -253.89 312s Investment_3 4.479 65.95 312s Investment_4 17.417 190.14 312s Investment_5 -28.673 -295.61 312s Investment_6 11.843 117.63 312s Investment_8 27.629 286.73 312s Investment_9 7.995 83.82 312s Investment_10 43.878 437.95 312s Investment_11 -25.218 -250.67 312s Investment_12 -21.091 -292.97 312s Investment_14 7.256 214.68 312s Investment_15 -5.080 -91.62 312s Investment_16 -0.541 -8.76 312s Investment_17 29.296 413.70 312s Investment_18 -7.713 -87.56 312s Investment_19 -67.010 -781.66 312s Investment_20 7.430 97.07 312s Investment_21 2.762 29.24 312s Investment_22 12.981 125.81 312s PrivateWages_2 0.000 0.00 312s PrivateWages_3 0.000 0.00 312s PrivateWages_4 0.000 0.00 312s PrivateWages_5 0.000 0.00 312s PrivateWages_6 0.000 0.00 312s PrivateWages_8 0.000 0.00 312s PrivateWages_9 0.000 0.00 312s PrivateWages_10 0.000 0.00 312s PrivateWages_11 0.000 0.00 312s PrivateWages_12 0.000 0.00 312s PrivateWages_13 0.000 0.00 312s PrivateWages_14 0.000 0.00 312s PrivateWages_15 0.000 0.00 312s PrivateWages_16 0.000 0.00 312s PrivateWages_17 0.000 0.00 312s PrivateWages_18 0.000 0.00 312s PrivateWages_19 0.000 0.00 312s PrivateWages_20 0.000 0.00 312s PrivateWages_21 0.000 0.00 312s PrivateWages_22 0.000 0.00 312s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 312s Consumption_2 0.0000 0.00 0.00 312s Consumption_3 0.0000 0.00 0.00 312s Consumption_4 0.0000 0.00 0.00 312s Consumption_5 0.0000 0.00 0.00 312s Consumption_6 0.0000 0.00 0.00 312s Consumption_8 0.0000 0.00 0.00 312s Consumption_9 0.0000 0.00 0.00 312s Consumption_11 0.0000 0.00 0.00 312s Consumption_12 0.0000 0.00 0.00 312s Consumption_14 0.0000 0.00 0.00 312s Consumption_15 0.0000 0.00 0.00 312s Consumption_16 0.0000 0.00 0.00 312s Consumption_17 0.0000 0.00 0.00 312s Consumption_18 0.0000 0.00 0.00 312s Consumption_19 0.0000 0.00 0.00 312s Consumption_20 0.0000 0.00 0.00 312s Consumption_21 0.0000 0.00 0.00 312s Consumption_22 0.0000 0.00 0.00 312s Investment_2 0.0000 0.00 0.00 312s Investment_3 0.0000 0.00 0.00 312s Investment_4 0.0000 0.00 0.00 312s Investment_5 0.0000 0.00 0.00 312s Investment_6 0.0000 0.00 0.00 312s Investment_8 0.0000 0.00 0.00 312s Investment_9 0.0000 0.00 0.00 312s Investment_10 0.0000 0.00 0.00 312s Investment_11 0.0000 0.00 0.00 312s Investment_12 0.0000 0.00 0.00 312s Investment_14 0.0000 0.00 0.00 312s Investment_15 0.0000 0.00 0.00 312s Investment_16 0.0000 0.00 0.00 312s Investment_17 0.0000 0.00 0.00 312s Investment_18 0.0000 0.00 0.00 312s Investment_19 0.0000 0.00 0.00 312s Investment_20 0.0000 0.00 0.00 312s Investment_21 0.0000 0.00 0.00 312s Investment_22 0.0000 0.00 0.00 312s PrivateWages_2 -1.9924 -93.78 -89.46 312s PrivateWages_3 0.4683 23.22 21.35 312s PrivateWages_4 1.4034 79.35 70.31 312s PrivateWages_5 -1.7870 -108.45 -102.22 312s PrivateWages_6 -0.3627 -21.98 -20.71 312s PrivateWages_8 1.1629 69.77 74.43 312s PrivateWages_9 1.2735 79.30 82.01 312s PrivateWages_10 2.2141 142.96 142.81 312s PrivateWages_11 -1.2912 -82.26 -86.51 312s PrivateWages_12 -0.0350 -1.92 -2.14 312s PrivateWages_13 -1.0438 -49.04 -55.74 312s PrivateWages_14 1.8016 75.90 79.81 312s PrivateWages_15 -0.3714 -19.02 -16.75 312s PrivateWages_16 -0.3904 -21.61 -19.40 312s PrivateWages_17 1.4934 85.71 81.24 312s PrivateWages_18 0.0279 1.88 1.75 312s PrivateWages_19 -3.8229 -261.91 -248.49 312s PrivateWages_20 0.7870 52.61 47.93 312s PrivateWages_21 -0.7415 -55.52 -51.54 312s PrivateWages_22 1.2062 104.79 91.31 312s PrivateWages_trend 312s Consumption_2 0.000 312s Consumption_3 0.000 312s Consumption_4 0.000 312s Consumption_5 0.000 312s Consumption_6 0.000 312s Consumption_8 0.000 312s Consumption_9 0.000 312s Consumption_11 0.000 312s Consumption_12 0.000 312s Consumption_14 0.000 312s Consumption_15 0.000 312s Consumption_16 0.000 312s Consumption_17 0.000 312s Consumption_18 0.000 312s Consumption_19 0.000 312s Consumption_20 0.000 312s Consumption_21 0.000 312s Consumption_22 0.000 312s Investment_2 0.000 312s Investment_3 0.000 312s Investment_4 0.000 312s Investment_5 0.000 312s Investment_6 0.000 312s Investment_8 0.000 312s Investment_9 0.000 312s Investment_10 0.000 312s Investment_11 0.000 312s Investment_12 0.000 312s Investment_14 0.000 312s Investment_15 0.000 312s Investment_16 0.000 312s Investment_17 0.000 312s Investment_18 0.000 312s Investment_19 0.000 312s Investment_20 0.000 312s Investment_21 0.000 312s Investment_22 0.000 312s PrivateWages_2 19.924 312s PrivateWages_3 -4.214 312s PrivateWages_4 -11.227 312s PrivateWages_5 12.509 312s PrivateWages_6 2.176 312s PrivateWages_8 -4.652 312s PrivateWages_9 -3.820 312s PrivateWages_10 -4.428 312s PrivateWages_11 1.291 312s PrivateWages_12 0.000 312s PrivateWages_13 -1.044 312s PrivateWages_14 3.603 312s PrivateWages_15 -1.114 312s PrivateWages_16 -1.562 312s PrivateWages_17 7.467 312s PrivateWages_18 0.168 312s PrivateWages_19 -26.760 312s PrivateWages_20 6.296 312s PrivateWages_21 -6.674 312s PrivateWages_22 12.062 312s [1] TRUE 312s > Bread 312s Consumption_(Intercept) Consumption_corpProf 312s Consumption_(Intercept) 118.21 -4.213 312s Consumption_corpProf -4.21 1.235 312s Consumption_corpProfLag 1.03 -0.689 312s Consumption_wages -1.44 -0.136 312s Investment_(Intercept) 0.00 0.000 312s Investment_corpProf 0.00 0.000 312s Investment_corpProfLag 0.00 0.000 312s Investment_capitalLag 0.00 0.000 312s PrivateWages_(Intercept) 0.00 0.000 312s PrivateWages_gnp 0.00 0.000 312s PrivateWages_gnpLag 0.00 0.000 312s PrivateWages_trend 0.00 0.000 312s Consumption_corpProfLag Consumption_wages 312s Consumption_(Intercept) 1.0298 -1.4384 312s Consumption_corpProf -0.6891 -0.1356 312s Consumption_corpProfLag 0.7104 -0.0191 312s Consumption_wages -0.0191 0.0972 312s Investment_(Intercept) 0.0000 0.0000 312s Investment_corpProf 0.0000 0.0000 312s Investment_corpProfLag 0.0000 0.0000 312s Investment_capitalLag 0.0000 0.0000 312s PrivateWages_(Intercept) 0.0000 0.0000 312s PrivateWages_gnp 0.0000 0.0000 312s PrivateWages_gnpLag 0.0000 0.0000 312s PrivateWages_trend 0.0000 0.0000 312s Investment_(Intercept) Investment_corpProf 312s Consumption_(Intercept) 0.0 0.000 312s Consumption_corpProf 0.0 0.000 312s Consumption_corpProfLag 0.0 0.000 312s Consumption_wages 0.0 0.000 312s Investment_(Intercept) 2314.8 -41.107 312s Investment_corpProf -41.1 1.637 312s Investment_corpProfLag 33.2 -1.272 312s Investment_capitalLag -10.7 0.169 312s PrivateWages_(Intercept) 0.0 0.000 312s PrivateWages_gnp 0.0 0.000 312s PrivateWages_gnpLag 0.0 0.000 312s PrivateWages_trend 0.0 0.000 312s Investment_corpProfLag Investment_capitalLag 312s Consumption_(Intercept) 0.000 0.0000 312s Consumption_corpProf 0.000 0.0000 312s Consumption_corpProfLag 0.000 0.0000 312s Consumption_wages 0.000 0.0000 312s Investment_(Intercept) 33.159 -10.7377 312s Investment_corpProf -1.272 0.1688 312s Investment_corpProfLag 1.204 -0.1550 312s Investment_capitalLag -0.155 0.0519 312s PrivateWages_(Intercept) 0.000 0.0000 312s PrivateWages_gnp 0.000 0.0000 312s PrivateWages_gnpLag 0.000 0.0000 312s PrivateWages_trend 0.000 0.0000 312s PrivateWages_(Intercept) PrivateWages_gnp 312s Consumption_(Intercept) 0.000 0.0000 312s Consumption_corpProf 0.000 0.0000 312s Consumption_corpProfLag 0.000 0.0000 312s Consumption_wages 0.000 0.0000 312s Investment_(Intercept) 0.000 0.0000 312s Investment_corpProf 0.000 0.0000 312s Investment_corpProfLag 0.000 0.0000 312s Investment_capitalLag 0.000 0.0000 312s PrivateWages_(Intercept) 162.179 -0.8825 312s PrivateWages_gnp -0.882 0.1501 312s PrivateWages_gnpLag -1.850 -0.1399 312s PrivateWages_trend 2.056 -0.0403 312s PrivateWages_gnpLag PrivateWages_trend 312s Consumption_(Intercept) 0.0000 0.0000 312s Consumption_corpProf 0.0000 0.0000 312s Consumption_corpProfLag 0.0000 0.0000 312s Consumption_wages 0.0000 0.0000 312s Investment_(Intercept) 0.0000 0.0000 312s Investment_corpProf 0.0000 0.0000 312s Investment_corpProfLag 0.0000 0.0000 312s Investment_capitalLag 0.0000 0.0000 312s PrivateWages_(Intercept) -1.8504 2.0559 312s PrivateWages_gnp -0.1399 -0.0403 312s PrivateWages_gnpLag 0.1768 0.0057 312s PrivateWages_trend 0.0057 0.1094 312s > 312s > # SUR 312s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 312s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 313s > summary 313s 313s systemfit results 313s method: SUR 313s 313s N DF SSR detRCov OLS-R2 McElroy-R2 313s system 59 47 45.1 0.168 0.976 0.992 313s 313s N DF SSR MSE RMSE R2 Adj R2 313s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 313s Investment 20 16 17.3 1.083 1.041 0.911 0.894 313s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 313s 313s The covariance matrix of the residuals used for estimation 313s Consumption Investment PrivateWages 313s Consumption 0.9286 0.0435 -0.369 313s Investment 0.0435 0.7653 0.109 313s PrivateWages -0.3690 0.1091 0.468 313s 313s The covariance matrix of the residuals 313s Consumption Investment PrivateWages 313s Consumption 0.9251 0.0748 -0.427 313s Investment 0.0748 0.7653 0.171 313s PrivateWages -0.4268 0.1706 0.492 313s 313s The correlations of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.0000 0.0888 -0.636 313s Investment 0.0888 1.0000 0.268 313s PrivateWages -0.6364 0.2678 1.000 313s 313s 313s SUR estimates for 'Consumption' (equation 1) 313s Model Formula: consump ~ corpProf + corpProfLag + wages 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 16.2684 1.2781 12.73 1.9e-09 *** 313s corpProf 0.1942 0.0927 2.10 0.054 . 313s corpProfLag 0.0746 0.0819 0.91 0.377 313s wages 0.8011 0.0372 21.53 1.1e-12 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.08 on 15 degrees of freedom 313s Number of observations: 19 Degrees of Freedom: 15 313s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 313s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 313s 313s 313s SUR estimates for 'Investment' (equation 2) 313s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 12.6462 4.6500 2.72 0.01515 * 313s corpProf 0.4707 0.0916 5.14 9.9e-05 *** 313s corpProfLag 0.3519 0.0874 4.03 0.00097 *** 313s capitalLag -0.1253 0.0229 -5.47 5.1e-05 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.041 on 16 degrees of freedom 313s Number of observations: 20 Degrees of Freedom: 16 313s SSR: 17.325 MSE: 1.083 Root MSE: 1.041 313s Multiple R-Squared: 0.911 Adjusted R-Squared: 0.894 313s 313s 313s SUR estimates for 'PrivateWages' (equation 3) 313s Model Formula: privWage ~ gnp + gnpLag + trend 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 1.3245 1.0946 1.21 0.24 313s gnp 0.4184 0.0260 16.08 2.7e-11 *** 313s gnpLag 0.1714 0.0307 5.59 4.1e-05 *** 313s trend 0.1455 0.0276 5.27 7.6e-05 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 0.801 on 16 degrees of freedom 313s Number of observations: 20 Degrees of Freedom: 16 313s SSR: 10.265 MSE: 0.642 Root MSE: 0.801 313s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 313s 313s > residuals 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 -0.3146 -0.2419 -1.1439 313s 3 -1.2707 -0.1795 0.5080 313s 4 -1.5428 1.0691 1.4208 313s 5 -0.4489 -1.4778 -0.1000 313s 6 0.0588 0.3168 -0.3599 313s 7 0.9215 1.4450 NA 313s 8 1.3791 0.8287 -0.7561 313s 9 1.0901 -0.5272 0.2880 313s 10 NA 1.2089 1.1795 313s 11 0.3577 0.4081 -0.3681 313s 12 -0.2286 0.2569 0.3439 313s 13 NA NA -0.1574 313s 14 0.2172 0.4743 0.4225 313s 15 -0.1124 -0.0607 0.3154 313s 16 -0.0876 0.0761 0.0151 313s 17 1.5611 1.0205 -0.8084 313s 18 -0.4529 0.0580 0.8611 313s 19 0.1999 -2.5444 -0.7635 313s 20 0.9266 -0.6202 -0.4039 313s 21 0.7589 -0.7478 -1.2175 313s 22 -2.2135 -0.6029 0.5611 313s > fitted 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 42.2 0.0419 26.6 313s 3 46.3 2.0795 28.8 313s 4 50.7 4.1309 32.7 313s 5 51.0 4.4778 34.0 313s 6 52.5 4.7832 35.8 313s 7 54.2 4.1550 NA 313s 8 54.8 3.3713 38.7 313s 9 56.2 3.5272 38.9 313s 10 NA 3.8911 40.1 313s 11 54.6 0.5919 38.3 313s 12 51.1 -3.6569 34.2 313s 13 NA NA 29.2 313s 14 46.3 -5.5743 28.1 313s 15 48.8 -2.9393 30.3 313s 16 51.4 -1.3761 33.2 313s 17 56.1 1.0795 37.6 313s 18 59.2 1.9420 40.1 313s 19 57.3 0.6444 39.0 313s 20 60.7 1.9202 42.0 313s 21 64.2 4.0478 46.2 313s 22 71.9 5.5029 52.7 313s > predict 313s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 313s 1 NA NA NA NA 313s 2 42.2 0.448 41.3 43.1 313s 3 46.3 0.476 45.3 47.2 313s 4 50.7 0.318 50.1 51.4 313s 5 51.0 0.373 50.3 51.8 313s 6 52.5 0.378 51.8 53.3 313s 7 54.2 0.337 53.5 54.9 313s 8 54.8 0.310 54.2 55.4 313s 9 56.2 0.343 55.5 56.9 313s 10 NA NA NA NA 313s 11 54.6 0.567 53.5 55.8 313s 12 51.1 0.509 50.1 52.2 313s 13 NA NA NA NA 313s 14 46.3 0.573 45.1 47.4 313s 15 48.8 0.382 48.0 49.6 313s 16 51.4 0.328 50.7 52.0 313s 17 56.1 0.336 55.5 56.8 313s 18 59.2 0.309 58.5 59.8 313s 19 57.3 0.370 56.6 58.0 313s 20 60.7 0.401 59.9 61.5 313s 21 64.2 0.405 63.4 65.1 313s 22 71.9 0.633 70.6 73.2 313s Investment.pred Investment.se.fit Investment.lwr Investment.upr 313s 1 NA NA NA NA 313s 2 0.0419 0.533 -1.0309 1.115 313s 3 2.0795 0.433 1.2082 2.951 313s 4 4.1309 0.387 3.3532 4.909 313s 5 4.4778 0.322 3.8307 5.125 313s 6 4.7832 0.305 4.1700 5.396 313s 7 4.1550 0.283 3.5852 4.725 313s 8 3.3713 0.253 2.8630 3.880 313s 9 3.5272 0.337 2.8488 4.206 313s 10 3.8911 0.386 3.1149 4.667 313s 11 0.5919 0.561 -0.5376 1.722 313s 12 -3.6569 0.530 -4.7223 -2.591 313s 13 NA NA NA NA 313s 14 -5.5743 0.618 -6.8176 -4.331 313s 15 -2.9393 0.362 -3.6671 -2.212 313s 16 -1.3761 0.296 -1.9710 -0.781 313s 17 1.0795 0.300 0.4763 1.683 313s 18 1.9420 0.216 1.5081 2.376 313s 19 0.6444 0.298 0.0451 1.244 313s 20 1.9202 0.318 1.2798 2.561 313s 21 4.0478 0.295 3.4537 4.642 313s 22 5.5029 0.417 4.6638 6.342 313s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 313s 1 NA NA NA NA 313s 2 26.6 0.312 26.0 27.3 313s 3 28.8 0.312 28.2 29.4 313s 4 32.7 0.307 32.1 33.3 313s 5 34.0 0.237 33.5 34.5 313s 6 35.8 0.235 35.3 36.2 313s 7 NA NA NA NA 313s 8 38.7 0.239 38.2 39.1 313s 9 38.9 0.228 38.5 39.4 313s 10 40.1 0.218 39.7 40.6 313s 11 38.3 0.293 37.7 38.9 313s 12 34.2 0.290 33.6 34.7 313s 13 29.2 0.343 28.5 29.8 313s 14 28.1 0.321 27.4 28.7 313s 15 30.3 0.320 29.6 30.9 313s 16 33.2 0.268 32.6 33.7 313s 17 37.6 0.263 37.1 38.1 313s 18 40.1 0.207 39.7 40.6 313s 19 39.0 0.293 38.4 39.6 313s 20 42.0 0.279 41.4 42.6 313s 21 46.2 0.295 45.6 46.8 313s 22 52.7 0.435 51.9 53.6 313s > model.frame 313s [1] TRUE 313s > model.matrix 313s [1] TRUE 313s > nobs 313s [1] 59 313s > linearHypothesis 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 48 313s 2 47 1 0.41 0.52 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 48 313s 2 47 1 0.52 0.47 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 48 313s 2 47 1 0.52 0.47 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 49 313s 2 47 2 0.31 0.73 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 49 313s 2 47 2 0.4 0.67 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 49 313s 2 47 2 0.79 0.67 313s > logLik 313s 'log Lik.' -67.3 (df=18) 313s 'log Lik.' -74.9 (df=18) 313s Estimating function 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_2 -0.5115 -6.342 313s Consumption_3 -2.0659 -34.913 313s Consumption_4 -2.5083 -46.152 313s Consumption_5 -0.7298 -14.158 313s Consumption_6 0.0957 1.923 313s Consumption_7 1.4982 29.364 313s Consumption_8 2.2421 44.394 313s Consumption_9 1.7723 37.396 313s Consumption_11 0.5815 9.072 313s Consumption_12 -0.3716 -4.237 313s Consumption_14 0.3531 3.954 313s Consumption_15 -0.1827 -2.248 313s Consumption_16 -0.1424 -1.993 313s Consumption_17 2.5380 44.669 313s Consumption_18 -0.7363 -12.738 313s Consumption_19 0.3251 4.973 313s Consumption_20 1.5064 28.622 313s Consumption_21 1.2337 26.032 313s Consumption_22 -3.5987 -84.568 313s Investment_2 0.0688 0.854 313s Investment_3 0.0511 0.863 313s Investment_4 -0.3043 -5.599 313s Investment_5 0.4206 8.160 313s Investment_6 -0.0902 -1.813 313s Investment_7 -0.4113 -8.061 313s Investment_8 -0.2359 -4.670 313s Investment_9 0.1501 3.166 313s Investment_10 0.0000 0.000 313s Investment_11 -0.1161 -1.812 313s Investment_12 -0.0731 -0.834 313s Investment_14 -0.1350 -1.512 313s Investment_15 0.0173 0.212 313s Investment_16 -0.0217 -0.303 313s Investment_17 -0.2904 -5.112 313s Investment_18 -0.0165 -0.286 313s Investment_19 0.7242 11.080 313s Investment_20 0.1765 3.354 313s Investment_21 0.2128 4.491 313s Investment_22 0.1716 4.032 313s PrivateWages_2 -1.5418 -19.118 313s PrivateWages_3 0.6847 11.571 313s PrivateWages_4 1.9149 35.234 313s PrivateWages_5 -0.1348 -2.615 313s PrivateWages_6 -0.4851 -9.750 313s PrivateWages_8 -1.0191 -20.178 313s PrivateWages_9 0.3882 8.190 313s PrivateWages_10 0.0000 0.000 313s PrivateWages_11 -0.4961 -7.739 313s PrivateWages_12 0.4635 5.284 313s PrivateWages_13 0.0000 0.000 313s PrivateWages_14 0.5694 6.377 313s PrivateWages_15 0.4251 5.229 313s PrivateWages_16 0.0204 0.286 313s PrivateWages_17 -1.0895 -19.175 313s PrivateWages_18 1.1605 20.077 313s PrivateWages_19 -1.0290 -15.743 313s PrivateWages_20 -0.5443 -10.343 313s PrivateWages_21 -1.6408 -34.622 313s PrivateWages_22 0.7563 17.772 313s Consumption_corpProfLag Consumption_wages 313s Consumption_2 -6.496 -14.423 313s Consumption_3 -25.617 -66.521 313s Consumption_4 -42.390 -92.806 313s Consumption_5 -13.428 -27.003 313s Consumption_6 1.856 3.693 313s Consumption_7 30.114 60.976 313s Consumption_8 43.945 93.047 313s Consumption_9 35.092 76.033 313s Consumption_11 12.619 24.482 313s Consumption_12 -5.798 -14.606 313s Consumption_14 2.471 12.039 313s Consumption_15 -2.047 -6.688 313s Consumption_16 -1.751 -5.595 313s Consumption_17 35.532 112.180 313s Consumption_18 -12.959 -35.121 313s Consumption_19 5.624 14.920 313s Consumption_20 23.048 74.417 313s Consumption_21 23.441 65.389 313s Consumption_22 -75.932 -222.397 313s Investment_2 0.874 1.941 313s Investment_3 0.633 1.645 313s Investment_4 -5.142 -11.258 313s Investment_5 7.739 15.562 313s Investment_6 -1.749 -3.481 313s Investment_7 -8.267 -16.739 313s Investment_8 -4.623 -9.788 313s Investment_9 2.971 6.437 313s Investment_10 0.000 0.000 313s Investment_11 -2.520 -4.889 313s Investment_12 -1.141 -2.873 313s Investment_14 -0.945 -4.603 313s Investment_15 0.193 0.632 313s Investment_16 -0.266 -0.851 313s Investment_17 -4.066 -12.838 313s Investment_18 -0.291 -0.787 313s Investment_19 12.528 33.240 313s Investment_20 2.701 8.720 313s Investment_21 4.044 11.280 313s Investment_22 3.620 10.604 313s PrivateWages_2 -19.580 -43.478 313s PrivateWages_3 8.490 22.046 313s PrivateWages_4 32.362 70.851 313s PrivateWages_5 -2.480 -4.987 313s PrivateWages_6 -9.410 -18.724 313s PrivateWages_8 -19.974 -42.291 313s PrivateWages_9 7.686 16.652 313s PrivateWages_10 0.000 0.000 313s PrivateWages_11 -10.765 -20.886 313s PrivateWages_12 7.230 18.215 313s PrivateWages_13 0.000 0.000 313s PrivateWages_14 3.986 19.417 313s PrivateWages_15 4.762 15.560 313s PrivateWages_16 0.251 0.802 313s PrivateWages_17 -15.253 -48.156 313s PrivateWages_18 20.425 55.356 313s PrivateWages_19 -17.801 -47.230 313s PrivateWages_20 -8.329 -26.891 313s PrivateWages_21 -31.176 -86.965 313s PrivateWages_22 15.957 46.737 313s Investment_(Intercept) Investment_corpProf 313s Consumption_2 0.08954 1.110 313s Consumption_3 0.36165 6.112 313s Consumption_4 0.43910 8.079 313s Consumption_5 0.12776 2.479 313s Consumption_6 -0.01675 -0.337 313s Consumption_7 -0.26227 -5.141 313s Consumption_8 -0.39250 -7.772 313s Consumption_9 -0.31026 -6.547 313s Consumption_11 -0.10180 -1.588 313s Consumption_12 0.06506 0.742 313s Consumption_14 -0.06181 -0.692 313s Consumption_15 0.03199 0.393 313s Consumption_16 0.02492 0.349 313s Consumption_17 -0.44431 -7.820 313s Consumption_18 0.12890 2.230 313s Consumption_19 -0.05691 -0.871 313s Consumption_20 -0.26372 -5.011 313s Consumption_21 -0.21598 -4.557 313s Consumption_22 0.62998 14.805 313s Investment_2 -0.33900 -4.204 313s Investment_3 -0.25149 -4.250 313s Investment_4 1.49825 27.568 313s Investment_5 -2.07104 -40.178 313s Investment_6 0.44402 8.925 313s Investment_7 2.02512 39.692 313s Investment_8 1.16134 22.995 313s Investment_9 -0.73888 -15.590 313s Investment_10 1.69419 36.764 313s Investment_11 0.57188 8.921 313s Investment_12 0.36002 4.104 313s Investment_14 0.66469 7.445 313s Investment_15 -0.08500 -1.046 313s Investment_16 0.10666 1.493 313s Investment_17 1.43016 25.171 313s Investment_18 0.08129 1.406 313s Investment_19 -3.56588 -54.558 313s Investment_20 -0.86923 -16.515 313s Investment_21 -1.04801 -22.113 313s Investment_22 -0.84488 -19.855 313s PrivateWages_2 0.63026 7.815 313s PrivateWages_3 -0.27988 -4.730 313s PrivateWages_4 -0.78278 -14.403 313s PrivateWages_5 0.05510 1.069 313s PrivateWages_6 0.19829 3.986 313s PrivateWages_8 0.41658 8.248 313s PrivateWages_9 -0.15868 -3.348 313s PrivateWages_10 -0.64985 -14.102 313s PrivateWages_11 0.20280 3.164 313s PrivateWages_12 -0.18947 -2.160 313s PrivateWages_13 0.00000 0.000 313s PrivateWages_14 -0.23276 -2.607 313s PrivateWages_15 -0.17379 -2.138 313s PrivateWages_16 -0.00834 -0.117 313s PrivateWages_17 0.44538 7.839 313s PrivateWages_18 -0.47440 -8.207 313s PrivateWages_19 0.42063 6.436 313s PrivateWages_20 0.22252 4.228 313s PrivateWages_21 0.67076 14.153 313s PrivateWages_22 -0.30915 -7.265 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_2 1.137 16.37 313s Consumption_3 4.484 66.04 313s Consumption_4 7.421 81.01 313s Consumption_5 2.351 24.24 313s Consumption_6 -0.325 -3.23 313s Consumption_7 -5.272 -51.88 313s Consumption_8 -7.693 -79.84 313s Consumption_9 -6.143 -64.41 313s Consumption_11 -2.209 -21.96 313s Consumption_12 1.015 14.10 313s Consumption_14 -0.433 -12.80 313s Consumption_15 0.358 6.46 313s Consumption_16 0.307 4.96 313s Consumption_17 -6.220 -87.84 313s Consumption_18 2.269 25.75 313s Consumption_19 -0.984 -11.48 313s Consumption_20 -4.035 -52.72 313s Consumption_21 -4.104 -43.46 313s Consumption_22 13.293 128.83 313s Investment_2 -4.305 -61.97 313s Investment_3 -3.118 -45.92 313s Investment_4 25.320 276.43 313s Investment_5 -38.107 -392.88 313s Investment_6 8.614 85.56 313s Investment_7 40.705 400.57 313s Investment_8 22.762 236.22 313s Investment_9 -14.630 -153.39 313s Investment_10 35.747 356.80 313s Investment_11 12.410 123.35 313s Investment_12 5.616 78.02 313s Investment_14 4.653 137.66 313s Investment_15 -0.952 -17.17 313s Investment_16 1.312 21.22 313s Investment_17 20.022 282.74 313s Investment_18 1.431 16.24 313s Investment_19 -61.690 -719.59 313s Investment_20 -13.299 -173.76 313s Investment_21 -19.912 -210.86 313s Investment_22 -17.827 -172.78 313s PrivateWages_2 8.004 115.21 313s PrivateWages_3 -3.471 -51.11 313s PrivateWages_4 -13.229 -144.42 313s PrivateWages_5 1.014 10.45 313s PrivateWages_6 3.847 38.21 313s PrivateWages_8 8.165 84.73 313s PrivateWages_9 -3.142 -32.94 313s PrivateWages_10 -13.712 -136.86 313s PrivateWages_11 4.401 43.74 313s PrivateWages_12 -2.956 -41.06 313s PrivateWages_13 0.000 0.00 313s PrivateWages_14 -1.629 -48.21 313s PrivateWages_15 -1.946 -35.11 313s PrivateWages_16 -0.103 -1.66 313s PrivateWages_17 6.235 88.05 313s PrivateWages_18 -8.349 -94.78 313s PrivateWages_19 7.277 84.88 313s PrivateWages_20 3.405 44.48 313s PrivateWages_21 12.744 134.96 313s PrivateWages_22 -6.523 -63.22 313s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 313s Consumption_2 -0.4240 -19.33 -19.04 313s Consumption_3 -1.7126 -85.80 -78.09 313s Consumption_4 -2.0793 -118.94 -104.17 313s Consumption_5 -0.6050 -34.54 -34.61 313s Consumption_6 0.0793 4.84 4.53 313s Consumption_7 0.0000 0.00 0.00 313s Consumption_8 1.8587 119.70 118.95 313s Consumption_9 1.4692 94.76 94.62 313s Consumption_11 0.4821 29.50 32.30 313s Consumption_12 -0.3081 -16.45 -18.85 313s Consumption_14 0.2927 13.20 12.97 313s Consumption_15 -0.1515 -7.53 -6.83 313s Consumption_16 -0.1180 -6.42 -5.87 313s Consumption_17 2.1040 131.92 114.46 313s Consumption_18 -0.6104 -39.67 -38.27 313s Consumption_19 0.2695 16.41 17.52 313s Consumption_20 1.2488 86.79 76.05 313s Consumption_21 1.0228 77.42 71.08 313s Consumption_22 -2.9832 -263.72 -225.83 313s Investment_2 0.1333 6.08 5.98 313s Investment_3 0.0989 4.95 4.51 313s Investment_4 -0.5890 -33.69 -29.51 313s Investment_5 0.8142 46.49 46.57 313s Investment_6 -0.1746 -10.65 -9.97 313s Investment_7 0.0000 0.00 0.00 313s Investment_8 -0.4566 -29.40 -29.22 313s Investment_9 0.2905 18.74 18.71 313s Investment_10 -0.6660 -44.62 -42.96 313s Investment_11 -0.2248 -13.76 -15.06 313s Investment_12 -0.1415 -7.56 -8.66 313s Investment_14 -0.2613 -11.79 -11.58 313s Investment_15 0.0334 1.66 1.51 313s Investment_16 -0.0419 -2.28 -2.08 313s Investment_17 -0.5622 -35.25 -30.59 313s Investment_18 -0.0320 -2.08 -2.00 313s Investment_19 1.4018 85.37 91.12 313s Investment_20 0.3417 23.75 20.81 313s Investment_21 0.4120 31.19 28.63 313s Investment_22 0.3321 29.36 25.14 313s PrivateWages_2 -3.8052 -173.52 -170.85 313s PrivateWages_3 1.6898 84.66 77.06 313s PrivateWages_4 4.7261 270.33 236.78 313s PrivateWages_5 -0.3327 -19.00 -19.03 313s PrivateWages_6 -1.1972 -73.03 -68.36 313s PrivateWages_8 -2.5152 -161.98 -160.97 313s PrivateWages_9 0.9580 61.79 61.70 313s PrivateWages_10 3.9235 262.88 253.07 313s PrivateWages_11 -1.2244 -74.93 -82.04 313s PrivateWages_12 1.1439 61.09 70.01 313s PrivateWages_13 -0.5236 -23.19 -27.96 313s PrivateWages_14 1.4053 63.38 62.26 313s PrivateWages_15 1.0493 52.15 47.32 313s PrivateWages_16 0.0503 2.74 2.50 313s PrivateWages_17 -2.6890 -168.60 -146.28 313s PrivateWages_18 2.8642 186.17 179.59 313s PrivateWages_19 -2.5396 -154.66 -165.07 313s PrivateWages_20 -1.3435 -93.37 -81.82 313s PrivateWages_21 -4.0497 -306.57 -281.46 313s PrivateWages_22 1.8665 165.00 141.30 313s PrivateWages_trend 313s Consumption_2 4.240 313s Consumption_3 15.413 313s Consumption_4 16.634 313s Consumption_5 4.235 313s Consumption_6 -0.476 313s Consumption_7 0.000 313s Consumption_8 -7.435 313s Consumption_9 -4.408 313s Consumption_11 -0.482 313s Consumption_12 0.000 313s Consumption_14 0.585 313s Consumption_15 -0.454 313s Consumption_16 -0.472 313s Consumption_17 10.520 313s Consumption_18 -3.662 313s Consumption_19 1.886 313s Consumption_20 9.990 313s Consumption_21 9.205 313s Consumption_22 -29.832 313s Investment_2 -1.333 313s Investment_3 -0.890 313s Investment_4 4.712 313s Investment_5 -5.699 313s Investment_6 1.047 313s Investment_7 0.000 313s Investment_8 1.826 313s Investment_9 -0.871 313s Investment_10 1.332 313s Investment_11 0.225 313s Investment_12 0.000 313s Investment_14 -0.523 313s Investment_15 0.100 313s Investment_16 -0.168 313s Investment_17 -2.811 313s Investment_18 -0.192 313s Investment_19 9.813 313s Investment_20 2.734 313s Investment_21 3.708 313s Investment_22 3.321 313s PrivateWages_2 38.052 313s PrivateWages_3 -15.208 313s PrivateWages_4 -37.809 313s PrivateWages_5 2.329 313s PrivateWages_6 7.183 313s PrivateWages_8 10.061 313s PrivateWages_9 -2.874 313s PrivateWages_10 -7.847 313s PrivateWages_11 1.224 313s PrivateWages_12 0.000 313s PrivateWages_13 -0.524 313s PrivateWages_14 2.811 313s PrivateWages_15 3.148 313s PrivateWages_16 0.201 313s PrivateWages_17 -13.445 313s PrivateWages_18 17.185 313s PrivateWages_19 -17.777 313s PrivateWages_20 -10.748 313s PrivateWages_21 -36.448 313s PrivateWages_22 18.665 313s [1] TRUE 313s > Bread 313s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 313s [1,] 9.64e+01 -1.01207 -0.67760 313s [2,] -1.01e+00 0.50717 -0.26912 313s [3,] -6.78e-01 -0.26912 0.39547 313s [4,] -1.57e+00 -0.07816 -0.02960 313s [5,] 4.72e+00 -0.06998 0.78589 313s [6,] -2.60e-01 0.05062 -0.04147 313s [7,] 5.84e-03 -0.03341 0.04369 313s [8,] -2.63e-04 -0.00132 -0.00391 313s [9,] -3.35e+01 0.06371 1.58512 313s [10,] 2.97e-01 -0.05279 0.03618 313s [11,] 2.54e-01 0.05334 -0.06435 313s [12,] 1.92e-01 0.03084 0.02478 313s Consumption_wages Investment_(Intercept) Investment_corpProf 313s [1,] -1.566759 4.725 -0.25994 313s [2,] -0.078160 -0.070 0.05062 313s [3,] -0.029602 0.786 -0.04147 313s [4,] 0.081697 -0.368 0.00116 313s [5,] -0.368191 1275.706 -12.07893 313s [6,] 0.001158 -12.079 0.49514 313s [7,] -0.003210 9.845 -0.37888 313s [8,] 0.001998 -6.140 0.04890 313s [9,] 0.126305 19.264 -0.14904 313s [10,] -0.000206 0.266 0.01283 313s [11,] -0.002055 -0.608 -0.01053 313s [12,] -0.027162 -0.549 0.00394 313s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 313s [1,] 0.00584 -0.000263 -33.5037 313s [2,] -0.03341 -0.001318 0.0637 313s [3,] 0.04369 -0.003914 1.5851 313s [4,] -0.00321 0.001998 0.1263 313s [5,] 9.84516 -6.139910 19.2637 313s [6,] -0.37888 0.048897 -0.1490 313s [7,] 0.45026 -0.053769 -0.4040 313s [8,] -0.05377 0.030940 -0.0490 313s [9,] -0.40395 -0.049007 70.6849 313s [10,] -0.00755 -0.001777 -0.2111 313s [11,] 0.01465 0.002709 -0.9817 313s [12,] -0.01065 0.003278 0.7839 313s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 313s [1,] 0.297134 0.25379 0.19157 313s [2,] -0.052789 0.05334 0.03084 313s [3,] 0.036177 -0.06435 0.02478 313s [4,] -0.000206 -0.00206 -0.02716 313s [5,] 0.265808 -0.60808 -0.54935 313s [6,] 0.012829 -0.01053 0.00394 313s [7,] -0.007548 0.01465 -0.01065 313s [8,] -0.001777 0.00271 0.00328 313s [9,] -0.211061 -0.98166 0.78387 313s [10,] 0.039911 -0.03744 -0.00955 313s [11,] -0.037441 0.05550 -0.00377 313s [12,] -0.009553 -0.00377 0.04488 313s > 313s > # 3SLS 313s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 313s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 313s > summary 313s 313s systemfit results 313s method: 3SLS 313s 313s N DF SSR detRCov OLS-R2 McElroy-R2 313s system 57 45 66.8 0.361 0.963 0.993 313s 313s N DF SSR MSE RMSE R2 Adj R2 313s Consumption 18 14 22.6 1.616 1.271 0.974 0.968 313s Investment 19 15 34.1 2.277 1.509 0.807 0.769 313s PrivateWages 20 16 10.1 0.628 0.793 0.987 0.985 313s 313s The covariance matrix of the residuals used for estimation 313s Consumption Investment PrivateWages 313s Consumption 1.237 0.518 -0.408 313s Investment 0.518 1.263 0.113 313s PrivateWages -0.408 0.113 0.468 313s 313s The covariance matrix of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.257 0.601 -0.421 313s Investment 0.601 1.601 0.214 313s PrivateWages -0.421 0.214 0.491 313s 313s The correlations of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.000 0.425 -0.537 313s Investment 0.425 1.000 0.239 313s PrivateWages -0.537 0.239 1.000 313s 313s 313s 3SLS estimates for 'Consumption' (equation 1) 313s Model Formula: consump ~ corpProf + corpProfLag + wages 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 18.2100 1.5273 11.92 1e-08 *** 313s corpProf -0.0639 0.1461 -0.44 0.67 313s corpProfLag 0.1687 0.1125 1.50 0.16 313s wages 0.8230 0.0431 19.07 2e-11 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.271 on 14 degrees of freedom 313s Number of observations: 18 Degrees of Freedom: 14 313s SSR: 22.626 MSE: 1.616 Root MSE: 1.271 313s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 313s 313s 313s 3SLS estimates for 'Investment' (equation 2) 313s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 24.7534 6.5548 3.78 0.00183 ** 313s corpProf 0.0524 0.1807 0.29 0.77600 313s corpProfLag 0.6584 0.1551 4.24 0.00071 *** 313s capitalLag -0.1756 0.0311 -5.64 4.7e-05 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.509 on 15 degrees of freedom 313s Number of observations: 19 Degrees of Freedom: 15 313s SSR: 34.149 MSE: 2.277 Root MSE: 1.509 313s Multiple R-Squared: 0.807 Adjusted R-Squared: 0.769 313s 313s 313s 3SLS estimates for 'PrivateWages' (equation 3) 313s Model Formula: privWage ~ gnp + gnpLag + trend 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 0.8154 1.0961 0.74 0.46772 313s gnp 0.4250 0.0299 14.19 1.7e-10 *** 313s gnpLag 0.1731 0.0331 5.23 8.3e-05 *** 313s trend 0.1255 0.0283 4.43 0.00042 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 0.793 on 16 degrees of freedom 313s Number of observations: 20 Degrees of Freedom: 16 313s SSR: 10.054 MSE: 0.628 Root MSE: 0.793 313s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 313s 313s > residuals 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 -0.8680 -1.857 -1.21010 313s 3 -0.7217 0.170 0.43075 313s 4 -1.1353 0.762 1.30899 313s 5 0.0755 -1.565 -0.20270 313s 6 0.6348 0.367 -0.46842 313s 7 NA NA NA 313s 8 1.7953 1.230 -0.85853 313s 9 1.7924 0.568 0.20422 313s 10 NA 2.308 1.09889 313s 11 -0.5211 -0.972 -0.39427 313s 12 -1.5560 -0.960 0.39889 313s 13 NA NA -0.00934 313s 14 -0.2384 1.327 0.59990 313s 15 -0.7342 -0.292 0.48094 313s 16 -0.4331 0.068 0.16188 313s 17 1.8775 1.932 -0.70448 313s 18 -0.6294 -0.154 0.95616 313s 19 -0.4252 -3.400 -0.62489 313s 20 1.3682 0.589 -0.29589 313s 21 1.3155 0.271 -1.14466 313s 22 -1.4276 0.942 0.55941 313s > fitted 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 42.8 1.657 26.7 313s 3 45.7 1.730 28.9 313s 4 50.3 4.438 32.8 313s 5 50.5 4.565 34.1 313s 6 52.0 4.733 35.9 313s 7 NA NA NA 313s 8 54.4 2.970 38.8 313s 9 55.5 2.432 39.0 313s 10 NA 2.792 40.2 313s 11 55.5 1.972 38.3 313s 12 52.5 -2.440 34.1 313s 13 NA NA 29.0 313s 14 46.7 -6.427 27.9 313s 15 49.4 -2.708 30.1 313s 16 51.7 -1.368 33.0 313s 17 55.8 0.168 37.5 313s 18 59.3 2.154 40.0 313s 19 57.9 1.500 38.8 313s 20 60.2 0.711 41.9 313s 21 63.7 3.029 46.1 313s 22 71.1 3.958 52.7 313s > predict 313s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 313s 1 NA NA NA NA 313s 2 42.8 0.542 39.8 45.7 313s 3 45.7 0.612 42.7 48.7 313s 4 50.3 0.407 47.5 53.2 313s 5 50.5 0.478 47.6 53.4 313s 6 52.0 0.488 49.0 54.9 313s 7 NA NA NA NA 313s 8 54.4 0.394 51.5 57.3 313s 9 55.5 0.464 52.6 58.4 313s 10 NA NA NA NA 313s 11 55.5 0.811 52.3 58.8 313s 12 52.5 0.773 49.3 55.6 313s 13 NA NA NA NA 313s 14 46.7 0.666 43.7 49.8 313s 15 49.4 0.463 46.5 52.3 313s 16 51.7 0.381 48.9 54.6 313s 17 55.8 0.424 52.9 58.7 313s 18 59.3 0.359 56.5 62.2 313s 19 57.9 0.492 55.0 60.8 313s 20 60.2 0.501 57.3 63.2 313s 21 63.7 0.491 60.8 66.6 313s 22 71.1 0.749 68.0 74.3 313s Investment.pred Investment.se.fit Investment.lwr Investment.upr 313s 1 NA NA NA NA 313s 2 1.657 0.831 -2.015 5.329 313s 3 1.730 0.574 -1.711 5.171 313s 4 4.438 0.507 1.045 7.831 313s 5 4.565 0.426 1.223 7.907 313s 6 4.733 0.406 1.402 8.064 313s 7 NA NA NA NA 313s 8 2.970 0.334 -0.324 6.263 313s 9 2.432 0.501 -0.957 5.820 313s 10 2.792 0.544 -0.627 6.211 313s 11 1.972 0.937 -1.814 5.757 313s 12 -2.440 0.849 -6.131 1.250 313s 13 NA NA NA NA 313s 14 -6.427 0.836 -10.104 -2.750 313s 15 -2.708 0.477 -6.081 0.665 313s 16 -1.368 0.381 -4.685 1.949 313s 17 0.168 0.473 -3.202 3.538 313s 18 2.154 0.311 -1.130 5.438 313s 19 1.500 0.518 -1.900 4.900 313s 20 0.711 0.541 -2.705 4.127 313s 21 3.029 0.467 -0.338 6.395 313s 22 3.958 0.677 0.432 7.483 313s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 313s 1 NA NA NA NA 313s 2 26.7 0.315 24.9 28.5 313s 3 28.9 0.322 27.1 30.7 313s 4 32.8 0.330 31.0 34.6 313s 5 34.1 0.241 32.3 35.9 313s 6 35.9 0.249 34.1 37.6 313s 7 NA NA NA NA 313s 8 38.8 0.243 37.0 40.5 313s 9 39.0 0.231 37.2 40.7 313s 10 40.2 0.225 38.5 41.9 313s 11 38.3 0.305 36.5 40.1 313s 12 34.1 0.317 32.3 35.9 313s 13 29.0 0.382 27.1 30.9 313s 14 27.9 0.321 26.1 29.7 313s 15 30.1 0.316 28.3 31.9 313s 16 33.0 0.265 31.3 34.8 313s 17 37.5 0.270 35.7 39.3 313s 18 40.0 0.207 38.3 41.8 313s 19 38.8 0.311 37.0 40.6 313s 20 41.9 0.287 40.1 43.7 313s 21 46.1 0.300 44.3 47.9 313s 22 52.7 0.463 50.8 54.7 313s > model.frame 313s [1] TRUE 313s > model.matrix 313s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 313s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 313s [3] "Numeric: lengths (708, 684) differ" 313s > nobs 313s [1] 57 313s > linearHypothesis 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 45 1 1.95 0.17 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 45 1 2.71 0.11 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 46 313s 2 45 1 2.71 0.1 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 47 313s 2 45 2 1.78 0.18 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 47 313s 2 45 2 2.48 0.095 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 47 313s 2 45 2 4.95 0.084 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s > logLik 313s 'log Lik.' -71.2 (df=18) 313s 'log Lik.' -81.7 (df=18) 313s Estimating function 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_2 -3.6474 -51.112 313s Consumption_3 -0.7759 -12.930 313s Consumption_4 0.5383 9.982 313s Consumption_5 -2.0601 -41.756 313s Consumption_6 1.0597 20.157 313s Consumption_8 5.0108 88.416 313s Consumption_9 4.4804 84.874 313s Consumption_11 -2.2103 -37.003 313s Consumption_12 -2.9903 -39.999 313s Consumption_14 0.5609 5.622 313s Consumption_15 -2.2997 -28.756 313s Consumption_16 -1.9032 -27.562 313s Consumption_17 6.4249 95.811 313s Consumption_18 -0.7235 -14.050 313s Consumption_19 -5.0805 -97.079 313s Consumption_20 3.4333 60.632 313s Consumption_21 1.6077 32.791 313s Consumption_22 -1.1313 -25.654 313s Investment_2 1.6537 23.174 313s Investment_3 -0.1564 -2.607 313s Investment_4 -0.6420 -11.906 313s Investment_5 1.4113 28.605 313s Investment_6 -0.3557 -6.767 313s Investment_8 -1.1680 -20.610 313s Investment_9 -0.5634 -10.672 313s Investment_10 0.0000 0.000 313s Investment_11 0.9137 15.295 313s Investment_12 0.9272 12.402 313s Investment_14 -1.2036 -12.064 313s Investment_15 0.2779 3.475 313s Investment_16 -0.0439 -0.636 313s Investment_17 -1.7918 -26.720 313s Investment_18 0.2271 4.411 313s Investment_19 3.1278 59.767 313s Investment_20 -0.5790 -10.225 313s Investment_21 -0.2789 -5.690 313s Investment_22 -0.8484 -19.238 313s PrivateWages_2 -3.1568 -44.237 313s PrivateWages_3 1.1209 18.679 313s PrivateWages_4 2.7328 50.677 313s PrivateWages_5 -2.9712 -60.223 313s PrivateWages_6 -0.5212 -9.913 313s PrivateWages_8 1.7420 30.738 313s PrivateWages_9 1.9832 37.569 313s PrivateWages_10 0.0000 0.000 313s PrivateWages_11 -2.5151 -42.105 313s PrivateWages_12 -0.3611 -4.830 313s PrivateWages_13 0.0000 0.000 313s PrivateWages_14 3.2055 32.130 313s PrivateWages_15 -0.2814 -3.519 313s PrivateWages_16 -0.4078 -5.906 313s PrivateWages_17 2.6678 39.784 313s PrivateWages_18 0.0554 1.076 313s PrivateWages_19 -6.6416 -126.909 313s PrivateWages_20 1.4327 25.301 313s PrivateWages_21 -1.3598 -27.735 313s PrivateWages_22 2.0747 47.044 313s Consumption_corpProfLag Consumption_wages 313s Consumption_2 -46.322 -108.77 313s Consumption_3 -9.621 -24.71 313s Consumption_4 9.097 18.98 313s Consumption_5 -37.905 -79.52 313s Consumption_6 20.558 40.85 313s Consumption_8 98.211 200.48 313s Consumption_9 88.711 187.18 313s Consumption_11 -47.964 -95.27 313s Consumption_12 -46.648 -118.58 313s Consumption_14 3.926 18.69 313s Consumption_15 -25.757 -85.85 313s Consumption_16 -23.410 -76.40 313s Consumption_17 89.949 268.43 313s Consumption_18 -12.733 -34.44 313s Consumption_19 -87.892 -250.13 313s Consumption_20 52.529 166.71 313s Consumption_21 30.546 85.88 313s Consumption_22 -23.871 -68.78 313s Investment_2 21.002 49.32 313s Investment_3 -1.940 -4.98 313s Investment_4 -10.851 -22.64 313s Investment_5 25.967 54.47 313s Investment_6 -6.901 -13.71 313s Investment_8 -22.893 -46.73 313s Investment_9 -11.154 -23.53 313s Investment_10 0.000 0.00 313s Investment_11 19.827 39.38 313s Investment_12 14.464 36.77 313s Investment_14 -8.425 -40.11 313s Investment_15 3.113 10.38 313s Investment_16 -0.540 -1.76 313s Investment_17 -25.085 -74.86 313s Investment_18 3.997 10.81 313s Investment_19 54.111 153.99 313s Investment_20 -8.858 -28.11 313s Investment_21 -5.300 -14.90 313s Investment_22 -17.901 -51.58 313s PrivateWages_2 -40.091 -94.14 313s PrivateWages_3 13.899 35.70 313s PrivateWages_4 46.184 96.34 313s PrivateWages_5 -54.670 -114.69 313s PrivateWages_6 -10.110 -20.09 313s PrivateWages_8 34.144 69.70 313s PrivateWages_9 39.267 82.85 313s PrivateWages_10 0.000 0.00 313s PrivateWages_11 -54.578 -108.40 313s PrivateWages_12 -5.633 -14.32 313s PrivateWages_13 0.000 0.00 313s PrivateWages_14 22.438 106.83 313s PrivateWages_15 -3.152 -10.51 313s PrivateWages_16 -5.016 -16.37 313s PrivateWages_17 37.350 111.46 313s PrivateWages_18 0.975 2.64 313s PrivateWages_19 -114.899 -326.98 313s PrivateWages_20 21.920 69.57 313s PrivateWages_21 -25.836 -72.64 313s PrivateWages_22 43.775 126.12 313s Investment_(Intercept) Investment_corpProf 313s Consumption_2 1.8176 24.384 313s Consumption_3 0.3867 6.453 313s Consumption_4 -0.2682 -5.040 313s Consumption_5 1.0266 21.198 313s Consumption_6 -0.5281 -10.172 313s Consumption_8 -2.4970 -43.782 313s Consumption_9 -2.2327 -43.602 313s Consumption_11 1.1015 18.940 313s Consumption_12 1.4902 20.151 313s Consumption_14 -0.2795 -2.793 313s Consumption_15 1.1460 14.736 313s Consumption_16 0.9485 13.590 313s Consumption_17 -3.2018 -47.918 313s Consumption_18 0.3605 6.983 313s Consumption_19 2.5318 49.008 313s Consumption_20 -1.7109 -29.898 313s Consumption_21 -0.8012 -16.122 313s Consumption_22 0.5638 12.844 313s Investment_2 -2.3696 -31.787 313s Investment_3 0.2241 3.741 313s Investment_4 0.9200 17.284 313s Investment_5 -2.0221 -41.754 313s Investment_6 0.5097 9.819 313s Investment_8 1.6736 29.344 313s Investment_9 0.8072 15.764 313s Investment_10 2.9560 59.913 313s Investment_11 -1.3092 -22.510 313s Investment_12 -1.3285 -17.964 313s Investment_14 1.7246 17.233 313s Investment_15 -0.3982 -5.120 313s Investment_16 0.0630 0.902 313s Investment_17 2.5674 38.424 313s Investment_18 -0.3254 -6.303 313s Investment_19 -4.4817 -86.752 313s Investment_20 0.8296 14.497 313s Investment_21 0.3997 8.043 313s Investment_22 1.2156 27.693 313s PrivateWages_2 1.9315 25.910 313s PrivateWages_3 -0.6858 -11.446 313s PrivateWages_4 -1.6720 -31.413 313s PrivateWages_5 1.8179 37.537 313s PrivateWages_6 0.3189 6.142 313s PrivateWages_8 -1.0659 -18.688 313s PrivateWages_9 -1.2134 -23.696 313s PrivateWages_10 -2.2443 -45.488 313s PrivateWages_11 1.5389 26.460 313s PrivateWages_12 0.2209 2.988 313s PrivateWages_13 0.0000 0.000 313s PrivateWages_14 -1.9613 -19.598 313s PrivateWages_15 0.1722 2.214 313s PrivateWages_16 0.2495 3.576 313s PrivateWages_17 -1.6323 -24.429 313s PrivateWages_18 -0.0339 -0.657 313s PrivateWages_19 4.0636 78.659 313s PrivateWages_20 -0.8766 -15.318 313s PrivateWages_21 0.8320 16.742 313s PrivateWages_22 -1.2694 -28.917 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_2 23.084 332.27 313s Consumption_3 4.795 70.60 313s Consumption_4 -4.533 -49.49 313s Consumption_5 18.890 194.75 313s Consumption_6 -10.245 -101.76 313s Consumption_8 -48.942 -507.90 313s Consumption_9 -44.208 -463.52 313s Consumption_11 23.902 237.59 313s Consumption_12 23.247 322.92 313s Consumption_14 -1.957 -57.89 313s Consumption_15 12.836 231.50 313s Consumption_16 11.666 188.74 313s Consumption_17 -44.825 -632.99 313s Consumption_18 6.345 72.04 313s Consumption_19 43.800 510.92 313s Consumption_20 -26.177 -342.01 313s Consumption_21 -15.222 -161.20 313s Consumption_22 11.896 115.30 313s Investment_2 -30.093 -433.16 313s Investment_3 2.779 40.93 313s Investment_4 15.547 169.73 313s Investment_5 -37.208 -383.60 313s Investment_6 9.888 98.22 313s Investment_8 32.803 340.41 313s Investment_9 15.983 167.58 313s Investment_10 62.371 622.53 313s Investment_11 -28.409 -282.39 313s Investment_12 -20.724 -287.88 313s Investment_14 12.072 357.16 313s Investment_15 -4.460 -80.44 313s Investment_16 0.774 12.53 313s Investment_17 35.944 507.58 313s Investment_18 -5.727 -65.02 313s Investment_19 -77.534 -904.41 313s Investment_20 12.693 165.84 313s Investment_21 7.594 80.42 313s Investment_22 25.650 248.60 313s PrivateWages_2 24.530 353.07 313s PrivateWages_3 -8.504 -125.23 313s PrivateWages_4 -28.257 -308.49 313s PrivateWages_5 33.450 344.86 313s PrivateWages_6 6.186 61.45 313s PrivateWages_8 -20.891 -216.79 313s PrivateWages_9 -24.025 -251.90 313s PrivateWages_10 -47.355 -472.65 313s PrivateWages_11 33.393 331.93 313s PrivateWages_12 3.447 47.88 313s PrivateWages_13 0.000 0.00 313s PrivateWages_14 -13.729 -406.18 313s PrivateWages_15 1.929 34.78 313s PrivateWages_16 3.069 49.66 313s PrivateWages_17 -22.852 -322.71 313s PrivateWages_18 -0.597 -6.77 313s PrivateWages_19 70.300 820.04 313s PrivateWages_20 -13.412 -175.23 313s PrivateWages_21 15.807 167.39 313s PrivateWages_22 -26.784 -259.59 313s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 313s Consumption_2 -3.6123 -170.03 -162.19 313s Consumption_3 -0.7684 -38.10 -35.04 313s Consumption_4 0.5331 30.14 26.71 313s Consumption_5 -2.0403 -123.82 -116.70 313s Consumption_6 1.0495 63.61 59.93 313s Consumption_8 4.9625 297.74 317.60 313s Consumption_9 4.4373 276.30 285.76 313s Consumption_11 -2.1891 -139.47 -146.67 313s Consumption_12 -2.9615 -162.39 -181.24 313s Consumption_14 0.5555 23.40 24.61 313s Consumption_15 -2.2776 -116.65 -102.72 313s Consumption_16 -1.8849 -104.31 -93.68 313s Consumption_17 6.3631 365.20 346.15 313s Consumption_18 -0.7165 -48.13 -44.93 313s Consumption_19 -5.0316 -344.73 -327.05 313s Consumption_20 3.4002 227.29 207.07 313s Consumption_21 1.5922 119.20 110.66 313s Consumption_22 -1.1205 -97.34 -84.82 313s Investment_2 2.0108 94.65 90.29 313s Investment_3 -0.1902 -9.43 -8.67 313s Investment_4 -0.7807 -44.14 -39.11 313s Investment_5 1.7160 104.14 98.16 313s Investment_6 -0.4326 -26.22 -24.70 313s Investment_8 -1.4203 -85.21 -90.90 313s Investment_9 -0.6850 -42.65 -44.11 313s Investment_10 -2.5085 -161.97 -161.80 313s Investment_11 1.1110 70.78 74.44 313s Investment_12 1.1274 61.82 69.00 313s Investment_14 -1.4635 -61.65 -64.83 313s Investment_15 0.3379 17.31 15.24 313s Investment_16 -0.0534 -2.96 -2.66 313s Investment_17 -2.1788 -125.05 -118.52 313s Investment_18 0.2762 18.55 17.32 313s Investment_19 3.8033 260.57 247.21 313s Investment_20 -0.7040 -47.06 -42.87 313s Investment_21 -0.3392 -25.39 -23.57 313s Investment_22 -1.0316 -89.62 -78.09 313s PrivateWages_2 -7.1301 -335.61 -320.14 313s PrivateWages_3 2.5317 125.52 115.44 313s PrivateWages_4 6.1723 349.00 309.23 313s PrivateWages_5 -6.7109 -407.26 -383.86 313s PrivateWages_6 -1.1771 -71.34 -67.21 313s PrivateWages_8 3.9346 236.07 251.82 313s PrivateWages_9 4.4793 278.92 288.47 313s PrivateWages_10 8.2849 534.95 534.38 313s PrivateWages_11 -5.6807 -361.93 -380.61 313s PrivateWages_12 -0.8156 -44.72 -49.92 313s PrivateWages_13 -4.4579 -209.42 -238.05 313s PrivateWages_14 7.2401 305.01 320.74 313s PrivateWages_15 -0.6357 -32.56 -28.67 313s PrivateWages_16 -0.9212 -50.98 -45.78 313s PrivateWages_17 6.0257 345.84 327.80 313s PrivateWages_18 0.1252 8.41 7.85 313s PrivateWages_19 -15.0009 -1027.75 -975.06 313s PrivateWages_20 3.2360 216.31 197.07 313s PrivateWages_21 -3.0713 -229.93 -213.45 313s PrivateWages_22 4.6859 407.11 354.72 313s PrivateWages_trend 313s Consumption_2 36.123 313s Consumption_3 6.916 313s Consumption_4 -4.265 313s Consumption_5 14.282 313s Consumption_6 -6.297 313s Consumption_8 -19.850 313s Consumption_9 -13.312 313s Consumption_11 2.189 313s Consumption_12 0.000 313s Consumption_14 1.111 313s Consumption_15 -6.833 313s Consumption_16 -7.540 313s Consumption_17 31.815 313s Consumption_18 -4.299 313s Consumption_19 -35.221 313s Consumption_20 27.202 313s Consumption_21 14.330 313s Consumption_22 -11.205 313s Investment_2 -20.108 313s Investment_3 1.712 313s Investment_4 6.246 313s Investment_5 -12.012 313s Investment_6 2.595 313s Investment_8 5.681 313s Investment_9 2.055 313s Investment_10 5.017 313s Investment_11 -1.111 313s Investment_12 0.000 313s Investment_14 -2.927 313s Investment_15 1.014 313s Investment_16 -0.214 313s Investment_17 -10.894 313s Investment_18 1.657 313s Investment_19 26.623 313s Investment_20 -5.632 313s Investment_21 -3.053 313s Investment_22 -10.316 313s PrivateWages_2 71.301 313s PrivateWages_3 -22.785 313s PrivateWages_4 -49.379 313s PrivateWages_5 46.976 313s PrivateWages_6 7.063 313s PrivateWages_8 -15.738 313s PrivateWages_9 -13.438 313s PrivateWages_10 -16.570 313s PrivateWages_11 5.681 313s PrivateWages_12 0.000 313s PrivateWages_13 -4.458 313s PrivateWages_14 14.480 313s PrivateWages_15 -1.907 313s PrivateWages_16 -3.685 313s PrivateWages_17 30.129 313s PrivateWages_18 0.751 313s PrivateWages_19 -105.007 313s PrivateWages_20 25.888 313s PrivateWages_21 -27.641 313s PrivateWages_22 46.859 313s [1] TRUE 313s > Bread 313s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 313s [1,] 132.9647 -4.1876 0.7762 313s [2,] -4.1876 1.2160 -0.6687 313s [3,] 0.7762 -0.6687 0.7219 313s [4,] -1.6897 -0.1344 -0.0278 313s [5,] 101.6483 3.2473 3.4997 313s [6,] -4.3150 0.5140 -0.4474 313s [7,] 1.5566 -0.3374 0.4240 313s [8,] -0.2539 -0.0329 -0.0138 313s [9,] -35.7522 0.3296 1.6708 313s [10,] 0.5355 -0.0797 0.0478 313s [11,] 0.0459 0.0759 -0.0780 313s [12,] 0.1973 0.0481 0.0250 313s Consumption_wages Investment_(Intercept) Investment_corpProf 313s [1,] -1.689687 101.65 -4.32e+00 313s [2,] -0.134421 3.25 5.14e-01 313s [3,] -0.027837 3.50 -4.47e-01 313s [4,] 0.106098 -5.00 6.63e-02 313s [5,] -4.996393 2449.02 -4.26e+01 313s [6,] 0.066338 -42.57 1.86e+00 313s [7,] -0.064579 34.21 -1.44e+00 313s [8,] 0.024569 -11.36 1.70e-01 313s [9,] 0.047220 27.91 -2.66e-01 313s [10,] 0.000172 1.31 3.12e-04 313s [11,] -0.000827 -1.84 4.41e-03 313s [12,] -0.034079 -0.80 1.58e-02 313s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 313s [1,] 1.55659 -0.25392 -35.7522 313s [2,] -0.33742 -0.03292 0.3296 313s [3,] 0.42396 -0.01383 1.6708 313s [4,] -0.06458 0.02457 0.0472 313s [5,] 34.20897 -11.35519 27.9136 313s [6,] -1.43523 0.17002 -0.2656 313s [7,] 1.37137 -0.15991 -0.3976 313s [8,] -0.15991 0.05521 -0.0847 313s [9,] -0.39759 -0.08475 68.4821 313s [10,] 0.00601 -0.00701 -0.3279 313s [11,] 0.00088 0.00875 -0.8283 313s [12,] -0.02279 0.00445 0.7887 313s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 313s [1,] 0.535460 0.045866 0.197271 313s [2,] -0.079666 0.075947 0.048142 313s [3,] 0.047829 -0.078006 0.025001 313s [4,] 0.000172 -0.000827 -0.034079 313s [5,] 1.306914 -1.841775 -0.800037 313s [6,] 0.000312 0.004408 0.015824 313s [7,] 0.006007 0.000880 -0.022790 313s [8,] -0.007006 0.008751 0.004448 313s [9,] -0.327909 -0.828330 0.788744 313s [10,] 0.051096 -0.046839 -0.013933 313s [11,] -0.046839 0.062505 0.000532 313s [12,] -0.013933 0.000532 0.045663 313s > 313s > # I3SLS 313s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 313s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 313s > summary 313s 313s systemfit results 313s method: iterated 3SLS 313s 313s convergence achieved after 9 iterations 313s 313s N DF SSR detRCov OLS-R2 McElroy-R2 313s system 57 45 75 0.422 0.959 0.993 313s 313s N DF SSR MSE RMSE R2 Adj R2 313s Consumption 18 14 22.7 1.622 1.273 0.973 0.968 313s Investment 19 15 42.1 2.809 1.676 0.762 0.715 313s PrivateWages 20 16 10.2 0.638 0.799 0.987 0.985 313s 313s The covariance matrix of the residuals used for estimation 313s Consumption Investment PrivateWages 313s Consumption 1.261 0.675 -0.439 313s Investment 0.675 1.949 0.237 313s PrivateWages -0.439 0.237 0.503 313s 313s The covariance matrix of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.261 0.675 -0.439 313s Investment 0.675 1.949 0.237 313s PrivateWages -0.439 0.237 0.503 313s 313s The correlations of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.000 0.431 -0.550 313s Investment 0.431 1.000 0.239 313s PrivateWages -0.550 0.239 1.000 313s 313s 313s 3SLS estimates for 'Consumption' (equation 1) 313s Model Formula: consump ~ corpProf + corpProfLag + wages 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 18.5887 1.5250 12.19 7.6e-09 *** 313s corpProf -0.0438 0.1441 -0.30 0.77 313s corpProfLag 0.1456 0.1109 1.31 0.21 313s wages 0.8141 0.0428 19.01 2.1e-11 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.273 on 14 degrees of freedom 313s Number of observations: 18 Degrees of Freedom: 14 313s SSR: 22.704 MSE: 1.622 Root MSE: 1.273 313s Multiple R-Squared: 0.973 Adjusted R-Squared: 0.968 313s 313s 313s 3SLS estimates for 'Investment' (equation 2) 313s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 29.4725 7.6857 3.83 0.0016 ** 313s corpProf -0.0183 0.2154 -0.09 0.9333 313s corpProfLag 0.7195 0.1850 3.89 0.0015 ** 313s capitalLag -0.1985 0.0366 -5.43 6.9e-05 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.676 on 15 degrees of freedom 313s Number of observations: 19 Degrees of Freedom: 15 313s SSR: 42.136 MSE: 2.809 Root MSE: 1.676 313s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.715 313s 313s 313s 3SLS estimates for 'PrivateWages' (equation 3) 313s Model Formula: privWage ~ gnp + gnpLag + trend 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 0.5385 1.1055 0.49 0.63277 313s gnp 0.4251 0.0287 14.80 9.3e-11 *** 313s gnpLag 0.1776 0.0322 5.51 4.7e-05 *** 313s trend 0.1211 0.0283 4.28 0.00057 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 0.799 on 16 degrees of freedom 313s Number of observations: 20 Degrees of Freedom: 16 313s SSR: 10.204 MSE: 0.638 Root MSE: 0.799 313s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 313s 313s > residuals 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 -0.9524 -2.2888 -1.1837 313s 3 -0.8681 0.0698 0.4581 313s 4 -1.1653 0.5368 1.3199 313s 5 0.0601 -1.6917 -0.2194 313s 6 0.6426 0.2972 -0.4805 313s 7 NA NA NA 313s 8 1.8394 1.3723 -0.8931 313s 9 1.8275 0.8861 0.1723 313s 10 NA 2.6574 1.0707 313s 11 -0.3387 -0.9736 -0.4288 313s 12 -1.4550 -0.8630 0.3956 313s 13 NA NA 0.0277 313s 14 -0.3782 1.7151 0.6823 313s 15 -0.7768 -0.1993 0.5638 313s 16 -0.4606 0.1448 0.2281 313s 17 1.8605 2.1295 -0.6557 313s 18 -0.5262 -0.1493 0.9718 313s 19 -0.3047 -3.4730 -0.6148 313s 20 1.3992 0.8566 -0.2636 313s 21 1.4216 0.4910 -1.1472 313s 22 -1.2431 1.2792 0.5323 313s > fitted 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 42.9 2.0888 26.7 313s 3 45.9 1.8302 28.8 313s 4 50.4 4.6632 32.8 313s 5 50.5 4.6917 34.1 313s 6 52.0 4.8028 35.9 313s 7 NA NA NA 313s 8 54.4 2.8277 38.8 313s 9 55.5 2.1139 39.0 313s 10 NA 2.4426 40.2 313s 11 55.3 1.9736 38.3 313s 12 52.4 -2.5370 34.1 313s 13 NA NA 29.0 313s 14 46.9 -6.8151 27.8 313s 15 49.5 -2.8007 30.0 313s 16 51.8 -1.4448 33.0 313s 17 55.8 -0.0295 37.5 313s 18 59.2 2.1493 40.0 313s 19 57.8 1.5730 38.8 313s 20 60.2 0.4434 41.9 313s 21 63.6 2.8090 46.1 313s 22 70.9 3.6208 52.8 313s > predict 313s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 313s 1 NA NA NA NA 313s 2 42.9 0.541 41.8 43.9 313s 3 45.9 0.608 44.6 47.1 313s 4 50.4 0.403 49.6 51.2 313s 5 50.5 0.472 49.6 51.5 313s 6 52.0 0.481 51.0 52.9 313s 7 NA NA NA NA 313s 8 54.4 0.388 53.6 55.1 313s 9 55.5 0.458 54.6 56.4 313s 10 NA NA NA NA 313s 11 55.3 0.795 53.7 56.9 313s 12 52.4 0.762 50.8 53.9 313s 13 NA NA NA NA 313s 14 46.9 0.663 45.5 48.2 313s 15 49.5 0.462 48.5 50.4 313s 16 51.8 0.381 51.0 52.5 313s 17 55.8 0.423 55.0 56.7 313s 18 59.2 0.355 58.5 59.9 313s 19 57.8 0.484 56.8 58.8 313s 20 60.2 0.500 59.2 61.2 313s 21 63.6 0.490 62.6 64.6 313s 22 70.9 0.747 69.4 72.4 313s Investment.pred Investment.se.fit Investment.lwr Investment.upr 313s 1 NA NA NA NA 313s 2 2.0888 0.985 0.105 4.072 313s 3 1.8302 0.708 0.404 3.257 313s 4 4.6632 0.612 3.430 5.897 313s 5 4.6917 0.519 3.645 5.738 313s 6 4.8028 0.498 3.800 5.806 313s 7 NA NA NA NA 313s 8 2.8277 0.410 2.003 3.653 313s 9 2.1139 0.599 0.908 3.320 313s 10 2.4426 0.651 1.131 3.754 313s 11 1.9736 1.138 -0.320 4.267 313s 12 -2.5370 1.038 -4.627 -0.447 313s 13 NA NA NA NA 313s 14 -6.8151 1.011 -8.851 -4.779 313s 15 -2.8007 0.587 -3.984 -1.617 313s 16 -1.4448 0.470 -2.392 -0.498 313s 17 -0.0295 0.573 -1.183 1.124 313s 18 2.1493 0.380 1.384 2.915 313s 19 1.5730 0.624 0.315 2.831 313s 20 0.4434 0.649 -0.864 1.751 313s 21 2.8090 0.565 1.671 3.947 313s 22 3.6208 0.814 1.982 5.260 313s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 313s 1 NA NA NA NA 313s 2 26.7 0.322 26.0 27.3 313s 3 28.8 0.328 28.2 29.5 313s 4 32.8 0.332 32.1 33.4 313s 5 34.1 0.244 33.6 34.6 313s 6 35.9 0.252 35.4 36.4 313s 7 NA NA NA NA 313s 8 38.8 0.246 38.3 39.3 313s 9 39.0 0.234 38.6 39.5 313s 10 40.2 0.230 39.8 40.7 313s 11 38.3 0.299 37.7 38.9 313s 12 34.1 0.304 33.5 34.7 313s 13 29.0 0.366 28.2 29.7 313s 14 27.8 0.321 27.2 28.5 313s 15 30.0 0.317 29.4 30.7 313s 16 33.0 0.266 32.4 33.5 313s 17 37.5 0.270 36.9 38.0 313s 18 40.0 0.211 39.6 40.5 313s 19 38.8 0.305 38.2 39.4 313s 20 41.9 0.290 41.3 42.4 313s 21 46.1 0.309 45.5 46.8 313s 22 52.8 0.468 51.8 53.7 313s > model.frame 313s [1] TRUE 313s > model.matrix 313s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 313s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 313s [3] "Numeric: lengths (708, 684) differ" 313s > nobs 313s [1] 57 313s > linearHypothesis 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 45 1 2.17 0.15 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 45 1 2.84 0.099 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 46 313s 2 45 1 2.84 0.092 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 47 313s 2 45 2 2.45 0.098 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 47 313s 2 45 2 3.2 0.05 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 47 313s 2 45 2 6.4 0.041 * 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s > logLik 313s 'log Lik.' -72.7 (df=18) 313s 'log Lik.' -83.9 (df=18) 313s Estimating function 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_2 -4.8293 -67.67 313s Consumption_3 -1.2969 -21.61 313s Consumption_4 0.5735 10.64 313s Consumption_5 -2.6416 -53.54 313s Consumption_6 1.4014 26.66 313s Consumption_8 6.4885 114.49 313s Consumption_9 5.8062 109.99 313s Consumption_11 -2.4210 -40.53 313s Consumption_12 -3.6335 -48.60 313s Consumption_14 0.4385 4.39 313s Consumption_15 -2.9914 -37.40 313s Consumption_16 -2.4677 -35.74 313s Consumption_17 8.1448 121.46 313s Consumption_18 -0.7823 -15.19 313s Consumption_19 -6.2524 -119.47 313s Consumption_20 4.4447 78.49 313s Consumption_21 2.3016 46.94 313s Consumption_22 -1.0069 -22.83 313s Investment_2 2.3888 33.48 313s Investment_3 -0.0694 -1.16 313s Investment_4 -0.5723 -10.61 313s Investment_5 1.7561 35.59 313s Investment_6 -0.2966 -5.64 313s Investment_8 -1.4003 -24.71 313s Investment_9 -0.9021 -17.09 313s Investment_10 0.0000 0.00 313s Investment_11 0.9937 16.63 313s Investment_12 0.8671 11.60 313s Investment_14 -1.7814 -17.86 313s Investment_15 0.1989 2.49 313s Investment_16 -0.1587 -2.30 313s Investment_17 -2.1900 -32.66 313s Investment_18 0.1172 2.28 313s Investment_19 3.5762 68.34 313s Investment_20 -0.8719 -15.40 313s Investment_21 -0.4978 -10.15 313s Investment_22 -1.3322 -30.21 313s PrivateWages_2 -4.3522 -60.99 313s PrivateWages_3 1.6337 27.22 313s PrivateWages_4 3.8487 71.37 313s PrivateWages_5 -4.1966 -85.06 313s PrivateWages_6 -0.7579 -14.42 313s PrivateWages_8 2.3542 41.54 313s PrivateWages_9 2.6975 51.10 313s PrivateWages_10 0.0000 0.00 313s PrivateWages_11 -3.6015 -60.29 313s PrivateWages_12 -0.5133 -6.87 313s PrivateWages_13 0.0000 0.00 313s PrivateWages_14 4.6825 46.94 313s PrivateWages_15 -0.1944 -2.43 313s PrivateWages_16 -0.4112 -5.96 313s PrivateWages_17 3.8500 57.41 313s PrivateWages_18 0.1148 2.23 313s PrivateWages_19 -9.2669 -177.08 313s PrivateWages_20 2.0821 36.77 313s PrivateWages_21 -1.9079 -38.91 313s PrivateWages_22 2.8370 64.33 313s Consumption_corpProfLag Consumption_wages 313s Consumption_2 -61.332 -144.02 313s Consumption_3 -16.082 -41.30 313s Consumption_4 9.693 20.22 313s Consumption_5 -48.605 -101.97 313s Consumption_6 27.187 54.02 313s Consumption_8 127.174 259.60 313s Consumption_9 114.963 242.56 313s Consumption_11 -52.537 -104.35 313s Consumption_12 -56.683 -144.08 313s Consumption_14 3.069 14.61 313s Consumption_15 -33.504 -111.68 313s Consumption_16 -30.352 -99.06 313s Consumption_17 114.027 340.28 313s Consumption_18 -13.768 -37.24 313s Consumption_19 -108.167 -307.82 313s Consumption_20 68.004 215.82 313s Consumption_21 43.729 122.95 313s Consumption_22 -21.245 -61.21 313s Investment_2 30.338 71.24 313s Investment_3 -0.861 -2.21 313s Investment_4 -9.672 -20.18 313s Investment_5 32.311 67.78 313s Investment_6 -5.754 -11.43 313s Investment_8 -27.445 -56.02 313s Investment_9 -17.861 -37.69 313s Investment_10 0.000 0.00 313s Investment_11 21.563 42.83 313s Investment_12 13.527 34.39 313s Investment_14 -12.470 -59.37 313s Investment_15 2.228 7.43 313s Investment_16 -1.952 -6.37 313s Investment_17 -30.659 -91.49 313s Investment_18 2.063 5.58 313s Investment_19 61.869 176.07 313s Investment_20 -13.340 -42.34 313s Investment_21 -9.458 -26.59 313s Investment_22 -28.109 -80.99 313s PrivateWages_2 -55.273 -129.79 313s PrivateWages_3 20.257 52.03 313s PrivateWages_4 65.044 135.69 313s PrivateWages_5 -77.218 -161.99 313s PrivateWages_6 -14.704 -29.21 313s PrivateWages_8 46.143 94.19 313s PrivateWages_9 53.410 112.69 313s PrivateWages_10 0.000 0.00 313s PrivateWages_11 -78.152 -155.23 313s PrivateWages_12 -8.008 -20.36 313s PrivateWages_13 0.000 0.00 313s PrivateWages_14 32.778 156.05 313s PrivateWages_15 -2.178 -7.26 313s PrivateWages_16 -5.058 -16.51 313s PrivateWages_17 53.901 160.85 313s PrivateWages_18 2.020 5.46 313s PrivateWages_19 -160.318 -456.23 313s PrivateWages_20 31.857 101.10 313s PrivateWages_21 -36.250 -101.92 313s PrivateWages_22 59.861 172.47 313s Investment_(Intercept) Investment_corpProf 313s Consumption_2 2.3171 31.08 313s Consumption_3 0.6223 10.39 313s Consumption_4 -0.2752 -5.17 313s Consumption_5 1.2675 26.17 313s Consumption_6 -0.6724 -12.95 313s Consumption_8 -3.1132 -54.59 313s Consumption_9 -2.7858 -54.40 313s Consumption_11 1.1616 19.97 313s Consumption_12 1.7434 23.57 313s Consumption_14 -0.2104 -2.10 313s Consumption_15 1.4353 18.46 313s Consumption_16 1.1840 16.97 313s Consumption_17 -3.9079 -58.49 313s Consumption_18 0.3753 7.27 313s Consumption_19 2.9999 58.07 313s Consumption_20 -2.1326 -37.27 313s Consumption_21 -1.1043 -22.22 313s Consumption_22 0.4831 11.01 313s Investment_2 -2.3817 -31.95 313s Investment_3 0.0692 1.16 313s Investment_4 0.5706 10.72 313s Investment_5 -1.7509 -36.15 313s Investment_6 0.2957 5.70 313s Investment_8 1.3961 24.48 313s Investment_9 0.8994 17.56 313s Investment_10 2.7604 55.95 313s Investment_11 -0.9907 -17.04 313s Investment_12 -0.8646 -11.69 313s Investment_14 1.7761 17.75 313s Investment_15 -0.1983 -2.55 313s Investment_16 0.1582 2.27 313s Investment_17 2.1835 32.68 313s Investment_18 -0.1169 -2.26 313s Investment_19 -3.5657 -69.02 313s Investment_20 0.8693 15.19 313s Investment_21 0.4963 9.99 313s Investment_22 1.3282 30.26 313s PrivateWages_2 2.5510 34.22 313s PrivateWages_3 -0.9575 -15.98 313s PrivateWages_4 -2.2559 -42.38 313s PrivateWages_5 2.4598 50.79 313s PrivateWages_6 0.4442 8.56 313s PrivateWages_8 -1.3799 -24.19 313s PrivateWages_9 -1.5811 -30.88 313s PrivateWages_10 -2.9678 -60.15 313s PrivateWages_11 2.1109 36.30 313s PrivateWages_12 0.3009 4.07 313s PrivateWages_13 0.0000 0.00 313s PrivateWages_14 -2.7446 -27.43 313s PrivateWages_15 0.1140 1.47 313s PrivateWages_16 0.2410 3.45 313s PrivateWages_17 -2.2567 -33.77 313s PrivateWages_18 -0.0673 -1.30 313s PrivateWages_19 5.4317 105.14 313s PrivateWages_20 -1.2204 -21.33 313s PrivateWages_21 1.1183 22.50 313s PrivateWages_22 -1.6629 -37.88 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_2 29.428 423.6 313s Consumption_3 7.716 113.6 313s Consumption_4 -4.651 -50.8 313s Consumption_5 23.321 240.4 313s Consumption_6 -13.045 -129.6 313s Consumption_8 -61.019 -633.2 313s Consumption_9 -55.160 -578.3 313s Consumption_11 25.207 250.6 313s Consumption_12 27.197 377.8 313s Consumption_14 -1.473 -43.6 313s Consumption_15 16.075 289.9 313s Consumption_16 14.563 235.6 313s Consumption_17 -54.711 -772.6 313s Consumption_18 6.606 75.0 313s Consumption_19 51.899 605.4 313s Consumption_20 -32.629 -426.3 313s Consumption_21 -20.982 -222.2 313s Consumption_22 10.194 98.8 313s Investment_2 -30.248 -435.4 313s Investment_3 0.858 12.6 313s Investment_4 9.643 105.3 313s Investment_5 -32.216 -332.1 313s Investment_6 5.737 57.0 313s Investment_8 27.364 284.0 313s Investment_9 17.808 186.7 313s Investment_10 58.244 581.3 313s Investment_11 -21.499 -213.7 313s Investment_12 -13.487 -187.4 313s Investment_14 12.433 367.8 313s Investment_15 -2.221 -40.1 313s Investment_16 1.946 31.5 313s Investment_17 30.569 431.7 313s Investment_18 -2.057 -23.4 313s Investment_19 -61.686 -719.5 313s Investment_20 13.301 173.8 313s Investment_21 9.430 99.9 313s Investment_22 28.026 271.6 313s PrivateWages_2 32.397 466.3 313s PrivateWages_3 -11.874 -174.8 313s PrivateWages_4 -38.124 -416.2 313s PrivateWages_5 45.260 466.6 313s PrivateWages_6 8.618 85.6 313s PrivateWages_8 -27.046 -280.7 313s PrivateWages_9 -31.306 -328.2 313s PrivateWages_10 -62.621 -625.0 313s PrivateWages_11 45.808 455.3 313s PrivateWages_12 4.694 65.2 313s PrivateWages_13 0.000 0.0 313s PrivateWages_14 -19.212 -568.4 313s PrivateWages_15 1.276 23.0 313s PrivateWages_16 2.965 48.0 313s PrivateWages_17 -31.593 -446.1 313s PrivateWages_18 -1.184 -13.4 313s PrivateWages_19 93.968 1096.1 313s PrivateWages_20 -18.672 -244.0 313s PrivateWages_21 21.247 225.0 313s PrivateWages_22 -35.087 -340.1 313s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 313s Consumption_2 -5.2993 -249.44 -237.94 313s Consumption_3 -1.4232 -70.56 -64.90 313s Consumption_4 0.6293 35.58 31.53 313s Consumption_5 -2.8987 -175.91 -165.80 313s Consumption_6 1.5378 93.21 87.81 313s Consumption_8 7.1199 427.18 455.67 313s Consumption_9 6.3712 396.73 410.31 313s Consumption_11 -2.6567 -169.26 -178.00 313s Consumption_12 -3.9871 -218.62 -244.01 313s Consumption_14 0.4811 20.27 21.31 313s Consumption_15 -3.2826 -168.12 -148.04 313s Consumption_16 -2.7078 -149.85 -134.58 313s Consumption_17 8.9374 512.95 486.20 313s Consumption_18 -0.8584 -57.66 -53.82 313s Consumption_19 -6.8609 -470.06 -445.96 313s Consumption_20 4.8772 326.02 297.02 313s Consumption_21 2.5255 189.08 175.52 313s Consumption_22 -1.1049 -95.99 -83.64 313s Investment_2 3.2022 150.73 143.78 313s Investment_3 -0.0931 -4.61 -4.24 313s Investment_4 -0.7671 -43.38 -38.43 313s Investment_5 2.3540 142.85 134.65 313s Investment_6 -0.3976 -24.10 -22.70 313s Investment_8 -1.8770 -112.62 -120.13 313s Investment_9 -1.2092 -75.30 -77.87 313s Investment_10 -3.7113 -239.64 -239.38 313s Investment_11 1.3320 84.87 89.25 313s Investment_12 1.1624 63.74 71.14 313s Investment_14 -2.3880 -100.60 -105.79 313s Investment_15 0.2667 13.66 12.03 313s Investment_16 -0.2127 -11.77 -10.57 313s Investment_17 -2.9356 -168.49 -159.70 313s Investment_18 0.1571 10.56 9.85 313s Investment_19 4.7939 328.45 311.61 313s Investment_20 -1.1688 -78.13 -71.18 313s Investment_21 -0.6673 -49.96 -46.38 313s Investment_22 -1.7858 -155.15 -135.18 313s PrivateWages_2 -8.5877 -404.22 -385.59 313s PrivateWages_3 3.2235 159.82 146.99 313s PrivateWages_4 7.5943 429.40 380.48 313s PrivateWages_5 -8.2808 -502.53 -473.66 313s PrivateWages_6 -1.4955 -90.64 -85.39 313s PrivateWages_8 4.6454 278.71 297.31 313s PrivateWages_9 5.3226 331.43 342.78 313s PrivateWages_10 9.9910 645.11 644.42 313s PrivateWages_11 -7.1064 -452.76 -476.13 313s PrivateWages_12 -1.0129 -55.54 -61.99 313s PrivateWages_13 -5.2725 -247.69 -281.55 313s PrivateWages_14 9.2395 389.24 409.31 313s PrivateWages_15 -0.3837 -19.65 -17.30 313s PrivateWages_16 -0.8115 -44.91 -40.33 313s PrivateWages_17 7.5969 436.02 413.27 313s PrivateWages_18 0.2264 15.21 14.20 313s PrivateWages_19 -18.2855 -1252.79 -1188.56 313s PrivateWages_20 4.1085 274.63 250.21 313s PrivateWages_21 -3.7647 -281.85 -261.64 313s PrivateWages_22 5.5980 486.35 423.77 313s PrivateWages_trend 313s Consumption_2 52.993 313s Consumption_3 12.808 313s Consumption_4 -5.035 313s Consumption_5 20.291 313s Consumption_6 -9.227 313s Consumption_8 -28.480 313s Consumption_9 -19.114 313s Consumption_11 2.657 313s Consumption_12 0.000 313s Consumption_14 0.962 313s Consumption_15 -9.848 313s Consumption_16 -10.831 313s Consumption_17 44.687 313s Consumption_18 -5.151 313s Consumption_19 -48.026 313s Consumption_20 39.018 313s Consumption_21 22.730 313s Consumption_22 -11.049 313s Investment_2 -32.022 313s Investment_3 0.838 313s Investment_4 6.137 313s Investment_5 -16.478 313s Investment_6 2.386 313s Investment_8 7.508 313s Investment_9 3.628 313s Investment_10 7.423 313s Investment_11 -1.332 313s Investment_12 0.000 313s Investment_14 -4.776 313s Investment_15 0.800 313s Investment_16 -0.851 313s Investment_17 -14.678 313s Investment_18 0.943 313s Investment_19 33.558 313s Investment_20 -9.351 313s Investment_21 -6.006 313s Investment_22 -17.858 313s PrivateWages_2 85.877 313s PrivateWages_3 -29.012 313s PrivateWages_4 -60.755 313s PrivateWages_5 57.966 313s PrivateWages_6 8.973 313s PrivateWages_8 -18.582 313s PrivateWages_9 -15.968 313s PrivateWages_10 -19.982 313s PrivateWages_11 7.106 313s PrivateWages_12 0.000 313s PrivateWages_13 -5.272 313s PrivateWages_14 18.479 313s PrivateWages_15 -1.151 313s PrivateWages_16 -3.246 313s PrivateWages_17 37.985 313s PrivateWages_18 1.359 313s PrivateWages_19 -127.998 313s PrivateWages_20 32.868 313s PrivateWages_21 -33.882 313s PrivateWages_22 55.980 313s [1] TRUE 313s > Bread 313s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 313s [1,] 132.5589 -4.1405 0.7711 313s [2,] -4.1405 1.1839 -0.6491 313s [3,] 0.7711 -0.6491 0.7009 313s [4,] -1.6944 -0.1297 -0.0283 313s [5,] 114.8656 3.1837 5.1587 313s [6,] -5.5704 0.7491 -0.6223 313s [7,] 1.9218 -0.4973 0.5817 313s [8,] -0.2370 -0.0398 -0.0201 313s [9,] -36.8131 0.3292 1.6643 313s [10,] 0.5110 -0.0698 0.0440 313s [11,] 0.0898 0.0655 -0.0737 313s [12,] 0.2835 0.0505 0.0244 313s Consumption_wages Investment_(Intercept) Investment_corpProf 313s [1,] -1.694379 114.87 -5.57043 313s [2,] -0.129702 3.18 0.74914 313s [3,] -0.028262 5.16 -0.62232 313s [4,] 0.104489 -5.87 0.06772 313s [5,] -5.874854 3366.95 -56.98587 313s [6,] 0.067720 -56.99 2.64551 313s [7,] -0.069795 45.44 -2.02544 313s [8,] 0.029271 -15.60 0.22292 313s [9,] 0.075832 53.51 -0.48750 313s [10,] -0.001892 2.12 0.00442 313s [11,] 0.000817 -3.12 0.00410 313s [12,] -0.036920 -1.40 0.02820 313s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 313s [1,] 1.92185 -0.23700 -36.8131 313s [2,] -0.49725 -0.03983 0.3292 313s [3,] 0.58170 -0.02007 1.6643 313s [4,] -0.06979 0.02927 0.0758 313s [5,] 45.44092 -15.60143 53.5110 313s [6,] -2.02544 0.22292 -0.4875 313s [7,] 1.95029 -0.21271 -0.7904 313s [8,] -0.21271 0.07616 -0.1618 313s [9,] -0.79038 -0.16180 69.6580 313s [10,] 0.00806 -0.01150 -0.3039 313s [11,] 0.00580 0.01472 -0.8753 313s [12,] -0.04133 0.00782 0.7539 313s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 313s [1,] 0.51104 0.089786 0.283482 313s [2,] -0.06979 0.065456 0.050508 313s [3,] 0.04399 -0.073692 0.024378 313s [4,] -0.00189 0.000817 -0.036920 313s [5,] 2.11576 -3.117775 -1.396100 313s [6,] 0.00442 0.004099 0.028202 313s [7,] 0.00806 0.005798 -0.041335 313s [8,] -0.01150 0.014719 0.007824 313s [9,] -0.30387 -0.875279 0.753905 313s [10,] 0.04699 -0.042862 -0.013049 313s [11,] -0.04286 0.059096 0.000172 313s [12,] -0.01305 0.000172 0.045631 313s > 313s > # OLS 313s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 313s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 313s > summary 313s 313s systemfit results 313s method: OLS 313s 313s N DF SSR detRCov OLS-R2 McElroy-R2 313s system 58 46 44.2 0.565 0.976 0.991 313s 313s N DF SSR MSE RMSE R2 Adj R2 313s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 313s Investment 19 15 17.11 1.140 1.07 0.907 0.889 313s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 313s 313s The covariance matrix of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.285 0.061 -0.511 313s Investment 0.061 1.059 0.151 313s PrivateWages -0.511 0.151 0.648 313s 313s The correlations of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.0000 0.0457 -0.568 313s Investment 0.0457 1.0000 0.168 313s PrivateWages -0.5681 0.1676 1.000 313s 313s 313s OLS estimates for 'Consumption' (equation 1) 313s Model Formula: consump ~ corpProf + corpProfLag + wages 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 16.2957 1.5438 10.56 2.4e-08 *** 313s corpProf 0.1796 0.1206 1.49 0.16 313s corpProfLag 0.1032 0.1031 1.00 0.33 313s wages 0.7962 0.0449 17.73 1.8e-11 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.076 on 15 degrees of freedom 313s Number of observations: 19 Degrees of Freedom: 15 313s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 313s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 313s 313s 313s OLS estimates for 'Investment' (equation 2) 313s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 10.1724 5.5758 1.82 0.08808 . 313s corpProf 0.5004 0.1092 4.58 0.00036 *** 313s corpProfLag 0.3270 0.1052 3.11 0.00718 ** 313s capitalLag -0.1134 0.0275 -4.13 0.00090 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.068 on 15 degrees of freedom 313s Number of observations: 19 Degrees of Freedom: 15 313s SSR: 17.105 MSE: 1.14 Root MSE: 1.068 313s Multiple R-Squared: 0.907 Adjusted R-Squared: 0.889 313s 313s 313s OLS estimates for 'PrivateWages' (equation 3) 313s Model Formula: privWage ~ gnp + gnpLag + trend 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 1.3550 1.3512 1.00 0.3309 313s gnp 0.4417 0.0342 12.92 7e-10 *** 313s gnpLag 0.1466 0.0393 3.73 0.0018 ** 313s trend 0.1244 0.0347 3.58 0.0025 ** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 0.78 on 16 degrees of freedom 313s Number of observations: 20 Degrees of Freedom: 16 313s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 313s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 313s 313s compare coef with single-equation OLS 313s [1] TRUE 313s > residuals 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 -0.3863 0.00693 -1.3389 313s 3 -1.2484 -0.06954 0.2462 313s 4 -1.6040 1.22401 1.1255 313s 5 -0.5384 -1.37697 -0.1959 313s 6 -0.0413 0.38610 -0.5284 313s 7 0.8043 1.48598 NA 313s 8 1.2830 0.78465 -0.7909 313s 9 1.0142 -0.65483 0.2819 313s 10 NA 1.06018 1.1384 313s 11 0.1429 0.39508 -0.1904 313s 12 -0.3439 0.20479 0.5813 313s 13 NA NA 0.1206 313s 14 0.3199 0.32778 0.4773 313s 15 -0.1016 -0.07450 0.3035 313s 16 -0.0702 NA 0.0284 313s 17 1.6064 0.96998 -0.8517 313s 18 -0.4980 0.08124 0.9908 313s 19 0.1253 -2.49295 -0.4597 313s 20 0.9805 -0.70609 -0.3819 313s 21 0.7551 -0.81928 -1.1062 313s 22 -2.1992 -0.73256 0.5501 313s > fitted 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 42.3 -0.207 26.8 313s 3 46.2 1.970 29.1 313s 4 50.8 3.976 33.0 313s 5 51.1 4.377 34.1 313s 6 52.6 4.714 35.9 313s 7 54.3 4.114 NA 313s 8 54.9 3.415 38.7 313s 9 56.3 3.655 38.9 313s 10 NA 4.040 40.2 313s 11 54.9 0.605 38.1 313s 12 51.2 -3.605 33.9 313s 13 NA NA 28.9 313s 14 46.2 -5.428 28.0 313s 15 48.8 -2.926 30.3 313s 16 51.4 NA 33.2 313s 17 56.1 1.130 37.7 313s 18 59.2 1.919 40.0 313s 19 57.4 0.593 38.7 313s 20 60.6 2.006 42.0 313s 21 64.2 4.119 46.1 313s 22 71.9 5.633 52.7 313s > predict 313s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 313s 1 NA NA NA NA 313s 2 42.3 0.543 39.9 44.7 313s 3 46.2 0.581 43.8 48.7 313s 4 50.8 0.394 48.5 53.1 313s 5 51.1 0.465 48.8 53.5 313s 6 52.6 0.474 50.3 55.0 313s 7 54.3 0.423 52.0 56.6 313s 8 54.9 0.389 52.6 57.2 313s 9 56.3 0.434 54.0 58.6 313s 10 NA NA NA NA 313s 11 54.9 0.727 52.2 57.5 313s 12 51.2 0.662 48.7 53.8 313s 13 NA NA NA NA 313s 14 46.2 0.698 43.6 48.8 313s 15 48.8 0.470 46.4 51.2 313s 16 51.4 0.398 49.1 53.7 313s 17 56.1 0.405 53.8 58.4 313s 18 59.2 0.375 56.9 61.5 313s 19 57.4 0.466 55.0 59.7 313s 20 60.6 0.482 58.2 63.0 313s 21 64.2 0.485 61.9 66.6 313s 22 71.9 0.755 69.3 74.5 313s Investment.pred Investment.se.fit Investment.lwr Investment.upr 313s 1 NA NA NA NA 313s 2 -0.207 0.645 -2.718 2.30 313s 3 1.970 0.523 -0.423 4.36 313s 4 3.976 0.462 1.634 6.32 313s 5 4.377 0.383 2.094 6.66 313s 6 4.714 0.362 2.444 6.98 313s 7 4.114 0.336 1.861 6.37 313s 8 3.415 0.298 1.184 5.65 313s 9 3.655 0.400 1.359 5.95 313s 10 4.040 0.458 1.701 6.38 313s 11 0.605 0.666 -1.928 3.14 313s 12 -3.605 0.637 -6.108 -1.10 313s 13 NA NA NA NA 313s 14 -5.428 0.767 -8.074 -2.78 313s 15 -2.926 0.453 -5.261 -0.59 313s 16 NA NA NA NA 313s 17 1.130 0.366 -1.142 3.40 313s 18 1.919 0.258 -0.293 4.13 313s 19 0.593 0.357 -1.674 2.86 313s 20 2.006 0.384 -0.278 4.29 313s 21 4.119 0.350 1.858 6.38 313s 22 5.633 0.495 3.263 8.00 313s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 313s 1 NA NA NA NA 313s 2 26.8 0.378 25.1 28.6 313s 3 29.1 0.381 27.3 30.8 313s 4 33.0 0.384 31.2 34.7 313s 5 34.1 0.297 32.4 35.8 313s 6 35.9 0.296 34.2 37.6 313s 7 NA NA NA NA 313s 8 38.7 0.303 37.0 40.4 313s 9 38.9 0.288 37.2 40.6 313s 10 40.2 0.274 38.5 41.8 313s 11 38.1 0.377 36.3 39.8 313s 12 33.9 0.381 32.2 35.7 313s 13 28.9 0.452 27.1 30.7 313s 14 28.0 0.397 26.3 29.8 313s 15 30.3 0.391 28.5 32.1 313s 16 33.2 0.327 31.5 34.9 313s 17 37.7 0.320 36.0 39.3 313s 18 40.0 0.250 38.4 41.7 313s 19 38.7 0.375 36.9 40.4 313s 20 42.0 0.337 40.3 43.7 313s 21 46.1 0.352 44.4 47.8 313s 22 52.7 0.530 50.9 54.6 313s > model.frame 313s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 313s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 313s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 313s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 313s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 313s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 313s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 313s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 313s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 313s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 313s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 313s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 313s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 313s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 313s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 313s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 313s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 313s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 313s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 313s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 313s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 313s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 313s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 313s trend 313s 1 -11 313s 2 -10 313s 3 -9 313s 4 -8 313s 5 -7 313s 6 -6 313s 7 -5 313s 8 -4 313s 9 -3 313s 10 -2 313s 11 -1 313s 12 0 313s 13 1 313s 14 2 313s 15 3 313s 16 4 313s 17 5 313s 18 6 313s 19 7 313s 20 8 313s 21 9 313s 22 10 313s > model.matrix 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_2 1 12.4 313s Consumption_3 1 16.9 313s Consumption_4 1 18.4 313s Consumption_5 1 19.4 313s Consumption_6 1 20.1 313s Consumption_7 1 19.6 313s Consumption_8 1 19.8 313s Consumption_9 1 21.1 313s Consumption_11 1 15.6 313s Consumption_12 1 11.4 313s Consumption_14 1 11.2 313s Consumption_15 1 12.3 313s Consumption_16 1 14.0 313s Consumption_17 1 17.6 313s Consumption_18 1 17.3 313s Consumption_19 1 15.3 313s Consumption_20 1 19.0 313s Consumption_21 1 21.1 313s Consumption_22 1 23.5 313s Investment_2 0 0.0 313s Investment_3 0 0.0 313s Investment_4 0 0.0 313s Investment_5 0 0.0 313s Investment_6 0 0.0 313s Investment_7 0 0.0 313s Investment_8 0 0.0 313s Investment_9 0 0.0 313s Investment_10 0 0.0 313s Investment_11 0 0.0 313s Investment_12 0 0.0 313s Investment_14 0 0.0 313s Investment_15 0 0.0 313s Investment_17 0 0.0 313s Investment_18 0 0.0 313s Investment_19 0 0.0 313s Investment_20 0 0.0 313s Investment_21 0 0.0 313s Investment_22 0 0.0 313s PrivateWages_2 0 0.0 313s PrivateWages_3 0 0.0 313s PrivateWages_4 0 0.0 313s PrivateWages_5 0 0.0 313s PrivateWages_6 0 0.0 313s PrivateWages_8 0 0.0 313s PrivateWages_9 0 0.0 313s PrivateWages_10 0 0.0 313s PrivateWages_11 0 0.0 313s PrivateWages_12 0 0.0 313s PrivateWages_13 0 0.0 313s PrivateWages_14 0 0.0 313s PrivateWages_15 0 0.0 313s PrivateWages_16 0 0.0 313s PrivateWages_17 0 0.0 313s PrivateWages_18 0 0.0 313s PrivateWages_19 0 0.0 313s PrivateWages_20 0 0.0 313s PrivateWages_21 0 0.0 313s PrivateWages_22 0 0.0 313s Consumption_corpProfLag Consumption_wages 313s Consumption_2 12.7 28.2 313s Consumption_3 12.4 32.2 313s Consumption_4 16.9 37.0 313s Consumption_5 18.4 37.0 313s Consumption_6 19.4 38.6 313s Consumption_7 20.1 40.7 313s Consumption_8 19.6 41.5 313s Consumption_9 19.8 42.9 313s Consumption_11 21.7 42.1 313s Consumption_12 15.6 39.3 313s Consumption_14 7.0 34.1 313s Consumption_15 11.2 36.6 313s Consumption_16 12.3 39.3 313s Consumption_17 14.0 44.2 313s Consumption_18 17.6 47.7 313s Consumption_19 17.3 45.9 313s Consumption_20 15.3 49.4 313s Consumption_21 19.0 53.0 313s Consumption_22 21.1 61.8 313s Investment_2 0.0 0.0 313s Investment_3 0.0 0.0 313s Investment_4 0.0 0.0 313s Investment_5 0.0 0.0 313s Investment_6 0.0 0.0 313s Investment_7 0.0 0.0 313s Investment_8 0.0 0.0 313s Investment_9 0.0 0.0 313s Investment_10 0.0 0.0 313s Investment_11 0.0 0.0 313s Investment_12 0.0 0.0 313s Investment_14 0.0 0.0 313s Investment_15 0.0 0.0 313s Investment_17 0.0 0.0 313s Investment_18 0.0 0.0 313s Investment_19 0.0 0.0 313s Investment_20 0.0 0.0 313s Investment_21 0.0 0.0 313s Investment_22 0.0 0.0 313s PrivateWages_2 0.0 0.0 313s PrivateWages_3 0.0 0.0 313s PrivateWages_4 0.0 0.0 313s PrivateWages_5 0.0 0.0 313s PrivateWages_6 0.0 0.0 313s PrivateWages_8 0.0 0.0 313s PrivateWages_9 0.0 0.0 313s PrivateWages_10 0.0 0.0 313s PrivateWages_11 0.0 0.0 313s PrivateWages_12 0.0 0.0 313s PrivateWages_13 0.0 0.0 313s PrivateWages_14 0.0 0.0 313s PrivateWages_15 0.0 0.0 313s PrivateWages_16 0.0 0.0 313s PrivateWages_17 0.0 0.0 313s PrivateWages_18 0.0 0.0 313s PrivateWages_19 0.0 0.0 313s PrivateWages_20 0.0 0.0 313s PrivateWages_21 0.0 0.0 313s PrivateWages_22 0.0 0.0 313s Investment_(Intercept) Investment_corpProf 313s Consumption_2 0 0.0 313s Consumption_3 0 0.0 313s Consumption_4 0 0.0 313s Consumption_5 0 0.0 313s Consumption_6 0 0.0 313s Consumption_7 0 0.0 313s Consumption_8 0 0.0 313s Consumption_9 0 0.0 313s Consumption_11 0 0.0 313s Consumption_12 0 0.0 313s Consumption_14 0 0.0 313s Consumption_15 0 0.0 313s Consumption_16 0 0.0 313s Consumption_17 0 0.0 313s Consumption_18 0 0.0 313s Consumption_19 0 0.0 313s Consumption_20 0 0.0 313s Consumption_21 0 0.0 313s Consumption_22 0 0.0 313s Investment_2 1 12.4 313s Investment_3 1 16.9 313s Investment_4 1 18.4 313s Investment_5 1 19.4 313s Investment_6 1 20.1 313s Investment_7 1 19.6 313s Investment_8 1 19.8 313s Investment_9 1 21.1 313s Investment_10 1 21.7 313s Investment_11 1 15.6 313s Investment_12 1 11.4 313s Investment_14 1 11.2 313s Investment_15 1 12.3 313s Investment_17 1 17.6 313s Investment_18 1 17.3 313s Investment_19 1 15.3 313s Investment_20 1 19.0 313s Investment_21 1 21.1 313s Investment_22 1 23.5 313s PrivateWages_2 0 0.0 313s PrivateWages_3 0 0.0 313s PrivateWages_4 0 0.0 313s PrivateWages_5 0 0.0 313s PrivateWages_6 0 0.0 313s PrivateWages_8 0 0.0 313s PrivateWages_9 0 0.0 313s PrivateWages_10 0 0.0 313s PrivateWages_11 0 0.0 313s PrivateWages_12 0 0.0 313s PrivateWages_13 0 0.0 313s PrivateWages_14 0 0.0 313s PrivateWages_15 0 0.0 313s PrivateWages_16 0 0.0 313s PrivateWages_17 0 0.0 313s PrivateWages_18 0 0.0 313s PrivateWages_19 0 0.0 313s PrivateWages_20 0 0.0 313s PrivateWages_21 0 0.0 313s PrivateWages_22 0 0.0 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_2 0.0 0 313s Consumption_3 0.0 0 313s Consumption_4 0.0 0 313s Consumption_5 0.0 0 313s Consumption_6 0.0 0 313s Consumption_7 0.0 0 313s Consumption_8 0.0 0 313s Consumption_9 0.0 0 313s Consumption_11 0.0 0 313s Consumption_12 0.0 0 313s Consumption_14 0.0 0 313s Consumption_15 0.0 0 313s Consumption_16 0.0 0 313s Consumption_17 0.0 0 313s Consumption_18 0.0 0 313s Consumption_19 0.0 0 313s Consumption_20 0.0 0 313s Consumption_21 0.0 0 313s Consumption_22 0.0 0 313s Investment_2 12.7 183 313s Investment_3 12.4 183 313s Investment_4 16.9 184 313s Investment_5 18.4 190 313s Investment_6 19.4 193 313s Investment_7 20.1 198 313s Investment_8 19.6 203 313s Investment_9 19.8 208 313s Investment_10 21.1 211 313s Investment_11 21.7 216 313s Investment_12 15.6 217 313s Investment_14 7.0 207 313s Investment_15 11.2 202 313s Investment_17 14.0 198 313s Investment_18 17.6 200 313s Investment_19 17.3 202 313s Investment_20 15.3 200 313s Investment_21 19.0 201 313s Investment_22 21.1 204 313s PrivateWages_2 0.0 0 313s PrivateWages_3 0.0 0 313s PrivateWages_4 0.0 0 313s PrivateWages_5 0.0 0 313s PrivateWages_6 0.0 0 313s PrivateWages_8 0.0 0 313s PrivateWages_9 0.0 0 313s PrivateWages_10 0.0 0 313s PrivateWages_11 0.0 0 313s PrivateWages_12 0.0 0 313s PrivateWages_13 0.0 0 313s PrivateWages_14 0.0 0 313s PrivateWages_15 0.0 0 313s PrivateWages_16 0.0 0 313s PrivateWages_17 0.0 0 313s PrivateWages_18 0.0 0 313s PrivateWages_19 0.0 0 313s PrivateWages_20 0.0 0 313s PrivateWages_21 0.0 0 313s PrivateWages_22 0.0 0 313s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 313s Consumption_2 0 0.0 0.0 313s Consumption_3 0 0.0 0.0 313s Consumption_4 0 0.0 0.0 313s Consumption_5 0 0.0 0.0 313s Consumption_6 0 0.0 0.0 313s Consumption_7 0 0.0 0.0 313s Consumption_8 0 0.0 0.0 313s Consumption_9 0 0.0 0.0 313s Consumption_11 0 0.0 0.0 313s Consumption_12 0 0.0 0.0 313s Consumption_14 0 0.0 0.0 313s Consumption_15 0 0.0 0.0 313s Consumption_16 0 0.0 0.0 313s Consumption_17 0 0.0 0.0 313s Consumption_18 0 0.0 0.0 313s Consumption_19 0 0.0 0.0 313s Consumption_20 0 0.0 0.0 313s Consumption_21 0 0.0 0.0 313s Consumption_22 0 0.0 0.0 313s Investment_2 0 0.0 0.0 313s Investment_3 0 0.0 0.0 313s Investment_4 0 0.0 0.0 313s Investment_5 0 0.0 0.0 313s Investment_6 0 0.0 0.0 313s Investment_7 0 0.0 0.0 313s Investment_8 0 0.0 0.0 313s Investment_9 0 0.0 0.0 313s Investment_10 0 0.0 0.0 313s Investment_11 0 0.0 0.0 313s Investment_12 0 0.0 0.0 313s Investment_14 0 0.0 0.0 313s Investment_15 0 0.0 0.0 313s Investment_17 0 0.0 0.0 313s Investment_18 0 0.0 0.0 313s Investment_19 0 0.0 0.0 313s Investment_20 0 0.0 0.0 313s Investment_21 0 0.0 0.0 313s Investment_22 0 0.0 0.0 313s PrivateWages_2 1 45.6 44.9 313s PrivateWages_3 1 50.1 45.6 313s PrivateWages_4 1 57.2 50.1 313s PrivateWages_5 1 57.1 57.2 313s PrivateWages_6 1 61.0 57.1 313s PrivateWages_8 1 64.4 64.0 313s PrivateWages_9 1 64.5 64.4 313s PrivateWages_10 1 67.0 64.5 313s PrivateWages_11 1 61.2 67.0 313s PrivateWages_12 1 53.4 61.2 313s PrivateWages_13 1 44.3 53.4 313s PrivateWages_14 1 45.1 44.3 313s PrivateWages_15 1 49.7 45.1 313s PrivateWages_16 1 54.4 49.7 313s PrivateWages_17 1 62.7 54.4 313s PrivateWages_18 1 65.0 62.7 313s PrivateWages_19 1 60.9 65.0 313s PrivateWages_20 1 69.5 60.9 313s PrivateWages_21 1 75.7 69.5 313s PrivateWages_22 1 88.4 75.7 313s PrivateWages_trend 313s Consumption_2 0 313s Consumption_3 0 313s Consumption_4 0 313s Consumption_5 0 313s Consumption_6 0 313s Consumption_7 0 313s Consumption_8 0 313s Consumption_9 0 313s Consumption_11 0 313s Consumption_12 0 313s Consumption_14 0 313s Consumption_15 0 313s Consumption_16 0 313s Consumption_17 0 313s Consumption_18 0 313s Consumption_19 0 313s Consumption_20 0 313s Consumption_21 0 313s Consumption_22 0 313s Investment_2 0 313s Investment_3 0 313s Investment_4 0 313s Investment_5 0 313s Investment_6 0 313s Investment_7 0 313s Investment_8 0 313s Investment_9 0 313s Investment_10 0 313s Investment_11 0 313s Investment_12 0 313s Investment_14 0 313s Investment_15 0 313s Investment_17 0 313s Investment_18 0 313s Investment_19 0 313s Investment_20 0 313s Investment_21 0 313s Investment_22 0 313s PrivateWages_2 -10 313s PrivateWages_3 -9 313s PrivateWages_4 -8 313s PrivateWages_5 -7 313s PrivateWages_6 -6 313s PrivateWages_8 -4 313s PrivateWages_9 -3 313s PrivateWages_10 -2 313s PrivateWages_11 -1 313s PrivateWages_12 0 313s PrivateWages_13 1 313s PrivateWages_14 2 313s PrivateWages_15 3 313s PrivateWages_16 4 313s PrivateWages_17 5 313s PrivateWages_18 6 313s PrivateWages_19 7 313s PrivateWages_20 8 313s PrivateWages_21 9 313s PrivateWages_22 10 313s > nobs 313s [1] 58 313s > linearHypothesis 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 47 313s 2 46 1 0.3 0.59 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 47 313s 2 46 1 0.29 0.6 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 47 313s 2 46 1 0.29 0.59 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 48 313s 2 46 2 0.16 0.85 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 48 313s 2 46 2 0.15 0.86 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 48 313s 2 46 2 0.3 0.86 313s > logLik 313s 'log Lik.' -68.8 (df=13) 313s 'log Lik.' -73.3 (df=13) 313s compare log likelihood value with single-equation OLS 313s [1] "Mean relative difference: 0.0011" 313s Estimating function 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_2 -0.3863 -4.791 313s Consumption_3 -1.2484 -21.098 313s Consumption_4 -1.6040 -29.514 313s Consumption_5 -0.5384 -10.446 313s Consumption_6 -0.0413 -0.830 313s Consumption_7 0.8043 15.763 313s Consumption_8 1.2830 25.403 313s Consumption_9 1.0142 21.399 313s Consumption_11 0.1429 2.229 313s Consumption_12 -0.3439 -3.920 313s Consumption_14 0.3199 3.583 313s Consumption_15 -0.1016 -1.250 313s Consumption_16 -0.0702 -0.983 313s Consumption_17 1.6064 28.272 313s Consumption_18 -0.4980 -8.616 313s Consumption_19 0.1253 1.917 313s Consumption_20 0.9805 18.629 313s Consumption_21 0.7551 15.933 313s Consumption_22 -2.1992 -51.681 313s Investment_2 0.0000 0.000 313s Investment_3 0.0000 0.000 313s Investment_4 0.0000 0.000 313s Investment_5 0.0000 0.000 313s Investment_6 0.0000 0.000 313s Investment_7 0.0000 0.000 313s Investment_8 0.0000 0.000 313s Investment_9 0.0000 0.000 313s Investment_10 0.0000 0.000 313s Investment_11 0.0000 0.000 313s Investment_12 0.0000 0.000 313s Investment_14 0.0000 0.000 313s Investment_15 0.0000 0.000 313s Investment_17 0.0000 0.000 313s Investment_18 0.0000 0.000 313s Investment_19 0.0000 0.000 313s Investment_20 0.0000 0.000 313s Investment_21 0.0000 0.000 313s Investment_22 0.0000 0.000 313s PrivateWages_2 0.0000 0.000 313s PrivateWages_3 0.0000 0.000 313s PrivateWages_4 0.0000 0.000 313s PrivateWages_5 0.0000 0.000 313s PrivateWages_6 0.0000 0.000 313s PrivateWages_8 0.0000 0.000 313s PrivateWages_9 0.0000 0.000 313s PrivateWages_10 0.0000 0.000 313s PrivateWages_11 0.0000 0.000 313s PrivateWages_12 0.0000 0.000 313s PrivateWages_13 0.0000 0.000 313s PrivateWages_14 0.0000 0.000 313s PrivateWages_15 0.0000 0.000 313s PrivateWages_16 0.0000 0.000 313s PrivateWages_17 0.0000 0.000 313s PrivateWages_18 0.0000 0.000 313s PrivateWages_19 0.0000 0.000 313s PrivateWages_20 0.0000 0.000 313s PrivateWages_21 0.0000 0.000 313s PrivateWages_22 0.0000 0.000 313s Consumption_corpProfLag Consumption_wages 313s Consumption_2 -4.907 -10.90 313s Consumption_3 -15.480 -40.20 313s Consumption_4 -27.108 -59.35 313s Consumption_5 -9.907 -19.92 313s Consumption_6 -0.801 -1.59 313s Consumption_7 16.166 32.73 313s Consumption_8 25.146 53.24 313s Consumption_9 20.081 43.51 313s Consumption_11 3.100 6.01 313s Consumption_12 -5.364 -13.51 313s Consumption_14 2.239 10.91 313s Consumption_15 -1.138 -3.72 313s Consumption_16 -0.864 -2.76 313s Consumption_17 22.489 71.00 313s Consumption_18 -8.765 -23.76 313s Consumption_19 2.168 5.75 313s Consumption_20 15.002 48.44 313s Consumption_21 14.348 40.02 313s Consumption_22 -46.403 -135.91 313s Investment_2 0.000 0.00 313s Investment_3 0.000 0.00 313s Investment_4 0.000 0.00 313s Investment_5 0.000 0.00 313s Investment_6 0.000 0.00 313s Investment_7 0.000 0.00 313s Investment_8 0.000 0.00 313s Investment_9 0.000 0.00 313s Investment_10 0.000 0.00 313s Investment_11 0.000 0.00 313s Investment_12 0.000 0.00 313s Investment_14 0.000 0.00 313s Investment_15 0.000 0.00 313s Investment_17 0.000 0.00 313s Investment_18 0.000 0.00 313s Investment_19 0.000 0.00 313s Investment_20 0.000 0.00 313s Investment_21 0.000 0.00 313s Investment_22 0.000 0.00 313s PrivateWages_2 0.000 0.00 313s PrivateWages_3 0.000 0.00 313s PrivateWages_4 0.000 0.00 313s PrivateWages_5 0.000 0.00 313s PrivateWages_6 0.000 0.00 313s PrivateWages_8 0.000 0.00 313s PrivateWages_9 0.000 0.00 313s PrivateWages_10 0.000 0.00 313s PrivateWages_11 0.000 0.00 313s PrivateWages_12 0.000 0.00 313s PrivateWages_13 0.000 0.00 313s PrivateWages_14 0.000 0.00 313s PrivateWages_15 0.000 0.00 313s PrivateWages_16 0.000 0.00 313s PrivateWages_17 0.000 0.00 313s PrivateWages_18 0.000 0.00 313s PrivateWages_19 0.000 0.00 313s PrivateWages_20 0.000 0.00 313s PrivateWages_21 0.000 0.00 313s PrivateWages_22 0.000 0.00 313s Investment_(Intercept) Investment_corpProf 313s Consumption_2 0.00000 0.000 313s Consumption_3 0.00000 0.000 313s Consumption_4 0.00000 0.000 313s Consumption_5 0.00000 0.000 313s Consumption_6 0.00000 0.000 313s Consumption_7 0.00000 0.000 313s Consumption_8 0.00000 0.000 313s Consumption_9 0.00000 0.000 313s Consumption_11 0.00000 0.000 313s Consumption_12 0.00000 0.000 313s Consumption_14 0.00000 0.000 313s Consumption_15 0.00000 0.000 313s Consumption_16 0.00000 0.000 313s Consumption_17 0.00000 0.000 313s Consumption_18 0.00000 0.000 313s Consumption_19 0.00000 0.000 313s Consumption_20 0.00000 0.000 313s Consumption_21 0.00000 0.000 313s Consumption_22 0.00000 0.000 313s Investment_2 0.00693 0.086 313s Investment_3 -0.06954 -1.175 313s Investment_4 1.22401 22.522 313s Investment_5 -1.37696 -26.713 313s Investment_6 0.38610 7.761 313s Investment_7 1.48598 29.125 313s Investment_8 0.78465 15.536 313s Investment_9 -0.65483 -13.817 313s Investment_10 1.06018 23.006 313s Investment_11 0.39508 6.163 313s Investment_12 0.20479 2.335 313s Investment_14 0.32778 3.671 313s Investment_15 -0.07450 -0.916 313s Investment_17 0.96998 17.072 313s Investment_18 0.08124 1.405 313s Investment_19 -2.49295 -38.142 313s Investment_20 -0.70609 -13.416 313s Investment_21 -0.81928 -17.287 313s Investment_22 -0.73256 -17.215 313s PrivateWages_2 0.00000 0.000 313s PrivateWages_3 0.00000 0.000 313s PrivateWages_4 0.00000 0.000 313s PrivateWages_5 0.00000 0.000 313s PrivateWages_6 0.00000 0.000 313s PrivateWages_8 0.00000 0.000 313s PrivateWages_9 0.00000 0.000 313s PrivateWages_10 0.00000 0.000 313s PrivateWages_11 0.00000 0.000 313s PrivateWages_12 0.00000 0.000 313s PrivateWages_13 0.00000 0.000 313s PrivateWages_14 0.00000 0.000 313s PrivateWages_15 0.00000 0.000 313s PrivateWages_16 0.00000 0.000 313s PrivateWages_17 0.00000 0.000 313s PrivateWages_18 0.00000 0.000 313s PrivateWages_19 0.00000 0.000 313s PrivateWages_20 0.00000 0.000 313s PrivateWages_21 0.00000 0.000 313s PrivateWages_22 0.00000 0.000 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_2 0.0000 0.00 313s Consumption_3 0.0000 0.00 313s Consumption_4 0.0000 0.00 313s Consumption_5 0.0000 0.00 313s Consumption_6 0.0000 0.00 313s Consumption_7 0.0000 0.00 313s Consumption_8 0.0000 0.00 313s Consumption_9 0.0000 0.00 313s Consumption_11 0.0000 0.00 313s Consumption_12 0.0000 0.00 313s Consumption_14 0.0000 0.00 313s Consumption_15 0.0000 0.00 313s Consumption_16 0.0000 0.00 313s Consumption_17 0.0000 0.00 313s Consumption_18 0.0000 0.00 313s Consumption_19 0.0000 0.00 313s Consumption_20 0.0000 0.00 313s Consumption_21 0.0000 0.00 313s Consumption_22 0.0000 0.00 313s Investment_2 0.0881 1.27 313s Investment_3 -0.8622 -12.70 313s Investment_4 20.6858 225.83 313s Investment_5 -25.3362 -261.21 313s Investment_6 7.4903 74.40 313s Investment_7 29.8681 293.93 313s Investment_8 15.3791 159.60 313s Investment_9 -12.9657 -135.94 313s Investment_10 22.3698 223.27 313s Investment_11 8.5733 85.22 313s Investment_12 3.1947 44.38 313s Investment_14 2.2945 67.88 313s Investment_15 -0.8344 -15.05 313s Investment_17 13.5797 191.77 313s Investment_18 1.4298 16.23 313s Investment_19 -43.1281 -503.08 313s Investment_20 -10.8032 -141.15 313s Investment_21 -15.5663 -164.84 313s Investment_22 -15.4570 -149.81 313s PrivateWages_2 0.0000 0.00 313s PrivateWages_3 0.0000 0.00 313s PrivateWages_4 0.0000 0.00 313s PrivateWages_5 0.0000 0.00 313s PrivateWages_6 0.0000 0.00 313s PrivateWages_8 0.0000 0.00 313s PrivateWages_9 0.0000 0.00 313s PrivateWages_10 0.0000 0.00 313s PrivateWages_11 0.0000 0.00 313s PrivateWages_12 0.0000 0.00 313s PrivateWages_13 0.0000 0.00 313s PrivateWages_14 0.0000 0.00 313s PrivateWages_15 0.0000 0.00 313s PrivateWages_16 0.0000 0.00 313s PrivateWages_17 0.0000 0.00 313s PrivateWages_18 0.0000 0.00 313s PrivateWages_19 0.0000 0.00 313s PrivateWages_20 0.0000 0.00 313s PrivateWages_21 0.0000 0.00 313s PrivateWages_22 0.0000 0.00 313s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 313s Consumption_2 0.0000 0.00 0.00 313s Consumption_3 0.0000 0.00 0.00 313s Consumption_4 0.0000 0.00 0.00 313s Consumption_5 0.0000 0.00 0.00 313s Consumption_6 0.0000 0.00 0.00 313s Consumption_7 0.0000 0.00 0.00 313s Consumption_8 0.0000 0.00 0.00 313s Consumption_9 0.0000 0.00 0.00 313s Consumption_11 0.0000 0.00 0.00 313s Consumption_12 0.0000 0.00 0.00 313s Consumption_14 0.0000 0.00 0.00 313s Consumption_15 0.0000 0.00 0.00 313s Consumption_16 0.0000 0.00 0.00 313s Consumption_17 0.0000 0.00 0.00 313s Consumption_18 0.0000 0.00 0.00 313s Consumption_19 0.0000 0.00 0.00 313s Consumption_20 0.0000 0.00 0.00 313s Consumption_21 0.0000 0.00 0.00 313s Consumption_22 0.0000 0.00 0.00 313s Investment_2 0.0000 0.00 0.00 313s Investment_3 0.0000 0.00 0.00 313s Investment_4 0.0000 0.00 0.00 313s Investment_5 0.0000 0.00 0.00 313s Investment_6 0.0000 0.00 0.00 313s Investment_7 0.0000 0.00 0.00 313s Investment_8 0.0000 0.00 0.00 313s Investment_9 0.0000 0.00 0.00 313s Investment_10 0.0000 0.00 0.00 313s Investment_11 0.0000 0.00 0.00 313s Investment_12 0.0000 0.00 0.00 313s Investment_14 0.0000 0.00 0.00 313s Investment_15 0.0000 0.00 0.00 313s Investment_17 0.0000 0.00 0.00 313s Investment_18 0.0000 0.00 0.00 313s Investment_19 0.0000 0.00 0.00 313s Investment_20 0.0000 0.00 0.00 313s Investment_21 0.0000 0.00 0.00 313s Investment_22 0.0000 0.00 0.00 313s PrivateWages_2 -1.3389 -61.06 -60.12 313s PrivateWages_3 0.2462 12.33 11.23 313s PrivateWages_4 1.1255 64.38 56.39 313s PrivateWages_5 -0.1959 -11.18 -11.20 313s PrivateWages_6 -0.5284 -32.23 -30.17 313s PrivateWages_8 -0.7909 -50.94 -50.62 313s PrivateWages_9 0.2819 18.18 18.15 313s PrivateWages_10 1.1384 76.28 73.43 313s PrivateWages_11 -0.1904 -11.65 -12.76 313s PrivateWages_12 0.5813 31.04 35.58 313s PrivateWages_13 0.1206 5.34 6.44 313s PrivateWages_14 0.4773 21.53 21.14 313s PrivateWages_15 0.3035 15.09 13.69 313s PrivateWages_16 0.0284 1.55 1.41 313s PrivateWages_17 -0.8517 -53.40 -46.33 313s PrivateWages_18 0.9908 64.40 62.12 313s PrivateWages_19 -0.4597 -28.00 -29.88 313s PrivateWages_20 -0.3819 -26.54 -23.26 313s PrivateWages_21 -1.1062 -83.74 -76.88 313s PrivateWages_22 0.5501 48.63 41.64 313s PrivateWages_trend 313s Consumption_2 0.000 313s Consumption_3 0.000 313s Consumption_4 0.000 313s Consumption_5 0.000 313s Consumption_6 0.000 313s Consumption_7 0.000 313s Consumption_8 0.000 313s Consumption_9 0.000 313s Consumption_11 0.000 313s Consumption_12 0.000 313s Consumption_14 0.000 313s Consumption_15 0.000 313s Consumption_16 0.000 313s Consumption_17 0.000 313s Consumption_18 0.000 313s Consumption_19 0.000 313s Consumption_20 0.000 313s Consumption_21 0.000 313s Consumption_22 0.000 313s Investment_2 0.000 313s Investment_3 0.000 313s Investment_4 0.000 313s Investment_5 0.000 313s Investment_6 0.000 313s Investment_7 0.000 313s Investment_8 0.000 313s Investment_9 0.000 313s Investment_10 0.000 313s Investment_11 0.000 313s Investment_12 0.000 313s Investment_14 0.000 313s Investment_15 0.000 313s Investment_17 0.000 313s Investment_18 0.000 313s Investment_19 0.000 313s Investment_20 0.000 313s Investment_21 0.000 313s Investment_22 0.000 313s PrivateWages_2 13.389 313s PrivateWages_3 -2.216 313s PrivateWages_4 -9.004 313s PrivateWages_5 1.371 313s PrivateWages_6 3.170 313s PrivateWages_8 3.164 313s PrivateWages_9 -0.846 313s PrivateWages_10 -2.277 313s PrivateWages_11 0.190 313s PrivateWages_12 0.000 313s PrivateWages_13 0.121 313s PrivateWages_14 0.955 313s PrivateWages_15 0.911 313s PrivateWages_16 0.114 313s PrivateWages_17 -4.258 313s PrivateWages_18 5.945 313s PrivateWages_19 -3.218 313s PrivateWages_20 -3.055 313s PrivateWages_21 -9.956 313s PrivateWages_22 5.501 313s [1] TRUE 313s > Bread 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_(Intercept) 107.542 -1.6123 313s Consumption_corpProf -1.612 0.6562 313s Consumption_corpProfLag -0.588 -0.3449 313s Consumption_wages -1.613 -0.0959 313s Investment_(Intercept) 0.000 0.0000 313s Investment_corpProf 0.000 0.0000 313s Investment_corpProfLag 0.000 0.0000 313s Investment_capitalLag 0.000 0.0000 313s PrivateWages_(Intercept) 0.000 0.0000 313s PrivateWages_gnp 0.000 0.0000 313s PrivateWages_gnpLag 0.000 0.0000 313s PrivateWages_trend 0.000 0.0000 313s Consumption_corpProfLag Consumption_wages 313s Consumption_(Intercept) -0.5878 -1.6130 313s Consumption_corpProf -0.3449 -0.0959 313s Consumption_corpProfLag 0.4797 -0.0326 313s Consumption_wages -0.0326 0.0910 313s Investment_(Intercept) 0.0000 0.0000 313s Investment_corpProf 0.0000 0.0000 313s Investment_corpProfLag 0.0000 0.0000 313s Investment_capitalLag 0.0000 0.0000 313s PrivateWages_(Intercept) 0.0000 0.0000 313s PrivateWages_gnp 0.0000 0.0000 313s PrivateWages_gnpLag 0.0000 0.0000 313s PrivateWages_trend 0.0000 0.0000 313s Investment_(Intercept) Investment_corpProf 313s Consumption_(Intercept) 0.00 0.000 313s Consumption_corpProf 0.00 0.000 313s Consumption_corpProfLag 0.00 0.000 313s Consumption_wages 0.00 0.000 313s Investment_(Intercept) 1702.08 -16.246 313s Investment_corpProf -16.25 0.653 313s Investment_corpProfLag 13.29 -0.499 313s Investment_capitalLag -8.19 0.066 313s PrivateWages_(Intercept) 0.00 0.000 313s PrivateWages_gnp 0.00 0.000 313s PrivateWages_gnpLag 0.00 0.000 313s PrivateWages_trend 0.00 0.000 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_(Intercept) 0.0000 0.0000 313s Consumption_corpProf 0.0000 0.0000 313s Consumption_corpProfLag 0.0000 0.0000 313s Consumption_wages 0.0000 0.0000 313s Investment_(Intercept) 13.2940 -8.1927 313s Investment_corpProf -0.4994 0.0660 313s Investment_corpProfLag 0.6054 -0.0737 313s Investment_capitalLag -0.0737 0.0414 313s PrivateWages_(Intercept) 0.0000 0.0000 313s PrivateWages_gnp 0.0000 0.0000 313s PrivateWages_gnpLag 0.0000 0.0000 313s PrivateWages_trend 0.0000 0.0000 313s PrivateWages_(Intercept) PrivateWages_gnp 313s Consumption_(Intercept) 0.000 0.0000 313s Consumption_corpProf 0.000 0.0000 313s Consumption_corpProfLag 0.000 0.0000 313s Consumption_wages 0.000 0.0000 313s Investment_(Intercept) 0.000 0.0000 313s Investment_corpProf 0.000 0.0000 313s Investment_corpProfLag 0.000 0.0000 313s Investment_capitalLag 0.000 0.0000 313s PrivateWages_(Intercept) 163.361 -0.6152 313s PrivateWages_gnp -0.615 0.1046 313s PrivateWages_gnpLag -2.146 -0.0975 313s PrivateWages_trend 2.016 -0.0281 313s PrivateWages_gnpLag PrivateWages_trend 313s Consumption_(Intercept) 0.00000 0.00000 313s Consumption_corpProf 0.00000 0.00000 313s Consumption_corpProfLag 0.00000 0.00000 313s Consumption_wages 0.00000 0.00000 313s Investment_(Intercept) 0.00000 0.00000 313s Investment_corpProf 0.00000 0.00000 313s Investment_corpProfLag 0.00000 0.00000 313s Investment_capitalLag 0.00000 0.00000 313s PrivateWages_(Intercept) -2.14647 2.01603 313s PrivateWages_gnp -0.09753 -0.02810 313s PrivateWages_gnpLag 0.13809 -0.00624 313s PrivateWages_trend -0.00624 0.10783 313s > 313s > # 2SLS 313s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 313s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 313s > summary 313s 313s systemfit results 313s method: 2SLS 313s 313s N DF SSR detRCov OLS-R2 McElroy-R2 313s system 56 44 57.9 0.391 0.968 0.992 313s 313s N DF SSR MSE RMSE R2 Adj R2 313s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 313s Investment 18 14 25.85 1.847 1.36 0.847 0.815 313s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 313s 313s The covariance matrix of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.307 0.540 -0.431 313s Investment 0.540 1.319 0.119 313s PrivateWages -0.431 0.119 0.496 313s 313s The correlations of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.000 0.414 -0.538 313s Investment 0.414 1.000 0.139 313s PrivateWages -0.538 0.139 1.000 313s 313s 313s 2SLS estimates for 'Consumption' (equation 1) 313s Model Formula: consump ~ corpProf + corpProfLag + wages 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 17.2849 1.6463 10.50 5.1e-08 *** 313s corpProf -0.0770 0.1683 -0.46 0.65 313s corpProfLag 0.2327 0.1276 1.82 0.09 . 313s wages 0.8259 0.0472 17.49 6.6e-11 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.261 on 14 degrees of freedom 313s Number of observations: 18 Degrees of Freedom: 14 313s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 313s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 313s 313s 313s 2SLS estimates for 'Investment' (equation 2) 313s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 18.2571 7.3132 2.50 0.02564 * 313s corpProf 0.1564 0.1942 0.81 0.43408 313s corpProfLag 0.5714 0.1672 3.42 0.00417 ** 313s capitalLag -0.1446 0.0346 -4.18 0.00093 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.359 on 14 degrees of freedom 313s Number of observations: 18 Degrees of Freedom: 14 313s SSR: 25.852 MSE: 1.847 Root MSE: 1.359 313s Multiple R-Squared: 0.847 Adjusted R-Squared: 0.815 313s 313s 313s 2SLS estimates for 'PrivateWages' (equation 3) 313s Model Formula: privWage ~ gnp + gnpLag + trend 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 1.3431 1.1879 1.13 0.275 313s gnp 0.4438 0.0361 12.28 1.5e-09 *** 313s gnpLag 0.1447 0.0392 3.69 0.002 ** 313s trend 0.1238 0.0308 4.01 0.001 ** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 0.78 on 16 degrees of freedom 313s Number of observations: 20 Degrees of Freedom: 16 313s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 313s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 313s 313s > residuals 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 -0.6754 -1.214 -1.3401 313s 3 -0.4627 0.325 0.2378 313s 4 -1.1585 1.094 1.1117 313s 5 -0.0305 -1.368 -0.1954 313s 6 0.4693 0.486 -0.5355 313s 7 NA NA NA 313s 8 1.6045 1.066 -0.7908 313s 9 1.6018 0.156 0.2831 313s 10 NA 1.853 1.1353 313s 11 -0.9031 -0.898 -0.1765 313s 12 -1.5948 -1.012 0.6007 313s 13 NA NA 0.1443 313s 14 0.2854 0.845 0.4826 313s 15 -0.4718 -0.365 0.3016 313s 16 -0.2268 NA 0.0261 313s 17 2.0079 1.685 -0.8614 313s 18 -0.7434 -0.121 0.9927 313s 19 -0.5410 -3.248 -0.4446 313s 20 1.4186 0.241 -0.3914 313s 21 1.1462 -0.013 -1.1115 313s 22 -1.7256 0.489 0.5312 313s > fitted 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 42.6 1.014 26.8 313s 3 45.5 1.575 29.1 313s 4 50.4 4.106 33.0 313s 5 50.6 4.368 34.1 313s 6 52.1 4.614 35.9 313s 7 NA NA NA 313s 8 54.6 3.134 38.7 313s 9 55.7 2.844 38.9 313s 10 NA 3.247 40.2 313s 11 55.9 1.898 38.1 313s 12 52.5 -2.388 33.9 313s 13 NA NA 28.9 313s 14 46.2 -5.945 28.0 313s 15 49.2 -2.635 30.3 313s 16 51.5 NA 33.2 313s 17 55.7 0.415 37.7 313s 18 59.4 2.121 40.0 313s 19 58.0 1.348 38.6 313s 20 60.2 1.059 42.0 313s 21 63.9 3.313 46.1 313s 22 71.4 4.411 52.8 313s > predict 313s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 313s 1 NA NA NA NA 313s 2 42.6 0.586 41.3 43.8 313s 3 45.5 0.674 44.0 46.9 313s 4 50.4 0.443 49.4 51.3 313s 5 50.6 0.524 49.5 51.8 313s 6 52.1 0.535 51.0 53.3 313s 7 NA NA NA NA 313s 8 54.6 0.431 53.7 55.5 313s 9 55.7 0.510 54.6 56.8 313s 10 NA NA NA NA 313s 11 55.9 0.936 53.9 57.9 313s 12 52.5 0.893 50.6 54.4 313s 13 NA NA NA NA 313s 14 46.2 0.713 44.7 47.7 313s 15 49.2 0.501 48.1 50.2 313s 16 51.5 0.407 50.7 52.4 313s 17 55.7 0.457 54.7 56.7 313s 18 59.4 0.397 58.6 60.3 313s 19 58.0 0.564 56.8 59.2 313s 20 60.2 0.543 59.0 61.3 313s 21 63.9 0.529 62.7 65.0 313s 22 71.4 0.808 69.7 73.2 313s Investment.pred Investment.se.fit Investment.lwr Investment.upr 313s 1 NA NA NA NA 313s 2 1.014 0.919 -0.957 2.985 313s 3 1.575 0.602 0.284 2.867 313s 4 4.106 0.544 2.940 5.272 313s 5 4.368 0.450 3.402 5.333 313s 6 4.614 0.425 3.703 5.526 313s 7 NA NA NA NA 313s 8 3.134 0.352 2.380 3.889 313s 9 2.844 0.544 1.677 4.012 313s 10 3.247 0.592 1.976 4.518 313s 11 1.898 0.978 -0.200 3.996 313s 12 -2.388 0.886 -4.289 -0.488 313s 13 NA NA NA NA 313s 14 -5.945 0.916 -7.909 -3.980 313s 15 -2.635 0.518 -3.745 -1.525 313s 16 NA NA NA NA 313s 17 0.415 0.507 -0.671 1.501 313s 18 2.121 0.329 1.416 2.826 313s 19 1.348 0.551 0.166 2.529 313s 20 1.059 0.582 -0.189 2.306 313s 21 3.313 0.496 2.248 4.377 313s 22 4.411 0.728 2.850 5.971 313s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 313s 1 NA NA NA NA 313s 2 26.8 0.330 26.1 27.5 313s 3 29.1 0.344 28.3 29.8 313s 4 33.0 0.363 32.2 33.8 313s 5 34.1 0.260 33.5 34.6 313s 6 35.9 0.268 35.4 36.5 313s 7 NA NA NA NA 313s 8 38.7 0.265 38.1 39.3 313s 9 38.9 0.252 38.4 39.5 313s 10 40.2 0.242 39.7 40.7 313s 11 38.1 0.358 37.3 38.8 313s 12 33.9 0.385 33.1 34.7 313s 13 28.9 0.460 27.9 29.8 313s 14 28.0 0.351 27.3 28.8 313s 15 30.3 0.343 29.6 31.0 313s 16 33.2 0.287 32.6 33.8 313s 17 37.7 0.296 37.0 38.3 313s 18 40.0 0.220 39.5 40.5 313s 19 38.6 0.361 37.9 39.4 313s 20 42.0 0.309 41.3 42.6 313s 21 46.1 0.312 45.4 46.8 313s 22 52.8 0.501 51.7 53.8 313s > model.frame 313s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 313s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 313s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 313s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 313s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 313s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 313s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 313s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 313s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 313s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 313s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 313s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 313s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 313s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 313s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 313s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 313s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 313s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 313s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 313s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 313s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 313s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 313s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 313s trend 313s 1 -11 313s 2 -10 313s 3 -9 313s 4 -8 313s 5 -7 313s 6 -6 313s 7 -5 313s 8 -4 313s 9 -3 313s 10 -2 313s 11 -1 313s 12 0 313s 13 1 313s 14 2 313s 15 3 313s 16 4 313s 17 5 313s 18 6 313s 19 7 313s 20 8 313s 21 9 313s 22 10 313s > Frames of instrumental variables 313s govExp taxes govWage trend capitalLag corpProfLag gnpLag 313s 1 2.4 3.4 2.2 -11 180 NA NA 313s 2 3.9 7.7 2.7 -10 183 12.7 44.9 313s 3 3.2 3.9 2.9 -9 183 12.4 45.6 313s 4 2.8 4.7 2.9 -8 184 16.9 50.1 313s 5 3.5 3.8 3.1 -7 190 18.4 57.2 313s 6 3.3 5.5 3.2 -6 193 19.4 57.1 313s 7 3.3 7.0 3.3 -5 198 20.1 NA 313s 8 4.0 6.7 3.6 -4 203 19.6 64.0 313s 9 4.2 4.2 3.7 -3 208 19.8 64.4 313s 10 4.1 4.0 4.0 -2 211 21.1 64.5 313s 11 5.2 7.7 4.2 -1 216 21.7 67.0 313s 12 5.9 7.5 4.8 0 217 15.6 61.2 313s 13 4.9 8.3 5.3 1 213 11.4 53.4 313s 14 3.7 5.4 5.6 2 207 7.0 44.3 313s 15 4.0 6.8 6.0 3 202 11.2 45.1 313s 16 4.4 7.2 6.1 4 199 12.3 49.7 313s 17 2.9 8.3 7.4 5 198 14.0 54.4 313s 18 4.3 6.7 6.7 6 200 17.6 62.7 313s 19 5.3 7.4 7.7 7 202 17.3 65.0 313s 20 6.6 8.9 7.8 8 200 15.3 60.9 313s 21 7.4 9.6 8.0 9 201 19.0 69.5 313s 22 13.8 11.6 8.5 10 204 21.1 75.7 313s govExp taxes govWage trend capitalLag corpProfLag gnpLag 313s 1 2.4 3.4 2.2 -11 180 NA NA 313s 2 3.9 7.7 2.7 -10 183 12.7 44.9 313s 3 3.2 3.9 2.9 -9 183 12.4 45.6 313s 4 2.8 4.7 2.9 -8 184 16.9 50.1 313s 5 3.5 3.8 3.1 -7 190 18.4 57.2 313s 6 3.3 5.5 3.2 -6 193 19.4 57.1 313s 7 3.3 7.0 3.3 -5 198 20.1 NA 313s 8 4.0 6.7 3.6 -4 203 19.6 64.0 313s 9 4.2 4.2 3.7 -3 208 19.8 64.4 313s 10 4.1 4.0 4.0 -2 211 21.1 64.5 313s 11 5.2 7.7 4.2 -1 216 21.7 67.0 313s 12 5.9 7.5 4.8 0 217 15.6 61.2 313s 13 4.9 8.3 5.3 1 213 11.4 53.4 313s 14 3.7 5.4 5.6 2 207 7.0 44.3 313s 15 4.0 6.8 6.0 3 202 11.2 45.1 313s 16 4.4 7.2 6.1 4 199 12.3 49.7 313s 17 2.9 8.3 7.4 5 198 14.0 54.4 313s 18 4.3 6.7 6.7 6 200 17.6 62.7 313s 19 5.3 7.4 7.7 7 202 17.3 65.0 313s 20 6.6 8.9 7.8 8 200 15.3 60.9 313s 21 7.4 9.6 8.0 9 201 19.0 69.5 313s 22 13.8 11.6 8.5 10 204 21.1 75.7 313s govExp taxes govWage trend capitalLag corpProfLag gnpLag 313s 1 2.4 3.4 2.2 -11 180 NA NA 313s 2 3.9 7.7 2.7 -10 183 12.7 44.9 313s 3 3.2 3.9 2.9 -9 183 12.4 45.6 313s 4 2.8 4.7 2.9 -8 184 16.9 50.1 313s 5 3.5 3.8 3.1 -7 190 18.4 57.2 313s 6 3.3 5.5 3.2 -6 193 19.4 57.1 313s 7 3.3 7.0 3.3 -5 198 20.1 NA 313s 8 4.0 6.7 3.6 -4 203 19.6 64.0 313s 9 4.2 4.2 3.7 -3 208 19.8 64.4 313s 10 4.1 4.0 4.0 -2 211 21.1 64.5 313s 11 5.2 7.7 4.2 -1 216 21.7 67.0 313s 12 5.9 7.5 4.8 0 217 15.6 61.2 313s 13 4.9 8.3 5.3 1 213 11.4 53.4 313s 14 3.7 5.4 5.6 2 207 7.0 44.3 313s 15 4.0 6.8 6.0 3 202 11.2 45.1 313s 16 4.4 7.2 6.1 4 199 12.3 49.7 313s 17 2.9 8.3 7.4 5 198 14.0 54.4 313s 18 4.3 6.7 6.7 6 200 17.6 62.7 313s 19 5.3 7.4 7.7 7 202 17.3 65.0 313s 20 6.6 8.9 7.8 8 200 15.3 60.9 313s 21 7.4 9.6 8.0 9 201 19.0 69.5 313s 22 13.8 11.6 8.5 10 204 21.1 75.7 313s > model.matrix 313s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 313s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 313s [3] "Numeric: lengths (696, 672) differ" 313s > matrix of instrumental variables 313s Consumption_(Intercept) Consumption_govExp Consumption_taxes 313s Consumption_2 1 3.9 7.7 313s Consumption_3 1 3.2 3.9 313s Consumption_4 1 2.8 4.7 313s Consumption_5 1 3.5 3.8 313s Consumption_6 1 3.3 5.5 313s Consumption_8 1 4.0 6.7 313s Consumption_9 1 4.2 4.2 313s Consumption_11 1 5.2 7.7 313s Consumption_12 1 5.9 7.5 313s Consumption_14 1 3.7 5.4 313s Consumption_15 1 4.0 6.8 313s Consumption_16 1 4.4 7.2 313s Consumption_17 1 2.9 8.3 313s Consumption_18 1 4.3 6.7 313s Consumption_19 1 5.3 7.4 313s Consumption_20 1 6.6 8.9 313s Consumption_21 1 7.4 9.6 313s Consumption_22 1 13.8 11.6 313s Investment_2 0 0.0 0.0 313s Investment_3 0 0.0 0.0 313s Investment_4 0 0.0 0.0 313s Investment_5 0 0.0 0.0 313s Investment_6 0 0.0 0.0 313s Investment_8 0 0.0 0.0 313s Investment_9 0 0.0 0.0 313s Investment_10 0 0.0 0.0 313s Investment_11 0 0.0 0.0 313s Investment_12 0 0.0 0.0 313s Investment_14 0 0.0 0.0 313s Investment_15 0 0.0 0.0 313s Investment_17 0 0.0 0.0 313s Investment_18 0 0.0 0.0 313s Investment_19 0 0.0 0.0 313s Investment_20 0 0.0 0.0 313s Investment_21 0 0.0 0.0 313s Investment_22 0 0.0 0.0 313s PrivateWages_2 0 0.0 0.0 313s PrivateWages_3 0 0.0 0.0 313s PrivateWages_4 0 0.0 0.0 313s PrivateWages_5 0 0.0 0.0 313s PrivateWages_6 0 0.0 0.0 313s PrivateWages_8 0 0.0 0.0 313s PrivateWages_9 0 0.0 0.0 313s PrivateWages_10 0 0.0 0.0 313s PrivateWages_11 0 0.0 0.0 313s PrivateWages_12 0 0.0 0.0 313s PrivateWages_13 0 0.0 0.0 313s PrivateWages_14 0 0.0 0.0 313s PrivateWages_15 0 0.0 0.0 313s PrivateWages_16 0 0.0 0.0 313s PrivateWages_17 0 0.0 0.0 313s PrivateWages_18 0 0.0 0.0 313s PrivateWages_19 0 0.0 0.0 313s PrivateWages_20 0 0.0 0.0 313s PrivateWages_21 0 0.0 0.0 313s PrivateWages_22 0 0.0 0.0 313s Consumption_govWage Consumption_trend Consumption_capitalLag 313s Consumption_2 2.7 -10 183 313s Consumption_3 2.9 -9 183 313s Consumption_4 2.9 -8 184 313s Consumption_5 3.1 -7 190 313s Consumption_6 3.2 -6 193 313s Consumption_8 3.6 -4 203 313s Consumption_9 3.7 -3 208 313s Consumption_11 4.2 -1 216 313s Consumption_12 4.8 0 217 313s Consumption_14 5.6 2 207 313s Consumption_15 6.0 3 202 313s Consumption_16 6.1 4 199 313s Consumption_17 7.4 5 198 313s Consumption_18 6.7 6 200 313s Consumption_19 7.7 7 202 313s Consumption_20 7.8 8 200 313s Consumption_21 8.0 9 201 313s Consumption_22 8.5 10 204 313s Investment_2 0.0 0 0 313s Investment_3 0.0 0 0 313s Investment_4 0.0 0 0 313s Investment_5 0.0 0 0 313s Investment_6 0.0 0 0 313s Investment_8 0.0 0 0 313s Investment_9 0.0 0 0 313s Investment_10 0.0 0 0 313s Investment_11 0.0 0 0 313s Investment_12 0.0 0 0 313s Investment_14 0.0 0 0 313s Investment_15 0.0 0 0 313s Investment_17 0.0 0 0 313s Investment_18 0.0 0 0 313s Investment_19 0.0 0 0 313s Investment_20 0.0 0 0 313s Investment_21 0.0 0 0 313s Investment_22 0.0 0 0 313s PrivateWages_2 0.0 0 0 313s PrivateWages_3 0.0 0 0 313s PrivateWages_4 0.0 0 0 313s PrivateWages_5 0.0 0 0 313s PrivateWages_6 0.0 0 0 313s PrivateWages_8 0.0 0 0 313s PrivateWages_9 0.0 0 0 313s PrivateWages_10 0.0 0 0 313s PrivateWages_11 0.0 0 0 313s PrivateWages_12 0.0 0 0 313s PrivateWages_13 0.0 0 0 313s PrivateWages_14 0.0 0 0 313s PrivateWages_15 0.0 0 0 313s PrivateWages_16 0.0 0 0 313s PrivateWages_17 0.0 0 0 313s PrivateWages_18 0.0 0 0 313s PrivateWages_19 0.0 0 0 313s PrivateWages_20 0.0 0 0 313s PrivateWages_21 0.0 0 0 313s PrivateWages_22 0.0 0 0 313s Consumption_corpProfLag Consumption_gnpLag 313s Consumption_2 12.7 44.9 313s Consumption_3 12.4 45.6 313s Consumption_4 16.9 50.1 313s Consumption_5 18.4 57.2 313s Consumption_6 19.4 57.1 313s Consumption_8 19.6 64.0 313s Consumption_9 19.8 64.4 313s Consumption_11 21.7 67.0 313s Consumption_12 15.6 61.2 313s Consumption_14 7.0 44.3 313s Consumption_15 11.2 45.1 313s Consumption_16 12.3 49.7 313s Consumption_17 14.0 54.4 313s Consumption_18 17.6 62.7 313s Consumption_19 17.3 65.0 313s Consumption_20 15.3 60.9 313s Consumption_21 19.0 69.5 313s Consumption_22 21.1 75.7 313s Investment_2 0.0 0.0 313s Investment_3 0.0 0.0 313s Investment_4 0.0 0.0 313s Investment_5 0.0 0.0 313s Investment_6 0.0 0.0 313s Investment_8 0.0 0.0 313s Investment_9 0.0 0.0 313s Investment_10 0.0 0.0 313s Investment_11 0.0 0.0 313s Investment_12 0.0 0.0 313s Investment_14 0.0 0.0 313s Investment_15 0.0 0.0 313s Investment_17 0.0 0.0 313s Investment_18 0.0 0.0 313s Investment_19 0.0 0.0 313s Investment_20 0.0 0.0 313s Investment_21 0.0 0.0 313s Investment_22 0.0 0.0 313s PrivateWages_2 0.0 0.0 313s PrivateWages_3 0.0 0.0 313s PrivateWages_4 0.0 0.0 313s PrivateWages_5 0.0 0.0 313s PrivateWages_6 0.0 0.0 313s PrivateWages_8 0.0 0.0 313s PrivateWages_9 0.0 0.0 313s PrivateWages_10 0.0 0.0 313s PrivateWages_11 0.0 0.0 313s PrivateWages_12 0.0 0.0 313s PrivateWages_13 0.0 0.0 313s PrivateWages_14 0.0 0.0 313s PrivateWages_15 0.0 0.0 313s PrivateWages_16 0.0 0.0 313s PrivateWages_17 0.0 0.0 313s PrivateWages_18 0.0 0.0 313s PrivateWages_19 0.0 0.0 313s PrivateWages_20 0.0 0.0 313s PrivateWages_21 0.0 0.0 313s PrivateWages_22 0.0 0.0 313s Investment_(Intercept) Investment_govExp Investment_taxes 313s Consumption_2 0 0.0 0.0 313s Consumption_3 0 0.0 0.0 313s Consumption_4 0 0.0 0.0 313s Consumption_5 0 0.0 0.0 313s Consumption_6 0 0.0 0.0 313s Consumption_8 0 0.0 0.0 313s Consumption_9 0 0.0 0.0 313s Consumption_11 0 0.0 0.0 313s Consumption_12 0 0.0 0.0 313s Consumption_14 0 0.0 0.0 313s Consumption_15 0 0.0 0.0 313s Consumption_16 0 0.0 0.0 313s Consumption_17 0 0.0 0.0 313s Consumption_18 0 0.0 0.0 313s Consumption_19 0 0.0 0.0 313s Consumption_20 0 0.0 0.0 313s Consumption_21 0 0.0 0.0 313s Consumption_22 0 0.0 0.0 313s Investment_2 1 3.9 7.7 313s Investment_3 1 3.2 3.9 313s Investment_4 1 2.8 4.7 313s Investment_5 1 3.5 3.8 313s Investment_6 1 3.3 5.5 313s Investment_8 1 4.0 6.7 313s Investment_9 1 4.2 4.2 313s Investment_10 1 4.1 4.0 313s Investment_11 1 5.2 7.7 313s Investment_12 1 5.9 7.5 313s Investment_14 1 3.7 5.4 313s Investment_15 1 4.0 6.8 313s Investment_17 1 2.9 8.3 313s Investment_18 1 4.3 6.7 313s Investment_19 1 5.3 7.4 313s Investment_20 1 6.6 8.9 313s Investment_21 1 7.4 9.6 313s Investment_22 1 13.8 11.6 313s PrivateWages_2 0 0.0 0.0 313s PrivateWages_3 0 0.0 0.0 313s PrivateWages_4 0 0.0 0.0 313s PrivateWages_5 0 0.0 0.0 313s PrivateWages_6 0 0.0 0.0 313s PrivateWages_8 0 0.0 0.0 313s PrivateWages_9 0 0.0 0.0 313s PrivateWages_10 0 0.0 0.0 313s PrivateWages_11 0 0.0 0.0 313s PrivateWages_12 0 0.0 0.0 313s PrivateWages_13 0 0.0 0.0 313s PrivateWages_14 0 0.0 0.0 313s PrivateWages_15 0 0.0 0.0 313s PrivateWages_16 0 0.0 0.0 313s PrivateWages_17 0 0.0 0.0 313s PrivateWages_18 0 0.0 0.0 313s PrivateWages_19 0 0.0 0.0 313s PrivateWages_20 0 0.0 0.0 313s PrivateWages_21 0 0.0 0.0 313s PrivateWages_22 0 0.0 0.0 313s Investment_govWage Investment_trend Investment_capitalLag 313s Consumption_2 0.0 0 0 313s Consumption_3 0.0 0 0 313s Consumption_4 0.0 0 0 313s Consumption_5 0.0 0 0 313s Consumption_6 0.0 0 0 313s Consumption_8 0.0 0 0 313s Consumption_9 0.0 0 0 313s Consumption_11 0.0 0 0 313s Consumption_12 0.0 0 0 313s Consumption_14 0.0 0 0 313s Consumption_15 0.0 0 0 313s Consumption_16 0.0 0 0 313s Consumption_17 0.0 0 0 313s Consumption_18 0.0 0 0 313s Consumption_19 0.0 0 0 313s Consumption_20 0.0 0 0 313s Consumption_21 0.0 0 0 313s Consumption_22 0.0 0 0 313s Investment_2 2.7 -10 183 313s Investment_3 2.9 -9 183 313s Investment_4 2.9 -8 184 313s Investment_5 3.1 -7 190 313s Investment_6 3.2 -6 193 313s Investment_8 3.6 -4 203 313s Investment_9 3.7 -3 208 313s Investment_10 4.0 -2 211 313s Investment_11 4.2 -1 216 313s Investment_12 4.8 0 217 313s Investment_14 5.6 2 207 313s Investment_15 6.0 3 202 313s Investment_17 7.4 5 198 313s Investment_18 6.7 6 200 313s Investment_19 7.7 7 202 313s Investment_20 7.8 8 200 313s Investment_21 8.0 9 201 313s Investment_22 8.5 10 204 313s PrivateWages_2 0.0 0 0 313s PrivateWages_3 0.0 0 0 313s PrivateWages_4 0.0 0 0 313s PrivateWages_5 0.0 0 0 313s PrivateWages_6 0.0 0 0 313s PrivateWages_8 0.0 0 0 313s PrivateWages_9 0.0 0 0 313s PrivateWages_10 0.0 0 0 313s PrivateWages_11 0.0 0 0 313s PrivateWages_12 0.0 0 0 313s PrivateWages_13 0.0 0 0 313s PrivateWages_14 0.0 0 0 313s PrivateWages_15 0.0 0 0 313s PrivateWages_16 0.0 0 0 313s PrivateWages_17 0.0 0 0 313s PrivateWages_18 0.0 0 0 313s PrivateWages_19 0.0 0 0 313s PrivateWages_20 0.0 0 0 313s PrivateWages_21 0.0 0 0 313s PrivateWages_22 0.0 0 0 313s Investment_corpProfLag Investment_gnpLag 313s Consumption_2 0.0 0.0 313s Consumption_3 0.0 0.0 313s Consumption_4 0.0 0.0 313s Consumption_5 0.0 0.0 313s Consumption_6 0.0 0.0 313s Consumption_8 0.0 0.0 313s Consumption_9 0.0 0.0 313s Consumption_11 0.0 0.0 313s Consumption_12 0.0 0.0 313s Consumption_14 0.0 0.0 313s Consumption_15 0.0 0.0 313s Consumption_16 0.0 0.0 313s Consumption_17 0.0 0.0 313s Consumption_18 0.0 0.0 313s Consumption_19 0.0 0.0 313s Consumption_20 0.0 0.0 313s Consumption_21 0.0 0.0 313s Consumption_22 0.0 0.0 313s Investment_2 12.7 44.9 313s Investment_3 12.4 45.6 313s Investment_4 16.9 50.1 313s Investment_5 18.4 57.2 313s Investment_6 19.4 57.1 313s Investment_8 19.6 64.0 313s Investment_9 19.8 64.4 313s Investment_10 21.1 64.5 313s Investment_11 21.7 67.0 313s Investment_12 15.6 61.2 313s Investment_14 7.0 44.3 313s Investment_15 11.2 45.1 313s Investment_17 14.0 54.4 313s Investment_18 17.6 62.7 313s Investment_19 17.3 65.0 313s Investment_20 15.3 60.9 313s Investment_21 19.0 69.5 313s Investment_22 21.1 75.7 313s PrivateWages_2 0.0 0.0 313s PrivateWages_3 0.0 0.0 313s PrivateWages_4 0.0 0.0 313s PrivateWages_5 0.0 0.0 313s PrivateWages_6 0.0 0.0 313s PrivateWages_8 0.0 0.0 313s PrivateWages_9 0.0 0.0 313s PrivateWages_10 0.0 0.0 313s PrivateWages_11 0.0 0.0 313s PrivateWages_12 0.0 0.0 313s PrivateWages_13 0.0 0.0 313s PrivateWages_14 0.0 0.0 313s PrivateWages_15 0.0 0.0 313s PrivateWages_16 0.0 0.0 313s PrivateWages_17 0.0 0.0 313s PrivateWages_18 0.0 0.0 313s PrivateWages_19 0.0 0.0 313s PrivateWages_20 0.0 0.0 313s PrivateWages_21 0.0 0.0 313s PrivateWages_22 0.0 0.0 313s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 313s Consumption_2 0 0.0 0.0 313s Consumption_3 0 0.0 0.0 313s Consumption_4 0 0.0 0.0 313s Consumption_5 0 0.0 0.0 313s Consumption_6 0 0.0 0.0 313s Consumption_8 0 0.0 0.0 313s Consumption_9 0 0.0 0.0 313s Consumption_11 0 0.0 0.0 313s Consumption_12 0 0.0 0.0 313s Consumption_14 0 0.0 0.0 313s Consumption_15 0 0.0 0.0 313s Consumption_16 0 0.0 0.0 313s Consumption_17 0 0.0 0.0 313s Consumption_18 0 0.0 0.0 313s Consumption_19 0 0.0 0.0 313s Consumption_20 0 0.0 0.0 313s Consumption_21 0 0.0 0.0 313s Consumption_22 0 0.0 0.0 313s Investment_2 0 0.0 0.0 313s Investment_3 0 0.0 0.0 313s Investment_4 0 0.0 0.0 313s Investment_5 0 0.0 0.0 313s Investment_6 0 0.0 0.0 313s Investment_8 0 0.0 0.0 313s Investment_9 0 0.0 0.0 313s Investment_10 0 0.0 0.0 313s Investment_11 0 0.0 0.0 313s Investment_12 0 0.0 0.0 313s Investment_14 0 0.0 0.0 313s Investment_15 0 0.0 0.0 313s Investment_17 0 0.0 0.0 313s Investment_18 0 0.0 0.0 313s Investment_19 0 0.0 0.0 313s Investment_20 0 0.0 0.0 313s Investment_21 0 0.0 0.0 313s Investment_22 0 0.0 0.0 313s PrivateWages_2 1 3.9 7.7 313s PrivateWages_3 1 3.2 3.9 313s PrivateWages_4 1 2.8 4.7 313s PrivateWages_5 1 3.5 3.8 313s PrivateWages_6 1 3.3 5.5 313s PrivateWages_8 1 4.0 6.7 313s PrivateWages_9 1 4.2 4.2 313s PrivateWages_10 1 4.1 4.0 313s PrivateWages_11 1 5.2 7.7 313s PrivateWages_12 1 5.9 7.5 313s PrivateWages_13 1 4.9 8.3 313s PrivateWages_14 1 3.7 5.4 313s PrivateWages_15 1 4.0 6.8 313s PrivateWages_16 1 4.4 7.2 313s PrivateWages_17 1 2.9 8.3 313s PrivateWages_18 1 4.3 6.7 313s PrivateWages_19 1 5.3 7.4 313s PrivateWages_20 1 6.6 8.9 313s PrivateWages_21 1 7.4 9.6 313s PrivateWages_22 1 13.8 11.6 313s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 313s Consumption_2 0.0 0 0 313s Consumption_3 0.0 0 0 313s Consumption_4 0.0 0 0 313s Consumption_5 0.0 0 0 313s Consumption_6 0.0 0 0 313s Consumption_8 0.0 0 0 313s Consumption_9 0.0 0 0 313s Consumption_11 0.0 0 0 313s Consumption_12 0.0 0 0 313s Consumption_14 0.0 0 0 313s Consumption_15 0.0 0 0 313s Consumption_16 0.0 0 0 313s Consumption_17 0.0 0 0 313s Consumption_18 0.0 0 0 313s Consumption_19 0.0 0 0 313s Consumption_20 0.0 0 0 313s Consumption_21 0.0 0 0 313s Consumption_22 0.0 0 0 313s Investment_2 0.0 0 0 313s Investment_3 0.0 0 0 313s Investment_4 0.0 0 0 313s Investment_5 0.0 0 0 313s Investment_6 0.0 0 0 313s Investment_8 0.0 0 0 313s Investment_9 0.0 0 0 313s Investment_10 0.0 0 0 313s Investment_11 0.0 0 0 313s Investment_12 0.0 0 0 313s Investment_14 0.0 0 0 313s Investment_15 0.0 0 0 313s Investment_17 0.0 0 0 313s Investment_18 0.0 0 0 313s Investment_19 0.0 0 0 313s Investment_20 0.0 0 0 313s Investment_21 0.0 0 0 313s Investment_22 0.0 0 0 313s PrivateWages_2 2.7 -10 183 313s PrivateWages_3 2.9 -9 183 313s PrivateWages_4 2.9 -8 184 313s PrivateWages_5 3.1 -7 190 313s PrivateWages_6 3.2 -6 193 313s PrivateWages_8 3.6 -4 203 313s PrivateWages_9 3.7 -3 208 313s PrivateWages_10 4.0 -2 211 313s PrivateWages_11 4.2 -1 216 313s PrivateWages_12 4.8 0 217 313s PrivateWages_13 5.3 1 213 313s PrivateWages_14 5.6 2 207 313s PrivateWages_15 6.0 3 202 313s PrivateWages_16 6.1 4 199 313s PrivateWages_17 7.4 5 198 313s PrivateWages_18 6.7 6 200 313s PrivateWages_19 7.7 7 202 313s PrivateWages_20 7.8 8 200 313s PrivateWages_21 8.0 9 201 313s PrivateWages_22 8.5 10 204 313s PrivateWages_corpProfLag PrivateWages_gnpLag 313s Consumption_2 0.0 0.0 313s Consumption_3 0.0 0.0 313s Consumption_4 0.0 0.0 313s Consumption_5 0.0 0.0 313s Consumption_6 0.0 0.0 313s Consumption_8 0.0 0.0 313s Consumption_9 0.0 0.0 313s Consumption_11 0.0 0.0 313s Consumption_12 0.0 0.0 313s Consumption_14 0.0 0.0 313s Consumption_15 0.0 0.0 313s Consumption_16 0.0 0.0 313s Consumption_17 0.0 0.0 313s Consumption_18 0.0 0.0 313s Consumption_19 0.0 0.0 313s Consumption_20 0.0 0.0 313s Consumption_21 0.0 0.0 313s Consumption_22 0.0 0.0 313s Investment_2 0.0 0.0 313s Investment_3 0.0 0.0 313s Investment_4 0.0 0.0 313s Investment_5 0.0 0.0 313s Investment_6 0.0 0.0 313s Investment_8 0.0 0.0 313s Investment_9 0.0 0.0 313s Investment_10 0.0 0.0 313s Investment_11 0.0 0.0 313s Investment_12 0.0 0.0 313s Investment_14 0.0 0.0 313s Investment_15 0.0 0.0 313s Investment_17 0.0 0.0 313s Investment_18 0.0 0.0 313s Investment_19 0.0 0.0 313s Investment_20 0.0 0.0 313s Investment_21 0.0 0.0 313s Investment_22 0.0 0.0 313s PrivateWages_2 12.7 44.9 313s PrivateWages_3 12.4 45.6 313s PrivateWages_4 16.9 50.1 313s PrivateWages_5 18.4 57.2 313s PrivateWages_6 19.4 57.1 313s PrivateWages_8 19.6 64.0 313s PrivateWages_9 19.8 64.4 313s PrivateWages_10 21.1 64.5 313s PrivateWages_11 21.7 67.0 313s PrivateWages_12 15.6 61.2 313s PrivateWages_13 11.4 53.4 313s PrivateWages_14 7.0 44.3 313s PrivateWages_15 11.2 45.1 313s PrivateWages_16 12.3 49.7 313s PrivateWages_17 14.0 54.4 313s PrivateWages_18 17.6 62.7 313s PrivateWages_19 17.3 65.0 313s PrivateWages_20 15.3 60.9 313s PrivateWages_21 19.0 69.5 313s PrivateWages_22 21.1 75.7 313s > matrix of fitted regressors 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_2 1 14.0 313s Consumption_3 1 16.7 313s Consumption_4 1 18.5 313s Consumption_5 1 20.3 313s Consumption_6 1 19.0 313s Consumption_8 1 17.6 313s Consumption_9 1 18.9 313s Consumption_11 1 16.7 313s Consumption_12 1 13.4 313s Consumption_14 1 10.0 313s Consumption_15 1 12.5 313s Consumption_16 1 14.5 313s Consumption_17 1 14.9 313s Consumption_18 1 19.4 313s Consumption_19 1 19.1 313s Consumption_20 1 17.7 313s Consumption_21 1 20.4 313s Consumption_22 1 22.7 313s Investment_2 0 0.0 313s Investment_3 0 0.0 313s Investment_4 0 0.0 313s Investment_5 0 0.0 313s Investment_6 0 0.0 313s Investment_8 0 0.0 313s Investment_9 0 0.0 313s Investment_10 0 0.0 313s Investment_11 0 0.0 313s Investment_12 0 0.0 313s Investment_14 0 0.0 313s Investment_15 0 0.0 313s Investment_17 0 0.0 313s Investment_18 0 0.0 313s Investment_19 0 0.0 313s Investment_20 0 0.0 313s Investment_21 0 0.0 313s Investment_22 0 0.0 313s PrivateWages_2 0 0.0 313s PrivateWages_3 0 0.0 313s PrivateWages_4 0 0.0 313s PrivateWages_5 0 0.0 313s PrivateWages_6 0 0.0 313s PrivateWages_8 0 0.0 313s PrivateWages_9 0 0.0 313s PrivateWages_10 0 0.0 313s PrivateWages_11 0 0.0 313s PrivateWages_12 0 0.0 313s PrivateWages_13 0 0.0 313s PrivateWages_14 0 0.0 313s PrivateWages_15 0 0.0 313s PrivateWages_16 0 0.0 313s PrivateWages_17 0 0.0 313s PrivateWages_18 0 0.0 313s PrivateWages_19 0 0.0 313s PrivateWages_20 0 0.0 313s PrivateWages_21 0 0.0 313s PrivateWages_22 0 0.0 313s Consumption_corpProfLag Consumption_wages 313s Consumption_2 12.7 29.8 313s Consumption_3 12.4 31.8 313s Consumption_4 16.9 35.3 313s Consumption_5 18.4 38.6 313s Consumption_6 19.4 38.5 313s Consumption_8 19.6 40.0 313s Consumption_9 19.8 41.8 313s Consumption_11 21.7 43.1 313s Consumption_12 15.6 39.7 313s Consumption_14 7.0 33.3 313s Consumption_15 11.2 37.3 313s Consumption_16 12.3 40.1 313s Consumption_17 14.0 41.8 313s Consumption_18 17.6 47.6 313s Consumption_19 17.3 49.2 313s Consumption_20 15.3 48.6 313s Consumption_21 19.0 53.4 313s Consumption_22 21.1 60.8 313s Investment_2 0.0 0.0 313s Investment_3 0.0 0.0 313s Investment_4 0.0 0.0 313s Investment_5 0.0 0.0 313s Investment_6 0.0 0.0 313s Investment_8 0.0 0.0 313s Investment_9 0.0 0.0 313s Investment_10 0.0 0.0 313s Investment_11 0.0 0.0 313s Investment_12 0.0 0.0 313s Investment_14 0.0 0.0 313s Investment_15 0.0 0.0 313s Investment_17 0.0 0.0 313s Investment_18 0.0 0.0 313s Investment_19 0.0 0.0 313s Investment_20 0.0 0.0 313s Investment_21 0.0 0.0 313s Investment_22 0.0 0.0 313s PrivateWages_2 0.0 0.0 313s PrivateWages_3 0.0 0.0 313s PrivateWages_4 0.0 0.0 313s PrivateWages_5 0.0 0.0 313s PrivateWages_6 0.0 0.0 313s PrivateWages_8 0.0 0.0 313s PrivateWages_9 0.0 0.0 313s PrivateWages_10 0.0 0.0 313s PrivateWages_11 0.0 0.0 313s PrivateWages_12 0.0 0.0 313s PrivateWages_13 0.0 0.0 313s PrivateWages_14 0.0 0.0 313s PrivateWages_15 0.0 0.0 313s PrivateWages_16 0.0 0.0 313s PrivateWages_17 0.0 0.0 313s PrivateWages_18 0.0 0.0 313s PrivateWages_19 0.0 0.0 313s PrivateWages_20 0.0 0.0 313s PrivateWages_21 0.0 0.0 313s PrivateWages_22 0.0 0.0 313s Investment_(Intercept) Investment_corpProf 313s Consumption_2 0 0.0 313s Consumption_3 0 0.0 313s Consumption_4 0 0.0 313s Consumption_5 0 0.0 313s Consumption_6 0 0.0 313s Consumption_8 0 0.0 313s Consumption_9 0 0.0 313s Consumption_11 0 0.0 313s Consumption_12 0 0.0 313s Consumption_14 0 0.0 313s Consumption_15 0 0.0 313s Consumption_16 0 0.0 313s Consumption_17 0 0.0 313s Consumption_18 0 0.0 313s Consumption_19 0 0.0 313s Consumption_20 0 0.0 313s Consumption_21 0 0.0 313s Consumption_22 0 0.0 313s Investment_2 1 13.4 313s Investment_3 1 16.7 313s Investment_4 1 18.8 313s Investment_5 1 20.6 313s Investment_6 1 19.3 313s Investment_8 1 17.5 313s Investment_9 1 19.5 313s Investment_10 1 20.2 313s Investment_11 1 17.2 313s Investment_12 1 13.5 313s Investment_14 1 10.1 313s Investment_15 1 13.0 313s Investment_17 1 14.9 313s Investment_18 1 19.5 313s Investment_19 1 19.3 313s Investment_20 1 17.5 313s Investment_21 1 20.2 313s Investment_22 1 22.8 313s PrivateWages_2 0 0.0 313s PrivateWages_3 0 0.0 313s PrivateWages_4 0 0.0 313s PrivateWages_5 0 0.0 313s PrivateWages_6 0 0.0 313s PrivateWages_8 0 0.0 313s PrivateWages_9 0 0.0 313s PrivateWages_10 0 0.0 313s PrivateWages_11 0 0.0 313s PrivateWages_12 0 0.0 313s PrivateWages_13 0 0.0 313s PrivateWages_14 0 0.0 313s PrivateWages_15 0 0.0 313s PrivateWages_16 0 0.0 313s PrivateWages_17 0 0.0 313s PrivateWages_18 0 0.0 313s PrivateWages_19 0 0.0 313s PrivateWages_20 0 0.0 313s PrivateWages_21 0 0.0 313s PrivateWages_22 0 0.0 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_2 0.0 0 313s Consumption_3 0.0 0 313s Consumption_4 0.0 0 313s Consumption_5 0.0 0 313s Consumption_6 0.0 0 313s Consumption_8 0.0 0 313s Consumption_9 0.0 0 313s Consumption_11 0.0 0 313s Consumption_12 0.0 0 313s Consumption_14 0.0 0 313s Consumption_15 0.0 0 313s Consumption_16 0.0 0 313s Consumption_17 0.0 0 313s Consumption_18 0.0 0 313s Consumption_19 0.0 0 313s Consumption_20 0.0 0 313s Consumption_21 0.0 0 313s Consumption_22 0.0 0 313s Investment_2 12.7 183 313s Investment_3 12.4 183 313s Investment_4 16.9 184 313s Investment_5 18.4 190 313s Investment_6 19.4 193 313s Investment_8 19.6 203 313s Investment_9 19.8 208 313s Investment_10 21.1 211 313s Investment_11 21.7 216 313s Investment_12 15.6 217 313s Investment_14 7.0 207 313s Investment_15 11.2 202 313s Investment_17 14.0 198 313s Investment_18 17.6 200 313s Investment_19 17.3 202 313s Investment_20 15.3 200 313s Investment_21 19.0 201 313s Investment_22 21.1 204 313s PrivateWages_2 0.0 0 313s PrivateWages_3 0.0 0 313s PrivateWages_4 0.0 0 313s PrivateWages_5 0.0 0 313s PrivateWages_6 0.0 0 313s PrivateWages_8 0.0 0 313s PrivateWages_9 0.0 0 313s PrivateWages_10 0.0 0 313s PrivateWages_11 0.0 0 313s PrivateWages_12 0.0 0 313s PrivateWages_13 0.0 0 313s PrivateWages_14 0.0 0 313s PrivateWages_15 0.0 0 313s PrivateWages_16 0.0 0 313s PrivateWages_17 0.0 0 313s PrivateWages_18 0.0 0 313s PrivateWages_19 0.0 0 313s PrivateWages_20 0.0 0 313s PrivateWages_21 0.0 0 313s PrivateWages_22 0.0 0 313s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 313s Consumption_2 0 0.0 0.0 313s Consumption_3 0 0.0 0.0 313s Consumption_4 0 0.0 0.0 313s Consumption_5 0 0.0 0.0 313s Consumption_6 0 0.0 0.0 313s Consumption_8 0 0.0 0.0 313s Consumption_9 0 0.0 0.0 313s Consumption_11 0 0.0 0.0 313s Consumption_12 0 0.0 0.0 313s Consumption_14 0 0.0 0.0 313s Consumption_15 0 0.0 0.0 313s Consumption_16 0 0.0 0.0 313s Consumption_17 0 0.0 0.0 313s Consumption_18 0 0.0 0.0 313s Consumption_19 0 0.0 0.0 313s Consumption_20 0 0.0 0.0 313s Consumption_21 0 0.0 0.0 313s Consumption_22 0 0.0 0.0 313s Investment_2 0 0.0 0.0 313s Investment_3 0 0.0 0.0 313s Investment_4 0 0.0 0.0 313s Investment_5 0 0.0 0.0 313s Investment_6 0 0.0 0.0 313s Investment_8 0 0.0 0.0 313s Investment_9 0 0.0 0.0 313s Investment_10 0 0.0 0.0 313s Investment_11 0 0.0 0.0 313s Investment_12 0 0.0 0.0 313s Investment_14 0 0.0 0.0 313s Investment_15 0 0.0 0.0 313s Investment_17 0 0.0 0.0 313s Investment_18 0 0.0 0.0 313s Investment_19 0 0.0 0.0 313s Investment_20 0 0.0 0.0 313s Investment_21 0 0.0 0.0 313s Investment_22 0 0.0 0.0 313s PrivateWages_2 1 47.1 44.9 313s PrivateWages_3 1 49.6 45.6 313s PrivateWages_4 1 56.5 50.1 313s PrivateWages_5 1 60.7 57.2 313s PrivateWages_6 1 60.6 57.1 313s PrivateWages_8 1 60.0 64.0 313s PrivateWages_9 1 62.3 64.4 313s PrivateWages_10 1 64.6 64.5 313s PrivateWages_11 1 63.7 67.0 313s PrivateWages_12 1 54.8 61.2 313s PrivateWages_13 1 47.0 53.4 313s PrivateWages_14 1 42.1 44.3 313s PrivateWages_15 1 51.2 45.1 313s PrivateWages_16 1 55.3 49.7 313s PrivateWages_17 1 57.4 54.4 313s PrivateWages_18 1 67.2 62.7 313s PrivateWages_19 1 68.5 65.0 313s PrivateWages_20 1 66.8 60.9 313s PrivateWages_21 1 74.9 69.5 313s PrivateWages_22 1 86.9 75.7 313s PrivateWages_trend 313s Consumption_2 0 313s Consumption_3 0 313s Consumption_4 0 313s Consumption_5 0 313s Consumption_6 0 313s Consumption_8 0 313s Consumption_9 0 313s Consumption_11 0 313s Consumption_12 0 313s Consumption_14 0 313s Consumption_15 0 313s Consumption_16 0 313s Consumption_17 0 313s Consumption_18 0 313s Consumption_19 0 313s Consumption_20 0 313s Consumption_21 0 313s Consumption_22 0 313s Investment_2 0 313s Investment_3 0 313s Investment_4 0 313s Investment_5 0 313s Investment_6 0 313s Investment_8 0 313s Investment_9 0 313s Investment_10 0 313s Investment_11 0 313s Investment_12 0 313s Investment_14 0 313s Investment_15 0 313s Investment_17 0 313s Investment_18 0 313s Investment_19 0 313s Investment_20 0 313s Investment_21 0 313s Investment_22 0 313s PrivateWages_2 -10 313s PrivateWages_3 -9 313s PrivateWages_4 -8 313s PrivateWages_5 -7 313s PrivateWages_6 -6 313s PrivateWages_8 -4 313s PrivateWages_9 -3 313s PrivateWages_10 -2 313s PrivateWages_11 -1 313s PrivateWages_12 0 313s PrivateWages_13 1 313s PrivateWages_14 2 313s PrivateWages_15 3 313s PrivateWages_16 4 313s PrivateWages_17 5 313s PrivateWages_18 6 313s PrivateWages_19 7 313s PrivateWages_20 8 313s PrivateWages_21 9 313s PrivateWages_22 10 313s > nobs 313s [1] 56 313s > linearHypothesis 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 45 313s 2 44 1 1.27 0.27 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 45 313s 2 44 1 1.66 0.2 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 45 313s 2 44 1 1.66 0.2 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 44 2 0.64 0.53 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 44 2 0.84 0.44 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 46 313s 2 44 2 1.68 0.43 313s > logLik 313s 'log Lik.' -69.5 (df=13) 313s 'log Lik.' -77.5 (df=13) 313s Estimating function 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_2 -1.891 -26.49 313s Consumption_3 -0.190 -3.16 313s Consumption_4 0.294 5.45 313s Consumption_5 -1.285 -26.05 313s Consumption_6 0.431 8.19 313s Consumption_8 2.670 47.11 313s Consumption_9 2.363 44.77 313s Consumption_11 -1.642 -27.49 313s Consumption_12 -1.735 -23.21 313s Consumption_14 0.834 8.35 313s Consumption_15 -1.061 -13.27 313s Consumption_16 -0.885 -12.82 313s Consumption_17 3.801 56.68 313s Consumption_18 -0.502 -9.76 313s Consumption_19 -3.000 -57.33 313s Consumption_20 2.012 35.52 313s Consumption_21 0.746 15.21 313s Consumption_22 -0.957 -21.70 313s Investment_2 0.000 0.00 313s Investment_3 0.000 0.00 313s Investment_4 0.000 0.00 313s Investment_5 0.000 0.00 313s Investment_6 0.000 0.00 313s Investment_8 0.000 0.00 313s Investment_9 0.000 0.00 313s Investment_10 0.000 0.00 313s Investment_11 0.000 0.00 313s Investment_12 0.000 0.00 313s Investment_14 0.000 0.00 313s Investment_15 0.000 0.00 313s Investment_17 0.000 0.00 313s Investment_18 0.000 0.00 313s Investment_19 0.000 0.00 313s Investment_20 0.000 0.00 313s Investment_21 0.000 0.00 313s Investment_22 0.000 0.00 313s PrivateWages_2 0.000 0.00 313s PrivateWages_3 0.000 0.00 313s PrivateWages_4 0.000 0.00 313s PrivateWages_5 0.000 0.00 313s PrivateWages_6 0.000 0.00 313s PrivateWages_8 0.000 0.00 313s PrivateWages_9 0.000 0.00 313s PrivateWages_10 0.000 0.00 313s PrivateWages_11 0.000 0.00 313s PrivateWages_12 0.000 0.00 313s PrivateWages_13 0.000 0.00 313s PrivateWages_14 0.000 0.00 313s PrivateWages_15 0.000 0.00 313s PrivateWages_16 0.000 0.00 313s PrivateWages_17 0.000 0.00 313s PrivateWages_18 0.000 0.00 313s PrivateWages_19 0.000 0.00 313s PrivateWages_20 0.000 0.00 313s PrivateWages_21 0.000 0.00 313s PrivateWages_22 0.000 0.00 313s Consumption_corpProfLag Consumption_wages 313s Consumption_2 -24.01 -56.38 313s Consumption_3 -2.35 -6.04 313s Consumption_4 4.96 10.35 313s Consumption_5 -23.65 -49.61 313s Consumption_6 8.35 16.60 313s Consumption_8 52.33 106.81 313s Consumption_9 46.80 98.74 313s Consumption_11 -35.64 -70.78 313s Consumption_12 -27.07 -68.81 313s Consumption_14 5.83 27.78 313s Consumption_15 -11.88 -39.61 313s Consumption_16 -10.89 -35.54 313s Consumption_17 53.21 158.79 313s Consumption_18 -8.84 -23.92 313s Consumption_19 -51.90 -147.70 313s Consumption_20 30.78 97.67 313s Consumption_21 14.17 39.83 313s Consumption_22 -20.20 -58.19 313s Investment_2 0.00 0.00 313s Investment_3 0.00 0.00 313s Investment_4 0.00 0.00 313s Investment_5 0.00 0.00 313s Investment_6 0.00 0.00 313s Investment_8 0.00 0.00 313s Investment_9 0.00 0.00 313s Investment_10 0.00 0.00 313s Investment_11 0.00 0.00 313s Investment_12 0.00 0.00 313s Investment_14 0.00 0.00 313s Investment_15 0.00 0.00 313s Investment_17 0.00 0.00 313s Investment_18 0.00 0.00 313s Investment_19 0.00 0.00 313s Investment_20 0.00 0.00 313s Investment_21 0.00 0.00 313s Investment_22 0.00 0.00 313s PrivateWages_2 0.00 0.00 313s PrivateWages_3 0.00 0.00 313s PrivateWages_4 0.00 0.00 313s PrivateWages_5 0.00 0.00 313s PrivateWages_6 0.00 0.00 313s PrivateWages_8 0.00 0.00 313s PrivateWages_9 0.00 0.00 313s PrivateWages_10 0.00 0.00 313s PrivateWages_11 0.00 0.00 313s PrivateWages_12 0.00 0.00 313s PrivateWages_13 0.00 0.00 313s PrivateWages_14 0.00 0.00 313s PrivateWages_15 0.00 0.00 313s PrivateWages_16 0.00 0.00 313s PrivateWages_17 0.00 0.00 313s PrivateWages_18 0.00 0.00 313s PrivateWages_19 0.00 0.00 313s PrivateWages_20 0.00 0.00 313s PrivateWages_21 0.00 0.00 313s PrivateWages_22 0.00 0.00 313s Investment_(Intercept) Investment_corpProf 313s Consumption_2 0.000 0.00 313s Consumption_3 0.000 0.00 313s Consumption_4 0.000 0.00 313s Consumption_5 0.000 0.00 313s Consumption_6 0.000 0.00 313s Consumption_8 0.000 0.00 313s Consumption_9 0.000 0.00 313s Consumption_11 0.000 0.00 313s Consumption_12 0.000 0.00 313s Consumption_14 0.000 0.00 313s Consumption_15 0.000 0.00 313s Consumption_16 0.000 0.00 313s Consumption_17 0.000 0.00 313s Consumption_18 0.000 0.00 313s Consumption_19 0.000 0.00 313s Consumption_20 0.000 0.00 313s Consumption_21 0.000 0.00 313s Consumption_22 0.000 0.00 313s Investment_2 -1.375 -18.47 313s Investment_3 0.361 6.02 313s Investment_4 1.027 19.33 313s Investment_5 -1.558 -32.12 313s Investment_6 0.610 11.77 313s Investment_8 1.420 24.90 313s Investment_9 0.404 7.88 313s Investment_10 2.082 42.13 313s Investment_11 -1.150 -19.79 313s Investment_12 -1.339 -18.06 313s Investment_14 1.019 10.28 313s Investment_15 -0.475 -6.17 313s Investment_17 2.105 31.39 313s Investment_18 -0.465 -9.06 313s Investment_19 -3.871 -74.65 313s Investment_20 0.469 8.23 313s Investment_21 0.132 2.65 313s Investment_22 0.603 13.74 313s PrivateWages_2 0.000 0.00 313s PrivateWages_3 0.000 0.00 313s PrivateWages_4 0.000 0.00 313s PrivateWages_5 0.000 0.00 313s PrivateWages_6 0.000 0.00 313s PrivateWages_8 0.000 0.00 313s PrivateWages_9 0.000 0.00 313s PrivateWages_10 0.000 0.00 313s PrivateWages_11 0.000 0.00 313s PrivateWages_12 0.000 0.00 313s PrivateWages_13 0.000 0.00 313s PrivateWages_14 0.000 0.00 313s PrivateWages_15 0.000 0.00 313s PrivateWages_16 0.000 0.00 313s PrivateWages_17 0.000 0.00 313s PrivateWages_18 0.000 0.00 313s PrivateWages_19 0.000 0.00 313s PrivateWages_20 0.000 0.00 313s PrivateWages_21 0.000 0.00 313s PrivateWages_22 0.000 0.00 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_2 0.00 0.0 313s Consumption_3 0.00 0.0 313s Consumption_4 0.00 0.0 313s Consumption_5 0.00 0.0 313s Consumption_6 0.00 0.0 313s Consumption_8 0.00 0.0 313s Consumption_9 0.00 0.0 313s Consumption_11 0.00 0.0 313s Consumption_12 0.00 0.0 313s Consumption_14 0.00 0.0 313s Consumption_15 0.00 0.0 313s Consumption_16 0.00 0.0 313s Consumption_17 0.00 0.0 313s Consumption_18 0.00 0.0 313s Consumption_19 0.00 0.0 313s Consumption_20 0.00 0.0 313s Consumption_21 0.00 0.0 313s Consumption_22 0.00 0.0 313s Investment_2 -17.46 -251.4 313s Investment_3 4.48 65.9 313s Investment_4 17.35 189.4 313s Investment_5 -28.67 -295.5 313s Investment_6 11.83 117.5 313s Investment_8 27.83 288.8 313s Investment_9 8.00 83.9 313s Investment_10 43.93 438.5 313s Investment_11 -24.96 -248.1 313s Investment_12 -20.88 -290.1 313s Investment_14 7.14 211.1 313s Investment_15 -5.32 -95.9 313s Investment_17 29.48 416.3 313s Investment_18 -8.18 -92.9 313s Investment_19 -66.97 -781.2 313s Investment_20 7.18 93.8 313s Investment_21 2.50 26.5 313s Investment_22 12.73 123.4 313s PrivateWages_2 0.00 0.0 313s PrivateWages_3 0.00 0.0 313s PrivateWages_4 0.00 0.0 313s PrivateWages_5 0.00 0.0 313s PrivateWages_6 0.00 0.0 313s PrivateWages_8 0.00 0.0 313s PrivateWages_9 0.00 0.0 313s PrivateWages_10 0.00 0.0 313s PrivateWages_11 0.00 0.0 313s PrivateWages_12 0.00 0.0 313s PrivateWages_13 0.00 0.0 313s PrivateWages_14 0.00 0.0 313s PrivateWages_15 0.00 0.0 313s PrivateWages_16 0.00 0.0 313s PrivateWages_17 0.00 0.0 313s PrivateWages_18 0.00 0.0 313s PrivateWages_19 0.00 0.0 313s PrivateWages_20 0.00 0.0 313s PrivateWages_21 0.00 0.0 313s PrivateWages_22 0.00 0.0 313s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 313s Consumption_2 0.0000 0.00 0.00 313s Consumption_3 0.0000 0.00 0.00 313s Consumption_4 0.0000 0.00 0.00 313s Consumption_5 0.0000 0.00 0.00 313s Consumption_6 0.0000 0.00 0.00 313s Consumption_8 0.0000 0.00 0.00 313s Consumption_9 0.0000 0.00 0.00 313s Consumption_11 0.0000 0.00 0.00 313s Consumption_12 0.0000 0.00 0.00 313s Consumption_14 0.0000 0.00 0.00 313s Consumption_15 0.0000 0.00 0.00 313s Consumption_16 0.0000 0.00 0.00 313s Consumption_17 0.0000 0.00 0.00 313s Consumption_18 0.0000 0.00 0.00 313s Consumption_19 0.0000 0.00 0.00 313s Consumption_20 0.0000 0.00 0.00 313s Consumption_21 0.0000 0.00 0.00 313s Consumption_22 0.0000 0.00 0.00 313s Investment_2 0.0000 0.00 0.00 313s Investment_3 0.0000 0.00 0.00 313s Investment_4 0.0000 0.00 0.00 313s Investment_5 0.0000 0.00 0.00 313s Investment_6 0.0000 0.00 0.00 313s Investment_8 0.0000 0.00 0.00 313s Investment_9 0.0000 0.00 0.00 313s Investment_10 0.0000 0.00 0.00 313s Investment_11 0.0000 0.00 0.00 313s Investment_12 0.0000 0.00 0.00 313s Investment_14 0.0000 0.00 0.00 313s Investment_15 0.0000 0.00 0.00 313s Investment_17 0.0000 0.00 0.00 313s Investment_18 0.0000 0.00 0.00 313s Investment_19 0.0000 0.00 0.00 313s Investment_20 0.0000 0.00 0.00 313s Investment_21 0.0000 0.00 0.00 313s Investment_22 0.0000 0.00 0.00 313s PrivateWages_2 -1.9924 -93.78 -89.46 313s PrivateWages_3 0.4683 23.22 21.35 313s PrivateWages_4 1.4034 79.35 70.31 313s PrivateWages_5 -1.7870 -108.45 -102.22 313s PrivateWages_6 -0.3627 -21.98 -20.71 313s PrivateWages_8 1.1629 69.77 74.43 313s PrivateWages_9 1.2735 79.30 82.01 313s PrivateWages_10 2.2141 142.96 142.81 313s PrivateWages_11 -1.2912 -82.26 -86.51 313s PrivateWages_12 -0.0350 -1.92 -2.14 313s PrivateWages_13 -1.0438 -49.04 -55.74 313s PrivateWages_14 1.8016 75.90 79.81 313s PrivateWages_15 -0.3714 -19.02 -16.75 313s PrivateWages_16 -0.3904 -21.61 -19.40 313s PrivateWages_17 1.4934 85.71 81.24 313s PrivateWages_18 0.0279 1.88 1.75 313s PrivateWages_19 -3.8229 -261.91 -248.49 313s PrivateWages_20 0.7870 52.61 47.93 313s PrivateWages_21 -0.7415 -55.52 -51.54 313s PrivateWages_22 1.2062 104.79 91.31 313s PrivateWages_trend 313s Consumption_2 0.000 313s Consumption_3 0.000 313s Consumption_4 0.000 313s Consumption_5 0.000 313s Consumption_6 0.000 313s Consumption_8 0.000 313s Consumption_9 0.000 313s Consumption_11 0.000 313s Consumption_12 0.000 313s Consumption_14 0.000 313s Consumption_15 0.000 313s Consumption_16 0.000 313s Consumption_17 0.000 313s Consumption_18 0.000 313s Consumption_19 0.000 313s Consumption_20 0.000 313s Consumption_21 0.000 313s Consumption_22 0.000 313s Investment_2 0.000 313s Investment_3 0.000 313s Investment_4 0.000 313s Investment_5 0.000 313s Investment_6 0.000 313s Investment_8 0.000 313s Investment_9 0.000 313s Investment_10 0.000 313s Investment_11 0.000 313s Investment_12 0.000 313s Investment_14 0.000 313s Investment_15 0.000 313s Investment_17 0.000 313s Investment_18 0.000 313s Investment_19 0.000 313s Investment_20 0.000 313s Investment_21 0.000 313s Investment_22 0.000 313s PrivateWages_2 19.924 313s PrivateWages_3 -4.214 313s PrivateWages_4 -11.227 313s PrivateWages_5 12.509 313s PrivateWages_6 2.176 313s PrivateWages_8 -4.652 313s PrivateWages_9 -3.820 313s PrivateWages_10 -4.428 313s PrivateWages_11 1.291 313s PrivateWages_12 0.000 313s PrivateWages_13 -1.044 313s PrivateWages_14 3.603 313s PrivateWages_15 -1.114 313s PrivateWages_16 -1.562 313s PrivateWages_17 7.467 313s PrivateWages_18 0.168 313s PrivateWages_19 -26.760 313s PrivateWages_20 6.296 313s PrivateWages_21 -6.674 313s PrivateWages_22 12.062 313s [1] TRUE 313s > Bread 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_(Intercept) 116.13 -4.139 313s Consumption_corpProf -4.14 1.213 313s Consumption_corpProfLag 1.01 -0.677 313s Consumption_wages -1.41 -0.133 313s Investment_(Intercept) 0.00 0.000 313s Investment_corpProf 0.00 0.000 313s Investment_corpProfLag 0.00 0.000 313s Investment_capitalLag 0.00 0.000 313s PrivateWages_(Intercept) 0.00 0.000 313s PrivateWages_gnp 0.00 0.000 313s PrivateWages_gnpLag 0.00 0.000 313s PrivateWages_trend 0.00 0.000 313s Consumption_corpProfLag Consumption_wages 313s Consumption_(Intercept) 1.0117 -1.4132 313s Consumption_corpProf -0.6770 -0.1333 313s Consumption_corpProfLag 0.6979 -0.0188 313s Consumption_wages -0.0188 0.0955 313s Investment_(Intercept) 0.0000 0.0000 313s Investment_corpProf 0.0000 0.0000 313s Investment_corpProfLag 0.0000 0.0000 313s Investment_capitalLag 0.0000 0.0000 313s PrivateWages_(Intercept) 0.0000 0.0000 313s PrivateWages_gnp 0.0000 0.0000 313s PrivateWages_gnpLag 0.0000 0.0000 313s PrivateWages_trend 0.0000 0.0000 313s Investment_(Intercept) Investment_corpProf 313s Consumption_(Intercept) 0.0 0.000 313s Consumption_corpProf 0.0 0.000 313s Consumption_corpProfLag 0.0 0.000 313s Consumption_wages 0.0 0.000 313s Investment_(Intercept) 2271.1 -40.229 313s Investment_corpProf -40.2 1.601 313s Investment_corpProfLag 32.3 -1.240 313s Investment_capitalLag -10.5 0.165 313s PrivateWages_(Intercept) 0.0 0.000 313s PrivateWages_gnp 0.0 0.000 313s PrivateWages_gnpLag 0.0 0.000 313s PrivateWages_trend 0.0 0.000 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_(Intercept) 0.000 0.0000 313s Consumption_corpProf 0.000 0.0000 313s Consumption_corpProfLag 0.000 0.0000 313s Consumption_wages 0.000 0.0000 313s Investment_(Intercept) 32.280 -10.5200 313s Investment_corpProf -1.240 0.1648 313s Investment_corpProfLag 1.187 -0.1522 313s Investment_capitalLag -0.152 0.0509 313s PrivateWages_(Intercept) 0.000 0.0000 313s PrivateWages_gnp 0.000 0.0000 313s PrivateWages_gnpLag 0.000 0.0000 313s PrivateWages_trend 0.000 0.0000 313s PrivateWages_(Intercept) PrivateWages_gnp 313s Consumption_(Intercept) 0.000 0.0000 313s Consumption_corpProf 0.000 0.0000 313s Consumption_corpProfLag 0.000 0.0000 313s Consumption_wages 0.000 0.0000 313s Investment_(Intercept) 0.000 0.0000 313s Investment_corpProf 0.000 0.0000 313s Investment_corpProfLag 0.000 0.0000 313s Investment_capitalLag 0.000 0.0000 313s PrivateWages_(Intercept) 159.333 -0.8670 313s PrivateWages_gnp -0.867 0.1475 313s PrivateWages_gnpLag -1.818 -0.1375 313s PrivateWages_trend 2.020 -0.0396 313s PrivateWages_gnpLag PrivateWages_trend 313s Consumption_(Intercept) 0.0000 0.0000 313s Consumption_corpProf 0.0000 0.0000 313s Consumption_corpProfLag 0.0000 0.0000 313s Consumption_wages 0.0000 0.0000 313s Investment_(Intercept) 0.0000 0.0000 313s Investment_corpProf 0.0000 0.0000 313s Investment_corpProfLag 0.0000 0.0000 313s Investment_capitalLag 0.0000 0.0000 313s PrivateWages_(Intercept) -1.8179 2.0198 313s PrivateWages_gnp -0.1375 -0.0396 313s PrivateWages_gnpLag 0.1737 0.0056 313s PrivateWages_trend 0.0056 0.1075 313s > 313s > # SUR 313s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 313s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 313s > summary 313s 313s systemfit results 313s method: SUR 313s 313s N DF SSR detRCov OLS-R2 McElroy-R2 313s system 58 46 45.1 0.199 0.975 0.993 313s 313s N DF SSR MSE RMSE R2 Adj R2 313s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 313s Investment 19 15 17.3 1.155 1.075 0.906 0.887 313s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 313s 313s The covariance matrix of the residuals used for estimation 313s Consumption Investment PrivateWages 313s Consumption 0.9830 0.0466 -0.391 313s Investment 0.0466 0.8101 0.115 313s PrivateWages -0.3906 0.1155 0.496 313s 313s The covariance matrix of the residuals 313s Consumption Investment PrivateWages 313s Consumption 0.979 0.080 -0.452 313s Investment 0.080 0.810 0.181 313s PrivateWages -0.452 0.181 0.521 313s 313s The correlations of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.0000 0.0907 -0.636 313s Investment 0.0907 1.0000 0.267 313s PrivateWages -0.6362 0.2671 1.000 313s 313s 313s SUR estimates for 'Consumption' (equation 1) 313s Model Formula: consump ~ corpProf + corpProfLag + wages 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 16.2670 1.3148 12.37 2.8e-09 *** 313s corpProf 0.1942 0.0954 2.04 0.06 . 313s corpProfLag 0.0747 0.0842 0.89 0.39 313s wages 0.8011 0.0383 20.93 1.6e-12 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.08 on 15 degrees of freedom 313s Number of observations: 19 Degrees of Freedom: 15 313s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 313s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 313s 313s 313s SUR estimates for 'Investment' (equation 2) 313s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 12.6390 4.7856 2.64 0.01852 * 313s corpProf 0.4708 0.0943 4.99 0.00016 *** 313s corpProfLag 0.3533 0.0907 3.89 0.00144 ** 313s capitalLag -0.1254 0.0236 -5.32 8.6e-05 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.075 on 15 degrees of freedom 313s Number of observations: 19 Degrees of Freedom: 15 313s SSR: 17.321 MSE: 1.155 Root MSE: 1.075 313s Multiple R-Squared: 0.906 Adjusted R-Squared: 0.887 313s 313s 313s SUR estimates for 'PrivateWages' (equation 3) 313s Model Formula: privWage ~ gnp + gnpLag + trend 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 1.3264 1.1240 1.18 0.2552 313s gnp 0.4184 0.0268 15.63 4.1e-11 *** 313s gnpLag 0.1714 0.0315 5.43 5.5e-05 *** 313s trend 0.1456 0.0284 5.13 0.0001 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 0.801 on 16 degrees of freedom 313s Number of observations: 20 Degrees of Freedom: 16 313s SSR: 10.266 MSE: 0.642 Root MSE: 0.801 313s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 313s 313s > residuals 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 -0.3143 -0.2326 -1.1434 313s 3 -1.2700 -0.1705 0.5084 313s 4 -1.5426 1.0718 1.4211 313s 5 -0.4489 -1.4767 -0.0992 313s 6 0.0588 0.3167 -0.3594 313s 7 0.9213 1.4446 NA 313s 8 1.3789 0.8296 -0.7554 313s 9 1.0900 -0.5263 0.2887 313s 10 NA 1.2083 1.1800 313s 11 0.3569 0.4082 -0.3673 313s 12 -0.2288 0.2663 0.3445 313s 13 NA NA -0.1571 313s 14 0.2181 0.4946 0.4220 313s 15 -0.1120 -0.0470 0.3147 313s 16 -0.0872 NA 0.0145 313s 17 1.5615 1.0289 -0.8091 313s 18 -0.4530 0.0617 0.8608 313s 19 0.1997 -2.5397 -0.7635 313s 20 0.9268 -0.6136 -0.4046 313s 21 0.7588 -0.7465 -1.2179 313s 22 -2.2137 -0.6044 0.5606 313s > fitted 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 42.2 0.0326 26.6 313s 3 46.3 2.0705 28.8 313s 4 50.7 4.1282 32.7 313s 5 51.0 4.4767 34.0 313s 6 52.5 4.7833 35.8 313s 7 54.2 4.1554 NA 313s 8 54.8 3.3704 38.7 313s 9 56.2 3.5263 38.9 313s 10 NA 3.8917 40.1 313s 11 54.6 0.5918 38.3 313s 12 51.1 -3.6663 34.2 313s 13 NA NA 29.2 313s 14 46.3 -5.5946 28.1 313s 15 48.8 -2.9530 30.3 313s 16 51.4 NA 33.2 313s 17 56.1 1.0711 37.6 313s 18 59.2 1.9383 40.1 313s 19 57.3 0.6397 39.0 313s 20 60.7 1.9136 42.0 313s 21 64.2 4.0465 46.2 313s 22 71.9 5.5044 52.7 313s > predict 313s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 313s 1 NA NA NA NA 313s 2 42.2 0.460 41.3 43.1 313s 3 46.3 0.489 45.3 47.3 313s 4 50.7 0.328 50.1 51.4 313s 5 51.0 0.384 50.3 51.8 313s 6 52.5 0.389 51.8 53.3 313s 7 54.2 0.347 53.5 54.9 313s 8 54.8 0.319 54.2 55.5 313s 9 56.2 0.353 55.5 56.9 313s 10 NA NA NA NA 313s 11 54.6 0.583 53.5 55.8 313s 12 51.1 0.524 50.1 52.2 313s 13 NA NA NA NA 313s 14 46.3 0.589 45.1 47.5 313s 15 48.8 0.393 48.0 49.6 313s 16 51.4 0.337 50.7 52.1 313s 17 56.1 0.345 55.4 56.8 313s 18 59.2 0.318 58.5 59.8 313s 19 57.3 0.381 56.5 58.1 313s 20 60.7 0.413 59.8 61.5 313s 21 64.2 0.417 63.4 65.1 313s 22 71.9 0.651 70.6 73.2 313s Investment.pred Investment.se.fit Investment.lwr Investment.upr 313s 1 NA NA NA NA 313s 2 0.0326 0.556 -1.0866 1.15 313s 3 2.0705 0.454 1.1575 2.98 313s 4 4.1282 0.399 3.3256 4.93 313s 5 4.4767 0.331 3.8101 5.14 313s 6 4.7833 0.314 4.1520 5.41 313s 7 4.1554 0.291 3.5687 4.74 313s 8 3.3704 0.260 2.8469 3.89 313s 9 3.5263 0.347 2.8278 4.22 313s 10 3.8917 0.397 3.0924 4.69 313s 11 0.5918 0.578 -0.5711 1.75 313s 12 -3.6663 0.551 -4.7762 -2.56 313s 13 NA NA NA NA 313s 14 -5.5946 0.661 -6.9261 -4.26 313s 15 -2.9530 0.392 -3.7430 -2.16 313s 16 NA NA NA NA 313s 17 1.0711 0.318 0.4315 1.71 313s 18 1.9383 0.225 1.4863 2.39 313s 19 0.6397 0.310 0.0165 1.26 313s 20 1.9136 0.333 1.2436 2.58 313s 21 4.0465 0.304 3.4345 4.66 313s 22 5.5044 0.429 4.6400 6.37 313s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 313s 1 NA NA NA NA 313s 2 26.6 0.321 26.0 27.3 313s 3 28.8 0.321 28.1 29.4 313s 4 32.7 0.316 32.0 33.3 313s 5 34.0 0.244 33.5 34.5 313s 6 35.8 0.242 35.3 36.2 313s 7 NA NA NA NA 313s 8 38.7 0.246 38.2 39.2 313s 9 38.9 0.234 38.4 39.4 313s 10 40.1 0.225 39.7 40.6 313s 11 38.3 0.301 37.7 38.9 313s 12 34.2 0.298 33.6 34.8 313s 13 29.2 0.353 28.4 29.9 313s 14 28.1 0.330 27.4 28.7 313s 15 30.3 0.328 29.6 30.9 313s 16 33.2 0.275 32.6 33.7 313s 17 37.6 0.270 37.1 38.2 313s 18 40.1 0.213 39.7 40.6 313s 19 39.0 0.301 38.4 39.6 313s 20 42.0 0.287 41.4 42.6 313s 21 46.2 0.304 45.6 46.8 313s 22 52.7 0.448 51.8 53.6 313s > model.frame 313s [1] TRUE 313s > model.matrix 313s [1] TRUE 313s > nobs 313s [1] 58 313s > linearHypothesis 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 47 313s 2 46 1 0.4 0.53 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 47 313s 2 46 1 0.49 0.49 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 47 313s 2 46 1 0.49 0.48 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 48 313s 2 46 2 0.31 0.74 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 48 313s 2 46 2 0.37 0.69 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 48 313s 2 46 2 0.75 0.69 313s > logLik 313s 'log Lik.' -66.4 (df=18) 313s 'log Lik.' -74.1 (df=18) 313s Estimating function 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_2 -0.4828 -5.986 313s Consumption_3 -1.9510 -32.972 313s Consumption_4 -2.3698 -43.605 313s Consumption_5 -0.6896 -13.377 313s Consumption_6 0.0903 1.814 313s Consumption_7 1.4152 27.739 313s Consumption_8 2.1183 41.942 313s Consumption_9 1.6745 35.332 313s Consumption_11 0.5483 8.553 313s Consumption_12 -0.3515 -4.008 313s Consumption_14 0.3350 3.752 313s Consumption_15 -0.1720 -2.116 313s Consumption_16 -0.1339 -1.875 313s Consumption_17 2.3987 42.218 313s Consumption_18 -0.6959 -12.040 313s Consumption_19 0.3068 4.694 313s Consumption_20 1.4238 27.052 313s Consumption_21 1.1656 24.594 313s Consumption_22 -3.4008 -79.918 313s Investment_2 0.0628 0.779 313s Investment_3 0.0460 0.778 313s Investment_4 -0.2893 -5.322 313s Investment_5 0.3986 7.732 313s Investment_6 -0.0855 -1.718 313s Investment_7 -0.3899 -7.642 313s Investment_8 -0.2239 -4.433 313s Investment_9 0.1420 2.997 313s Investment_10 0.0000 0.000 313s Investment_11 -0.1102 -1.719 313s Investment_12 -0.0719 -0.819 313s Investment_14 -0.1335 -1.495 313s Investment_15 0.0127 0.156 313s Investment_17 -0.2777 -4.887 313s Investment_18 -0.0167 -0.288 313s Investment_19 0.6855 10.488 313s Investment_20 0.1656 3.146 313s Investment_21 0.2015 4.251 313s Investment_22 0.1631 3.834 313s PrivateWages_2 -1.4560 -18.055 313s PrivateWages_3 0.6473 10.940 313s PrivateWages_4 1.8097 33.298 313s PrivateWages_5 -0.1264 -2.452 313s PrivateWages_6 -0.4576 -9.199 313s PrivateWages_8 -0.9619 -19.046 313s PrivateWages_9 0.3676 7.757 313s PrivateWages_10 0.0000 0.000 313s PrivateWages_11 -0.4677 -7.296 313s PrivateWages_12 0.4387 5.001 313s PrivateWages_13 0.0000 0.000 313s PrivateWages_14 0.5373 6.018 313s PrivateWages_15 0.4008 4.929 313s PrivateWages_16 0.0184 0.258 313s PrivateWages_17 -1.0303 -18.134 313s PrivateWages_18 1.0961 18.963 313s PrivateWages_19 -0.9722 -14.875 313s PrivateWages_20 -0.5153 -9.790 313s PrivateWages_21 -1.5509 -32.724 313s PrivateWages_22 0.7139 16.776 313s Consumption_corpProfLag Consumption_wages 313s Consumption_2 -6.131 -13.614 313s Consumption_3 -24.192 -62.822 313s Consumption_4 -40.050 -87.684 313s Consumption_5 -12.688 -25.514 313s Consumption_6 1.751 3.484 313s Consumption_7 28.447 57.601 313s Consumption_8 41.518 87.909 313s Consumption_9 33.155 71.835 313s Consumption_11 11.898 23.083 313s Consumption_12 -5.484 -13.816 313s Consumption_14 2.345 11.425 313s Consumption_15 -1.926 -6.295 313s Consumption_16 -1.647 -5.263 313s Consumption_17 33.582 106.024 313s Consumption_18 -12.249 -33.196 313s Consumption_19 5.307 14.081 313s Consumption_20 21.784 70.336 313s Consumption_21 22.146 61.777 313s Consumption_22 -71.756 -210.167 313s Investment_2 0.797 1.770 313s Investment_3 0.571 1.482 313s Investment_4 -4.889 -10.703 313s Investment_5 7.333 14.747 313s Investment_6 -1.658 -3.300 313s Investment_7 -7.837 -15.869 313s Investment_8 -4.389 -9.292 313s Investment_9 2.812 6.093 313s Investment_10 0.000 0.000 313s Investment_11 -2.391 -4.638 313s Investment_12 -1.121 -2.825 313s Investment_14 -0.934 -4.552 313s Investment_15 0.142 0.464 313s Investment_17 -3.888 -12.274 313s Investment_18 -0.293 -0.794 313s Investment_19 11.859 31.463 313s Investment_20 2.534 8.181 313s Investment_21 3.828 10.678 313s Investment_22 3.442 10.082 313s PrivateWages_2 -18.491 -41.059 313s PrivateWages_3 8.027 20.845 313s PrivateWages_4 30.584 66.958 313s PrivateWages_5 -2.325 -4.676 313s PrivateWages_6 -8.878 -17.665 313s PrivateWages_8 -18.854 -39.920 313s PrivateWages_9 7.279 15.770 313s PrivateWages_10 0.000 0.000 313s PrivateWages_11 -10.149 -19.690 313s PrivateWages_12 6.843 17.240 313s PrivateWages_13 0.000 0.000 313s PrivateWages_14 3.761 18.323 313s PrivateWages_15 4.489 14.668 313s PrivateWages_16 0.227 0.725 313s PrivateWages_17 -14.424 -45.540 313s PrivateWages_18 19.292 52.286 313s PrivateWages_19 -16.820 -44.626 313s PrivateWages_20 -7.884 -25.455 313s PrivateWages_21 -29.467 -82.197 313s PrivateWages_22 15.062 44.116 313s Investment_(Intercept) Investment_corpProf 313s Consumption_2 0.0848 1.052 313s Consumption_3 0.3428 5.793 313s Consumption_4 0.4164 7.661 313s Consumption_5 0.1211 2.350 313s Consumption_6 -0.0159 -0.319 313s Consumption_7 -0.2486 -4.873 313s Consumption_8 -0.3722 -7.369 313s Consumption_9 -0.2942 -6.207 313s Consumption_11 -0.0963 -1.503 313s Consumption_12 0.0618 0.704 313s Consumption_14 -0.0589 -0.659 313s Consumption_15 0.0302 0.372 313s Consumption_16 0.0000 0.000 313s Consumption_17 -0.4214 -7.417 313s Consumption_18 0.1223 2.115 313s Consumption_19 -0.0539 -0.825 313s Consumption_20 -0.2501 -4.753 313s Consumption_21 -0.2048 -4.321 313s Consumption_22 0.5975 14.041 313s Investment_2 -0.3080 -3.820 313s Investment_3 -0.2258 -3.815 313s Investment_4 1.4192 26.112 313s Investment_5 -1.9554 -37.935 313s Investment_6 0.4194 8.430 313s Investment_7 1.9129 37.493 313s Investment_8 1.0985 21.751 313s Investment_9 -0.6968 -14.703 313s Investment_10 1.6000 34.719 313s Investment_11 0.5405 8.432 313s Investment_12 0.3526 4.020 313s Investment_14 0.6549 7.335 313s Investment_15 -0.0622 -0.766 313s Investment_17 1.3624 23.978 313s Investment_18 0.0817 1.413 313s Investment_19 -3.3630 -51.454 313s Investment_20 -0.8125 -15.437 313s Investment_21 -0.9884 -20.856 313s Investment_22 -0.8004 -18.809 313s PrivateWages_2 0.5958 7.388 313s PrivateWages_3 -0.2649 -4.477 313s PrivateWages_4 -0.7405 -13.626 313s PrivateWages_5 0.0517 1.003 313s PrivateWages_6 0.1873 3.764 313s PrivateWages_8 0.3936 7.794 313s PrivateWages_9 -0.1504 -3.174 313s PrivateWages_10 -0.6149 -13.343 313s PrivateWages_11 0.1914 2.986 313s PrivateWages_12 -0.1795 -2.046 313s PrivateWages_13 0.0000 0.000 313s PrivateWages_14 -0.2199 -2.463 313s PrivateWages_15 -0.1640 -2.017 313s PrivateWages_16 0.0000 0.000 313s PrivateWages_17 0.4216 7.420 313s PrivateWages_18 -0.4485 -7.760 313s PrivateWages_19 0.3978 6.087 313s PrivateWages_20 0.2109 4.006 313s PrivateWages_21 0.6346 13.391 313s PrivateWages_22 -0.2921 -6.865 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_2 1.077 15.50 313s Consumption_3 4.250 62.59 313s Consumption_4 7.036 76.82 313s Consumption_5 2.229 22.98 313s Consumption_6 -0.308 -3.06 313s Consumption_7 -4.998 -49.18 313s Consumption_8 -7.294 -75.70 313s Consumption_9 -5.825 -61.07 313s Consumption_11 -2.090 -20.78 313s Consumption_12 0.963 13.38 313s Consumption_14 -0.412 -12.19 313s Consumption_15 0.338 6.10 313s Consumption_16 0.000 0.00 313s Consumption_17 -5.900 -83.32 313s Consumption_18 2.152 24.43 313s Consumption_19 -0.932 -10.88 313s Consumption_20 -3.827 -50.00 313s Consumption_21 -3.891 -41.20 313s Consumption_22 12.607 122.18 313s Investment_2 -3.912 -56.31 313s Investment_3 -2.799 -41.22 313s Investment_4 23.984 261.83 313s Investment_5 -35.979 -370.94 313s Investment_6 8.137 80.82 313s Investment_7 38.449 378.37 313s Investment_8 21.531 223.44 313s Investment_9 -13.797 -144.66 313s Investment_10 33.759 336.95 313s Investment_11 11.729 116.59 313s Investment_12 5.501 76.41 313s Investment_14 4.584 135.62 313s Investment_15 -0.697 -12.57 313s Investment_17 19.074 269.35 313s Investment_18 1.438 16.32 313s Investment_19 -58.180 -678.65 313s Investment_20 -12.431 -162.42 313s Investment_21 -18.780 -198.88 313s Investment_22 -16.888 -163.68 313s PrivateWages_2 7.567 108.91 313s PrivateWages_3 -3.285 -48.37 313s PrivateWages_4 -12.515 -136.63 313s PrivateWages_5 0.951 9.81 313s PrivateWages_6 3.633 36.09 313s PrivateWages_8 7.715 80.06 313s PrivateWages_9 -2.978 -31.23 313s PrivateWages_10 -12.974 -129.50 313s PrivateWages_11 4.153 41.28 313s PrivateWages_12 -2.800 -38.90 313s PrivateWages_13 0.000 0.00 313s PrivateWages_14 -1.539 -45.54 313s PrivateWages_15 -1.837 -33.13 313s PrivateWages_16 0.000 0.00 313s PrivateWages_17 5.903 83.35 313s PrivateWages_18 -7.894 -89.62 313s PrivateWages_19 6.883 80.29 313s PrivateWages_20 3.226 42.15 313s PrivateWages_21 12.058 127.69 313s PrivateWages_22 -6.164 -59.74 313s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 313s Consumption_2 -0.4002 -18.25 -17.97 313s Consumption_3 -1.6172 -81.02 -73.75 313s Consumption_4 -1.9644 -112.37 -98.42 313s Consumption_5 -0.5716 -32.64 -32.70 313s Consumption_6 0.0748 4.56 4.27 313s Consumption_7 0.0000 0.00 0.00 313s Consumption_8 1.7559 113.08 112.38 313s Consumption_9 1.3880 89.53 89.39 313s Consumption_11 0.4545 27.81 30.45 313s Consumption_12 -0.2914 -15.56 -17.83 313s Consumption_14 0.2777 12.53 12.30 313s Consumption_15 -0.1426 -7.09 -6.43 313s Consumption_16 -0.1110 -6.04 -5.52 313s Consumption_17 1.9884 124.67 108.17 313s Consumption_18 -0.5769 -37.50 -36.17 313s Consumption_19 0.2543 15.49 16.53 313s Consumption_20 1.1803 82.03 71.88 313s Consumption_21 0.9662 73.14 67.15 313s Consumption_22 -2.8190 -249.20 -213.40 313s Investment_2 0.1212 5.53 5.44 313s Investment_3 0.0888 4.45 4.05 313s Investment_4 -0.5585 -31.95 -27.98 313s Investment_5 0.7695 43.94 44.02 313s Investment_6 -0.1651 -10.07 -9.42 313s Investment_7 0.0000 0.00 0.00 313s Investment_8 -0.4323 -27.84 -27.67 313s Investment_9 0.2742 17.69 17.66 313s Investment_10 -0.6296 -42.19 -40.61 313s Investment_11 -0.2127 -13.02 -14.25 313s Investment_12 -0.1388 -7.41 -8.49 313s Investment_14 -0.2577 -11.62 -11.42 313s Investment_15 0.0245 1.22 1.10 313s Investment_17 -0.5361 -33.62 -29.17 313s Investment_18 -0.0322 -2.09 -2.02 313s Investment_19 1.3234 80.60 86.02 313s Investment_20 0.3197 22.22 19.47 313s Investment_21 0.3890 29.45 27.03 313s Investment_22 0.3150 27.84 23.84 313s PrivateWages_2 -3.5926 -163.82 -161.31 313s PrivateWages_3 1.5973 80.02 72.84 313s PrivateWages_4 4.4653 255.42 223.71 313s PrivateWages_5 -0.3118 -17.80 -17.84 313s PrivateWages_6 -1.1292 -68.88 -64.48 313s PrivateWages_8 -2.3735 -152.85 -151.90 313s PrivateWages_9 0.9071 58.50 58.41 313s PrivateWages_10 3.7077 248.42 239.15 313s PrivateWages_11 -1.1540 -70.63 -77.32 313s PrivateWages_12 1.0824 57.80 66.24 313s PrivateWages_13 -0.4937 -21.87 -26.36 313s PrivateWages_14 1.3258 59.79 58.73 313s PrivateWages_15 0.9889 49.15 44.60 313s PrivateWages_16 0.0455 2.48 2.26 313s PrivateWages_17 -2.5423 -159.40 -138.30 313s PrivateWages_18 2.7047 175.80 169.58 313s PrivateWages_19 -2.3990 -146.10 -155.93 313s PrivateWages_20 -1.2714 -88.36 -77.43 313s PrivateWages_21 -3.8267 -289.68 -265.96 313s PrivateWages_22 1.7614 155.71 133.34 313s PrivateWages_trend 313s Consumption_2 4.0019 313s Consumption_3 14.5552 313s Consumption_4 15.7155 313s Consumption_5 4.0012 313s Consumption_6 -0.4490 313s Consumption_7 0.0000 313s Consumption_8 -7.0237 313s Consumption_9 -4.1641 313s Consumption_11 -0.4545 313s Consumption_12 0.0000 313s Consumption_14 0.5555 313s Consumption_15 -0.4277 313s Consumption_16 -0.4440 313s Consumption_17 9.9420 313s Consumption_18 -3.4614 313s Consumption_19 1.7801 313s Consumption_20 9.4420 313s Consumption_21 8.6959 313s Consumption_22 -28.1902 313s Investment_2 -1.2122 313s Investment_3 -0.7996 313s Investment_4 4.4678 313s Investment_5 -5.3865 313s Investment_6 0.9903 313s Investment_7 0.0000 313s Investment_8 1.7292 313s Investment_9 -0.8227 313s Investment_10 1.2593 313s Investment_11 0.2127 313s Investment_12 0.0000 313s Investment_14 -0.5154 313s Investment_15 0.0735 313s Investment_17 -2.6807 313s Investment_18 -0.1929 313s Investment_19 9.2640 313s Investment_20 2.5579 313s Investment_21 3.5008 313s Investment_22 3.1497 313s PrivateWages_2 35.9264 313s PrivateWages_3 -14.3757 313s PrivateWages_4 -35.7225 313s PrivateWages_5 2.1827 313s PrivateWages_6 6.7753 313s PrivateWages_8 9.4940 313s PrivateWages_9 -2.7212 313s PrivateWages_10 -7.4154 313s PrivateWages_11 1.1540 313s PrivateWages_12 0.0000 313s PrivateWages_13 -0.4937 313s PrivateWages_14 2.6517 313s PrivateWages_15 2.9666 313s PrivateWages_16 0.1820 313s PrivateWages_17 -12.7113 313s PrivateWages_18 16.2281 313s PrivateWages_19 -16.7928 313s PrivateWages_20 -10.1714 313s PrivateWages_21 -34.4407 313s PrivateWages_22 17.6141 313s [1] TRUE 313s > Bread 313s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 313s [1,] 1.00e+02 -1.05144 -0.70595 313s [2,] -1.05e+00 0.52767 -0.28007 313s [3,] -7.06e-01 -0.28007 0.41162 313s [4,] -1.63e+00 -0.08132 -0.03081 313s [5,] 5.03e+00 -0.06375 0.80965 313s [6,] -2.73e-01 0.05286 -0.04323 313s [7,] 4.77e-03 -0.03564 0.04677 313s [8,] -4.66e-04 -0.00135 -0.00415 313s [9,] -3.50e+01 0.07154 1.64913 313s [10,] 3.09e-01 -0.05491 0.03767 313s [11,] 2.66e-01 0.05541 -0.06699 313s [12,] 1.98e-01 0.03217 0.02582 313s Consumption_wages Investment_(Intercept) Investment_corpProf 313s [1,] -1.63020 5.0343 -0.27333 313s [2,] -0.08132 -0.0638 0.05286 313s [3,] -0.03081 0.8097 -0.04323 313s [4,] 0.08501 -0.3863 0.00122 313s [5,] -0.38629 1328.3034 -12.58281 313s [6,] 0.00122 -12.5828 0.51550 313s [7,] -0.00347 10.1576 -0.39286 313s [8,] 0.00211 -6.3831 0.05078 313s [9,] 0.13121 19.8408 -0.15336 313s [10,] -0.00022 0.2731 0.01339 313s [11,] -0.00213 -0.6257 -0.01103 313s [12,] -0.02827 -0.5788 0.00418 313s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 313s [1,] 0.00477 -0.000466 -34.9530 313s [2,] -0.03564 -0.001347 0.0715 313s [3,] 0.04677 -0.004153 1.6491 313s [4,] -0.00347 0.002105 0.1312 313s [5,] 10.15755 -6.383136 19.8408 313s [6,] -0.39286 0.050784 -0.1534 313s [7,] 0.47726 -0.056526 -0.3957 313s [8,] -0.05653 0.032233 -0.0526 313s [9,] -0.39566 -0.052599 73.2779 313s [10,] -0.00743 -0.001878 -0.2209 313s [11,] 0.01439 0.002876 -1.0159 313s [12,] -0.01026 0.003357 0.8108 313s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 313s [1,] 0.30855 0.26619 0.19754 313s [2,] -0.05491 0.05541 0.03217 313s [3,] 0.03767 -0.06699 0.02582 313s [4,] -0.00022 -0.00213 -0.02827 313s [5,] 0.27312 -0.62569 -0.57877 313s [6,] 0.01339 -0.01103 0.00418 313s [7,] -0.00743 0.01439 -0.01026 313s [8,] -0.00188 0.00288 0.00336 313s [9,] -0.22091 -1.01587 0.81082 313s [10,] 0.04154 -0.03895 -0.00995 313s [11,] -0.03895 0.05766 -0.00383 313s [12,] -0.00995 -0.00383 0.04664 313s > 313s > # 3SLS 313s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 313s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 313s > summary 313s 313s systemfit results 313s method: 3SLS 313s 313s N DF SSR detRCov OLS-R2 McElroy-R2 313s system 56 44 67.5 0.436 0.963 0.993 313s 313s N DF SSR MSE RMSE R2 Adj R2 313s Consumption 18 14 22.4 1.598 1.264 0.974 0.968 313s Investment 18 14 35.0 2.503 1.582 0.793 0.749 313s PrivateWages 20 16 10.1 0.629 0.793 0.987 0.985 313s 313s The covariance matrix of the residuals used for estimation 313s Consumption Investment PrivateWages 313s Consumption 1.307 0.540 -0.431 313s Investment 0.540 1.319 0.119 313s PrivateWages -0.431 0.119 0.496 313s 313s The covariance matrix of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.309 0.638 -0.440 313s Investment 0.638 1.749 0.233 313s PrivateWages -0.440 0.233 0.519 313s 313s The correlations of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.000 0.422 -0.532 313s Investment 0.422 1.000 0.247 313s PrivateWages -0.532 0.247 1.000 313s 313s 313s 3SLS estimates for 'Consumption' (equation 1) 313s Model Formula: consump ~ corpProf + corpProfLag + wages 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 18.0338 1.5648 11.52 1.6e-08 *** 313s corpProf -0.0632 0.1500 -0.42 0.68 313s corpProfLag 0.1784 0.1154 1.55 0.14 313s wages 0.8224 0.0444 18.54 3.0e-11 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.264 on 14 degrees of freedom 313s Number of observations: 18 Degrees of Freedom: 14 313s SSR: 22.377 MSE: 1.598 Root MSE: 1.264 313s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 313s 313s 313s 3SLS estimates for 'Investment' (equation 2) 313s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 24.6766 6.7008 3.68 0.00246 ** 313s corpProf 0.0472 0.1843 0.26 0.80149 313s corpProfLag 0.6874 0.1577 4.36 0.00065 *** 313s capitalLag -0.1776 0.0318 -5.59 6.7e-05 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.582 on 14 degrees of freedom 313s Number of observations: 18 Degrees of Freedom: 14 313s SSR: 35.037 MSE: 2.503 Root MSE: 1.582 313s Multiple R-Squared: 0.793 Adjusted R-Squared: 0.749 313s 313s 313s 3SLS estimates for 'PrivateWages' (equation 3) 313s Model Formula: privWage ~ gnp + gnpLag + trend 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 0.7823 1.1254 0.70 0.49695 313s gnp 0.4257 0.0308 13.80 2.6e-10 *** 313s gnpLag 0.1728 0.0341 5.07 0.00011 *** 313s trend 0.1252 0.0291 4.30 0.00055 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 0.793 on 16 degrees of freedom 313s Number of observations: 20 Degrees of Freedom: 16 313s SSR: 10.057 MSE: 0.629 Root MSE: 0.793 313s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 313s 313s > residuals 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 -0.8058 -1.721 -1.20135 313s 3 -0.6573 0.337 0.43696 313s 4 -1.1124 0.810 1.31177 313s 5 0.0833 -1.544 -0.19794 313s 6 0.6334 0.368 -0.46596 313s 7 NA NA NA 313s 8 1.7939 1.245 -0.85614 313s 9 1.7891 0.593 0.20698 313s 10 NA 2.303 1.10034 313s 11 -0.5397 -1.015 -0.38801 313s 12 -1.5147 -0.846 0.40949 313s 13 NA NA 0.00602 313s 14 -0.1171 1.670 0.61306 313s 15 -0.6526 -0.075 0.49152 313s 16 -0.3617 NA 0.17066 313s 17 1.9331 2.086 -0.69991 313s 18 -0.6063 -0.101 0.96136 313s 19 -0.3990 -3.345 -0.61606 313s 20 1.4134 0.717 -0.29343 313s 21 1.3257 0.306 -1.14412 313s 22 -1.4340 0.935 0.55310 313s > fitted 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 42.7 1.5213 26.7 313s 3 45.7 1.5632 28.9 313s 4 50.3 4.3898 32.8 313s 5 50.5 4.5444 34.1 313s 6 52.0 4.7320 35.9 313s 7 NA NA NA 313s 8 54.4 2.9547 38.8 313s 9 55.5 2.4075 39.0 313s 10 NA 2.7965 40.2 313s 11 55.5 2.0150 38.3 313s 12 52.4 -2.5541 34.1 313s 13 NA NA 29.0 313s 14 46.6 -6.7699 27.9 313s 15 49.4 -2.9250 30.1 313s 16 51.7 NA 33.0 313s 17 55.8 0.0139 37.5 313s 18 59.3 2.1013 40.0 313s 19 57.9 1.4453 38.8 313s 20 60.2 0.5828 41.9 313s 21 63.7 2.9944 46.1 313s 22 71.1 3.9651 52.7 313s > predict 313s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 313s 1 NA NA NA NA 313s 2 42.7 0.555 39.7 45.7 313s 3 45.7 0.628 42.6 48.7 313s 4 50.3 0.418 47.5 53.2 313s 5 50.5 0.492 47.6 53.4 313s 6 52.0 0.501 49.0 54.9 313s 7 NA NA NA NA 313s 8 54.4 0.405 51.6 57.3 313s 9 55.5 0.477 52.6 58.4 313s 10 NA NA NA NA 313s 11 55.5 0.832 52.3 58.8 313s 12 52.4 0.792 49.2 55.6 313s 13 NA NA NA NA 313s 14 46.6 0.676 43.5 49.7 313s 15 49.4 0.470 46.5 52.2 313s 16 51.7 0.386 48.8 54.5 313s 17 55.8 0.433 52.9 58.6 313s 18 59.3 0.368 56.5 62.1 313s 19 57.9 0.504 55.0 60.8 313s 20 60.2 0.513 57.3 63.1 313s 21 63.7 0.505 60.8 66.6 313s 22 71.1 0.771 68.0 74.3 313s Investment.pred Investment.se.fit Investment.lwr Investment.upr 313s 1 NA NA NA NA 313s 2 1.5213 0.857 -2.337 5.380 313s 3 1.5632 0.589 -2.058 5.184 313s 4 4.3898 0.519 0.819 7.961 313s 5 4.5444 0.436 1.025 8.064 313s 6 4.7320 0.415 1.224 8.240 313s 7 NA NA NA NA 313s 8 2.9547 0.342 -0.517 6.426 313s 9 2.4075 0.511 -1.158 5.973 313s 10 2.7965 0.556 -0.800 6.393 313s 11 2.0150 0.955 -1.948 5.978 313s 12 -2.5541 0.874 -6.431 1.323 313s 13 NA NA NA NA 313s 14 -6.7699 0.865 -10.637 -2.903 313s 15 -2.9250 0.503 -6.485 0.635 313s 16 NA NA NA NA 313s 17 0.0139 0.483 -3.534 3.561 313s 18 2.1013 0.320 -1.361 5.563 313s 19 1.4453 0.532 -2.134 5.025 313s 20 0.5828 0.550 -3.010 4.175 313s 21 2.9944 0.476 -0.549 6.538 313s 22 3.9651 0.692 0.261 7.669 313s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 313s 1 NA NA NA NA 313s 2 26.7 0.324 24.9 28.5 313s 3 28.9 0.331 27.0 30.7 313s 4 32.8 0.339 31.0 34.6 313s 5 34.1 0.248 32.3 35.9 313s 6 35.9 0.256 34.1 37.6 313s 7 NA NA NA NA 313s 8 38.8 0.251 37.0 40.5 313s 9 39.0 0.238 37.2 40.7 313s 10 40.2 0.232 38.4 42.0 313s 11 38.3 0.314 36.5 40.1 313s 12 34.1 0.327 32.3 35.9 313s 13 29.0 0.393 27.1 30.9 313s 14 27.9 0.329 26.1 29.7 313s 15 30.1 0.324 28.3 31.9 313s 16 33.0 0.271 31.3 34.8 313s 17 37.5 0.277 35.7 39.3 313s 18 40.0 0.213 38.3 41.8 313s 19 38.8 0.320 37.0 40.6 313s 20 41.9 0.295 40.1 43.7 313s 21 46.1 0.309 44.3 47.9 313s 22 52.7 0.476 50.8 54.7 313s > model.frame 313s [1] TRUE 313s > model.matrix 313s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 313s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 313s [3] "Numeric: lengths (696, 672) differ" 313s > nobs 313s [1] 56 313s > linearHypothesis 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 45 313s 2 44 1 1.91 0.17 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 45 313s 2 44 1 2.6 0.11 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 45 313s 2 44 1 2.6 0.11 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 44 2 1.62 0.21 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 44 2 2.2 0.12 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 46 313s 2 44 2 4.41 0.11 313s > logLik 313s 'log Lik.' -70.1 (df=18) 313s 'log Lik.' -80.6 (df=18) 313s Estimating function 313s Consumption_(Intercept) Consumption_corpProf 313s Consumption_2 -3.3369 -46.76 313s Consumption_3 -0.6260 -10.43 313s Consumption_4 0.5431 10.07 313s Consumption_5 -1.9287 -39.09 313s Consumption_6 0.9979 18.98 313s Consumption_8 4.7224 83.33 313s Consumption_9 4.2195 79.93 313s Consumption_11 -2.1144 -35.40 313s Consumption_12 -2.7531 -36.83 313s Consumption_14 0.7280 7.30 313s Consumption_15 -2.0340 -25.43 313s Consumption_16 -1.6770 -24.29 313s Consumption_17 6.1486 91.69 313s Consumption_18 -0.6466 -12.56 313s Consumption_19 -4.7474 -90.72 313s Consumption_20 3.3112 58.48 313s Consumption_21 1.5335 31.28 313s Consumption_22 -1.0772 -24.43 313s Investment_2 1.4470 20.28 313s Investment_3 -0.2844 -4.74 313s Investment_4 -0.6458 -11.98 313s Investment_5 1.3096 26.54 313s Investment_6 -0.3315 -6.31 313s Investment_8 -1.1056 -19.51 313s Investment_9 -0.5457 -10.34 313s Investment_10 0.0000 0.00 313s Investment_11 0.8919 14.93 313s Investment_12 0.7723 10.33 313s Investment_14 -1.4083 -14.12 313s Investment_15 0.0885 1.11 313s Investment_17 -1.8093 -26.98 313s Investment_18 0.1676 3.25 313s Investment_19 2.8888 55.20 313s Investment_20 -0.6425 -11.35 313s Investment_21 -0.2855 -5.82 313s Investment_22 -0.7925 -17.97 313s PrivateWages_2 -2.9611 -41.49 313s PrivateWages_3 1.0665 17.77 313s PrivateWages_4 2.5794 47.83 313s PrivateWages_5 -2.7951 -56.65 313s PrivateWages_6 -0.4865 -9.25 313s PrivateWages_8 1.6497 29.11 313s PrivateWages_9 1.8751 35.52 313s PrivateWages_10 0.0000 0.00 313s PrivateWages_11 -2.3618 -39.54 313s PrivateWages_12 -0.3246 -4.34 313s PrivateWages_13 0.0000 0.00 313s PrivateWages_14 3.0441 30.51 313s PrivateWages_15 -0.2496 -3.12 313s PrivateWages_16 -0.3710 -5.37 313s PrivateWages_17 2.5263 37.67 313s PrivateWages_18 0.0583 1.13 313s PrivateWages_19 -6.2503 -119.43 313s PrivateWages_20 1.3565 23.96 313s PrivateWages_21 -1.2791 -26.09 313s PrivateWages_22 1.9457 44.12 313s Consumption_corpProfLag Consumption_wages 313s Consumption_2 -42.379 -99.51 313s Consumption_3 -7.762 -19.94 313s Consumption_4 9.179 19.15 313s Consumption_5 -35.489 -74.45 313s Consumption_6 19.359 38.46 313s Consumption_8 92.559 188.94 313s Consumption_9 83.547 176.28 313s Consumption_11 -45.883 -91.13 313s Consumption_12 -42.949 -109.17 313s Consumption_14 5.096 24.26 313s Consumption_15 -22.780 -75.93 313s Consumption_16 -20.627 -67.32 313s Consumption_17 86.080 256.88 313s Consumption_18 -11.379 -30.78 313s Consumption_19 -82.131 -233.73 313s Consumption_20 50.662 160.78 313s Consumption_21 29.137 81.92 313s Consumption_22 -22.729 -65.49 313s Investment_2 18.377 43.15 313s Investment_3 -3.526 -9.06 313s Investment_4 -10.914 -22.77 313s Investment_5 24.097 50.55 313s Investment_6 -6.431 -12.78 313s Investment_8 -21.669 -44.23 313s Investment_9 -10.805 -22.80 313s Investment_10 0.000 0.00 313s Investment_11 19.355 38.44 313s Investment_12 12.047 30.62 313s Investment_14 -9.858 -46.93 313s Investment_15 0.992 3.31 313s Investment_17 -25.331 -75.59 313s Investment_18 2.950 7.98 313s Investment_19 49.976 142.22 313s Investment_20 -9.831 -31.20 313s Investment_21 -5.425 -15.25 313s Investment_22 -16.723 -48.18 313s PrivateWages_2 -37.606 -88.31 313s PrivateWages_3 13.225 33.97 313s PrivateWages_4 43.593 90.94 313s PrivateWages_5 -51.429 -107.89 313s PrivateWages_6 -9.438 -18.75 313s PrivateWages_8 32.333 66.00 313s PrivateWages_9 37.126 78.33 313s PrivateWages_10 0.000 0.00 313s PrivateWages_11 -51.251 -101.80 313s PrivateWages_12 -5.063 -12.87 313s PrivateWages_13 0.000 0.00 313s PrivateWages_14 21.309 101.45 313s PrivateWages_15 -2.796 -9.32 313s PrivateWages_16 -4.563 -14.89 313s PrivateWages_17 35.368 105.55 313s PrivateWages_18 1.025 2.77 313s PrivateWages_19 -108.130 -307.72 313s PrivateWages_20 20.754 65.87 313s PrivateWages_21 -24.303 -68.33 313s PrivateWages_22 41.055 118.29 313s Investment_(Intercept) Investment_corpProf 313s Consumption_2 1.6657 22.369 313s Consumption_3 0.3125 5.208 313s Consumption_4 -0.2711 -5.105 313s Consumption_5 0.9628 19.850 313s Consumption_6 -0.4981 -9.617 313s Consumption_8 -2.3573 -41.335 313s Consumption_9 -2.1063 -41.098 313s Consumption_11 1.0555 18.165 313s Consumption_12 1.3743 18.540 313s Consumption_14 -0.3634 -3.664 313s Consumption_15 1.0153 13.204 313s Consumption_16 0.0000 0.000 313s Consumption_17 -3.0693 -45.765 313s Consumption_18 0.3228 6.293 313s Consumption_19 2.3698 45.702 313s Consumption_20 -1.6529 -29.000 313s Consumption_21 -0.7655 -15.445 313s Consumption_22 0.5377 12.243 313s Investment_2 -2.0943 -28.124 313s Investment_3 0.4116 6.860 313s Investment_4 0.9347 17.600 313s Investment_5 -1.8955 -39.080 313s Investment_6 0.4798 9.263 313s Investment_8 1.6002 28.058 313s Investment_9 0.7899 15.412 313s Investment_10 2.8075 56.810 313s Investment_11 -1.2910 -22.218 313s Investment_12 -1.1178 -15.079 313s Investment_14 2.0383 20.552 313s Investment_15 -0.1282 -1.667 313s Investment_17 2.6188 39.047 313s Investment_18 -0.2426 -4.730 313s Investment_19 -4.1811 -80.631 313s Investment_20 0.9300 16.316 313s Investment_21 0.4133 8.338 313s Investment_22 1.1471 26.118 313s PrivateWages_2 1.8190 24.427 313s PrivateWages_3 -0.6551 -10.919 313s PrivateWages_4 -1.5845 -29.835 313s PrivateWages_5 1.7170 35.400 313s PrivateWages_6 0.2989 5.770 313s PrivateWages_8 -1.0134 -17.769 313s PrivateWages_9 -1.1518 -22.474 313s PrivateWages_10 -2.1257 -43.013 313s PrivateWages_11 1.4508 24.969 313s PrivateWages_12 0.1994 2.690 313s PrivateWages_13 0.0000 0.000 313s PrivateWages_14 -1.8700 -18.855 313s PrivateWages_15 0.1533 1.994 313s PrivateWages_16 0.0000 0.000 313s PrivateWages_17 -1.5519 -23.140 313s PrivateWages_18 -0.0358 -0.698 313s PrivateWages_19 3.8395 74.045 313s PrivateWages_20 -0.8333 -14.620 313s PrivateWages_21 0.7858 15.853 313s PrivateWages_22 -1.1953 -27.215 313s Investment_corpProfLag Investment_capitalLag 313s Consumption_2 21.15 304.50 313s Consumption_3 3.87 57.06 313s Consumption_4 -4.58 -50.02 313s Consumption_5 17.72 182.64 313s Consumption_6 -9.66 -95.99 313s Consumption_8 -46.20 -479.48 313s Consumption_9 -41.70 -437.27 313s Consumption_11 22.90 227.67 313s Consumption_12 21.44 297.81 313s Consumption_14 -2.54 -75.26 313s Consumption_15 11.37 205.09 313s Consumption_16 0.00 0.00 313s Consumption_17 -42.97 -606.79 313s Consumption_18 5.68 64.49 313s Consumption_19 41.00 478.23 313s Consumption_20 -25.29 -330.42 313s Consumption_21 -14.54 -154.02 313s Consumption_22 11.35 109.96 313s Investment_2 -26.60 -382.84 313s Investment_3 5.10 75.16 313s Investment_4 15.80 172.46 313s Investment_5 -34.88 -359.58 313s Investment_6 9.31 92.46 313s Investment_8 31.36 325.47 313s Investment_9 15.64 163.98 313s Investment_10 59.24 591.25 313s Investment_11 -28.01 -278.46 313s Investment_12 -17.44 -242.22 313s Investment_14 14.27 422.14 313s Investment_15 -1.44 -25.89 313s Investment_17 36.66 517.73 313s Investment_18 -4.27 -48.47 313s Investment_19 -72.33 -843.75 313s Investment_20 14.23 185.90 313s Investment_21 7.85 83.15 313s Investment_22 24.20 234.58 313s PrivateWages_2 23.10 332.51 313s PrivateWages_3 -8.12 -119.63 313s PrivateWages_4 -26.78 -292.35 313s PrivateWages_5 31.59 325.71 313s PrivateWages_6 5.80 57.59 313s PrivateWages_8 -19.86 -206.12 313s PrivateWages_9 -22.81 -239.12 313s PrivateWages_10 -44.85 -447.66 313s PrivateWages_11 31.48 312.95 313s PrivateWages_12 3.11 43.21 313s PrivateWages_13 0.00 0.00 313s PrivateWages_14 -13.09 -387.28 313s PrivateWages_15 1.72 30.97 313s PrivateWages_16 0.00 0.00 313s PrivateWages_17 -21.73 -306.81 313s PrivateWages_18 -0.63 -7.15 313s PrivateWages_19 66.42 774.82 313s PrivateWages_20 -12.75 -166.57 313s PrivateWages_21 14.93 158.09 313s PrivateWages_22 -25.22 -244.43 313s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 313s Consumption_2 -3.302 -155.43 -148.27 313s Consumption_3 -0.619 -30.71 -28.25 313s Consumption_4 0.537 30.39 26.93 313s Consumption_5 -1.909 -115.83 -109.18 313s Consumption_6 0.987 59.85 56.39 313s Consumption_8 4.673 280.38 299.09 313s Consumption_9 4.176 260.01 268.91 313s Consumption_11 -2.092 -133.31 -140.19 313s Consumption_12 -2.724 -149.39 -166.74 313s Consumption_14 0.720 30.35 31.91 313s Consumption_15 -2.013 -103.09 -90.78 313s Consumption_16 -1.660 -91.84 -82.48 313s Consumption_17 6.085 349.22 331.00 313s Consumption_18 -0.640 -42.98 -40.12 313s Consumption_19 -4.698 -321.88 -305.37 313s Consumption_20 3.277 219.03 199.56 313s Consumption_21 1.518 113.62 105.47 313s Consumption_22 -1.066 -92.61 -80.70 313s Investment_2 1.762 82.94 79.12 313s Investment_3 -0.346 -17.17 -15.79 313s Investment_4 -0.786 -44.47 -39.40 313s Investment_5 1.595 96.79 91.23 313s Investment_6 -0.404 -24.47 -23.05 313s Investment_8 -1.346 -80.78 -86.17 313s Investment_9 -0.665 -41.38 -42.80 313s Investment_10 -2.362 -152.52 -152.36 313s Investment_11 1.086 69.20 72.78 313s Investment_12 0.940 51.57 57.56 313s Investment_14 -1.715 -72.25 -75.98 313s Investment_15 0.108 5.52 4.86 313s Investment_17 -2.203 -126.46 -119.87 313s Investment_18 0.204 13.71 12.80 313s Investment_19 3.518 241.02 228.67 313s Investment_20 -0.782 -52.30 -47.65 313s Investment_21 -0.348 -26.03 -24.17 313s Investment_22 -0.965 -83.85 -73.06 313s PrivateWages_2 -6.697 -315.21 -300.67 313s PrivateWages_3 2.412 119.58 109.98 313s PrivateWages_4 5.833 329.84 292.25 313s PrivateWages_5 -6.321 -383.60 -361.56 313s PrivateWages_6 -1.100 -66.69 -62.82 313s PrivateWages_8 3.731 223.83 238.77 313s PrivateWages_9 4.240 264.05 273.09 313s PrivateWages_10 7.826 505.29 504.75 313s PrivateWages_11 -5.341 -340.30 -357.86 313s PrivateWages_12 -0.734 -40.25 -44.92 313s PrivateWages_13 -4.155 -195.19 -221.87 313s PrivateWages_14 6.884 290.02 304.97 313s PrivateWages_15 -0.565 -28.91 -25.46 313s PrivateWages_16 -0.839 -46.43 -41.70 313s PrivateWages_17 5.713 327.90 310.80 313s PrivateWages_18 0.132 8.85 8.26 313s PrivateWages_19 -14.135 -968.43 -918.78 313s PrivateWages_20 3.068 205.06 186.82 313s PrivateWages_21 -2.893 -216.57 -201.04 313s PrivateWages_22 4.400 382.29 333.10 313s PrivateWages_trend 313s Consumption_2 33.022 313s Consumption_3 5.575 313s Consumption_4 -4.300 313s Consumption_5 13.361 313s Consumption_6 -5.925 313s Consumption_8 -18.693 313s Consumption_9 -12.527 313s Consumption_11 2.092 313s Consumption_12 0.000 313s Consumption_14 1.441 313s Consumption_15 -6.038 313s Consumption_16 -6.638 313s Consumption_17 30.423 313s Consumption_18 -3.839 313s Consumption_19 -32.886 313s Consumption_20 26.214 313s Consumption_21 13.658 313s Consumption_22 -10.660 313s Investment_2 -17.621 313s Investment_3 3.117 313s Investment_4 6.292 313s Investment_5 -11.164 313s Investment_6 2.422 313s Investment_8 5.385 313s Investment_9 1.994 313s Investment_10 4.724 313s Investment_11 -1.086 313s Investment_12 0.000 313s Investment_14 -3.430 313s Investment_15 0.323 313s Investment_17 -11.017 313s Investment_18 1.225 313s Investment_19 24.626 313s Investment_20 -6.260 313s Investment_21 -3.129 313s Investment_22 -9.652 313s PrivateWages_2 66.965 313s PrivateWages_3 -21.707 313s PrivateWages_4 -46.667 313s PrivateWages_5 44.247 313s PrivateWages_6 6.602 313s PrivateWages_8 -14.923 313s PrivateWages_9 -12.721 313s PrivateWages_10 -15.651 313s PrivateWages_11 5.341 313s PrivateWages_12 0.000 313s PrivateWages_13 -4.155 313s PrivateWages_14 13.769 313s PrivateWages_15 -1.694 313s PrivateWages_16 -3.356 313s PrivateWages_17 28.566 313s PrivateWages_18 0.791 313s PrivateWages_19 -98.946 313s PrivateWages_20 24.542 313s PrivateWages_21 -26.035 313s PrivateWages_22 44.003 313s [1] TRUE 313s > Bread 313s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 313s [1,] 137.1267 -4.2997 0.8463 313s [2,] -4.2997 1.2597 -0.6942 313s [3,] 0.8463 -0.6942 0.7454 313s [4,] -1.7733 -0.1394 -0.0281 313s [5,] 105.0265 3.4241 3.4807 313s [6,] -4.4721 0.5244 -0.4530 313s [7,] 1.6442 -0.3454 0.4268 313s [8,] -0.2644 -0.0340 -0.0134 313s [9,] -38.0151 0.3680 1.7655 313s [10,] 0.5379 -0.0825 0.0502 313s [11,] 0.0809 0.0782 -0.0821 313s [12,] 0.1895 0.0505 0.0265 313s Consumption_wages Investment_(Intercept) Investment_corpProf 313s [1,] -1.773256 105.03 -4.47211 313s [2,] -0.139424 3.42 0.52437 313s [3,] -0.028067 3.48 -0.45300 313s [4,] 0.110155 -5.14 0.06784 313s [5,] -5.138461 2514.46 -43.59967 313s [6,] 0.067843 -43.60 1.90216 313s [7,] -0.064178 34.75 -1.45456 313s [8,] 0.025084 -11.63 0.17310 313s [9,] 0.044238 27.92 -0.25822 313s [10,] 0.000203 1.31 0.00136 313s [11,] -0.000811 -1.85 0.00316 313s [12,] -0.035488 -0.85 0.01679 313s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 313s [1,] 1.64420 -0.26436 -38.0151 313s [2,] -0.34536 -0.03402 0.3680 313s [3,] 0.42680 -0.01343 1.7655 313s [4,] -0.06418 0.02508 0.0442 313s [5,] 34.75055 -11.63252 27.9186 313s [6,] -1.45456 0.17310 -0.2582 313s [7,] 1.39257 -0.16270 -0.3518 313s [8,] -0.16270 0.05655 -0.0905 313s [9,] -0.35175 -0.09046 70.9283 313s [10,] 0.00769 -0.00730 -0.3444 313s [11,] -0.00156 0.00915 -0.8533 313s [12,] -0.02239 0.00456 0.8163 313s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 313s [1,] 0.537909 0.080946 0.189459 313s [2,] -0.082456 0.078164 0.050460 313s [3,] 0.050248 -0.082092 0.026511 313s [4,] 0.000203 -0.000811 -0.035488 313s [5,] 1.312267 -1.847095 -0.850461 313s [6,] 0.001362 0.003160 0.016792 313s [7,] 0.007689 -0.001565 -0.022388 313s [8,] -0.007301 0.009148 0.004555 313s [9,] -0.344428 -0.853347 0.816265 313s [10,] 0.053258 -0.048785 -0.014522 313s [11,] -0.048785 0.064956 0.000648 313s [12,] -0.014522 0.000648 0.047452 313s > 313s > # I3SLS 313s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 313s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 313s > summary 313s 313s systemfit results 313s method: iterated 3SLS 313s 313s convergence achieved after 10 iterations 313s 313s N DF SSR detRCov OLS-R2 McElroy-R2 313s system 56 44 79.4 0.55 0.956 0.994 313s 313s N DF SSR MSE RMSE R2 Adj R2 313s Consumption 18 14 22.3 1.595 1.263 0.974 0.968 313s Investment 18 14 46.8 3.346 1.829 0.724 0.664 313s PrivateWages 20 16 10.2 0.639 0.799 0.987 0.985 313s 313s The covariance matrix of the residuals used for estimation 313s Consumption Investment PrivateWages 313s Consumption 1.307 0.750 -0.452 313s Investment 0.750 2.318 0.272 313s PrivateWages -0.452 0.272 0.530 313s 313s The covariance matrix of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.307 0.750 -0.452 313s Investment 0.750 2.318 0.272 313s PrivateWages -0.452 0.272 0.530 313s 313s The correlations of the residuals 313s Consumption Investment PrivateWages 313s Consumption 1.000 0.424 -0.542 313s Investment 0.424 1.000 0.254 313s PrivateWages -0.542 0.254 1.000 313s 313s 313s 3SLS estimates for 'Consumption' (equation 1) 313s Model Formula: consump ~ corpProf + corpProfLag + wages 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 18.3252 1.5452 11.86 1.1e-08 *** 313s corpProf -0.0436 0.1470 -0.30 0.77 313s corpProfLag 0.1614 0.1127 1.43 0.17 313s wages 0.8127 0.0436 18.65 2.8e-11 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.263 on 14 degrees of freedom 313s Number of observations: 18 Degrees of Freedom: 14 313s SSR: 22.337 MSE: 1.595 Root MSE: 1.263 313s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 313s 313s 313s 3SLS estimates for 'Investment' (equation 2) 313s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 30.2418 8.3674 3.61 0.00282 ** 313s corpProf -0.0437 0.2341 -0.19 0.85457 313s corpProfLag 0.7856 0.1993 3.94 0.00147 ** 313s capitalLag -0.2065 0.0397 -5.20 0.00014 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 1.829 on 14 degrees of freedom 313s Number of observations: 18 Degrees of Freedom: 14 313s SSR: 46.838 MSE: 3.346 Root MSE: 1.829 313s Multiple R-Squared: 0.724 Adjusted R-Squared: 0.664 313s 313s 313s 3SLS estimates for 'PrivateWages' (equation 3) 313s Model Formula: privWage ~ gnp + gnpLag + trend 313s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 313s gnpLag 313s 313s Estimate Std. Error t value Pr(>|t|) 313s (Intercept) 0.4741 1.1280 0.42 0.67983 313s gnp 0.4268 0.0296 14.44 1.4e-10 *** 313s gnpLag 0.1767 0.0330 5.35 6.5e-05 *** 313s trend 0.1201 0.0290 4.14 0.00076 *** 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s 313s Residual standard error: 0.799 on 16 degrees of freedom 313s Number of observations: 20 Degrees of Freedom: 16 313s SSR: 10.218 MSE: 0.639 Root MSE: 0.799 313s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 313s 313s > residuals 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 -0.8546 -2.1226 -1.1687 313s 3 -0.7611 0.3684 0.4670 313s 4 -1.1233 0.5912 1.3216 313s 5 0.0781 -1.6694 -0.2108 313s 6 0.6467 0.2952 -0.4776 313s 7 NA NA NA 313s 8 1.8444 1.4348 -0.8884 313s 9 1.8309 1.0020 0.1781 313s 10 NA 2.7265 1.0734 313s 11 -0.3652 -1.0581 -0.4134 313s 12 -1.3877 -0.6431 0.4203 313s 13 NA NA 0.0623 313s 14 -0.1818 2.4214 0.7091 313s 15 -0.6438 0.2168 0.5845 313s 16 -0.3417 NA 0.2455 313s 17 1.9583 2.4607 -0.6474 313s 18 -0.4806 -0.0468 0.9840 313s 19 -0.2563 -3.3855 -0.5930 313s 20 1.4832 1.1550 -0.2586 313s 21 1.4514 0.6086 -1.1446 313s 22 -1.2351 1.3453 0.5196 313s > fitted 313s Consumption Investment PrivateWages 313s 1 NA NA NA 313s 2 42.8 1.923 26.7 313s 3 45.8 1.532 28.8 313s 4 50.3 4.609 32.8 313s 5 50.5 4.669 34.1 313s 6 52.0 4.805 35.9 313s 7 NA NA NA 313s 8 54.4 2.765 38.8 313s 9 55.5 1.998 39.0 313s 10 NA 2.373 40.2 313s 11 55.4 2.058 38.3 313s 12 52.3 -2.757 34.1 313s 13 NA NA 28.9 313s 14 46.7 -7.521 27.8 313s 15 49.3 -3.217 30.0 313s 16 51.6 NA 33.0 313s 17 55.7 -0.361 37.4 313s 18 59.2 2.047 40.0 313s 19 57.8 1.485 38.8 313s 20 60.1 0.145 41.9 313s 21 63.5 2.691 46.1 313s 22 70.9 3.555 52.8 313s > predict 313s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 313s 1 NA NA NA NA 313s 2 42.8 0.548 41.7 43.9 313s 3 45.8 0.618 44.5 47.0 313s 4 50.3 0.411 49.5 51.2 313s 5 50.5 0.481 49.6 51.5 313s 6 52.0 0.490 51.0 52.9 313s 7 NA NA NA NA 313s 8 54.4 0.396 53.6 55.2 313s 9 55.5 0.467 54.5 56.4 313s 10 NA NA NA NA 313s 11 55.4 0.811 53.7 57.0 313s 12 52.3 0.775 50.7 53.8 313s 13 NA NA NA NA 313s 14 46.7 0.665 45.3 48.0 313s 15 49.3 0.463 48.4 50.3 313s 16 51.6 0.381 50.9 52.4 313s 17 55.7 0.428 54.9 56.6 313s 18 59.2 0.360 58.5 59.9 313s 19 57.8 0.492 56.8 58.7 313s 20 60.1 0.508 59.1 61.1 313s 21 63.5 0.499 62.5 64.6 313s 22 70.9 0.761 69.4 72.5 313s Investment.pred Investment.se.fit Investment.lwr Investment.upr 313s 1 NA NA NA NA 313s 2 1.923 1.079 -0.2526 4.098 313s 3 1.532 0.766 -0.0119 3.075 313s 4 4.609 0.668 3.2632 5.954 313s 5 4.669 0.566 3.5280 5.811 313s 6 4.805 0.543 3.7104 5.899 313s 7 NA NA NA NA 313s 8 2.765 0.447 1.8648 3.665 313s 9 1.998 0.651 0.6860 3.310 313s 10 2.373 0.710 0.9434 3.804 313s 11 2.058 1.237 -0.4350 4.551 313s 12 -2.757 1.139 -5.0532 -0.461 313s 13 NA NA NA NA 313s 14 -7.521 1.094 -9.7261 -5.317 313s 15 -3.217 0.648 -4.5217 -1.912 313s 16 NA NA NA NA 313s 17 -0.361 0.615 -1.6007 0.879 313s 18 2.047 0.417 1.2060 2.888 313s 19 1.485 0.684 0.1062 2.865 313s 20 0.145 0.699 -1.2632 1.553 313s 21 2.691 0.614 1.4548 3.928 313s 22 3.555 0.887 1.7674 5.342 313s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 313s 1 NA NA NA NA 313s 2 26.7 0.330 26.0 27.3 313s 3 28.8 0.336 28.2 29.5 313s 4 32.8 0.340 32.1 33.5 313s 5 34.1 0.251 33.6 34.6 313s 6 35.9 0.259 35.4 36.4 313s 7 NA NA NA NA 313s 8 38.8 0.253 38.3 39.3 313s 9 39.0 0.240 38.5 39.5 313s 10 40.2 0.236 39.8 40.7 313s 11 38.3 0.307 37.7 38.9 313s 12 34.1 0.313 33.4 34.7 313s 13 28.9 0.376 28.2 29.7 313s 14 27.8 0.327 27.1 28.4 313s 15 30.0 0.322 29.4 30.7 313s 16 33.0 0.270 32.4 33.5 313s 17 37.4 0.275 36.9 38.0 313s 18 40.0 0.216 39.6 40.5 313s 19 38.8 0.314 38.2 39.4 313s 20 41.9 0.296 41.3 42.5 313s 21 46.1 0.317 45.5 46.8 313s 22 52.8 0.480 51.8 53.7 313s > model.frame 313s [1] TRUE 313s > model.matrix 313s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 313s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 313s [3] "Numeric: lengths (696, 672) differ" 313s > nobs 313s [1] 56 313s > linearHypothesis 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 45 313s 2 44 1 2.29 0.14 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 45 313s 2 44 1 2.89 0.096 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s Linear hypothesis test (Chi^2 statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df Chisq Pr(>Chisq) 313s 1 45 313s 2 44 1 2.89 0.089 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 313s Linear hypothesis test (Theil's F test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 44 2 2.3 0.11 313s Linear hypothesis test (F statistic of a Wald test) 313s 313s Hypothesis: 313s Consumption_corpProf + Investment_capitalLag = 0 313s Consumption_corpProfLag - PrivateWages_trend = 0 313s 313s Model 1: restricted model 313s Model 2: kleinModel 313s 313s Res.Df Df F Pr(>F) 313s 1 46 313s 2 44 2 2.9 0.066 . 313s --- 313s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 314s Linear hypothesis test (Chi^2 statistic of a Wald test) 314s 314s Hypothesis: 314s Consumption_corpProf + Investment_capitalLag = 0 314s Consumption_corpProfLag - PrivateWages_trend = 0 314s 314s Model 1: restricted model 314s Model 2: kleinModel 314s 314s Res.Df Df Chisq Pr(>Chisq) 314s 1 46 314s 2 44 2 5.79 0.055 . 314s --- 314s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 314s > logLik 314s 'log Lik.' -72.2 (df=18) 314s 'log Lik.' -83.4 (df=18) 314s Estimating function 314s Consumption_(Intercept) Consumption_corpProf 314s Consumption_2 -4.4102 -61.801 314s Consumption_3 -1.0169 -16.947 314s Consumption_4 0.6316 11.712 314s Consumption_5 -2.4849 -50.366 314s Consumption_6 1.3496 25.671 314s Consumption_8 6.2136 109.641 314s Consumption_9 5.5588 105.303 314s Consumption_11 -2.3690 -39.659 314s Consumption_12 -3.3344 -44.601 314s Consumption_14 0.8298 8.317 314s Consumption_15 -2.5803 -32.264 314s Consumption_16 -2.1088 -30.539 314s Consumption_17 7.9903 119.154 314s Consumption_18 -0.6538 -12.697 314s Consumption_19 -5.8714 -112.192 314s Consumption_20 4.4259 78.161 314s Consumption_21 2.2655 46.209 314s Consumption_22 -0.9489 -21.517 314s Investment_2 1.9674 27.570 314s Investment_3 -0.3392 -5.652 314s Investment_4 -0.5776 -10.712 314s Investment_5 1.5305 31.021 314s Investment_6 -0.2467 -4.692 314s Investment_8 -1.2650 -22.320 314s Investment_9 -0.8831 -16.728 314s Investment_10 0.0000 0.000 314s Investment_11 0.9353 15.658 314s Investment_12 0.5224 6.988 314s Investment_14 -2.2467 -22.520 314s Investment_15 -0.2344 -2.931 314s Investment_17 -2.2188 -33.088 314s Investment_18 -0.0466 -0.905 314s Investment_19 3.0409 58.107 314s Investment_20 -1.0335 -18.251 314s Investment_21 -0.5381 -10.975 314s Investment_22 -1.2437 -28.202 314s PrivateWages_2 -4.0943 -57.374 314s PrivateWages_3 1.5700 26.162 314s PrivateWages_4 3.6522 67.727 314s PrivateWages_5 -3.9696 -80.460 314s PrivateWages_6 -0.7099 -13.503 314s PrivateWages_8 2.2578 39.840 314s PrivateWages_9 2.5772 48.821 314s PrivateWages_10 0.0000 0.000 314s PrivateWages_11 -3.3861 -56.686 314s PrivateWages_12 -0.4354 -5.824 314s PrivateWages_13 0.0000 0.000 314s PrivateWages_14 4.5081 45.187 314s PrivateWages_15 -0.1430 -1.788 314s PrivateWages_16 -0.3534 -5.118 314s PrivateWages_17 3.6864 54.972 314s PrivateWages_18 0.1281 2.488 314s PrivateWages_19 -8.7578 -167.347 314s PrivateWages_20 1.9940 35.215 314s PrivateWages_21 -1.7982 -36.678 314s PrivateWages_22 2.6643 60.414 314s Consumption_corpProfLag Consumption_wages 314s Consumption_2 -56.01 -131.52 314s Consumption_3 -12.61 -32.39 314s Consumption_4 10.67 22.27 314s Consumption_5 -45.72 -95.92 314s Consumption_6 26.18 52.02 314s Consumption_8 121.79 248.60 314s Consumption_9 110.06 232.23 314s Consumption_11 -51.41 -102.11 314s Consumption_12 -52.02 -132.22 314s Consumption_14 5.81 27.65 314s Consumption_15 -28.90 -96.33 314s Consumption_16 -25.94 -84.65 314s Consumption_17 111.86 333.82 314s Consumption_18 -11.51 -31.13 314s Consumption_19 -101.57 -289.06 314s Consumption_20 67.72 214.91 314s Consumption_21 43.05 121.02 314s Consumption_22 -20.02 -57.69 314s Investment_2 24.99 58.67 314s Investment_3 -4.21 -10.80 314s Investment_4 -9.76 -20.36 314s Investment_5 28.16 59.08 314s Investment_6 -4.79 -9.51 314s Investment_8 -24.79 -50.61 314s Investment_9 -17.48 -36.89 314s Investment_10 0.00 0.00 314s Investment_11 20.30 40.31 314s Investment_12 8.15 20.72 314s Investment_14 -15.73 -74.88 314s Investment_15 -2.63 -8.75 314s Investment_17 -31.06 -92.70 314s Investment_18 -0.82 -2.22 314s Investment_19 52.61 149.71 314s Investment_20 -15.81 -50.18 314s Investment_21 -10.22 -28.74 314s Investment_22 -26.24 -75.61 314s PrivateWages_2 -52.00 -122.10 314s PrivateWages_3 19.47 50.00 314s PrivateWages_4 61.72 128.76 314s PrivateWages_5 -73.04 -153.23 314s PrivateWages_6 -13.77 -27.36 314s PrivateWages_8 44.25 90.33 314s PrivateWages_9 51.03 107.67 314s PrivateWages_10 0.00 0.00 314s PrivateWages_11 -73.48 -145.95 314s PrivateWages_12 -6.79 -17.27 314s PrivateWages_13 0.00 0.00 314s PrivateWages_14 31.56 150.24 314s PrivateWages_15 -1.60 -5.34 314s PrivateWages_16 -4.35 -14.19 314s PrivateWages_17 51.61 154.01 314s PrivateWages_18 2.25 6.10 314s PrivateWages_19 -151.51 -431.17 314s PrivateWages_20 30.51 96.82 314s PrivateWages_21 -34.17 -96.06 314s PrivateWages_22 56.22 161.97 314s Investment_(Intercept) Investment_corpProf 314s Consumption_2 1.9908 26.734 314s Consumption_3 0.4591 7.651 314s Consumption_4 -0.2851 -5.368 314s Consumption_5 1.1217 23.127 314s Consumption_6 -0.6092 -11.762 314s Consumption_8 -2.8049 -49.183 314s Consumption_9 -2.5093 -48.961 314s Consumption_11 1.0694 18.405 314s Consumption_12 1.5052 20.306 314s Consumption_14 -0.3746 -3.777 314s Consumption_15 1.1648 15.147 314s Consumption_16 0.0000 0.000 314s Consumption_17 -3.6069 -53.782 314s Consumption_18 0.2951 5.754 314s Consumption_19 2.6504 51.112 314s Consumption_20 -1.9979 -35.052 314s Consumption_21 -1.0227 -20.634 314s Consumption_22 0.4283 9.753 314s Investment_2 -1.8422 -24.739 314s Investment_3 0.3176 5.293 314s Investment_4 0.5409 10.184 314s Investment_5 -1.4331 -29.546 314s Investment_6 0.2310 4.459 314s Investment_8 1.1844 20.769 314s Investment_9 0.8269 16.134 314s Investment_10 2.3608 47.771 314s Investment_11 -0.8758 -15.072 314s Investment_12 -0.4892 -6.600 314s Investment_14 2.1037 21.212 314s Investment_15 0.2195 2.854 314s Investment_17 2.0776 30.979 314s Investment_18 0.0436 0.851 314s Investment_19 -2.8474 -54.911 314s Investment_20 0.9677 16.978 314s Investment_21 0.5038 10.165 314s Investment_22 1.1646 26.516 314s PrivateWages_2 2.2726 30.518 314s PrivateWages_3 -0.8714 -14.524 314s PrivateWages_4 -2.0272 -38.170 314s PrivateWages_5 2.2034 45.428 314s PrivateWages_6 0.3940 7.607 314s PrivateWages_8 -1.2532 -21.975 314s PrivateWages_9 -1.4305 -27.911 314s PrivateWages_10 -2.6709 -54.046 314s PrivateWages_11 1.8795 32.347 314s PrivateWages_12 0.2417 3.260 314s PrivateWages_13 0.0000 0.000 314s PrivateWages_14 -2.5023 -25.230 314s PrivateWages_15 0.0794 1.032 314s PrivateWages_16 0.0000 0.000 314s PrivateWages_17 -2.0461 -30.509 314s PrivateWages_18 -0.0711 -1.386 314s PrivateWages_19 4.8611 93.745 314s PrivateWages_20 -1.1068 -19.419 314s PrivateWages_21 0.9981 20.138 314s PrivateWages_22 -1.4788 -33.672 314s Investment_corpProfLag Investment_capitalLag 314s Consumption_2 25.283 363.92 314s Consumption_3 5.692 83.82 314s Consumption_4 -4.818 -52.60 314s Consumption_5 20.639 212.79 314s Consumption_6 -11.819 -117.39 314s Consumption_8 -54.976 -570.52 314s Consumption_9 -49.684 -520.93 314s Consumption_11 23.206 230.67 314s Consumption_12 23.481 326.17 314s Consumption_14 -2.622 -77.57 314s Consumption_15 13.045 235.28 314s Consumption_16 0.000 0.00 314s Consumption_17 -50.497 -713.09 314s Consumption_18 5.194 58.97 314s Consumption_19 45.852 534.85 314s Consumption_20 -30.568 -399.38 314s Consumption_21 -19.431 -205.77 314s Consumption_22 9.038 87.60 314s Investment_2 -23.396 -336.76 314s Investment_3 3.938 57.99 314s Investment_4 9.141 99.79 314s Investment_5 -26.369 -271.86 314s Investment_6 4.481 44.51 314s Investment_8 23.215 240.92 314s Investment_9 16.372 171.66 314s Investment_10 49.812 497.18 314s Investment_11 -19.004 -188.91 314s Investment_12 -7.631 -106.01 314s Investment_14 14.726 435.68 314s Investment_15 2.458 44.34 314s Investment_17 29.086 410.74 314s Investment_18 0.768 8.72 314s Investment_19 -49.260 -574.60 314s Investment_20 14.806 193.44 314s Investment_21 9.573 101.37 314s Investment_22 24.572 238.15 314s PrivateWages_2 28.862 415.43 314s PrivateWages_3 -10.806 -159.12 314s PrivateWages_4 -34.259 -374.01 314s PrivateWages_5 40.542 417.98 314s PrivateWages_6 7.644 75.93 314s PrivateWages_8 -24.563 -254.91 314s PrivateWages_9 -28.324 -296.97 314s PrivateWages_10 -56.356 -562.49 314s PrivateWages_11 40.785 405.41 314s PrivateWages_12 3.770 52.37 314s PrivateWages_13 0.000 0.00 314s PrivateWages_14 -17.516 -518.22 314s PrivateWages_15 0.889 16.03 314s PrivateWages_16 0.000 0.00 314s PrivateWages_17 -28.646 -404.52 314s PrivateWages_18 -1.251 -14.21 314s PrivateWages_19 84.097 980.97 314s PrivateWages_20 -16.934 -221.25 314s PrivateWages_21 18.964 200.82 314s PrivateWages_22 -31.204 -302.42 314s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 314s Consumption_2 -4.7927 -225.59 -215.2 314s Consumption_3 -1.1051 -54.79 -50.4 314s Consumption_4 0.6863 38.81 34.4 314s Consumption_5 -2.7004 -163.88 -154.5 314s Consumption_6 1.4666 88.89 83.7 314s Consumption_8 6.7526 405.14 432.2 314s Consumption_9 6.0409 376.16 389.0 314s Consumption_11 -2.5745 -164.03 -172.5 314s Consumption_12 -3.6236 -198.69 -221.8 314s Consumption_14 0.9017 37.99 39.9 314s Consumption_15 -2.8041 -143.62 -126.5 314s Consumption_16 -2.2917 -126.82 -113.9 314s Consumption_17 8.6833 498.37 472.4 314s Consumption_18 -0.7105 -47.73 -44.5 314s Consumption_19 -6.3806 -437.15 -414.7 314s Consumption_20 4.8097 321.50 292.9 314s Consumption_21 2.4620 184.32 171.1 314s Consumption_22 -1.0312 -89.59 -78.1 314s Investment_2 2.6290 123.75 118.0 314s Investment_3 -0.4532 -22.47 -20.7 314s Investment_4 -0.7719 -43.64 -38.7 314s Investment_5 2.0451 124.11 117.0 314s Investment_6 -0.3296 -19.98 -18.8 314s Investment_8 -1.6903 -101.41 -108.2 314s Investment_9 -1.1800 -73.48 -76.0 314s Investment_10 -3.3690 -217.54 -217.3 314s Investment_11 1.2498 79.63 83.7 314s Investment_12 0.6981 38.28 42.7 314s Investment_14 -3.0022 -126.47 -133.0 314s Investment_15 -0.3132 -16.04 -14.1 314s Investment_17 -2.9649 -170.17 -161.3 314s Investment_18 -0.0623 -4.18 -3.9 314s Investment_19 4.0635 278.40 264.1 314s Investment_20 -1.3810 -92.31 -84.1 314s Investment_21 -0.7190 -53.83 -50.0 314s Investment_22 -1.6619 -144.39 -125.8 314s PrivateWages_2 -8.0595 -379.36 -361.9 314s PrivateWages_3 3.0904 153.23 140.9 314s PrivateWages_4 7.1892 406.50 360.2 314s PrivateWages_5 -7.8142 -474.21 -447.0 314s PrivateWages_6 -1.3974 -84.70 -79.8 314s PrivateWages_8 4.4445 266.66 284.4 314s PrivateWages_9 5.0731 315.90 326.7 314s PrivateWages_10 9.4721 611.61 611.0 314s PrivateWages_11 -6.6655 -424.67 -446.6 314s PrivateWages_12 -0.8571 -46.99 -52.5 314s PrivateWages_13 -4.8476 -227.73 -258.9 314s PrivateWages_14 8.8741 373.85 393.1 314s PrivateWages_15 -0.2815 -14.42 -12.7 314s PrivateWages_16 -0.6957 -38.50 -34.6 314s PrivateWages_17 7.2565 416.48 394.8 314s PrivateWages_18 0.2522 16.94 15.8 314s PrivateWages_19 -17.2396 -1181.13 -1120.6 314s PrivateWages_20 3.9252 262.38 239.0 314s PrivateWages_21 -3.5398 -265.01 -246.0 314s PrivateWages_22 5.2446 455.65 397.0 314s PrivateWages_trend 314s Consumption_2 47.927 314s Consumption_3 9.946 314s Consumption_4 -5.491 314s Consumption_5 18.903 314s Consumption_6 -8.800 314s Consumption_8 -27.010 314s Consumption_9 -18.123 314s Consumption_11 2.574 314s Consumption_12 0.000 314s Consumption_14 1.803 314s Consumption_15 -8.412 314s Consumption_16 -9.167 314s Consumption_17 43.417 314s Consumption_18 -4.263 314s Consumption_19 -44.664 314s Consumption_20 38.478 314s Consumption_21 22.158 314s Consumption_22 -10.312 314s Investment_2 -26.290 314s Investment_3 4.079 314s Investment_4 6.175 314s Investment_5 -14.316 314s Investment_6 1.978 314s Investment_8 6.761 314s Investment_9 3.540 314s Investment_10 6.738 314s Investment_11 -1.250 314s Investment_12 0.000 314s Investment_14 -6.004 314s Investment_15 -0.940 314s Investment_17 -14.825 314s Investment_18 -0.374 314s Investment_19 28.444 314s Investment_20 -11.048 314s Investment_21 -6.471 314s Investment_22 -16.619 314s PrivateWages_2 80.595 314s PrivateWages_3 -27.814 314s PrivateWages_4 -57.514 314s PrivateWages_5 54.699 314s PrivateWages_6 8.384 314s PrivateWages_8 -17.778 314s PrivateWages_9 -15.219 314s PrivateWages_10 -18.944 314s PrivateWages_11 6.666 314s PrivateWages_12 0.000 314s PrivateWages_13 -4.848 314s PrivateWages_14 17.748 314s PrivateWages_15 -0.844 314s PrivateWages_16 -2.783 314s PrivateWages_17 36.283 314s PrivateWages_18 1.513 314s PrivateWages_19 -120.677 314s PrivateWages_20 31.402 314s PrivateWages_21 -31.858 314s PrivateWages_22 52.446 314s [1] TRUE 314s > Bread 314s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 314s [1,] 133.708 -4.1980 0.8576 314s [2,] -4.198 1.2100 -0.6653 314s [3,] 0.858 -0.6653 0.7119 314s [4,] -1.738 -0.1324 -0.0277 314s [5,] 125.235 3.6584 5.4171 314s [6,] -6.184 0.8150 -0.6677 314s [7,] 2.270 -0.5431 0.6187 314s [8,] -0.265 -0.0441 -0.0204 314s [9,] -39.027 0.3871 1.7425 314s [10,] 0.490 -0.0701 0.0456 314s [11,] 0.147 0.0648 -0.0766 314s [12,] 0.260 0.0523 0.0256 314s Consumption_wages Investment_(Intercept) Investment_corpProf 314s [1,] -1.73822 125.23 -6.18369 314s [2,] -0.13241 3.66 0.81500 314s [3,] -0.02768 5.42 -0.66769 314s [4,] 0.10634 -6.40 0.07260 314s [5,] -6.40260 3920.72 -66.16832 314s [6,] 0.07260 -66.17 3.06783 314s [7,] -0.07286 52.35 -2.32206 314s [8,] 0.03170 -18.13 0.25629 314s [9,] 0.06731 57.07 -0.51824 314s [10,] -0.00202 2.27 0.00785 314s [11,] 0.00109 -3.34 0.00101 314s [12,] -0.03773 -1.63 0.03241 314s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 314s [1,] 2.27003 -0.26469 -39.0267 314s [2,] -0.54312 -0.04408 0.3871 314s [3,] 0.61867 -0.02038 1.7425 314s [4,] -0.07286 0.03170 0.0673 314s [5,] 52.35486 -18.13066 57.0659 314s [6,] -2.32206 0.25629 -0.5182 314s [7,] 2.22379 -0.24386 -0.7311 314s [8,] -0.24386 0.08845 -0.1851 314s [9,] -0.73109 -0.18506 71.2482 314s [10,] 0.01103 -0.01288 -0.3220 314s [11,] 0.00202 0.01653 -0.8851 314s [12,] -0.04341 0.00871 0.7698 314s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 314s [1,] 0.49031 0.147339 0.260437 314s [2,] -0.07008 0.064790 0.052347 314s [3,] 0.04558 -0.076595 0.025629 314s [4,] -0.00202 0.001086 -0.037728 314s [5,] 2.27149 -3.339873 -1.627913 314s [6,] 0.00785 0.001013 0.032414 314s [7,] 0.01103 0.002018 -0.043407 314s [8,] -0.01288 0.016530 0.008714 314s [9,] -0.32199 -0.885080 0.769761 314s [10,] 0.04892 -0.044549 -0.013616 314s [11,] -0.04455 0.061046 0.000449 314s [12,] -0.01362 0.000449 0.047057 314s > 314s BEGIN TEST KleinI_noMat.R 314s 314s R version 4.3.2 (2023-10-31) -- "Eye Holes" 314s Copyright (C) 2023 The R Foundation for Statistical Computing 314s Platform: x86_64-pc-linux-gnu (64-bit) 314s 314s R is free software and comes with ABSOLUTELY NO WARRANTY. 314s You are welcome to redistribute it under certain conditions. 314s Type 'license()' or 'licence()' for distribution details. 314s 314s R is a collaborative project with many contributors. 314s Type 'contributors()' for more information and 314s 'citation()' on how to cite R or R packages in publications. 314s 314s Type 'demo()' for some demos, 'help()' for on-line help, or 314s 'help.start()' for an HTML browser interface to help. 314s Type 'q()' to quit R. 314s 314s > library( "systemfit" ) 314s Loading required package: Matrix 315s Loading required package: car 315s Loading required package: carData 315s Loading required package: lmtest 315s Loading required package: zoo 315s 315s Attaching package: ‘zoo’ 315s 315s The following objects are masked from ‘package:base’: 315s 315s as.Date, as.Date.numeric 315s 315s 315s Please cite the 'systemfit' package as: 315s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 315s 315s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 315s https://r-forge.r-project.org/projects/systemfit/ 315s > options( warn = 1 ) 315s > options( digits = 3 ) 315s > 315s > data( "KleinI" ) 315s > eqConsump <- consump ~ corpProf + corpProfLag + wages 315s > eqInvest <- invest ~ corpProf + corpProfLag + capitalLag 315s > eqPrivWage <- privWage ~ gnp + gnpLag + trend 315s > inst <- ~ govExp + taxes + govWage + trend + capitalLag + corpProfLag + gnpLag 315s > system <- list( Consumption = eqConsump, Investment = eqInvest, 315s + PrivateWages = eqPrivWage ) 315s > restrict <- c( "Consumption_corpProf + Investment_capitalLag = 0" ) 315s > restrict2 <- c( restrict, "Consumption_corpProfLag - PrivateWages_trend = 0" ) 315s > 315s > for( dataNo in 1:5 ) { 315s + # set some values of some variables to NA 315s + if( dataNo == 2 ) { 315s + KleinI$gnpLag[ 7 ] <- NA 315s + } else if( dataNo == 3 ) { 315s + KleinI$wages[ 10 ] <- NA 315s + } else if( dataNo == 4 ) { 315s + KleinI$corpProf[ 13 ] <- NA 315s + } else if( dataNo == 5 ) { 315s + KleinI$invest[ 16 ] <- NA 315s + } 315s + 315s + # single-equation OLS 315s + lmConsump <- lm( eqConsump, data = KleinI ) 315s + lmInvest <- lm( eqInvest, data = KleinI ) 315s + lmPrivWage <- lm( eqPrivWage, data = KleinI ) 315s + 315s + for( methodNo in 1:5 ) { 315s + method <- c( "OLS", "2SLS", "SUR", "3SLS", "3SLS" )[ methodNo ] 315s + maxit <- ifelse( methodNo == 5, 500, 1 ) 315s + 315s + cat( "> \n> # ", ifelse( maxit == 1, "", "I" ), method, "\n", sep = "" ) 315s + if( method %in% c( "OLS", "WLS", "SUR" ) ) { 315s + kleinModel <- systemfit( system, method = method, data = KleinI, 315s + methodResidCov = ifelse( method == "OLS", "geomean", "noDfCor" ), 315s + maxit = maxit, useMatrix = FALSE ) 315s + } else { 315s + kleinModel <- systemfit( system, method = method, data = KleinI, 315s + inst = inst, methodResidCov = "noDfCor", maxit = maxit, 315s + useMatrix = FALSE ) 315s + } 315s + cat( "> summary\n" ) 315s + print( summary( kleinModel ) ) 315s + if( method == "OLS" ) { 315s + cat( "compare coef with single-equation OLS\n" ) 315s + print( all.equal( coef( kleinModel ), 315s + c( coef( lmConsump ), coef( lmInvest ), coef( lmPrivWage ) ), 315s + check.attributes = FALSE ) ) 315s + } 315s + cat( "> residuals\n" ) 315s + print( residuals( kleinModel ) ) 315s + cat( "> fitted\n" ) 315s + print( fitted( kleinModel ) ) 315s + cat( "> predict\n" ) 315s + print( predict( kleinModel, se.fit = TRUE, 315s + interval = ifelse( methodNo %in% c( 1, 4 ), "prediction", "confidence" ), 315s + useDfSys = methodNo %in% c( 1, 3, 5 ) ) ) 315s + cat( "> model.frame\n" ) 315s + if( methodNo == 1 ) { 315s + mfOls <- model.frame( kleinModel ) 315s + print( mfOls ) 315s + } else if( methodNo == 2 ) { 315s + mf2sls <- model.frame( kleinModel ) 315s + print( mf2sls ) 315s + } else if( methodNo == 3 ) { 315s + print( all.equal( mfOls, model.frame( kleinModel ) ) ) 315s + } else { 315s + print( all.equal( mf2sls, model.frame( kleinModel ) ) ) 315s + } 315s + cat( "> model.matrix\n" ) 315s + if( methodNo == 1 ) { 315s + mmOls <- model.matrix( kleinModel ) 315s + print( mmOls ) 315s + } else { 315s + print( all.equal( mmOls, model.matrix( kleinModel ) ) ) 315s + } 315s + cat( "> nobs\n" ) 315s + print( nobs( kleinModel ) ) 315s + cat( "> linearHypothesis\n" ) 315s + print( linearHypothesis( kleinModel, restrict ) ) 315s + print( linearHypothesis( kleinModel, restrict, test = "F" ) ) 315s + print( linearHypothesis( kleinModel, restrict, test = "Chisq" ) ) 315s + print( linearHypothesis( kleinModel, restrict2 ) ) 315s + print( linearHypothesis( kleinModel, restrict2, test = "F" ) ) 315s + print( linearHypothesis( kleinModel, restrict2, test = "Chisq" ) ) 315s + cat( "> logLik\n" ) 315s + print( logLik( kleinModel ) ) 315s + print( logLik( kleinModel, residCovDiag = TRUE ) ) 315s + if( method == "OLS" ) { 315s + cat( "compare log likelihood value with single-equation OLS\n" ) 315s + print( all.equal( logLik( kleinModel, residCovDiag = TRUE ), 315s + logLik( lmConsump ) + logLik( lmInvest ) + logLik( lmPrivWage ), 315s + check.attributes = FALSE ) ) 315s + } 315s + } 315s + } 315s > 315s > # OLS 315s > summary 315s 315s systemfit results 315s method: OLS 315s 315s N DF SSR detRCov OLS-R2 McElroy-R2 315s system 63 51 45.2 0.371 0.977 0.991 315s 315s N DF SSR MSE RMSE R2 Adj R2 315s Consumption 21 17 17.9 1.052 1.026 0.981 0.978 315s Investment 21 17 17.3 1.019 1.009 0.931 0.919 315s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 315s 315s The covariance matrix of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.0517 0.0611 -0.470 315s Investment 0.0611 1.0190 0.150 315s PrivateWages -0.4704 0.1497 0.589 315s 315s The correlations of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.0000 0.0591 -0.598 315s Investment 0.0591 1.0000 0.193 315s PrivateWages -0.5979 0.1933 1.000 315s 315s 315s OLS estimates for 'Consumption' (equation 1) 315s Model Formula: consump ~ corpProf + corpProfLag + wages 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 16.2366 1.3027 12.46 5.6e-10 *** 315s corpProf 0.1929 0.0912 2.12 0.049 * 315s corpProfLag 0.0899 0.0906 0.99 0.335 315s wages 0.7962 0.0399 19.93 3.2e-13 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.026 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 315s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 315s 315s 315s OLS estimates for 'Investment' (equation 2) 315s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 10.1258 5.4655 1.85 0.08137 . 315s corpProf 0.4796 0.0971 4.94 0.00012 *** 315s corpProfLag 0.3330 0.1009 3.30 0.00421 ** 315s capitalLag -0.1118 0.0267 -4.18 0.00062 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.009 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 315s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 315s 315s 315s OLS estimates for 'PrivateWages' (equation 3) 315s Model Formula: privWage ~ gnp + gnpLag + trend 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 1.4970 1.2700 1.18 0.25474 315s gnp 0.4395 0.0324 13.56 1.5e-10 *** 315s gnpLag 0.1461 0.0374 3.90 0.00114 ** 315s trend 0.1302 0.0319 4.08 0.00078 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 0.767 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 315s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 315s 315s compare coef with single-equation OLS 315s [1] TRUE 315s > residuals 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 -0.32389 -0.0668 -1.2942 315s 3 -1.25001 -0.0476 0.2957 315s 4 -1.56574 1.2467 1.1877 315s 5 -0.49350 -1.3512 -0.1358 315s 6 0.00761 0.4154 -0.4654 315s 7 0.86910 1.4923 -0.4838 315s 8 1.33848 0.7889 -0.7281 315s 9 1.05498 -0.6317 0.3392 315s 10 -0.58856 1.0830 1.1957 315s 11 0.28231 0.2791 -0.1508 315s 12 -0.22965 0.0369 0.5942 315s 13 -0.32213 0.3659 0.1027 315s 14 0.32228 0.2237 0.4503 315s 15 -0.05801 -0.1728 0.2816 315s 16 -0.03466 0.0101 0.0138 315s 17 1.61650 0.9719 -0.8508 315s 18 -0.43597 0.0516 0.9956 315s 19 0.21005 -2.5656 -0.4688 315s 20 0.98920 -0.6866 -0.3795 315s 21 0.78508 -0.7807 -1.0909 315s 22 -2.17345 -0.6623 0.5917 315s > fitted 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 42.2 -0.133 26.8 315s 3 46.3 1.948 29.0 315s 4 50.8 3.953 32.9 315s 5 51.1 4.351 34.0 315s 6 52.6 4.685 35.9 315s 7 54.2 4.108 37.9 315s 8 54.9 3.411 38.6 315s 9 56.2 3.632 38.9 315s 10 58.4 4.017 40.1 315s 11 54.7 0.721 38.1 315s 12 51.1 -3.437 33.9 315s 13 45.9 -6.566 28.9 315s 14 46.2 -5.324 28.0 315s 15 48.8 -2.827 30.3 315s 16 51.3 -1.310 33.2 315s 17 56.1 1.128 37.7 315s 18 59.1 1.948 40.0 315s 19 57.3 0.666 38.7 315s 20 60.6 1.987 42.0 315s 21 64.2 4.081 46.1 315s 22 71.9 5.562 52.7 315s > predict 315s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 315s 1 NA NA NA NA 315s 2 42.2 0.462 40.0 44.5 315s 3 46.3 0.518 43.9 48.6 315s 4 50.8 0.341 48.6 52.9 315s 5 51.1 0.396 48.9 53.3 315s 6 52.6 0.397 50.4 54.8 315s 7 54.2 0.359 52.0 56.4 315s 8 54.9 0.327 52.7 57.0 315s 9 56.2 0.350 54.1 58.4 315s 10 58.4 0.370 56.2 60.6 315s 11 54.7 0.606 52.3 57.1 315s 12 51.1 0.484 48.9 53.4 315s 13 45.9 0.629 43.5 48.3 315s 14 46.2 0.602 43.8 48.6 315s 15 48.8 0.374 46.6 50.9 315s 16 51.3 0.333 49.2 53.5 315s 17 56.1 0.366 53.9 58.3 315s 18 59.1 0.321 57.0 61.3 315s 19 57.3 0.371 55.1 59.5 315s 20 60.6 0.434 58.4 62.8 315s 21 64.2 0.425 62.0 66.4 315s 22 71.9 0.666 69.4 74.3 315s Investment.pred Investment.se.fit Investment.lwr Investment.upr 315s 1 NA NA NA NA 315s 2 -0.133 0.607 -2.498 2.231 315s 3 1.948 0.499 -0.313 4.208 315s 4 3.953 0.449 1.735 6.171 315s 5 4.351 0.371 2.192 6.510 315s 6 4.685 0.349 2.540 6.829 315s 7 4.108 0.329 1.976 6.239 315s 8 3.411 0.292 1.301 5.521 315s 9 3.632 0.389 1.460 5.804 315s 10 4.017 0.447 1.801 6.233 315s 11 0.721 0.601 -1.638 3.080 315s 12 -3.437 0.507 -5.704 -1.169 315s 13 -6.566 0.616 -8.940 -4.192 315s 14 -5.324 0.694 -7.783 -2.865 315s 15 -2.827 0.373 -4.988 -0.667 315s 16 -1.310 0.320 -3.436 0.816 315s 17 1.128 0.347 -1.015 3.271 315s 18 1.948 0.243 -0.136 4.033 315s 19 0.666 0.312 -1.456 2.787 315s 20 1.987 0.366 -0.169 4.143 315s 21 4.081 0.332 1.948 6.214 315s 22 5.562 0.461 3.334 7.790 315s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 315s 1 NA NA NA NA 315s 2 26.8 0.354 25.1 28.5 315s 3 29.0 0.355 27.3 30.7 315s 4 32.9 0.354 31.2 34.6 315s 5 34.0 0.269 32.4 35.7 315s 6 35.9 0.266 34.2 37.5 315s 7 37.9 0.266 36.3 39.5 315s 8 38.6 0.273 37.0 40.3 315s 9 38.9 0.261 37.2 40.5 315s 10 40.1 0.247 38.5 41.7 315s 11 38.1 0.354 36.4 39.7 315s 12 33.9 0.363 32.2 35.6 315s 13 28.9 0.429 27.1 30.7 315s 14 28.0 0.376 26.3 29.8 315s 15 30.3 0.371 28.6 32.0 315s 16 33.2 0.310 31.5 34.8 315s 17 37.7 0.305 36.0 39.3 315s 18 40.0 0.238 38.4 41.6 315s 19 38.7 0.357 37.0 40.4 315s 20 42.0 0.321 40.3 43.6 315s 21 46.1 0.335 44.4 47.8 315s 22 52.7 0.502 50.9 54.5 315s > model.frame 315s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 315s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 315s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 315s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 315s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 315s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 315s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 315s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 315s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 315s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 315s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 315s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 315s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 315s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 315s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 315s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 315s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 315s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 315s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 315s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 315s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 315s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 315s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 315s trend 315s 1 -11 315s 2 -10 315s 3 -9 315s 4 -8 315s 5 -7 315s 6 -6 315s 7 -5 315s 8 -4 315s 9 -3 315s 10 -2 315s 11 -1 315s 12 0 315s 13 1 315s 14 2 315s 15 3 315s 16 4 315s 17 5 315s 18 6 315s 19 7 315s 20 8 315s 21 9 315s 22 10 315s > model.matrix 315s Consumption_(Intercept) Consumption_corpProf 315s Consumption_2 1 12.4 315s Consumption_3 1 16.9 315s Consumption_4 1 18.4 315s Consumption_5 1 19.4 315s Consumption_6 1 20.1 315s Consumption_7 1 19.6 315s Consumption_8 1 19.8 315s Consumption_9 1 21.1 315s Consumption_10 1 21.7 315s Consumption_11 1 15.6 315s Consumption_12 1 11.4 315s Consumption_13 1 7.0 315s Consumption_14 1 11.2 315s Consumption_15 1 12.3 315s Consumption_16 1 14.0 315s Consumption_17 1 17.6 315s Consumption_18 1 17.3 315s Consumption_19 1 15.3 315s Consumption_20 1 19.0 315s Consumption_21 1 21.1 315s Consumption_22 1 23.5 315s Investment_2 0 0.0 315s Investment_3 0 0.0 315s Investment_4 0 0.0 315s Investment_5 0 0.0 315s Investment_6 0 0.0 315s Investment_7 0 0.0 315s Investment_8 0 0.0 315s Investment_9 0 0.0 315s Investment_10 0 0.0 315s Investment_11 0 0.0 315s Investment_12 0 0.0 315s Investment_13 0 0.0 315s Investment_14 0 0.0 315s Investment_15 0 0.0 315s Investment_16 0 0.0 315s Investment_17 0 0.0 315s Investment_18 0 0.0 315s Investment_19 0 0.0 315s Investment_20 0 0.0 315s Investment_21 0 0.0 315s Investment_22 0 0.0 315s PrivateWages_2 0 0.0 315s PrivateWages_3 0 0.0 315s PrivateWages_4 0 0.0 315s PrivateWages_5 0 0.0 315s PrivateWages_6 0 0.0 315s PrivateWages_7 0 0.0 315s PrivateWages_8 0 0.0 315s PrivateWages_9 0 0.0 315s PrivateWages_10 0 0.0 315s PrivateWages_11 0 0.0 315s PrivateWages_12 0 0.0 315s PrivateWages_13 0 0.0 315s PrivateWages_14 0 0.0 315s PrivateWages_15 0 0.0 315s PrivateWages_16 0 0.0 315s PrivateWages_17 0 0.0 315s PrivateWages_18 0 0.0 315s PrivateWages_19 0 0.0 315s PrivateWages_20 0 0.0 315s PrivateWages_21 0 0.0 315s PrivateWages_22 0 0.0 315s Consumption_corpProfLag Consumption_wages 315s Consumption_2 12.7 28.2 315s Consumption_3 12.4 32.2 315s Consumption_4 16.9 37.0 315s Consumption_5 18.4 37.0 315s Consumption_6 19.4 38.6 315s Consumption_7 20.1 40.7 315s Consumption_8 19.6 41.5 315s Consumption_9 19.8 42.9 315s Consumption_10 21.1 45.3 315s Consumption_11 21.7 42.1 315s Consumption_12 15.6 39.3 315s Consumption_13 11.4 34.3 315s Consumption_14 7.0 34.1 315s Consumption_15 11.2 36.6 315s Consumption_16 12.3 39.3 315s Consumption_17 14.0 44.2 315s Consumption_18 17.6 47.7 315s Consumption_19 17.3 45.9 315s Consumption_20 15.3 49.4 315s Consumption_21 19.0 53.0 315s Consumption_22 21.1 61.8 315s Investment_2 0.0 0.0 315s Investment_3 0.0 0.0 315s Investment_4 0.0 0.0 315s Investment_5 0.0 0.0 315s Investment_6 0.0 0.0 315s Investment_7 0.0 0.0 315s Investment_8 0.0 0.0 315s Investment_9 0.0 0.0 315s Investment_10 0.0 0.0 315s Investment_11 0.0 0.0 315s Investment_12 0.0 0.0 315s Investment_13 0.0 0.0 315s Investment_14 0.0 0.0 315s Investment_15 0.0 0.0 315s Investment_16 0.0 0.0 315s Investment_17 0.0 0.0 315s Investment_18 0.0 0.0 315s Investment_19 0.0 0.0 315s Investment_20 0.0 0.0 315s Investment_21 0.0 0.0 315s Investment_22 0.0 0.0 315s PrivateWages_2 0.0 0.0 315s PrivateWages_3 0.0 0.0 315s PrivateWages_4 0.0 0.0 315s PrivateWages_5 0.0 0.0 315s PrivateWages_6 0.0 0.0 315s PrivateWages_7 0.0 0.0 315s PrivateWages_8 0.0 0.0 315s PrivateWages_9 0.0 0.0 315s PrivateWages_10 0.0 0.0 315s PrivateWages_11 0.0 0.0 315s PrivateWages_12 0.0 0.0 315s PrivateWages_13 0.0 0.0 315s PrivateWages_14 0.0 0.0 315s PrivateWages_15 0.0 0.0 315s PrivateWages_16 0.0 0.0 315s PrivateWages_17 0.0 0.0 315s PrivateWages_18 0.0 0.0 315s PrivateWages_19 0.0 0.0 315s PrivateWages_20 0.0 0.0 315s PrivateWages_21 0.0 0.0 315s PrivateWages_22 0.0 0.0 315s Investment_(Intercept) Investment_corpProf 315s Consumption_2 0 0.0 315s Consumption_3 0 0.0 315s Consumption_4 0 0.0 315s Consumption_5 0 0.0 315s Consumption_6 0 0.0 315s Consumption_7 0 0.0 315s Consumption_8 0 0.0 315s Consumption_9 0 0.0 315s Consumption_10 0 0.0 315s Consumption_11 0 0.0 315s Consumption_12 0 0.0 315s Consumption_13 0 0.0 315s Consumption_14 0 0.0 315s Consumption_15 0 0.0 315s Consumption_16 0 0.0 315s Consumption_17 0 0.0 315s Consumption_18 0 0.0 315s Consumption_19 0 0.0 315s Consumption_20 0 0.0 315s Consumption_21 0 0.0 315s Consumption_22 0 0.0 315s Investment_2 1 12.4 315s Investment_3 1 16.9 315s Investment_4 1 18.4 315s Investment_5 1 19.4 315s Investment_6 1 20.1 315s Investment_7 1 19.6 315s Investment_8 1 19.8 315s Investment_9 1 21.1 315s Investment_10 1 21.7 315s Investment_11 1 15.6 315s Investment_12 1 11.4 315s Investment_13 1 7.0 315s Investment_14 1 11.2 315s Investment_15 1 12.3 315s Investment_16 1 14.0 315s Investment_17 1 17.6 315s Investment_18 1 17.3 315s Investment_19 1 15.3 315s Investment_20 1 19.0 315s Investment_21 1 21.1 315s Investment_22 1 23.5 315s PrivateWages_2 0 0.0 315s PrivateWages_3 0 0.0 315s PrivateWages_4 0 0.0 315s PrivateWages_5 0 0.0 315s PrivateWages_6 0 0.0 315s PrivateWages_7 0 0.0 315s PrivateWages_8 0 0.0 315s PrivateWages_9 0 0.0 315s PrivateWages_10 0 0.0 315s PrivateWages_11 0 0.0 315s PrivateWages_12 0 0.0 315s PrivateWages_13 0 0.0 315s PrivateWages_14 0 0.0 315s PrivateWages_15 0 0.0 315s PrivateWages_16 0 0.0 315s PrivateWages_17 0 0.0 315s PrivateWages_18 0 0.0 315s PrivateWages_19 0 0.0 315s PrivateWages_20 0 0.0 315s PrivateWages_21 0 0.0 315s PrivateWages_22 0 0.0 315s Investment_corpProfLag Investment_capitalLag 315s Consumption_2 0.0 0 315s Consumption_3 0.0 0 315s Consumption_4 0.0 0 315s Consumption_5 0.0 0 315s Consumption_6 0.0 0 315s Consumption_7 0.0 0 315s Consumption_8 0.0 0 315s Consumption_9 0.0 0 315s Consumption_10 0.0 0 315s Consumption_11 0.0 0 315s Consumption_12 0.0 0 315s Consumption_13 0.0 0 315s Consumption_14 0.0 0 315s Consumption_15 0.0 0 315s Consumption_16 0.0 0 315s Consumption_17 0.0 0 315s Consumption_18 0.0 0 315s Consumption_19 0.0 0 315s Consumption_20 0.0 0 315s Consumption_21 0.0 0 315s Consumption_22 0.0 0 315s Investment_2 12.7 183 315s Investment_3 12.4 183 315s Investment_4 16.9 184 315s Investment_5 18.4 190 315s Investment_6 19.4 193 315s Investment_7 20.1 198 315s Investment_8 19.6 203 315s Investment_9 19.8 208 315s Investment_10 21.1 211 315s Investment_11 21.7 216 315s Investment_12 15.6 217 315s Investment_13 11.4 213 315s Investment_14 7.0 207 315s Investment_15 11.2 202 315s Investment_16 12.3 199 315s Investment_17 14.0 198 315s Investment_18 17.6 200 315s Investment_19 17.3 202 315s Investment_20 15.3 200 315s Investment_21 19.0 201 315s Investment_22 21.1 204 315s PrivateWages_2 0.0 0 315s PrivateWages_3 0.0 0 315s PrivateWages_4 0.0 0 315s PrivateWages_5 0.0 0 315s PrivateWages_6 0.0 0 315s PrivateWages_7 0.0 0 315s PrivateWages_8 0.0 0 315s PrivateWages_9 0.0 0 315s PrivateWages_10 0.0 0 315s PrivateWages_11 0.0 0 315s PrivateWages_12 0.0 0 315s PrivateWages_13 0.0 0 315s PrivateWages_14 0.0 0 315s PrivateWages_15 0.0 0 315s PrivateWages_16 0.0 0 315s PrivateWages_17 0.0 0 315s PrivateWages_18 0.0 0 315s PrivateWages_19 0.0 0 315s PrivateWages_20 0.0 0 315s PrivateWages_21 0.0 0 315s PrivateWages_22 0.0 0 315s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 315s Consumption_2 0 0.0 0.0 315s Consumption_3 0 0.0 0.0 315s Consumption_4 0 0.0 0.0 315s Consumption_5 0 0.0 0.0 315s Consumption_6 0 0.0 0.0 315s Consumption_7 0 0.0 0.0 315s Consumption_8 0 0.0 0.0 315s Consumption_9 0 0.0 0.0 315s Consumption_10 0 0.0 0.0 315s Consumption_11 0 0.0 0.0 315s Consumption_12 0 0.0 0.0 315s Consumption_13 0 0.0 0.0 315s Consumption_14 0 0.0 0.0 315s Consumption_15 0 0.0 0.0 315s Consumption_16 0 0.0 0.0 315s Consumption_17 0 0.0 0.0 315s Consumption_18 0 0.0 0.0 315s Consumption_19 0 0.0 0.0 315s Consumption_20 0 0.0 0.0 315s Consumption_21 0 0.0 0.0 315s Consumption_22 0 0.0 0.0 315s Investment_2 0 0.0 0.0 315s Investment_3 0 0.0 0.0 315s Investment_4 0 0.0 0.0 315s Investment_5 0 0.0 0.0 315s Investment_6 0 0.0 0.0 315s Investment_7 0 0.0 0.0 315s Investment_8 0 0.0 0.0 315s Investment_9 0 0.0 0.0 315s Investment_10 0 0.0 0.0 315s Investment_11 0 0.0 0.0 315s Investment_12 0 0.0 0.0 315s Investment_13 0 0.0 0.0 315s Investment_14 0 0.0 0.0 315s Investment_15 0 0.0 0.0 315s Investment_16 0 0.0 0.0 315s Investment_17 0 0.0 0.0 315s Investment_18 0 0.0 0.0 315s Investment_19 0 0.0 0.0 315s Investment_20 0 0.0 0.0 315s Investment_21 0 0.0 0.0 315s Investment_22 0 0.0 0.0 315s PrivateWages_2 1 45.6 44.9 315s PrivateWages_3 1 50.1 45.6 315s PrivateWages_4 1 57.2 50.1 315s PrivateWages_5 1 57.1 57.2 315s PrivateWages_6 1 61.0 57.1 315s PrivateWages_7 1 64.0 61.0 315s PrivateWages_8 1 64.4 64.0 315s PrivateWages_9 1 64.5 64.4 315s PrivateWages_10 1 67.0 64.5 315s PrivateWages_11 1 61.2 67.0 315s PrivateWages_12 1 53.4 61.2 315s PrivateWages_13 1 44.3 53.4 315s PrivateWages_14 1 45.1 44.3 315s PrivateWages_15 1 49.7 45.1 315s PrivateWages_16 1 54.4 49.7 315s PrivateWages_17 1 62.7 54.4 315s PrivateWages_18 1 65.0 62.7 315s PrivateWages_19 1 60.9 65.0 315s PrivateWages_20 1 69.5 60.9 315s PrivateWages_21 1 75.7 69.5 315s PrivateWages_22 1 88.4 75.7 315s PrivateWages_trend 315s Consumption_2 0 315s Consumption_3 0 315s Consumption_4 0 315s Consumption_5 0 315s Consumption_6 0 315s Consumption_7 0 315s Consumption_8 0 315s Consumption_9 0 315s Consumption_10 0 315s Consumption_11 0 315s Consumption_12 0 315s Consumption_13 0 315s Consumption_14 0 315s Consumption_15 0 315s Consumption_16 0 315s Consumption_17 0 315s Consumption_18 0 315s Consumption_19 0 315s Consumption_20 0 315s Consumption_21 0 315s Consumption_22 0 315s Investment_2 0 315s Investment_3 0 315s Investment_4 0 315s Investment_5 0 315s Investment_6 0 315s Investment_7 0 315s Investment_8 0 315s Investment_9 0 315s Investment_10 0 315s Investment_11 0 315s Investment_12 0 315s Investment_13 0 315s Investment_14 0 315s Investment_15 0 315s Investment_16 0 315s Investment_17 0 315s Investment_18 0 315s Investment_19 0 315s Investment_20 0 315s Investment_21 0 315s Investment_22 0 315s PrivateWages_2 -10 315s PrivateWages_3 -9 315s PrivateWages_4 -8 315s PrivateWages_5 -7 315s PrivateWages_6 -6 315s PrivateWages_7 -5 315s PrivateWages_8 -4 315s PrivateWages_9 -3 315s PrivateWages_10 -2 315s PrivateWages_11 -1 315s PrivateWages_12 0 315s PrivateWages_13 1 315s PrivateWages_14 2 315s PrivateWages_15 3 315s PrivateWages_16 4 315s PrivateWages_17 5 315s PrivateWages_18 6 315s PrivateWages_19 7 315s PrivateWages_20 8 315s PrivateWages_21 9 315s PrivateWages_22 10 315s > nobs 315s [1] 63 315s > linearHypothesis 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 0.82 0.37 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 0.73 0.4 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 52 315s 2 51 1 0.73 0.39 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.42 0.66 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.37 0.69 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 53 315s 2 51 2 0.74 0.69 315s > logLik 315s 'log Lik.' -72.3 (df=13) 315s 'log Lik.' -77.9 (df=13) 315s compare log likelihood value with single-equation OLS 315s [1] TRUE 315s > 315s > # 2SLS 315s > summary 315s 315s systemfit results 315s method: 2SLS 315s 315s N DF SSR detRCov OLS-R2 McElroy-R2 315s system 63 51 61 0.288 0.969 0.992 315s 315s N DF SSR MSE RMSE R2 Adj R2 315s Consumption 21 17 21.9 1.290 1.136 0.977 0.973 315s Investment 21 17 29.0 1.709 1.307 0.885 0.865 315s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 315s 315s The covariance matrix of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.044 0.438 -0.385 315s Investment 0.438 1.383 0.193 315s PrivateWages -0.385 0.193 0.476 315s 315s The correlations of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.000 0.364 -0.546 315s Investment 0.364 1.000 0.237 315s PrivateWages -0.546 0.237 1.000 315s 315s 315s 2SLS estimates for 'Consumption' (equation 1) 315s Model Formula: consump ~ corpProf + corpProfLag + wages 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 16.5548 1.3208 12.53 5.2e-10 *** 315s corpProf 0.0173 0.1180 0.15 0.89 315s corpProfLag 0.2162 0.1073 2.02 0.06 . 315s wages 0.8102 0.0402 20.13 2.7e-13 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.136 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 21.925 MSE: 1.29 Root MSE: 1.136 315s Multiple R-Squared: 0.977 Adjusted R-Squared: 0.973 315s 315s 315s 2SLS estimates for 'Investment' (equation 2) 315s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 20.2782 7.5427 2.69 0.01555 * 315s corpProf 0.1502 0.1732 0.87 0.39792 315s corpProfLag 0.6159 0.1628 3.78 0.00148 ** 315s capitalLag -0.1578 0.0361 -4.37 0.00042 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.307 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 29.047 MSE: 1.709 Root MSE: 1.307 315s Multiple R-Squared: 0.885 Adjusted R-Squared: 0.865 315s 315s 315s 2SLS estimates for 'PrivateWages' (equation 3) 315s Model Formula: privWage ~ gnp + gnpLag + trend 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 1.5003 1.1478 1.31 0.20857 315s gnp 0.4389 0.0356 12.32 6.8e-10 *** 315s gnpLag 0.1467 0.0388 3.78 0.00150 ** 315s trend 0.1304 0.0291 4.47 0.00033 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 0.767 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 315s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 315s 315s > residuals 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 -0.46263 -1.320 -1.2940 315s 3 -0.61635 0.257 0.2981 315s 4 -1.30423 0.860 1.1918 315s 5 -0.24588 -1.594 -0.1361 315s 6 0.22948 0.259 -0.4634 315s 7 0.88538 1.207 -0.4824 315s 8 1.44189 0.969 -0.7284 315s 9 1.34190 0.113 0.3387 315s 10 -0.39403 1.796 1.1965 315s 11 -0.62564 -0.953 -0.1552 315s 12 -1.06543 -0.807 0.5882 315s 13 -1.33021 -0.895 0.0955 315s 14 0.61059 1.306 0.4487 315s 15 -0.14208 -0.151 0.2822 315s 16 0.00315 0.142 0.0145 315s 17 2.00337 1.749 -0.8478 315s 18 -0.60552 -0.192 0.9950 315s 19 -0.24771 -3.291 -0.4734 315s 20 1.38510 0.285 -0.3766 315s 21 1.03204 -0.104 -1.0893 315s 22 -1.89319 0.363 0.5974 315s > fitted 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 42.4 1.120 26.8 315s 3 45.6 1.643 29.0 315s 4 50.5 4.340 32.9 315s 5 50.8 4.594 34.0 315s 6 52.4 4.841 35.9 315s 7 54.2 4.393 37.9 315s 8 54.8 3.231 38.6 315s 9 56.0 2.887 38.9 315s 10 58.2 3.304 40.1 315s 11 55.6 1.953 38.1 315s 12 52.0 -2.593 33.9 315s 13 46.9 -5.305 28.9 315s 14 45.9 -6.406 28.1 315s 15 48.8 -2.849 30.3 315s 16 51.3 -1.442 33.2 315s 17 55.7 0.351 37.6 315s 18 59.3 2.192 40.0 315s 19 57.7 1.391 38.7 315s 20 60.2 1.015 42.0 315s 21 64.0 3.404 46.1 315s 22 71.6 4.537 52.7 315s > predict 315s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 315s 1 NA NA NA NA 315s 2 42.4 0.471 41.4 43.4 315s 3 45.6 0.577 44.4 46.8 315s 4 50.5 0.354 49.8 51.3 315s 5 50.8 0.405 50.0 51.7 315s 6 52.4 0.404 51.5 53.2 315s 7 54.2 0.359 53.5 55.0 315s 8 54.8 0.328 54.1 55.4 315s 9 56.0 0.368 55.2 56.7 315s 10 58.2 0.377 57.4 59.0 315s 11 55.6 0.728 54.1 57.2 315s 12 52.0 0.604 50.7 53.2 315s 13 46.9 0.765 45.3 48.5 315s 14 45.9 0.615 44.6 47.2 315s 15 48.8 0.374 48.1 49.6 315s 16 51.3 0.333 50.6 52.0 315s 17 55.7 0.409 54.8 56.6 315s 18 59.3 0.326 58.6 60.0 315s 19 57.7 0.414 56.9 58.6 315s 20 60.2 0.478 59.2 61.2 315s 21 64.0 0.446 63.0 64.9 315s 22 71.6 0.689 70.1 73.0 315s Investment.pred Investment.se.fit Investment.lwr Investment.upr 315s 1 NA NA NA NA 315s 2 1.120 0.865 -0.706 2.946 315s 3 1.643 0.594 0.390 2.895 315s 4 4.340 0.545 3.190 5.490 315s 5 4.594 0.443 3.660 5.527 315s 6 4.841 0.411 3.973 5.709 315s 7 4.393 0.399 3.550 5.235 315s 8 3.231 0.348 2.497 3.965 315s 9 2.887 0.542 1.744 4.030 315s 10 3.304 0.593 2.054 4.555 315s 11 1.953 0.855 0.148 3.757 315s 12 -2.593 0.679 -4.026 -1.160 315s 13 -5.305 0.876 -7.152 -3.457 315s 14 -6.406 0.916 -8.338 -4.473 315s 15 -2.849 0.435 -3.765 -1.932 315s 16 -1.442 0.376 -2.236 -0.649 315s 17 0.351 0.510 -0.724 1.426 315s 18 2.192 0.299 1.560 2.823 315s 19 1.391 0.464 0.411 2.371 315s 20 1.015 0.576 -0.201 2.230 315s 21 3.404 0.471 2.410 4.398 315s 22 4.537 0.675 3.114 5.961 315s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 315s 1 NA NA NA NA 315s 2 26.8 0.318 26.1 27.5 315s 3 29.0 0.330 28.3 29.7 315s 4 32.9 0.346 32.2 33.6 315s 5 34.0 0.242 33.5 34.5 315s 6 35.9 0.248 35.3 36.4 315s 7 37.9 0.244 37.4 38.4 315s 8 38.6 0.246 38.1 39.1 315s 9 38.9 0.235 38.4 39.4 315s 10 40.1 0.224 39.6 40.6 315s 11 38.1 0.350 37.3 38.8 315s 12 33.9 0.382 33.1 34.7 315s 13 28.9 0.454 27.9 29.9 315s 14 28.1 0.342 27.3 28.8 315s 15 30.3 0.335 29.6 31.0 315s 16 33.2 0.280 32.6 33.8 315s 17 37.6 0.291 37.0 38.3 315s 18 40.0 0.215 39.6 40.5 315s 19 38.7 0.356 37.9 39.4 315s 20 42.0 0.304 41.3 42.6 315s 21 46.1 0.306 45.4 46.7 315s 22 52.7 0.489 51.7 53.7 315s > model.frame 315s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 315s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 315s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 315s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 315s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 315s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 315s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 315s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 315s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 315s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 315s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 315s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 315s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 315s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 315s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 315s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 315s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 315s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 315s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 315s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 315s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 315s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 315s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 315s trend 315s 1 -11 315s 2 -10 315s 3 -9 315s 4 -8 315s 5 -7 315s 6 -6 315s 7 -5 315s 8 -4 315s 9 -3 315s 10 -2 315s 11 -1 315s 12 0 315s 13 1 315s 14 2 315s 15 3 315s 16 4 315s 17 5 315s 18 6 315s 19 7 315s 20 8 315s 21 9 315s 22 10 315s > model.matrix 315s [1] TRUE 315s > nobs 315s [1] 63 315s > linearHypothesis 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 1.08 0.3 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 1.29 0.26 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 52 315s 2 51 1 1.29 0.26 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.54 0.58 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.65 0.53 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 53 315s 2 51 2 1.3 0.52 315s > logLik 315s 'log Lik.' -76.3 (df=13) 315s 'log Lik.' -85.5 (df=13) 315s > 315s > # SUR 315s > summary 315s 315s systemfit results 315s method: SUR 315s 315s N DF SSR detRCov OLS-R2 McElroy-R2 315s system 63 51 46.5 0.158 0.977 0.993 315s 315s N DF SSR MSE RMSE R2 Adj R2 315s Consumption 21 17 18.1 1.065 1.032 0.981 0.977 315s Investment 21 17 17.6 1.036 1.018 0.930 0.918 315s PrivateWages 21 17 10.8 0.633 0.796 0.986 0.984 315s 315s The covariance matrix of the residuals used for estimation 315s Consumption Investment PrivateWages 315s Consumption 0.8514 0.0495 -0.381 315s Investment 0.0495 0.8249 0.121 315s PrivateWages -0.3808 0.1212 0.476 315s 315s The covariance matrix of the residuals 315s Consumption Investment PrivateWages 315s Consumption 0.8618 0.0766 -0.437 315s Investment 0.0766 0.8384 0.203 315s PrivateWages -0.4368 0.2027 0.513 315s 315s The correlations of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.0000 0.0901 -0.657 315s Investment 0.0901 1.0000 0.309 315s PrivateWages -0.6572 0.3092 1.000 315s 315s 315s SUR estimates for 'Consumption' (equation 1) 315s Model Formula: consump ~ corpProf + corpProfLag + wages 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 15.9805 1.1687 13.67 1.3e-10 *** 315s corpProf 0.2302 0.0767 3.00 0.008 ** 315s corpProfLag 0.0673 0.0769 0.87 0.394 315s wages 0.7962 0.0353 22.58 4.1e-14 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.032 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 18.098 MSE: 1.065 Root MSE: 1.032 315s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 315s 315s 315s SUR estimates for 'Investment' (equation 2) 315s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 12.9293 4.8014 2.69 0.01540 * 315s corpProf 0.4429 0.0861 5.15 8.1e-05 *** 315s corpProfLag 0.3655 0.0894 4.09 0.00077 *** 315s capitalLag -0.1253 0.0235 -5.34 5.4e-05 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.018 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 17.606 MSE: 1.036 Root MSE: 1.018 315s Multiple R-Squared: 0.93 Adjusted R-Squared: 0.918 315s 315s 315s SUR estimates for 'PrivateWages' (equation 3) 315s Model Formula: privWage ~ gnp + gnpLag + trend 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 1.6347 1.1173 1.46 0.16 315s gnp 0.4098 0.0273 15.04 3.0e-11 *** 315s gnpLag 0.1744 0.0312 5.59 3.2e-05 *** 315s trend 0.1558 0.0276 5.65 2.9e-05 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 0.796 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 10.763 MSE: 0.633 Root MSE: 0.796 315s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 315s 315s > residuals 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 -0.24064 -0.3522 -1.0960 315s 3 -1.34080 -0.1605 0.5818 315s 4 -1.61038 1.0687 1.5313 315s 5 -0.54147 -1.4707 -0.0220 315s 6 -0.04372 0.3299 -0.2587 315s 7 0.85234 1.4346 -0.3243 315s 8 1.30302 0.8306 -0.6674 315s 9 0.97574 -0.4918 0.3660 315s 10 -0.66060 1.2434 1.2682 315s 11 0.45069 0.2647 -0.3467 315s 12 -0.04295 0.0795 0.3057 315s 13 -0.06686 0.3369 -0.2602 315s 14 0.32177 0.4080 0.3434 315s 15 -0.00441 -0.1533 0.2628 315s 16 -0.01931 0.0158 -0.0216 315s 17 1.53656 1.0372 -0.7988 315s 18 -0.42317 0.0176 0.8550 315s 19 0.29041 -2.6364 -0.8217 315s 20 0.88685 -0.5822 -0.3869 315s 21 0.68839 -0.7015 -1.1838 315s 22 -2.31147 -0.5183 0.6742 315s > fitted 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 42.1 0.152 26.6 315s 3 46.3 2.060 28.7 315s 4 50.8 4.131 32.6 315s 5 51.1 4.471 33.9 315s 6 52.6 4.770 35.7 315s 7 54.2 4.165 37.7 315s 8 54.9 3.369 38.6 315s 9 56.3 3.492 38.8 315s 10 58.5 3.857 40.0 315s 11 54.5 0.735 38.2 315s 12 50.9 -3.479 34.2 315s 13 45.7 -6.537 29.3 315s 14 46.2 -5.508 28.2 315s 15 48.7 -2.847 30.3 315s 16 51.3 -1.316 33.2 315s 17 56.2 1.063 37.6 315s 18 59.1 1.982 40.1 315s 19 57.2 0.736 39.0 315s 20 60.7 1.882 42.0 315s 21 64.3 4.002 46.2 315s 22 72.0 5.418 52.6 315s > predict 315s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 315s 1 NA NA NA NA 315s 2 42.1 0.415 41.3 43.0 315s 3 46.3 0.449 45.4 47.2 315s 4 50.8 0.300 50.2 51.4 315s 5 51.1 0.348 50.4 51.8 315s 6 52.6 0.350 51.9 53.3 315s 7 54.2 0.317 53.6 54.9 315s 8 54.9 0.289 54.3 55.5 315s 9 56.3 0.309 55.7 56.9 315s 10 58.5 0.328 57.8 59.1 315s 11 54.5 0.516 53.5 55.6 315s 12 50.9 0.414 50.1 51.8 315s 13 45.7 0.544 44.6 46.8 315s 14 46.2 0.527 45.1 47.2 315s 15 48.7 0.332 48.0 49.4 315s 16 51.3 0.295 50.7 51.9 315s 17 56.2 0.319 55.5 56.8 315s 18 59.1 0.286 58.5 59.7 315s 19 57.2 0.323 56.6 57.9 315s 20 60.7 0.381 59.9 61.5 315s 21 64.3 0.381 63.5 65.1 315s 22 72.0 0.597 70.8 73.2 315s Investment.pred Investment.se.fit Investment.lwr Investment.upr 315s 1 NA NA NA NA 315s 2 0.152 0.536 -0.924 1.229 315s 3 2.060 0.446 1.166 2.955 315s 4 4.131 0.397 3.334 4.929 315s 5 4.471 0.329 3.809 5.132 315s 6 4.770 0.311 4.145 5.395 315s 7 4.165 0.294 3.575 4.756 315s 8 3.369 0.263 2.842 3.897 315s 9 3.492 0.347 2.796 4.188 315s 10 3.857 0.398 3.058 4.656 315s 11 0.735 0.539 -0.346 1.816 315s 12 -3.479 0.454 -4.390 -2.569 315s 13 -6.537 0.552 -7.646 -5.428 315s 14 -5.508 0.617 -6.747 -4.269 315s 15 -2.847 0.335 -3.519 -2.175 315s 16 -1.316 0.287 -1.892 -0.739 315s 17 1.063 0.311 0.439 1.686 315s 18 1.982 0.218 1.545 2.420 315s 19 0.736 0.279 0.176 1.296 315s 20 1.882 0.327 1.227 2.538 315s 21 4.002 0.297 3.405 4.598 315s 22 5.418 0.412 4.591 6.245 315s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 315s 1 NA NA NA NA 315s 2 26.6 0.313 26.0 27.2 315s 3 28.7 0.310 28.1 29.3 315s 4 32.6 0.305 32.0 33.2 315s 5 33.9 0.236 33.4 34.4 315s 6 35.7 0.233 35.2 36.1 315s 7 37.7 0.234 37.3 38.2 315s 8 38.6 0.239 38.1 39.0 315s 9 38.8 0.229 38.4 39.3 315s 10 40.0 0.219 39.6 40.5 315s 11 38.2 0.301 37.6 38.9 315s 12 34.2 0.308 33.6 34.8 315s 13 29.3 0.370 28.5 30.0 315s 14 28.2 0.332 27.5 28.8 315s 15 30.3 0.324 29.7 31.0 315s 16 33.2 0.271 32.7 33.8 315s 17 37.6 0.263 37.1 38.1 315s 18 40.1 0.211 39.7 40.6 315s 19 39.0 0.306 38.4 39.6 315s 20 42.0 0.280 41.4 42.5 315s 21 46.2 0.298 45.6 46.8 315s 22 52.6 0.445 51.7 53.5 315s > model.frame 315s [1] TRUE 315s > model.matrix 315s [1] TRUE 315s > nobs 315s [1] 63 315s > linearHypothesis 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 1.44 0.24 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 1.69 0.2 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 52 315s 2 51 1 1.69 0.19 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.77 0.47 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.91 0.41 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 53 315s 2 51 2 1.83 0.4 315s > logLik 315s 'log Lik.' -70 (df=18) 315s 'log Lik.' -79 (df=18) 315s > 315s > # 3SLS 315s > summary 315s 315s systemfit results 315s method: 3SLS 315s 315s N DF SSR detRCov OLS-R2 McElroy-R2 315s system 63 51 73.6 0.283 0.963 0.995 315s 315s N DF SSR MSE RMSE R2 Adj R2 315s Consumption 21 17 18.7 1.102 1.050 0.980 0.977 315s Investment 21 17 44.0 2.586 1.608 0.826 0.795 315s PrivateWages 21 17 10.9 0.642 0.801 0.986 0.984 315s 315s The covariance matrix of the residuals used for estimation 315s Consumption Investment PrivateWages 315s Consumption 1.044 0.438 -0.385 315s Investment 0.438 1.383 0.193 315s PrivateWages -0.385 0.193 0.476 315s 315s The covariance matrix of the residuals 315s Consumption Investment PrivateWages 315s Consumption 0.892 0.411 -0.394 315s Investment 0.411 2.093 0.403 315s PrivateWages -0.394 0.403 0.520 315s 315s The correlations of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.000 0.301 -0.578 315s Investment 0.301 1.000 0.386 315s PrivateWages -0.578 0.386 1.000 315s 315s 315s 3SLS estimates for 'Consumption' (equation 1) 315s Model Formula: consump ~ corpProf + corpProfLag + wages 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 16.4408 1.3045 12.60 4.7e-10 *** 315s corpProf 0.1249 0.1081 1.16 0.26 315s corpProfLag 0.1631 0.1004 1.62 0.12 315s wages 0.7901 0.0379 20.83 1.5e-13 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.05 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 18.727 MSE: 1.102 Root MSE: 1.05 315s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 315s 315s 315s 3SLS estimates for 'Investment' (equation 2) 315s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 28.1778 6.7938 4.15 0.00067 *** 315s corpProf -0.0131 0.1619 -0.08 0.93655 315s corpProfLag 0.7557 0.1529 4.94 0.00012 *** 315s capitalLag -0.1948 0.0325 -5.99 1.5e-05 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.608 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 43.954 MSE: 2.586 Root MSE: 1.608 315s Multiple R-Squared: 0.826 Adjusted R-Squared: 0.795 315s 315s 315s 3SLS estimates for 'PrivateWages' (equation 3) 315s Model Formula: privWage ~ gnp + gnpLag + trend 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 1.7972 1.1159 1.61 0.13 315s gnp 0.4005 0.0318 12.59 4.8e-10 *** 315s gnpLag 0.1813 0.0342 5.31 5.8e-05 *** 315s trend 0.1497 0.0279 5.36 5.2e-05 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 0.801 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 10.921 MSE: 0.642 Root MSE: 0.801 315s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 315s 315s > residuals 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 -0.4416 -2.1951 -1.20287 315s 3 -1.0150 0.1515 0.51834 315s 4 -1.5289 0.4406 1.50936 315s 5 -0.4985 -1.8667 -0.08743 315s 6 -0.0132 0.0713 -0.28089 315s 7 0.7759 1.0294 -0.33908 315s 8 1.3004 1.1011 -0.69282 315s 9 1.0993 0.5853 0.34494 315s 10 -0.5839 2.2952 1.27590 315s 11 -0.1917 -1.3443 -0.40414 315s 12 -0.5598 -0.9944 0.22151 315s 13 -0.6746 -1.3404 -0.36962 315s 14 0.5767 1.9316 0.31006 315s 15 -0.0211 -0.1217 0.27309 315s 16 0.0539 0.1847 0.00716 315s 17 1.8555 2.0937 -0.71866 315s 18 -0.4596 -0.3216 0.90582 315s 19 0.0613 -3.6314 -0.81881 315s 20 1.2602 0.7582 -0.26942 315s 21 0.9500 0.2428 -1.06125 315s 22 -1.9451 0.9302 0.87883 315s > fitted 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 42.3 1.99510 26.7 315s 3 46.0 1.74850 28.8 315s 4 50.7 4.75942 32.6 315s 5 51.1 4.86672 34.0 315s 6 52.6 5.02874 35.7 315s 7 54.3 4.57056 37.7 315s 8 54.9 3.09893 38.6 315s 9 56.2 2.41471 38.9 315s 10 58.4 2.80476 40.0 315s 11 55.2 2.34425 38.3 315s 12 51.5 -2.40558 34.3 315s 13 46.3 -4.85959 29.4 315s 14 45.9 -7.03164 28.2 315s 15 48.7 -2.87827 30.3 315s 16 51.2 -1.48466 33.2 315s 17 55.8 0.00629 37.5 315s 18 59.2 2.32164 40.1 315s 19 57.4 1.73138 39.0 315s 20 60.3 0.54175 41.9 315s 21 64.1 3.05716 46.1 315s 22 71.6 3.96979 52.4 315s > predict 315s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 315s 1 NA NA NA NA 315s 2 42.3 0.464 39.9 44.8 315s 3 46.0 0.541 43.5 48.5 315s 4 50.7 0.337 48.4 53.1 315s 5 51.1 0.385 48.7 53.5 315s 6 52.6 0.386 50.3 55.0 315s 7 54.3 0.349 52.0 56.7 315s 8 54.9 0.320 52.6 57.2 315s 9 56.2 0.355 53.9 58.5 315s 10 58.4 0.370 56.0 60.7 315s 11 55.2 0.682 52.6 57.8 315s 12 51.5 0.563 48.9 54.0 315s 13 46.3 0.719 43.6 49.0 315s 14 45.9 0.597 43.4 48.5 315s 15 48.7 0.370 46.4 51.1 315s 16 51.2 0.327 48.9 53.6 315s 17 55.8 0.391 53.5 58.2 315s 18 59.2 0.316 56.8 61.5 315s 19 57.4 0.389 55.1 59.8 315s 20 60.3 0.459 57.9 62.8 315s 21 64.1 0.438 61.7 66.4 315s 22 71.6 0.674 69.0 74.3 315s Investment.pred Investment.se.fit Investment.lwr Investment.upr 315s 1 NA NA NA NA 315s 2 1.99510 0.792 -1.787 5.777 315s 3 1.74850 0.585 -1.861 5.358 315s 4 4.75942 0.510 1.200 8.319 315s 5 4.86672 0.423 1.359 8.375 315s 6 5.02874 0.400 1.533 8.525 315s 7 4.57056 0.391 1.079 8.062 315s 8 3.09893 0.345 -0.371 6.568 315s 9 2.41471 0.511 -1.145 5.974 315s 10 2.80476 0.560 -0.788 6.397 315s 11 2.34425 0.839 -1.482 6.170 315s 12 -2.40558 0.673 -6.083 1.272 315s 13 -4.85959 0.862 -8.708 -1.011 315s 14 -7.03164 0.874 -10.893 -3.171 315s 15 -2.87827 0.433 -6.392 0.635 315s 16 -1.48466 0.375 -4.968 1.999 315s 17 0.00629 0.491 -3.541 3.554 315s 18 2.32164 0.294 -1.127 5.771 315s 19 1.73138 0.446 -1.789 5.252 315s 20 0.54175 0.547 -3.042 4.125 315s 21 3.05716 0.454 -0.468 6.582 315s 22 3.96979 0.642 0.317 7.623 315s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 315s 1 NA NA NA NA 315s 2 26.7 0.314 24.9 28.5 315s 3 28.8 0.318 27.0 30.6 315s 4 32.6 0.325 30.8 34.4 315s 5 34.0 0.235 32.2 35.7 315s 6 35.7 0.241 33.9 37.4 315s 7 37.7 0.238 36.0 39.5 315s 8 38.6 0.237 36.8 40.4 315s 9 38.9 0.227 37.1 40.6 315s 10 40.0 0.219 38.3 41.8 315s 11 38.3 0.317 36.5 40.1 315s 12 34.3 0.344 32.4 36.1 315s 13 29.4 0.419 27.5 31.3 315s 14 28.2 0.334 26.4 30.0 315s 15 30.3 0.320 28.5 32.1 315s 16 33.2 0.268 31.4 35.0 315s 17 37.5 0.269 35.7 39.3 315s 18 40.1 0.212 38.3 41.8 315s 19 39.0 0.331 37.2 40.8 315s 20 41.9 0.287 40.1 43.7 315s 21 46.1 0.301 44.3 47.9 315s 22 52.4 0.471 50.5 54.4 315s > model.frame 315s [1] TRUE 315s > model.matrix 315s [1] TRUE 315s > nobs 315s [1] 63 315s > linearHypothesis 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 0.29 0.59 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 0.39 0.54 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 52 315s 2 51 1 0.39 0.53 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.3 0.74 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.4 0.67 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 53 315s 2 51 2 0.8 0.67 315s > logLik 315s 'log Lik.' -76.1 (df=18) 315s 'log Lik.' -89.1 (df=18) 315s > 315s > # I3SLS 315s > summary 315s 315s systemfit results 315s method: iterated 3SLS 315s 315s convergence achieved after 20 iterations 315s 315s N DF SSR detRCov OLS-R2 McElroy-R2 315s system 63 51 128 0.509 0.936 0.996 315s 315s N DF SSR MSE RMSE R2 Adj R2 315s Consumption 21 17 19.2 1.130 1.063 0.980 0.976 315s Investment 21 17 95.7 5.627 2.372 0.621 0.554 315s PrivateWages 21 17 12.7 0.748 0.865 0.984 0.981 315s 315s The covariance matrix of the residuals used for estimation 315s Consumption Investment PrivateWages 315s Consumption 0.915 0.642 -0.435 315s Investment 0.642 4.555 0.734 315s PrivateWages -0.435 0.734 0.606 315s 315s The covariance matrix of the residuals 315s Consumption Investment PrivateWages 315s Consumption 0.915 0.642 -0.435 315s Investment 0.642 4.555 0.734 315s PrivateWages -0.435 0.734 0.606 315s 315s The correlations of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.000 0.314 -0.584 315s Investment 0.314 1.000 0.442 315s PrivateWages -0.584 0.442 1.000 315s 315s 315s 3SLS estimates for 'Consumption' (equation 1) 315s Model Formula: consump ~ corpProf + corpProfLag + wages 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 16.5590 1.2244 13.52 1.6e-10 *** 315s corpProf 0.1645 0.0962 1.71 0.105 315s corpProfLag 0.1766 0.0901 1.96 0.067 . 315s wages 0.7658 0.0348 22.03 6.1e-14 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.063 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 19.213 MSE: 1.13 Root MSE: 1.063 315s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 315s 315s 315s 3SLS estimates for 'Investment' (equation 2) 315s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 42.8959 10.5937 4.05 0.00083 *** 315s corpProf -0.3565 0.2602 -1.37 0.18838 315s corpProfLag 1.0113 0.2488 4.07 0.00081 *** 315s capitalLag -0.2602 0.0509 -5.12 8.6e-05 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 2.372 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 95.661 MSE: 5.627 Root MSE: 2.372 315s Multiple R-Squared: 0.621 Adjusted R-Squared: 0.554 315s 315s 315s 3SLS estimates for 'PrivateWages' (equation 3) 315s Model Formula: privWage ~ gnp + gnpLag + trend 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 2.6247 1.1956 2.20 0.042 * 315s gnp 0.3748 0.0311 12.05 9.4e-10 *** 315s gnpLag 0.1937 0.0324 5.98 1.5e-05 *** 315s trend 0.1679 0.0289 5.80 2.1e-05 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 0.865 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 12.719 MSE: 0.748 Root MSE: 0.865 315s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.981 315s 315s > residuals 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 -0.537 -3.95419 -1.2303 315s 3 -1.187 0.00151 0.5797 315s 4 -1.705 -0.22015 1.6794 315s 5 -0.734 -2.22753 -0.0260 315s 6 -0.251 -0.10866 -0.1362 315s 7 0.600 0.83218 -0.1837 315s 8 1.142 1.46624 -0.5825 315s 9 0.921 1.62030 0.4347 315s 10 -0.745 3.40013 1.4104 315s 11 -0.197 -2.15443 -0.4679 315s 12 -0.385 -1.62274 0.0106 315s 13 -0.390 -2.62869 -0.7363 315s 14 0.749 2.80517 0.0581 315s 15 0.112 -0.27710 0.1113 315s 16 0.170 0.13598 -0.1089 315s 17 1.925 2.76200 -0.6976 315s 18 -0.341 -0.53919 0.8651 315s 19 0.219 -4.32845 -1.0116 315s 20 1.383 1.71889 -0.2087 315s 21 1.028 1.06406 -0.9656 315s 22 -1.777 2.25466 1.2061 315s > fitted 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 42.4 3.754 26.7 315s 3 46.2 1.898 28.7 315s 4 50.9 5.420 32.4 315s 5 51.3 5.228 33.9 315s 6 52.9 5.209 35.5 315s 7 54.5 4.768 37.6 315s 8 55.1 2.734 38.5 315s 9 56.4 1.380 38.8 315s 10 58.5 1.700 39.9 315s 11 55.2 3.154 38.4 315s 12 51.3 -1.777 34.5 315s 13 46.0 -3.571 29.7 315s 14 45.8 -7.905 28.4 315s 15 48.6 -2.723 30.5 315s 16 51.1 -1.436 33.3 315s 17 55.8 -0.662 37.5 315s 18 59.0 2.539 40.1 315s 19 57.3 2.428 39.2 315s 20 60.2 -0.419 41.8 315s 21 64.0 2.236 46.0 315s 22 71.5 2.645 52.1 315s > predict 315s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 315s 1 NA NA NA NA 315s 2 42.4 0.434 41.6 43.3 315s 3 46.2 0.491 45.2 47.2 315s 4 50.9 0.309 50.3 51.5 315s 5 51.3 0.351 50.6 52.0 315s 6 52.9 0.352 52.1 53.6 315s 7 54.5 0.320 53.9 55.1 315s 8 55.1 0.293 54.5 55.6 315s 9 56.4 0.324 55.7 57.0 315s 10 58.5 0.340 57.9 59.2 315s 11 55.2 0.613 54.0 56.4 315s 12 51.3 0.506 50.3 52.3 315s 13 46.0 0.649 44.7 47.3 315s 14 45.8 0.546 44.7 46.8 315s 15 48.6 0.341 47.9 49.3 315s 16 51.1 0.301 50.5 51.7 315s 17 55.8 0.357 55.1 56.5 315s 18 59.0 0.293 58.5 59.6 315s 19 57.3 0.353 56.6 58.0 315s 20 60.2 0.421 59.4 61.1 315s 21 64.0 0.409 63.2 64.8 315s 22 71.5 0.630 70.2 72.7 315s Investment.pred Investment.se.fit Investment.lwr Investment.upr 315s 1 NA NA NA NA 315s 2 3.754 1.263 1.218 6.2906 315s 3 1.898 1.022 -0.153 3.9503 315s 4 5.420 0.853 3.709 7.1317 315s 5 5.228 0.727 3.767 6.6877 315s 6 5.209 0.703 3.797 6.6200 315s 7 4.768 0.688 3.387 6.1487 315s 8 2.734 0.615 1.499 3.9683 315s 9 1.380 0.852 -0.330 3.0893 315s 10 1.700 0.938 -0.184 3.5836 315s 11 3.154 1.437 0.269 6.0398 315s 12 -1.777 1.173 -4.133 0.5780 315s 13 -3.571 1.494 -6.570 -0.5725 315s 14 -7.905 1.479 -10.875 -4.9350 315s 15 -2.723 0.778 -4.285 -1.1613 315s 16 -1.436 0.672 -2.784 -0.0875 315s 17 -0.662 0.832 -2.333 1.0088 315s 18 2.539 0.522 1.491 3.5875 315s 19 2.428 0.753 0.918 3.9392 315s 20 -0.419 0.907 -2.240 1.4019 315s 21 2.236 0.775 0.679 3.7928 315s 22 2.645 1.076 0.486 4.8047 315s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 315s 1 NA NA NA NA 315s 2 26.7 0.340 26.0 27.4 315s 3 28.7 0.339 28.0 29.4 315s 4 32.4 0.340 31.7 33.1 315s 5 33.9 0.250 33.4 34.4 315s 6 35.5 0.258 35.0 36.1 315s 7 37.6 0.256 37.1 38.1 315s 8 38.5 0.252 38.0 39.0 315s 9 38.8 0.241 38.3 39.2 315s 10 39.9 0.239 39.4 40.4 315s 11 38.4 0.314 37.7 39.0 315s 12 34.5 0.342 33.8 35.2 315s 13 29.7 0.430 28.9 30.6 315s 14 28.4 0.361 27.7 29.2 315s 15 30.5 0.336 29.8 31.2 315s 16 33.3 0.281 32.7 33.9 315s 17 37.5 0.270 37.0 38.0 315s 18 40.1 0.231 39.7 40.6 315s 19 39.2 0.343 38.5 39.9 315s 20 41.8 0.294 41.2 42.4 315s 21 46.0 0.326 45.3 46.6 315s 22 52.1 0.501 51.1 53.1 315s > model.frame 315s [1] TRUE 315s > model.matrix 315s [1] TRUE 315s > nobs 315s [1] 63 315s > linearHypothesis 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 0.59 0.45 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 51 1 0.73 0.4 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 52 315s 2 51 1 0.73 0.39 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.72 0.49 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 53 315s 2 51 2 0.88 0.42 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 53 315s 2 51 2 1.77 0.41 315s > logLik 315s 'log Lik.' -82.3 (df=18) 315s 'log Lik.' -99.1 (df=18) 315s > 315s > # OLS 315s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 315s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 315s > summary 315s 315s systemfit results 315s method: OLS 315s 315s N DF SSR detRCov OLS-R2 McElroy-R2 315s system 62 50 44.9 0.372 0.977 0.991 315s 315s N DF SSR MSE RMSE R2 Adj R2 315s Consumption 21 17 17.88 1.052 1.03 0.981 0.978 315s Investment 21 17 17.32 1.019 1.01 0.931 0.919 315s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 315s 315s The covariance matrix of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.0703 -0.0161 -0.463 315s Investment -0.0161 0.9435 0.199 315s PrivateWages -0.4633 0.1993 0.609 315s 315s The correlations of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.0000 -0.0201 -0.575 315s Investment -0.0201 1.0000 0.264 315s PrivateWages -0.5747 0.2639 1.000 315s 315s 315s OLS estimates for 'Consumption' (equation 1) 315s Model Formula: consump ~ corpProf + corpProfLag + wages 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 16.2366 1.3141 12.36 6.4e-10 *** 315s corpProf 0.1929 0.0920 2.10 0.051 . 315s corpProfLag 0.0899 0.0914 0.98 0.339 315s wages 0.7962 0.0403 19.76 3.6e-13 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.026 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 315s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 315s 315s 315s OLS estimates for 'Investment' (equation 2) 315s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 10.1258 5.2592 1.93 0.07108 . 315s corpProf 0.4796 0.0934 5.13 8.3e-05 *** 315s corpProfLag 0.3330 0.0971 3.43 0.00318 ** 315s capitalLag -0.1118 0.0257 -4.35 0.00044 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.009 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 315s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 315s 315s 315s OLS estimates for 'PrivateWages' (equation 3) 315s Model Formula: privWage ~ gnp + gnpLag + trend 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 1.3550 1.3093 1.03 0.3161 315s gnp 0.4417 0.0331 13.33 4.4e-10 *** 315s gnpLag 0.1466 0.0381 3.85 0.0014 ** 315s trend 0.1244 0.0336 3.70 0.0020 ** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 0.78 on 16 degrees of freedom 315s Number of observations: 20 Degrees of Freedom: 16 315s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 315s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 315s 315s compare coef with single-equation OLS 315s [1] TRUE 315s > residuals 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 -0.32389 -0.0668 -1.3389 315s 3 -1.25001 -0.0476 0.2462 315s 4 -1.56574 1.2467 1.1255 315s 5 -0.49350 -1.3512 -0.1959 315s 6 0.00761 0.4154 -0.5284 315s 7 0.86910 1.4923 NA 315s 8 1.33848 0.7889 -0.7909 315s 9 1.05498 -0.6317 0.2819 315s 10 -0.58856 1.0830 1.1384 315s 11 0.28231 0.2791 -0.1904 315s 12 -0.22965 0.0369 0.5813 315s 13 -0.32213 0.3659 0.1206 315s 14 0.32228 0.2237 0.4773 315s 15 -0.05801 -0.1728 0.3035 315s 16 -0.03466 0.0101 0.0284 315s 17 1.61650 0.9719 -0.8517 315s 18 -0.43597 0.0516 0.9908 315s 19 0.21005 -2.5656 -0.4597 315s 20 0.98920 -0.6866 -0.3819 315s 21 0.78508 -0.7807 -1.1062 315s 22 -2.17345 -0.6623 0.5501 315s > fitted 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 42.2 -0.133 26.8 315s 3 46.3 1.948 29.1 315s 4 50.8 3.953 33.0 315s 5 51.1 4.351 34.1 315s 6 52.6 4.685 35.9 315s 7 54.2 4.108 NA 315s 8 54.9 3.411 38.7 315s 9 56.2 3.632 38.9 315s 10 58.4 4.017 40.2 315s 11 54.7 0.721 38.1 315s 12 51.1 -3.437 33.9 315s 13 45.9 -6.566 28.9 315s 14 46.2 -5.324 28.0 315s 15 48.8 -2.827 30.3 315s 16 51.3 -1.310 33.2 315s 17 56.1 1.128 37.7 315s 18 59.1 1.948 40.0 315s 19 57.3 0.666 38.7 315s 20 60.6 1.987 42.0 315s 21 64.2 4.081 46.1 315s 22 71.9 5.562 52.7 315s > predict 315s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 315s 1 NA NA NA NA 315s 2 42.2 0.466 40.0 44.5 315s 3 46.3 0.523 43.9 48.6 315s 4 50.8 0.344 48.6 52.9 315s 5 51.1 0.399 48.9 53.3 315s 6 52.6 0.401 50.4 54.8 315s 7 54.2 0.363 52.0 56.4 315s 8 54.9 0.330 52.7 57.0 315s 9 56.2 0.354 54.1 58.4 315s 10 58.4 0.373 56.2 60.6 315s 11 54.7 0.612 52.3 57.1 315s 12 51.1 0.489 48.8 53.4 315s 13 45.9 0.634 43.5 48.3 315s 14 46.2 0.608 43.8 48.6 315s 15 48.8 0.378 46.6 51.0 315s 16 51.3 0.336 49.2 53.5 315s 17 56.1 0.369 53.9 58.3 315s 18 59.1 0.324 57.0 61.3 315s 19 57.3 0.375 55.1 59.5 315s 20 60.6 0.437 58.4 62.9 315s 21 64.2 0.429 62.0 66.4 315s 22 71.9 0.672 69.4 74.3 315s Investment.pred Investment.se.fit Investment.lwr Investment.upr 315s 1 NA NA NA NA 315s 2 -0.133 0.584 -2.476 2.209 315s 3 1.948 0.480 -0.297 4.193 315s 4 3.953 0.432 1.748 6.159 315s 5 4.351 0.357 2.201 6.502 315s 6 4.685 0.336 2.548 6.821 315s 7 4.108 0.316 1.983 6.232 315s 8 3.411 0.281 1.306 5.516 315s 9 3.632 0.374 1.469 5.794 315s 10 4.017 0.430 1.813 6.221 315s 11 0.721 0.579 -1.616 3.058 315s 12 -3.437 0.488 -5.688 -1.185 315s 13 -6.566 0.592 -8.917 -4.215 315s 14 -5.324 0.667 -7.754 -2.893 315s 15 -2.827 0.359 -4.979 -0.675 315s 16 -1.310 0.308 -3.430 0.810 315s 17 1.128 0.334 -1.008 3.264 315s 18 1.948 0.234 -0.133 4.030 315s 19 0.666 0.300 -1.450 2.781 315s 20 1.987 0.353 -0.161 4.134 315s 21 4.081 0.319 1.954 6.207 315s 22 5.562 0.444 3.348 7.777 315s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 315s 1 NA NA NA NA 315s 2 26.8 0.366 25.1 28.6 315s 3 29.1 0.369 27.3 30.8 315s 4 33.0 0.372 31.2 34.7 315s 5 34.1 0.288 32.4 35.8 315s 6 35.9 0.287 34.3 37.6 315s 7 NA NA NA NA 315s 8 38.7 0.293 37.0 40.4 315s 9 38.9 0.279 37.3 40.6 315s 10 40.2 0.266 38.5 41.8 315s 11 38.1 0.365 36.4 39.8 315s 12 33.9 0.369 32.2 35.7 315s 13 28.9 0.438 27.1 30.7 315s 14 28.0 0.385 26.3 29.8 315s 15 30.3 0.379 28.6 32.0 315s 16 33.2 0.316 31.5 34.9 315s 17 37.7 0.310 36.0 39.3 315s 18 40.0 0.243 38.4 41.7 315s 19 38.7 0.363 36.9 40.4 315s 20 42.0 0.326 40.3 43.7 315s 21 46.1 0.341 44.4 47.8 315s 22 52.7 0.514 50.9 54.6 315s > model.frame 315s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 315s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 315s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 315s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 315s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 315s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 315s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 315s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 315s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 315s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 315s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 315s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 315s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 315s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 315s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 315s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 315s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 315s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 315s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 315s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 315s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 315s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 315s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 315s trend 315s 1 -11 315s 2 -10 315s 3 -9 315s 4 -8 315s 5 -7 315s 6 -6 315s 7 -5 315s 8 -4 315s 9 -3 315s 10 -2 315s 11 -1 315s 12 0 315s 13 1 315s 14 2 315s 15 3 315s 16 4 315s 17 5 315s 18 6 315s 19 7 315s 20 8 315s 21 9 315s 22 10 315s > model.matrix 315s Consumption_(Intercept) Consumption_corpProf 315s Consumption_2 1 12.4 315s Consumption_3 1 16.9 315s Consumption_4 1 18.4 315s Consumption_5 1 19.4 315s Consumption_6 1 20.1 315s Consumption_7 1 19.6 315s Consumption_8 1 19.8 315s Consumption_9 1 21.1 315s Consumption_10 1 21.7 315s Consumption_11 1 15.6 315s Consumption_12 1 11.4 315s Consumption_13 1 7.0 315s Consumption_14 1 11.2 315s Consumption_15 1 12.3 315s Consumption_16 1 14.0 315s Consumption_17 1 17.6 315s Consumption_18 1 17.3 315s Consumption_19 1 15.3 315s Consumption_20 1 19.0 315s Consumption_21 1 21.1 315s Consumption_22 1 23.5 315s Investment_2 0 0.0 315s Investment_3 0 0.0 315s Investment_4 0 0.0 315s Investment_5 0 0.0 315s Investment_6 0 0.0 315s Investment_7 0 0.0 315s Investment_8 0 0.0 315s Investment_9 0 0.0 315s Investment_10 0 0.0 315s Investment_11 0 0.0 315s Investment_12 0 0.0 315s Investment_13 0 0.0 315s Investment_14 0 0.0 315s Investment_15 0 0.0 315s Investment_16 0 0.0 315s Investment_17 0 0.0 315s Investment_18 0 0.0 315s Investment_19 0 0.0 315s Investment_20 0 0.0 315s Investment_21 0 0.0 315s Investment_22 0 0.0 315s PrivateWages_2 0 0.0 315s PrivateWages_3 0 0.0 315s PrivateWages_4 0 0.0 315s PrivateWages_5 0 0.0 315s PrivateWages_6 0 0.0 315s PrivateWages_8 0 0.0 315s PrivateWages_9 0 0.0 315s PrivateWages_10 0 0.0 315s PrivateWages_11 0 0.0 315s PrivateWages_12 0 0.0 315s PrivateWages_13 0 0.0 315s PrivateWages_14 0 0.0 315s PrivateWages_15 0 0.0 315s PrivateWages_16 0 0.0 315s PrivateWages_17 0 0.0 315s PrivateWages_18 0 0.0 315s PrivateWages_19 0 0.0 315s PrivateWages_20 0 0.0 315s PrivateWages_21 0 0.0 315s PrivateWages_22 0 0.0 315s Consumption_corpProfLag Consumption_wages 315s Consumption_2 12.7 28.2 315s Consumption_3 12.4 32.2 315s Consumption_4 16.9 37.0 315s Consumption_5 18.4 37.0 315s Consumption_6 19.4 38.6 315s Consumption_7 20.1 40.7 315s Consumption_8 19.6 41.5 315s Consumption_9 19.8 42.9 315s Consumption_10 21.1 45.3 315s Consumption_11 21.7 42.1 315s Consumption_12 15.6 39.3 315s Consumption_13 11.4 34.3 315s Consumption_14 7.0 34.1 315s Consumption_15 11.2 36.6 315s Consumption_16 12.3 39.3 315s Consumption_17 14.0 44.2 315s Consumption_18 17.6 47.7 315s Consumption_19 17.3 45.9 315s Consumption_20 15.3 49.4 315s Consumption_21 19.0 53.0 315s Consumption_22 21.1 61.8 315s Investment_2 0.0 0.0 315s Investment_3 0.0 0.0 315s Investment_4 0.0 0.0 315s Investment_5 0.0 0.0 315s Investment_6 0.0 0.0 315s Investment_7 0.0 0.0 315s Investment_8 0.0 0.0 315s Investment_9 0.0 0.0 315s Investment_10 0.0 0.0 315s Investment_11 0.0 0.0 315s Investment_12 0.0 0.0 315s Investment_13 0.0 0.0 315s Investment_14 0.0 0.0 315s Investment_15 0.0 0.0 315s Investment_16 0.0 0.0 315s Investment_17 0.0 0.0 315s Investment_18 0.0 0.0 315s Investment_19 0.0 0.0 315s Investment_20 0.0 0.0 315s Investment_21 0.0 0.0 315s Investment_22 0.0 0.0 315s PrivateWages_2 0.0 0.0 315s PrivateWages_3 0.0 0.0 315s PrivateWages_4 0.0 0.0 315s PrivateWages_5 0.0 0.0 315s PrivateWages_6 0.0 0.0 315s PrivateWages_8 0.0 0.0 315s PrivateWages_9 0.0 0.0 315s PrivateWages_10 0.0 0.0 315s PrivateWages_11 0.0 0.0 315s PrivateWages_12 0.0 0.0 315s PrivateWages_13 0.0 0.0 315s PrivateWages_14 0.0 0.0 315s PrivateWages_15 0.0 0.0 315s PrivateWages_16 0.0 0.0 315s PrivateWages_17 0.0 0.0 315s PrivateWages_18 0.0 0.0 315s PrivateWages_19 0.0 0.0 315s PrivateWages_20 0.0 0.0 315s PrivateWages_21 0.0 0.0 315s PrivateWages_22 0.0 0.0 315s Investment_(Intercept) Investment_corpProf 315s Consumption_2 0 0.0 315s Consumption_3 0 0.0 315s Consumption_4 0 0.0 315s Consumption_5 0 0.0 315s Consumption_6 0 0.0 315s Consumption_7 0 0.0 315s Consumption_8 0 0.0 315s Consumption_9 0 0.0 315s Consumption_10 0 0.0 315s Consumption_11 0 0.0 315s Consumption_12 0 0.0 315s Consumption_13 0 0.0 315s Consumption_14 0 0.0 315s Consumption_15 0 0.0 315s Consumption_16 0 0.0 315s Consumption_17 0 0.0 315s Consumption_18 0 0.0 315s Consumption_19 0 0.0 315s Consumption_20 0 0.0 315s Consumption_21 0 0.0 315s Consumption_22 0 0.0 315s Investment_2 1 12.4 315s Investment_3 1 16.9 315s Investment_4 1 18.4 315s Investment_5 1 19.4 315s Investment_6 1 20.1 315s Investment_7 1 19.6 315s Investment_8 1 19.8 315s Investment_9 1 21.1 315s Investment_10 1 21.7 315s Investment_11 1 15.6 315s Investment_12 1 11.4 315s Investment_13 1 7.0 315s Investment_14 1 11.2 315s Investment_15 1 12.3 315s Investment_16 1 14.0 315s Investment_17 1 17.6 315s Investment_18 1 17.3 315s Investment_19 1 15.3 315s Investment_20 1 19.0 315s Investment_21 1 21.1 315s Investment_22 1 23.5 315s PrivateWages_2 0 0.0 315s PrivateWages_3 0 0.0 315s PrivateWages_4 0 0.0 315s PrivateWages_5 0 0.0 315s PrivateWages_6 0 0.0 315s PrivateWages_8 0 0.0 315s PrivateWages_9 0 0.0 315s PrivateWages_10 0 0.0 315s PrivateWages_11 0 0.0 315s PrivateWages_12 0 0.0 315s PrivateWages_13 0 0.0 315s PrivateWages_14 0 0.0 315s PrivateWages_15 0 0.0 315s PrivateWages_16 0 0.0 315s PrivateWages_17 0 0.0 315s PrivateWages_18 0 0.0 315s PrivateWages_19 0 0.0 315s PrivateWages_20 0 0.0 315s PrivateWages_21 0 0.0 315s PrivateWages_22 0 0.0 315s Investment_corpProfLag Investment_capitalLag 315s Consumption_2 0.0 0 315s Consumption_3 0.0 0 315s Consumption_4 0.0 0 315s Consumption_5 0.0 0 315s Consumption_6 0.0 0 315s Consumption_7 0.0 0 315s Consumption_8 0.0 0 315s Consumption_9 0.0 0 315s Consumption_10 0.0 0 315s Consumption_11 0.0 0 315s Consumption_12 0.0 0 315s Consumption_13 0.0 0 315s Consumption_14 0.0 0 315s Consumption_15 0.0 0 315s Consumption_16 0.0 0 315s Consumption_17 0.0 0 315s Consumption_18 0.0 0 315s Consumption_19 0.0 0 315s Consumption_20 0.0 0 315s Consumption_21 0.0 0 315s Consumption_22 0.0 0 315s Investment_2 12.7 183 315s Investment_3 12.4 183 315s Investment_4 16.9 184 315s Investment_5 18.4 190 315s Investment_6 19.4 193 315s Investment_7 20.1 198 315s Investment_8 19.6 203 315s Investment_9 19.8 208 315s Investment_10 21.1 211 315s Investment_11 21.7 216 315s Investment_12 15.6 217 315s Investment_13 11.4 213 315s Investment_14 7.0 207 315s Investment_15 11.2 202 315s Investment_16 12.3 199 315s Investment_17 14.0 198 315s Investment_18 17.6 200 315s Investment_19 17.3 202 315s Investment_20 15.3 200 315s Investment_21 19.0 201 315s Investment_22 21.1 204 315s PrivateWages_2 0.0 0 315s PrivateWages_3 0.0 0 315s PrivateWages_4 0.0 0 315s PrivateWages_5 0.0 0 315s PrivateWages_6 0.0 0 315s PrivateWages_8 0.0 0 315s PrivateWages_9 0.0 0 315s PrivateWages_10 0.0 0 315s PrivateWages_11 0.0 0 315s PrivateWages_12 0.0 0 315s PrivateWages_13 0.0 0 315s PrivateWages_14 0.0 0 315s PrivateWages_15 0.0 0 315s PrivateWages_16 0.0 0 315s PrivateWages_17 0.0 0 315s PrivateWages_18 0.0 0 315s PrivateWages_19 0.0 0 315s PrivateWages_20 0.0 0 315s PrivateWages_21 0.0 0 315s PrivateWages_22 0.0 0 315s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 315s Consumption_2 0 0.0 0.0 315s Consumption_3 0 0.0 0.0 315s Consumption_4 0 0.0 0.0 315s Consumption_5 0 0.0 0.0 315s Consumption_6 0 0.0 0.0 315s Consumption_7 0 0.0 0.0 315s Consumption_8 0 0.0 0.0 315s Consumption_9 0 0.0 0.0 315s Consumption_10 0 0.0 0.0 315s Consumption_11 0 0.0 0.0 315s Consumption_12 0 0.0 0.0 315s Consumption_13 0 0.0 0.0 315s Consumption_14 0 0.0 0.0 315s Consumption_15 0 0.0 0.0 315s Consumption_16 0 0.0 0.0 315s Consumption_17 0 0.0 0.0 315s Consumption_18 0 0.0 0.0 315s Consumption_19 0 0.0 0.0 315s Consumption_20 0 0.0 0.0 315s Consumption_21 0 0.0 0.0 315s Consumption_22 0 0.0 0.0 315s Investment_2 0 0.0 0.0 315s Investment_3 0 0.0 0.0 315s Investment_4 0 0.0 0.0 315s Investment_5 0 0.0 0.0 315s Investment_6 0 0.0 0.0 315s Investment_7 0 0.0 0.0 315s Investment_8 0 0.0 0.0 315s Investment_9 0 0.0 0.0 315s Investment_10 0 0.0 0.0 315s Investment_11 0 0.0 0.0 315s Investment_12 0 0.0 0.0 315s Investment_13 0 0.0 0.0 315s Investment_14 0 0.0 0.0 315s Investment_15 0 0.0 0.0 315s Investment_16 0 0.0 0.0 315s Investment_17 0 0.0 0.0 315s Investment_18 0 0.0 0.0 315s Investment_19 0 0.0 0.0 315s Investment_20 0 0.0 0.0 315s Investment_21 0 0.0 0.0 315s Investment_22 0 0.0 0.0 315s PrivateWages_2 1 45.6 44.9 315s PrivateWages_3 1 50.1 45.6 315s PrivateWages_4 1 57.2 50.1 315s PrivateWages_5 1 57.1 57.2 315s PrivateWages_6 1 61.0 57.1 315s PrivateWages_8 1 64.4 64.0 315s PrivateWages_9 1 64.5 64.4 315s PrivateWages_10 1 67.0 64.5 315s PrivateWages_11 1 61.2 67.0 315s PrivateWages_12 1 53.4 61.2 315s PrivateWages_13 1 44.3 53.4 315s PrivateWages_14 1 45.1 44.3 315s PrivateWages_15 1 49.7 45.1 315s PrivateWages_16 1 54.4 49.7 315s PrivateWages_17 1 62.7 54.4 315s PrivateWages_18 1 65.0 62.7 315s PrivateWages_19 1 60.9 65.0 315s PrivateWages_20 1 69.5 60.9 315s PrivateWages_21 1 75.7 69.5 315s PrivateWages_22 1 88.4 75.7 315s PrivateWages_trend 315s Consumption_2 0 315s Consumption_3 0 315s Consumption_4 0 315s Consumption_5 0 315s Consumption_6 0 315s Consumption_7 0 315s Consumption_8 0 315s Consumption_9 0 315s Consumption_10 0 315s Consumption_11 0 315s Consumption_12 0 315s Consumption_13 0 315s Consumption_14 0 315s Consumption_15 0 315s Consumption_16 0 315s Consumption_17 0 315s Consumption_18 0 315s Consumption_19 0 315s Consumption_20 0 315s Consumption_21 0 315s Consumption_22 0 315s Investment_2 0 315s Investment_3 0 315s Investment_4 0 315s Investment_5 0 315s Investment_6 0 315s Investment_7 0 315s Investment_8 0 315s Investment_9 0 315s Investment_10 0 315s Investment_11 0 315s Investment_12 0 315s Investment_13 0 315s Investment_14 0 315s Investment_15 0 315s Investment_16 0 315s Investment_17 0 315s Investment_18 0 315s Investment_19 0 315s Investment_20 0 315s Investment_21 0 315s Investment_22 0 315s PrivateWages_2 -10 315s PrivateWages_3 -9 315s PrivateWages_4 -8 315s PrivateWages_5 -7 315s PrivateWages_6 -6 315s PrivateWages_8 -4 315s PrivateWages_9 -3 315s PrivateWages_10 -2 315s PrivateWages_11 -1 315s PrivateWages_12 0 315s PrivateWages_13 1 315s PrivateWages_14 2 315s PrivateWages_15 3 315s PrivateWages_16 4 315s PrivateWages_17 5 315s PrivateWages_18 6 315s PrivateWages_19 7 315s PrivateWages_20 8 315s PrivateWages_21 9 315s PrivateWages_22 10 315s > nobs 315s [1] 62 315s > linearHypothesis 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 51 315s 2 50 1 0.8 0.37 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 51 315s 2 50 1 0.72 0.4 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 51 315s 2 50 1 0.72 0.4 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 50 2 0.42 0.66 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 50 2 0.37 0.69 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 52 315s 2 50 2 0.75 0.69 315s > logLik 315s 'log Lik.' -71.9 (df=13) 315s 'log Lik.' -77.1 (df=13) 315s compare log likelihood value with single-equation OLS 315s [1] "Mean relative difference: 0.000555" 315s > 315s > # 2SLS 315s > summary 315s 315s systemfit results 315s method: 2SLS 315s 315s N DF SSR detRCov OLS-R2 McElroy-R2 315s system 60 48 53.4 0.274 0.973 0.992 315s 315s N DF SSR MSE RMSE R2 Adj R2 315s Consumption 20 16 20.67 1.292 1.14 0.978 0.974 315s Investment 20 16 23.02 1.438 1.20 0.901 0.883 315s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 315s 315s The covariance matrix of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.034 0.309 -0.383 315s Investment 0.309 1.151 0.202 315s PrivateWages -0.383 0.202 0.487 315s 315s The correlations of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.000 0.284 -0.540 315s Investment 0.284 1.000 0.269 315s PrivateWages -0.540 0.269 1.000 315s 315s 315s 2SLS estimates for 'Consumption' (equation 1) 315s Model Formula: consump ~ corpProf + corpProfLag + wages 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 16.5093 1.3121 12.58 1.0e-09 *** 315s corpProf 0.0219 0.1159 0.19 0.85 315s corpProfLag 0.1931 0.1071 1.80 0.09 . 315s wages 0.8174 0.0408 20.05 9.2e-13 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.137 on 16 degrees of freedom 315s Number of observations: 20 Degrees of Freedom: 16 315s SSR: 20.671 MSE: 1.292 Root MSE: 1.137 315s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.974 315s 315s 315s 2SLS estimates for 'Investment' (equation 2) 315s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 17.843 6.850 2.60 0.01915 * 315s corpProf 0.217 0.155 1.40 0.18106 315s corpProfLag 0.542 0.148 3.65 0.00216 ** 315s capitalLag -0.145 0.033 -4.41 0.00044 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.199 on 16 degrees of freedom 315s Number of observations: 20 Degrees of Freedom: 16 315s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 315s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 315s 315s 315s 2SLS estimates for 'PrivateWages' (equation 3) 315s Model Formula: privWage ~ gnp + gnpLag + trend 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 1.3431 1.1772 1.14 0.27070 315s gnp 0.4438 0.0358 12.39 1.3e-09 *** 315s gnpLag 0.1447 0.0389 3.72 0.00185 ** 315s trend 0.1238 0.0306 4.05 0.00093 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 0.78 on 16 degrees of freedom 315s Number of observations: 20 Degrees of Freedom: 16 315s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 315s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 315s 315s > residuals 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 -0.383 -1.0104 -1.3401 315s 3 -0.593 0.2478 0.2378 315s 4 -1.219 1.0621 1.1117 315s 5 -0.130 -1.4104 -0.1954 315s 6 0.354 0.4328 -0.5355 315s 7 NA NA NA 315s 8 1.551 1.0463 -0.7908 315s 9 1.440 0.0674 0.2831 315s 10 -0.286 1.7698 1.1353 315s 11 -0.453 -0.5912 -0.1765 315s 12 -0.994 -0.6318 0.6007 315s 13 -1.300 -0.6983 0.1443 315s 14 0.521 0.9724 0.4826 315s 15 -0.157 -0.1827 0.3016 315s 16 -0.014 0.1167 0.0261 315s 17 1.974 1.6266 -0.8614 315s 18 -0.576 -0.0525 0.9927 315s 19 -0.203 -3.0656 -0.4446 315s 20 1.342 0.1393 -0.3914 315s 21 1.039 -0.1305 -1.1115 315s 22 -1.912 0.2922 0.5312 315s > fitted 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 42.3 0.810 26.8 315s 3 45.6 1.652 29.1 315s 4 50.4 4.138 33.0 315s 5 50.7 4.410 34.1 315s 6 52.2 4.667 35.9 315s 7 NA NA NA 315s 8 54.6 3.154 38.7 315s 9 55.9 2.933 38.9 315s 10 58.1 3.330 40.2 315s 11 55.5 1.591 38.1 315s 12 51.9 -2.768 33.9 315s 13 46.9 -5.502 28.9 315s 14 46.0 -6.072 28.0 315s 15 48.9 -2.817 30.3 315s 16 51.3 -1.417 33.2 315s 17 55.7 0.473 37.7 315s 18 59.3 2.053 40.0 315s 19 57.7 1.166 38.6 315s 20 60.3 1.161 42.0 315s 21 64.0 3.431 46.1 315s 22 71.6 4.608 52.8 315s > predict 315s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 315s 1 NA NA NA NA 315s 2 42.3 0.473 41.3 43.3 315s 3 45.6 0.573 44.4 46.8 315s 4 50.4 0.366 49.6 51.2 315s 5 50.7 0.423 49.8 51.6 315s 6 52.2 0.426 51.3 53.1 315s 7 NA NA NA NA 315s 8 54.6 0.347 53.9 55.4 315s 9 55.9 0.384 55.0 56.7 315s 10 58.1 0.395 57.2 58.9 315s 11 55.5 0.729 53.9 57.0 315s 12 51.9 0.594 50.6 53.2 315s 13 46.9 0.752 45.3 48.5 315s 14 46.0 0.616 44.7 47.3 315s 15 48.9 0.373 48.1 49.6 315s 16 51.3 0.331 50.6 52.0 315s 17 55.7 0.403 54.9 56.6 315s 18 59.3 0.326 58.6 60.0 315s 19 57.7 0.411 56.8 58.6 315s 20 60.3 0.472 59.3 61.3 315s 21 64.0 0.443 63.0 64.9 315s 22 71.6 0.683 70.2 73.1 315s Investment.pred Investment.se.fit Investment.lwr Investment.upr 315s 1 NA NA NA NA 315s 2 0.810 0.786 -0.8569 2.48 315s 3 1.652 0.541 0.5056 2.80 315s 4 4.138 0.511 3.0552 5.22 315s 5 4.410 0.421 3.5172 5.30 315s 6 4.667 0.395 3.8294 5.51 315s 7 NA NA NA NA 315s 8 3.154 0.327 2.4602 3.85 315s 9 2.933 0.489 1.8967 3.97 315s 10 3.330 0.537 2.1915 4.47 315s 11 1.591 0.786 -0.0748 3.26 315s 12 -2.768 0.615 -4.0716 -1.46 315s 13 -5.502 0.787 -7.1696 -3.83 315s 14 -6.072 0.842 -7.8568 -4.29 315s 15 -2.817 0.397 -3.6591 -1.98 315s 16 -1.417 0.343 -2.1436 -0.69 315s 17 0.473 0.457 -0.4954 1.44 315s 18 2.053 0.286 1.4471 2.66 315s 19 1.166 0.430 0.2549 2.08 315s 20 1.161 0.515 0.0698 2.25 315s 21 3.431 0.426 2.5282 4.33 315s 22 4.608 0.606 3.3223 5.89 315s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 315s 1 NA NA NA NA 315s 2 26.8 0.328 26.1 27.5 315s 3 29.1 0.340 28.3 29.8 315s 4 33.0 0.360 32.2 33.8 315s 5 34.1 0.258 33.5 34.6 315s 6 35.9 0.266 35.4 36.5 315s 7 NA NA NA NA 315s 8 38.7 0.262 38.1 39.2 315s 9 38.9 0.250 38.4 39.4 315s 10 40.2 0.240 39.7 40.7 315s 11 38.1 0.355 37.3 38.8 315s 12 33.9 0.382 33.1 34.7 315s 13 28.9 0.456 27.9 29.8 315s 14 28.0 0.348 27.3 28.8 315s 15 30.3 0.339 29.6 31.0 315s 16 33.2 0.284 32.6 33.8 315s 17 37.7 0.293 37.0 38.3 315s 18 40.0 0.218 39.5 40.5 315s 19 38.6 0.358 37.9 39.4 315s 20 42.0 0.307 41.3 42.6 315s 21 46.1 0.310 45.5 46.8 315s 22 52.8 0.496 51.7 53.8 315s > model.frame 315s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 315s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 315s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 315s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 315s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 315s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 315s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 315s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 315s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 315s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 315s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 315s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 315s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 315s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 315s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 315s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 315s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 315s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 315s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 315s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 315s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 315s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 315s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 315s trend 315s 1 -11 315s 2 -10 315s 3 -9 315s 4 -8 315s 5 -7 315s 6 -6 315s 7 -5 315s 8 -4 315s 9 -3 315s 10 -2 315s 11 -1 315s 12 0 315s 13 1 315s 14 2 315s 15 3 315s 16 4 315s 17 5 315s 18 6 315s 19 7 315s 20 8 315s 21 9 315s 22 10 315s > model.matrix 315s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 315s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 315s [3] "Numeric: lengths (744, 720) differ" 315s > nobs 315s [1] 60 315s > linearHypothesis 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 49 315s 2 48 1 0.95 0.34 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 49 315s 2 48 1 1.05 0.31 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 49 315s 2 48 1 1.05 0.3 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 50 315s 2 48 2 0.48 0.62 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 50 315s 2 48 2 0.53 0.59 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 50 315s 2 48 2 1.06 0.59 315s > logLik 315s 'log Lik.' -72.2 (df=13) 315s 'log Lik.' -79.7 (df=13) 315s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 315s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 315s > 315s > # SUR 315s > summary 315s 315s systemfit results 315s method: SUR 315s 315s N DF SSR detRCov OLS-R2 McElroy-R2 315s system 62 50 46.2 0.154 0.977 0.993 315s 315s N DF SSR MSE RMSE R2 Adj R2 315s Consumption 21 17 18.1 1.062 1.031 0.981 0.977 315s Investment 21 17 17.5 1.030 1.015 0.931 0.918 315s PrivateWages 20 16 10.6 0.663 0.814 0.987 0.984 315s 315s The covariance matrix of the residuals used for estimation 315s Consumption Investment PrivateWages 315s Consumption 0.8562 -0.0129 -0.371 315s Investment -0.0129 0.7548 0.159 315s PrivateWages -0.3706 0.1594 0.487 315s 315s The covariance matrix of the residuals 315s Consumption Investment PrivateWages 315s Consumption 0.8684 0.0078 -0.442 315s Investment 0.0078 0.7702 0.237 315s PrivateWages -0.4416 0.2366 0.531 315s 315s The correlations of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.00000 0.00562 -0.651 315s Investment 0.00562 1.00000 0.372 315s PrivateWages -0.65109 0.37198 1.000 315s 315s 315s SUR estimates for 'Consumption' (equation 1) 315s Model Formula: consump ~ corpProf + corpProfLag + wages 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 16.0647 1.1729 13.70 1.3e-10 *** 315s corpProf 0.2283 0.0775 2.94 0.0091 ** 315s corpProfLag 0.0723 0.0771 0.94 0.3615 315s wages 0.7930 0.0352 22.51 4.3e-14 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.031 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 18.06 MSE: 1.062 Root MSE: 1.031 315s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 315s 315s 315s SUR estimates for 'Investment' (equation 2) 315s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 12.3516 4.5762 2.70 0.01520 * 315s corpProf 0.4461 0.0818 5.45 4.3e-05 *** 315s corpProfLag 0.3609 0.0849 4.25 0.00054 *** 315s capitalLag -0.1224 0.0223 -5.47 4.1e-05 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.015 on 17 degrees of freedom 315s Number of observations: 21 Degrees of Freedom: 17 315s SSR: 17.514 MSE: 1.03 Root MSE: 1.015 315s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 315s 315s 315s SUR estimates for 'PrivateWages' (equation 3) 315s Model Formula: privWage ~ gnp + gnpLag + trend 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 1.5433 1.1371 1.36 0.19 315s gnp 0.4117 0.0279 14.77 9.6e-11 *** 315s gnpLag 0.1743 0.0317 5.50 4.8e-05 *** 315s trend 0.1550 0.0283 5.49 5.0e-05 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 0.814 on 16 degrees of freedom 315s Number of observations: 20 Degrees of Freedom: 16 315s SSR: 10.611 MSE: 0.663 Root MSE: 0.814 315s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 315s 315s > residuals 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 -0.27628 -0.3003 -1.0910 315s 3 -1.35400 -0.1239 0.5795 315s 4 -1.62816 1.1154 1.5172 315s 5 -0.56494 -1.4358 -0.0341 315s 6 -0.06584 0.3581 -0.2772 315s 7 0.83245 1.4526 NA 315s 8 1.28855 0.8290 -0.6896 315s 9 0.96709 -0.5092 0.3445 315s 10 -0.66705 1.2210 1.2429 315s 11 0.41992 0.2497 -0.3602 315s 12 -0.05971 0.0470 0.3068 315s 13 -0.08649 0.3096 -0.2426 315s 14 0.33124 0.3652 0.3591 315s 15 -0.00604 -0.1652 0.2710 315s 16 -0.01478 0.0124 -0.0207 315s 17 1.55472 1.0339 -0.8117 315s 18 -0.41250 0.0255 0.8398 315s 19 0.29322 -2.6293 -0.8283 315s 20 0.91756 -0.5906 -0.4091 315s 21 0.71583 -0.7036 -1.2154 315s 22 -2.26223 -0.5283 0.6207 315s > fitted 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 42.2 0.100 26.6 315s 3 46.4 2.024 28.7 315s 4 50.8 4.085 32.6 315s 5 51.2 4.436 33.9 315s 6 52.7 4.742 35.7 315s 7 54.3 4.147 NA 315s 8 54.9 3.371 38.6 315s 9 56.3 3.509 38.9 315s 10 58.5 3.879 40.1 315s 11 54.6 0.750 38.3 315s 12 51.0 -3.447 34.2 315s 13 45.7 -6.510 29.2 315s 14 46.2 -5.465 28.1 315s 15 48.7 -2.835 30.3 315s 16 51.3 -1.312 33.2 315s 17 56.1 1.066 37.6 315s 18 59.1 1.974 40.2 315s 19 57.2 0.729 39.0 315s 20 60.7 1.891 42.0 315s 21 64.3 4.004 46.2 315s 22 72.0 5.428 52.7 315s > predict 315s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 315s 1 NA NA NA NA 315s 2 42.2 0.414 41.3 43.0 315s 3 46.4 0.451 45.4 47.3 315s 4 50.8 0.296 50.2 51.4 315s 5 51.2 0.342 50.5 51.9 315s 6 52.7 0.342 52.0 53.4 315s 7 54.3 0.309 53.6 54.9 315s 8 54.9 0.282 54.3 55.5 315s 9 56.3 0.303 55.7 56.9 315s 10 58.5 0.321 57.8 59.1 315s 11 54.6 0.515 53.5 55.6 315s 12 51.0 0.418 50.1 51.8 315s 13 45.7 0.548 44.6 46.8 315s 14 46.2 0.528 45.1 47.2 315s 15 48.7 0.333 48.0 49.4 315s 16 51.3 0.296 50.7 51.9 315s 17 56.1 0.321 55.5 56.8 315s 18 59.1 0.287 58.5 59.7 315s 19 57.2 0.325 56.6 57.9 315s 20 60.7 0.383 59.9 61.5 315s 21 64.3 0.382 63.5 65.1 315s 22 72.0 0.599 70.8 73.2 315s Investment.pred Investment.se.fit Investment.lwr Investment.upr 315s 1 NA NA NA NA 315s 2 0.100 0.511 -0.926 1.127 315s 3 2.024 0.425 1.170 2.878 315s 4 4.085 0.378 3.325 4.845 315s 5 4.436 0.313 3.806 5.065 315s 6 4.742 0.296 4.147 5.336 315s 7 4.147 0.279 3.586 4.709 315s 8 3.371 0.250 2.868 3.874 315s 9 3.509 0.331 2.845 4.174 315s 10 3.879 0.380 3.116 4.642 315s 11 0.750 0.512 -0.279 1.779 315s 12 -3.447 0.433 -4.316 -2.578 315s 13 -6.510 0.527 -7.568 -5.451 315s 14 -5.465 0.587 -6.645 -4.285 315s 15 -2.835 0.320 -3.477 -2.193 315s 16 -1.312 0.274 -1.863 -0.761 315s 17 1.066 0.296 0.472 1.661 315s 18 1.974 0.208 1.558 2.391 315s 19 0.729 0.265 0.197 1.262 315s 20 1.891 0.311 1.266 2.515 315s 21 4.004 0.283 3.435 4.572 315s 22 5.428 0.393 4.640 6.217 315s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 315s 1 NA NA NA NA 315s 2 26.6 0.318 26.0 27.2 315s 3 28.7 0.317 28.1 29.4 315s 4 32.6 0.315 32.0 33.2 315s 5 33.9 0.243 33.4 34.4 315s 6 35.7 0.242 35.2 36.2 315s 7 NA NA NA NA 315s 8 38.6 0.247 38.1 39.1 315s 9 38.9 0.236 38.4 39.3 315s 10 40.1 0.227 39.6 40.5 315s 11 38.3 0.306 37.6 38.9 315s 12 34.2 0.312 33.6 34.8 315s 13 29.2 0.376 28.5 30.0 315s 14 28.1 0.337 27.5 28.8 315s 15 30.3 0.328 29.7 31.0 315s 16 33.2 0.274 32.7 33.8 315s 17 37.6 0.266 37.1 38.1 315s 18 40.2 0.213 39.7 40.6 315s 19 39.0 0.310 38.4 39.7 315s 20 42.0 0.282 41.4 42.6 315s 21 46.2 0.300 45.6 46.8 315s 22 52.7 0.451 51.8 53.6 315s > model.frame 315s [1] TRUE 315s > model.matrix 315s [1] TRUE 315s > nobs 315s [1] 62 315s > linearHypothesis 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 51 315s 2 50 1 1.39 0.24 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 51 315s 2 50 1 1.7 0.2 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 51 315s 2 50 1 1.7 0.19 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 50 2 0.72 0.49 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 52 315s 2 50 2 0.87 0.42 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 52 315s 2 50 2 1.75 0.42 315s > logLik 315s 'log Lik.' -69.4 (df=18) 315s 'log Lik.' -78.2 (df=18) 315s > 315s > # 3SLS 315s > summary 315s 315s systemfit results 315s method: 3SLS 315s 315s N DF SSR detRCov OLS-R2 McElroy-R2 315s system 60 48 62.6 0.265 0.968 0.994 315s 315s N DF SSR MSE RMSE R2 Adj R2 315s Consumption 20 16 17.8 1.114 1.06 0.981 0.977 315s Investment 20 16 34.3 2.143 1.46 0.853 0.825 315s PrivateWages 20 16 10.5 0.656 0.81 0.987 0.984 315s 315s The covariance matrix of the residuals used for estimation 315s Consumption Investment PrivateWages 315s Consumption 1.034 0.309 -0.383 315s Investment 0.309 1.151 0.202 315s PrivateWages -0.383 0.202 0.487 315s 315s The covariance matrix of the residuals 315s Consumption Investment PrivateWages 315s Consumption 0.891 0.304 -0.391 315s Investment 0.304 1.715 0.388 315s PrivateWages -0.391 0.388 0.525 315s 315s The correlations of the residuals 315s Consumption Investment PrivateWages 315s Consumption 1.000 0.246 -0.571 315s Investment 0.246 1.000 0.409 315s PrivateWages -0.571 0.409 1.000 315s 315s 315s 3SLS estimates for 'Consumption' (equation 1) 315s Model Formula: consump ~ corpProf + corpProfLag + wages 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 16.3668 1.3024 12.57 1.1e-09 *** 315s corpProf 0.1186 0.1073 1.10 0.29 315s corpProfLag 0.1448 0.1008 1.44 0.17 315s wages 0.8006 0.0391 20.47 6.7e-13 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.056 on 16 degrees of freedom 315s Number of observations: 20 Degrees of Freedom: 16 315s SSR: 17.825 MSE: 1.114 Root MSE: 1.056 315s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 315s 315s 315s 3SLS estimates for 'Investment' (equation 2) 315s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 24.8872 6.2956 3.95 0.00114 ** 315s corpProf 0.0702 0.1458 0.48 0.63648 315s corpProfLag 0.6688 0.1402 4.77 0.00021 *** 315s capitalLag -0.1786 0.0303 -5.90 2.3e-05 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 1.464 on 16 degrees of freedom 315s Number of observations: 20 Degrees of Freedom: 16 315s SSR: 34.295 MSE: 2.143 Root MSE: 1.464 315s Multiple R-Squared: 0.853 Adjusted R-Squared: 0.825 315s 315s 315s 3SLS estimates for 'PrivateWages' (equation 3) 315s Model Formula: privWage ~ gnp + gnpLag + trend 315s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 315s gnpLag 315s 315s Estimate Std. Error t value Pr(>|t|) 315s (Intercept) 1.6387 1.1457 1.43 0.17188 315s gnp 0.4062 0.0324 12.52 1.1e-09 *** 315s gnpLag 0.1784 0.0347 5.14 1.0e-04 *** 315s trend 0.1435 0.0292 4.91 0.00016 *** 315s --- 315s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 315s 315s Residual standard error: 0.81 on 16 degrees of freedom 315s Number of observations: 20 Degrees of Freedom: 16 315s SSR: 10.497 MSE: 0.656 Root MSE: 0.81 315s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 315s 315s > residuals 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 -0.3538 -1.795 -1.2388 315s 3 -0.9465 0.154 0.4649 315s 4 -1.4189 0.678 1.4344 315s 5 -0.3546 -1.666 -0.1354 315s 6 0.1366 0.251 -0.3452 315s 7 NA NA NA 315s 8 1.4213 1.150 -0.7445 315s 9 1.2173 0.476 0.3001 315s 10 -0.4636 2.200 1.2232 315s 11 -0.0650 -0.962 -0.4104 315s 12 -0.5422 -0.808 0.2495 315s 13 -0.7092 -1.098 -0.3057 315s 14 0.4898 1.542 0.3497 315s 15 -0.0502 -0.155 0.2949 315s 16 0.0272 0.154 0.0214 315s 17 1.8311 1.932 -0.7322 315s 18 -0.4567 -0.180 0.9090 315s 19 0.0650 -3.381 -0.7795 315s 20 1.2135 0.557 -0.2847 315s 21 0.9466 0.167 -1.0812 315s 22 -1.9877 0.784 0.8102 315s > fitted 315s Consumption Investment PrivateWages 315s 1 NA NA NA 315s 2 42.3 1.595 26.7 315s 3 45.9 1.746 28.8 315s 4 50.6 4.522 32.7 315s 5 51.0 4.666 34.0 315s 6 52.5 4.849 35.7 315s 7 NA NA NA 315s 8 54.8 3.050 38.6 315s 9 56.1 2.524 38.9 315s 10 58.3 2.900 40.1 315s 11 55.1 1.962 38.3 315s 12 51.4 -2.592 34.3 315s 13 46.3 -5.102 29.3 315s 14 46.0 -6.642 28.2 315s 15 48.8 -2.845 30.3 315s 16 51.3 -1.454 33.2 315s 17 55.9 0.168 37.5 315s 18 59.2 2.180 40.1 315s 19 57.4 1.481 39.0 315s 20 60.4 0.743 41.9 315s 21 64.1 3.133 46.1 315s 22 71.7 4.116 52.5 315s > predict 315s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 315s 1 NA NA NA NA 315s 2 42.3 0.468 39.8 44.7 315s 3 45.9 0.543 43.4 48.5 315s 4 50.6 0.352 48.3 53.0 315s 5 51.0 0.407 48.6 53.4 315s 6 52.5 0.411 50.1 54.9 315s 7 NA NA NA NA 315s 8 54.8 0.340 52.4 57.1 315s 9 56.1 0.372 53.7 58.5 315s 10 58.3 0.387 55.9 60.6 315s 11 55.1 0.687 52.4 57.7 315s 12 51.4 0.558 48.9 54.0 315s 13 46.3 0.713 43.6 49.0 315s 14 46.0 0.599 43.4 48.6 315s 15 48.8 0.368 46.4 51.1 315s 16 51.3 0.326 48.9 53.6 315s 17 55.9 0.388 53.5 58.3 315s 18 59.2 0.319 56.8 61.5 315s 19 57.4 0.391 55.0 59.8 315s 20 60.4 0.457 57.9 62.8 315s 21 64.1 0.437 61.6 66.5 315s 22 71.7 0.674 69.0 74.3 315s Investment.pred Investment.se.fit Investment.lwr Investment.upr 315s 1 NA NA NA NA 315s 2 1.595 0.731 -1.8742 5.065 315s 3 1.746 0.533 -1.5566 5.050 315s 4 4.522 0.484 1.2530 7.791 315s 5 4.666 0.406 1.4458 7.887 315s 6 4.849 0.386 1.6390 8.058 315s 7 NA NA NA NA 315s 8 3.050 0.325 -0.1296 6.229 315s 9 2.524 0.467 -0.7334 5.782 315s 10 2.900 0.515 -0.3900 6.190 315s 11 1.962 0.769 -1.5438 5.467 315s 12 -2.592 0.608 -5.9519 0.769 315s 13 -5.102 0.774 -8.6129 -1.592 315s 14 -6.642 0.807 -10.1867 -3.098 315s 15 -2.845 0.395 -6.0599 0.370 315s 16 -1.454 0.341 -4.6409 1.733 315s 17 0.168 0.442 -3.0739 3.410 315s 18 2.180 0.281 -0.9807 5.340 315s 19 1.481 0.414 -1.7440 4.706 315s 20 0.743 0.492 -2.5310 4.017 315s 21 3.133 0.414 -0.0924 6.358 315s 22 4.116 0.583 0.7756 7.457 315s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 315s 1 NA NA NA NA 315s 2 26.7 0.322 24.9 28.6 315s 3 28.8 0.328 27.0 30.7 315s 4 32.7 0.340 30.8 34.5 315s 5 34.0 0.250 32.2 35.8 315s 6 35.7 0.257 33.9 37.5 315s 7 NA NA NA NA 315s 8 38.6 0.254 36.8 40.4 315s 9 38.9 0.241 37.1 40.7 315s 10 40.1 0.235 38.3 41.9 315s 11 38.3 0.325 36.5 40.2 315s 12 34.3 0.349 32.4 36.1 315s 13 29.3 0.425 27.4 31.2 315s 14 28.2 0.340 26.3 30.0 315s 15 30.3 0.326 28.5 32.2 315s 16 33.2 0.272 31.4 35.0 315s 17 37.5 0.273 35.7 39.3 315s 18 40.1 0.214 38.3 41.9 315s 19 39.0 0.336 37.1 40.8 315s 20 41.9 0.290 40.1 43.7 315s 21 46.1 0.305 44.2 47.9 315s 22 52.5 0.479 50.5 54.5 315s > model.frame 315s [1] TRUE 315s > model.matrix 315s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 315s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 315s [3] "Numeric: lengths (744, 720) differ" 315s > nobs 315s [1] 60 315s > linearHypothesis 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 49 315s 2 48 1 0.22 0.64 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 49 315s 2 48 1 0.29 0.59 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 49 315s 2 48 1 0.29 0.59 315s Linear hypothesis test (Theil's F test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 50 315s 2 48 2 0.29 0.75 315s Linear hypothesis test (F statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df F Pr(>F) 315s 1 50 315s 2 48 2 0.38 0.68 315s Linear hypothesis test (Chi^2 statistic of a Wald test) 315s 315s Hypothesis: 315s Consumption_corpProf + Investment_capitalLag = 0 315s Consumption_corpProfLag - PrivateWages_trend = 0 315s 315s Model 1: restricted model 315s Model 2: kleinModel 315s 315s Res.Df Df Chisq Pr(>Chisq) 315s 1 50 315s 2 48 2 0.77 0.68 315s > logLik 315s 'log Lik.' -71.9 (df=18) 315s 'log Lik.' -82.9 (df=18) 315s > 315s > # I3SLS 316s > summary 316s 316s systemfit results 316s method: iterated 3SLS 316s 316s convergence achieved after 22 iterations 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 60 48 107 0.47 0.946 0.996 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 20 16 18.1 1.13 1.063 0.981 0.977 316s Investment 20 16 76.4 4.77 2.185 0.672 0.610 316s PrivateWages 20 16 12.3 0.77 0.877 0.984 0.982 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 0.905 0.509 -0.437 316s Investment 0.509 3.819 0.709 316s PrivateWages -0.437 0.709 0.616 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 0.905 0.509 -0.437 316s Investment 0.509 3.819 0.709 316s PrivateWages -0.437 0.709 0.616 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.274 -0.585 316s Investment 0.274 1.000 0.462 316s PrivateWages -0.585 0.462 1.000 316s 316s 316s 3SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.4728 1.2187 13.52 3.6e-10 *** 316s corpProf 0.1642 0.0952 1.73 0.10 316s corpProfLag 0.1552 0.0903 1.72 0.11 316s wages 0.7756 0.0356 21.82 2.5e-13 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.063 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 18.095 MSE: 1.131 Root MSE: 1.063 316s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 316s 316s 316s 3SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 38.7938 9.7249 3.99 0.00106 ** 316s corpProf -0.2501 0.2337 -1.07 0.30036 316s corpProfLag 0.9129 0.2271 4.02 0.00099 *** 316s capitalLag -0.2409 0.0469 -5.14 9.9e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 2.185 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 76.371 MSE: 4.773 Root MSE: 2.185 316s Multiple R-Squared: 0.672 Adjusted R-Squared: 0.61 316s 316s 316s 3SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 2.4620 1.2228 2.01 0.061 . 316s gnp 0.3776 0.0318 11.88 2.4e-09 *** 316s gnpLag 0.1937 0.0331 5.85 2.5e-05 *** 316s trend 0.1619 0.0300 5.40 5.9e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.877 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 12.318 MSE: 0.77 Root MSE: 0.877 316s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.982 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.4522 -3.4485 -1.2596 316s 3 -1.1470 0.0027 0.5437 316s 4 -1.6147 0.0274 1.6290 316s 5 -0.6117 -2.0392 -0.0707 316s 6 -0.1229 0.0457 -0.1859 316s 7 NA NA NA 316s 8 1.2461 1.4658 -0.6304 316s 9 1.0158 1.4202 0.3924 316s 10 -0.6460 3.2062 1.3671 316s 11 -0.0554 -1.7386 -0.4891 316s 12 -0.3472 -1.3793 0.0179 316s 13 -0.3947 -2.2646 -0.6968 316s 14 0.6536 2.4092 0.1021 316s 15 0.0821 -0.2787 0.1482 316s 16 0.1381 0.1196 -0.0796 316s 17 1.8826 2.5548 -0.6862 316s 18 -0.3415 -0.4009 0.8755 316s 19 0.2296 -4.0454 -0.9839 316s 20 1.3178 1.4481 -0.1989 316s 21 1.0065 0.9087 -0.9681 316s 22 -1.8388 1.9868 1.1734 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.4 3.249 26.8 316s 3 46.1 1.897 28.8 316s 4 50.8 5.173 32.5 316s 5 51.2 5.039 34.0 316s 6 52.7 5.054 35.6 316s 7 NA NA NA 316s 8 55.0 2.734 38.5 316s 9 56.3 1.580 38.8 316s 10 58.4 1.894 39.9 316s 11 55.1 2.739 38.4 316s 12 51.2 -2.021 34.5 316s 13 46.0 -3.935 29.7 316s 14 45.8 -7.509 28.4 316s 15 48.6 -2.721 30.5 316s 16 51.2 -1.420 33.3 316s 17 55.8 -0.455 37.5 316s 18 59.0 2.401 40.1 316s 19 57.3 2.145 39.2 316s 20 60.3 -0.148 41.8 316s 21 64.0 2.391 46.0 316s 22 71.5 2.913 52.1 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.4 0.437 41.5 43.2 316s 3 46.1 0.492 45.2 47.1 316s 4 50.8 0.321 50.2 51.5 316s 5 51.2 0.369 50.5 52.0 316s 6 52.7 0.372 52.0 53.5 316s 7 NA NA NA NA 316s 8 55.0 0.310 54.3 55.6 316s 9 56.3 0.338 55.6 57.0 316s 10 58.4 0.355 57.7 59.2 316s 11 55.1 0.618 53.8 56.3 316s 12 51.2 0.501 50.2 52.3 316s 13 46.0 0.642 44.7 47.3 316s 14 45.8 0.547 44.7 46.9 316s 15 48.6 0.340 47.9 49.3 316s 16 51.2 0.300 50.6 51.8 316s 17 55.8 0.354 55.1 56.5 316s 18 59.0 0.294 58.4 59.6 316s 19 57.3 0.354 56.6 58.0 316s 20 60.3 0.418 59.4 61.1 316s 21 64.0 0.407 63.2 64.8 316s 22 71.5 0.628 70.3 72.8 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 3.249 1.160 0.91672 5.580 316s 3 1.897 0.934 0.02009 3.775 316s 4 5.173 0.803 3.55865 6.787 316s 5 5.039 0.693 3.64486 6.433 316s 6 5.054 0.674 3.69840 6.410 316s 7 NA NA NA NA 316s 8 2.734 0.584 1.56002 3.908 316s 9 1.580 0.783 0.00466 3.155 316s 10 1.894 0.868 0.14846 3.639 316s 11 2.739 1.321 0.08241 5.395 316s 12 -2.021 1.064 -4.16036 0.119 316s 13 -3.935 1.349 -6.64712 -1.224 316s 14 -7.509 1.360 -10.24349 -4.775 316s 15 -2.721 0.712 -4.15288 -1.290 316s 16 -1.420 0.614 -2.65412 -0.185 316s 17 -0.455 0.751 -1.96433 1.055 316s 18 2.401 0.498 1.39939 3.402 316s 19 2.145 0.698 0.74152 3.549 316s 20 -0.148 0.816 -1.78957 1.493 316s 21 2.391 0.713 0.95855 3.824 316s 22 2.913 0.984 0.93419 4.892 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.8 0.347 26.1 27.5 316s 3 28.8 0.348 28.1 29.5 316s 4 32.5 0.354 31.8 33.2 316s 5 34.0 0.263 33.4 34.5 316s 6 35.6 0.274 35.0 36.1 316s 7 NA NA NA NA 316s 8 38.5 0.268 38.0 39.1 316s 9 38.8 0.256 38.3 39.3 316s 10 39.9 0.254 39.4 40.4 316s 11 38.4 0.323 37.7 39.0 316s 12 34.5 0.347 33.8 35.2 316s 13 29.7 0.435 28.8 30.6 316s 14 28.4 0.366 27.7 29.1 316s 15 30.5 0.341 29.8 31.1 316s 16 33.3 0.285 32.7 33.9 316s 17 37.5 0.275 36.9 38.0 316s 18 40.1 0.233 39.7 40.6 316s 19 39.2 0.346 38.5 39.9 316s 20 41.8 0.298 41.2 42.4 316s 21 46.0 0.329 45.3 46.6 316s 22 52.1 0.510 51.1 53.2 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 316s [3] "Numeric: lengths (744, 720) differ" 316s > nobs 316s [1] 60 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 48 1 0.4 0.53 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 48 1 0.5 0.49 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 49 316s 2 48 1 0.5 0.48 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 50 316s 2 48 2 0.66 0.52 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 50 316s 2 48 2 0.83 0.44 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 50 316s 2 48 2 1.66 0.44 316s > logLik 316s 'log Lik.' -77.6 (df=18) 316s 'log Lik.' -92.7 (df=18) 316s > 316s > # OLS 316s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: OLS 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 61 49 44.5 0.382 0.977 0.99 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 20 16 17.48 1.093 1.04 0.981 0.978 316s Investment 21 17 17.32 1.019 1.01 0.931 0.919 316s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.124 0.034 -0.442 316s Investment 0.034 0.928 0.130 316s PrivateWages -0.442 0.130 0.563 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.0000 0.0266 -0.563 316s Investment 0.0266 1.0000 0.169 316s PrivateWages -0.5630 0.1689 1.000 316s 316s 316s OLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.1357 1.3571 11.89 2.4e-09 *** 316s corpProf 0.1994 0.0949 2.10 0.052 . 316s corpProfLag 0.0969 0.0944 1.03 0.320 316s wages 0.7940 0.0415 19.16 1.9e-12 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.045 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 17.481 MSE: 1.093 Root MSE: 1.045 316s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 316s 316s 316s OLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 10.1258 5.2164 1.94 0.06901 . 316s corpProf 0.4796 0.0927 5.17 7.6e-05 *** 316s corpProfLag 0.3330 0.0963 3.46 0.00299 ** 316s capitalLag -0.1118 0.0255 -4.38 0.00041 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.009 on 17 degrees of freedom 316s Number of observations: 21 Degrees of Freedom: 17 316s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 316s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 316s 316s 316s OLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3550 1.2591 1.08 0.2978 316s gnp 0.4417 0.0319 13.86 2.5e-10 *** 316s gnpLag 0.1466 0.0366 4.01 0.0010 ** 316s trend 0.1244 0.0323 3.85 0.0014 ** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.78 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 316s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 316s 316s compare coef with single-equation OLS 316s [1] TRUE 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.3304 -0.0668 -1.3389 316s 3 -1.2748 -0.0476 0.2462 316s 4 -1.6213 1.2467 1.1255 316s 5 -0.5661 -1.3512 -0.1959 316s 6 -0.0730 0.4154 -0.5284 316s 7 0.7915 1.4923 NA 316s 8 1.2648 0.7889 -0.7909 316s 9 0.9746 -0.6317 0.2819 316s 10 NA 1.0830 1.1384 316s 11 0.2225 0.2791 -0.1904 316s 12 -0.2256 0.0369 0.5813 316s 13 -0.2711 0.3659 0.1206 316s 14 0.3765 0.2237 0.4773 316s 15 -0.0349 -0.1728 0.3035 316s 16 -0.0243 0.0101 0.0284 316s 17 1.6023 0.9719 -0.8517 316s 18 -0.4658 0.0516 0.9908 316s 19 0.1914 -2.5656 -0.4597 316s 20 0.9683 -0.6866 -0.3819 316s 21 0.7325 -0.7807 -1.1062 316s 22 -2.2370 -0.6623 0.5501 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.2 -0.133 26.8 316s 3 46.3 1.948 29.1 316s 4 50.8 3.953 33.0 316s 5 51.2 4.351 34.1 316s 6 52.7 4.685 35.9 316s 7 54.3 4.108 NA 316s 8 54.9 3.411 38.7 316s 9 56.3 3.632 38.9 316s 10 NA 4.017 40.2 316s 11 54.8 0.721 38.1 316s 12 51.1 -3.437 33.9 316s 13 45.9 -6.566 28.9 316s 14 46.1 -5.324 28.0 316s 15 48.7 -2.827 30.3 316s 16 51.3 -1.310 33.2 316s 17 56.1 1.128 37.7 316s 18 59.2 1.948 40.0 316s 19 57.3 0.666 38.7 316s 20 60.6 1.987 42.0 316s 21 64.3 4.081 46.1 316s 22 71.9 5.562 52.7 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.2 0.478 39.9 44.5 316s 3 46.3 0.537 43.9 48.6 316s 4 50.8 0.364 48.6 53.0 316s 5 51.2 0.427 48.9 53.4 316s 6 52.7 0.433 50.4 54.9 316s 7 54.3 0.394 52.1 56.6 316s 8 54.9 0.360 52.7 57.2 316s 9 56.3 0.387 54.1 58.6 316s 10 NA NA NA NA 316s 11 54.8 0.635 52.3 57.2 316s 12 51.1 0.501 48.8 53.5 316s 13 45.9 0.656 43.4 48.4 316s 14 46.1 0.629 43.7 48.6 316s 15 48.7 0.389 46.5 51.0 316s 16 51.3 0.345 49.1 53.5 316s 17 56.1 0.379 53.9 58.3 316s 18 59.2 0.336 57.0 61.4 316s 19 57.3 0.385 55.1 59.5 316s 20 60.6 0.450 58.3 62.9 316s 21 64.3 0.448 62.0 66.6 316s 22 71.9 0.697 69.4 74.5 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 -0.133 0.579 -2.472 2.206 316s 3 1.948 0.476 -0.295 4.190 316s 4 3.953 0.428 1.750 6.157 316s 5 4.351 0.354 2.202 6.501 316s 6 4.685 0.333 2.548 6.821 316s 7 4.108 0.314 1.983 6.232 316s 8 3.411 0.279 1.306 5.516 316s 9 3.632 0.371 1.470 5.793 316s 10 4.017 0.426 1.815 6.219 316s 11 0.721 0.574 -1.613 3.054 316s 12 -3.437 0.484 -5.686 -1.188 316s 13 -6.566 0.588 -8.913 -4.219 316s 14 -5.324 0.662 -7.750 -2.898 316s 15 -2.827 0.356 -4.978 -0.676 316s 16 -1.310 0.305 -3.429 0.809 316s 17 1.128 0.332 -1.007 3.263 316s 18 1.948 0.232 -0.133 4.030 316s 19 0.666 0.298 -1.449 2.781 316s 20 1.987 0.350 -0.160 4.133 316s 21 4.081 0.317 1.955 6.207 316s 22 5.562 0.440 3.349 7.775 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.8 0.352 25.1 28.6 316s 3 29.1 0.355 27.3 30.8 316s 4 33.0 0.358 31.2 34.7 316s 5 34.1 0.277 32.4 35.8 316s 6 35.9 0.276 34.3 37.6 316s 7 NA NA NA NA 316s 8 38.7 0.282 37.0 40.4 316s 9 38.9 0.268 37.3 40.6 316s 10 40.2 0.255 38.5 41.8 316s 11 38.1 0.351 36.4 39.8 316s 12 33.9 0.355 32.2 35.6 316s 13 28.9 0.421 27.1 30.7 316s 14 28.0 0.370 26.3 29.8 316s 15 30.3 0.364 28.6 32.0 316s 16 33.2 0.304 31.5 34.9 316s 17 37.7 0.298 36.0 39.3 316s 18 40.0 0.233 38.4 41.6 316s 19 38.7 0.349 36.9 40.4 316s 20 42.0 0.314 40.3 43.7 316s 21 46.1 0.328 44.4 47.8 316s 22 52.7 0.494 50.9 54.6 316s > model.frame 316s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 316s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 316s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 316s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 316s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 316s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 316s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 316s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 316s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 316s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 316s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 316s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 316s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 316s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 316s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 316s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 316s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 316s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 316s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 316s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 316s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 316s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 316s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 316s trend 316s 1 -11 316s 2 -10 316s 3 -9 316s 4 -8 316s 5 -7 316s 6 -6 316s 7 -5 316s 8 -4 316s 9 -3 316s 10 -2 316s 11 -1 316s 12 0 316s 13 1 316s 14 2 316s 15 3 316s 16 4 316s 17 5 316s 18 6 316s 19 7 316s 20 8 316s 21 9 316s 22 10 316s > model.matrix 316s Consumption_(Intercept) Consumption_corpProf 316s Consumption_2 1 12.4 316s Consumption_3 1 16.9 316s Consumption_4 1 18.4 316s Consumption_5 1 19.4 316s Consumption_6 1 20.1 316s Consumption_7 1 19.6 316s Consumption_8 1 19.8 316s Consumption_9 1 21.1 316s Consumption_11 1 15.6 316s Consumption_12 1 11.4 316s Consumption_13 1 7.0 316s Consumption_14 1 11.2 316s Consumption_15 1 12.3 316s Consumption_16 1 14.0 316s Consumption_17 1 17.6 316s Consumption_18 1 17.3 316s Consumption_19 1 15.3 316s Consumption_20 1 19.0 316s Consumption_21 1 21.1 316s Consumption_22 1 23.5 316s Investment_2 0 0.0 316s Investment_3 0 0.0 316s Investment_4 0 0.0 316s Investment_5 0 0.0 316s Investment_6 0 0.0 316s Investment_7 0 0.0 316s Investment_8 0 0.0 316s Investment_9 0 0.0 316s Investment_10 0 0.0 316s Investment_11 0 0.0 316s Investment_12 0 0.0 316s Investment_13 0 0.0 316s Investment_14 0 0.0 316s Investment_15 0 0.0 316s Investment_16 0 0.0 316s Investment_17 0 0.0 316s Investment_18 0 0.0 316s Investment_19 0 0.0 316s Investment_20 0 0.0 316s Investment_21 0 0.0 316s Investment_22 0 0.0 316s PrivateWages_2 0 0.0 316s PrivateWages_3 0 0.0 316s PrivateWages_4 0 0.0 316s PrivateWages_5 0 0.0 316s PrivateWages_6 0 0.0 316s PrivateWages_8 0 0.0 316s PrivateWages_9 0 0.0 316s PrivateWages_10 0 0.0 316s PrivateWages_11 0 0.0 316s PrivateWages_12 0 0.0 316s PrivateWages_13 0 0.0 316s PrivateWages_14 0 0.0 316s PrivateWages_15 0 0.0 316s PrivateWages_16 0 0.0 316s PrivateWages_17 0 0.0 316s PrivateWages_18 0 0.0 316s PrivateWages_19 0 0.0 316s PrivateWages_20 0 0.0 316s PrivateWages_21 0 0.0 316s PrivateWages_22 0 0.0 316s Consumption_corpProfLag Consumption_wages 316s Consumption_2 12.7 28.2 316s Consumption_3 12.4 32.2 316s Consumption_4 16.9 37.0 316s Consumption_5 18.4 37.0 316s Consumption_6 19.4 38.6 316s Consumption_7 20.1 40.7 316s Consumption_8 19.6 41.5 316s Consumption_9 19.8 42.9 316s Consumption_11 21.7 42.1 316s Consumption_12 15.6 39.3 316s Consumption_13 11.4 34.3 316s Consumption_14 7.0 34.1 316s Consumption_15 11.2 36.6 316s Consumption_16 12.3 39.3 316s Consumption_17 14.0 44.2 316s Consumption_18 17.6 47.7 316s Consumption_19 17.3 45.9 316s Consumption_20 15.3 49.4 316s Consumption_21 19.0 53.0 316s Consumption_22 21.1 61.8 316s Investment_2 0.0 0.0 316s Investment_3 0.0 0.0 316s Investment_4 0.0 0.0 316s Investment_5 0.0 0.0 316s Investment_6 0.0 0.0 316s Investment_7 0.0 0.0 316s Investment_8 0.0 0.0 316s Investment_9 0.0 0.0 316s Investment_10 0.0 0.0 316s Investment_11 0.0 0.0 316s Investment_12 0.0 0.0 316s Investment_13 0.0 0.0 316s Investment_14 0.0 0.0 316s Investment_15 0.0 0.0 316s Investment_16 0.0 0.0 316s Investment_17 0.0 0.0 316s Investment_18 0.0 0.0 316s Investment_19 0.0 0.0 316s Investment_20 0.0 0.0 316s Investment_21 0.0 0.0 316s Investment_22 0.0 0.0 316s PrivateWages_2 0.0 0.0 316s PrivateWages_3 0.0 0.0 316s PrivateWages_4 0.0 0.0 316s PrivateWages_5 0.0 0.0 316s PrivateWages_6 0.0 0.0 316s PrivateWages_8 0.0 0.0 316s PrivateWages_9 0.0 0.0 316s PrivateWages_10 0.0 0.0 316s PrivateWages_11 0.0 0.0 316s PrivateWages_12 0.0 0.0 316s PrivateWages_13 0.0 0.0 316s PrivateWages_14 0.0 0.0 316s PrivateWages_15 0.0 0.0 316s PrivateWages_16 0.0 0.0 316s PrivateWages_17 0.0 0.0 316s PrivateWages_18 0.0 0.0 316s PrivateWages_19 0.0 0.0 316s PrivateWages_20 0.0 0.0 316s PrivateWages_21 0.0 0.0 316s PrivateWages_22 0.0 0.0 316s Investment_(Intercept) Investment_corpProf 316s Consumption_2 0 0.0 316s Consumption_3 0 0.0 316s Consumption_4 0 0.0 316s Consumption_5 0 0.0 316s Consumption_6 0 0.0 316s Consumption_7 0 0.0 316s Consumption_8 0 0.0 316s Consumption_9 0 0.0 316s Consumption_11 0 0.0 316s Consumption_12 0 0.0 316s Consumption_13 0 0.0 316s Consumption_14 0 0.0 316s Consumption_15 0 0.0 316s Consumption_16 0 0.0 316s Consumption_17 0 0.0 316s Consumption_18 0 0.0 316s Consumption_19 0 0.0 316s Consumption_20 0 0.0 316s Consumption_21 0 0.0 316s Consumption_22 0 0.0 316s Investment_2 1 12.4 316s Investment_3 1 16.9 316s Investment_4 1 18.4 316s Investment_5 1 19.4 316s Investment_6 1 20.1 316s Investment_7 1 19.6 316s Investment_8 1 19.8 316s Investment_9 1 21.1 316s Investment_10 1 21.7 316s Investment_11 1 15.6 316s Investment_12 1 11.4 316s Investment_13 1 7.0 316s Investment_14 1 11.2 316s Investment_15 1 12.3 316s Investment_16 1 14.0 316s Investment_17 1 17.6 316s Investment_18 1 17.3 316s Investment_19 1 15.3 316s Investment_20 1 19.0 316s Investment_21 1 21.1 316s Investment_22 1 23.5 316s PrivateWages_2 0 0.0 316s PrivateWages_3 0 0.0 316s PrivateWages_4 0 0.0 316s PrivateWages_5 0 0.0 316s PrivateWages_6 0 0.0 316s PrivateWages_8 0 0.0 316s PrivateWages_9 0 0.0 316s PrivateWages_10 0 0.0 316s PrivateWages_11 0 0.0 316s PrivateWages_12 0 0.0 316s PrivateWages_13 0 0.0 316s PrivateWages_14 0 0.0 316s PrivateWages_15 0 0.0 316s PrivateWages_16 0 0.0 316s PrivateWages_17 0 0.0 316s PrivateWages_18 0 0.0 316s PrivateWages_19 0 0.0 316s PrivateWages_20 0 0.0 316s PrivateWages_21 0 0.0 316s PrivateWages_22 0 0.0 316s Investment_corpProfLag Investment_capitalLag 316s Consumption_2 0.0 0 316s Consumption_3 0.0 0 316s Consumption_4 0.0 0 316s Consumption_5 0.0 0 316s Consumption_6 0.0 0 316s Consumption_7 0.0 0 316s Consumption_8 0.0 0 316s Consumption_9 0.0 0 316s Consumption_11 0.0 0 316s Consumption_12 0.0 0 316s Consumption_13 0.0 0 316s Consumption_14 0.0 0 316s Consumption_15 0.0 0 316s Consumption_16 0.0 0 316s Consumption_17 0.0 0 316s Consumption_18 0.0 0 316s Consumption_19 0.0 0 316s Consumption_20 0.0 0 316s Consumption_21 0.0 0 316s Consumption_22 0.0 0 316s Investment_2 12.7 183 316s Investment_3 12.4 183 316s Investment_4 16.9 184 316s Investment_5 18.4 190 316s Investment_6 19.4 193 316s Investment_7 20.1 198 316s Investment_8 19.6 203 316s Investment_9 19.8 208 316s Investment_10 21.1 211 316s Investment_11 21.7 216 316s Investment_12 15.6 217 316s Investment_13 11.4 213 316s Investment_14 7.0 207 316s Investment_15 11.2 202 316s Investment_16 12.3 199 316s Investment_17 14.0 198 316s Investment_18 17.6 200 316s Investment_19 17.3 202 316s Investment_20 15.3 200 316s Investment_21 19.0 201 316s Investment_22 21.1 204 316s PrivateWages_2 0.0 0 316s PrivateWages_3 0.0 0 316s PrivateWages_4 0.0 0 316s PrivateWages_5 0.0 0 316s PrivateWages_6 0.0 0 316s PrivateWages_8 0.0 0 316s PrivateWages_9 0.0 0 316s PrivateWages_10 0.0 0 316s PrivateWages_11 0.0 0 316s PrivateWages_12 0.0 0 316s PrivateWages_13 0.0 0 316s PrivateWages_14 0.0 0 316s PrivateWages_15 0.0 0 316s PrivateWages_16 0.0 0 316s PrivateWages_17 0.0 0 316s PrivateWages_18 0.0 0 316s PrivateWages_19 0.0 0 316s PrivateWages_20 0.0 0 316s PrivateWages_21 0.0 0 316s PrivateWages_22 0.0 0 316s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 316s Consumption_2 0 0.0 0.0 316s Consumption_3 0 0.0 0.0 316s Consumption_4 0 0.0 0.0 316s Consumption_5 0 0.0 0.0 316s Consumption_6 0 0.0 0.0 316s Consumption_7 0 0.0 0.0 316s Consumption_8 0 0.0 0.0 316s Consumption_9 0 0.0 0.0 316s Consumption_11 0 0.0 0.0 316s Consumption_12 0 0.0 0.0 316s Consumption_13 0 0.0 0.0 316s Consumption_14 0 0.0 0.0 316s Consumption_15 0 0.0 0.0 316s Consumption_16 0 0.0 0.0 316s Consumption_17 0 0.0 0.0 316s Consumption_18 0 0.0 0.0 316s Consumption_19 0 0.0 0.0 316s Consumption_20 0 0.0 0.0 316s Consumption_21 0 0.0 0.0 316s Consumption_22 0 0.0 0.0 316s Investment_2 0 0.0 0.0 316s Investment_3 0 0.0 0.0 316s Investment_4 0 0.0 0.0 316s Investment_5 0 0.0 0.0 316s Investment_6 0 0.0 0.0 316s Investment_7 0 0.0 0.0 316s Investment_8 0 0.0 0.0 316s Investment_9 0 0.0 0.0 316s Investment_10 0 0.0 0.0 316s Investment_11 0 0.0 0.0 316s Investment_12 0 0.0 0.0 316s Investment_13 0 0.0 0.0 316s Investment_14 0 0.0 0.0 316s Investment_15 0 0.0 0.0 316s Investment_16 0 0.0 0.0 316s Investment_17 0 0.0 0.0 316s Investment_18 0 0.0 0.0 316s Investment_19 0 0.0 0.0 316s Investment_20 0 0.0 0.0 316s Investment_21 0 0.0 0.0 316s Investment_22 0 0.0 0.0 316s PrivateWages_2 1 45.6 44.9 316s PrivateWages_3 1 50.1 45.6 316s PrivateWages_4 1 57.2 50.1 316s PrivateWages_5 1 57.1 57.2 316s PrivateWages_6 1 61.0 57.1 316s PrivateWages_8 1 64.4 64.0 316s PrivateWages_9 1 64.5 64.4 316s PrivateWages_10 1 67.0 64.5 316s PrivateWages_11 1 61.2 67.0 316s PrivateWages_12 1 53.4 61.2 316s PrivateWages_13 1 44.3 53.4 316s PrivateWages_14 1 45.1 44.3 316s PrivateWages_15 1 49.7 45.1 316s PrivateWages_16 1 54.4 49.7 316s PrivateWages_17 1 62.7 54.4 316s PrivateWages_18 1 65.0 62.7 316s PrivateWages_19 1 60.9 65.0 316s PrivateWages_20 1 69.5 60.9 316s PrivateWages_21 1 75.7 69.5 316s PrivateWages_22 1 88.4 75.7 316s PrivateWages_trend 316s Consumption_2 0 316s Consumption_3 0 316s Consumption_4 0 316s Consumption_5 0 316s Consumption_6 0 316s Consumption_7 0 316s Consumption_8 0 316s Consumption_9 0 316s Consumption_11 0 316s Consumption_12 0 316s Consumption_13 0 316s Consumption_14 0 316s Consumption_15 0 316s Consumption_16 0 316s Consumption_17 0 316s Consumption_18 0 316s Consumption_19 0 316s Consumption_20 0 316s Consumption_21 0 316s Consumption_22 0 316s Investment_2 0 316s Investment_3 0 316s Investment_4 0 316s Investment_5 0 316s Investment_6 0 316s Investment_7 0 316s Investment_8 0 316s Investment_9 0 316s Investment_10 0 316s Investment_11 0 316s Investment_12 0 316s Investment_13 0 316s Investment_14 0 316s Investment_15 0 316s Investment_16 0 316s Investment_17 0 316s Investment_18 0 316s Investment_19 0 316s Investment_20 0 316s Investment_21 0 316s Investment_22 0 316s PrivateWages_2 -10 316s PrivateWages_3 -9 316s PrivateWages_4 -8 316s PrivateWages_5 -7 316s PrivateWages_6 -6 316s PrivateWages_8 -4 316s PrivateWages_9 -3 316s PrivateWages_10 -2 316s PrivateWages_11 -1 316s PrivateWages_12 0 316s PrivateWages_13 1 316s PrivateWages_14 2 316s PrivateWages_15 3 316s PrivateWages_16 4 316s PrivateWages_17 5 316s PrivateWages_18 6 316s PrivateWages_19 7 316s PrivateWages_20 8 316s PrivateWages_21 9 316s PrivateWages_22 10 316s > nobs 316s [1] 61 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 50 316s 2 49 1 0.87 0.35 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 50 316s 2 49 1 0.8 0.38 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 50 316s 2 49 1 0.8 0.37 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 51 316s 2 49 2 0.48 0.62 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 51 316s 2 49 2 0.43 0.65 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 51 316s 2 49 2 0.87 0.65 316s > logLik 316s 'log Lik.' -71.7 (df=13) 316s 'log Lik.' -76.1 (df=13) 316s compare log likelihood value with single-equation OLS 316s [1] "Mean relative difference: 0.00159" 316s > 316s > # 2SLS 316s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: 2SLS 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 59 47 53.2 0.251 0.973 0.991 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 19 15 20.49 1.366 1.17 0.978 0.973 316s Investment 20 16 23.02 1.438 1.20 0.901 0.883 316s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.079 0.354 -0.383 316s Investment 0.354 1.047 0.107 316s PrivateWages -0.383 0.107 0.445 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.335 -0.556 316s Investment 0.335 1.000 0.149 316s PrivateWages -0.556 0.149 1.000 316s 316s 316s 2SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.4657 1.3505 12.19 3.5e-09 *** 316s corpProf 0.0243 0.1180 0.21 0.839 316s corpProfLag 0.1981 0.1087 1.82 0.088 . 316s wages 0.8159 0.0420 19.45 4.7e-12 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.169 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 20.493 MSE: 1.366 Root MSE: 1.169 316s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.973 316s 316s 316s 2SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 17.8425 6.5319 2.73 0.01478 * 316s corpProf 0.2167 0.1478 1.47 0.16189 316s corpProfLag 0.5416 0.1415 3.83 0.00149 ** 316s capitalLag -0.1455 0.0314 -4.63 0.00028 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.199 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 316s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 316s 316s 316s 2SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3431 1.1250 1.19 0.24995 316s gnp 0.4438 0.0342 12.97 6.6e-10 *** 316s gnpLag 0.1447 0.0371 3.90 0.00128 ** 316s trend 0.1238 0.0292 4.24 0.00063 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.78 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 316s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.39161 -1.0104 -1.3401 316s 3 -0.60524 0.2478 0.2378 316s 4 -1.24952 1.0621 1.1117 316s 5 -0.17101 -1.4104 -0.1954 316s 6 0.30841 0.4328 -0.5355 316s 7 NA NA NA 316s 8 1.50999 1.0463 -0.7908 316s 9 1.39649 0.0674 0.2831 316s 10 NA 1.7698 1.1353 316s 11 -0.49339 -0.5912 -0.1765 316s 12 -0.99824 -0.6318 0.6007 316s 13 -1.27965 -0.6983 0.1443 316s 14 0.55302 0.9724 0.4826 316s 15 -0.14553 -0.1827 0.3016 316s 16 -0.00773 0.1167 0.0261 316s 17 1.97001 1.6266 -0.8614 316s 18 -0.59152 -0.0525 0.9927 316s 19 -0.21481 -3.0656 -0.4446 316s 20 1.33575 0.1393 -0.3914 316s 21 1.01443 -0.1305 -1.1115 316s 22 -1.93986 0.2922 0.5312 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.3 0.810 26.8 316s 3 45.6 1.652 29.1 316s 4 50.4 4.138 33.0 316s 5 50.8 4.410 34.1 316s 6 52.3 4.667 35.9 316s 7 NA NA NA 316s 8 54.7 3.154 38.7 316s 9 55.9 2.933 38.9 316s 10 NA 3.330 40.2 316s 11 55.5 1.591 38.1 316s 12 51.9 -2.768 33.9 316s 13 46.9 -5.502 28.9 316s 14 45.9 -6.072 28.0 316s 15 48.8 -2.817 30.3 316s 16 51.3 -1.417 33.2 316s 17 55.7 0.473 37.7 316s 18 59.3 2.053 40.0 316s 19 57.7 1.166 38.6 316s 20 60.3 1.161 42.0 316s 21 64.0 3.431 46.1 316s 22 71.6 4.608 52.8 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.3 0.483 41.3 43.3 316s 3 45.6 0.586 44.4 46.9 316s 4 50.4 0.390 49.6 51.3 316s 5 50.8 0.456 49.8 51.7 316s 6 52.3 0.463 51.3 53.3 316s 7 NA NA NA NA 316s 8 54.7 0.382 53.9 55.5 316s 9 55.9 0.422 55.0 56.8 316s 10 NA NA NA NA 316s 11 55.5 0.742 53.9 57.1 316s 12 51.9 0.600 50.6 53.2 316s 13 46.9 0.770 45.2 48.5 316s 14 45.9 0.635 44.6 47.3 316s 15 48.8 0.383 48.0 49.7 316s 16 51.3 0.339 50.6 52.0 316s 17 55.7 0.410 54.9 56.6 316s 18 59.3 0.336 58.6 60.0 316s 19 57.7 0.418 56.8 58.6 316s 20 60.3 0.481 59.2 61.3 316s 21 64.0 0.462 63.0 65.0 316s 22 71.6 0.706 70.1 73.1 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 0.810 0.750 -0.77956 2.400 316s 3 1.652 0.516 0.55883 2.746 316s 4 4.138 0.487 3.10541 5.170 316s 5 4.410 0.402 3.55860 5.262 316s 6 4.667 0.377 3.86830 5.466 316s 7 NA NA NA NA 316s 8 3.154 0.312 2.49238 3.815 316s 9 2.933 0.466 1.94478 3.920 316s 10 3.330 0.512 2.24435 4.416 316s 11 1.591 0.749 0.00249 3.180 316s 12 -2.768 0.586 -4.01111 -1.525 316s 13 -5.502 0.750 -7.09222 -3.911 316s 14 -6.072 0.803 -7.77404 -4.371 316s 15 -2.817 0.379 -3.62002 -2.015 316s 16 -1.417 0.327 -2.10985 -0.723 316s 17 0.473 0.436 -0.45046 1.397 316s 18 2.053 0.272 1.47523 2.630 316s 19 1.166 0.410 0.29710 2.034 316s 20 1.161 0.491 0.12044 2.201 316s 21 3.431 0.406 2.57004 4.291 316s 22 4.608 0.578 3.38197 5.834 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.8 0.313 26.2 27.5 316s 3 29.1 0.325 28.4 29.8 316s 4 33.0 0.344 32.3 33.7 316s 5 34.1 0.246 33.6 34.6 316s 6 35.9 0.254 35.4 36.5 316s 7 NA NA NA NA 316s 8 38.7 0.251 38.2 39.2 316s 9 38.9 0.239 38.4 39.4 316s 10 40.2 0.229 39.7 40.7 316s 11 38.1 0.339 37.4 38.8 316s 12 33.9 0.365 33.1 34.7 316s 13 28.9 0.436 27.9 29.8 316s 14 28.0 0.333 27.3 28.7 316s 15 30.3 0.324 29.6 31.0 316s 16 33.2 0.271 32.6 33.7 316s 17 37.7 0.280 37.1 38.3 316s 18 40.0 0.208 39.6 40.4 316s 19 38.6 0.342 37.9 39.4 316s 20 42.0 0.293 41.4 42.6 316s 21 46.1 0.296 45.5 46.7 316s 22 52.8 0.474 51.8 53.8 316s > model.frame 316s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 316s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 316s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 316s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 316s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 316s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 316s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 316s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 316s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 316s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 316s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 316s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 316s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 316s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 316s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 316s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 316s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 316s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 316s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 316s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 316s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 316s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 316s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 316s trend 316s 1 -11 316s 2 -10 316s 3 -9 316s 4 -8 316s 5 -7 316s 6 -6 316s 7 -5 316s 8 -4 316s 9 -3 316s 10 -2 316s 11 -1 316s 12 0 316s 13 1 316s 14 2 316s 15 3 316s 16 4 316s 17 5 316s 18 6 316s 19 7 316s 20 8 316s 21 9 316s 22 10 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 316s [3] "Numeric: lengths (732, 708) differ" 316s > nobs 316s [1] 59 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.87 0.36 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.98 0.33 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 48 316s 2 47 1 0.98 0.32 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 0.43 0.65 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 0.49 0.61 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 49 316s 2 47 2 0.98 0.61 316s > logLik 316s 'log Lik.' -71.5 (df=13) 316s 'log Lik.' -78.7 (df=13) 316s > 316s > # SUR 316s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: SUR 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 61 49 45.4 0.151 0.977 0.992 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 20 16 17.6 1.102 1.050 0.981 0.977 316s Investment 21 17 17.5 1.029 1.015 0.931 0.918 316s PrivateWages 20 16 10.3 0.643 0.802 0.987 0.985 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 0.8871 0.0268 -0.349 316s Investment 0.0268 0.7328 0.103 316s PrivateWages -0.3492 0.1029 0.444 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 0.8852 0.0508 -0.406 316s Investment 0.0508 0.7313 0.161 316s PrivateWages -0.4063 0.1609 0.467 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.065 -0.635 316s Investment 0.065 1.000 0.262 316s PrivateWages -0.635 0.262 1.000 316s 316s 316s SUR estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.0876 1.2010 13.39 4.1e-10 *** 316s corpProf 0.2173 0.0799 2.72 0.015 * 316s corpProfLag 0.0694 0.0793 0.88 0.394 316s wages 0.7975 0.0360 22.15 2.0e-13 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.05 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 17.63 MSE: 1.102 Root MSE: 1.05 316s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 316s 316s 316s SUR estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 12.3518 4.5615 2.71 0.01493 * 316s corpProf 0.4511 0.0814 5.54 3.6e-05 *** 316s corpProfLag 0.3570 0.0846 4.22 0.00058 *** 316s capitalLag -0.1225 0.0223 -5.49 4.0e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.015 on 17 degrees of freedom 316s Number of observations: 21 Degrees of Freedom: 17 316s SSR: 17.5 MSE: 1.029 Root MSE: 1.015 316s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 316s 316s 316s SUR estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3964 1.0825 1.29 0.22 316s gnp 0.4177 0.0269 15.55 4.4e-11 *** 316s gnpLag 0.1709 0.0306 5.59 4.0e-05 *** 316s trend 0.1467 0.0272 5.40 5.9e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.802 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 10.284 MSE: 0.643 Root MSE: 0.802 316s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.2529 -0.2920 -1.15193 316s 3 -1.2998 -0.1392 0.50193 316s 4 -1.5662 1.1106 1.42026 316s 5 -0.4876 -1.4391 -0.09801 316s 6 0.0149 0.3556 -0.35678 316s 7 0.9002 1.4558 NA 316s 8 1.3535 0.8299 -0.74964 316s 9 1.0406 -0.5136 0.29355 316s 10 NA 1.2191 1.18544 316s 11 0.4417 0.2810 -0.36558 316s 12 -0.0892 0.0754 0.33733 316s 13 -0.1541 0.3429 -0.17490 316s 14 0.2984 0.3597 0.39941 316s 15 -0.0260 -0.1602 0.29441 316s 16 -0.0250 0.0130 -0.00177 316s 17 1.5671 1.0231 -0.81891 316s 18 -0.4089 0.0306 0.85516 316s 19 0.2819 -2.6153 -0.77184 316s 20 0.9257 -0.6030 -0.41040 316s 21 0.7415 -0.7118 -1.21679 316s 22 -2.2437 -0.5398 0.57166 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.2 0.092 26.7 316s 3 46.3 2.039 28.8 316s 4 50.8 4.089 32.7 316s 5 51.1 4.439 34.0 316s 6 52.6 4.744 35.8 316s 7 54.2 4.144 NA 316s 8 54.8 3.370 38.6 316s 9 56.3 3.514 38.9 316s 10 NA 3.881 40.1 316s 11 54.6 0.719 38.3 316s 12 51.0 -3.475 34.2 316s 13 45.8 -6.543 29.2 316s 14 46.2 -5.460 28.1 316s 15 48.7 -2.840 30.3 316s 16 51.3 -1.313 33.2 316s 17 56.1 1.077 37.6 316s 18 59.1 1.969 40.1 316s 19 57.2 0.715 39.0 316s 20 60.7 1.903 42.0 316s 21 64.3 4.012 46.2 316s 22 71.9 5.440 52.7 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.2 0.422 41.3 43.0 316s 3 46.3 0.462 45.4 47.2 316s 4 50.8 0.309 50.1 51.4 316s 5 51.1 0.359 50.4 51.8 316s 6 52.6 0.362 51.9 53.3 316s 7 54.2 0.328 53.5 54.9 316s 8 54.8 0.300 54.2 55.4 316s 9 56.3 0.323 55.6 56.9 316s 10 NA NA NA NA 316s 11 54.6 0.531 53.5 55.6 316s 12 51.0 0.427 50.1 51.8 316s 13 45.8 0.564 44.6 46.9 316s 14 46.2 0.543 45.1 47.3 316s 15 48.7 0.341 48.0 49.4 316s 16 51.3 0.302 50.7 51.9 316s 17 56.1 0.328 55.5 56.8 316s 18 59.1 0.294 58.5 59.7 316s 19 57.2 0.332 56.6 57.9 316s 20 60.7 0.392 59.9 61.5 316s 21 64.3 0.394 63.5 65.0 316s 22 71.9 0.615 70.7 73.2 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 0.092 0.508 -0.929 1.113 316s 3 2.039 0.421 1.193 2.885 316s 4 4.089 0.376 3.333 4.846 316s 5 4.439 0.311 3.813 5.065 316s 6 4.744 0.294 4.154 5.335 316s 7 4.144 0.277 3.587 4.701 316s 8 3.370 0.247 2.873 3.867 316s 9 3.514 0.328 2.855 4.172 316s 10 3.881 0.376 3.126 4.636 316s 11 0.719 0.508 -0.301 1.739 316s 12 -3.475 0.428 -4.336 -2.615 316s 13 -6.543 0.521 -7.590 -5.496 316s 14 -5.460 0.583 -6.632 -4.288 316s 15 -2.840 0.316 -3.474 -2.205 316s 16 -1.313 0.271 -1.857 -0.769 316s 17 1.077 0.293 0.488 1.666 316s 18 1.969 0.205 1.557 2.382 316s 19 0.715 0.263 0.187 1.244 316s 20 1.903 0.309 1.283 2.523 316s 21 4.012 0.280 3.449 4.574 316s 22 5.440 0.389 4.659 6.221 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.7 0.306 26.0 27.3 316s 3 28.8 0.305 28.2 29.4 316s 4 32.7 0.302 32.1 33.3 316s 5 34.0 0.231 33.5 34.5 316s 6 35.8 0.230 35.3 36.2 316s 7 NA NA NA NA 316s 8 38.6 0.233 38.2 39.1 316s 9 38.9 0.222 38.5 39.4 316s 10 40.1 0.213 39.7 40.5 316s 11 38.3 0.292 37.7 38.9 316s 12 34.2 0.300 33.6 34.8 316s 13 29.2 0.361 28.4 29.9 316s 14 28.1 0.322 27.5 28.7 316s 15 30.3 0.314 29.7 30.9 316s 16 33.2 0.263 32.7 33.7 316s 17 37.6 0.256 37.1 38.1 316s 18 40.1 0.204 39.7 40.6 316s 19 39.0 0.298 38.4 39.6 316s 20 42.0 0.272 41.5 42.6 316s 21 46.2 0.288 45.6 46.8 316s 22 52.7 0.431 51.9 53.6 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] TRUE 316s > nobs 316s [1] 61 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 50 316s 2 49 1 1.01 0.32 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 50 316s 2 49 1 1.3 0.26 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 50 316s 2 49 1 1.3 0.25 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 51 316s 2 49 2 0.53 0.59 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 51 316s 2 49 2 0.69 0.51 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 51 316s 2 49 2 1.38 0.5 316s > logLik 316s 'log Lik.' -69.6 (df=18) 316s 'log Lik.' -76.9 (df=18) 316s > 316s > # 3SLS 316s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: 3SLS 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 59 47 59.5 0.241 0.97 0.994 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 19 15 18.1 1.203 1.097 0.980 0.977 316s Investment 20 16 31.1 1.945 1.395 0.866 0.841 316s PrivateWages 20 16 10.3 0.645 0.803 0.987 0.985 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 1.079 0.354 -0.383 316s Investment 0.354 1.047 0.107 316s PrivateWages -0.383 0.107 0.445 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 0.950 0.324 -0.395 316s Investment 0.324 1.385 0.242 316s PrivateWages -0.395 0.242 0.475 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.293 -0.582 316s Investment 0.293 1.000 0.292 316s PrivateWages -0.582 0.292 1.000 316s 316s 316s 3SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.5606 1.3295 12.46 2.6e-09 *** 316s corpProf 0.1100 0.1098 1.00 0.33 316s corpProfLag 0.1155 0.1007 1.15 0.27 316s wages 0.8086 0.0401 20.18 2.8e-12 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.097 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 18.051 MSE: 1.203 Root MSE: 1.097 316s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 316s 316s 316s 3SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 23.6871 6.1159 3.87 0.00135 ** 316s corpProf 0.1072 0.1414 0.76 0.45918 316s corpProfLag 0.6278 0.1361 4.61 0.00029 *** 316s capitalLag -0.1726 0.0295 -5.85 2.5e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.395 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 31.126 MSE: 1.945 Root MSE: 1.395 316s Multiple R-Squared: 0.866 Adjusted R-Squared: 0.841 316s 316s 316s 3SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3603 1.0927 1.24 0.23109 316s gnp 0.4117 0.0315 13.06 6.0e-10 *** 316s gnpLag 0.1782 0.0336 5.31 7.1e-05 *** 316s trend 0.1370 0.0280 4.89 0.00016 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.803 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 10.318 MSE: 0.645 Root MSE: 0.803 316s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.29542 -1.636 -1.2658 316s 3 -0.89033 0.135 0.4198 316s 4 -1.25669 0.777 1.3578 316s 5 -0.14000 -1.574 -0.2036 316s 6 0.37365 0.341 -0.4283 316s 7 NA NA NA 316s 8 1.63850 1.194 -0.8319 316s 9 1.44030 0.454 0.2186 316s 10 NA 2.192 1.1346 316s 11 0.17274 -0.750 -0.4603 316s 12 -0.49629 -0.698 0.2476 316s 13 -0.78384 -0.976 -0.2528 316s 14 0.32420 1.365 0.4028 316s 15 -0.10364 -0.170 0.3295 316s 16 -0.00105 0.140 0.0377 316s 17 1.84421 1.862 -0.7540 316s 18 -0.36893 -0.103 0.8827 316s 19 0.14129 -3.255 -0.7764 316s 20 1.23511 0.475 -0.3230 316s 21 1.06553 0.152 -1.1453 316s 22 -1.85709 0.746 0.6843 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.2 1.436 26.8 316s 3 45.9 1.765 28.9 316s 4 50.5 4.423 32.7 316s 5 50.7 4.574 34.1 316s 6 52.2 4.759 35.8 316s 7 NA NA NA 316s 8 54.6 3.006 38.7 316s 9 55.9 2.546 39.0 316s 10 NA 2.908 40.2 316s 11 54.8 1.750 38.4 316s 12 51.4 -2.702 34.3 316s 13 46.4 -5.224 29.3 316s 14 46.2 -6.465 28.1 316s 15 48.8 -2.830 30.3 316s 16 51.3 -1.440 33.2 316s 17 55.9 0.238 37.6 316s 18 59.1 2.103 40.1 316s 19 57.4 1.355 39.0 316s 20 60.4 0.825 41.9 316s 21 63.9 3.148 46.1 316s 22 71.6 4.154 52.6 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.2 0.475 39.6 44.7 316s 3 45.9 0.557 43.3 48.5 316s 4 50.5 0.372 48.0 52.9 316s 5 50.7 0.433 48.2 53.3 316s 6 52.2 0.438 49.7 54.7 316s 7 NA NA NA NA 316s 8 54.6 0.362 52.1 57.0 316s 9 55.9 0.401 53.4 58.3 316s 10 NA NA NA NA 316s 11 54.8 0.684 52.1 57.6 316s 12 51.4 0.563 48.8 54.0 316s 13 46.4 0.733 43.6 49.2 316s 14 46.2 0.612 43.5 48.9 316s 15 48.8 0.379 46.3 51.3 316s 16 51.3 0.334 48.9 53.7 316s 17 55.9 0.394 53.4 58.3 316s 18 59.1 0.322 56.6 61.5 316s 19 57.4 0.392 54.9 59.8 316s 20 60.4 0.462 57.8 62.9 316s 21 63.9 0.448 61.4 66.5 316s 22 71.6 0.686 68.8 74.3 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 1.436 0.709 -1.8811 4.754 316s 3 1.765 0.512 -1.3848 4.915 316s 4 4.423 0.470 1.3027 7.543 316s 5 4.574 0.392 1.5029 7.645 316s 6 4.759 0.370 1.7000 7.818 316s 7 NA NA NA NA 316s 8 3.006 0.306 -0.0214 6.033 316s 9 2.546 0.444 -0.5575 5.649 316s 10 2.908 0.488 -0.2245 6.041 316s 11 1.750 0.738 -1.5953 5.096 316s 12 -2.702 0.583 -5.9068 0.503 316s 13 -5.224 0.743 -8.5738 -1.874 316s 14 -6.465 0.780 -9.8530 -3.077 316s 15 -2.830 0.378 -5.8936 0.233 316s 16 -1.440 0.326 -4.4762 1.597 316s 17 0.238 0.426 -2.8533 3.329 316s 18 2.103 0.268 -0.9077 5.114 316s 19 1.355 0.399 -1.7201 4.431 316s 20 0.825 0.474 -2.2981 3.947 316s 21 3.148 0.393 0.0761 6.220 316s 22 4.154 0.555 0.9719 7.336 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.8 0.309 24.9 28.6 316s 3 28.9 0.315 27.1 30.7 316s 4 32.7 0.326 30.9 34.6 316s 5 34.1 0.236 32.3 35.9 316s 6 35.8 0.244 34.0 37.6 316s 7 NA NA NA NA 316s 8 38.7 0.237 37.0 40.5 316s 9 39.0 0.225 37.2 40.7 316s 10 40.2 0.219 38.4 41.9 316s 11 38.4 0.309 36.5 40.2 316s 12 34.3 0.336 32.4 36.1 316s 13 29.3 0.411 27.3 31.2 316s 14 28.1 0.326 26.3 29.9 316s 15 30.3 0.313 28.4 32.1 316s 16 33.2 0.262 31.4 35.0 316s 17 37.6 0.265 35.8 39.3 316s 18 40.1 0.205 38.4 41.9 316s 19 39.0 0.323 37.1 40.8 316s 20 41.9 0.282 40.1 43.7 316s 21 46.1 0.293 44.3 48.0 316s 22 52.6 0.463 50.7 54.6 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 316s [3] "Numeric: lengths (732, 708) differ" 316s > nobs 316s [1] 59 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.23 0.64 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.31 0.58 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 48 316s 2 47 1 0.31 0.58 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 0.5 0.61 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 0.68 0.51 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 49 316s 2 47 2 1.37 0.5 316s > logLik 316s 'log Lik.' -71 (df=18) 316s 'log Lik.' -81.1 (df=18) 316s > 316s > # I3SLS 316s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: iterated 3SLS 316s 316s convergence achieved after 15 iterations 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 59 47 81.3 0.349 0.958 0.995 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 19 15 18.1 1.209 1.100 0.980 0.976 316s Investment 20 16 52.0 3.250 1.803 0.776 0.735 316s PrivateWages 20 16 11.2 0.699 0.836 0.986 0.983 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 0.955 0.456 -0.421 316s Investment 0.456 2.294 0.375 316s PrivateWages -0.421 0.375 0.522 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 0.955 0.456 -0.421 316s Investment 0.456 2.294 0.375 316s PrivateWages -0.421 0.375 0.522 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.322 -0.582 316s Investment 0.322 1.000 0.341 316s PrivateWages -0.582 0.341 1.000 316s 316s 316s 3SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.8311 1.2489 13.48 8.7e-10 *** 316s corpProf 0.1468 0.0991 1.48 0.16 316s corpProfLag 0.0924 0.0906 1.02 0.32 316s wages 0.7945 0.0371 21.43 1.2e-12 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.1 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 18.14 MSE: 1.209 Root MSE: 1.1 316s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 316s 316s 316s 3SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 32.4128 8.2695 3.92 0.00122 ** 316s corpProf -0.0799 0.1934 -0.41 0.68498 316s corpProfLag 0.7607 0.1878 4.05 0.00093 *** 316s capitalLag -0.2114 0.0400 -5.29 7.4e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.803 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 51.999 MSE: 3.25 Root MSE: 1.803 316s Multiple R-Squared: 0.776 Adjusted R-Squared: 0.735 316s 316s 316s 3SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.5421 1.1496 1.34 0.19852 316s gnp 0.3936 0.0313 12.57 1.0e-09 *** 316s gnpLag 0.1945 0.0328 5.93 2.1e-05 *** 316s trend 0.1416 0.0286 4.95 0.00014 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.836 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 11.181 MSE: 0.699 Root MSE: 0.836 316s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.983 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.3309 -2.6308 -1.3061 316s 3 -1.0419 0.0146 0.4450 316s 4 -1.2918 0.4128 1.4338 316s 5 -0.1772 -1.7488 -0.2494 316s 6 0.3563 0.2807 -0.4066 316s 7 NA NA NA 316s 8 1.6778 1.4671 -0.8700 316s 9 1.4561 1.1068 0.1712 316s 10 NA 2.9002 1.1262 316s 11 0.4237 -1.0652 -0.6189 316s 12 -0.2711 -0.9488 0.0375 316s 13 -0.5643 -1.6241 -0.5055 316s 14 0.2845 1.8477 0.3080 316s 15 -0.0514 -0.2379 0.3003 316s 16 0.0521 0.1268 0.0141 316s 17 1.8733 2.2462 -0.7083 316s 18 -0.1962 -0.1724 0.8305 316s 19 0.3553 -3.5810 -0.9448 316s 20 1.3161 1.0343 -0.2738 316s 21 1.2055 0.6622 -1.1283 316s 22 -1.6327 1.5541 0.8257 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.2 2.431 26.8 316s 3 46.0 1.885 28.9 316s 4 50.5 4.787 32.7 316s 5 50.8 4.749 34.1 316s 6 52.2 4.819 35.8 316s 7 NA NA NA 316s 8 54.5 2.733 38.8 316s 9 55.8 1.893 39.0 316s 10 NA 2.200 40.2 316s 11 54.6 2.065 38.5 316s 12 51.2 -2.451 34.5 316s 13 46.2 -4.576 29.5 316s 14 46.2 -6.948 28.2 316s 15 48.8 -2.762 30.3 316s 16 51.2 -1.427 33.2 316s 17 55.8 -0.146 37.5 316s 18 58.9 2.172 40.2 316s 19 57.1 1.681 39.1 316s 20 60.3 0.266 41.9 316s 21 63.8 2.638 46.1 316s 22 71.3 3.346 52.5 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.2 0.446 41.3 43.1 316s 3 46.0 0.511 45.0 47.1 316s 4 50.5 0.340 49.8 51.2 316s 5 50.8 0.393 50.0 51.6 316s 6 52.2 0.396 51.4 53.0 316s 7 NA NA NA NA 316s 8 54.5 0.326 53.9 55.2 316s 9 55.8 0.362 55.1 56.6 316s 10 NA NA NA NA 316s 11 54.6 0.612 53.3 55.8 316s 12 51.2 0.511 50.1 52.2 316s 13 46.2 0.671 44.8 47.5 316s 14 46.2 0.563 45.1 47.3 316s 15 48.8 0.354 48.0 49.5 316s 16 51.2 0.311 50.6 51.9 316s 17 55.8 0.362 55.1 56.6 316s 18 58.9 0.297 58.3 59.5 316s 19 57.1 0.357 56.4 57.9 316s 20 60.3 0.427 59.4 61.1 316s 21 63.8 0.416 63.0 64.6 316s 22 71.3 0.640 70.0 72.6 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 2.431 0.970 0.4798 4.382 316s 3 1.885 0.745 0.3859 3.385 316s 4 4.787 0.664 3.4506 6.124 316s 5 4.749 0.562 3.6174 5.880 316s 6 4.819 0.537 3.7391 5.900 316s 7 NA NA NA NA 316s 8 2.733 0.446 1.8351 3.631 316s 9 1.893 0.620 0.6455 3.141 316s 10 2.200 0.684 0.8232 3.576 316s 11 2.065 1.055 -0.0569 4.187 316s 12 -2.451 0.845 -4.1517 -0.751 316s 13 -4.576 1.070 -6.7293 -2.423 316s 14 -6.948 1.103 -9.1676 -4.728 316s 15 -2.762 0.556 -3.8806 -1.644 316s 16 -1.427 0.480 -2.3919 -0.462 316s 17 -0.146 0.603 -1.3588 1.066 316s 18 2.172 0.390 1.3869 2.958 316s 19 1.681 0.563 0.5476 2.815 316s 20 0.266 0.661 -1.0634 1.595 316s 21 2.638 0.558 1.5144 3.761 316s 22 3.346 0.778 1.7808 4.911 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.8 0.326 26.2 27.5 316s 3 28.9 0.328 28.2 29.5 316s 4 32.7 0.334 32.0 33.3 316s 5 34.1 0.242 33.7 34.6 316s 6 35.8 0.252 35.3 36.3 316s 7 NA NA NA NA 316s 8 38.8 0.244 38.3 39.3 316s 9 39.0 0.232 38.6 39.5 316s 10 40.2 0.230 39.7 40.6 316s 11 38.5 0.308 37.9 39.1 316s 12 34.5 0.336 33.8 35.1 316s 13 29.5 0.420 28.7 30.4 316s 14 28.2 0.345 27.5 28.9 316s 15 30.3 0.325 29.6 31.0 316s 16 33.2 0.271 32.6 33.7 316s 17 37.5 0.267 37.0 38.0 316s 18 40.2 0.218 39.7 40.6 316s 19 39.1 0.331 38.5 39.8 316s 20 41.9 0.289 41.3 42.5 316s 21 46.1 0.311 45.5 46.8 316s 22 52.5 0.485 51.5 53.5 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 316s [3] "Numeric: lengths (732, 708) differ" 316s > nobs 316s [1] 59 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.28 0.6 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.37 0.55 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 48 316s 2 47 1 0.37 0.54 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 1.25 0.3 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 1.64 0.21 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 49 316s 2 47 2 3.28 0.19 316s > logLik 316s 'log Lik.' -74.5 (df=18) 316s 'log Lik.' -87.1 (df=18) 316s > 316s > # OLS 316s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: OLS 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 59 47 44.2 0.453 0.976 0.99 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 316s Investment 20 16 17.11 1.069 1.03 0.912 0.895 316s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.1939 0.0559 -0.474 316s Investment 0.0559 0.9839 0.140 316s PrivateWages -0.4745 0.1403 0.602 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.0000 0.0447 -0.568 316s Investment 0.0447 1.0000 0.169 316s PrivateWages -0.5680 0.1689 1.000 316s 316s 316s OLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.2957 1.4879 10.95 1.5e-08 *** 316s corpProf 0.1796 0.1162 1.55 0.14 316s corpProfLag 0.1032 0.0994 1.04 0.32 316s wages 0.7962 0.0433 18.39 1.1e-11 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.076 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 316s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 316s 316s 316s OLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 10.1813 5.3720 1.90 0.07627 . 316s corpProf 0.5003 0.1052 4.75 0.00022 *** 316s corpProfLag 0.3259 0.1003 3.25 0.00502 ** 316s capitalLag -0.1134 0.0265 -4.28 0.00057 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.034 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 17.109 MSE: 1.069 Root MSE: 1.034 316s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.895 316s 316s 316s OLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3550 1.3021 1.04 0.3135 316s gnp 0.4417 0.0330 13.40 4.1e-10 *** 316s gnpLag 0.1466 0.0379 3.87 0.0013 ** 316s trend 0.1244 0.0335 3.72 0.0019 ** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.78 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 316s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 316s 316s compare coef with single-equation OLS 316s [1] TRUE 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.3863 -0.000301 -1.3389 316s 3 -1.2484 -0.076489 0.2462 316s 4 -1.6040 1.221792 1.1255 316s 5 -0.5384 -1.377872 -0.1959 316s 6 -0.0413 0.386104 -0.5284 316s 7 0.8043 1.486279 NA 316s 8 1.2830 0.784055 -0.7909 316s 9 1.0142 -0.655354 0.2819 316s 10 NA 1.060871 1.1384 316s 11 0.1429 0.395249 -0.1904 316s 12 -0.3439 0.198005 0.5813 316s 13 NA NA 0.1206 316s 14 0.3199 0.312725 0.4773 316s 15 -0.1016 -0.084685 0.3035 316s 16 -0.0702 0.066194 0.0284 316s 17 1.6064 0.963697 -0.8517 316s 18 -0.4980 0.078506 0.9908 316s 19 0.1253 -2.496401 -0.4597 316s 20 0.9805 -0.711004 -0.3819 316s 21 0.7551 -0.820172 -1.1062 316s 22 -2.1992 -0.731199 0.5501 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.3 -0.200 26.8 316s 3 46.2 1.976 29.1 316s 4 50.8 3.978 33.0 316s 5 51.1 4.378 34.1 316s 6 52.6 4.714 35.9 316s 7 54.3 4.114 NA 316s 8 54.9 3.416 38.7 316s 9 56.3 3.655 38.9 316s 10 NA 4.039 40.2 316s 11 54.9 0.605 38.1 316s 12 51.2 -3.598 33.9 316s 13 NA NA 28.9 316s 14 46.2 -5.413 28.0 316s 15 48.8 -2.915 30.3 316s 16 51.4 -1.366 33.2 316s 17 56.1 1.136 37.7 316s 18 59.2 1.921 40.0 316s 19 57.4 0.596 38.7 316s 20 60.6 2.011 42.0 316s 21 64.2 4.120 46.1 316s 22 71.9 5.631 52.7 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.3 0.523 39.9 44.7 316s 3 46.2 0.560 43.8 48.7 316s 4 50.8 0.379 48.5 53.1 316s 5 51.1 0.448 48.8 53.5 316s 6 52.6 0.457 50.3 55.0 316s 7 54.3 0.408 52.0 56.6 316s 8 54.9 0.375 52.6 57.2 316s 9 56.3 0.418 54.0 58.6 316s 10 NA NA NA NA 316s 11 54.9 0.701 52.3 57.4 316s 12 51.2 0.638 48.7 53.8 316s 13 NA NA NA NA 316s 14 46.2 0.673 43.6 48.7 316s 15 48.8 0.453 46.5 51.2 316s 16 51.4 0.384 49.1 53.7 316s 17 56.1 0.391 53.8 58.4 316s 18 59.2 0.361 56.9 61.5 316s 19 57.4 0.449 55.0 59.7 316s 20 60.6 0.465 58.3 63.0 316s 21 64.2 0.468 61.9 66.6 316s 22 71.9 0.728 69.3 74.5 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 -0.200 0.613 -2.618 2.219 316s 3 1.976 0.494 -0.329 4.282 316s 4 3.978 0.444 1.714 6.242 316s 5 4.378 0.369 2.169 6.587 316s 6 4.714 0.349 2.519 6.909 316s 7 4.114 0.323 1.934 6.293 316s 8 3.416 0.287 1.257 5.575 316s 9 3.655 0.386 1.435 5.876 316s 10 4.039 0.441 1.777 6.301 316s 11 0.605 0.641 -1.843 3.053 316s 12 -3.598 0.606 -6.010 -1.186 316s 13 NA NA NA NA 316s 14 -5.413 0.708 -7.934 -2.892 316s 15 -2.915 0.412 -5.155 -0.676 316s 16 -1.366 0.336 -3.554 0.821 316s 17 1.136 0.342 -1.055 3.327 316s 18 1.921 0.246 -0.217 4.060 316s 19 0.596 0.341 -1.594 2.787 316s 20 2.011 0.364 -0.194 4.216 316s 21 4.120 0.337 1.932 6.308 316s 22 5.631 0.477 3.341 7.922 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.8 0.364 25.1 28.6 316s 3 29.1 0.367 27.3 30.8 316s 4 33.0 0.370 31.2 34.7 316s 5 34.1 0.286 32.4 35.8 316s 6 35.9 0.285 34.3 37.6 316s 7 NA NA NA NA 316s 8 38.7 0.292 37.0 40.4 316s 9 38.9 0.277 37.3 40.6 316s 10 40.2 0.264 38.5 41.8 316s 11 38.1 0.363 36.4 39.8 316s 12 33.9 0.367 32.2 35.7 316s 13 28.9 0.435 27.1 30.7 316s 14 28.0 0.383 26.3 29.8 316s 15 30.3 0.377 28.6 32.0 316s 16 33.2 0.315 31.5 34.9 316s 17 37.7 0.308 36.0 39.3 316s 18 40.0 0.241 38.4 41.7 316s 19 38.7 0.361 36.9 40.4 316s 20 42.0 0.324 40.3 43.7 316s 21 46.1 0.339 44.4 47.8 316s 22 52.7 0.511 50.9 54.6 316s > model.frame 316s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 316s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 316s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 316s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 316s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 316s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 316s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 316s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 316s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 316s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 316s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 316s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 316s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 316s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 316s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 316s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 316s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 316s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 316s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 316s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 316s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 316s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 316s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 316s trend 316s 1 -11 316s 2 -10 316s 3 -9 316s 4 -8 316s 5 -7 316s 6 -6 316s 7 -5 316s 8 -4 316s 9 -3 316s 10 -2 316s 11 -1 316s 12 0 316s 13 1 316s 14 2 316s 15 3 316s 16 4 316s 17 5 316s 18 6 316s 19 7 316s 20 8 316s 21 9 316s 22 10 316s > model.matrix 316s Consumption_(Intercept) Consumption_corpProf 316s Consumption_2 1 12.4 316s Consumption_3 1 16.9 316s Consumption_4 1 18.4 316s Consumption_5 1 19.4 316s Consumption_6 1 20.1 316s Consumption_7 1 19.6 316s Consumption_8 1 19.8 316s Consumption_9 1 21.1 316s Consumption_11 1 15.6 316s Consumption_12 1 11.4 316s Consumption_14 1 11.2 316s Consumption_15 1 12.3 316s Consumption_16 1 14.0 316s Consumption_17 1 17.6 316s Consumption_18 1 17.3 316s Consumption_19 1 15.3 316s Consumption_20 1 19.0 316s Consumption_21 1 21.1 316s Consumption_22 1 23.5 316s Investment_2 0 0.0 316s Investment_3 0 0.0 316s Investment_4 0 0.0 316s Investment_5 0 0.0 316s Investment_6 0 0.0 316s Investment_7 0 0.0 316s Investment_8 0 0.0 316s Investment_9 0 0.0 316s Investment_10 0 0.0 316s Investment_11 0 0.0 316s Investment_12 0 0.0 316s Investment_14 0 0.0 316s Investment_15 0 0.0 316s Investment_16 0 0.0 316s Investment_17 0 0.0 316s Investment_18 0 0.0 316s Investment_19 0 0.0 316s Investment_20 0 0.0 316s Investment_21 0 0.0 316s Investment_22 0 0.0 316s PrivateWages_2 0 0.0 316s PrivateWages_3 0 0.0 316s PrivateWages_4 0 0.0 316s PrivateWages_5 0 0.0 316s PrivateWages_6 0 0.0 316s PrivateWages_8 0 0.0 316s PrivateWages_9 0 0.0 316s PrivateWages_10 0 0.0 316s PrivateWages_11 0 0.0 316s PrivateWages_12 0 0.0 316s PrivateWages_13 0 0.0 316s PrivateWages_14 0 0.0 316s PrivateWages_15 0 0.0 316s PrivateWages_16 0 0.0 316s PrivateWages_17 0 0.0 316s PrivateWages_18 0 0.0 316s PrivateWages_19 0 0.0 316s PrivateWages_20 0 0.0 316s PrivateWages_21 0 0.0 316s PrivateWages_22 0 0.0 316s Consumption_corpProfLag Consumption_wages 316s Consumption_2 12.7 28.2 316s Consumption_3 12.4 32.2 316s Consumption_4 16.9 37.0 316s Consumption_5 18.4 37.0 316s Consumption_6 19.4 38.6 316s Consumption_7 20.1 40.7 316s Consumption_8 19.6 41.5 316s Consumption_9 19.8 42.9 316s Consumption_11 21.7 42.1 316s Consumption_12 15.6 39.3 316s Consumption_14 7.0 34.1 316s Consumption_15 11.2 36.6 316s Consumption_16 12.3 39.3 316s Consumption_17 14.0 44.2 316s Consumption_18 17.6 47.7 316s Consumption_19 17.3 45.9 316s Consumption_20 15.3 49.4 316s Consumption_21 19.0 53.0 316s Consumption_22 21.1 61.8 316s Investment_2 0.0 0.0 316s Investment_3 0.0 0.0 316s Investment_4 0.0 0.0 316s Investment_5 0.0 0.0 316s Investment_6 0.0 0.0 316s Investment_7 0.0 0.0 316s Investment_8 0.0 0.0 316s Investment_9 0.0 0.0 316s Investment_10 0.0 0.0 316s Investment_11 0.0 0.0 316s Investment_12 0.0 0.0 316s Investment_14 0.0 0.0 316s Investment_15 0.0 0.0 316s Investment_16 0.0 0.0 316s Investment_17 0.0 0.0 316s Investment_18 0.0 0.0 316s Investment_19 0.0 0.0 316s Investment_20 0.0 0.0 316s Investment_21 0.0 0.0 316s Investment_22 0.0 0.0 316s PrivateWages_2 0.0 0.0 316s PrivateWages_3 0.0 0.0 316s PrivateWages_4 0.0 0.0 316s PrivateWages_5 0.0 0.0 316s PrivateWages_6 0.0 0.0 316s PrivateWages_8 0.0 0.0 316s PrivateWages_9 0.0 0.0 316s PrivateWages_10 0.0 0.0 316s PrivateWages_11 0.0 0.0 316s PrivateWages_12 0.0 0.0 316s PrivateWages_13 0.0 0.0 316s PrivateWages_14 0.0 0.0 316s PrivateWages_15 0.0 0.0 316s PrivateWages_16 0.0 0.0 316s PrivateWages_17 0.0 0.0 316s PrivateWages_18 0.0 0.0 316s PrivateWages_19 0.0 0.0 316s PrivateWages_20 0.0 0.0 316s PrivateWages_21 0.0 0.0 316s PrivateWages_22 0.0 0.0 316s Investment_(Intercept) Investment_corpProf 316s Consumption_2 0 0.0 316s Consumption_3 0 0.0 316s Consumption_4 0 0.0 316s Consumption_5 0 0.0 316s Consumption_6 0 0.0 316s Consumption_7 0 0.0 316s Consumption_8 0 0.0 316s Consumption_9 0 0.0 316s Consumption_11 0 0.0 316s Consumption_12 0 0.0 316s Consumption_14 0 0.0 316s Consumption_15 0 0.0 316s Consumption_16 0 0.0 316s Consumption_17 0 0.0 316s Consumption_18 0 0.0 316s Consumption_19 0 0.0 316s Consumption_20 0 0.0 316s Consumption_21 0 0.0 316s Consumption_22 0 0.0 316s Investment_2 1 12.4 316s Investment_3 1 16.9 316s Investment_4 1 18.4 316s Investment_5 1 19.4 316s Investment_6 1 20.1 316s Investment_7 1 19.6 316s Investment_8 1 19.8 316s Investment_9 1 21.1 316s Investment_10 1 21.7 316s Investment_11 1 15.6 316s Investment_12 1 11.4 316s Investment_14 1 11.2 316s Investment_15 1 12.3 316s Investment_16 1 14.0 316s Investment_17 1 17.6 316s Investment_18 1 17.3 316s Investment_19 1 15.3 316s Investment_20 1 19.0 316s Investment_21 1 21.1 316s Investment_22 1 23.5 316s PrivateWages_2 0 0.0 316s PrivateWages_3 0 0.0 316s PrivateWages_4 0 0.0 316s PrivateWages_5 0 0.0 316s PrivateWages_6 0 0.0 316s PrivateWages_8 0 0.0 316s PrivateWages_9 0 0.0 316s PrivateWages_10 0 0.0 316s PrivateWages_11 0 0.0 316s PrivateWages_12 0 0.0 316s PrivateWages_13 0 0.0 316s PrivateWages_14 0 0.0 316s PrivateWages_15 0 0.0 316s PrivateWages_16 0 0.0 316s PrivateWages_17 0 0.0 316s PrivateWages_18 0 0.0 316s PrivateWages_19 0 0.0 316s PrivateWages_20 0 0.0 316s PrivateWages_21 0 0.0 316s PrivateWages_22 0 0.0 316s Investment_corpProfLag Investment_capitalLag 316s Consumption_2 0.0 0 316s Consumption_3 0.0 0 316s Consumption_4 0.0 0 316s Consumption_5 0.0 0 316s Consumption_6 0.0 0 316s Consumption_7 0.0 0 316s Consumption_8 0.0 0 316s Consumption_9 0.0 0 316s Consumption_11 0.0 0 316s Consumption_12 0.0 0 316s Consumption_14 0.0 0 316s Consumption_15 0.0 0 316s Consumption_16 0.0 0 316s Consumption_17 0.0 0 316s Consumption_18 0.0 0 316s Consumption_19 0.0 0 316s Consumption_20 0.0 0 316s Consumption_21 0.0 0 316s Consumption_22 0.0 0 316s Investment_2 12.7 183 316s Investment_3 12.4 183 316s Investment_4 16.9 184 316s Investment_5 18.4 190 316s Investment_6 19.4 193 316s Investment_7 20.1 198 316s Investment_8 19.6 203 316s Investment_9 19.8 208 316s Investment_10 21.1 211 316s Investment_11 21.7 216 316s Investment_12 15.6 217 316s Investment_14 7.0 207 316s Investment_15 11.2 202 316s Investment_16 12.3 199 316s Investment_17 14.0 198 316s Investment_18 17.6 200 316s Investment_19 17.3 202 316s Investment_20 15.3 200 316s Investment_21 19.0 201 316s Investment_22 21.1 204 316s PrivateWages_2 0.0 0 316s PrivateWages_3 0.0 0 316s PrivateWages_4 0.0 0 316s PrivateWages_5 0.0 0 316s PrivateWages_6 0.0 0 316s PrivateWages_8 0.0 0 316s PrivateWages_9 0.0 0 316s PrivateWages_10 0.0 0 316s PrivateWages_11 0.0 0 316s PrivateWages_12 0.0 0 316s PrivateWages_13 0.0 0 316s PrivateWages_14 0.0 0 316s PrivateWages_15 0.0 0 316s PrivateWages_16 0.0 0 316s PrivateWages_17 0.0 0 316s PrivateWages_18 0.0 0 316s PrivateWages_19 0.0 0 316s PrivateWages_20 0.0 0 316s PrivateWages_21 0.0 0 316s PrivateWages_22 0.0 0 316s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 316s Consumption_2 0 0.0 0.0 316s Consumption_3 0 0.0 0.0 316s Consumption_4 0 0.0 0.0 316s Consumption_5 0 0.0 0.0 316s Consumption_6 0 0.0 0.0 316s Consumption_7 0 0.0 0.0 316s Consumption_8 0 0.0 0.0 316s Consumption_9 0 0.0 0.0 316s Consumption_11 0 0.0 0.0 316s Consumption_12 0 0.0 0.0 316s Consumption_14 0 0.0 0.0 316s Consumption_15 0 0.0 0.0 316s Consumption_16 0 0.0 0.0 316s Consumption_17 0 0.0 0.0 316s Consumption_18 0 0.0 0.0 316s Consumption_19 0 0.0 0.0 316s Consumption_20 0 0.0 0.0 316s Consumption_21 0 0.0 0.0 316s Consumption_22 0 0.0 0.0 316s Investment_2 0 0.0 0.0 316s Investment_3 0 0.0 0.0 316s Investment_4 0 0.0 0.0 316s Investment_5 0 0.0 0.0 316s Investment_6 0 0.0 0.0 316s Investment_7 0 0.0 0.0 316s Investment_8 0 0.0 0.0 316s Investment_9 0 0.0 0.0 316s Investment_10 0 0.0 0.0 316s Investment_11 0 0.0 0.0 316s Investment_12 0 0.0 0.0 316s Investment_14 0 0.0 0.0 316s Investment_15 0 0.0 0.0 316s Investment_16 0 0.0 0.0 316s Investment_17 0 0.0 0.0 316s Investment_18 0 0.0 0.0 316s Investment_19 0 0.0 0.0 316s Investment_20 0 0.0 0.0 316s Investment_21 0 0.0 0.0 316s Investment_22 0 0.0 0.0 316s PrivateWages_2 1 45.6 44.9 316s PrivateWages_3 1 50.1 45.6 316s PrivateWages_4 1 57.2 50.1 316s PrivateWages_5 1 57.1 57.2 316s PrivateWages_6 1 61.0 57.1 316s PrivateWages_8 1 64.4 64.0 316s PrivateWages_9 1 64.5 64.4 316s PrivateWages_10 1 67.0 64.5 316s PrivateWages_11 1 61.2 67.0 316s PrivateWages_12 1 53.4 61.2 316s PrivateWages_13 1 44.3 53.4 316s PrivateWages_14 1 45.1 44.3 316s PrivateWages_15 1 49.7 45.1 316s PrivateWages_16 1 54.4 49.7 316s PrivateWages_17 1 62.7 54.4 316s PrivateWages_18 1 65.0 62.7 316s PrivateWages_19 1 60.9 65.0 316s PrivateWages_20 1 69.5 60.9 316s PrivateWages_21 1 75.7 69.5 316s PrivateWages_22 1 88.4 75.7 316s PrivateWages_trend 316s Consumption_2 0 316s Consumption_3 0 316s Consumption_4 0 316s Consumption_5 0 316s Consumption_6 0 316s Consumption_7 0 316s Consumption_8 0 316s Consumption_9 0 316s Consumption_11 0 316s Consumption_12 0 316s Consumption_14 0 316s Consumption_15 0 316s Consumption_16 0 316s Consumption_17 0 316s Consumption_18 0 316s Consumption_19 0 316s Consumption_20 0 316s Consumption_21 0 316s Consumption_22 0 316s Investment_2 0 316s Investment_3 0 316s Investment_4 0 316s Investment_5 0 316s Investment_6 0 316s Investment_7 0 316s Investment_8 0 316s Investment_9 0 316s Investment_10 0 316s Investment_11 0 316s Investment_12 0 316s Investment_14 0 316s Investment_15 0 316s Investment_16 0 316s Investment_17 0 316s Investment_18 0 316s Investment_19 0 316s Investment_20 0 316s Investment_21 0 316s Investment_22 0 316s PrivateWages_2 -10 316s PrivateWages_3 -9 316s PrivateWages_4 -8 316s PrivateWages_5 -7 316s PrivateWages_6 -6 316s PrivateWages_8 -4 316s PrivateWages_9 -3 316s PrivateWages_10 -2 316s PrivateWages_11 -1 316s PrivateWages_12 0 316s PrivateWages_13 1 316s PrivateWages_14 2 316s PrivateWages_15 3 316s PrivateWages_16 4 316s PrivateWages_17 5 316s PrivateWages_18 6 316s PrivateWages_19 7 316s PrivateWages_20 8 316s PrivateWages_21 9 316s PrivateWages_22 10 316s > nobs 316s [1] 59 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.33 0.57 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.31 0.58 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 48 316s 2 47 1 0.31 0.58 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 0.17 0.84 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 0.16 0.85 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 49 316s 2 47 2 0.33 0.85 316s > logLik 316s 'log Lik.' -69.6 (df=13) 316s 'log Lik.' -74.2 (df=13) 316s compare log likelihood value with single-equation OLS 316s [1] "Mean relative difference: 0.00099" 316s > 316s > # 2SLS 316s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: 2SLS 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 57 45 58.2 0.333 0.968 0.991 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 316s Investment 19 15 26.21 1.748 1.32 0.852 0.823 316s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.237 0.518 -0.408 316s Investment 0.518 1.263 0.113 316s PrivateWages -0.408 0.113 0.468 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.416 -0.538 316s Investment 0.416 1.000 0.139 316s PrivateWages -0.538 0.139 1.000 316s 316s 316s 2SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 17.2849 1.6018 10.79 3.6e-08 *** 316s corpProf -0.0770 0.1637 -0.47 0.645 316s corpProfLag 0.2327 0.1242 1.87 0.082 . 316s wages 0.8259 0.0459 17.98 4.5e-11 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.261 on 14 degrees of freedom 316s Number of observations: 18 Degrees of Freedom: 14 316s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 316s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 316s 316s 316s 2SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 18.4005 7.1627 2.57 0.02138 * 316s corpProf 0.1507 0.1905 0.79 0.44118 316s corpProfLag 0.5757 0.1634 3.52 0.00307 ** 316s capitalLag -0.1452 0.0339 -4.28 0.00065 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.322 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 26.213 MSE: 1.748 Root MSE: 1.322 316s Multiple R-Squared: 0.852 Adjusted R-Squared: 0.823 316s 316s 316s 2SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3431 1.1544 1.16 0.26172 316s gnp 0.4438 0.0351 12.64 9.7e-10 *** 316s gnpLag 0.1447 0.0381 3.80 0.00158 ** 316s trend 0.1238 0.0300 4.13 0.00078 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.78 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 316s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.6754 -1.23599 -1.3401 316s 3 -0.4627 0.32957 0.2378 316s 4 -1.1585 1.08894 1.1117 316s 5 -0.0305 -1.37017 -0.1954 316s 6 0.4693 0.48431 -0.5355 316s 7 NA NA NA 316s 8 1.6045 1.06811 -0.7908 316s 9 1.6018 0.16695 0.2831 316s 10 NA 1.86380 1.1353 316s 11 -0.9031 -0.92183 -0.1765 316s 12 -1.5948 -1.03217 0.6007 316s 13 NA NA 0.1443 316s 14 0.2854 0.85468 0.4826 316s 15 -0.4718 -0.36943 0.3016 316s 16 -0.2268 0.00554 0.0261 316s 17 2.0079 1.69566 -0.8614 316s 18 -0.7434 -0.12659 0.9927 316s 19 -0.5410 -3.26209 -0.4446 316s 20 1.4186 0.25579 -0.3914 316s 21 1.1462 -0.00185 -1.1115 316s 22 -1.7256 0.50679 0.5312 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.6 1.036 26.8 316s 3 45.5 1.570 29.1 316s 4 50.4 4.111 33.0 316s 5 50.6 4.370 34.1 316s 6 52.1 4.616 35.9 316s 7 NA NA NA 316s 8 54.6 3.132 38.7 316s 9 55.7 2.833 38.9 316s 10 NA 3.236 40.2 316s 11 55.9 1.922 38.1 316s 12 52.5 -2.368 33.9 316s 13 NA NA 28.9 316s 14 46.2 -5.955 28.0 316s 15 49.2 -2.631 30.3 316s 16 51.5 -1.306 33.2 316s 17 55.7 0.404 37.7 316s 18 59.4 2.127 40.0 316s 19 58.0 1.362 38.6 316s 20 60.2 1.044 42.0 316s 21 63.9 3.302 46.1 316s 22 71.4 4.393 52.8 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.6 0.571 41.4 43.8 316s 3 45.5 0.656 44.1 46.9 316s 4 50.4 0.431 49.4 51.3 316s 5 50.6 0.510 49.5 51.7 316s 6 52.1 0.521 51.0 53.2 316s 7 NA NA NA NA 316s 8 54.6 0.419 53.7 55.5 316s 9 55.7 0.496 54.6 56.8 316s 10 NA NA NA NA 316s 11 55.9 0.910 54.0 57.9 316s 12 52.5 0.869 50.6 54.4 316s 13 NA NA NA NA 316s 14 46.2 0.694 44.7 47.7 316s 15 49.2 0.487 48.1 50.2 316s 16 51.5 0.396 50.7 52.4 316s 17 55.7 0.445 54.7 56.6 316s 18 59.4 0.386 58.6 60.3 316s 19 58.0 0.548 56.9 59.2 316s 20 60.2 0.528 59.0 61.3 316s 21 63.9 0.515 62.8 65.0 316s 22 71.4 0.786 69.7 73.1 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 1.036 0.892 -0.865 2.937 316s 3 1.570 0.579 0.335 2.805 316s 4 4.111 0.531 2.979 5.243 316s 5 4.370 0.440 3.432 5.308 316s 6 4.616 0.416 3.729 5.502 316s 7 NA NA NA NA 316s 8 3.132 0.344 2.398 3.866 316s 9 2.833 0.533 1.696 3.970 316s 10 3.236 0.580 2.000 4.473 316s 11 1.922 0.959 -0.122 3.966 316s 12 -2.368 0.860 -4.201 -0.534 316s 13 NA NA NA NA 316s 14 -5.955 0.865 -7.799 -4.110 316s 15 -2.631 0.479 -3.652 -1.610 316s 16 -1.306 0.382 -2.120 -0.491 316s 17 0.404 0.487 -0.635 1.443 316s 18 2.127 0.319 1.447 2.806 316s 19 1.362 0.537 0.218 2.506 316s 20 1.044 0.566 -0.162 2.250 316s 21 3.302 0.486 2.265 4.339 316s 22 4.393 0.713 2.874 5.912 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.8 0.321 26.2 27.5 316s 3 29.1 0.334 28.4 29.8 316s 4 33.0 0.353 32.2 33.7 316s 5 34.1 0.253 33.6 34.6 316s 6 35.9 0.261 35.4 36.5 316s 7 NA NA NA NA 316s 8 38.7 0.257 38.1 39.2 316s 9 38.9 0.245 38.4 39.4 316s 10 40.2 0.235 39.7 40.7 316s 11 38.1 0.348 37.3 38.8 316s 12 33.9 0.374 33.1 34.7 316s 13 28.9 0.447 27.9 29.8 316s 14 28.0 0.341 27.3 28.7 316s 15 30.3 0.333 29.6 31.0 316s 16 33.2 0.278 32.6 33.8 316s 17 37.7 0.288 37.1 38.3 316s 18 40.0 0.214 39.6 40.5 316s 19 38.6 0.351 37.9 39.4 316s 20 42.0 0.301 41.4 42.6 316s 21 46.1 0.304 45.5 46.8 316s 22 52.8 0.486 51.7 53.8 316s > model.frame 316s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 316s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 316s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 316s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 316s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 316s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 316s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 316s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 316s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 316s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 316s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 316s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 316s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 316s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 316s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 316s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 316s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 316s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 316s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 316s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 316s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 316s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 316s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 316s trend 316s 1 -11 316s 2 -10 316s 3 -9 316s 4 -8 316s 5 -7 316s 6 -6 316s 7 -5 316s 8 -4 316s 9 -3 316s 10 -2 316s 11 -1 316s 12 0 316s 13 1 316s 14 2 316s 15 3 316s 16 4 316s 17 5 316s 18 6 316s 19 7 316s 20 8 316s 21 9 316s 22 10 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 316s [3] "Numeric: lengths (708, 684) differ" 316s > nobs 316s [1] 57 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 45 1 1.37 0.25 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 45 1 1.77 0.19 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 46 316s 2 45 1 1.77 0.18 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 45 2 0.69 0.51 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 45 2 0.89 0.42 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 47 316s 2 45 2 1.78 0.41 316s > logLik 316s 'log Lik.' -70.6 (df=13) 316s 'log Lik.' -78.7 (df=13) 316s > 316s > # SUR 316s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: SUR 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 59 47 45.1 0.168 0.976 0.992 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 316s Investment 20 16 17.3 1.083 1.041 0.911 0.894 316s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 0.9286 0.0435 -0.369 316s Investment 0.0435 0.7653 0.109 316s PrivateWages -0.3690 0.1091 0.468 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 0.9251 0.0748 -0.427 316s Investment 0.0748 0.7653 0.171 316s PrivateWages -0.4268 0.1706 0.492 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.0000 0.0888 -0.636 316s Investment 0.0888 1.0000 0.268 316s PrivateWages -0.6364 0.2678 1.000 316s 316s 316s SUR estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.2684 1.2781 12.73 1.9e-09 *** 316s corpProf 0.1942 0.0927 2.10 0.054 . 316s corpProfLag 0.0746 0.0819 0.91 0.377 316s wages 0.8011 0.0372 21.53 1.1e-12 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.08 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 316s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 316s 316s 316s SUR estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 12.6462 4.6500 2.72 0.01515 * 316s corpProf 0.4707 0.0916 5.14 9.9e-05 *** 316s corpProfLag 0.3519 0.0874 4.03 0.00097 *** 316s capitalLag -0.1253 0.0229 -5.47 5.1e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.041 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 17.325 MSE: 1.083 Root MSE: 1.041 316s Multiple R-Squared: 0.911 Adjusted R-Squared: 0.894 316s 316s 316s SUR estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3245 1.0946 1.21 0.24 316s gnp 0.4184 0.0260 16.08 2.7e-11 *** 316s gnpLag 0.1714 0.0307 5.59 4.1e-05 *** 316s trend 0.1455 0.0276 5.27 7.6e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.801 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 10.265 MSE: 0.642 Root MSE: 0.801 316s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.3146 -0.2419 -1.1439 316s 3 -1.2707 -0.1795 0.5080 316s 4 -1.5428 1.0691 1.4208 316s 5 -0.4489 -1.4778 -0.1000 316s 6 0.0588 0.3168 -0.3599 316s 7 0.9215 1.4450 NA 316s 8 1.3791 0.8287 -0.7561 316s 9 1.0901 -0.5272 0.2880 316s 10 NA 1.2089 1.1795 316s 11 0.3577 0.4081 -0.3681 316s 12 -0.2286 0.2569 0.3439 316s 13 NA NA -0.1574 316s 14 0.2172 0.4743 0.4225 316s 15 -0.1124 -0.0607 0.3154 316s 16 -0.0876 0.0761 0.0151 316s 17 1.5611 1.0205 -0.8084 316s 18 -0.4529 0.0580 0.8611 316s 19 0.1999 -2.5444 -0.7635 316s 20 0.9266 -0.6202 -0.4039 316s 21 0.7589 -0.7478 -1.2175 316s 22 -2.2135 -0.6029 0.5611 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.2 0.0419 26.6 316s 3 46.3 2.0795 28.8 316s 4 50.7 4.1309 32.7 316s 5 51.0 4.4778 34.0 316s 6 52.5 4.7832 35.8 316s 7 54.2 4.1550 NA 316s 8 54.8 3.3713 38.7 316s 9 56.2 3.5272 38.9 316s 10 NA 3.8911 40.1 316s 11 54.6 0.5919 38.3 316s 12 51.1 -3.6569 34.2 316s 13 NA NA 29.2 316s 14 46.3 -5.5743 28.1 316s 15 48.8 -2.9393 30.3 316s 16 51.4 -1.3761 33.2 316s 17 56.1 1.0795 37.6 316s 18 59.2 1.9420 40.1 316s 19 57.3 0.6444 39.0 316s 20 60.7 1.9202 42.0 316s 21 64.2 4.0478 46.2 316s 22 71.9 5.5029 52.7 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.2 0.448 41.3 43.1 316s 3 46.3 0.476 45.3 47.2 316s 4 50.7 0.318 50.1 51.4 316s 5 51.0 0.373 50.3 51.8 316s 6 52.5 0.378 51.8 53.3 316s 7 54.2 0.337 53.5 54.9 316s 8 54.8 0.310 54.2 55.4 316s 9 56.2 0.343 55.5 56.9 316s 10 NA NA NA NA 316s 11 54.6 0.567 53.5 55.8 316s 12 51.1 0.509 50.1 52.2 316s 13 NA NA NA NA 316s 14 46.3 0.573 45.1 47.4 316s 15 48.8 0.382 48.0 49.6 316s 16 51.4 0.328 50.7 52.0 316s 17 56.1 0.336 55.5 56.8 316s 18 59.2 0.309 58.5 59.8 316s 19 57.3 0.370 56.6 58.0 316s 20 60.7 0.401 59.9 61.5 316s 21 64.2 0.405 63.4 65.1 316s 22 71.9 0.633 70.6 73.2 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 0.0419 0.533 -1.0309 1.115 316s 3 2.0795 0.433 1.2082 2.951 316s 4 4.1309 0.387 3.3532 4.909 316s 5 4.4778 0.322 3.8307 5.125 316s 6 4.7832 0.305 4.1700 5.396 316s 7 4.1550 0.283 3.5852 4.725 316s 8 3.3713 0.253 2.8630 3.880 316s 9 3.5272 0.337 2.8488 4.206 316s 10 3.8911 0.386 3.1149 4.667 316s 11 0.5919 0.561 -0.5376 1.722 316s 12 -3.6569 0.530 -4.7223 -2.591 316s 13 NA NA NA NA 316s 14 -5.5743 0.618 -6.8176 -4.331 316s 15 -2.9393 0.362 -3.6671 -2.212 316s 16 -1.3761 0.296 -1.9710 -0.781 316s 17 1.0795 0.300 0.4763 1.683 316s 18 1.9420 0.216 1.5081 2.376 316s 19 0.6444 0.298 0.0451 1.244 316s 20 1.9202 0.318 1.2798 2.561 316s 21 4.0478 0.295 3.4537 4.642 316s 22 5.5029 0.417 4.6638 6.342 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.6 0.312 26.0 27.3 316s 3 28.8 0.312 28.2 29.4 316s 4 32.7 0.307 32.1 33.3 316s 5 34.0 0.237 33.5 34.5 316s 6 35.8 0.235 35.3 36.2 316s 7 NA NA NA NA 316s 8 38.7 0.239 38.2 39.1 316s 9 38.9 0.228 38.5 39.4 316s 10 40.1 0.218 39.7 40.6 316s 11 38.3 0.293 37.7 38.9 316s 12 34.2 0.290 33.6 34.7 316s 13 29.2 0.343 28.5 29.8 316s 14 28.1 0.321 27.4 28.7 316s 15 30.3 0.320 29.6 30.9 316s 16 33.2 0.268 32.6 33.7 316s 17 37.6 0.263 37.1 38.1 316s 18 40.1 0.207 39.7 40.6 316s 19 39.0 0.293 38.4 39.6 316s 20 42.0 0.279 41.4 42.6 316s 21 46.2 0.295 45.6 46.8 316s 22 52.7 0.435 51.9 53.6 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] TRUE 316s > nobs 316s [1] 59 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.41 0.52 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 47 1 0.52 0.47 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 48 316s 2 47 1 0.52 0.47 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 0.31 0.73 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 49 316s 2 47 2 0.4 0.67 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 49 316s 2 47 2 0.79 0.67 316s > logLik 316s 'log Lik.' -67.3 (df=18) 316s 'log Lik.' -74.9 (df=18) 316s > 316s > # 3SLS 316s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: 3SLS 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 57 45 66.8 0.361 0.963 0.993 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 18 14 22.6 1.616 1.271 0.974 0.968 316s Investment 19 15 34.1 2.277 1.509 0.807 0.769 316s PrivateWages 20 16 10.1 0.628 0.793 0.987 0.985 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 1.237 0.518 -0.408 316s Investment 0.518 1.263 0.113 316s PrivateWages -0.408 0.113 0.468 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.257 0.601 -0.421 316s Investment 0.601 1.601 0.214 316s PrivateWages -0.421 0.214 0.491 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.425 -0.537 316s Investment 0.425 1.000 0.239 316s PrivateWages -0.537 0.239 1.000 316s 316s 316s 3SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 18.2100 1.5273 11.92 1e-08 *** 316s corpProf -0.0639 0.1461 -0.44 0.67 316s corpProfLag 0.1687 0.1125 1.50 0.16 316s wages 0.8230 0.0431 19.07 2e-11 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.271 on 14 degrees of freedom 316s Number of observations: 18 Degrees of Freedom: 14 316s SSR: 22.626 MSE: 1.616 Root MSE: 1.271 316s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 316s 316s 316s 3SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 24.7534 6.5548 3.78 0.00183 ** 316s corpProf 0.0524 0.1807 0.29 0.77600 316s corpProfLag 0.6584 0.1551 4.24 0.00071 *** 316s capitalLag -0.1756 0.0311 -5.64 4.7e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.509 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 34.149 MSE: 2.277 Root MSE: 1.509 316s Multiple R-Squared: 0.807 Adjusted R-Squared: 0.769 316s 316s 316s 3SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 0.8154 1.0961 0.74 0.46772 316s gnp 0.4250 0.0299 14.19 1.7e-10 *** 316s gnpLag 0.1731 0.0331 5.23 8.3e-05 *** 316s trend 0.1255 0.0283 4.43 0.00042 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.793 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 10.054 MSE: 0.628 Root MSE: 0.793 316s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.8680 -1.857 -1.21010 316s 3 -0.7217 0.170 0.43075 316s 4 -1.1353 0.762 1.30899 316s 5 0.0755 -1.565 -0.20270 316s 6 0.6348 0.367 -0.46842 316s 7 NA NA NA 316s 8 1.7953 1.230 -0.85853 316s 9 1.7924 0.568 0.20422 316s 10 NA 2.308 1.09889 316s 11 -0.5211 -0.972 -0.39427 316s 12 -1.5560 -0.960 0.39889 316s 13 NA NA -0.00934 316s 14 -0.2384 1.327 0.59990 316s 15 -0.7342 -0.292 0.48094 316s 16 -0.4331 0.068 0.16188 316s 17 1.8775 1.932 -0.70448 316s 18 -0.6294 -0.154 0.95616 316s 19 -0.4252 -3.400 -0.62489 316s 20 1.3682 0.589 -0.29589 316s 21 1.3155 0.271 -1.14466 316s 22 -1.4276 0.942 0.55941 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.8 1.657 26.7 316s 3 45.7 1.730 28.9 316s 4 50.3 4.438 32.8 316s 5 50.5 4.565 34.1 316s 6 52.0 4.733 35.9 316s 7 NA NA NA 316s 8 54.4 2.970 38.8 316s 9 55.5 2.432 39.0 316s 10 NA 2.792 40.2 316s 11 55.5 1.972 38.3 316s 12 52.5 -2.440 34.1 316s 13 NA NA 29.0 316s 14 46.7 -6.427 27.9 316s 15 49.4 -2.708 30.1 316s 16 51.7 -1.368 33.0 316s 17 55.8 0.168 37.5 316s 18 59.3 2.154 40.0 316s 19 57.9 1.500 38.8 316s 20 60.2 0.711 41.9 316s 21 63.7 3.029 46.1 316s 22 71.1 3.958 52.7 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.8 0.542 39.8 45.7 316s 3 45.7 0.612 42.7 48.7 316s 4 50.3 0.407 47.5 53.2 316s 5 50.5 0.478 47.6 53.4 316s 6 52.0 0.488 49.0 54.9 316s 7 NA NA NA NA 316s 8 54.4 0.394 51.5 57.3 316s 9 55.5 0.464 52.6 58.4 316s 10 NA NA NA NA 316s 11 55.5 0.811 52.3 58.8 316s 12 52.5 0.773 49.3 55.6 316s 13 NA NA NA NA 316s 14 46.7 0.666 43.7 49.8 316s 15 49.4 0.463 46.5 52.3 316s 16 51.7 0.381 48.9 54.6 316s 17 55.8 0.424 52.9 58.7 316s 18 59.3 0.359 56.5 62.2 316s 19 57.9 0.492 55.0 60.8 316s 20 60.2 0.501 57.3 63.2 316s 21 63.7 0.491 60.8 66.6 316s 22 71.1 0.749 68.0 74.3 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 1.657 0.831 -2.015 5.329 316s 3 1.730 0.574 -1.711 5.171 316s 4 4.438 0.507 1.045 7.831 316s 5 4.565 0.426 1.223 7.907 316s 6 4.733 0.406 1.402 8.064 316s 7 NA NA NA NA 316s 8 2.970 0.334 -0.324 6.263 316s 9 2.432 0.501 -0.957 5.820 316s 10 2.792 0.544 -0.627 6.211 316s 11 1.972 0.937 -1.814 5.757 316s 12 -2.440 0.849 -6.131 1.250 316s 13 NA NA NA NA 316s 14 -6.427 0.836 -10.104 -2.750 316s 15 -2.708 0.477 -6.081 0.665 316s 16 -1.368 0.381 -4.685 1.949 316s 17 0.168 0.473 -3.202 3.538 316s 18 2.154 0.311 -1.130 5.438 316s 19 1.500 0.518 -1.900 4.900 316s 20 0.711 0.541 -2.705 4.127 316s 21 3.029 0.467 -0.338 6.395 316s 22 3.958 0.677 0.432 7.483 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.7 0.315 24.9 28.5 316s 3 28.9 0.322 27.1 30.7 316s 4 32.8 0.330 31.0 34.6 316s 5 34.1 0.241 32.3 35.9 316s 6 35.9 0.249 34.1 37.6 316s 7 NA NA NA NA 316s 8 38.8 0.243 37.0 40.5 316s 9 39.0 0.231 37.2 40.7 316s 10 40.2 0.225 38.5 41.9 316s 11 38.3 0.305 36.5 40.1 316s 12 34.1 0.317 32.3 35.9 316s 13 29.0 0.382 27.1 30.9 316s 14 27.9 0.321 26.1 29.7 316s 15 30.1 0.316 28.3 31.9 316s 16 33.0 0.265 31.3 34.8 316s 17 37.5 0.270 35.7 39.3 316s 18 40.0 0.207 38.3 41.8 316s 19 38.8 0.311 37.0 40.6 316s 20 41.9 0.287 40.1 43.7 316s 21 46.1 0.300 44.3 47.9 316s 22 52.7 0.463 50.8 54.7 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 316s [3] "Numeric: lengths (708, 684) differ" 316s > nobs 316s [1] 57 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 45 1 1.95 0.17 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 45 1 2.71 0.11 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 46 316s 2 45 1 2.71 0.1 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 45 2 1.78 0.18 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 45 2 2.48 0.095 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 47 316s 2 45 2 4.95 0.084 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s > logLik 316s 'log Lik.' -71.2 (df=18) 316s 'log Lik.' -81.7 (df=18) 316s > 316s > # I3SLS 316s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: iterated 3SLS 316s 316s convergence achieved after 9 iterations 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 57 45 75 0.422 0.959 0.993 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 18 14 22.7 1.622 1.273 0.973 0.968 316s Investment 19 15 42.1 2.809 1.676 0.762 0.715 316s PrivateWages 20 16 10.2 0.638 0.799 0.987 0.985 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 1.261 0.675 -0.439 316s Investment 0.675 1.949 0.237 316s PrivateWages -0.439 0.237 0.503 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.261 0.675 -0.439 316s Investment 0.675 1.949 0.237 316s PrivateWages -0.439 0.237 0.503 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.431 -0.550 316s Investment 0.431 1.000 0.239 316s PrivateWages -0.550 0.239 1.000 316s 316s 316s 3SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 18.5887 1.5250 12.19 7.6e-09 *** 316s corpProf -0.0438 0.1441 -0.30 0.77 316s corpProfLag 0.1456 0.1109 1.31 0.21 316s wages 0.8141 0.0428 19.01 2.1e-11 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.273 on 14 degrees of freedom 316s Number of observations: 18 Degrees of Freedom: 14 316s SSR: 22.704 MSE: 1.622 Root MSE: 1.273 316s Multiple R-Squared: 0.973 Adjusted R-Squared: 0.968 316s 316s 316s 3SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 29.4725 7.6857 3.83 0.0016 ** 316s corpProf -0.0183 0.2154 -0.09 0.9333 316s corpProfLag 0.7195 0.1850 3.89 0.0015 ** 316s capitalLag -0.1985 0.0366 -5.43 6.9e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.676 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 42.136 MSE: 2.809 Root MSE: 1.676 316s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.715 316s 316s 316s 3SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 0.5385 1.1055 0.49 0.63277 316s gnp 0.4251 0.0287 14.80 9.3e-11 *** 316s gnpLag 0.1776 0.0322 5.51 4.7e-05 *** 316s trend 0.1211 0.0283 4.28 0.00057 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.799 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 10.204 MSE: 0.638 Root MSE: 0.799 316s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.9524 -2.2888 -1.1837 316s 3 -0.8681 0.0698 0.4581 316s 4 -1.1653 0.5368 1.3199 316s 5 0.0601 -1.6917 -0.2194 316s 6 0.6426 0.2972 -0.4805 316s 7 NA NA NA 316s 8 1.8394 1.3723 -0.8931 316s 9 1.8275 0.8861 0.1723 316s 10 NA 2.6574 1.0707 316s 11 -0.3387 -0.9736 -0.4288 316s 12 -1.4550 -0.8630 0.3956 316s 13 NA NA 0.0277 316s 14 -0.3782 1.7151 0.6823 316s 15 -0.7768 -0.1993 0.5638 316s 16 -0.4606 0.1448 0.2281 316s 17 1.8605 2.1295 -0.6557 316s 18 -0.5262 -0.1493 0.9718 316s 19 -0.3047 -3.4730 -0.6148 316s 20 1.3992 0.8566 -0.2636 316s 21 1.4216 0.4910 -1.1472 316s 22 -1.2431 1.2792 0.5323 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.9 2.0888 26.7 316s 3 45.9 1.8302 28.8 316s 4 50.4 4.6632 32.8 316s 5 50.5 4.6917 34.1 316s 6 52.0 4.8028 35.9 316s 7 NA NA NA 316s 8 54.4 2.8277 38.8 316s 9 55.5 2.1139 39.0 316s 10 NA 2.4426 40.2 316s 11 55.3 1.9736 38.3 316s 12 52.4 -2.5370 34.1 316s 13 NA NA 29.0 316s 14 46.9 -6.8151 27.8 316s 15 49.5 -2.8007 30.0 316s 16 51.8 -1.4448 33.0 316s 17 55.8 -0.0295 37.5 316s 18 59.2 2.1493 40.0 316s 19 57.8 1.5730 38.8 316s 20 60.2 0.4434 41.9 316s 21 63.6 2.8090 46.1 316s 22 70.9 3.6208 52.8 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.9 0.541 41.8 43.9 316s 3 45.9 0.608 44.6 47.1 316s 4 50.4 0.403 49.6 51.2 316s 5 50.5 0.472 49.6 51.5 316s 6 52.0 0.481 51.0 52.9 316s 7 NA NA NA NA 316s 8 54.4 0.388 53.6 55.1 316s 9 55.5 0.458 54.6 56.4 316s 10 NA NA NA NA 316s 11 55.3 0.795 53.7 56.9 316s 12 52.4 0.762 50.8 53.9 316s 13 NA NA NA NA 316s 14 46.9 0.663 45.5 48.2 316s 15 49.5 0.462 48.5 50.4 316s 16 51.8 0.381 51.0 52.5 316s 17 55.8 0.423 55.0 56.7 316s 18 59.2 0.355 58.5 59.9 316s 19 57.8 0.484 56.8 58.8 316s 20 60.2 0.500 59.2 61.2 316s 21 63.6 0.490 62.6 64.6 316s 22 70.9 0.747 69.4 72.4 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 2.0888 0.985 0.105 4.072 316s 3 1.8302 0.708 0.404 3.257 316s 4 4.6632 0.612 3.430 5.897 316s 5 4.6917 0.519 3.645 5.738 316s 6 4.8028 0.498 3.800 5.806 316s 7 NA NA NA NA 316s 8 2.8277 0.410 2.003 3.653 316s 9 2.1139 0.599 0.908 3.320 316s 10 2.4426 0.651 1.131 3.754 316s 11 1.9736 1.138 -0.320 4.267 316s 12 -2.5370 1.038 -4.627 -0.447 316s 13 NA NA NA NA 316s 14 -6.8151 1.011 -8.851 -4.779 316s 15 -2.8007 0.587 -3.984 -1.617 316s 16 -1.4448 0.470 -2.392 -0.498 316s 17 -0.0295 0.573 -1.183 1.124 316s 18 2.1493 0.380 1.384 2.915 316s 19 1.5730 0.624 0.315 2.831 316s 20 0.4434 0.649 -0.864 1.751 316s 21 2.8090 0.565 1.671 3.947 316s 22 3.6208 0.814 1.982 5.260 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.7 0.322 26.0 27.3 316s 3 28.8 0.328 28.2 29.5 316s 4 32.8 0.332 32.1 33.4 316s 5 34.1 0.244 33.6 34.6 316s 6 35.9 0.252 35.4 36.4 316s 7 NA NA NA NA 316s 8 38.8 0.246 38.3 39.3 316s 9 39.0 0.234 38.6 39.5 316s 10 40.2 0.230 39.8 40.7 316s 11 38.3 0.299 37.7 38.9 316s 12 34.1 0.304 33.5 34.7 316s 13 29.0 0.366 28.2 29.7 316s 14 27.8 0.321 27.2 28.5 316s 15 30.0 0.317 29.4 30.7 316s 16 33.0 0.266 32.4 33.5 316s 17 37.5 0.270 36.9 38.0 316s 18 40.0 0.211 39.6 40.5 316s 19 38.8 0.305 38.2 39.4 316s 20 41.9 0.290 41.3 42.4 316s 21 46.1 0.309 45.5 46.8 316s 22 52.8 0.468 51.8 53.7 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 316s [3] "Numeric: lengths (708, 684) differ" 316s > nobs 316s [1] 57 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 45 1 2.17 0.15 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 45 1 2.84 0.099 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 46 316s 2 45 1 2.84 0.092 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 45 2 2.45 0.098 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 45 2 3.2 0.05 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 47 316s 2 45 2 6.4 0.041 * 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s > logLik 316s 'log Lik.' -72.7 (df=18) 316s 'log Lik.' -83.9 (df=18) 316s > 316s > # OLS 316s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: OLS 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 58 46 44.2 0.565 0.976 0.991 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 316s Investment 19 15 17.11 1.140 1.07 0.907 0.889 316s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.285 0.061 -0.511 316s Investment 0.061 1.059 0.151 316s PrivateWages -0.511 0.151 0.648 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.0000 0.0457 -0.568 316s Investment 0.0457 1.0000 0.168 316s PrivateWages -0.5681 0.1676 1.000 316s 316s 316s OLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.2957 1.5438 10.56 2.4e-08 *** 316s corpProf 0.1796 0.1206 1.49 0.16 316s corpProfLag 0.1032 0.1031 1.00 0.33 316s wages 0.7962 0.0449 17.73 1.8e-11 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.076 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 316s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 316s 316s 316s OLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 10.1724 5.5758 1.82 0.08808 . 316s corpProf 0.5004 0.1092 4.58 0.00036 *** 316s corpProfLag 0.3270 0.1052 3.11 0.00718 ** 316s capitalLag -0.1134 0.0275 -4.13 0.00090 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.068 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 17.105 MSE: 1.14 Root MSE: 1.068 316s Multiple R-Squared: 0.907 Adjusted R-Squared: 0.889 316s 316s 316s OLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3550 1.3512 1.00 0.3309 316s gnp 0.4417 0.0342 12.92 7e-10 *** 316s gnpLag 0.1466 0.0393 3.73 0.0018 ** 316s trend 0.1244 0.0347 3.58 0.0025 ** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.78 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 316s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 316s 316s compare coef with single-equation OLS 316s [1] TRUE 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.3863 0.00693 -1.3389 316s 3 -1.2484 -0.06954 0.2462 316s 4 -1.6040 1.22401 1.1255 316s 5 -0.5384 -1.37697 -0.1959 316s 6 -0.0413 0.38610 -0.5284 316s 7 0.8043 1.48598 NA 316s 8 1.2830 0.78465 -0.7909 316s 9 1.0142 -0.65483 0.2819 316s 10 NA 1.06018 1.1384 316s 11 0.1429 0.39508 -0.1904 316s 12 -0.3439 0.20479 0.5813 316s 13 NA NA 0.1206 316s 14 0.3199 0.32778 0.4773 316s 15 -0.1016 -0.07450 0.3035 316s 16 -0.0702 NA 0.0284 316s 17 1.6064 0.96998 -0.8517 316s 18 -0.4980 0.08124 0.9908 316s 19 0.1253 -2.49295 -0.4597 316s 20 0.9805 -0.70609 -0.3819 316s 21 0.7551 -0.81928 -1.1062 316s 22 -2.1992 -0.73256 0.5501 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.3 -0.207 26.8 316s 3 46.2 1.970 29.1 316s 4 50.8 3.976 33.0 316s 5 51.1 4.377 34.1 316s 6 52.6 4.714 35.9 316s 7 54.3 4.114 NA 316s 8 54.9 3.415 38.7 316s 9 56.3 3.655 38.9 316s 10 NA 4.040 40.2 316s 11 54.9 0.605 38.1 316s 12 51.2 -3.605 33.9 316s 13 NA NA 28.9 316s 14 46.2 -5.428 28.0 316s 15 48.8 -2.926 30.3 316s 16 51.4 NA 33.2 316s 17 56.1 1.130 37.7 316s 18 59.2 1.919 40.0 316s 19 57.4 0.593 38.7 316s 20 60.6 2.006 42.0 316s 21 64.2 4.119 46.1 316s 22 71.9 5.633 52.7 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.3 0.543 39.9 44.7 316s 3 46.2 0.581 43.8 48.7 316s 4 50.8 0.394 48.5 53.1 316s 5 51.1 0.465 48.8 53.5 316s 6 52.6 0.474 50.3 55.0 316s 7 54.3 0.423 52.0 56.6 316s 8 54.9 0.389 52.6 57.2 316s 9 56.3 0.434 54.0 58.6 316s 10 NA NA NA NA 316s 11 54.9 0.727 52.2 57.5 316s 12 51.2 0.662 48.7 53.8 316s 13 NA NA NA NA 316s 14 46.2 0.698 43.6 48.8 316s 15 48.8 0.470 46.4 51.2 316s 16 51.4 0.398 49.1 53.7 316s 17 56.1 0.405 53.8 58.4 316s 18 59.2 0.375 56.9 61.5 316s 19 57.4 0.466 55.0 59.7 316s 20 60.6 0.482 58.2 63.0 316s 21 64.2 0.485 61.9 66.6 316s 22 71.9 0.755 69.3 74.5 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 -0.207 0.645 -2.718 2.30 316s 3 1.970 0.523 -0.423 4.36 316s 4 3.976 0.462 1.634 6.32 316s 5 4.377 0.383 2.094 6.66 316s 6 4.714 0.362 2.444 6.98 316s 7 4.114 0.336 1.861 6.37 316s 8 3.415 0.298 1.184 5.65 316s 9 3.655 0.400 1.359 5.95 316s 10 4.040 0.458 1.701 6.38 316s 11 0.605 0.666 -1.928 3.14 316s 12 -3.605 0.637 -6.108 -1.10 316s 13 NA NA NA NA 316s 14 -5.428 0.767 -8.074 -2.78 316s 15 -2.926 0.453 -5.261 -0.59 316s 16 NA NA NA NA 316s 17 1.130 0.366 -1.142 3.40 316s 18 1.919 0.258 -0.293 4.13 316s 19 0.593 0.357 -1.674 2.86 316s 20 2.006 0.384 -0.278 4.29 316s 21 4.119 0.350 1.858 6.38 316s 22 5.633 0.495 3.263 8.00 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.8 0.378 25.1 28.6 316s 3 29.1 0.381 27.3 30.8 316s 4 33.0 0.384 31.2 34.7 316s 5 34.1 0.297 32.4 35.8 316s 6 35.9 0.296 34.2 37.6 316s 7 NA NA NA NA 316s 8 38.7 0.303 37.0 40.4 316s 9 38.9 0.288 37.2 40.6 316s 10 40.2 0.274 38.5 41.8 316s 11 38.1 0.377 36.3 39.8 316s 12 33.9 0.381 32.2 35.7 316s 13 28.9 0.452 27.1 30.7 316s 14 28.0 0.397 26.3 29.8 316s 15 30.3 0.391 28.5 32.1 316s 16 33.2 0.327 31.5 34.9 316s 17 37.7 0.320 36.0 39.3 316s 18 40.0 0.250 38.4 41.7 316s 19 38.7 0.375 36.9 40.4 316s 20 42.0 0.337 40.3 43.7 316s 21 46.1 0.352 44.4 47.8 316s 22 52.7 0.530 50.9 54.6 316s > model.frame 316s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 316s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 316s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 316s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 316s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 316s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 316s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 316s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 316s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 316s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 316s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 316s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 316s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 316s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 316s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 316s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 316s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 316s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 316s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 316s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 316s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 316s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 316s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 316s trend 316s 1 -11 316s 2 -10 316s 3 -9 316s 4 -8 316s 5 -7 316s 6 -6 316s 7 -5 316s 8 -4 316s 9 -3 316s 10 -2 316s 11 -1 316s 12 0 316s 13 1 316s 14 2 316s 15 3 316s 16 4 316s 17 5 316s 18 6 316s 19 7 316s 20 8 316s 21 9 316s 22 10 316s > model.matrix 316s Consumption_(Intercept) Consumption_corpProf 316s Consumption_2 1 12.4 316s Consumption_3 1 16.9 316s Consumption_4 1 18.4 316s Consumption_5 1 19.4 316s Consumption_6 1 20.1 316s Consumption_7 1 19.6 316s Consumption_8 1 19.8 316s Consumption_9 1 21.1 316s Consumption_11 1 15.6 316s Consumption_12 1 11.4 316s Consumption_14 1 11.2 316s Consumption_15 1 12.3 316s Consumption_16 1 14.0 316s Consumption_17 1 17.6 316s Consumption_18 1 17.3 316s Consumption_19 1 15.3 316s Consumption_20 1 19.0 316s Consumption_21 1 21.1 316s Consumption_22 1 23.5 316s Investment_2 0 0.0 316s Investment_3 0 0.0 316s Investment_4 0 0.0 316s Investment_5 0 0.0 316s Investment_6 0 0.0 316s Investment_7 0 0.0 316s Investment_8 0 0.0 316s Investment_9 0 0.0 316s Investment_10 0 0.0 316s Investment_11 0 0.0 316s Investment_12 0 0.0 316s Investment_14 0 0.0 316s Investment_15 0 0.0 316s Investment_17 0 0.0 316s Investment_18 0 0.0 316s Investment_19 0 0.0 316s Investment_20 0 0.0 316s Investment_21 0 0.0 316s Investment_22 0 0.0 316s PrivateWages_2 0 0.0 316s PrivateWages_3 0 0.0 316s PrivateWages_4 0 0.0 316s PrivateWages_5 0 0.0 316s PrivateWages_6 0 0.0 316s PrivateWages_8 0 0.0 316s PrivateWages_9 0 0.0 316s PrivateWages_10 0 0.0 316s PrivateWages_11 0 0.0 316s PrivateWages_12 0 0.0 316s PrivateWages_13 0 0.0 316s PrivateWages_14 0 0.0 316s PrivateWages_15 0 0.0 316s PrivateWages_16 0 0.0 316s PrivateWages_17 0 0.0 316s PrivateWages_18 0 0.0 316s PrivateWages_19 0 0.0 316s PrivateWages_20 0 0.0 316s PrivateWages_21 0 0.0 316s PrivateWages_22 0 0.0 316s Consumption_corpProfLag Consumption_wages 316s Consumption_2 12.7 28.2 316s Consumption_3 12.4 32.2 316s Consumption_4 16.9 37.0 316s Consumption_5 18.4 37.0 316s Consumption_6 19.4 38.6 316s Consumption_7 20.1 40.7 316s Consumption_8 19.6 41.5 316s Consumption_9 19.8 42.9 316s Consumption_11 21.7 42.1 316s Consumption_12 15.6 39.3 316s Consumption_14 7.0 34.1 316s Consumption_15 11.2 36.6 316s Consumption_16 12.3 39.3 316s Consumption_17 14.0 44.2 316s Consumption_18 17.6 47.7 316s Consumption_19 17.3 45.9 316s Consumption_20 15.3 49.4 316s Consumption_21 19.0 53.0 316s Consumption_22 21.1 61.8 316s Investment_2 0.0 0.0 316s Investment_3 0.0 0.0 316s Investment_4 0.0 0.0 316s Investment_5 0.0 0.0 316s Investment_6 0.0 0.0 316s Investment_7 0.0 0.0 316s Investment_8 0.0 0.0 316s Investment_9 0.0 0.0 316s Investment_10 0.0 0.0 316s Investment_11 0.0 0.0 316s Investment_12 0.0 0.0 316s Investment_14 0.0 0.0 316s Investment_15 0.0 0.0 316s Investment_17 0.0 0.0 316s Investment_18 0.0 0.0 316s Investment_19 0.0 0.0 316s Investment_20 0.0 0.0 316s Investment_21 0.0 0.0 316s Investment_22 0.0 0.0 316s PrivateWages_2 0.0 0.0 316s PrivateWages_3 0.0 0.0 316s PrivateWages_4 0.0 0.0 316s PrivateWages_5 0.0 0.0 316s PrivateWages_6 0.0 0.0 316s PrivateWages_8 0.0 0.0 316s PrivateWages_9 0.0 0.0 316s PrivateWages_10 0.0 0.0 316s PrivateWages_11 0.0 0.0 316s PrivateWages_12 0.0 0.0 316s PrivateWages_13 0.0 0.0 316s PrivateWages_14 0.0 0.0 316s PrivateWages_15 0.0 0.0 316s PrivateWages_16 0.0 0.0 316s PrivateWages_17 0.0 0.0 316s PrivateWages_18 0.0 0.0 316s PrivateWages_19 0.0 0.0 316s PrivateWages_20 0.0 0.0 316s PrivateWages_21 0.0 0.0 316s PrivateWages_22 0.0 0.0 316s Investment_(Intercept) Investment_corpProf 316s Consumption_2 0 0.0 316s Consumption_3 0 0.0 316s Consumption_4 0 0.0 316s Consumption_5 0 0.0 316s Consumption_6 0 0.0 316s Consumption_7 0 0.0 316s Consumption_8 0 0.0 316s Consumption_9 0 0.0 316s Consumption_11 0 0.0 316s Consumption_12 0 0.0 316s Consumption_14 0 0.0 316s Consumption_15 0 0.0 316s Consumption_16 0 0.0 316s Consumption_17 0 0.0 316s Consumption_18 0 0.0 316s Consumption_19 0 0.0 316s Consumption_20 0 0.0 316s Consumption_21 0 0.0 316s Consumption_22 0 0.0 316s Investment_2 1 12.4 316s Investment_3 1 16.9 316s Investment_4 1 18.4 316s Investment_5 1 19.4 316s Investment_6 1 20.1 316s Investment_7 1 19.6 316s Investment_8 1 19.8 316s Investment_9 1 21.1 316s Investment_10 1 21.7 316s Investment_11 1 15.6 316s Investment_12 1 11.4 316s Investment_14 1 11.2 316s Investment_15 1 12.3 316s Investment_17 1 17.6 316s Investment_18 1 17.3 316s Investment_19 1 15.3 316s Investment_20 1 19.0 316s Investment_21 1 21.1 316s Investment_22 1 23.5 316s PrivateWages_2 0 0.0 316s PrivateWages_3 0 0.0 316s PrivateWages_4 0 0.0 316s PrivateWages_5 0 0.0 316s PrivateWages_6 0 0.0 316s PrivateWages_8 0 0.0 316s PrivateWages_9 0 0.0 316s PrivateWages_10 0 0.0 316s PrivateWages_11 0 0.0 316s PrivateWages_12 0 0.0 316s PrivateWages_13 0 0.0 316s PrivateWages_14 0 0.0 316s PrivateWages_15 0 0.0 316s PrivateWages_16 0 0.0 316s PrivateWages_17 0 0.0 316s PrivateWages_18 0 0.0 316s PrivateWages_19 0 0.0 316s PrivateWages_20 0 0.0 316s PrivateWages_21 0 0.0 316s PrivateWages_22 0 0.0 316s Investment_corpProfLag Investment_capitalLag 316s Consumption_2 0.0 0 316s Consumption_3 0.0 0 316s Consumption_4 0.0 0 316s Consumption_5 0.0 0 316s Consumption_6 0.0 0 316s Consumption_7 0.0 0 316s Consumption_8 0.0 0 316s Consumption_9 0.0 0 316s Consumption_11 0.0 0 316s Consumption_12 0.0 0 316s Consumption_14 0.0 0 316s Consumption_15 0.0 0 316s Consumption_16 0.0 0 316s Consumption_17 0.0 0 316s Consumption_18 0.0 0 316s Consumption_19 0.0 0 316s Consumption_20 0.0 0 316s Consumption_21 0.0 0 316s Consumption_22 0.0 0 316s Investment_2 12.7 183 316s Investment_3 12.4 183 316s Investment_4 16.9 184 316s Investment_5 18.4 190 316s Investment_6 19.4 193 316s Investment_7 20.1 198 316s Investment_8 19.6 203 316s Investment_9 19.8 208 316s Investment_10 21.1 211 316s Investment_11 21.7 216 316s Investment_12 15.6 217 316s Investment_14 7.0 207 316s Investment_15 11.2 202 316s Investment_17 14.0 198 316s Investment_18 17.6 200 316s Investment_19 17.3 202 316s Investment_20 15.3 200 316s Investment_21 19.0 201 316s Investment_22 21.1 204 316s PrivateWages_2 0.0 0 316s PrivateWages_3 0.0 0 316s PrivateWages_4 0.0 0 316s PrivateWages_5 0.0 0 316s PrivateWages_6 0.0 0 316s PrivateWages_8 0.0 0 316s PrivateWages_9 0.0 0 316s PrivateWages_10 0.0 0 316s PrivateWages_11 0.0 0 316s PrivateWages_12 0.0 0 316s PrivateWages_13 0.0 0 316s PrivateWages_14 0.0 0 316s PrivateWages_15 0.0 0 316s PrivateWages_16 0.0 0 316s PrivateWages_17 0.0 0 316s PrivateWages_18 0.0 0 316s PrivateWages_19 0.0 0 316s PrivateWages_20 0.0 0 316s PrivateWages_21 0.0 0 316s PrivateWages_22 0.0 0 316s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 316s Consumption_2 0 0.0 0.0 316s Consumption_3 0 0.0 0.0 316s Consumption_4 0 0.0 0.0 316s Consumption_5 0 0.0 0.0 316s Consumption_6 0 0.0 0.0 316s Consumption_7 0 0.0 0.0 316s Consumption_8 0 0.0 0.0 316s Consumption_9 0 0.0 0.0 316s Consumption_11 0 0.0 0.0 316s Consumption_12 0 0.0 0.0 316s Consumption_14 0 0.0 0.0 316s Consumption_15 0 0.0 0.0 316s Consumption_16 0 0.0 0.0 316s Consumption_17 0 0.0 0.0 316s Consumption_18 0 0.0 0.0 316s Consumption_19 0 0.0 0.0 316s Consumption_20 0 0.0 0.0 316s Consumption_21 0 0.0 0.0 316s Consumption_22 0 0.0 0.0 316s Investment_2 0 0.0 0.0 316s Investment_3 0 0.0 0.0 316s Investment_4 0 0.0 0.0 316s Investment_5 0 0.0 0.0 316s Investment_6 0 0.0 0.0 316s Investment_7 0 0.0 0.0 316s Investment_8 0 0.0 0.0 316s Investment_9 0 0.0 0.0 316s Investment_10 0 0.0 0.0 316s Investment_11 0 0.0 0.0 316s Investment_12 0 0.0 0.0 316s Investment_14 0 0.0 0.0 316s Investment_15 0 0.0 0.0 316s Investment_17 0 0.0 0.0 316s Investment_18 0 0.0 0.0 316s Investment_19 0 0.0 0.0 316s Investment_20 0 0.0 0.0 316s Investment_21 0 0.0 0.0 316s Investment_22 0 0.0 0.0 316s PrivateWages_2 1 45.6 44.9 316s PrivateWages_3 1 50.1 45.6 316s PrivateWages_4 1 57.2 50.1 316s PrivateWages_5 1 57.1 57.2 316s PrivateWages_6 1 61.0 57.1 316s PrivateWages_8 1 64.4 64.0 316s PrivateWages_9 1 64.5 64.4 316s PrivateWages_10 1 67.0 64.5 316s PrivateWages_11 1 61.2 67.0 316s PrivateWages_12 1 53.4 61.2 316s PrivateWages_13 1 44.3 53.4 316s PrivateWages_14 1 45.1 44.3 316s PrivateWages_15 1 49.7 45.1 316s PrivateWages_16 1 54.4 49.7 316s PrivateWages_17 1 62.7 54.4 316s PrivateWages_18 1 65.0 62.7 316s PrivateWages_19 1 60.9 65.0 316s PrivateWages_20 1 69.5 60.9 316s PrivateWages_21 1 75.7 69.5 316s PrivateWages_22 1 88.4 75.7 316s PrivateWages_trend 316s Consumption_2 0 316s Consumption_3 0 316s Consumption_4 0 316s Consumption_5 0 316s Consumption_6 0 316s Consumption_7 0 316s Consumption_8 0 316s Consumption_9 0 316s Consumption_11 0 316s Consumption_12 0 316s Consumption_14 0 316s Consumption_15 0 316s Consumption_16 0 316s Consumption_17 0 316s Consumption_18 0 316s Consumption_19 0 316s Consumption_20 0 316s Consumption_21 0 316s Consumption_22 0 316s Investment_2 0 316s Investment_3 0 316s Investment_4 0 316s Investment_5 0 316s Investment_6 0 316s Investment_7 0 316s Investment_8 0 316s Investment_9 0 316s Investment_10 0 316s Investment_11 0 316s Investment_12 0 316s Investment_14 0 316s Investment_15 0 316s Investment_17 0 316s Investment_18 0 316s Investment_19 0 316s Investment_20 0 316s Investment_21 0 316s Investment_22 0 316s PrivateWages_2 -10 316s PrivateWages_3 -9 316s PrivateWages_4 -8 316s PrivateWages_5 -7 316s PrivateWages_6 -6 316s PrivateWages_8 -4 316s PrivateWages_9 -3 316s PrivateWages_10 -2 316s PrivateWages_11 -1 316s PrivateWages_12 0 316s PrivateWages_13 1 316s PrivateWages_14 2 316s PrivateWages_15 3 316s PrivateWages_16 4 316s PrivateWages_17 5 316s PrivateWages_18 6 316s PrivateWages_19 7 316s PrivateWages_20 8 316s PrivateWages_21 9 316s PrivateWages_22 10 316s > nobs 316s [1] 58 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 46 1 0.3 0.59 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 46 1 0.29 0.6 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 47 316s 2 46 1 0.29 0.59 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 46 2 0.16 0.85 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 46 2 0.15 0.86 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 48 316s 2 46 2 0.3 0.86 316s > logLik 316s 'log Lik.' -68.8 (df=13) 316s 'log Lik.' -73.3 (df=13) 316s compare log likelihood value with single-equation OLS 316s [1] "Mean relative difference: 0.0011" 316s > 316s > # 2SLS 316s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: 2SLS 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 56 44 57.9 0.391 0.968 0.992 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 316s Investment 18 14 25.85 1.847 1.36 0.847 0.815 316s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.307 0.540 -0.431 316s Investment 0.540 1.319 0.119 316s PrivateWages -0.431 0.119 0.496 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.414 -0.538 316s Investment 0.414 1.000 0.139 316s PrivateWages -0.538 0.139 1.000 316s 316s 316s 2SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 17.2849 1.6463 10.50 5.1e-08 *** 316s corpProf -0.0770 0.1683 -0.46 0.65 316s corpProfLag 0.2327 0.1276 1.82 0.09 . 316s wages 0.8259 0.0472 17.49 6.6e-11 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.261 on 14 degrees of freedom 316s Number of observations: 18 Degrees of Freedom: 14 316s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 316s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 316s 316s 316s 2SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 18.2571 7.3132 2.50 0.02564 * 316s corpProf 0.1564 0.1942 0.81 0.43408 316s corpProfLag 0.5714 0.1672 3.42 0.00417 ** 316s capitalLag -0.1446 0.0346 -4.18 0.00093 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.359 on 14 degrees of freedom 316s Number of observations: 18 Degrees of Freedom: 14 316s SSR: 25.852 MSE: 1.847 Root MSE: 1.359 316s Multiple R-Squared: 0.847 Adjusted R-Squared: 0.815 316s 316s 316s 2SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3431 1.1879 1.13 0.275 316s gnp 0.4438 0.0361 12.28 1.5e-09 *** 316s gnpLag 0.1447 0.0392 3.69 0.002 ** 316s trend 0.1238 0.0308 4.01 0.001 ** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.78 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 316s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.6754 -1.214 -1.3401 316s 3 -0.4627 0.325 0.2378 316s 4 -1.1585 1.094 1.1117 316s 5 -0.0305 -1.368 -0.1954 316s 6 0.4693 0.486 -0.5355 316s 7 NA NA NA 316s 8 1.6045 1.066 -0.7908 316s 9 1.6018 0.156 0.2831 316s 10 NA 1.853 1.1353 316s 11 -0.9031 -0.898 -0.1765 316s 12 -1.5948 -1.012 0.6007 316s 13 NA NA 0.1443 316s 14 0.2854 0.845 0.4826 316s 15 -0.4718 -0.365 0.3016 316s 16 -0.2268 NA 0.0261 316s 17 2.0079 1.685 -0.8614 316s 18 -0.7434 -0.121 0.9927 316s 19 -0.5410 -3.248 -0.4446 316s 20 1.4186 0.241 -0.3914 316s 21 1.1462 -0.013 -1.1115 316s 22 -1.7256 0.489 0.5312 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.6 1.014 26.8 316s 3 45.5 1.575 29.1 316s 4 50.4 4.106 33.0 316s 5 50.6 4.368 34.1 316s 6 52.1 4.614 35.9 316s 7 NA NA NA 316s 8 54.6 3.134 38.7 316s 9 55.7 2.844 38.9 316s 10 NA 3.247 40.2 316s 11 55.9 1.898 38.1 316s 12 52.5 -2.388 33.9 316s 13 NA NA 28.9 316s 14 46.2 -5.945 28.0 316s 15 49.2 -2.635 30.3 316s 16 51.5 NA 33.2 316s 17 55.7 0.415 37.7 316s 18 59.4 2.121 40.0 316s 19 58.0 1.348 38.6 316s 20 60.2 1.059 42.0 316s 21 63.9 3.313 46.1 316s 22 71.4 4.411 52.8 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.6 0.586 41.3 43.8 316s 3 45.5 0.674 44.0 46.9 316s 4 50.4 0.443 49.4 51.3 316s 5 50.6 0.524 49.5 51.8 316s 6 52.1 0.535 51.0 53.3 316s 7 NA NA NA NA 316s 8 54.6 0.431 53.7 55.5 316s 9 55.7 0.510 54.6 56.8 316s 10 NA NA NA NA 316s 11 55.9 0.936 53.9 57.9 316s 12 52.5 0.893 50.6 54.4 316s 13 NA NA NA NA 316s 14 46.2 0.713 44.7 47.7 316s 15 49.2 0.501 48.1 50.2 316s 16 51.5 0.407 50.7 52.4 316s 17 55.7 0.457 54.7 56.7 316s 18 59.4 0.397 58.6 60.3 316s 19 58.0 0.564 56.8 59.2 316s 20 60.2 0.543 59.0 61.3 316s 21 63.9 0.529 62.7 65.0 316s 22 71.4 0.808 69.7 73.2 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 1.014 0.919 -0.957 2.985 316s 3 1.575 0.602 0.284 2.867 316s 4 4.106 0.544 2.940 5.272 316s 5 4.368 0.450 3.402 5.333 316s 6 4.614 0.425 3.703 5.526 316s 7 NA NA NA NA 316s 8 3.134 0.352 2.380 3.889 316s 9 2.844 0.544 1.677 4.012 316s 10 3.247 0.592 1.976 4.518 316s 11 1.898 0.978 -0.200 3.996 316s 12 -2.388 0.886 -4.289 -0.488 316s 13 NA NA NA NA 316s 14 -5.945 0.916 -7.909 -3.980 316s 15 -2.635 0.518 -3.745 -1.525 316s 16 NA NA NA NA 316s 17 0.415 0.507 -0.671 1.501 316s 18 2.121 0.329 1.416 2.826 316s 19 1.348 0.551 0.166 2.529 316s 20 1.059 0.582 -0.189 2.306 316s 21 3.313 0.496 2.248 4.377 316s 22 4.411 0.728 2.850 5.971 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.8 0.330 26.1 27.5 316s 3 29.1 0.344 28.3 29.8 316s 4 33.0 0.363 32.2 33.8 316s 5 34.1 0.260 33.5 34.6 316s 6 35.9 0.268 35.4 36.5 316s 7 NA NA NA NA 316s 8 38.7 0.265 38.1 39.3 316s 9 38.9 0.252 38.4 39.5 316s 10 40.2 0.242 39.7 40.7 316s 11 38.1 0.358 37.3 38.8 316s 12 33.9 0.385 33.1 34.7 316s 13 28.9 0.460 27.9 29.8 316s 14 28.0 0.351 27.3 28.8 316s 15 30.3 0.343 29.6 31.0 316s 16 33.2 0.287 32.6 33.8 316s 17 37.7 0.296 37.0 38.3 316s 18 40.0 0.220 39.5 40.5 316s 19 38.6 0.361 37.9 39.4 316s 20 42.0 0.309 41.3 42.6 316s 21 46.1 0.312 45.4 46.8 316s 22 52.8 0.501 51.7 53.8 316s > model.frame 316s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 316s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 316s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 316s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 316s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 316s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 316s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 316s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 316s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 316s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 316s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 316s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 316s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 316s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 316s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 316s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 316s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 316s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 316s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 316s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 316s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 316s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 316s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 316s trend 316s 1 -11 316s 2 -10 316s 3 -9 316s 4 -8 316s 5 -7 316s 6 -6 316s 7 -5 316s 8 -4 316s 9 -3 316s 10 -2 316s 11 -1 316s 12 0 316s 13 1 316s 14 2 316s 15 3 316s 16 4 316s 17 5 316s 18 6 316s 19 7 316s 20 8 316s 21 9 316s 22 10 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 316s [3] "Numeric: lengths (696, 672) differ" 316s > nobs 316s [1] 56 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 45 316s 2 44 1 1.27 0.27 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 45 316s 2 44 1 1.66 0.2 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 45 316s 2 44 1 1.66 0.2 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 44 2 0.64 0.53 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 44 2 0.84 0.44 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 46 316s 2 44 2 1.68 0.43 316s > logLik 316s 'log Lik.' -69.5 (df=13) 316s 'log Lik.' -77.5 (df=13) 316s > 316s > # SUR 316s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: SUR 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 58 46 45.1 0.199 0.975 0.993 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 316s Investment 19 15 17.3 1.155 1.075 0.906 0.887 316s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 0.9830 0.0466 -0.391 316s Investment 0.0466 0.8101 0.115 316s PrivateWages -0.3906 0.1155 0.496 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 0.979 0.080 -0.452 316s Investment 0.080 0.810 0.181 316s PrivateWages -0.452 0.181 0.521 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.0000 0.0907 -0.636 316s Investment 0.0907 1.0000 0.267 316s PrivateWages -0.6362 0.2671 1.000 316s 316s 316s SUR estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 16.2670 1.3148 12.37 2.8e-09 *** 316s corpProf 0.1942 0.0954 2.04 0.06 . 316s corpProfLag 0.0747 0.0842 0.89 0.39 316s wages 0.8011 0.0383 20.93 1.6e-12 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.08 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 316s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 316s 316s 316s SUR estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 12.6390 4.7856 2.64 0.01852 * 316s corpProf 0.4708 0.0943 4.99 0.00016 *** 316s corpProfLag 0.3533 0.0907 3.89 0.00144 ** 316s capitalLag -0.1254 0.0236 -5.32 8.6e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.075 on 15 degrees of freedom 316s Number of observations: 19 Degrees of Freedom: 15 316s SSR: 17.321 MSE: 1.155 Root MSE: 1.075 316s Multiple R-Squared: 0.906 Adjusted R-Squared: 0.887 316s 316s 316s SUR estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 1.3264 1.1240 1.18 0.2552 316s gnp 0.4184 0.0268 15.63 4.1e-11 *** 316s gnpLag 0.1714 0.0315 5.43 5.5e-05 *** 316s trend 0.1456 0.0284 5.13 0.0001 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.801 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 10.266 MSE: 0.642 Root MSE: 0.801 316s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.3143 -0.2326 -1.1434 316s 3 -1.2700 -0.1705 0.5084 316s 4 -1.5426 1.0718 1.4211 316s 5 -0.4489 -1.4767 -0.0992 316s 6 0.0588 0.3167 -0.3594 316s 7 0.9213 1.4446 NA 316s 8 1.3789 0.8296 -0.7554 316s 9 1.0900 -0.5263 0.2887 316s 10 NA 1.2083 1.1800 316s 11 0.3569 0.4082 -0.3673 316s 12 -0.2288 0.2663 0.3445 316s 13 NA NA -0.1571 316s 14 0.2181 0.4946 0.4220 316s 15 -0.1120 -0.0470 0.3147 316s 16 -0.0872 NA 0.0145 316s 17 1.5615 1.0289 -0.8091 316s 18 -0.4530 0.0617 0.8608 316s 19 0.1997 -2.5397 -0.7635 316s 20 0.9268 -0.6136 -0.4046 316s 21 0.7588 -0.7465 -1.2179 316s 22 -2.2137 -0.6044 0.5606 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.2 0.0326 26.6 316s 3 46.3 2.0705 28.8 316s 4 50.7 4.1282 32.7 316s 5 51.0 4.4767 34.0 316s 6 52.5 4.7833 35.8 316s 7 54.2 4.1554 NA 316s 8 54.8 3.3704 38.7 316s 9 56.2 3.5263 38.9 316s 10 NA 3.8917 40.1 316s 11 54.6 0.5918 38.3 316s 12 51.1 -3.6663 34.2 316s 13 NA NA 29.2 316s 14 46.3 -5.5946 28.1 316s 15 48.8 -2.9530 30.3 316s 16 51.4 NA 33.2 316s 17 56.1 1.0711 37.6 316s 18 59.2 1.9383 40.1 316s 19 57.3 0.6397 39.0 316s 20 60.7 1.9136 42.0 316s 21 64.2 4.0465 46.2 316s 22 71.9 5.5044 52.7 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.2 0.460 41.3 43.1 316s 3 46.3 0.489 45.3 47.3 316s 4 50.7 0.328 50.1 51.4 316s 5 51.0 0.384 50.3 51.8 316s 6 52.5 0.389 51.8 53.3 316s 7 54.2 0.347 53.5 54.9 316s 8 54.8 0.319 54.2 55.5 316s 9 56.2 0.353 55.5 56.9 316s 10 NA NA NA NA 316s 11 54.6 0.583 53.5 55.8 316s 12 51.1 0.524 50.1 52.2 316s 13 NA NA NA NA 316s 14 46.3 0.589 45.1 47.5 316s 15 48.8 0.393 48.0 49.6 316s 16 51.4 0.337 50.7 52.1 316s 17 56.1 0.345 55.4 56.8 316s 18 59.2 0.318 58.5 59.8 316s 19 57.3 0.381 56.5 58.1 316s 20 60.7 0.413 59.8 61.5 316s 21 64.2 0.417 63.4 65.1 316s 22 71.9 0.651 70.6 73.2 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 0.0326 0.556 -1.0866 1.15 316s 3 2.0705 0.454 1.1575 2.98 316s 4 4.1282 0.399 3.3256 4.93 316s 5 4.4767 0.331 3.8101 5.14 316s 6 4.7833 0.314 4.1520 5.41 316s 7 4.1554 0.291 3.5687 4.74 316s 8 3.3704 0.260 2.8469 3.89 316s 9 3.5263 0.347 2.8278 4.22 316s 10 3.8917 0.397 3.0924 4.69 316s 11 0.5918 0.578 -0.5711 1.75 316s 12 -3.6663 0.551 -4.7762 -2.56 316s 13 NA NA NA NA 316s 14 -5.5946 0.661 -6.9261 -4.26 316s 15 -2.9530 0.392 -3.7430 -2.16 316s 16 NA NA NA NA 316s 17 1.0711 0.318 0.4315 1.71 316s 18 1.9383 0.225 1.4863 2.39 316s 19 0.6397 0.310 0.0165 1.26 316s 20 1.9136 0.333 1.2436 2.58 316s 21 4.0465 0.304 3.4345 4.66 316s 22 5.5044 0.429 4.6400 6.37 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.6 0.321 26.0 27.3 316s 3 28.8 0.321 28.1 29.4 316s 4 32.7 0.316 32.0 33.3 316s 5 34.0 0.244 33.5 34.5 316s 6 35.8 0.242 35.3 36.2 316s 7 NA NA NA NA 316s 8 38.7 0.246 38.2 39.2 316s 9 38.9 0.234 38.4 39.4 316s 10 40.1 0.225 39.7 40.6 316s 11 38.3 0.301 37.7 38.9 316s 12 34.2 0.298 33.6 34.8 316s 13 29.2 0.353 28.4 29.9 316s 14 28.1 0.330 27.4 28.7 316s 15 30.3 0.328 29.6 30.9 316s 16 33.2 0.275 32.6 33.7 316s 17 37.6 0.270 37.1 38.2 316s 18 40.1 0.213 39.7 40.6 316s 19 39.0 0.301 38.4 39.6 316s 20 42.0 0.287 41.4 42.6 316s 21 46.2 0.304 45.6 46.8 316s 22 52.7 0.448 51.8 53.6 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] TRUE 316s > nobs 316s [1] 58 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 46 1 0.4 0.53 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 47 316s 2 46 1 0.49 0.49 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 47 316s 2 46 1 0.49 0.48 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 46 2 0.31 0.74 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 48 316s 2 46 2 0.37 0.69 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 48 316s 2 46 2 0.75 0.69 316s > logLik 316s 'log Lik.' -66.4 (df=18) 316s 'log Lik.' -74.1 (df=18) 316s > 316s > # 3SLS 316s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: 3SLS 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 56 44 67.5 0.436 0.963 0.993 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 18 14 22.4 1.598 1.264 0.974 0.968 316s Investment 18 14 35.0 2.503 1.582 0.793 0.749 316s PrivateWages 20 16 10.1 0.629 0.793 0.987 0.985 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 1.307 0.540 -0.431 316s Investment 0.540 1.319 0.119 316s PrivateWages -0.431 0.119 0.496 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.309 0.638 -0.440 316s Investment 0.638 1.749 0.233 316s PrivateWages -0.440 0.233 0.519 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.422 -0.532 316s Investment 0.422 1.000 0.247 316s PrivateWages -0.532 0.247 1.000 316s 316s 316s 3SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 18.0338 1.5648 11.52 1.6e-08 *** 316s corpProf -0.0632 0.1500 -0.42 0.68 316s corpProfLag 0.1784 0.1154 1.55 0.14 316s wages 0.8224 0.0444 18.54 3.0e-11 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.264 on 14 degrees of freedom 316s Number of observations: 18 Degrees of Freedom: 14 316s SSR: 22.377 MSE: 1.598 Root MSE: 1.264 316s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 316s 316s 316s 3SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 24.6766 6.7008 3.68 0.00246 ** 316s corpProf 0.0472 0.1843 0.26 0.80149 316s corpProfLag 0.6874 0.1577 4.36 0.00065 *** 316s capitalLag -0.1776 0.0318 -5.59 6.7e-05 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.582 on 14 degrees of freedom 316s Number of observations: 18 Degrees of Freedom: 14 316s SSR: 35.037 MSE: 2.503 Root MSE: 1.582 316s Multiple R-Squared: 0.793 Adjusted R-Squared: 0.749 316s 316s 316s 3SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 0.7823 1.1254 0.70 0.49695 316s gnp 0.4257 0.0308 13.80 2.6e-10 *** 316s gnpLag 0.1728 0.0341 5.07 0.00011 *** 316s trend 0.1252 0.0291 4.30 0.00055 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.793 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 10.057 MSE: 0.629 Root MSE: 0.793 316s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.8058 -1.721 -1.20135 316s 3 -0.6573 0.337 0.43696 316s 4 -1.1124 0.810 1.31177 316s 5 0.0833 -1.544 -0.19794 316s 6 0.6334 0.368 -0.46596 316s 7 NA NA NA 316s 8 1.7939 1.245 -0.85614 316s 9 1.7891 0.593 0.20698 316s 10 NA 2.303 1.10034 316s 11 -0.5397 -1.015 -0.38801 316s 12 -1.5147 -0.846 0.40949 316s 13 NA NA 0.00602 316s 14 -0.1171 1.670 0.61306 316s 15 -0.6526 -0.075 0.49152 316s 16 -0.3617 NA 0.17066 316s 17 1.9331 2.086 -0.69991 316s 18 -0.6063 -0.101 0.96136 316s 19 -0.3990 -3.345 -0.61606 316s 20 1.4134 0.717 -0.29343 316s 21 1.3257 0.306 -1.14412 316s 22 -1.4340 0.935 0.55310 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.7 1.5213 26.7 316s 3 45.7 1.5632 28.9 316s 4 50.3 4.3898 32.8 316s 5 50.5 4.5444 34.1 316s 6 52.0 4.7320 35.9 316s 7 NA NA NA 316s 8 54.4 2.9547 38.8 316s 9 55.5 2.4075 39.0 316s 10 NA 2.7965 40.2 316s 11 55.5 2.0150 38.3 316s 12 52.4 -2.5541 34.1 316s 13 NA NA 29.0 316s 14 46.6 -6.7699 27.9 316s 15 49.4 -2.9250 30.1 316s 16 51.7 NA 33.0 316s 17 55.8 0.0139 37.5 316s 18 59.3 2.1013 40.0 316s 19 57.9 1.4453 38.8 316s 20 60.2 0.5828 41.9 316s 21 63.7 2.9944 46.1 316s 22 71.1 3.9651 52.7 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.7 0.555 39.7 45.7 316s 3 45.7 0.628 42.6 48.7 316s 4 50.3 0.418 47.5 53.2 316s 5 50.5 0.492 47.6 53.4 316s 6 52.0 0.501 49.0 54.9 316s 7 NA NA NA NA 316s 8 54.4 0.405 51.6 57.3 316s 9 55.5 0.477 52.6 58.4 316s 10 NA NA NA NA 316s 11 55.5 0.832 52.3 58.8 316s 12 52.4 0.792 49.2 55.6 316s 13 NA NA NA NA 316s 14 46.6 0.676 43.5 49.7 316s 15 49.4 0.470 46.5 52.2 316s 16 51.7 0.386 48.8 54.5 316s 17 55.8 0.433 52.9 58.6 316s 18 59.3 0.368 56.5 62.1 316s 19 57.9 0.504 55.0 60.8 316s 20 60.2 0.513 57.3 63.1 316s 21 63.7 0.505 60.8 66.6 316s 22 71.1 0.771 68.0 74.3 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 1.5213 0.857 -2.337 5.380 316s 3 1.5632 0.589 -2.058 5.184 316s 4 4.3898 0.519 0.819 7.961 316s 5 4.5444 0.436 1.025 8.064 316s 6 4.7320 0.415 1.224 8.240 316s 7 NA NA NA NA 316s 8 2.9547 0.342 -0.517 6.426 316s 9 2.4075 0.511 -1.158 5.973 316s 10 2.7965 0.556 -0.800 6.393 316s 11 2.0150 0.955 -1.948 5.978 316s 12 -2.5541 0.874 -6.431 1.323 316s 13 NA NA NA NA 316s 14 -6.7699 0.865 -10.637 -2.903 316s 15 -2.9250 0.503 -6.485 0.635 316s 16 NA NA NA NA 316s 17 0.0139 0.483 -3.534 3.561 316s 18 2.1013 0.320 -1.361 5.563 316s 19 1.4453 0.532 -2.134 5.025 316s 20 0.5828 0.550 -3.010 4.175 316s 21 2.9944 0.476 -0.549 6.538 316s 22 3.9651 0.692 0.261 7.669 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.7 0.324 24.9 28.5 316s 3 28.9 0.331 27.0 30.7 316s 4 32.8 0.339 31.0 34.6 316s 5 34.1 0.248 32.3 35.9 316s 6 35.9 0.256 34.1 37.6 316s 7 NA NA NA NA 316s 8 38.8 0.251 37.0 40.5 316s 9 39.0 0.238 37.2 40.7 316s 10 40.2 0.232 38.4 42.0 316s 11 38.3 0.314 36.5 40.1 316s 12 34.1 0.327 32.3 35.9 316s 13 29.0 0.393 27.1 30.9 316s 14 27.9 0.329 26.1 29.7 316s 15 30.1 0.324 28.3 31.9 316s 16 33.0 0.271 31.3 34.8 316s 17 37.5 0.277 35.7 39.3 316s 18 40.0 0.213 38.3 41.8 316s 19 38.8 0.320 37.0 40.6 316s 20 41.9 0.295 40.1 43.7 316s 21 46.1 0.309 44.3 47.9 316s 22 52.7 0.476 50.8 54.7 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 316s [3] "Numeric: lengths (696, 672) differ" 316s > nobs 316s [1] 56 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 45 316s 2 44 1 1.91 0.17 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 45 316s 2 44 1 2.6 0.11 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 45 316s 2 44 1 2.6 0.11 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 44 2 1.62 0.21 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 44 2 2.2 0.12 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 46 316s 2 44 2 4.41 0.11 316s > logLik 316s 'log Lik.' -70.1 (df=18) 316s 'log Lik.' -80.6 (df=18) 316s > 316s > # I3SLS 316s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 316s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 316s > summary 316s 316s systemfit results 316s method: iterated 3SLS 316s 316s convergence achieved after 10 iterations 316s 316s N DF SSR detRCov OLS-R2 McElroy-R2 316s system 56 44 79.4 0.55 0.956 0.994 316s 316s N DF SSR MSE RMSE R2 Adj R2 316s Consumption 18 14 22.3 1.595 1.263 0.974 0.968 316s Investment 18 14 46.8 3.346 1.829 0.724 0.664 316s PrivateWages 20 16 10.2 0.639 0.799 0.987 0.985 316s 316s The covariance matrix of the residuals used for estimation 316s Consumption Investment PrivateWages 316s Consumption 1.307 0.750 -0.452 316s Investment 0.750 2.318 0.272 316s PrivateWages -0.452 0.272 0.530 316s 316s The covariance matrix of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.307 0.750 -0.452 316s Investment 0.750 2.318 0.272 316s PrivateWages -0.452 0.272 0.530 316s 316s The correlations of the residuals 316s Consumption Investment PrivateWages 316s Consumption 1.000 0.424 -0.542 316s Investment 0.424 1.000 0.254 316s PrivateWages -0.542 0.254 1.000 316s 316s 316s 3SLS estimates for 'Consumption' (equation 1) 316s Model Formula: consump ~ corpProf + corpProfLag + wages 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 18.3252 1.5452 11.86 1.1e-08 *** 316s corpProf -0.0436 0.1470 -0.30 0.77 316s corpProfLag 0.1614 0.1127 1.43 0.17 316s wages 0.8127 0.0436 18.65 2.8e-11 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.263 on 14 degrees of freedom 316s Number of observations: 18 Degrees of Freedom: 14 316s SSR: 22.337 MSE: 1.595 Root MSE: 1.263 316s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 316s 316s 316s 3SLS estimates for 'Investment' (equation 2) 316s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 30.2418 8.3674 3.61 0.00282 ** 316s corpProf -0.0437 0.2341 -0.19 0.85457 316s corpProfLag 0.7856 0.1993 3.94 0.00147 ** 316s capitalLag -0.2065 0.0397 -5.20 0.00014 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 1.829 on 14 degrees of freedom 316s Number of observations: 18 Degrees of Freedom: 14 316s SSR: 46.838 MSE: 3.346 Root MSE: 1.829 316s Multiple R-Squared: 0.724 Adjusted R-Squared: 0.664 316s 316s 316s 3SLS estimates for 'PrivateWages' (equation 3) 316s Model Formula: privWage ~ gnp + gnpLag + trend 316s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 316s gnpLag 316s 316s Estimate Std. Error t value Pr(>|t|) 316s (Intercept) 0.4741 1.1280 0.42 0.67983 316s gnp 0.4268 0.0296 14.44 1.4e-10 *** 316s gnpLag 0.1767 0.0330 5.35 6.5e-05 *** 316s trend 0.1201 0.0290 4.14 0.00076 *** 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s 316s Residual standard error: 0.799 on 16 degrees of freedom 316s Number of observations: 20 Degrees of Freedom: 16 316s SSR: 10.218 MSE: 0.639 Root MSE: 0.799 316s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 316s 316s > residuals 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 -0.8546 -2.1226 -1.1687 316s 3 -0.7611 0.3684 0.4670 316s 4 -1.1233 0.5912 1.3216 316s 5 0.0781 -1.6694 -0.2108 316s 6 0.6467 0.2952 -0.4776 316s 7 NA NA NA 316s 8 1.8444 1.4348 -0.8884 316s 9 1.8309 1.0020 0.1781 316s 10 NA 2.7265 1.0734 316s 11 -0.3652 -1.0581 -0.4134 316s 12 -1.3877 -0.6431 0.4203 316s 13 NA NA 0.0623 316s 14 -0.1818 2.4214 0.7091 316s 15 -0.6438 0.2168 0.5845 316s 16 -0.3417 NA 0.2455 316s 17 1.9583 2.4607 -0.6474 316s 18 -0.4806 -0.0468 0.9840 316s 19 -0.2563 -3.3855 -0.5930 316s 20 1.4832 1.1550 -0.2586 316s 21 1.4514 0.6086 -1.1446 316s 22 -1.2351 1.3453 0.5196 316s > fitted 316s Consumption Investment PrivateWages 316s 1 NA NA NA 316s 2 42.8 1.923 26.7 316s 3 45.8 1.532 28.8 316s 4 50.3 4.609 32.8 316s 5 50.5 4.669 34.1 316s 6 52.0 4.805 35.9 316s 7 NA NA NA 316s 8 54.4 2.765 38.8 316s 9 55.5 1.998 39.0 316s 10 NA 2.373 40.2 316s 11 55.4 2.058 38.3 316s 12 52.3 -2.757 34.1 316s 13 NA NA 28.9 316s 14 46.7 -7.521 27.8 316s 15 49.3 -3.217 30.0 316s 16 51.6 NA 33.0 316s 17 55.7 -0.361 37.4 316s 18 59.2 2.047 40.0 316s 19 57.8 1.485 38.8 316s 20 60.1 0.145 41.9 316s 21 63.5 2.691 46.1 316s 22 70.9 3.555 52.8 316s > predict 316s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 316s 1 NA NA NA NA 316s 2 42.8 0.548 41.7 43.9 316s 3 45.8 0.618 44.5 47.0 316s 4 50.3 0.411 49.5 51.2 316s 5 50.5 0.481 49.6 51.5 316s 6 52.0 0.490 51.0 52.9 316s 7 NA NA NA NA 316s 8 54.4 0.396 53.6 55.2 316s 9 55.5 0.467 54.5 56.4 316s 10 NA NA NA NA 316s 11 55.4 0.811 53.7 57.0 316s 12 52.3 0.775 50.7 53.8 316s 13 NA NA NA NA 316s 14 46.7 0.665 45.3 48.0 316s 15 49.3 0.463 48.4 50.3 316s 16 51.6 0.381 50.9 52.4 316s 17 55.7 0.428 54.9 56.6 316s 18 59.2 0.360 58.5 59.9 316s 19 57.8 0.492 56.8 58.7 316s 20 60.1 0.508 59.1 61.1 316s 21 63.5 0.499 62.5 64.6 316s 22 70.9 0.761 69.4 72.5 316s Investment.pred Investment.se.fit Investment.lwr Investment.upr 316s 1 NA NA NA NA 316s 2 1.923 1.079 -0.2526 4.098 316s 3 1.532 0.766 -0.0119 3.075 316s 4 4.609 0.668 3.2632 5.954 316s 5 4.669 0.566 3.5280 5.811 316s 6 4.805 0.543 3.7104 5.899 316s 7 NA NA NA NA 316s 8 2.765 0.447 1.8648 3.665 316s 9 1.998 0.651 0.6860 3.310 316s 10 2.373 0.710 0.9434 3.804 316s 11 2.058 1.237 -0.4350 4.551 316s 12 -2.757 1.139 -5.0532 -0.461 316s 13 NA NA NA NA 316s 14 -7.521 1.094 -9.7261 -5.317 316s 15 -3.217 0.648 -4.5217 -1.912 316s 16 NA NA NA NA 316s 17 -0.361 0.615 -1.6007 0.879 316s 18 2.047 0.417 1.2060 2.888 316s 19 1.485 0.684 0.1062 2.865 316s 20 0.145 0.699 -1.2632 1.553 316s 21 2.691 0.614 1.4548 3.928 316s 22 3.555 0.887 1.7674 5.342 316s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 316s 1 NA NA NA NA 316s 2 26.7 0.330 26.0 27.3 316s 3 28.8 0.336 28.2 29.5 316s 4 32.8 0.340 32.1 33.5 316s 5 34.1 0.251 33.6 34.6 316s 6 35.9 0.259 35.4 36.4 316s 7 NA NA NA NA 316s 8 38.8 0.253 38.3 39.3 316s 9 39.0 0.240 38.5 39.5 316s 10 40.2 0.236 39.8 40.7 316s 11 38.3 0.307 37.7 38.9 316s 12 34.1 0.313 33.4 34.7 316s 13 28.9 0.376 28.2 29.7 316s 14 27.8 0.327 27.1 28.4 316s 15 30.0 0.322 29.4 30.7 316s 16 33.0 0.270 32.4 33.5 316s 17 37.4 0.275 36.9 38.0 316s 18 40.0 0.216 39.6 40.5 316s 19 38.8 0.314 38.2 39.4 316s 20 41.9 0.296 41.3 42.5 316s 21 46.1 0.317 45.5 46.8 316s 22 52.8 0.480 51.8 53.7 316s > model.frame 316s [1] TRUE 316s > model.matrix 316s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 316s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 316s [3] "Numeric: lengths (696, 672) differ" 316s > nobs 316s [1] 56 316s > linearHypothesis 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 45 316s 2 44 1 2.29 0.14 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 45 316s 2 44 1 2.89 0.096 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 45 316s 2 44 1 2.89 0.089 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s Linear hypothesis test (Theil's F test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 44 2 2.3 0.11 316s Linear hypothesis test (F statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df F Pr(>F) 316s 1 46 316s 2 44 2 2.9 0.066 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s Linear hypothesis test (Chi^2 statistic of a Wald test) 316s 316s Hypothesis: 316s Consumption_corpProf + Investment_capitalLag = 0 316s Consumption_corpProfLag - PrivateWages_trend = 0 316s 316s Model 1: restricted model 316s Model 2: kleinModel 316s 316s Res.Df Df Chisq Pr(>Chisq) 316s 1 46 316s 2 44 2 5.79 0.055 . 316s --- 316s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 316s > logLik 316s 'log Lik.' -72.2 (df=18) 316s 'log Lik.' -83.4 (df=18) 316s > 316s BEGIN TEST test_2sls.R 316s 316s R version 4.3.2 (2023-10-31) -- "Eye Holes" 316s Copyright (C) 2023 The R Foundation for Statistical Computing 316s Platform: x86_64-pc-linux-gnu (64-bit) 316s 316s R is free software and comes with ABSOLUTELY NO WARRANTY. 316s You are welcome to redistribute it under certain conditions. 316s Type 'license()' or 'licence()' for distribution details. 316s 316s R is a collaborative project with many contributors. 316s Type 'contributors()' for more information and 316s 'citation()' on how to cite R or R packages in publications. 316s 316s Type 'demo()' for some demos, 'help()' for on-line help, or 316s 'help.start()' for an HTML browser interface to help. 316s Type 'q()' to quit R. 316s 317s > library( systemfit ) 317s Loading required package: Matrix 318s Loading required package: car 318s Loading required package: carData 318s Loading required package: lmtest 318s Loading required package: zoo 318s 318s Attaching package: ‘zoo’ 318s 318s The following objects are masked from ‘package:base’: 318s 318s as.Date, as.Date.numeric 318s 318s 318s Please cite the 'systemfit' package as: 318s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 318s 318s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 318s https://r-forge.r-project.org/projects/systemfit/ 318s > options( digits = 3 ) 318s > 318s > data( "Kmenta" ) 318s > useMatrix <- FALSE 318s > 318s > demand <- consump ~ price + income 318s > supply <- consump ~ price + farmPrice + trend 318s > inst <- ~ income + farmPrice + trend 318s > inst1 <- ~ income + farmPrice 318s > instlist <- list( inst1, inst ) 318s > system <- list( demand = demand, supply = supply ) 318s > restrm <- matrix(0,1,7) # restriction matrix "R" 318s > restrm[1,3] <- 1 318s > restrm[1,7] <- -1 318s > restrict <- "demand_income - supply_trend = 0" 318s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 318s > restr2m[1,3] <- 1 318s > restr2m[1,7] <- -1 318s > restr2m[2,2] <- -1 318s > restr2m[2,5] <- 1 318s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 318s > restrict2 <- c( "demand_income - supply_trend = 0", 318s + "- demand_price + supply_price = 0.5" ) 318s > tc <- matrix(0,7,6) 318s > tc[1,1] <- 1 318s > tc[2,2] <- 1 318s > tc[3,3] <- 1 318s > tc[4,4] <- 1 318s > tc[5,5] <- 1 318s > tc[6,6] <- 1 318s > tc[7,3] <- 1 318s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 318s > restr3m[1,2] <- -1 318s > restr3m[1,5] <- 1 318s > restr3q <- c( 0.5 ) # restriction vector "q" 2 318s > restrict3 <- "- C2 + C5 = 0.5" 318s > 318s > # It is not possible to estimate 2SLS with systemfit exactly 318s > # as EViews does, because EViews uses 318s > # methodResidCov == "geomean" for the coefficient covariance matrix and 318s > # methodResidCov == "noDfCor" for the residual covariance matrix. 318s > # systemfit uses always the same formulas for both calculations. 318s > 318s > ## *************** 2SLS estimation ************************ 318s > ## ************ 2SLS estimation (default)********************* 318s > fit2sls1 <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 318s + x = TRUE, useMatrix = useMatrix ) 318s > print( summary( fit2sls1 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 162 4.36 0.697 0.548 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 65.7 3.87 1.97 0.755 0.726 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.87 4.36 318s supply 4.36 6.04 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.902 318s supply 0.902 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 318s price -0.2436 0.0965 -2.52 0.022 * 318s income 0.3140 0.0469 6.69 3.8e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.966 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 318s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 318s price 0.2401 0.0999 2.40 0.0288 * 318s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 318s trend 0.2529 0.0997 2.54 0.0219 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2sls1 ) 318s [1] 40 318s > 318s > ## *************** 2SLS estimation (singleEqSigma=F)******************* 318s > fit2sls1s <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 318s + singleEqSigma = FALSE, useMatrix = useMatrix ) 318s > print( summary( fit2sls1s ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 162 4.36 0.697 0.548 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 65.7 3.87 1.97 0.755 0.726 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.87 4.36 318s supply 4.36 6.04 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.902 318s supply 0.902 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.633 8.935 10.59 6.6e-09 *** 318s price -0.244 0.109 -2.24 0.039 * 318s income 0.314 0.053 5.93 1.6e-05 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.966 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 318s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 10.8404 4.57 0.00032 *** 318s price 0.2401 0.0902 2.66 0.01706 * 318s farmPrice 0.2556 0.0426 5.99 1.9e-05 *** 318s trend 0.2529 0.0899 2.81 0.01253 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2sls1s ) 318s [1] 40 318s > 318s > ## ********************* 2SLS (useDfSys = TRUE) ***************** 318s > print( summary( fit2sls1, useDfSys = TRUE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 162 4.36 0.697 0.548 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 65.7 3.87 1.97 0.755 0.726 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.87 4.36 318s supply 4.36 6.04 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.902 318s supply 0.902 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 318s price -0.2436 0.0965 -2.52 0.017 * 318s income 0.3140 0.0469 6.69 1.3e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.966 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 318s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 318s price 0.2401 0.0999 2.40 0.02208 * 318s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 318s trend 0.2529 0.0997 2.54 0.01605 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2sls1 ) 318s [1] 40 318s > 318s > ## ********************* 2SLS (methodResidCov = "noDfCor" ) ***************** 318s > fit2sls1r <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 318s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 318s > print( summary( fit2sls1r ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 162 2.97 0.697 0.525 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 65.7 3.87 1.97 0.755 0.726 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.29 3.59 318s supply 3.59 4.83 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.902 318s supply 0.902 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.6333 7.3027 12.96 3.1e-10 *** 318s price -0.2436 0.0890 -2.74 0.014 * 318s income 0.3140 0.0433 7.25 1.3e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.966 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 318s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 10.7425 4.61 0.00029 *** 318s price 0.2401 0.0894 2.69 0.01623 * 318s farmPrice 0.2556 0.0423 6.05 1.7e-05 *** 318s trend 0.2529 0.0891 2.84 0.01188 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2sls1r ) 318s [1] 40 318s > 318s > ## *************** 2SLS (methodResidCov="noDfCor", singleEqSigma=F) ************* 318s > fit2sls1rs <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 318s + methodResidCov = "noDfCor", singleEqSigma = FALSE, useMatrix = useMatrix ) 318s > print( summary( fit2sls1rs ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 162 2.97 0.697 0.525 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 65.7 3.87 1.97 0.755 0.726 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.29 3.59 318s supply 3.59 4.83 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.902 318s supply 0.902 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.6333 8.1158 11.66 1.6e-09 *** 318s price -0.2436 0.0989 -2.46 0.025 * 318s income 0.3140 0.0481 6.53 5.2e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.966 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 318s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 9.8463 5.03 0.00012 *** 318s price 0.2401 0.0819 2.93 0.00980 ** 318s farmPrice 0.2556 0.0387 6.60 6.1e-06 *** 318s trend 0.2529 0.0817 3.10 0.00694 ** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2sls1rs ) 318s [1] 40 318s > 318s > ## ********************* 2SLS with restriction ******************** 318s > ## **************** 2SLS with restriction (default)******************** 318s > fit2sls2 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 318s + inst = inst, useMatrix = useMatrix ) 318s > print( summary( fit2sls2 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 166 3.6 0.691 0.553 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.749 0.719 318s supply 20 16 98.2 6.13 2.48 0.634 0.565 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.97 4.55 318s supply 4.55 6.13 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.923 318s supply 0.923 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.2816 8.8693 10.63 2.4e-12 *** 318s price -0.2247 0.1034 -2.17 0.037 * 318s income 0.2983 0.0454 6.57 1.6e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.991 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 318s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 48.1843 10.5384 4.57 6.1e-05 *** 318s price 0.2427 0.0896 2.71 0.011 * 318s farmPrice 0.2619 0.0411 6.38 2.8e-07 *** 318s trend 0.2983 0.0454 6.57 1.6e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.477 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 318s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 318s 318s > nobs( fit2sls2 ) 318s [1] 40 318s > # the same with symbolically specified restrictions 318s > fit2sls2Sym <- systemfit( system, "2SLS", data = Kmenta, 318s + restrict.matrix = restrict, inst = inst, useMatrix = useMatrix ) 318s > all.equal( fit2sls2, fit2sls2Sym ) 318s [1] "Component “call”: target, current do not match when deparsed" 318s > nobs( fit2sls2Sym ) 318s [1] 40 318s > 318s > ## ************* 2SLS with restriction (singleEqSigma=T) ***************** 318s > fit2sls2s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 318s + inst = inst, singleEqSigma = TRUE, x = TRUE, 318s + useMatrix = useMatrix ) 318s > print( summary( fit2sls2s ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 166 3.6 0.691 0.553 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.749 0.719 318s supply 20 16 98.2 6.13 2.48 0.634 0.565 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.97 4.55 318s supply 4.55 6.13 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.923 318s supply 0.923 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.2816 8.0090 11.77 1.5e-13 *** 318s price -0.2247 0.0946 -2.37 0.023 * 318s income 0.2983 0.0430 6.94 5.3e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.991 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 318s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 48.1843 11.8001 4.08 0.00025 *** 318s price 0.2427 0.1006 2.41 0.02135 * 318s farmPrice 0.2619 0.0459 5.70 2.1e-06 *** 318s trend 0.2983 0.0430 6.94 5.3e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.477 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 318s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 318s 318s > nobs( fit2sls2s ) 318s [1] 40 318s > 318s > ## ********************* 2SLS with restriction (useDfSys=T) ************** 318s > print( summary( fit2sls2, useDfSys = TRUE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 166 3.6 0.691 0.553 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.749 0.719 318s supply 20 16 98.2 6.13 2.48 0.634 0.565 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.97 4.55 318s supply 4.55 6.13 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.923 318s supply 0.923 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.2816 8.8693 10.63 2.4e-12 *** 318s price -0.2247 0.1034 -2.17 0.037 * 318s income 0.2983 0.0454 6.57 1.6e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.991 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 318s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 48.1843 10.5384 4.57 6.1e-05 *** 318s price 0.2427 0.0896 2.71 0.011 * 318s farmPrice 0.2619 0.0411 6.38 2.8e-07 *** 318s trend 0.2983 0.0454 6.57 1.6e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.477 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 318s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 318s 318s > nobs( fit2sls2 ) 318s [1] 40 318s > 318s > ## ********************* 2SLS with restriction (methodResidCov = "noDfCor") ************** 318s > fit2sls2r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 318s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 318s > print( summary( fit2sls2r ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 166 2.45 0.691 0.526 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.749 0.719 318s supply 20 16 98.2 6.13 2.48 0.634 0.565 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.37 3.75 318s supply 3.75 4.91 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.923 318s supply 0.923 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.2816 8.1771 11.53 2.7e-13 *** 318s price -0.2247 0.0954 -2.36 0.024 * 318s income 0.2983 0.0419 7.13 3.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.991 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 318s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 48.1843 9.7159 4.96 1.9e-05 *** 318s price 0.2427 0.0826 2.94 0.0059 ** 318s farmPrice 0.2619 0.0379 6.92 5.7e-08 *** 318s trend 0.2983 0.0419 7.13 3.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.477 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 318s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 318s 318s > nobs( fit2sls2r ) 318s [1] 40 318s > 318s > ## ******** 2SLS with restriction (methodResidCov="noDfCor", singleEqSigma=TRUE) ********* 318s > fit2sls2rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 318s + inst = inst, methodResidCov = "noDfCor", singleEqSigma = TRUE, 318s + useMatrix = useMatrix ) 318s > print( summary( fit2sls2rs ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 166 2.45 0.691 0.526 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.749 0.719 318s supply 20 16 98.2 6.13 2.48 0.634 0.565 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.37 3.75 318s supply 3.75 4.91 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.923 318s supply 0.923 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.2816 7.3834 12.77 1.6e-14 *** 318s price -0.2247 0.0871 -2.58 0.014 * 318s income 0.2983 0.0394 7.57 8.5e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.991 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 318s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 48.1843 10.5574 4.56 6.3e-05 *** 318s price 0.2427 0.0900 2.70 0.011 * 318s farmPrice 0.2619 0.0411 6.37 2.8e-07 *** 318s trend 0.2983 0.0394 7.57 8.5e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.477 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 318s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 318s 318s > nobs( fit2sls2rs ) 318s [1] 40 318s > 318s > ## ********************* 2SLS with restriction via restrict.regMat ****************** 318s > ## *************** 2SLS with restriction via restrict.regMat (default )*************** 318s > fit2sls3 <- systemfit( system, "2SLS", data = Kmenta, restrict.regMat = tc, 318s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 318s > print( summary( fit2sls3, useDfSys = TRUE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 166 2.45 0.691 0.526 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.749 0.719 318s supply 20 16 98.2 6.13 2.48 0.634 0.565 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.37 3.75 318s supply 3.75 4.91 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.923 318s supply 0.923 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.2816 8.1771 11.53 2.7e-13 *** 318s price -0.2247 0.0954 -2.36 0.024 * 318s income 0.2983 0.0419 7.13 3.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.991 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 318s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 48.1843 9.7159 4.96 1.9e-05 *** 318s price 0.2427 0.0826 2.94 0.0059 ** 318s farmPrice 0.2619 0.0379 6.92 5.7e-08 *** 318s trend 0.2983 0.0419 7.13 3.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.477 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 318s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 318s 318s > nobs( fit2sls3 ) 318s [1] 40 318s > 318s > 318s > ## ***************** 2SLS with 2 restrictions ******************* 318s > ## ************** 2SLS with 2 restrictions (default) ************** 318s > fit2sls4 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 318s + restrict.rhs = restr2q, inst = inst, useMatrix = useMatrix ) 318s > print( summary( fit2sls4 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 3.78 0.69 0.568 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.89 4.53 318s supply 4.53 6.25 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 318s price -0.2433 0.0663 -3.67 0.00081 *** 318s income 0.3027 0.0408 7.42 1.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 318s price 0.2567 0.0663 3.87 0.00045 *** 318s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 318s trend 0.3027 0.0408 7.42 1.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls4 ) 318s [1] 40 318s > # the same with symbolically specified restrictions 318s > fit2sls4Sym <- systemfit( system, "2SLS", data = Kmenta, 318s + restrict.matrix = restrict2, inst = inst, useMatrix = useMatrix ) 318s > all.equal( fit2sls4, fit2sls4Sym ) 318s [1] "Component “call”: target, current do not match when deparsed" 318s > nobs( fit2sls4Sym ) 318s [1] 40 318s > 318s > ## ************ 2SLS with 2 restrictions (singleEqSigma=T) ************** 318s > fit2sls4s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 318s + restrict.rhs = restr2q, inst = inst, singleEqSigma = TRUE, 318s + useMatrix = useMatrix ) 318s > print( summary( fit2sls4s ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 3.78 0.69 0.568 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.89 4.53 318s supply 4.53 6.25 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 6.3056 15.18 < 2e-16 *** 318s price -0.2433 0.0684 -3.56 0.0011 ** 318s income 0.3027 0.0394 7.69 5.1e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 8.3296 5.59 2.7e-06 *** 318s price 0.2567 0.0684 3.75 0.00064 *** 318s farmPrice 0.2637 0.0455 5.79 1.5e-06 *** 318s trend 0.3027 0.0394 7.69 5.1e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls4s ) 318s [1] 40 318s > 318s > ## ***************** 2SLS with 2 restrictions (useDfSys=T) ************** 318s > print( summary( fit2sls4, useDfSys = TRUE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 3.78 0.69 0.568 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.89 4.53 318s supply 4.53 6.25 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 318s price -0.2433 0.0663 -3.67 0.00081 *** 318s income 0.3027 0.0408 7.42 1.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 318s price 0.2567 0.0663 3.87 0.00045 *** 318s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 318s trend 0.3027 0.0408 7.42 1.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls4 ) 318s [1] 40 318s > 318s > ## ***************** 2SLS with 2 restrictions (methodResidCov="noDfCor") ************** 318s > fit2sls4r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 318s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 318s + x = TRUE, useMatrix = useMatrix ) 318s > print( summary( fit2sls4r ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 2.57 0.69 0.54 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.30 3.73 318s supply 3.73 5.00 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 6.0044 15.94 < 2e-16 *** 318s price -0.2433 0.0621 -3.92 0.00039 *** 318s income 0.3027 0.0382 7.93 2.5e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 7.3842 6.31 3.1e-07 *** 318s price 0.2567 0.0621 4.14 0.00021 *** 318s farmPrice 0.2637 0.0373 7.08 3.0e-08 *** 318s trend 0.3027 0.0382 7.93 2.5e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls4r ) 318s [1] 40 318s > 318s > ## ***** 2SLS with 2 restrictions (methodResidCov="noDfCor", singleEqSigma=T) ******* 318s > fit2sls4rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 318s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 318s + singleEqSigma = TRUE, useMatrix = useMatrix ) 318s > print( summary( fit2sls4rs ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 2.57 0.69 0.54 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.30 3.73 318s supply 3.73 5.00 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 5.7579 16.62 < 2e-16 *** 318s price -0.2433 0.0621 -3.92 4e-04 *** 318s income 0.3027 0.0360 8.40 6.6e-10 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 7.5360 6.18 4.5e-07 *** 318s price 0.2567 0.0621 4.13 0.00021 *** 318s farmPrice 0.2637 0.0407 6.47 1.8e-07 *** 318s trend 0.3027 0.0360 8.40 6.6e-10 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls4rs ) 318s [1] 40 318s > 318s > ## ************* 2SLS with 2 restrictions via R and restrict.regMat ****************** 318s > ## ******** 2SLS with 2 restrictions via R and restrict.regMat (default) ************* 318s > fit2sls5 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 318s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 318s + useMatrix = useMatrix ) 318s > print( summary( fit2sls5 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 3.78 0.69 0.568 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.89 4.53 318s supply 4.53 6.25 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 318s price -0.2433 0.0663 -3.67 0.00081 *** 318s income 0.3027 0.0408 7.42 1.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 318s price 0.2567 0.0663 3.87 0.00045 *** 318s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 318s trend 0.3027 0.0408 7.42 1.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls5 ) 318s [1] 40 318s > # the same with symbolically specified restrictions 318s > fit2sls5Sym <- systemfit( system, "2SLS", data = Kmenta, 318s + restrict.matrix = restrict3, restrict.regMat = tc, inst = inst, 318s + useMatrix = useMatrix ) 318s > all.equal( fit2sls5, fit2sls5Sym ) 318s [1] "Component “call”: target, current do not match when deparsed" 318s > nobs( fit2sls5Sym ) 318s [1] 40 318s > 318s > ## ******* 2SLS with 2 restrictions via R and restrict.regMat (singleEqSigma=T) ****** 318s > fit2sls5s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 318s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 318s + singleEqSigma = TRUE, useMatrix = useMatrix ) 318s > print( summary( fit2sls5s ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 3.78 0.69 0.568 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.89 4.53 318s supply 4.53 6.25 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 6.3056 15.18 < 2e-16 *** 318s price -0.2433 0.0684 -3.56 0.0011 ** 318s income 0.3027 0.0394 7.69 5.1e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 8.3296 5.59 2.7e-06 *** 318s price 0.2567 0.0684 3.75 0.00064 *** 318s farmPrice 0.2637 0.0455 5.79 1.5e-06 *** 318s trend 0.3027 0.0394 7.69 5.1e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls5s ) 318s [1] 40 318s > 318s > ## ********** 2SLS with 2 restrictions via R and restrict.regMat (useDfSys=T) ******* 318s > print( summary( fit2sls5, useDfSys = TRUE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 3.78 0.69 0.568 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.89 4.53 318s supply 4.53 6.25 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 318s price -0.2433 0.0663 -3.67 0.00081 *** 318s income 0.3027 0.0408 7.42 1.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 318s price 0.2567 0.0663 3.87 0.00045 *** 318s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 318s trend 0.3027 0.0408 7.42 1.1e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls5 ) 318s [1] 40 318s > 318s > ## ************* 2SLS with 2 restrictions via R and restrict.regMat (methodResidCov="noDfCor") ********* 318s > fit2sls5r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 318s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 318s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 318s > print( summary( fit2sls5r ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 2.57 0.69 0.54 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.30 3.73 318s supply 3.73 5.00 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 6.0044 15.94 < 2e-16 *** 318s price -0.2433 0.0621 -3.92 0.00039 *** 318s income 0.3027 0.0382 7.93 2.5e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 7.3842 6.31 3.1e-07 *** 318s price 0.2567 0.0621 4.14 0.00021 *** 318s farmPrice 0.2637 0.0373 7.08 3.0e-08 *** 318s trend 0.3027 0.0382 7.93 2.5e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls5r ) 318s [1] 40 318s > 318s > ## ** 2SLS with 2 restrictions via R and restrict.regMat (methodResidCov="noDfCor", singleEqSigma=T) ** 318s > fit2sls5rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 318s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 318s + methodResidCov = "noDfCor", singleEqSigma = TRUE, 318s + x = TRUE, useMatrix = useMatrix ) 318s > print( summary( fit2sls5rs ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 2.57 0.69 0.54 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.30 3.73 318s supply 3.73 5.00 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.919 318s supply 0.919 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 95.7059 5.7579 16.62 < 2e-16 *** 318s price -0.2433 0.0621 -3.92 4e-04 *** 318s income 0.3027 0.0360 8.40 6.6e-10 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.972 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 318s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.5637 7.5360 6.18 4.5e-07 *** 318s price 0.2567 0.0621 4.13 0.00021 *** 318s farmPrice 0.2637 0.0407 6.47 1.8e-07 *** 318s trend 0.3027 0.0360 8.40 6.6e-10 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.5 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 318s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 318s 318s > nobs( fit2sls5rs ) 318s [1] 40 318s > 318s > ## *********** 2SLS estimation with different instruments ************** 318s > ## ******* 2SLS estimation with different instruments (default) ********* 318s > fit2slsd1 <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 318s + useMatrix = useMatrix ) 318s > print( summary( fit2slsd1 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 164 9.25 0.694 0.512 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.748 0.719 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.97 3.84 318s supply 3.84 6.04 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.784 318s supply 0.784 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 318s price -0.4116 0.1448 -2.84 0.011 * 318s income 0.3617 0.0564 6.41 6.4e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.992 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 318s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 318s price 0.2401 0.0999 2.40 0.0288 * 318s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 318s trend 0.2529 0.0997 2.54 0.0219 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2slsd1 ) 318s [1] 40 318s > 318s > ## *********** 2SLS estimation with different instruments (singleEqSigma=F)***** 318s > fit2slsd1s <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 318s + singleEqSigma = FALSE, useMatrix = useMatrix ) 318s > print( summary( fit2slsd1s ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 164 9.25 0.694 0.512 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.748 0.719 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.97 3.84 318s supply 3.84 6.04 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.784 318s supply 0.784 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 106.7894 12.4749 8.56 1.4e-07 *** 318s price -0.4116 0.1622 -2.54 0.021 * 318s income 0.3617 0.0631 5.73 2.5e-05 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.992 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 318s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 10.8976 4.55 0.00033 *** 318s price 0.2401 0.0907 2.65 0.01755 * 318s farmPrice 0.2556 0.0429 5.96 2e-05 *** 318s trend 0.2529 0.0904 2.80 0.01292 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2slsd1s ) 318s [1] 40 318s > 318s > ## ********* 2SLS estimation with different instruments (useDfSys=T) ******* 318s > print( summary( fit2slsd1, useDfSys = TRUE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 164 9.25 0.694 0.512 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.748 0.719 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.97 3.84 318s supply 3.84 6.04 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.784 318s supply 0.784 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 318s price -0.4116 0.1448 -2.84 0.0076 ** 318s income 0.3617 0.0564 6.41 2.9e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.992 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 318s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 318s price 0.2401 0.0999 2.40 0.02208 * 318s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 318s trend 0.2529 0.0997 2.54 0.01605 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2slsd1 ) 318s [1] 40 318s > 318s > ## ********* 2SLS estimation with different instruments (methodResidCov="noDfCor") ****** 318s > fit2slsd1r <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 318s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 318s > print( summary( fit2slsd1r ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 164 6.29 0.694 0.5 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.748 0.719 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.37 3.16 318s supply 3.16 4.83 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.784 318s supply 0.784 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 106.789 10.274 10.39 8.8e-09 *** 318s price -0.412 0.134 -3.08 0.0068 ** 318s income 0.362 0.052 6.95 2.3e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.992 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 318s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 10.7425 4.61 0.00029 *** 318s price 0.2401 0.0894 2.69 0.01623 * 318s farmPrice 0.2556 0.0423 6.05 1.7e-05 *** 318s trend 0.2529 0.0891 2.84 0.01188 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2slsd1r ) 318s [1] 40 318s > 318s > ## 2SLS estimation with different instruments (methodResidCov="noDfCor",singleEqSigma=F) 318s > fit2slsd1r <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 318s + methodResidCov = "noDfCor", singleEqSigma = FALSE, 318s + useMatrix = useMatrix ) 318s > print( summary( fit2slsd1r ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 164 6.29 0.694 0.5 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.748 0.719 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.37 3.16 318s supply 3.16 4.83 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.784 318s supply 0.784 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 106.7894 11.3309 9.42 3.7e-08 *** 318s price -0.4116 0.1473 -2.79 0.012 * 318s income 0.3617 0.0574 6.31 7.9e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.992 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 318s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 9.8982 5.00 0.00013 *** 318s price 0.2401 0.0824 2.92 0.01012 * 318s farmPrice 0.2556 0.0389 6.56 6.5e-06 *** 318s trend 0.2529 0.0821 3.08 0.00718 ** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > nobs( fit2slsd1r ) 318s [1] 40 318s > 318s > ## **** 2SLS estimation with different instruments and restriction ******* 318s > ## ** 2SLS estimation with different instruments and restriction (default) **** 318s > fit2slsd2 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 318s + inst = instlist, useMatrix = useMatrix ) 318s > print( summary( fit2slsd2 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 165 4.89 0.693 0.56 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 64.4 3.79 1.95 0.760 0.731 318s supply 20 16 100.3 6.27 2.50 0.626 0.556 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.79 4.35 318s supply 4.35 6.27 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.891 318s supply 0.891 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 103.5936 11.8930 8.71 3.5e-10 *** 318s price -0.3449 0.1455 -2.37 0.024 * 318s income 0.3260 0.0511 6.38 2.8e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.947 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 318s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 47.3592 10.5362 4.49 7.7e-05 *** 318s price 0.2443 0.0894 2.73 0.0099 ** 318s farmPrice 0.2657 0.0411 6.47 2.1e-07 *** 318s trend 0.3260 0.0511 6.38 2.8e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.504 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 318s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 318s 318s > nobs( fit2slsd2 ) 318s [1] 40 318s > 318s > ## 2SLS estimation with different instruments and restriction (singleEqSigma=T) 318s > fit2slsd2s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 318s + inst = instlist, singleEqSigma = TRUE, useMatrix = useMatrix ) 318s > print( summary( fit2slsd2s ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 165 4.89 0.693 0.56 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 64.4 3.79 1.95 0.760 0.731 318s supply 20 16 100.3 6.27 2.50 0.626 0.556 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.79 4.35 318s supply 4.35 6.27 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.891 318s supply 0.891 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 103.5936 10.6344 9.74 2.3e-11 *** 318s price -0.3449 0.1327 -2.60 0.014 * 318s income 0.3260 0.0485 6.73 9.9e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.947 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 318s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 47.3592 11.9466 3.96 0.00036 *** 318s price 0.2443 0.1017 2.40 0.02188 * 318s farmPrice 0.2657 0.0465 5.71 2.0e-06 *** 318s trend 0.3260 0.0485 6.73 9.9e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.504 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 318s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 318s 318s > nobs( fit2slsd2s ) 318s [1] 40 318s > 318s > ## **** 2SLS estimation with different instruments and restriction (useDfSys=F) 318s > print( summary( fit2slsd2, useDfSys = FALSE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 165 4.89 0.693 0.56 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 64.4 3.79 1.95 0.760 0.731 318s supply 20 16 100.3 6.27 2.50 0.626 0.556 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.79 4.35 318s supply 4.35 6.27 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.891 318s supply 0.891 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 103.5936 11.8930 8.71 1.1e-07 *** 318s price -0.3449 0.1455 -2.37 0.03 * 318s income 0.3260 0.0511 6.38 6.9e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.947 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 318s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 47.3592 10.5362 4.49 0.00037 *** 318s price 0.2443 0.0894 2.73 0.01475 * 318s farmPrice 0.2657 0.0411 6.47 7.8e-06 *** 318s trend 0.3260 0.0511 6.38 9.1e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.504 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 318s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 318s 318s > nobs( fit2slsd2 ) 318s [1] 40 318s > 318s > ## **** 2SLS estimation with different instruments and restriction (methodResidCov="noDfCor") 318s > fit2slsd2r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 318s + inst = instlist, methodResidCov = "noDfCor", useMatrix = useMatrix ) 318s > print( summary( fit2slsd2r ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 165 3.32 0.693 0.537 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 64.4 3.79 1.95 0.760 0.731 318s supply 20 16 100.3 6.27 2.50 0.626 0.556 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.22 3.58 318s supply 3.58 5.02 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.891 318s supply 0.891 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 103.5936 10.9648 9.45 4.9e-11 *** 318s price -0.3449 0.1341 -2.57 0.015 * 318s income 0.3260 0.0471 6.92 5.7e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.947 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 318s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 47.3592 9.7139 4.88 2.5e-05 *** 318s price 0.2443 0.0824 2.96 0.0055 ** 318s farmPrice 0.2657 0.0379 7.01 4.3e-08 *** 318s trend 0.3260 0.0471 6.92 5.7e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.504 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 318s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 318s 318s > nobs( fit2slsd2r ) 318s [1] 40 318s > 318s > ## 2SLS estimation with different instr. and restr. (methodResidCov="noDfCor", singleEqSigma=T) 318s > fit2slsd2rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 318s + inst = instlist, methodResidCov = "noDfCor", singleEqSigma = TRUE, 318s + useMatrix = useMatrix ) 318s > print( summary( fit2slsd2rs ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 165 3.32 0.693 0.537 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 64.4 3.79 1.95 0.760 0.731 318s supply 20 16 100.3 6.27 2.50 0.626 0.556 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.22 3.58 318s supply 3.58 5.02 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.891 318s supply 0.891 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 103.5936 9.7929 10.58 2.7e-12 *** 318s price -0.3449 0.1220 -2.83 0.0078 ** 318s income 0.3260 0.0444 7.35 1.6e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.947 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 318s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 47.3592 10.6890 4.43 9.3e-05 *** 318s price 0.2443 0.0910 2.69 0.011 * 318s farmPrice 0.2657 0.0416 6.38 2.8e-07 *** 318s trend 0.3260 0.0444 7.35 1.6e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.504 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 318s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 318s 318s > nobs( fit2slsd2rs ) 318s [1] 40 318s > 318s > ## **** 2SLS estimation with different instruments and restriction via restrict.regMat * 318s > ## 2SLS estimation with different instruments and restriction via restrict.regMat (default) 318s > fit2slsd3 <- systemfit( system, "2SLS", data = Kmenta, restrict.regMat = tc, 318s + inst = instlist, useMatrix = useMatrix ) 318s > print( summary( fit2slsd3 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 165 4.89 0.693 0.56 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 64.4 3.79 1.95 0.760 0.731 318s supply 20 16 100.3 6.27 2.50 0.626 0.556 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.79 4.35 318s supply 4.35 6.27 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.891 318s supply 0.891 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 103.5936 11.8930 8.71 3.5e-10 *** 318s price -0.3449 0.1455 -2.37 0.024 * 318s income 0.3260 0.0511 6.38 2.8e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.947 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 318s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 47.3592 10.5362 4.49 7.7e-05 *** 318s price 0.2443 0.0894 2.73 0.0099 ** 318s farmPrice 0.2657 0.0411 6.47 2.1e-07 *** 318s trend 0.3260 0.0511 6.38 2.8e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.504 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 318s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 318s 318s > nobs( fit2slsd3 ) 318s [1] 40 318s > 318s > ## **** 2SLS estimation with different instr. and restr. via restrict.regMat (methodResidCov="noDfCor") 318s > fit2slsd3r <- systemfit( system, "2SLS", data = Kmenta, restrict.regMat = tc, 318s + inst = instlist, methodResidCov = "noDfCor", useMatrix = useMatrix ) 318s > print( summary( fit2slsd3r ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 165 3.32 0.693 0.537 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 64.4 3.79 1.95 0.760 0.731 318s supply 20 16 100.3 6.27 2.50 0.626 0.556 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.22 3.58 318s supply 3.58 5.02 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.891 318s supply 0.891 1.000 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 103.5936 10.9648 9.45 4.9e-11 *** 318s price -0.3449 0.1341 -2.57 0.015 * 318s income 0.3260 0.0471 6.92 5.7e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.947 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 318s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 47.3592 9.7139 4.88 2.5e-05 *** 318s price 0.2443 0.0824 2.96 0.0055 ** 318s farmPrice 0.2657 0.0379 7.01 4.3e-08 *** 318s trend 0.3260 0.0471 6.92 5.7e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.504 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 318s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 318s 318s > nobs( fit2slsd3r ) 318s [1] 40 318s > 318s > 318s > ## *********** estimations with a single regressor ************ 318s > fit2slsS1 <- systemfit( 318s + list( consump ~ price - 1, price ~ consump + trend ), "2SLS", 318s + data = Kmenta, inst = ~ farmPrice + trend + income, useMatrix = useMatrix ) 318s > print( summary( fit2slsS1 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 36 1544 179 -0.65 0.852 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s eq1 20 19 861 45.3 6.73 -2.213 -2.213 318s eq2 20 17 682 40.1 6.33 -0.022 -0.143 318s 318s The covariance matrix of the residuals 318s eq1 eq2 318s eq1 45.3 -40.5 318s eq2 -40.5 40.1 318s 318s The correlations of the residuals 318s eq1 eq2 318s eq1 1.00 -0.95 318s eq2 -0.95 1.00 318s 318s 318s 2SLS estimates for 'eq1' (equation 1) 318s Model Formula: consump ~ price - 1 318s Instruments: ~farmPrice + trend + income 318s 318s Estimate Std. Error t value Pr(>|t|) 318s price 1.006 0.015 66.9 <2e-16 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 6.734 on 19 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 19 318s SSR: 861.48 MSE: 45.341 Root MSE: 6.734 318s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 318s 318s 318s 2SLS estimates for 'eq2' (equation 2) 318s Model Formula: price ~ consump + trend 318s Instruments: ~farmPrice + trend + income 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 55.5365 46.2668 1.20 0.25 318s consump 0.4453 0.4622 0.96 0.35 318s trend -0.0426 0.2496 -0.17 0.87 318s 318s Residual standard error: 6.335 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 682.257 MSE: 40.133 Root MSE: 6.335 318s Multiple R-Squared: -0.022 Adjusted R-Squared: -0.143 318s 318s > nobs( fit2slsS1 ) 318s [1] 40 318s > fit2slsS2 <- systemfit( 318s + list( consump ~ price - 1, consump ~ trend - 1 ), "2SLS", 318s + data = Kmenta, inst = ~ farmPrice + price + income, useMatrix = useMatrix ) 318s > print( summary( fit2slsS2 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 38 47456 111148 -87.5 -5.28 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s eq1 20 19 861 45.3 6.73 -2.21 -2.21 318s eq2 20 19 46595 2452.3 49.52 -172.79 -172.79 318s 318s The covariance matrix of the residuals 318s eq1 eq2 318s eq1 45.34 -6.33 318s eq2 -6.33 2452.34 318s 318s The correlations of the residuals 318s eq1 eq2 318s eq1 1.0000 -0.0448 318s eq2 -0.0448 1.0000 318s 318s 318s 2SLS estimates for 'eq1' (equation 1) 318s Model Formula: consump ~ price - 1 318s Instruments: ~farmPrice + price + income 318s 318s Estimate Std. Error t value Pr(>|t|) 318s price 1.006 0.015 66.9 <2e-16 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 6.733 on 19 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 19 318s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 318s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 318s 318s 318s 2SLS estimates for 'eq2' (equation 2) 318s Model Formula: consump ~ trend - 1 318s Instruments: ~farmPrice + price + income 318s 318s Estimate Std. Error t value Pr(>|t|) 318s trend 7.578 0.934 8.11 1.4e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 49.521 on 19 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 19 318s SSR: 46594.549 MSE: 2452.345 Root MSE: 49.521 318s Multiple R-Squared: -172.786 Adjusted R-Squared: -172.786 318s 318s > nobs( fit2slsS2 ) 318s [1] 40 318s > fit2slsS3 <- systemfit( 318s + list( consump ~ trend - 1, price ~ trend - 1 ), "2SLS", 318s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 318s > print( summary( fit2slsS3 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 38 97978 687515 -104 -10.6 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s eq1 20 19 50950 2682 51.8 -189.0 -189.0 318s eq2 20 19 47028 2475 49.8 -69.5 -69.5 318s 318s The covariance matrix of the residuals 318s eq1 eq2 318s eq1 2682 2439 318s eq2 2439 2475 318s 318s The correlations of the residuals 318s eq1 eq2 318s eq1 1.000 0.989 318s eq2 0.989 1.000 318s 318s 318s 2SLS estimates for 'eq1' (equation 1) 318s Model Formula: consump ~ trend - 1 318s Instruments: ~income + farmPrice 318s 318s Estimate Std. Error t value Pr(>|t|) 318s trend 8.65 1.05 8.27 1e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 51.784 on 19 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 19 318s SSR: 50949.985 MSE: 2681.578 Root MSE: 51.784 318s Multiple R-Squared: -189.031 Adjusted R-Squared: -189.031 318s 318s 318s 2SLS estimates for 'eq2' (equation 2) 318s Model Formula: price ~ trend - 1 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s trend 7.318 0.929 7.88 2.1e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 49.751 on 19 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 19 318s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 318s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 318s 318s > nobs( fit2slsS3 ) 318s [1] 40 318s > fit2slsS4 <- systemfit( 318s + list( consump ~ trend - 1, price ~ trend - 1 ), "2SLS", 318s + data = Kmenta, inst = ~ farmPrice + trend + income, 318s + restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), useMatrix = useMatrix ) 318s > print( summary( fit2slsS4 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 39 93548 111736 -99 -1.03 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s eq1 20 19 46514 2448 49.5 -172.5 -172.5 318s eq2 20 19 47033 2475 49.8 -69.5 -69.5 318s 318s The covariance matrix of the residuals 318s eq1 eq2 318s eq1 2448 2439 318s eq2 2439 2475 318s 318s The correlations of the residuals 318s eq1 eq2 318s eq1 1.000 0.988 318s eq2 0.988 1.000 318s 318s 318s 2SLS estimates for 'eq1' (equation 1) 318s Model Formula: consump ~ trend - 1 318s Instruments: ~farmPrice + trend + income 318s 318s Estimate Std. Error t value Pr(>|t|) 318s trend 7.362 0.646 11.4 5.7e-14 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 49.478 on 19 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 19 318s SSR: 46514.283 MSE: 2448.12 Root MSE: 49.478 318s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 318s 318s 318s 2SLS estimates for 'eq2' (equation 2) 318s Model Formula: price ~ trend - 1 318s Instruments: ~farmPrice + trend + income 318s 318s Estimate Std. Error t value Pr(>|t|) 318s trend 7.362 0.646 11.4 5.7e-14 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 49.754 on 19 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 19 318s SSR: 47033.469 MSE: 2475.446 Root MSE: 49.754 318s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 318s 318s > nobs( fit2slsS4 ) 318s [1] 40 318s > fit2slsS5 <- systemfit( 318s + list( consump ~ 1, price ~ 1 ), "2SLS", 318s + data = Kmenta, inst = ~ farmPrice, useMatrix = useMatrix ) 318s > print( summary( fit2slsS1 ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 36 1544 179 -0.65 0.852 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s eq1 20 19 861 45.3 6.73 -2.213 -2.213 318s eq2 20 17 682 40.1 6.33 -0.022 -0.143 318s 318s The covariance matrix of the residuals 318s eq1 eq2 318s eq1 45.3 -40.5 318s eq2 -40.5 40.1 318s 318s The correlations of the residuals 318s eq1 eq2 318s eq1 1.00 -0.95 318s eq2 -0.95 1.00 318s 318s 318s 2SLS estimates for 'eq1' (equation 1) 318s Model Formula: consump ~ price - 1 318s Instruments: ~farmPrice + trend + income 318s 318s Estimate Std. Error t value Pr(>|t|) 318s price 1.006 0.015 66.9 <2e-16 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 6.734 on 19 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 19 318s SSR: 861.48 MSE: 45.341 Root MSE: 6.734 318s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 318s 318s 318s 2SLS estimates for 'eq2' (equation 2) 318s Model Formula: price ~ consump + trend 318s Instruments: ~farmPrice + trend + income 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 55.5365 46.2668 1.20 0.25 318s consump 0.4453 0.4622 0.96 0.35 318s trend -0.0426 0.2496 -0.17 0.87 318s 318s Residual standard error: 6.335 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 682.257 MSE: 40.133 Root MSE: 6.335 318s Multiple R-Squared: -0.022 Adjusted R-Squared: -0.143 318s 318s > 318s > 318s > ## **************** shorter summaries ********************** 318s > print( summary( fit2sls1, useDfSys = TRUE, residCov = FALSE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 162 4.36 0.697 0.548 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 65.7 3.87 1.97 0.755 0.726 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 318s price -0.2436 0.0965 -2.52 0.017 * 318s income 0.3140 0.0469 6.69 1.3e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.966 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 318s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 318s price 0.2401 0.0999 2.40 0.02208 * 318s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 318s trend 0.2529 0.0997 2.54 0.01605 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.458 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 318s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 318s 318s > 318s > print( summary( fit2sls1, equations = FALSE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 162 4.36 0.697 0.548 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 65.7 3.87 1.97 0.755 0.726 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.87 4.36 318s supply 4.36 6.04 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.902 318s supply 0.902 1.000 318s 318s 318s Coefficients: 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 318s demand_price -0.2436 0.0965 -2.52 0.0218 * 318s demand_income 0.3140 0.0469 6.69 3.8e-06 *** 318s supply_(Intercept) 49.5324 12.0105 4.12 0.0008 *** 318s supply_price 0.2401 0.0999 2.40 0.0288 * 318s supply_farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 318s supply_trend 0.2529 0.0997 2.54 0.0219 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s > 318s > print( summary( fit2sls1rs, residCov = FALSE, equations = FALSE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 162 2.97 0.697 0.525 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 65.7 3.87 1.97 0.755 0.726 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s 318s Coefficients: 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 94.6333 8.1158 11.66 1.6e-09 *** 318s demand_price -0.2436 0.0989 -2.46 0.02471 * 318s demand_income 0.3140 0.0481 6.53 5.2e-06 *** 318s supply_(Intercept) 49.5324 9.8463 5.03 0.00012 *** 318s supply_price 0.2401 0.0819 2.93 0.00980 ** 318s supply_farmPrice 0.2556 0.0387 6.60 6.1e-06 *** 318s supply_trend 0.2529 0.0817 3.10 0.00694 ** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s > 318s > print( summary( fit2sls2Sym, useDfSys = FALSE ), equations = FALSE ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 166 3.6 0.691 0.553 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.749 0.719 318s supply 20 16 98.2 6.13 2.48 0.634 0.565 318s 318s The covariance matrix of the residuals 318s demand supply 318s demand 3.97 4.55 318s supply 4.55 6.13 318s 318s The correlations of the residuals 318s demand supply 318s demand 1.000 0.923 318s supply 0.923 1.000 318s 318s 318s Coefficients: 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 94.2816 8.8693 10.63 6.3e-09 *** 318s demand_price -0.2247 0.1034 -2.17 0.04425 * 318s demand_income 0.2983 0.0454 6.57 4.8e-06 *** 318s supply_(Intercept) 48.1843 10.5384 4.57 0.00031 *** 318s supply_price 0.2427 0.0896 2.71 0.01551 * 318s supply_farmPrice 0.2619 0.0411 6.38 9.1e-06 *** 318s supply_trend 0.2983 0.0454 6.57 6.4e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s > 318s > print( summary( fit2sls2 ), residCov = FALSE ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 166 3.6 0.691 0.553 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.749 0.719 318s supply 20 16 98.2 6.13 2.48 0.634 0.565 318s 318s 318s 2SLS estimates for 'demand' (equation 1) 318s Model Formula: consump ~ price + income 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.2816 8.8693 10.63 2.4e-12 *** 318s price -0.2247 0.1034 -2.17 0.037 * 318s income 0.2983 0.0454 6.57 1.6e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 1.991 on 17 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 17 318s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 318s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 318s 318s 318s 2SLS estimates for 'supply' (equation 2) 318s Model Formula: consump ~ price + farmPrice + trend 318s Instruments: ~income + farmPrice + trend 318s 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 48.1843 10.5384 4.57 6.1e-05 *** 318s price 0.2427 0.0896 2.71 0.011 * 318s farmPrice 0.2619 0.0411 6.38 2.8e-07 *** 318s trend 0.2983 0.0454 6.57 1.6e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s 318s Residual standard error: 2.477 on 16 degrees of freedom 318s Number of observations: 20 Degrees of Freedom: 16 318s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 318s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 318s 318s > 318s > print( summary( fit2sls3, useDfSys = FALSE, residCov = FALSE, 318s + equations = FALSE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 166 2.45 0.691 0.526 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.749 0.719 318s supply 20 16 98.2 6.13 2.48 0.634 0.565 318s 318s 318s Coefficients: 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 94.2816 8.1771 11.53 1.8e-09 *** 318s demand_price -0.2247 0.0954 -2.36 0.03071 * 318s demand_income 0.2983 0.0419 7.13 1.7e-06 *** 318s supply_(Intercept) 48.1843 9.7159 4.96 0.00014 *** 318s supply_price 0.2427 0.0826 2.94 0.00966 ** 318s supply_farmPrice 0.2619 0.0379 6.92 3.5e-06 *** 318s supply_trend 0.2983 0.0419 7.13 2.4e-06 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s > 318s > print( summary( fit2sls4s ), equations = FALSE, residCov = FALSE ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 3.78 0.69 0.568 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s 318s Coefficients: 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 95.7059 6.3056 15.18 < 2e-16 *** 318s demand_price -0.2433 0.0684 -3.56 0.00110 ** 318s demand_income 0.3027 0.0394 7.69 5.1e-09 *** 318s supply_(Intercept) 46.5637 8.3296 5.59 2.7e-06 *** 318s supply_price 0.2567 0.0684 3.75 0.00064 *** 318s supply_farmPrice 0.2637 0.0455 5.79 1.5e-06 *** 318s supply_trend 0.3027 0.0394 7.69 5.1e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s > 318s > print( summary( fit2sls5r, equations = FALSE, residCov = FALSE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 35 166 2.57 0.69 0.54 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 66.1 3.89 1.97 0.754 0.725 318s supply 20 16 100.0 6.25 2.50 0.627 0.557 318s 318s 318s Coefficients: 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 95.7059 6.0044 15.94 < 2e-16 *** 318s demand_price -0.2433 0.0621 -3.92 0.00039 *** 318s demand_income 0.3027 0.0382 7.93 2.5e-09 *** 318s supply_(Intercept) 46.5637 7.3842 6.31 3.1e-07 *** 318s supply_price 0.2567 0.0621 4.14 0.00021 *** 318s supply_farmPrice 0.2637 0.0373 7.08 3.0e-08 *** 318s supply_trend 0.3027 0.0382 7.93 2.5e-09 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s > 318s > print( summary( fit2slsd1s ), residCov = FALSE, equations = FALSE ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 33 164 9.25 0.694 0.512 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 67.4 3.97 1.99 0.748 0.719 318s supply 20 16 96.6 6.04 2.46 0.640 0.572 318s 318s 318s Coefficients: 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 106.7894 12.4749 8.56 1.4e-07 *** 318s demand_price -0.4116 0.1622 -2.54 0.02121 * 318s demand_income 0.3617 0.0631 5.73 2.5e-05 *** 318s supply_(Intercept) 49.5324 10.8976 4.55 0.00033 *** 318s supply_price 0.2401 0.0907 2.65 0.01755 * 318s supply_farmPrice 0.2556 0.0429 5.96 2.0e-05 *** 318s supply_trend 0.2529 0.0904 2.80 0.01292 * 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s > 318s > print( summary( fit2slsd2, residCov = FALSE, equations = FALSE ) ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 165 4.89 0.693 0.56 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 64.4 3.79 1.95 0.760 0.731 318s supply 20 16 100.3 6.27 2.50 0.626 0.556 318s 318s 318s Coefficients: 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 103.5936 11.8930 8.71 3.5e-10 *** 318s demand_price -0.3449 0.1455 -2.37 0.0236 * 318s demand_income 0.3260 0.0511 6.38 2.8e-07 *** 318s supply_(Intercept) 47.3592 10.5362 4.49 7.7e-05 *** 318s supply_price 0.2443 0.0894 2.73 0.0099 ** 318s supply_farmPrice 0.2657 0.0411 6.47 2.1e-07 *** 318s supply_trend 0.3260 0.0511 6.38 2.8e-07 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s > 318s > print( summary( fit2slsd3r ), residCov = FALSE, equations = FALSE ) 318s 318s systemfit results 318s method: 2SLS 318s 318s N DF SSR detRCov OLS-R2 McElroy-R2 318s system 40 34 165 3.32 0.693 0.537 318s 318s N DF SSR MSE RMSE R2 Adj R2 318s demand 20 17 64.4 3.79 1.95 0.760 0.731 318s supply 20 16 100.3 6.27 2.50 0.626 0.556 318s 318s 318s Coefficients: 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 103.5936 10.9648 9.45 4.9e-11 *** 318s demand_price -0.3449 0.1341 -2.57 0.0147 * 318s demand_income 0.3260 0.0471 6.92 5.7e-08 *** 318s supply_(Intercept) 47.3592 9.7139 4.88 2.5e-05 *** 318s supply_price 0.2443 0.0824 2.96 0.0055 ** 318s supply_farmPrice 0.2657 0.0379 7.01 4.3e-08 *** 318s supply_trend 0.3260 0.0471 6.92 5.7e-08 *** 318s --- 318s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 318s > 318s > 318s > ## ****************** residuals ************************** 318s > print( residuals( fit2sls1 ) ) 318s demand supply 318s 1 0.843 -0.4348 318s 2 -0.698 -1.2131 318s 3 2.359 1.7090 318s 4 1.490 0.7956 318s 5 2.139 1.5942 318s 6 1.277 0.6595 318s 7 1.571 1.4346 318s 8 -3.066 -4.8724 318s 9 -1.125 -2.3975 318s 10 2.492 3.1427 318s 11 -0.108 0.0689 318s 12 -2.292 -1.3978 318s 13 -1.598 -1.1136 318s 14 -0.271 1.1684 318s 15 1.958 3.4865 318s 16 -3.430 -3.8285 318s 17 -0.313 0.6793 318s 18 -2.151 -2.7713 318s 19 1.592 2.6668 318s 20 -0.668 0.6235 318s > print( residuals( fit2sls1$eq[[ 1 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 318s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 318s 12 13 14 15 16 17 18 19 20 318s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 318s > 318s > print( residuals( fit2sls2s ) ) 318s demand supply 318s 1 0.678 -0.0135 318s 2 -0.777 -0.8544 318s 3 2.281 2.0245 318s 4 1.416 1.0692 318s 5 2.213 1.7598 318s 6 1.334 0.7923 318s 7 1.640 1.5342 318s 8 -2.994 -4.8544 318s 9 -1.072 -2.3959 318s 10 2.522 3.1637 318s 11 -0.330 0.1628 318s 12 -2.593 -1.2864 318s 13 -1.856 -1.0729 318s 14 -0.356 1.1087 318s 15 2.138 3.2597 318s 16 -3.282 -4.1265 318s 17 -0.076 0.3331 318s 18 -2.119 -3.0961 318s 19 1.690 2.3122 318s 20 -0.458 0.1799 318s > print( residuals( fit2sls2s$eq[[ 2 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 318s -0.0135 -0.8544 2.0245 1.0692 1.7598 0.7923 1.5342 -4.8544 -2.3959 3.1637 318s 11 12 13 14 15 16 17 18 19 20 318s 0.1628 -1.2864 -1.0729 1.1087 3.2597 -4.1265 0.3331 -3.0961 2.3122 0.1799 318s > 318s > print( residuals( fit2sls3 ) ) 318s demand supply 318s 1 0.678 -0.0135 318s 2 -0.777 -0.8544 318s 3 2.281 2.0245 318s 4 1.416 1.0692 318s 5 2.213 1.7598 318s 6 1.334 0.7923 318s 7 1.640 1.5342 318s 8 -2.994 -4.8544 318s 9 -1.072 -2.3959 318s 10 2.522 3.1637 318s 11 -0.330 0.1628 318s 12 -2.593 -1.2864 318s 13 -1.856 -1.0729 318s 14 -0.356 1.1087 318s 15 2.138 3.2597 318s 16 -3.282 -4.1265 318s 17 -0.076 0.3331 318s 18 -2.119 -3.0961 318s 19 1.690 2.3122 318s 20 -0.458 0.1799 318s > print( residuals( fit2sls3$eq[[ 1 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 318s 0.678 -0.777 2.281 1.416 2.213 1.334 1.640 -2.994 -1.072 2.522 -0.330 318s 12 13 14 15 16 17 18 19 20 318s -2.593 -1.856 -0.356 2.138 -3.282 -0.076 -2.119 1.690 -0.458 318s > 318s > print( residuals( fit2sls4r ) ) 318s demand supply 318s 1 0.729 0.0219 318s 2 -0.698 -0.8806 318s 3 2.349 2.0055 318s 4 1.496 1.0326 318s 5 2.165 1.7870 318s 6 1.310 0.7993 318s 7 1.635 1.5189 318s 8 -2.951 -4.9334 318s 9 -1.134 -2.3609 318s 10 2.397 3.2818 318s 11 -0.359 0.2857 318s 12 -2.524 -1.2257 318s 13 -1.745 -1.0782 318s 14 -0.349 1.1382 318s 15 2.022 3.2981 318s 16 -3.345 -4.1440 318s 17 -0.322 0.4686 318s 18 -2.075 -3.1779 318s 19 1.738 2.2072 318s 20 -0.339 -0.0444 318s > print( residuals( fit2sls4r$eq[[ 2 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 318s 0.0219 -0.8806 2.0055 1.0326 1.7870 0.7993 1.5189 -4.9334 -2.3609 3.2818 318s 11 12 13 14 15 16 17 18 19 20 318s 0.2857 -1.2257 -1.0782 1.1382 3.2981 -4.1440 0.4686 -3.1779 2.2072 -0.0444 318s > 318s > print( residuals( fit2sls5rs ) ) 318s demand supply 318s 1 0.729 0.0219 318s 2 -0.698 -0.8806 318s 3 2.349 2.0055 318s 4 1.496 1.0326 318s 5 2.165 1.7870 318s 6 1.310 0.7993 318s 7 1.635 1.5189 318s 8 -2.951 -4.9334 318s 9 -1.134 -2.3609 318s 10 2.397 3.2818 318s 11 -0.359 0.2857 318s 12 -2.524 -1.2257 318s 13 -1.745 -1.0782 318s 14 -0.349 1.1382 318s 15 2.022 3.2981 318s 16 -3.345 -4.1440 318s 17 -0.322 0.4686 318s 18 -2.075 -3.1779 318s 19 1.738 2.2072 318s 20 -0.339 -0.0444 318s > print( residuals( fit2sls5rs$eq[[ 1 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 318s 0.729 -0.698 2.349 1.496 2.165 1.310 1.635 -2.951 -1.134 2.397 -0.359 318s 12 13 14 15 16 17 18 19 20 318s -2.524 -1.745 -0.349 2.022 -3.345 -0.322 -2.075 1.738 -0.339 318s > 318s > print( residuals( fit2slsd1 ) ) 318s demand supply 318s 1 1.3775 -0.4348 318s 2 0.0125 -1.2131 318s 3 2.9728 1.7090 318s 4 2.2121 0.7956 318s 5 1.6920 1.5942 318s 6 1.0407 0.6595 318s 7 1.4768 1.4346 318s 8 -2.7583 -4.8724 318s 9 -1.6807 -2.3975 318s 10 1.4265 3.1427 318s 11 -0.2029 0.0689 318s 12 -1.5123 -1.3978 318s 13 -0.4958 -1.1136 318s 14 -0.1528 1.1684 318s 15 0.8692 3.4865 318s 16 -4.0547 -3.8285 318s 17 -2.5309 0.6793 318s 18 -1.8070 -2.7713 318s 19 1.9299 2.6668 318s 20 0.1853 0.6235 318s > print( residuals( fit2slsd1$eq[[ 2 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 318s -0.4348 -1.2131 1.7090 0.7956 1.5942 0.6595 1.4346 -4.8724 -2.3975 3.1427 318s 11 12 13 14 15 16 17 18 19 20 318s 0.0689 -1.3978 -1.1136 1.1684 3.4865 -3.8285 0.6793 -2.7713 2.6668 0.6235 318s > 318s > print( residuals( fit2slsd2r ) ) 318s demand supply 318s 1 0.996 0.2444 318s 2 -0.268 -0.6349 318s 3 2.715 2.2177 318s 4 1.936 1.2367 318s 5 1.907 1.8612 318s 6 1.184 0.8736 318s 7 1.609 1.5951 318s 8 -2.709 -4.8434 318s 9 -1.476 -2.3949 318s 10 1.705 3.1765 318s 11 -0.540 0.2202 318s 12 -2.167 -1.2182 318s 13 -1.150 -1.0480 318s 14 -0.316 1.0722 318s 15 1.395 3.1209 318s 16 -3.680 -4.3088 318s 17 -1.669 0.1212 318s 18 -1.829 -3.2948 318s 19 2.016 2.0952 318s 20 0.341 -0.0916 318s > print( residuals( fit2slsd2r$eq[[ 1 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 318s 0.996 -0.268 2.715 1.936 1.907 1.184 1.609 -2.709 -1.476 1.705 -0.540 318s 12 13 14 15 16 17 18 19 20 318s -2.167 -1.150 -0.316 1.395 -3.680 -1.669 -1.829 2.016 0.341 318s > 318s > 318s > ## *************** coefficients ********************* 318s > print( round( coef( fit2sls1s ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s 94.633 -0.244 0.314 49.532 318s supply_price supply_farmPrice supply_trend 318s 0.240 0.256 0.253 318s > print( round( coef( fit2sls1s$eq[[ 1 ]] ), digits = 6 ) ) 318s (Intercept) price income 318s 94.633 -0.244 0.314 318s > 318s > print( round( coef( fit2sls2 ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s 94.282 -0.225 0.298 48.184 318s supply_price supply_farmPrice supply_trend 318s 0.243 0.262 0.298 318s > print( round( coef( fit2sls2$eq[[ 2 ]] ), digits = 6 ) ) 318s (Intercept) price farmPrice trend 318s 48.184 0.243 0.262 0.298 318s > 318s > print( round( coef( fit2sls3 ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s 94.282 -0.225 0.298 48.184 318s supply_price supply_farmPrice supply_trend 318s 0.243 0.262 0.298 318s > print( round( coef( fit2sls3, modified.regMat = TRUE ), digits = 6 ) ) 318s C1 C2 C3 C4 C5 C6 318s 94.282 -0.225 0.298 48.184 0.243 0.262 318s > print( round( coef( fit2sls3$eq[[ 1 ]] ), digits = 6 ) ) 318s (Intercept) price income 318s 94.282 -0.225 0.298 318s > 318s > print( round( coef( fit2sls4s ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s 95.706 -0.243 0.303 46.564 318s supply_price supply_farmPrice supply_trend 318s 0.257 0.264 0.303 318s > print( round( coef( fit2sls4s$eq[[ 2 ]] ), digits = 6 ) ) 318s (Intercept) price farmPrice trend 318s 46.564 0.257 0.264 0.303 318s > 318s > print( round( coef( fit2sls5r ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s 95.706 -0.243 0.303 46.564 318s supply_price supply_farmPrice supply_trend 318s 0.257 0.264 0.303 318s > print( round( coef( fit2sls5r, modified.regMat = TRUE ), digits = 6 ) ) 318s C1 C2 C3 C4 C5 C6 318s 95.706 -0.243 0.303 46.564 0.257 0.264 318s > print( round( coef( fit2sls5r$eq[[ 2 ]] ), digits = 6 ) ) 318s (Intercept) price farmPrice trend 318s 46.564 0.257 0.264 0.303 318s > 318s > 318s > ## *************** coefficients with stats ********************* 318s > print( round( coef( summary( fit2sls1s ) ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 94.633 8.9352 10.59 0.000000 318s demand_price -0.244 0.1088 -2.24 0.038916 318s demand_income 0.314 0.0530 5.93 0.000016 318s supply_(Intercept) 49.532 10.8404 4.57 0.000315 318s supply_price 0.240 0.0902 2.66 0.017058 318s supply_farmPrice 0.256 0.0426 5.99 0.000019 318s supply_trend 0.253 0.0899 2.81 0.012528 318s > print( round( coef( summary( fit2sls1s$eq[[ 1 ]] ) ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.633 8.935 10.59 0.000000 318s price -0.244 0.109 -2.24 0.038916 318s income 0.314 0.053 5.93 0.000016 318s > 318s > print( round( coef( summary( fit2sls2, useDfSys = FALSE ) ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 94.282 8.8693 10.63 0.000000 318s demand_price -0.225 0.1034 -2.17 0.044246 318s demand_income 0.298 0.0454 6.57 0.000005 318s supply_(Intercept) 48.184 10.5384 4.57 0.000313 318s supply_price 0.243 0.0896 2.71 0.015508 318s supply_farmPrice 0.262 0.0411 6.38 0.000009 318s supply_trend 0.298 0.0454 6.57 0.000006 318s > print( round( coef( summary( fit2sls2$eq[[ 2 ]], useDfSys = FALSE ) ), 318s + digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 48.184 10.5384 4.57 0.000313 318s price 0.243 0.0896 2.71 0.015508 318s farmPrice 0.262 0.0411 6.38 0.000009 318s trend 0.298 0.0454 6.57 0.000006 318s > 318s > print( round( coef( summary( fit2sls3 ) ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 94.282 8.1771 11.53 0.000000 318s demand_price -0.225 0.0954 -2.36 0.024352 318s demand_income 0.298 0.0419 7.13 0.000000 318s supply_(Intercept) 48.184 9.7159 4.96 0.000019 318s supply_price 0.243 0.0826 2.94 0.005903 318s supply_farmPrice 0.262 0.0379 6.92 0.000000 318s supply_trend 0.298 0.0419 7.13 0.000000 318s > print( round( coef( summary( fit2sls3 ), modified.regMat = TRUE ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s C1 94.282 8.1771 11.53 0.000000 318s C2 -0.225 0.0954 -2.36 0.024352 318s C3 0.298 0.0419 7.13 0.000000 318s C4 48.184 9.7159 4.96 0.000019 318s C5 0.243 0.0826 2.94 0.005903 318s C6 0.262 0.0379 6.92 0.000000 318s > print( round( coef( summary( fit2sls3$eq[[ 1 ]] ) ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 94.282 8.1771 11.53 0.0000 318s price -0.225 0.0954 -2.36 0.0244 318s income 0.298 0.0419 7.13 0.0000 318s > 318s > print( round( coef( summary( fit2sls4s ) ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 95.706 6.3056 15.18 0.000000 318s demand_price -0.243 0.0684 -3.56 0.001104 318s demand_income 0.303 0.0394 7.69 0.000000 318s supply_(Intercept) 46.564 8.3296 5.59 0.000003 318s supply_price 0.257 0.0684 3.75 0.000635 318s supply_farmPrice 0.264 0.0455 5.79 0.000001 318s supply_trend 0.303 0.0394 7.69 0.000000 318s > print( round( coef( summary( fit2sls4s$eq[[ 2 ]] ) ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.564 8.3296 5.59 0.000003 318s price 0.257 0.0684 3.75 0.000635 318s farmPrice 0.264 0.0455 5.79 0.000001 318s trend 0.303 0.0394 7.69 0.000000 318s > 318s > print( round( coef( summary( fit2sls5r, useDfSys = FALSE ) ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s demand_(Intercept) 95.706 6.0044 15.94 0.000000 318s demand_price -0.243 0.0621 -3.92 0.001102 318s demand_income 0.303 0.0382 7.93 0.000000 318s supply_(Intercept) 46.564 7.3842 6.31 0.000010 318s supply_price 0.257 0.0621 4.14 0.000774 318s supply_farmPrice 0.264 0.0373 7.08 0.000003 318s supply_trend 0.303 0.0382 7.93 0.000001 318s > print( round( coef( summary( fit2sls5r, useDfSys = FALSE ), 318s + modified.regMat = TRUE ), digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s C1 95.706 6.0044 15.94 NA 318s C2 -0.243 0.0621 -3.92 NA 318s C3 0.303 0.0382 7.93 NA 318s C4 46.564 7.3842 6.31 NA 318s C5 0.257 0.0621 4.14 NA 318s C6 0.264 0.0373 7.08 NA 318s > print( round( coef( summary( fit2sls5r$eq[[ 2 ]], useDfSys = FALSE ) ), 318s + digits = 6 ) ) 318s Estimate Std. Error t value Pr(>|t|) 318s (Intercept) 46.564 7.3842 6.31 0.000010 318s price 0.257 0.0621 4.14 0.000774 318s farmPrice 0.264 0.0373 7.08 0.000003 318s trend 0.303 0.0382 7.93 0.000001 318s > 318s > 318s > ## *********** variance covariance matrix of the coefficients ******* 318s > print( round( vcov( fit2sls1s ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 79.8371 -0.85694 0.06274 318s demand_price -0.8569 0.01185 -0.00336 318s demand_income 0.0627 -0.00336 0.00280 318s supply_(Intercept) 0.0000 0.00000 0.00000 318s supply_price 0.0000 0.00000 0.00000 318s supply_farmPrice 0.0000 0.00000 0.00000 318s supply_trend 0.0000 0.00000 0.00000 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) 0.000 0.000000 0.000000 318s demand_price 0.000 0.000000 0.000000 318s demand_income 0.000 0.000000 0.000000 318s supply_(Intercept) 117.514 -0.892363 -0.263795 318s supply_price -0.892 0.008136 0.000763 318s supply_farmPrice -0.264 0.000763 0.001819 318s supply_trend -0.241 0.000472 0.001122 318s supply_trend 318s demand_(Intercept) 0.000000 318s demand_price 0.000000 318s demand_income 0.000000 318s supply_(Intercept) -0.240505 318s supply_price 0.000472 318s supply_farmPrice 0.001122 318s supply_trend 0.008090 318s > print( round( vcov( fit2sls1s$eq[[ 1 ]] ), digits = 6 ) ) 318s (Intercept) price income 318s (Intercept) 79.8371 -0.85694 0.06274 318s price -0.8569 0.01185 -0.00336 318s income 0.0627 -0.00336 0.00280 318s > 318s > print( round( vcov( fit2sls1r ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 53.3287 -0.57241 0.04191 318s demand_price -0.5724 0.00791 -0.00225 318s demand_income 0.0419 -0.00225 0.00187 318s supply_(Intercept) 0.0000 0.00000 0.00000 318s supply_price 0.0000 0.00000 0.00000 318s supply_farmPrice 0.0000 0.00000 0.00000 318s supply_trend 0.0000 0.00000 0.00000 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) 0.000 0.000000 0.000000 318s demand_price 0.000 0.000000 0.000000 318s demand_income 0.000 0.000000 0.000000 318s supply_(Intercept) 115.402 -0.876328 -0.259055 318s supply_price -0.876 0.007989 0.000749 318s supply_farmPrice -0.259 0.000749 0.001786 318s supply_trend -0.236 0.000463 0.001101 318s supply_trend 318s demand_(Intercept) 0.000000 318s demand_price 0.000000 318s demand_income 0.000000 318s supply_(Intercept) -0.236183 318s supply_price 0.000463 318s supply_farmPrice 0.001101 318s supply_trend 0.007945 318s > print( round( vcov( fit2sls1r$eq[[ 2 ]] ), digits = 6 ) ) 318s (Intercept) price farmPrice trend 318s (Intercept) 115.402 -0.876328 -0.259055 -0.236183 318s price -0.876 0.007989 0.000749 0.000463 318s farmPrice -0.259 0.000749 0.001786 0.001101 318s trend -0.236 0.000463 0.001101 0.007945 318s > 318s > print( round( vcov( fit2sls2 ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 78.66379 -0.829021 0.046112 318s demand_price -0.82902 0.010698 -0.002471 318s demand_income 0.04611 -0.002471 0.002061 318s supply_(Intercept) -1.37081 0.073457 -0.061273 318s supply_price 0.00269 -0.000144 0.000120 318s supply_farmPrice 0.00639 -0.000343 0.000286 318s supply_trend 0.04611 -0.002471 0.002061 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) -1.3708 0.002689 0.006393 318s demand_price 0.0735 -0.000144 -0.000343 318s demand_income -0.0613 0.000120 0.000286 318s supply_(Intercept) 111.0580 -0.872938 -0.236592 318s supply_price -0.8729 0.008032 0.000707 318s supply_farmPrice -0.2366 0.000707 0.001686 318s supply_trend -0.0613 0.000120 0.000286 318s supply_trend 318s demand_(Intercept) 0.046112 318s demand_price -0.002471 318s demand_income 0.002061 318s supply_(Intercept) -0.061273 318s supply_price 0.000120 318s supply_farmPrice 0.000286 318s supply_trend 0.002061 318s > print( round( vcov( fit2sls2$eq[[ 1 ]] ), digits = 6 ) ) 318s (Intercept) price income 318s (Intercept) 78.6638 -0.82902 0.04611 318s price -0.8290 0.01070 -0.00247 318s income 0.0461 -0.00247 0.00206 318s > 318s > print( round( vcov( fit2sls3 ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 66.86423 -0.704668 0.039196 318s demand_price -0.70467 0.009094 -0.002100 318s demand_income 0.03920 -0.002100 0.001752 318s supply_(Intercept) -1.16519 0.062438 -0.052082 318s supply_price 0.00229 -0.000122 0.000102 318s supply_farmPrice 0.00543 -0.000291 0.000243 318s supply_trend 0.03920 -0.002100 0.001752 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) -1.1652 0.002285 0.005434 318s demand_price 0.0624 -0.000122 -0.000291 318s demand_income -0.0521 0.000102 0.000243 318s supply_(Intercept) 94.3993 -0.741997 -0.201104 318s supply_price -0.7420 0.006827 0.000601 318s supply_farmPrice -0.2011 0.000601 0.001433 318s supply_trend -0.0521 0.000102 0.000243 318s supply_trend 318s demand_(Intercept) 0.039196 318s demand_price -0.002100 318s demand_income 0.001752 318s supply_(Intercept) -0.052082 318s supply_price 0.000102 318s supply_farmPrice 0.000243 318s supply_trend 0.001752 318s > print( round( vcov( fit2sls3, modified.regMat = TRUE ), digits = 6 ) ) 318s C1 C2 C3 C4 C5 C6 318s C1 66.86423 -0.704668 0.039196 -1.1652 0.002285 0.005434 318s C2 -0.70467 0.009094 -0.002100 0.0624 -0.000122 -0.000291 318s C3 0.03920 -0.002100 0.001752 -0.0521 0.000102 0.000243 318s C4 -1.16519 0.062438 -0.052082 94.3993 -0.741997 -0.201104 318s C5 0.00229 -0.000122 0.000102 -0.7420 0.006827 0.000601 318s C6 0.00543 -0.000291 0.000243 -0.2011 0.000601 0.001433 318s > print( round( vcov( fit2sls3$eq[[ 2 ]] ), digits = 6 ) ) 318s (Intercept) price farmPrice trend 318s (Intercept) 94.3993 -0.741997 -0.201104 -0.052082 318s price -0.7420 0.006827 0.000601 0.000102 318s farmPrice -0.2011 0.000601 0.001433 0.000243 318s trend -0.0521 0.000102 0.000243 0.001752 318s > 318s > print( round( vcov( fit2sls4s ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 39.7610 -0.358128 -0.03842 318s demand_price -0.3581 0.004681 -0.00113 318s demand_income -0.0384 -0.001129 0.00155 318s supply_(Intercept) 39.6949 -0.480685 0.08595 318s supply_price -0.3581 0.004681 -0.00113 318s supply_farmPrice -0.0359 0.000252 0.00011 318s supply_trend -0.0384 -0.001129 0.00155 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) 39.6949 -0.358128 -0.035932 318s demand_price -0.4807 0.004681 0.000252 318s demand_income 0.0859 -0.001129 0.000110 318s supply_(Intercept) 69.3817 -0.480685 -0.226588 318s supply_price -0.4807 0.004681 0.000252 318s supply_farmPrice -0.2266 0.000252 0.002072 318s supply_trend 0.0859 -0.001129 0.000110 318s supply_trend 318s demand_(Intercept) -0.03842 318s demand_price -0.00113 318s demand_income 0.00155 318s supply_(Intercept) 0.08595 318s supply_price -0.00113 318s supply_farmPrice 0.00011 318s supply_trend 0.00155 318s > print( round( vcov( fit2sls4s$eq[[ 1 ]] ), digits = 6 ) ) 318s (Intercept) price income 318s (Intercept) 39.7610 -0.35813 -0.03842 318s price -0.3581 0.00468 -0.00113 318s income -0.0384 -0.00113 0.00155 318s > 318s > print( round( vcov( fit2sls5r ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 36.0523 -0.302514 -0.057288 318s demand_price -0.3025 0.003851 -0.000847 318s demand_income -0.0573 -0.000847 0.001456 318s supply_(Intercept) 34.1121 -0.397307 0.057684 318s supply_price -0.3025 0.003851 -0.000847 318s supply_farmPrice -0.0337 0.000218 0.000122 318s supply_trend -0.0573 -0.000847 0.001456 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) 34.1121 -0.302514 -0.033671 318s demand_price -0.3973 0.003851 0.000218 318s demand_income 0.0577 -0.000847 0.000122 318s supply_(Intercept) 54.5267 -0.397307 -0.157170 318s supply_price -0.3973 0.003851 0.000218 318s supply_farmPrice -0.1572 0.000218 0.001388 318s supply_trend 0.0577 -0.000847 0.000122 318s supply_trend 318s demand_(Intercept) -0.057288 318s demand_price -0.000847 318s demand_income 0.001456 318s supply_(Intercept) 0.057684 318s supply_price -0.000847 318s supply_farmPrice 0.000122 318s supply_trend 0.001456 318s > print( round( vcov( fit2sls5r, modified.regMat = TRUE ), digits = 6 ) ) 318s C1 C2 C3 C4 C5 C6 318s C1 36.0523 -0.302514 -0.057288 34.1121 -0.302514 -0.033671 318s C2 -0.3025 0.003851 -0.000847 -0.3973 0.003851 0.000218 318s C3 -0.0573 -0.000847 0.001456 0.0577 -0.000847 0.000122 318s C4 34.1121 -0.397307 0.057684 54.5267 -0.397307 -0.157170 318s C5 -0.3025 0.003851 -0.000847 -0.3973 0.003851 0.000218 318s C6 -0.0337 0.000218 0.000122 -0.1572 0.000218 0.001388 318s > print( round( vcov( fit2sls5r$eq[[ 2 ]] ), digits = 6 ) ) 318s (Intercept) price farmPrice trend 318s (Intercept) 54.5267 -0.397307 -0.157170 0.057684 318s price -0.3973 0.003851 0.000218 -0.000847 318s farmPrice -0.1572 0.000218 0.001388 0.000122 318s trend 0.0577 -0.000847 0.000122 0.001456 318s > 318s > print( round( vcov( fit2slsd1 ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 124.179 -1.51767 0.28519 318s demand_price -1.518 0.02098 -0.00595 318s demand_income 0.285 -0.00595 0.00318 318s supply_(Intercept) 0.000 0.00000 0.00000 318s supply_price 0.000 0.00000 0.00000 318s supply_farmPrice 0.000 0.00000 0.00000 318s supply_trend 0.000 0.00000 0.00000 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) 0.000 0.000000 0.000000 318s demand_price 0.000 0.000000 0.000000 318s demand_income 0.000 0.000000 0.000000 318s supply_(Intercept) 144.253 -1.095410 -0.323818 318s supply_price -1.095 0.009987 0.000936 318s supply_farmPrice -0.324 0.000936 0.002233 318s supply_trend -0.295 0.000579 0.001377 318s supply_trend 318s demand_(Intercept) 0.000000 318s demand_price 0.000000 318s demand_income 0.000000 318s supply_(Intercept) -0.295229 318s supply_price 0.000579 318s supply_farmPrice 0.001377 318s supply_trend 0.009931 318s > print( round( vcov( fit2slsd1$eq[[ 1 ]] ), digits = 6 ) ) 318s (Intercept) price income 318s (Intercept) 124.179 -1.51767 0.28519 318s price -1.518 0.02098 -0.00595 318s income 0.285 -0.00595 0.00318 318s > 318s > print( round( vcov( fit2slsd2rs ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 95.9017 -1.129212 0.176368 318s demand_price -1.1292 0.014881 -0.003682 318s demand_income 0.1764 -0.003682 0.001968 318s supply_(Intercept) -5.2430 0.109460 -0.058492 318s supply_price 0.0103 -0.000215 0.000115 318s supply_farmPrice 0.0245 -0.000510 0.000273 318s supply_trend 0.1764 -0.003682 0.001968 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) -5.2430 0.010284 0.024451 318s demand_price 0.1095 -0.000215 -0.000510 318s demand_income -0.0585 0.000115 0.000273 318s supply_(Intercept) 114.2555 -0.898881 -0.243056 318s supply_price -0.8989 0.008273 0.000727 318s supply_farmPrice -0.2431 0.000727 0.001733 318s supply_trend -0.0585 0.000115 0.000273 318s supply_trend 318s demand_(Intercept) 0.176368 318s demand_price -0.003682 318s demand_income 0.001968 318s supply_(Intercept) -0.058492 318s supply_price 0.000115 318s supply_farmPrice 0.000273 318s supply_trend 0.001968 318s > print( round( vcov( fit2slsd2rs$eq[[ 2 ]] ), digits = 6 ) ) 318s (Intercept) price farmPrice trend 318s (Intercept) 114.2555 -0.898881 -0.243056 -0.058492 318s price -0.8989 0.008273 0.000727 0.000115 318s farmPrice -0.2431 0.000727 0.001733 0.000273 318s trend -0.0585 0.000115 0.000273 0.001968 318s > 318s > print( round( vcov( fit2slsd3 ), digits = 6 ) ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 141.4425 -1.640068 0.234151 318s demand_price -1.6401 0.021165 -0.004888 318s demand_income 0.2342 -0.004888 0.002612 318s supply_(Intercept) -6.9607 0.145321 -0.077656 318s supply_price 0.0137 -0.000285 0.000152 318s supply_farmPrice 0.0325 -0.000678 0.000362 318s supply_trend 0.2342 -0.004888 0.002612 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) -6.9607 0.013653 0.032462 318s demand_price 0.1453 -0.000285 -0.000678 318s demand_income -0.0777 0.000152 0.000362 318s supply_(Intercept) 111.0123 -0.869653 -0.237751 318s supply_price -0.8697 0.007995 0.000708 318s supply_farmPrice -0.2378 0.000708 0.001688 318s supply_trend -0.0777 0.000152 0.000362 318s supply_trend 318s demand_(Intercept) 0.234151 318s demand_price -0.004888 318s demand_income 0.002612 318s supply_(Intercept) -0.077656 318s supply_price 0.000152 318s supply_farmPrice 0.000362 318s supply_trend 0.002612 318s > print( round( vcov( fit2slsd3, modified.regMat = TRUE ), digits = 6 ) ) 318s C1 C2 C3 C4 C5 C6 318s C1 141.4425 -1.640068 0.234151 -6.9607 0.013653 0.032462 318s C2 -1.6401 0.021165 -0.004888 0.1453 -0.000285 -0.000678 318s C3 0.2342 -0.004888 0.002612 -0.0777 0.000152 0.000362 318s C4 -6.9607 0.145321 -0.077656 111.0123 -0.869653 -0.237751 318s C5 0.0137 -0.000285 0.000152 -0.8697 0.007995 0.000708 318s C6 0.0325 -0.000678 0.000362 -0.2378 0.000708 0.001688 318s > print( round( vcov( fit2slsd3$eq[[ 1 ]] ), digits = 6 ) ) 318s (Intercept) price income 318s (Intercept) 141.442 -1.64007 0.23415 318s price -1.640 0.02116 -0.00489 318s income 0.234 -0.00489 0.00261 318s > 318s > 318s > ## *********** confidence intervals of coefficients ************* 318s > print( confint( fit2sls1 ) ) 318s 2.5 % 97.5 % 318s demand_(Intercept) 77.922 111.345 318s demand_price -0.447 -0.040 318s demand_income 0.215 0.413 318s supply_(Intercept) 24.071 74.994 318s supply_price 0.028 0.452 318s supply_farmPrice 0.155 0.356 318s supply_trend 0.042 0.464 318s > print( confint( fit2sls1$eq[[ 1 ]], level = 0.9 ) ) 318s 5 % 95 % 318s (Intercept) 80.854 108.412 318s price -0.411 -0.076 318s income 0.232 0.396 318s > 318s > print( confint( fit2sls2s, level = 0.9 ) ) 318s 5 % 95 % 318s demand_(Intercept) 78.005 110.558 318s demand_price -0.417 -0.032 318s demand_income 0.211 0.386 318s supply_(Intercept) 24.204 72.165 318s supply_price 0.038 0.447 318s supply_farmPrice 0.169 0.355 318s supply_trend 0.211 0.386 318s > print( confint( fit2sls2s$eq[[ 2 ]], level = 0.99 ) ) 318s 0.5 % 99.5 % 318s (Intercept) 15.989 80.380 318s price -0.032 0.517 318s farmPrice 0.137 0.387 318s trend 0.181 0.416 318s > 318s > print( confint( fit2sls3, level = 0.99, useDfSys = TRUE ) ) 318s 0.5 % 99.5 % 318s demand_(Intercept) 77.664 110.899 318s demand_price -0.419 -0.031 318s demand_income 0.213 0.383 318s supply_(Intercept) 28.439 67.929 318s supply_price 0.075 0.411 318s supply_farmPrice 0.185 0.339 318s supply_trend 0.213 0.383 318s > print( confint( fit2sls3$eq[[ 1 ]], level = 0.5, useDfSys = TRUE ) ) 318s 25 % 75 % 318s (Intercept) 88.71 99.857 318s price -0.29 -0.160 318s income 0.27 0.327 318s > 318s > print( confint( fit2sls4r, level = 0.5 ) ) 318s 25 % 75 % 318s demand_(Intercept) 83.516 107.895 318s demand_price -0.369 -0.117 318s demand_income 0.225 0.380 318s supply_(Intercept) 31.573 61.554 318s supply_price 0.131 0.383 318s supply_farmPrice 0.188 0.339 318s supply_trend 0.225 0.380 318s > print( confint( fit2sls4r$eq[[ 2 ]], level = 0.25 ) ) 318s 37.5 % 62.5 % 318s (Intercept) 44.192 48.935 318s price 0.237 0.277 318s farmPrice 0.252 0.276 318s trend 0.290 0.315 318s > 318s > print( confint( fit2sls5rs, level = 0.25 ) ) 318s 37.5 % 62.5 % 318s demand_(Intercept) 84.017 107.395 318s demand_price -0.369 -0.117 318s demand_income 0.230 0.376 318s supply_(Intercept) 31.265 61.863 318s supply_price 0.131 0.383 318s supply_farmPrice 0.181 0.346 318s supply_trend 0.230 0.376 318s > print( confint( fit2sls5rs$eq[[ 1 ]], level = 0.975 ) ) 318s 1.3 % 98.8 % 318s (Intercept) 82.221 109.191 318s price -0.389 -0.098 318s income 0.218 0.387 318s > 318s > print( confint( fit2slsd1, level = 0.975, useDfSys = TRUE ) ) 318s 1.3 % 98.8 % 318s demand_(Intercept) 84.118 129.461 318s demand_price -0.706 -0.117 318s demand_income 0.247 0.476 318s supply_(Intercept) 25.097 73.968 318s supply_price 0.037 0.443 318s supply_farmPrice 0.159 0.352 318s supply_trend 0.050 0.456 318s > print( confint( fit2slsd1$eq[[ 2 ]], level = 0.999, useDfSys = TRUE ) ) 318s 0.1 % 100 % 318s (Intercept) 6.163 92.901 318s price -0.121 0.601 318s farmPrice 0.085 0.426 318s trend -0.107 0.613 318s > 318s > print( confint( fit2slsd2r, level = 0.999 ) ) 318s 0.1 % 100 % 318s demand_(Intercept) 81.311 125.877 318s demand_price -0.617 -0.072 318s demand_income 0.230 0.422 318s supply_(Intercept) 27.618 67.100 318s supply_price 0.077 0.412 318s supply_farmPrice 0.189 0.343 318s supply_trend 0.230 0.422 318s > print( confint( fit2slsd2r$eq[[ 1 ]] ) ) 318s 2.5 % 97.5 % 318s (Intercept) 81.311 125.877 318s price -0.617 -0.072 318s income 0.230 0.422 318s > 318s > 318s > ## *********** fitted values ************* 318s > print( fitted( fit2sls1, se.fit = TRUE, interval = "prediction" ) ) 318s demand supply 318s 1 97.6 98.9 318s 2 99.9 100.4 318s 3 99.8 100.5 318s 4 100.0 100.7 318s 5 102.1 102.6 318s 6 102.0 102.6 318s 7 102.4 102.6 318s 8 103.0 104.8 318s 9 101.5 102.7 318s 10 100.3 99.7 318s 11 95.5 95.4 318s 12 94.7 93.8 318s 13 96.1 95.6 318s 14 99.0 97.6 318s 15 103.8 102.3 318s 16 103.7 104.1 318s 17 103.8 102.8 318s 18 102.1 102.7 318s 19 103.6 102.6 318s 20 106.9 105.6 318s > print( fitted( fit2sls1$eq[[ 1 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 12 13 318s 97.6 99.9 99.8 100.0 102.1 102.0 102.4 103.0 101.5 100.3 95.5 94.7 96.1 318s 14 15 16 17 18 19 20 318s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 318s > 318s > print( fitted( fit2sls2s ) ) 318s demand supply 318s 1 97.8 98.5 318s 2 100.0 100.0 318s 3 99.9 100.1 318s 4 100.1 100.4 318s 5 102.0 102.5 318s 6 101.9 102.5 318s 7 102.4 102.5 318s 8 102.9 104.8 318s 9 101.4 102.7 318s 10 100.3 99.7 318s 11 95.8 95.3 318s 12 95.0 93.7 318s 13 96.4 95.6 318s 14 99.1 97.6 318s 15 103.7 102.5 318s 16 103.5 104.4 318s 17 103.6 103.2 318s 18 102.0 103.0 318s 19 103.5 102.9 318s 20 106.7 106.1 318s > print( fitted( fit2sls2s$eq[[ 2 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 12 13 318s 98.5 100.0 100.1 100.4 102.5 102.5 102.5 104.8 102.7 99.7 95.3 93.7 95.6 318s 14 15 16 17 18 19 20 318s 97.6 102.5 104.4 103.2 103.0 102.9 106.1 318s > 318s > print( fitted( fit2sls3 ) ) 318s demand supply 318s 1 97.8 98.5 318s 2 100.0 100.0 318s 3 99.9 100.1 318s 4 100.1 100.4 318s 5 102.0 102.5 318s 6 101.9 102.5 318s 7 102.4 102.5 318s 8 102.9 104.8 318s 9 101.4 102.7 318s 10 100.3 99.7 318s 11 95.8 95.3 318s 12 95.0 93.7 318s 13 96.4 95.6 318s 14 99.1 97.6 318s 15 103.7 102.5 318s 16 103.5 104.4 318s 17 103.6 103.2 318s 18 102.0 103.0 318s 19 103.5 102.9 318s 20 106.7 106.1 318s > print( fitted( fit2sls3$eq[[ 1 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 12 13 318s 97.8 100.0 99.9 100.1 102.0 101.9 102.4 102.9 101.4 100.3 95.8 95.0 96.4 318s 14 15 16 17 18 19 20 318s 99.1 103.7 103.5 103.6 102.0 103.5 106.7 318s > 318s > print( fitted( fit2sls4r ) ) 318s demand supply 318s 1 97.8 98.5 318s 2 99.9 100.1 318s 3 99.8 100.2 318s 4 100.0 100.5 318s 5 102.1 102.5 318s 6 101.9 102.4 318s 7 102.4 102.5 318s 8 102.9 104.8 318s 9 101.5 102.7 318s 10 100.4 99.5 318s 11 95.8 95.1 318s 12 94.9 93.6 318s 13 96.3 95.6 318s 14 99.1 97.6 318s 15 103.8 102.5 318s 16 103.6 104.4 318s 17 103.8 103.1 318s 18 102.0 103.1 318s 19 103.5 103.0 318s 20 106.6 106.3 318s > print( fitted( fit2sls4r$eq[[ 2 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 12 13 318s 98.5 100.1 100.2 100.5 102.5 102.4 102.5 104.8 102.7 99.5 95.1 93.6 95.6 318s 14 15 16 17 18 19 20 318s 97.6 102.5 104.4 103.1 103.1 103.0 106.3 318s > 318s > print( fitted( fit2sls5rs ) ) 318s demand supply 318s 1 97.8 98.5 318s 2 99.9 100.1 318s 3 99.8 100.2 318s 4 100.0 100.5 318s 5 102.1 102.5 318s 6 101.9 102.4 318s 7 102.4 102.5 318s 8 102.9 104.8 318s 9 101.5 102.7 318s 10 100.4 99.5 318s 11 95.8 95.1 318s 12 94.9 93.6 318s 13 96.3 95.6 318s 14 99.1 97.6 318s 15 103.8 102.5 318s 16 103.6 104.4 318s 17 103.8 103.1 318s 18 102.0 103.1 318s 19 103.5 103.0 318s 20 106.6 106.3 318s > print( fitted( fit2sls5rs$eq[[ 1 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 12 13 318s 97.8 99.9 99.8 100.0 102.1 101.9 102.4 102.9 101.5 100.4 95.8 94.9 96.3 318s 14 15 16 17 18 19 20 318s 99.1 103.8 103.6 103.8 102.0 103.5 106.6 318s > 318s > print( fitted( fit2slsd1 ) ) 318s demand supply 318s 1 97.1 98.9 318s 2 99.2 100.4 318s 3 99.2 100.5 318s 4 99.3 100.7 318s 5 102.5 102.6 318s 6 102.2 102.6 318s 7 102.5 102.6 318s 8 102.7 104.8 318s 9 102.0 102.7 318s 10 101.4 99.7 318s 11 95.6 95.4 318s 12 93.9 93.8 318s 13 95.0 95.6 318s 14 98.9 97.6 318s 15 104.9 102.3 318s 16 104.3 104.1 318s 17 106.1 102.8 318s 18 101.7 102.7 318s 19 103.3 102.6 318s 20 106.0 105.6 318s > print( fitted( fit2slsd1$eq[[ 2 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 12 13 318s 98.9 100.4 100.5 100.7 102.6 102.6 102.6 104.8 102.7 99.7 95.4 93.8 95.6 318s 14 15 16 17 18 19 20 318s 97.6 102.3 104.1 102.8 102.7 102.6 105.6 318s > 318s > print( fitted( fit2slsd2r ) ) 318s demand supply 318s 1 97.5 98.2 318s 2 99.5 99.8 318s 3 99.4 99.9 318s 4 99.6 100.3 318s 5 102.3 102.4 318s 6 102.1 102.4 318s 7 102.4 102.4 318s 8 102.6 104.7 318s 9 101.8 102.7 318s 10 101.1 99.6 318s 11 96.0 95.2 318s 12 94.6 93.6 318s 13 95.7 95.6 318s 14 99.1 97.7 318s 15 104.4 102.7 318s 16 103.9 104.5 318s 17 105.2 103.4 318s 18 101.8 103.2 318s 19 103.2 103.1 318s 20 105.9 106.3 318s > print( fitted( fit2slsd2r$eq[[ 1 ]] ) ) 318s 1 2 3 4 5 6 7 8 9 10 11 12 13 318s 97.5 99.5 99.4 99.6 102.3 102.1 102.4 102.6 101.8 101.1 96.0 94.6 95.7 318s 14 15 16 17 18 19 20 318s 99.1 104.4 103.9 105.2 101.8 103.2 105.9 318s > 318s > 318s > ## *********** predicted values ************* 318s > predictData <- Kmenta 318s > predictData$consump <- NULL 318s > predictData$price <- Kmenta$price * 0.9 318s > predictData$income <- Kmenta$income * 1.1 318s > 318s > print( predict( fit2sls1, se.fit = TRUE, interval = "prediction" ) ) 318s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 318s 1 97.6 0.661 93.3 102.0 98.9 1.079 318s 2 99.9 0.600 95.5 104.2 100.4 1.064 318s 3 99.8 0.564 95.5 104.1 100.5 0.962 318s 4 100.0 0.605 95.7 104.4 100.7 0.938 318s 5 102.1 0.516 97.8 106.4 102.6 0.914 318s 6 102.0 0.474 97.7 106.2 102.6 0.808 318s 7 102.4 0.493 98.1 106.7 102.6 0.736 318s 8 103.0 0.615 98.6 107.3 104.8 0.994 318s 9 101.5 0.544 97.2 105.8 102.7 0.808 318s 10 100.3 0.822 95.8 104.8 99.7 1.023 318s 11 95.5 0.963 90.9 100.2 95.4 1.228 318s 12 94.7 1.006 90.1 99.4 93.8 1.428 318s 13 96.1 0.915 91.6 100.7 95.6 1.272 318s 14 99.0 0.518 94.7 103.3 97.6 0.917 318s 15 103.8 0.793 99.4 108.3 102.3 0.899 318s 16 103.7 0.636 99.3 108.0 104.1 0.936 318s 17 103.8 1.348 98.8 108.9 102.8 1.665 318s 18 102.1 0.549 97.8 106.4 102.7 0.988 318s 19 103.6 0.695 99.2 108.0 102.6 1.129 318s 20 106.9 1.306 101.9 111.9 105.6 1.733 318s supply.lwr supply.upr 318s 1 93.2 104.6 318s 2 94.7 106.1 318s 3 94.9 106.0 318s 4 95.1 106.3 318s 5 97.1 108.2 318s 6 97.1 108.1 318s 7 97.1 108.0 318s 8 99.2 110.4 318s 9 97.3 108.2 318s 10 94.0 105.3 318s 11 89.5 101.2 318s 12 87.8 99.8 318s 13 89.8 101.5 318s 14 92.0 103.1 318s 15 96.8 107.9 318s 16 98.5 109.6 318s 17 96.5 109.1 318s 18 97.1 108.3 318s 19 96.8 108.3 318s 20 99.2 112.0 318s > print( predict( fit2sls1$eq[[ 1 ]], se.fit = TRUE, interval = "prediction" ) ) 318s fit se.fit lwr upr 318s 1 97.6 0.661 93.3 102.0 318s 2 99.9 0.600 95.5 104.2 318s 3 99.8 0.564 95.5 104.1 318s 4 100.0 0.605 95.7 104.4 318s 5 102.1 0.516 97.8 106.4 318s 6 102.0 0.474 97.7 106.2 318s 7 102.4 0.493 98.1 106.7 318s 8 103.0 0.615 98.6 107.3 318s 9 101.5 0.544 97.2 105.8 318s 10 100.3 0.822 95.8 104.8 318s 11 95.5 0.963 90.9 100.2 318s 12 94.7 1.006 90.1 99.4 318s 13 96.1 0.915 91.6 100.7 318s 14 99.0 0.518 94.7 103.3 318s 15 103.8 0.793 99.4 108.3 318s 16 103.7 0.636 99.3 108.0 318s 17 103.8 1.348 98.8 108.9 318s 18 102.1 0.549 97.8 106.4 318s 19 103.6 0.695 99.2 108.0 318s 20 106.9 1.306 101.9 111.9 318s > 318s > print( predict( fit2sls2s, se.pred = TRUE, interval = "confidence", 318s + level = 0.999, newdata = predictData ) ) 318s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 318s 1 102.7 2.23 99.1 106 96.1 2.75 318s 2 105.2 2.23 101.6 109 97.5 2.64 318s 3 105.1 2.24 101.4 109 97.6 2.65 318s 4 105.4 2.23 101.8 109 97.9 2.62 318s 5 107.2 2.52 101.7 113 100.1 2.83 318s 6 107.1 2.46 101.9 112 100.0 2.77 318s 7 107.7 2.45 102.6 113 100.0 2.70 318s 8 108.5 2.41 103.6 113 102.2 2.65 318s 9 106.5 2.53 100.9 112 100.4 2.87 318s 10 105.0 2.66 98.7 111 97.4 3.10 318s 11 100.1 2.42 95.1 105 93.0 3.17 318s 12 99.5 2.22 96.0 103 91.3 3.14 318s 13 101.2 2.13 98.5 104 93.1 2.95 318s 14 104.0 2.32 99.7 108 95.3 2.91 318s 15 108.9 2.74 102.1 116 100.2 2.92 318s 16 108.9 2.62 102.7 115 102.0 2.79 318s 17 108.4 3.09 99.9 117 101.1 3.37 318s 18 107.5 2.36 102.9 112 100.5 2.65 318s 19 109.2 2.44 104.1 114 100.3 2.64 318s 20 113.0 2.67 106.6 119 103.3 2.58 318s supply.lwr supply.upr 318s 1 91.8 100.4 318s 2 94.3 100.8 318s 3 94.2 101.0 318s 4 94.8 101.0 318s 5 95.2 105.0 318s 6 95.6 104.5 318s 7 96.1 103.9 318s 8 98.9 105.6 318s 9 95.2 105.6 318s 10 90.7 104.1 318s 11 85.9 100.2 318s 12 84.4 98.3 318s 13 87.3 98.9 318s 14 89.7 100.8 318s 15 94.7 105.8 318s 16 97.3 106.6 318s 17 92.9 109.3 318s 18 97.1 103.9 318s 19 97.1 103.6 318s 20 100.7 105.9 318s > print( predict( fit2sls2s$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 318s + level = 0.999, newdata = predictData ) ) 318s fit se.pred lwr upr 318s 1 96.1 2.75 91.8 100.4 318s 2 97.5 2.64 94.3 100.8 318s 3 97.6 2.65 94.2 101.0 318s 4 97.9 2.62 94.8 101.0 318s 5 100.1 2.83 95.2 105.0 318s 6 100.0 2.77 95.6 104.5 318s 7 100.0 2.70 96.1 103.9 318s 8 102.2 2.65 98.9 105.6 318s 9 100.4 2.87 95.2 105.6 318s 10 97.4 3.10 90.7 104.1 318s 11 93.0 3.17 85.9 100.2 318s 12 91.3 3.14 84.4 98.3 318s 13 93.1 2.95 87.3 98.9 318s 14 95.3 2.91 89.7 100.8 318s 15 100.2 2.92 94.7 105.8 318s 16 102.0 2.79 97.3 106.6 318s 17 101.1 3.37 92.9 109.3 318s 18 100.5 2.65 97.1 103.9 318s 19 100.3 2.64 97.1 103.6 318s 20 103.3 2.58 100.7 105.9 318s > 318s > print( predict( fit2sls3, se.pred = TRUE, interval = "prediction", 318s + level = 0.975, useDfSys = TRUE ) ) 318s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 318s 1 97.8 2.09 92.9 103 98.5 2.55 318s 2 100.0 2.08 95.1 105 100.0 2.57 318s 3 99.9 2.07 95.0 105 100.1 2.55 318s 4 100.1 2.08 95.2 105 100.4 2.56 318s 5 102.0 2.06 97.2 107 102.5 2.58 318s 6 101.9 2.05 97.1 107 102.5 2.56 318s 7 102.4 2.05 97.5 107 102.5 2.55 318s 8 102.9 2.09 98.0 108 104.8 2.61 318s 9 101.4 2.07 96.6 106 102.7 2.57 318s 10 100.3 2.17 95.2 105 99.7 2.62 318s 11 95.8 2.20 90.6 101 95.3 2.67 318s 12 95.0 2.20 89.9 100 93.7 2.74 318s 13 96.4 2.17 91.3 101 95.6 2.69 318s 14 99.1 2.06 94.3 104 97.6 2.59 318s 15 103.7 2.14 98.7 109 102.5 2.56 318s 16 103.5 2.08 98.6 108 104.4 2.55 318s 17 103.6 2.40 98.0 109 103.2 2.78 318s 18 102.0 2.07 97.2 107 103.0 2.56 318s 19 103.5 2.11 98.6 108 102.9 2.59 318s 20 106.7 2.38 101.1 112 106.1 2.78 318s supply.lwr supply.upr 318s 1 92.5 104 318s 2 94.0 106 318s 3 94.1 106 318s 4 94.4 106 318s 5 96.4 109 318s 6 96.5 108 318s 7 96.5 108 318s 8 98.6 111 318s 9 96.7 109 318s 10 93.5 106 318s 11 89.0 102 318s 12 87.3 100 318s 13 89.3 102 318s 14 91.6 104 318s 15 96.5 109 318s 16 98.4 110 318s 17 96.7 110 318s 18 97.0 109 318s 19 96.8 109 318s 20 99.5 113 318s > print( predict( fit2sls3$eq[[ 1 ]], se.pred = TRUE, interval = "prediction", 318s + level = 0.975, useDfSys = TRUE ) ) 318s fit se.pred lwr upr 318s 1 97.8 2.09 92.9 103 318s 2 100.0 2.08 95.1 105 318s 3 99.9 2.07 95.0 105 318s 4 100.1 2.08 95.2 105 318s 5 102.0 2.06 97.2 107 318s 6 101.9 2.05 97.1 107 318s 7 102.4 2.05 97.5 107 318s 8 102.9 2.09 98.0 108 318s 9 101.4 2.07 96.6 106 318s 10 100.3 2.17 95.2 105 318s 11 95.8 2.20 90.6 101 318s 12 95.0 2.20 89.9 100 318s 13 96.4 2.17 91.3 101 318s 14 99.1 2.06 94.3 104 318s 15 103.7 2.14 98.7 109 318s 16 103.5 2.08 98.6 108 318s 17 103.6 2.40 98.0 109 318s 18 102.0 2.07 97.2 107 318s 19 103.5 2.11 98.6 108 318s 20 106.7 2.38 101.1 112 318s > 318s > print( predict( fit2sls4r, se.fit = TRUE, interval = "confidence", 318s + level = 0.25 ) ) 318s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 318s 1 97.8 0.602 97.6 97.9 98.5 0.586 318s 2 99.9 0.526 99.7 100.1 100.1 0.672 318s 3 99.8 0.508 99.7 100.0 100.2 0.621 318s 4 100.0 0.530 99.8 100.2 100.5 0.632 318s 5 102.1 0.488 101.9 102.2 102.5 0.704 318s 6 101.9 0.474 101.8 102.1 102.4 0.636 318s 7 102.4 0.498 102.2 102.5 102.5 0.587 318s 8 102.9 0.604 102.7 103.0 104.8 0.764 318s 9 101.5 0.502 101.3 101.6 102.7 0.656 318s 10 100.4 0.696 100.2 100.6 99.5 0.710 318s 11 95.8 0.928 95.5 96.1 95.1 0.885 318s 12 94.9 0.889 94.7 95.2 93.6 1.146 318s 13 96.3 0.739 96.0 96.5 95.6 1.052 318s 14 99.1 0.519 98.9 99.3 97.6 0.746 318s 15 103.8 0.626 103.6 104.0 102.5 0.637 318s 16 103.6 0.566 103.4 103.8 104.4 0.615 318s 17 103.8 0.942 103.5 104.1 103.1 1.153 318s 18 102.0 0.540 101.8 102.2 103.1 0.556 318s 19 103.5 0.677 103.3 103.7 103.0 0.631 318s 20 106.6 1.226 106.2 107.0 106.3 0.900 318s supply.lwr supply.upr 318s 1 98.3 98.7 318s 2 99.9 100.3 318s 3 100.0 100.4 318s 4 100.3 100.7 318s 5 102.2 102.7 318s 6 102.2 102.6 318s 7 102.3 102.7 318s 8 104.6 105.1 318s 9 102.5 102.9 318s 10 99.3 99.8 318s 11 94.9 95.4 318s 12 93.3 94.0 318s 13 95.3 96.0 318s 14 97.4 97.9 318s 15 102.3 102.7 318s 16 104.2 104.6 318s 17 102.7 103.4 318s 18 102.9 103.3 318s 19 102.8 103.2 318s 20 106.0 106.6 318s > print( predict( fit2sls4r$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 318s + level = 0.25 ) ) 318s fit se.fit lwr upr 318s 1 98.5 0.586 98.3 98.7 318s 2 100.1 0.672 99.9 100.3 318s 3 100.2 0.621 100.0 100.4 318s 4 100.5 0.632 100.3 100.7 318s 5 102.5 0.704 102.2 102.7 318s 6 102.4 0.636 102.2 102.6 318s 7 102.5 0.587 102.3 102.7 318s 8 104.8 0.764 104.6 105.1 318s 9 102.7 0.656 102.5 102.9 318s 10 99.5 0.710 99.3 99.8 318s 11 95.1 0.885 94.9 95.4 318s 12 93.6 1.146 93.3 94.0 318s 13 95.6 1.052 95.3 96.0 318s 14 97.6 0.746 97.4 97.9 318s 15 102.5 0.637 102.3 102.7 318s 16 104.4 0.615 104.2 104.6 318s 17 103.1 1.153 102.7 103.4 318s 18 103.1 0.556 102.9 103.3 318s 19 103.0 0.631 102.8 103.2 318s 20 106.3 0.900 106.0 106.6 318s > 318s > print( predict( fit2sls5rs, se.fit = TRUE, se.pred = TRUE, 318s + interval = "prediction", level = 0.5, newdata = predictData ) ) 318s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 318s 1 102.8 0.713 2.10 101.4 104 95.9 318s 2 105.4 0.742 2.11 103.9 107 97.4 318s 3 105.3 0.751 2.11 103.8 107 97.5 318s 4 105.5 0.749 2.11 104.1 107 97.8 318s 5 107.5 1.080 2.25 105.9 109 99.9 318s 6 107.4 1.031 2.23 105.9 109 99.9 318s 7 107.9 1.040 2.23 106.4 109 99.9 318s 8 108.7 1.044 2.23 107.1 110 102.1 318s 9 106.8 1.073 2.24 105.2 108 100.2 318s 10 105.3 1.188 2.30 103.8 107 97.2 318s 11 100.3 1.013 2.22 98.8 102 92.8 318s 12 99.7 0.770 2.12 98.2 101 91.1 318s 13 101.3 0.584 2.06 99.9 103 93.0 318s 14 104.3 0.833 2.14 102.8 106 95.1 318s 15 109.2 1.310 2.37 107.6 111 100.1 318s 16 109.1 1.214 2.32 107.6 111 101.8 318s 17 108.9 1.582 2.53 107.1 111 100.8 318s 18 107.7 0.958 2.19 106.2 109 100.4 318s 19 109.4 1.111 2.26 107.9 111 100.3 318s 20 113.2 1.529 2.50 111.5 115 103.4 318s supply.se.fit supply.se.pred supply.lwr supply.upr 318s 1 0.746 2.61 94.1 97.7 318s 2 0.628 2.58 95.6 99.1 318s 3 0.642 2.58 95.7 99.3 318s 4 0.607 2.57 96.0 99.5 318s 5 0.978 2.68 98.1 101.8 318s 6 0.881 2.65 98.1 101.7 318s 7 0.786 2.62 98.1 101.7 318s 8 0.780 2.62 100.4 103.9 318s 9 1.031 2.70 98.4 102.1 318s 10 1.212 2.78 95.3 99.1 318s 11 1.339 2.84 90.8 94.7 318s 12 1.478 2.90 89.1 93.1 318s 13 1.292 2.81 91.1 94.9 318s 14 1.123 2.74 93.2 97.0 318s 15 1.105 2.73 98.2 101.9 318s 16 0.996 2.69 100.0 103.7 318s 17 1.636 2.99 98.8 102.9 318s 18 0.777 2.62 98.7 102.2 318s 19 0.775 2.62 98.5 102.1 318s 20 0.600 2.57 101.6 105.1 318s > print( predict( fit2sls5rs$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 318s + interval = "prediction", level = 0.5, newdata = predictData ) ) 318s fit se.fit se.pred lwr upr 318s 1 102.8 0.713 2.10 101.4 104 318s 2 105.4 0.742 2.11 103.9 107 318s 3 105.3 0.751 2.11 103.8 107 318s 4 105.5 0.749 2.11 104.1 107 318s 5 107.5 1.080 2.25 105.9 109 318s 6 107.4 1.031 2.23 105.9 109 318s 7 107.9 1.040 2.23 106.4 109 318s 8 108.7 1.044 2.23 107.1 110 318s 9 106.8 1.073 2.24 105.2 108 318s 10 105.3 1.188 2.30 103.8 107 318s 11 100.3 1.013 2.22 98.8 102 318s 12 99.7 0.770 2.12 98.2 101 318s 13 101.3 0.584 2.06 99.9 103 318s 14 104.3 0.833 2.14 102.8 106 318s 15 109.2 1.310 2.37 107.6 111 318s 16 109.1 1.214 2.32 107.6 111 318s 17 108.9 1.582 2.53 107.1 111 318s 18 107.7 0.958 2.19 106.2 109 318s 19 109.4 1.111 2.26 107.9 111 318s 20 113.2 1.529 2.50 111.5 115 318s > 318s > print( predict( fit2slsd1, se.fit = TRUE, se.pred = TRUE, 318s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 318s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 318s 1 97.1 0.751 2.13 95.1 99.2 98.9 318s 2 99.2 0.757 2.13 97.1 101.2 100.4 318s 3 99.2 0.692 2.11 97.3 101.1 100.5 318s 4 99.3 0.766 2.13 97.2 101.4 100.7 318s 5 102.5 0.595 2.08 100.9 104.2 102.6 318s 6 102.2 0.503 2.05 100.8 103.6 102.6 318s 7 102.5 0.503 2.05 101.1 103.9 102.6 318s 8 102.7 0.653 2.10 100.9 104.4 104.8 318s 9 102.0 0.655 2.10 100.2 103.8 102.7 318s 10 101.4 1.074 2.26 98.5 104.3 99.7 318s 11 95.6 0.978 2.22 93.0 98.3 95.4 318s 12 93.9 1.134 2.29 90.8 97.0 93.8 318s 13 95.0 1.162 2.31 91.9 98.2 95.6 318s 14 98.9 0.530 2.06 97.5 100.4 97.6 318s 15 104.9 1.061 2.26 102.0 107.8 102.3 318s 16 104.3 0.757 2.13 102.2 106.3 104.1 318s 17 106.1 1.963 2.80 100.7 111.4 102.8 318s 18 101.7 0.597 2.08 100.1 103.4 102.7 318s 19 103.3 0.736 2.12 101.3 105.3 102.6 318s 20 106.0 1.430 2.45 102.1 110.0 105.6 318s supply.se.fit supply.se.pred supply.lwr supply.upr 318s 1 1.079 2.68 96.0 101.9 318s 2 1.064 2.68 97.5 103.3 318s 3 0.962 2.64 97.8 103.1 318s 4 0.938 2.63 98.1 103.3 318s 5 0.914 2.62 100.1 105.1 318s 6 0.808 2.59 100.4 104.8 318s 7 0.736 2.57 100.5 104.6 318s 8 0.994 2.65 102.1 107.5 318s 9 0.808 2.59 100.5 105.0 318s 10 1.023 2.66 96.9 102.5 318s 11 1.228 2.75 92.0 98.7 318s 12 1.428 2.84 89.9 97.7 318s 13 1.272 2.77 92.2 99.1 318s 14 0.917 2.62 95.1 100.1 318s 15 0.899 2.62 99.9 104.8 318s 16 0.936 2.63 101.5 106.6 318s 17 1.665 2.97 98.3 107.4 318s 18 0.988 2.65 100.0 105.4 318s 19 1.129 2.70 99.5 105.6 318s 20 1.733 3.01 100.9 110.3 318s > print( predict( fit2slsd1$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 318s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 318s fit se.fit se.pred lwr upr 318s 1 98.9 1.079 2.68 96.0 101.9 318s 2 100.4 1.064 2.68 97.5 103.3 318s 3 100.5 0.962 2.64 97.8 103.1 318s 4 100.7 0.938 2.63 98.1 103.3 318s 5 102.6 0.914 2.62 100.1 105.1 318s 6 102.6 0.808 2.59 100.4 104.8 318s 7 102.6 0.736 2.57 100.5 104.6 318s 8 104.8 0.994 2.65 102.1 107.5 318s 9 102.7 0.808 2.59 100.5 105.0 318s 10 99.7 1.023 2.66 96.9 102.5 318s 11 95.4 1.228 2.75 92.0 98.7 318s 12 93.8 1.428 2.84 89.9 97.7 318s 13 95.6 1.272 2.77 92.2 99.1 318s 14 97.6 0.917 2.62 95.1 100.1 318s 15 102.3 0.899 2.62 99.9 104.8 318s 16 104.1 0.936 2.63 101.5 106.6 318s 17 102.8 1.665 2.97 98.3 107.4 318s 18 102.7 0.988 2.65 100.0 105.4 318s 19 102.6 1.129 2.70 99.5 105.6 318s 20 105.6 1.733 3.01 100.9 110.3 318s > 318s > print( predict( fit2slsd2r, se.fit = TRUE, interval = "prediction", 318s + level = 0.9, newdata = predictData ) ) 318s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 318s 1 104 1.34 99.8 108 95.8 1.026 318s 2 106 1.27 102.3 110 97.3 0.786 318s 3 106 1.32 102.2 110 97.4 0.804 318s 4 106 1.27 102.4 110 97.7 0.734 318s 5 109 2.06 104.2 114 100.0 1.130 318s 6 109 1.92 104.1 113 99.9 1.014 318s 7 109 1.86 104.7 114 99.9 0.893 318s 8 110 1.67 105.4 114 102.2 0.765 318s 9 108 2.12 103.4 113 100.4 1.187 318s 10 107 2.45 101.9 112 97.4 1.525 318s 11 102 1.85 97.1 106 92.9 1.627 318s 12 101 1.26 96.6 104 91.2 1.587 318s 13 102 0.98 98.3 106 93.1 1.314 318s 14 105 1.63 101.1 110 95.3 1.253 318s 15 111 2.53 105.6 116 100.4 1.269 318s 16 111 2.23 105.7 116 102.1 1.075 318s 17 111 3.28 104.9 118 101.3 1.888 318s 18 109 1.59 104.5 113 100.7 0.796 318s 19 110 1.70 106.1 115 100.5 0.772 318s 20 114 1.87 109.4 119 103.6 0.656 318s supply.lwr supply.upr 318s 1 91.2 100.4 318s 2 92.8 101.7 318s 3 93.0 101.9 318s 4 93.3 102.1 318s 5 95.3 104.6 318s 6 95.4 104.5 318s 7 95.4 104.4 318s 8 97.8 106.6 318s 9 95.7 105.1 318s 10 92.5 102.4 318s 11 87.9 98.0 318s 12 86.2 96.2 318s 13 88.3 97.9 318s 14 90.5 100.0 318s 15 95.6 105.1 318s 16 97.5 106.7 318s 17 96.0 106.6 318s 18 96.2 105.1 318s 19 96.1 105.0 318s 20 99.2 107.9 318s > print( predict( fit2slsd2r$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 318s + level = 0.9, newdata = predictData ) ) 318s fit se.fit lwr upr 318s 1 104 1.34 99.8 108 318s 2 106 1.27 102.3 110 318s 3 106 1.32 102.2 110 318s 4 106 1.27 102.4 110 318s 5 109 2.06 104.2 114 318s 6 109 1.92 104.1 113 318s 7 109 1.86 104.7 114 318s 8 110 1.67 105.4 114 318s 9 108 2.12 103.4 113 318s 10 107 2.45 101.9 112 318s 11 102 1.85 97.1 106 318s 12 101 1.26 96.6 104 318s 13 102 0.98 98.3 106 318s 14 105 1.63 101.1 110 318s 15 111 2.53 105.6 116 318s 16 111 2.23 105.7 116 318s 17 111 3.28 104.9 118 318s 18 109 1.59 104.5 113 318s 19 110 1.70 106.1 115 318s 20 114 1.87 109.4 119 318s > 318s > # predict just one observation 318s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 318s + trend = 25 ) 318s > 318s > print( predict( fit2sls1rs, newdata = smallData ) ) 318s demand.pred supply.pred 318s 1 110 118 318s > print( predict( fit2sls1rs$eq[[ 1 ]], newdata = smallData ) ) 318s fit 318s 1 110 318s > 318s > print( predict( fit2sls2, se.fit = TRUE, level = 0.9, 318s + newdata = smallData ) ) 318s demand.pred demand.se.fit supply.pred supply.se.fit 318s 1 110 2.79 119 3.18 318s > print( predict( fit2sls2$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 318s + newdata = smallData ) ) 318s fit se.pred 318s 1 110 3.42 318s > 318s > print( predict( fit2sls3, interval = "prediction", level = 0.975, 318s + newdata = smallData ) ) 318s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 318s 1 110 102 117 119 110 128 318s > print( predict( fit2sls3$eq[[ 1 ]], interval = "confidence", level = 0.8, 318s + newdata = smallData ) ) 318s fit lwr upr 318s 1 110 106 113 318s > 318s > print( predict( fit2sls4r, se.fit = TRUE, interval = "confidence", 318s + level = 0.999, newdata = smallData ) ) 318s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 318s 1 109 2.24 101 118 119 2.09 318s supply.lwr supply.upr 318s 1 112 127 318s > print( predict( fit2sls4r$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 318s + level = 0.75, newdata = smallData ) ) 318s fit se.pred lwr upr 318s 1 119 3.26 115 123 318s > 318s > print( predict( fit2sls5s, se.fit = TRUE, interval = "prediction", 318s + newdata = smallData ) ) 318s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 318s 1 109 2.26 103 116 119 2.33 318s supply.lwr supply.upr 318s 1 112 126 318s > print( predict( fit2sls5s$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 318s + newdata = smallData ) ) 318s fit se.pred lwr upr 318s 1 109 3 105 114 318s > 318s > print( predict( fit2slsd3, se.fit = TRUE, se.pred = TRUE, 318s + interval = "prediction", level = 0.5, newdata = smallData ) ) 318s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 318s 1 108 3.33 3.86 105 110 119 318s supply.se.fit supply.se.pred supply.lwr supply.upr 318s 1 3.2 4.07 116 122 318s > print( predict( fit2slsd3$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 318s + interval = "confidence", level = 0.25, newdata = smallData ) ) 318s fit se.fit se.pred lwr upr 318s 1 108 3.33 3.86 107 109 318s > 318s > 318s > ## ************ correlation of predicted values *************** 318s > print( correlation.systemfit( fit2sls1, 1, 2 ) ) 318s [,1] 318s [1,] 0 318s [2,] 0 318s [3,] 0 318s [4,] 0 318s [5,] 0 318s [6,] 0 318s [7,] 0 318s [8,] 0 318s [9,] 0 318s [10,] 0 318s [11,] 0 318s [12,] 0 318s [13,] 0 318s [14,] 0 318s [15,] 0 318s [16,] 0 318s [17,] 0 318s [18,] 0 318s [19,] 0 318s [20,] 0 318s > 318s > print( correlation.systemfit( fit2sls2s, 2, 1 ) ) 318s [,1] 318s [1,] 0.413453 318s [2,] 0.153759 318s [3,] 0.152962 318s [4,] 0.112671 318s [5,] -0.071442 318s [6,] -0.053943 318s [7,] -0.050961 318s [8,] -0.005442 318s [9,] -0.000476 318s [10,] -0.001894 318s [11,] 0.047351 318s [12,] 0.064973 318s [13,] 0.024591 318s [14,] -0.028036 318s [15,] 0.175326 318s [16,] 0.254878 318s [17,] 0.104540 318s [18,] 0.065579 318s [19,] 0.147008 318s [20,] 0.124593 318s > 318s > print( correlation.systemfit( fit2sls3, 1, 2 ) ) 318s [,1] 318s [1,] 0.44877 318s [2,] 0.16875 318s [3,] 0.16850 318s [4,] 0.12519 318s [5,] -0.08079 318s [6,] -0.06096 318s [7,] -0.05780 318s [8,] -0.00618 318s [9,] -0.00054 318s [10,] -0.00214 318s [11,] 0.05454 318s [12,] 0.07607 318s [13,] 0.02868 318s [14,] -0.03197 318s [15,] 0.19899 318s [16,] 0.28551 318s [17,] 0.11838 318s [18,] 0.07184 318s [19,] 0.16271 318s [20,] 0.13995 318s > 318s > print( correlation.systemfit( fit2sls4r, 2, 1 ) ) 318s [,1] 318s [1,] 0.4078 318s [2,] 0.2866 318s [3,] 0.2528 318s [4,] 0.2836 318s [5,] -0.0300 318s [6,] -0.0537 318s [7,] -0.0627 318s [8,] 0.1044 318s [9,] 0.1003 318s [10,] 0.4530 318s [11,] 0.1293 318s [12,] 0.0184 318s [13,] 0.0449 318s [14,] -0.0409 318s [15,] 0.4229 318s [16,] 0.2649 318s [17,] 0.6554 318s [18,] 0.2693 318s [19,] 0.3831 318s [20,] 0.5784 318s > 318s > print( correlation.systemfit( fit2sls5rs, 1, 2 ) ) 318s [,1] 318s [1,] 0.38438 318s [2,] 0.30697 318s [3,] 0.26690 318s [4,] 0.30163 318s [5,] -0.02768 318s [6,] -0.05086 318s [7,] -0.05895 318s [8,] 0.10102 318s [9,] 0.10072 318s [10,] 0.45547 318s [11,] 0.10817 318s [12,] 0.00552 318s [13,] 0.04219 318s [14,] -0.04054 318s [15,] 0.42100 318s [16,] 0.24974 318s [17,] 0.65722 318s [18,] 0.24286 318s [19,] 0.34336 318s [20,] 0.54717 318s > 318s > print( correlation.systemfit( fit2slsd1, 2, 1 ) ) 318s [,1] 318s [1,] 0 318s [2,] 0 318s [3,] 0 318s [4,] 0 318s [5,] 0 318s [6,] 0 318s [7,] 0 318s [8,] 0 318s [9,] 0 318s [10,] 0 318s [11,] 0 318s [12,] 0 318s [13,] 0 318s [14,] 0 318s [15,] 0 318s [16,] 0 318s [17,] 0 318s [18,] 0 318s [19,] 0 318s [20,] 0 318s > 318s > print( correlation.systemfit( fit2slsd2r, 1, 2 ) ) 318s [,1] 318s [1,] 0.51320 318s [2,] 0.27263 318s [3,] 0.26221 318s [4,] 0.21307 318s [5,] -0.11973 318s [6,] -0.08282 318s [7,] -0.06158 318s [8,] -0.00225 318s [9,] -0.00103 318s [10,] -0.00892 318s [11,] 0.04576 318s [12,] 0.08710 318s [13,] 0.03423 318s [14,] -0.03425 318s [15,] 0.25625 318s [16,] 0.35070 318s [17,] 0.17505 318s [18,] -0.02443 318s [19,] 0.07277 318s [20,] 0.05142 318s > 318s > 318s > ## ************ Log-Likelihood values *************** 318s > print( logLik( fit2sls1 ) ) 318s 'log Lik.' -67.6 (df=8) 318s > print( logLik( fit2sls1, residCovDiag = TRUE ) ) 318s 'log Lik.' -84.4 (df=8) 318s > 318s > print( logLik( fit2sls2s ) ) 318s 'log Lik.' -65.7 (df=7) 318s > print( logLik( fit2sls2s, residCovDiag = TRUE ) ) 318s 'log Lik.' -84.8 (df=7) 318s > 318s > print( logLik( fit2sls3 ) ) 318s 'log Lik.' -65.7 (df=7) 318s > print( logLik( fit2sls3, residCovDiag = TRUE ) ) 318s 'log Lik.' -84.8 (df=7) 318s > 318s > print( logLik( fit2sls4r ) ) 318s 'log Lik.' -66.2 (df=6) 318s > print( logLik( fit2sls4r, residCovDiag = TRUE ) ) 318s 'log Lik.' -84.8 (df=6) 318s > 318s > print( logLik( fit2sls5rs ) ) 318s 'log Lik.' -66.2 (df=6) 318s > print( logLik( fit2sls5rs, residCovDiag = TRUE ) ) 318s 'log Lik.' -84.8 (df=6) 318s > 318s > print( logLik( fit2slsd1 ) ) 318s 'log Lik.' -75.1 (df=8) 318s > print( logLik( fit2slsd1, residCovDiag = TRUE ) ) 318s 'log Lik.' -84.7 (df=8) 318s > 318s > print( logLik( fit2slsd2r ) ) 318s 'log Lik.' -68.8 (df=7) 318s > print( logLik( fit2slsd2r, residCovDiag = TRUE ) ) 318s 'log Lik.' -84.6 (df=7) 318s > 318s > 318s > ## ************** F tests **************** 318s > # testing first restriction 318s > print( linearHypothesis( fit2sls1, restrm ) ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0.06 0.8 318s > linearHypothesis( fit2sls1, restrict ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0.06 0.8 318s > 318s > print( linearHypothesis( fit2sls1s, restrm ) ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1s 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0.07 0.79 318s > linearHypothesis( fit2sls1s, restrict ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1s 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0.07 0.79 318s > 318s > print( linearHypothesis( fit2sls1, restrm ) ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0.06 0.8 318s > linearHypothesis( fit2sls1, restrict ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0.06 0.8 318s > 318s > print( linearHypothesis( fit2sls1r, restrm ) ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1r 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0.08 0.78 318s > linearHypothesis( fit2sls1r, restrict ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1r 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0.08 0.78 318s > 318s > # testing second restriction 318s > restrOnly2m <- matrix(0,1,7) 318s > restrOnly2q <- 0.5 318s > restrOnly2m[1,2] <- -1 318s > restrOnly2m[1,5] <- 1 318s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 318s > # first restriction not imposed 318s > print( linearHypothesis( fit2sls1, restrOnly2m, restrOnly2q ) ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0 0.96 318s > linearHypothesis( fit2sls1, restrictOnly2 ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df F Pr(>F) 318s 1 34 318s 2 33 1 0 0.96 318s > 318s > # first restriction imposed 318s > print( linearHypothesis( fit2sls2, restrOnly2m, restrOnly2q ) ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls2 318s 318s Res.Df Df F Pr(>F) 318s 1 35 318s 2 34 1 0.01 0.92 318s > linearHypothesis( fit2sls2, restrictOnly2 ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls2 318s 318s Res.Df Df F Pr(>F) 318s 1 35 318s 2 34 1 0.01 0.92 318s > 318s > print( linearHypothesis( fit2sls2r, restrOnly2m, restrOnly2q ) ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls2r 318s 318s Res.Df Df F Pr(>F) 318s 1 35 318s 2 34 1 0.01 0.91 318s > linearHypothesis( fit2sls2r, restrictOnly2 ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls2r 318s 318s Res.Df Df F Pr(>F) 318s 1 35 318s 2 34 1 0.01 0.91 318s > 318s > print( linearHypothesis( fit2sls3, restrOnly2m, restrOnly2q ) ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls3 318s 318s Res.Df Df F Pr(>F) 318s 1 35 318s 2 34 1 0.01 0.91 318s > linearHypothesis( fit2sls3, restrictOnly2 ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls3 318s 318s Res.Df Df F Pr(>F) 318s 1 35 318s 2 34 1 0.01 0.91 318s > 318s > # testing both of the restrictions 318s > print( linearHypothesis( fit2sls1, restr2m, restr2q ) ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df F Pr(>F) 318s 1 35 318s 2 33 2 0.04 0.97 318s > linearHypothesis( fit2sls1, restrict2 ) 318s Linear hypothesis test (Theil's F test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df F Pr(>F) 318s 1 35 318s 2 33 2 0.04 0.97 318s > 318s > 318s > ## ************** Wald tests **************** 318s > # testing first restriction 318s > print( linearHypothesis( fit2sls1, restrm, test = "Chisq" ) ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.31 0.58 318s > linearHypothesis( fit2sls1, restrict, test = "Chisq" ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.31 0.58 318s > 318s > print( linearHypothesis( fit2sls1s, restrm, test = "Chisq" ) ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1s 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.34 0.56 318s > linearHypothesis( fit2sls1s, restrict, test = "Chisq" ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1s 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.34 0.56 318s > 318s > print( linearHypothesis( fit2sls1, restrm, test = "Chisq" ) ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.31 0.58 318s > linearHypothesis( fit2sls1, restrict, test = "Chisq" ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.31 0.58 318s > 318s > print( linearHypothesis( fit2sls1r, restrm, test = "Chisq" ) ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1r 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.38 0.54 318s > linearHypothesis( fit2sls1r, restrict, test = "Chisq" ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s 318s Model 1: restricted model 318s Model 2: fit2sls1r 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.38 0.54 318s > 318s > # testing second restriction 318s > # first restriction not imposed 318s > print( linearHypothesis( fit2sls1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.01 0.91 318s > linearHypothesis( fit2sls1, restrictOnly2, test = "Chisq" ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 34 318s 2 33 1 0.01 0.91 318s > # first restriction imposed 318s > print( linearHypothesis( fit2sls2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls2 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 35 318s 2 34 1 0.06 0.81 318s > linearHypothesis( fit2sls2, restrictOnly2, test = "Chisq" ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls2 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 35 318s 2 34 1 0.06 0.81 318s > 318s > print( linearHypothesis( fit2sls2r, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls2r 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 35 318s 2 34 1 0.07 0.8 318s > linearHypothesis( fit2sls2r, restrictOnly2, test = "Chisq" ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls2r 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 35 318s 2 34 1 0.07 0.8 318s > 318s > print( linearHypothesis( fit2sls3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls3 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 35 318s 2 34 1 0.07 0.8 318s > linearHypothesis( fit2sls3, restrictOnly2, test = "Chisq" ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls3 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 35 318s 2 34 1 0.07 0.8 318s > 318s > # testing both of the restrictions 318s > print( linearHypothesis( fit2sls1, restr2m, restr2q, test = "Chisq" ) ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 35 318s 2 33 2 0.35 0.84 318s > linearHypothesis( fit2sls1, restrict2, test = "Chisq" ) 318s Linear hypothesis test (Chi^2 statistic of a Wald test) 318s 318s Hypothesis: 318s demand_income - supply_trend = 0 318s - demand_price + supply_price = 0.5 318s 318s Model 1: restricted model 318s Model 2: fit2sls1 318s 318s Res.Df Df Chisq Pr(>Chisq) 318s 1 35 318s 2 33 2 0.35 0.84 318s > 318s > 318s > ## **************** model frame ************************ 318s > print( mf <- model.frame( fit2sls1 ) ) 318s consump price income farmPrice trend 318s 1 98.5 100.3 87.4 98.0 1 318s 2 99.2 104.3 97.6 99.1 2 318s 3 102.2 103.4 96.7 99.1 3 318s 4 101.5 104.5 98.2 98.1 4 318s 5 104.2 98.0 99.8 110.8 5 318s 6 103.2 99.5 100.5 108.2 6 318s 7 104.0 101.1 103.2 105.6 7 318s 8 99.9 104.8 107.8 109.8 8 318s 9 100.3 96.4 96.6 108.7 9 318s 10 102.8 91.2 88.9 100.6 10 318s 11 95.4 93.1 75.1 81.0 11 318s 12 92.4 98.8 76.9 68.6 12 318s 13 94.5 102.9 84.6 70.9 13 318s 14 98.8 98.8 90.6 81.4 14 318s 15 105.8 95.1 103.1 102.3 15 318s 16 100.2 98.5 105.1 105.0 16 318s 17 103.5 86.5 96.4 110.5 17 318s 18 99.9 104.0 104.4 92.5 18 318s 19 105.2 105.8 110.7 89.3 19 318s 20 106.2 113.5 127.1 93.0 20 318s > print( mf1 <- model.frame( fit2sls1$eq[[ 1 ]] ) ) 318s consump price income 318s 1 98.5 100.3 87.4 318s 2 99.2 104.3 97.6 318s 3 102.2 103.4 96.7 318s 4 101.5 104.5 98.2 318s 5 104.2 98.0 99.8 318s 6 103.2 99.5 100.5 318s 7 104.0 101.1 103.2 318s 8 99.9 104.8 107.8 318s 9 100.3 96.4 96.6 318s 10 102.8 91.2 88.9 318s 11 95.4 93.1 75.1 318s 12 92.4 98.8 76.9 318s 13 94.5 102.9 84.6 318s 14 98.8 98.8 90.6 318s 15 105.8 95.1 103.1 318s 16 100.2 98.5 105.1 318s 17 103.5 86.5 96.4 318s 18 99.9 104.0 104.4 318s 19 105.2 105.8 110.7 318s 20 106.2 113.5 127.1 318s > print( attributes( mf1 )$terms ) 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s > print( mf2 <- model.frame( fit2sls1$eq[[ 2 ]] ) ) 318s consump price farmPrice trend 318s 1 98.5 100.3 98.0 1 318s 2 99.2 104.3 99.1 2 318s 3 102.2 103.4 99.1 3 318s 4 101.5 104.5 98.1 4 318s 5 104.2 98.0 110.8 5 318s 6 103.2 99.5 108.2 6 318s 7 104.0 101.1 105.6 7 318s 8 99.9 104.8 109.8 8 318s 9 100.3 96.4 108.7 9 318s 10 102.8 91.2 100.6 10 318s 11 95.4 93.1 81.0 11 318s 12 92.4 98.8 68.6 12 318s 13 94.5 102.9 70.9 13 318s 14 98.8 98.8 81.4 14 318s 15 105.8 95.1 102.3 15 318s 16 100.2 98.5 105.0 16 318s 17 103.5 86.5 110.5 17 318s 18 99.9 104.0 92.5 18 318s 19 105.2 105.8 89.3 19 318s 20 106.2 113.5 93.0 20 318s > print( attributes( mf2 )$terms ) 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s > 318s > print( all.equal( mf, model.frame( fit2sls2s ) ) ) 318s [1] TRUE 318s > print( all.equal( mf2, model.frame( fit2sls2s$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > 318s > print( all.equal( mf, model.frame( fit2sls3 ) ) ) 318s [1] TRUE 318s > print( all.equal( mf1, model.frame( fit2sls3$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > 318s > print( all.equal( mf, model.frame( fit2sls4r ) ) ) 318s [1] TRUE 318s > print( all.equal( mf2, model.frame( fit2sls4r$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > 318s > print( all.equal( mf, model.frame( fit2sls5rs ) ) ) 318s [1] TRUE 318s > print( all.equal( mf1, model.frame( fit2sls5rs$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > 318s > fit2sls1$eq[[ 1 ]]$modelInst 318s income farmPrice trend 318s 1 87.4 98.0 1 318s 2 97.6 99.1 2 318s 3 96.7 99.1 3 318s 4 98.2 98.1 4 318s 5 99.8 110.8 5 318s 6 100.5 108.2 6 318s 7 103.2 105.6 7 318s 8 107.8 109.8 8 318s 9 96.6 108.7 9 318s 10 88.9 100.6 10 318s 11 75.1 81.0 11 318s 12 76.9 68.6 12 318s 13 84.6 70.9 13 318s 14 90.6 81.4 14 318s 15 103.1 102.3 15 318s 16 105.1 105.0 16 318s 17 96.4 110.5 17 318s 18 104.4 92.5 18 318s 19 110.7 89.3 19 318s 20 127.1 93.0 20 318s > fit2sls1$eq[[ 2 ]]$modelInst 318s income farmPrice trend 318s 1 87.4 98.0 1 318s 2 97.6 99.1 2 318s 3 96.7 99.1 3 318s 4 98.2 98.1 4 318s 5 99.8 110.8 5 318s 6 100.5 108.2 6 318s 7 103.2 105.6 7 318s 8 107.8 109.8 8 318s 9 96.6 108.7 9 318s 10 88.9 100.6 10 318s 11 75.1 81.0 11 318s 12 76.9 68.6 12 318s 13 84.6 70.9 13 318s 14 90.6 81.4 14 318s 15 103.1 102.3 15 318s 16 105.1 105.0 16 318s 17 96.4 110.5 17 318s 18 104.4 92.5 18 318s 19 110.7 89.3 19 318s 20 127.1 93.0 20 318s > 318s > fit2sls2s$eq[[ 1 ]]$modelInst 318s income farmPrice trend 318s 1 87.4 98.0 1 318s 2 97.6 99.1 2 318s 3 96.7 99.1 3 318s 4 98.2 98.1 4 318s 5 99.8 110.8 5 318s 6 100.5 108.2 6 318s 7 103.2 105.6 7 318s 8 107.8 109.8 8 318s 9 96.6 108.7 9 318s 10 88.9 100.6 10 318s 11 75.1 81.0 11 318s 12 76.9 68.6 12 318s 13 84.6 70.9 13 318s 14 90.6 81.4 14 318s 15 103.1 102.3 15 318s 16 105.1 105.0 16 318s 17 96.4 110.5 17 318s 18 104.4 92.5 18 318s 19 110.7 89.3 19 318s 20 127.1 93.0 20 318s > fit2sls2s$eq[[ 2 ]]$modelInst 318s income farmPrice trend 318s 1 87.4 98.0 1 318s 2 97.6 99.1 2 318s 3 96.7 99.1 3 318s 4 98.2 98.1 4 318s 5 99.8 110.8 5 318s 6 100.5 108.2 6 318s 7 103.2 105.6 7 318s 8 107.8 109.8 8 318s 9 96.6 108.7 9 318s 10 88.9 100.6 10 318s 11 75.1 81.0 11 318s 12 76.9 68.6 12 318s 13 84.6 70.9 13 318s 14 90.6 81.4 14 318s 15 103.1 102.3 15 318s 16 105.1 105.0 16 318s 17 96.4 110.5 17 318s 18 104.4 92.5 18 318s 19 110.7 89.3 19 318s 20 127.1 93.0 20 318s > 318s > fit2sls5rs$eq[[ 1 ]]$modelInst 318s income farmPrice trend 318s 1 87.4 98.0 1 318s 2 97.6 99.1 2 318s 3 96.7 99.1 3 318s 4 98.2 98.1 4 318s 5 99.8 110.8 5 318s 6 100.5 108.2 6 318s 7 103.2 105.6 7 318s 8 107.8 109.8 8 318s 9 96.6 108.7 9 318s 10 88.9 100.6 10 318s 11 75.1 81.0 11 318s 12 76.9 68.6 12 318s 13 84.6 70.9 13 318s 14 90.6 81.4 14 318s 15 103.1 102.3 15 318s 16 105.1 105.0 16 318s 17 96.4 110.5 17 318s 18 104.4 92.5 18 318s 19 110.7 89.3 19 318s 20 127.1 93.0 20 318s > fit2sls5rs$eq[[ 2 ]]$modelInst 318s income farmPrice trend 318s 1 87.4 98.0 1 318s 2 97.6 99.1 2 318s 3 96.7 99.1 3 318s 4 98.2 98.1 4 318s 5 99.8 110.8 5 318s 6 100.5 108.2 6 318s 7 103.2 105.6 7 318s 8 107.8 109.8 8 318s 9 96.6 108.7 9 318s 10 88.9 100.6 10 318s 11 75.1 81.0 11 318s 12 76.9 68.6 12 318s 13 84.6 70.9 13 318s 14 90.6 81.4 14 318s 15 103.1 102.3 15 318s 16 105.1 105.0 16 318s 17 96.4 110.5 17 318s 18 104.4 92.5 18 318s 19 110.7 89.3 19 318s 20 127.1 93.0 20 318s > 318s > 318s > ## **************** model matrix ************************ 318s > # with x (returnModelMatrix) = TRUE 318s > print( !is.null( fit2sls1$eq[[ 1 ]]$x ) ) 318s [1] TRUE 318s > print( mm <- model.matrix( fit2sls1 ) ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s demand_1 1 100.3 87.4 0 318s demand_2 1 104.3 97.6 0 318s demand_3 1 103.4 96.7 0 318s demand_4 1 104.5 98.2 0 318s demand_5 1 98.0 99.8 0 318s demand_6 1 99.5 100.5 0 318s demand_7 1 101.1 103.2 0 318s demand_8 1 104.8 107.8 0 318s demand_9 1 96.4 96.6 0 318s demand_10 1 91.2 88.9 0 318s demand_11 1 93.1 75.1 0 318s demand_12 1 98.8 76.9 0 318s demand_13 1 102.9 84.6 0 318s demand_14 1 98.8 90.6 0 318s demand_15 1 95.1 103.1 0 318s demand_16 1 98.5 105.1 0 318s demand_17 1 86.5 96.4 0 318s demand_18 1 104.0 104.4 0 318s demand_19 1 105.8 110.7 0 318s demand_20 1 113.5 127.1 0 318s supply_1 0 0.0 0.0 1 318s supply_2 0 0.0 0.0 1 318s supply_3 0 0.0 0.0 1 318s supply_4 0 0.0 0.0 1 318s supply_5 0 0.0 0.0 1 318s supply_6 0 0.0 0.0 1 318s supply_7 0 0.0 0.0 1 318s supply_8 0 0.0 0.0 1 318s supply_9 0 0.0 0.0 1 318s supply_10 0 0.0 0.0 1 318s supply_11 0 0.0 0.0 1 318s supply_12 0 0.0 0.0 1 318s supply_13 0 0.0 0.0 1 318s supply_14 0 0.0 0.0 1 318s supply_15 0 0.0 0.0 1 318s supply_16 0 0.0 0.0 1 318s supply_17 0 0.0 0.0 1 318s supply_18 0 0.0 0.0 1 318s supply_19 0 0.0 0.0 1 318s supply_20 0 0.0 0.0 1 318s supply_price supply_farmPrice supply_trend 318s demand_1 0.0 0.0 0 318s demand_2 0.0 0.0 0 318s demand_3 0.0 0.0 0 318s demand_4 0.0 0.0 0 318s demand_5 0.0 0.0 0 318s demand_6 0.0 0.0 0 318s demand_7 0.0 0.0 0 318s demand_8 0.0 0.0 0 318s demand_9 0.0 0.0 0 318s demand_10 0.0 0.0 0 318s demand_11 0.0 0.0 0 318s demand_12 0.0 0.0 0 318s demand_13 0.0 0.0 0 318s demand_14 0.0 0.0 0 318s demand_15 0.0 0.0 0 318s demand_16 0.0 0.0 0 318s demand_17 0.0 0.0 0 318s demand_18 0.0 0.0 0 318s demand_19 0.0 0.0 0 318s demand_20 0.0 0.0 0 318s supply_1 100.3 98.0 1 318s supply_2 104.3 99.1 2 318s supply_3 103.4 99.1 3 318s supply_4 104.5 98.1 4 318s supply_5 98.0 110.8 5 318s supply_6 99.5 108.2 6 318s supply_7 101.1 105.6 7 318s supply_8 104.8 109.8 8 318s supply_9 96.4 108.7 9 318s supply_10 91.2 100.6 10 318s supply_11 93.1 81.0 11 318s supply_12 98.8 68.6 12 318s supply_13 102.9 70.9 13 318s supply_14 98.8 81.4 14 318s supply_15 95.1 102.3 15 318s supply_16 98.5 105.0 16 318s supply_17 86.5 110.5 17 318s supply_18 104.0 92.5 18 318s supply_19 105.8 89.3 19 318s supply_20 113.5 93.0 20 318s > print( mm1 <- model.matrix( fit2sls1$eq[[ 1 ]] ) ) 318s (Intercept) price income 318s 1 1 100.3 87.4 318s 2 1 104.3 97.6 318s 3 1 103.4 96.7 318s 4 1 104.5 98.2 318s 5 1 98.0 99.8 318s 6 1 99.5 100.5 318s 7 1 101.1 103.2 318s 8 1 104.8 107.8 318s 9 1 96.4 96.6 318s 10 1 91.2 88.9 318s 11 1 93.1 75.1 318s 12 1 98.8 76.9 318s 13 1 102.9 84.6 318s 14 1 98.8 90.6 318s 15 1 95.1 103.1 318s 16 1 98.5 105.1 318s 17 1 86.5 96.4 318s 18 1 104.0 104.4 318s 19 1 105.8 110.7 318s 20 1 113.5 127.1 318s attr(,"assign") 318s [1] 0 1 2 318s > print( mm2 <- model.matrix( fit2sls1$eq[[ 2 ]] ) ) 318s (Intercept) price farmPrice trend 318s 1 1 100.3 98.0 1 318s 2 1 104.3 99.1 2 318s 3 1 103.4 99.1 3 318s 4 1 104.5 98.1 4 318s 5 1 98.0 110.8 5 318s 6 1 99.5 108.2 6 318s 7 1 101.1 105.6 7 318s 8 1 104.8 109.8 8 318s 9 1 96.4 108.7 9 318s 10 1 91.2 100.6 10 318s 11 1 93.1 81.0 11 318s 12 1 98.8 68.6 12 318s 13 1 102.9 70.9 13 318s 14 1 98.8 81.4 14 318s 15 1 95.1 102.3 15 318s 16 1 98.5 105.0 16 318s 17 1 86.5 110.5 17 318s 18 1 104.0 92.5 18 318s 19 1 105.8 89.3 19 318s 20 1 113.5 93.0 20 318s attr(,"assign") 318s [1] 0 1 2 3 318s > 318s > # with x (returnModelMatrix) = FALSE 318s > print( all.equal( mm, model.matrix( fit2sls1s ) ) ) 318s [1] TRUE 318s > print( all.equal( mm1, model.matrix( fit2sls1s$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > print( all.equal( mm2, model.matrix( fit2sls1s$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > print( !is.null( fit2sls1s$eq[[ 1 ]]$x ) ) 318s [1] FALSE 318s > 318s > # with x (returnModelMatrix) = TRUE 318s > print( !is.null( fit2sls2s$eq[[ 1 ]]$x ) ) 318s [1] TRUE 318s > print( all.equal( mm, model.matrix( fit2sls2s ) ) ) 318s [1] TRUE 318s > print( all.equal( mm1, model.matrix( fit2sls2s$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > print( all.equal( mm2, model.matrix( fit2sls2s$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > 318s > # with x (returnModelMatrix) = FALSE 318s > print( all.equal( mm, model.matrix( fit2sls2Sym ) ) ) 318s [1] TRUE 318s > print( all.equal( mm1, model.matrix( fit2sls2Sym$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > print( all.equal( mm2, model.matrix( fit2sls2Sym$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > print( !is.null( fit2sls2Sym$eq[[ 1 ]]$x ) ) 318s [1] FALSE 318s > 318s > # with x (returnModelMatrix) = FALSE 318s > print( all.equal( mm, model.matrix( fit2sls3 ) ) ) 318s [1] TRUE 318s > print( all.equal( mm1, model.matrix( fit2sls3$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > print( all.equal( mm2, model.matrix( fit2sls3$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > print( !is.null( fit2sls3$eq[[ 1 ]]$x ) ) 318s [1] FALSE 318s > 318s > # with x (returnModelMatrix) = TRUE 318s > print( !is.null( fit2sls4r$eq[[ 1 ]]$x ) ) 318s [1] TRUE 318s > print( all.equal( mm, model.matrix( fit2sls4r ) ) ) 318s [1] TRUE 318s > print( all.equal( mm1, model.matrix( fit2sls4r$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > print( all.equal( mm2, model.matrix( fit2sls4r$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > 318s > # with x (returnModelMatrix) = FALSE 318s > print( all.equal( mm, model.matrix( fit2sls4s ) ) ) 318s [1] TRUE 318s > print( all.equal( mm1, model.matrix( fit2sls4s$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > print( all.equal( mm2, model.matrix( fit2sls4s$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > print( !is.null( fit2sls4s$eq[[ 1 ]]$x ) ) 318s [1] FALSE 318s > 318s > # with x (returnModelMatrix) = TRUE 318s > print( !is.null( fit2sls5rs$eq[[ 1 ]]$x ) ) 318s [1] TRUE 318s > print( all.equal( mm, model.matrix( fit2sls5rs ) ) ) 318s [1] TRUE 318s > print( all.equal( mm1, model.matrix( fit2sls5rs$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > print( all.equal( mm2, model.matrix( fit2sls5rs$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > 318s > # with x (returnModelMatrix) = FALSE 318s > print( all.equal( mm, model.matrix( fit2sls5r ) ) ) 318s [1] TRUE 318s > print( all.equal( mm1, model.matrix( fit2sls5r$eq[[ 1 ]] ) ) ) 318s [1] TRUE 318s > print( all.equal( mm2, model.matrix( fit2sls5r$eq[[ 2 ]] ) ) ) 318s [1] TRUE 318s > print( !is.null( fit2sls5r$eq[[ 1 ]]$x ) ) 318s [1] FALSE 318s > 318s > # matrices of instrumental variables 318s > model.matrix( fit2sls1, which = "z" ) 318s demand_(Intercept) demand_income demand_farmPrice demand_trend 318s demand_1 1 87.4 98.0 1 318s demand_2 1 97.6 99.1 2 318s demand_3 1 96.7 99.1 3 318s demand_4 1 98.2 98.1 4 318s demand_5 1 99.8 110.8 5 318s demand_6 1 100.5 108.2 6 318s demand_7 1 103.2 105.6 7 318s demand_8 1 107.8 109.8 8 318s demand_9 1 96.6 108.7 9 318s demand_10 1 88.9 100.6 10 318s demand_11 1 75.1 81.0 11 318s demand_12 1 76.9 68.6 12 318s demand_13 1 84.6 70.9 13 318s demand_14 1 90.6 81.4 14 318s demand_15 1 103.1 102.3 15 318s demand_16 1 105.1 105.0 16 318s demand_17 1 96.4 110.5 17 318s demand_18 1 104.4 92.5 18 318s demand_19 1 110.7 89.3 19 318s demand_20 1 127.1 93.0 20 318s supply_1 0 0.0 0.0 0 318s supply_2 0 0.0 0.0 0 318s supply_3 0 0.0 0.0 0 318s supply_4 0 0.0 0.0 0 318s supply_5 0 0.0 0.0 0 318s supply_6 0 0.0 0.0 0 318s supply_7 0 0.0 0.0 0 318s supply_8 0 0.0 0.0 0 318s supply_9 0 0.0 0.0 0 318s supply_10 0 0.0 0.0 0 318s supply_11 0 0.0 0.0 0 318s supply_12 0 0.0 0.0 0 318s supply_13 0 0.0 0.0 0 318s supply_14 0 0.0 0.0 0 318s supply_15 0 0.0 0.0 0 318s supply_16 0 0.0 0.0 0 318s supply_17 0 0.0 0.0 0 318s supply_18 0 0.0 0.0 0 318s supply_19 0 0.0 0.0 0 318s supply_20 0 0.0 0.0 0 318s supply_(Intercept) supply_income supply_farmPrice supply_trend 318s demand_1 0 0.0 0.0 0 318s demand_2 0 0.0 0.0 0 318s demand_3 0 0.0 0.0 0 318s demand_4 0 0.0 0.0 0 318s demand_5 0 0.0 0.0 0 318s demand_6 0 0.0 0.0 0 318s demand_7 0 0.0 0.0 0 318s demand_8 0 0.0 0.0 0 318s demand_9 0 0.0 0.0 0 318s demand_10 0 0.0 0.0 0 318s demand_11 0 0.0 0.0 0 318s demand_12 0 0.0 0.0 0 318s demand_13 0 0.0 0.0 0 318s demand_14 0 0.0 0.0 0 318s demand_15 0 0.0 0.0 0 318s demand_16 0 0.0 0.0 0 318s demand_17 0 0.0 0.0 0 318s demand_18 0 0.0 0.0 0 318s demand_19 0 0.0 0.0 0 318s demand_20 0 0.0 0.0 0 318s supply_1 1 87.4 98.0 1 318s supply_2 1 97.6 99.1 2 318s supply_3 1 96.7 99.1 3 318s supply_4 1 98.2 98.1 4 318s supply_5 1 99.8 110.8 5 318s supply_6 1 100.5 108.2 6 318s supply_7 1 103.2 105.6 7 318s supply_8 1 107.8 109.8 8 318s supply_9 1 96.6 108.7 9 318s supply_10 1 88.9 100.6 10 318s supply_11 1 75.1 81.0 11 318s supply_12 1 76.9 68.6 12 318s supply_13 1 84.6 70.9 13 318s supply_14 1 90.6 81.4 14 318s supply_15 1 103.1 102.3 15 318s supply_16 1 105.1 105.0 16 318s supply_17 1 96.4 110.5 17 318s supply_18 1 104.4 92.5 18 318s supply_19 1 110.7 89.3 19 318s supply_20 1 127.1 93.0 20 318s > model.matrix( fit2sls1$eq[[ 1 ]], which = "z" ) 318s (Intercept) income farmPrice trend 318s 1 1 87.4 98.0 1 318s 2 1 97.6 99.1 2 318s 3 1 96.7 99.1 3 318s 4 1 98.2 98.1 4 318s 5 1 99.8 110.8 5 318s 6 1 100.5 108.2 6 318s 7 1 103.2 105.6 7 318s 8 1 107.8 109.8 8 318s 9 1 96.6 108.7 9 318s 10 1 88.9 100.6 10 318s 11 1 75.1 81.0 11 318s 12 1 76.9 68.6 12 318s 13 1 84.6 70.9 13 318s 14 1 90.6 81.4 14 318s 15 1 103.1 102.3 15 318s 16 1 105.1 105.0 16 318s 17 1 96.4 110.5 17 318s 18 1 104.4 92.5 18 318s 19 1 110.7 89.3 19 318s 20 1 127.1 93.0 20 318s attr(,"assign") 318s [1] 0 1 2 3 318s > model.matrix( fit2sls1$eq[[ 2 ]], which = "z" ) 318s (Intercept) income farmPrice trend 318s 1 1 87.4 98.0 1 318s 2 1 97.6 99.1 2 318s 3 1 96.7 99.1 3 318s 4 1 98.2 98.1 4 318s 5 1 99.8 110.8 5 318s 6 1 100.5 108.2 6 318s 7 1 103.2 105.6 7 318s 8 1 107.8 109.8 8 318s 9 1 96.6 108.7 9 318s 10 1 88.9 100.6 10 318s 11 1 75.1 81.0 11 318s 12 1 76.9 68.6 12 318s 13 1 84.6 70.9 13 318s 14 1 90.6 81.4 14 318s 15 1 103.1 102.3 15 318s 16 1 105.1 105.0 16 318s 17 1 96.4 110.5 17 318s 18 1 104.4 92.5 18 318s 19 1 110.7 89.3 19 318s 20 1 127.1 93.0 20 318s attr(,"assign") 318s [1] 0 1 2 3 318s > 318s > # matrices of fitted regressors 318s > model.matrix( fit2sls5r, which = "xHat" ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s demand_1 1 99.6 87.4 0 318s demand_2 1 105.1 97.6 0 318s demand_3 1 103.8 96.7 0 318s demand_4 1 104.5 98.2 0 318s demand_5 1 98.7 99.8 0 318s demand_6 1 99.6 100.5 0 318s demand_7 1 102.0 103.2 0 318s demand_8 1 102.2 107.8 0 318s demand_9 1 94.6 96.6 0 318s demand_10 1 92.7 88.9 0 318s demand_11 1 92.4 75.1 0 318s demand_12 1 98.9 76.9 0 318s demand_13 1 102.2 84.6 0 318s demand_14 1 100.3 90.6 0 318s demand_15 1 97.6 103.1 0 318s demand_16 1 96.9 105.1 0 318s demand_17 1 87.7 96.4 0 318s demand_18 1 101.1 104.4 0 318s demand_19 1 106.1 110.7 0 318s demand_20 1 114.4 127.1 0 318s supply_1 0 0.0 0.0 1 318s supply_2 0 0.0 0.0 1 318s supply_3 0 0.0 0.0 1 318s supply_4 0 0.0 0.0 1 318s supply_5 0 0.0 0.0 1 318s supply_6 0 0.0 0.0 1 318s supply_7 0 0.0 0.0 1 318s supply_8 0 0.0 0.0 1 318s supply_9 0 0.0 0.0 1 318s supply_10 0 0.0 0.0 1 318s supply_11 0 0.0 0.0 1 318s supply_12 0 0.0 0.0 1 318s supply_13 0 0.0 0.0 1 318s supply_14 0 0.0 0.0 1 318s supply_15 0 0.0 0.0 1 318s supply_16 0 0.0 0.0 1 318s supply_17 0 0.0 0.0 1 318s supply_18 0 0.0 0.0 1 318s supply_19 0 0.0 0.0 1 318s supply_20 0 0.0 0.0 1 318s supply_price supply_farmPrice supply_trend 318s demand_1 0.0 0.0 0 318s demand_2 0.0 0.0 0 318s demand_3 0.0 0.0 0 318s demand_4 0.0 0.0 0 318s demand_5 0.0 0.0 0 318s demand_6 0.0 0.0 0 318s demand_7 0.0 0.0 0 318s demand_8 0.0 0.0 0 318s demand_9 0.0 0.0 0 318s demand_10 0.0 0.0 0 318s demand_11 0.0 0.0 0 318s demand_12 0.0 0.0 0 318s demand_13 0.0 0.0 0 318s demand_14 0.0 0.0 0 318s demand_15 0.0 0.0 0 318s demand_16 0.0 0.0 0 318s demand_17 0.0 0.0 0 318s demand_18 0.0 0.0 0 318s demand_19 0.0 0.0 0 318s demand_20 0.0 0.0 0 318s supply_1 99.6 98.0 1 318s supply_2 105.1 99.1 2 318s supply_3 103.8 99.1 3 318s supply_4 104.5 98.1 4 318s supply_5 98.7 110.8 5 318s supply_6 99.6 108.2 6 318s supply_7 102.0 105.6 7 318s supply_8 102.2 109.8 8 318s supply_9 94.6 108.7 9 318s supply_10 92.7 100.6 10 318s supply_11 92.4 81.0 11 318s supply_12 98.9 68.6 12 318s supply_13 102.2 70.9 13 318s supply_14 100.3 81.4 14 318s supply_15 97.6 102.3 15 318s supply_16 96.9 105.0 16 318s supply_17 87.7 110.5 17 318s supply_18 101.1 92.5 18 318s supply_19 106.1 89.3 19 318s supply_20 114.4 93.0 20 318s > model.matrix( fit2sls5r$eq[[ 1 ]], which = "xHat" ) 318s (Intercept) price income 318s 1 1 99.6 87.4 318s 2 1 105.1 97.6 318s 3 1 103.8 96.7 318s 4 1 104.5 98.2 318s 5 1 98.7 99.8 318s 6 1 99.6 100.5 318s 7 1 102.0 103.2 318s 8 1 102.2 107.8 318s 9 1 94.6 96.6 318s 10 1 92.7 88.9 318s 11 1 92.4 75.1 318s 12 1 98.9 76.9 318s 13 1 102.2 84.6 318s 14 1 100.3 90.6 318s 15 1 97.6 103.1 318s 16 1 96.9 105.1 318s 17 1 87.7 96.4 318s 18 1 101.1 104.4 318s 19 1 106.1 110.7 318s 20 1 114.4 127.1 318s > model.matrix( fit2sls5r$eq[[ 2 ]], which = "xHat" ) 318s (Intercept) price farmPrice trend 318s 1 1 99.6 98.0 1 318s 2 1 105.1 99.1 2 318s 3 1 103.8 99.1 3 318s 4 1 104.5 98.1 4 318s 5 1 98.7 110.8 5 318s 6 1 99.6 108.2 6 318s 7 1 102.0 105.6 7 318s 8 1 102.2 109.8 8 318s 9 1 94.6 108.7 9 318s 10 1 92.7 100.6 10 318s 11 1 92.4 81.0 11 318s 12 1 98.9 68.6 12 318s 13 1 102.2 70.9 13 318s 14 1 100.3 81.4 14 318s 15 1 97.6 102.3 15 318s 16 1 96.9 105.0 16 318s 17 1 87.7 110.5 17 318s 18 1 101.1 92.5 18 318s 19 1 106.1 89.3 19 318s 20 1 114.4 93.0 20 318s > 318s > 318s > ## **************** formulas ************************ 318s > formula( fit2sls1 ) 318s $demand 318s consump ~ price + income 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s 318s > formula( fit2sls1$eq[[ 1 ]] ) 318s consump ~ price + income 318s > 318s > formula( fit2sls2s ) 318s $demand 318s consump ~ price + income 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s 318s > formula( fit2sls2s$eq[[ 2 ]] ) 318s consump ~ price + farmPrice + trend 318s > 318s > formula( fit2sls3 ) 318s $demand 318s consump ~ price + income 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s 318s > formula( fit2sls3$eq[[ 1 ]] ) 318s consump ~ price + income 318s > 318s > formula( fit2sls4r ) 318s $demand 318s consump ~ price + income 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s 318s > formula( fit2sls4r$eq[[ 2 ]] ) 318s consump ~ price + farmPrice + trend 318s > 318s > formula( fit2sls5rs ) 318s $demand 318s consump ~ price + income 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s 318s > formula( fit2sls5rs$eq[[ 1 ]] ) 318s consump ~ price + income 318s > 318s > formula( fit2slsd1 ) 318s $demand 318s consump ~ price + income 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s 318s > formula( fit2slsd1$eq[[ 2 ]] ) 318s consump ~ price + farmPrice + trend 318s > 318s > formula( fit2slsd2r ) 318s $demand 318s consump ~ price + income 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s 318s > formula( fit2slsd2r$eq[[ 1 ]] ) 318s consump ~ price + income 318s > 318s > 318s > ## **************** model terms ******************* 318s > terms( fit2sls1 ) 318s $demand 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s 318s > terms( fit2sls1$eq[[ 1 ]] ) 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s > 318s > terms( fit2sls2s ) 318s $demand 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s 318s > terms( fit2sls2s$eq[[ 2 ]] ) 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s > 318s > terms( fit2sls3 ) 318s $demand 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s 318s > terms( fit2sls3$eq[[ 1 ]] ) 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s > 318s > terms( fit2sls4r ) 318s $demand 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s 318s > terms( fit2sls4r$eq[[ 2 ]] ) 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s > 318s > terms( fit2sls5rs ) 318s $demand 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s 318s > terms( fit2sls5rs$eq[[ 1 ]] ) 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s > 318s > terms( fit2slsd1 ) 318s $demand 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s 318s > terms( fit2slsd1$eq[[ 2 ]] ) 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s > 318s > terms( fit2slsd2r ) 318s $demand 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s 318s $supply 318s consump ~ price + farmPrice + trend 318s attr(,"variables") 318s list(consump, price, farmPrice, trend) 318s attr(,"factors") 318s price farmPrice trend 318s consump 0 0 0 318s price 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "price" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, farmPrice, trend) 318s attr(,"dataClasses") 318s consump price farmPrice trend 318s "numeric" "numeric" "numeric" "numeric" 318s 318s > terms( fit2slsd2r$eq[[ 1 ]] ) 318s consump ~ price + income 318s attr(,"variables") 318s list(consump, price, income) 318s attr(,"factors") 318s price income 318s consump 0 0 318s price 1 0 318s income 0 1 318s attr(,"term.labels") 318s [1] "price" "income" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 1 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(consump, price, income) 318s attr(,"dataClasses") 318s consump price income 318s "numeric" "numeric" "numeric" 318s > 318s > 318s > ## **************** terms of instruments ******************* 318s > fit2sls1$eq[[ 1 ]]$termsInst 318s ~income + farmPrice + trend 318s attr(,"variables") 318s list(income, farmPrice, trend) 318s attr(,"factors") 318s income farmPrice trend 318s income 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "income" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 0 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(income, farmPrice, trend) 318s attr(,"dataClasses") 318s income farmPrice trend 318s "numeric" "numeric" "numeric" 318s > 318s > fit2sls2s$eq[[ 2 ]]$termsInst 318s ~income + farmPrice + trend 318s attr(,"variables") 318s list(income, farmPrice, trend) 318s attr(,"factors") 318s income farmPrice trend 318s income 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "income" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 0 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(income, farmPrice, trend) 318s attr(,"dataClasses") 318s income farmPrice trend 318s "numeric" "numeric" "numeric" 318s > 318s > fit2sls3$eq[[ 1 ]]$termsInst 318s ~income + farmPrice + trend 318s attr(,"variables") 318s list(income, farmPrice, trend) 318s attr(,"factors") 318s income farmPrice trend 318s income 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "income" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 0 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(income, farmPrice, trend) 318s attr(,"dataClasses") 318s income farmPrice trend 318s "numeric" "numeric" "numeric" 318s > 318s > fit2sls4r$eq[[ 2 ]]$termsInst 318s ~income + farmPrice + trend 318s attr(,"variables") 318s list(income, farmPrice, trend) 318s attr(,"factors") 318s income farmPrice trend 318s income 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "income" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 0 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(income, farmPrice, trend) 318s attr(,"dataClasses") 318s income farmPrice trend 318s "numeric" "numeric" "numeric" 318s > 318s > fit2sls5rs$eq[[ 1 ]]$termsInst 318s ~income + farmPrice + trend 318s attr(,"variables") 318s list(income, farmPrice, trend) 318s attr(,"factors") 318s income farmPrice trend 318s income 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "income" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 0 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(income, farmPrice, trend) 318s attr(,"dataClasses") 318s income farmPrice trend 318s "numeric" "numeric" "numeric" 318s > 318s > fit2slsd1$eq[[ 2 ]]$termsInst 318s ~income + farmPrice + trend 318s attr(,"variables") 318s list(income, farmPrice, trend) 318s attr(,"factors") 318s income farmPrice trend 318s income 1 0 0 318s farmPrice 0 1 0 318s trend 0 0 1 318s attr(,"term.labels") 318s [1] "income" "farmPrice" "trend" 318s attr(,"order") 318s [1] 1 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 0 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(income, farmPrice, trend) 318s attr(,"dataClasses") 318s income farmPrice trend 318s "numeric" "numeric" "numeric" 318s > 318s > fit2slsd2r$eq[[ 1 ]]$termsInst 318s ~income + farmPrice 318s attr(,"variables") 318s list(income, farmPrice) 318s attr(,"factors") 318s income farmPrice 318s income 1 0 318s farmPrice 0 1 318s attr(,"term.labels") 318s [1] "income" "farmPrice" 318s attr(,"order") 318s [1] 1 1 318s attr(,"intercept") 318s [1] 1 318s attr(,"response") 318s [1] 0 318s attr(,".Environment") 318s 318s attr(,"predvars") 318s list(income, farmPrice) 318s attr(,"dataClasses") 318s income farmPrice 318s "numeric" "numeric" 318s > 318s > 318s > ## **************** estfun ************************ 318s > library( "sandwich" ) 318s > 318s > estfun( fit2sls1 ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s demand_1 0.6738 67.13 58.89 0.000 318s demand_2 -0.4897 -51.48 -47.80 0.000 318s demand_3 2.4440 253.65 236.33 0.000 318s demand_4 1.4958 156.35 146.88 0.000 318s demand_5 2.2975 226.65 229.29 0.000 318s demand_6 1.3235 131.89 133.02 0.000 318s demand_7 1.7917 182.70 184.90 0.000 318s demand_8 -3.6818 -376.41 -396.90 0.000 318s demand_9 -1.5729 -148.80 -151.94 0.000 318s demand_10 2.8552 264.73 253.83 0.000 318s demand_11 -0.2736 -25.29 -20.55 0.000 318s demand_12 -2.2634 -223.89 -174.06 0.000 318s demand_13 -1.7795 -181.80 -150.55 0.000 318s demand_14 0.0991 9.93 8.98 0.000 318s demand_15 2.5674 250.64 264.70 0.000 318s demand_16 -3.8102 -369.18 -400.45 0.000 318s demand_17 -0.0206 -1.81 -1.99 0.000 318s demand_18 -2.8715 -290.19 -299.78 0.000 318s demand_19 1.6632 176.41 184.12 0.000 318s demand_20 -0.4478 -51.23 -56.92 0.000 318s supply_1 0.0000 0.00 0.00 -0.268 318s supply_2 0.0000 0.00 0.00 -1.418 318s supply_3 0.0000 0.00 0.00 1.625 318s supply_4 0.0000 0.00 0.00 0.790 318s supply_5 0.0000 0.00 0.00 1.438 318s supply_6 0.0000 0.00 0.00 0.613 318s supply_7 0.0000 0.00 0.00 1.217 318s supply_8 0.0000 0.00 0.00 -4.265 318s supply_9 0.0000 0.00 0.00 -1.956 318s supply_10 0.0000 0.00 0.00 2.785 318s supply_11 0.0000 0.00 0.00 0.233 318s supply_12 0.0000 0.00 0.00 -1.426 318s supply_13 0.0000 0.00 0.00 -0.935 318s supply_14 0.0000 0.00 0.00 0.803 318s supply_15 0.0000 0.00 0.00 2.886 318s supply_16 0.0000 0.00 0.00 -3.454 318s supply_17 0.0000 0.00 0.00 0.391 318s supply_18 0.0000 0.00 0.00 -2.061 318s supply_19 0.0000 0.00 0.00 2.596 318s supply_20 0.0000 0.00 0.00 0.406 318s supply_price supply_farmPrice supply_trend 318s demand_1 0.0 0.0 0.000 318s demand_2 0.0 0.0 0.000 318s demand_3 0.0 0.0 0.000 318s demand_4 0.0 0.0 0.000 318s demand_5 0.0 0.0 0.000 318s demand_6 0.0 0.0 0.000 318s demand_7 0.0 0.0 0.000 318s demand_8 0.0 0.0 0.000 318s demand_9 0.0 0.0 0.000 318s demand_10 0.0 0.0 0.000 318s demand_11 0.0 0.0 0.000 318s demand_12 0.0 0.0 0.000 318s demand_13 0.0 0.0 0.000 318s demand_14 0.0 0.0 0.000 318s demand_15 0.0 0.0 0.000 318s demand_16 0.0 0.0 0.000 318s demand_17 0.0 0.0 0.000 318s demand_18 0.0 0.0 0.000 318s demand_19 0.0 0.0 0.000 318s demand_20 0.0 0.0 0.000 318s supply_1 -26.7 -26.3 -0.268 318s supply_2 -149.1 -140.5 -2.836 318s supply_3 168.7 161.1 4.876 318s supply_4 82.6 77.5 3.159 318s supply_5 141.9 159.3 7.190 318s supply_6 61.1 66.4 3.680 318s supply_7 124.1 128.5 8.520 318s supply_8 -436.1 -468.3 -34.122 318s supply_9 -185.0 -212.6 -17.602 318s supply_10 258.2 280.1 27.848 318s supply_11 21.5 18.8 2.558 318s supply_12 -141.0 -97.8 -17.107 318s supply_13 -95.5 -66.3 -12.152 318s supply_14 80.6 65.4 11.246 318s supply_15 281.7 295.2 43.286 318s supply_16 -334.7 -362.7 -55.267 318s supply_17 34.3 43.2 6.650 318s supply_18 -208.3 -190.7 -37.106 318s supply_19 275.4 231.8 49.327 318s supply_20 46.5 37.8 8.122 318s > round( colSums( estfun( fit2sls1 ) ), digits = 7 ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s 0 0 0 0 318s supply_price supply_farmPrice supply_trend 318s 0 0 0 318s > 318s > estfun( fit2sls1s ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s demand_1 0.6738 67.13 58.89 0.000 318s demand_2 -0.4897 -51.48 -47.80 0.000 318s demand_3 2.4440 253.65 236.33 0.000 318s demand_4 1.4958 156.35 146.88 0.000 318s demand_5 2.2975 226.65 229.29 0.000 318s demand_6 1.3235 131.89 133.02 0.000 318s demand_7 1.7917 182.70 184.90 0.000 318s demand_8 -3.6818 -376.41 -396.90 0.000 318s demand_9 -1.5729 -148.80 -151.94 0.000 318s demand_10 2.8552 264.73 253.83 0.000 318s demand_11 -0.2736 -25.29 -20.55 0.000 318s demand_12 -2.2634 -223.89 -174.06 0.000 318s demand_13 -1.7795 -181.80 -150.55 0.000 318s demand_14 0.0991 9.93 8.98 0.000 318s demand_15 2.5674 250.64 264.70 0.000 318s demand_16 -3.8102 -369.18 -400.45 0.000 318s demand_17 -0.0206 -1.81 -1.99 0.000 318s demand_18 -2.8715 -290.19 -299.78 0.000 318s demand_19 1.6632 176.41 184.12 0.000 318s demand_20 -0.4478 -51.23 -56.92 0.000 318s supply_1 0.0000 0.00 0.00 -0.268 318s supply_2 0.0000 0.00 0.00 -1.418 318s supply_3 0.0000 0.00 0.00 1.625 318s supply_4 0.0000 0.00 0.00 0.790 318s supply_5 0.0000 0.00 0.00 1.438 318s supply_6 0.0000 0.00 0.00 0.613 318s supply_7 0.0000 0.00 0.00 1.217 318s supply_8 0.0000 0.00 0.00 -4.265 318s supply_9 0.0000 0.00 0.00 -1.956 318s supply_10 0.0000 0.00 0.00 2.785 318s supply_11 0.0000 0.00 0.00 0.233 318s supply_12 0.0000 0.00 0.00 -1.426 318s supply_13 0.0000 0.00 0.00 -0.935 318s supply_14 0.0000 0.00 0.00 0.803 318s supply_15 0.0000 0.00 0.00 2.886 318s supply_16 0.0000 0.00 0.00 -3.454 318s supply_17 0.0000 0.00 0.00 0.391 318s supply_18 0.0000 0.00 0.00 -2.061 318s supply_19 0.0000 0.00 0.00 2.596 318s supply_20 0.0000 0.00 0.00 0.406 318s supply_price supply_farmPrice supply_trend 318s demand_1 0.0 0.0 0.000 318s demand_2 0.0 0.0 0.000 318s demand_3 0.0 0.0 0.000 318s demand_4 0.0 0.0 0.000 318s demand_5 0.0 0.0 0.000 318s demand_6 0.0 0.0 0.000 318s demand_7 0.0 0.0 0.000 318s demand_8 0.0 0.0 0.000 318s demand_9 0.0 0.0 0.000 318s demand_10 0.0 0.0 0.000 318s demand_11 0.0 0.0 0.000 318s demand_12 0.0 0.0 0.000 318s demand_13 0.0 0.0 0.000 318s demand_14 0.0 0.0 0.000 318s demand_15 0.0 0.0 0.000 318s demand_16 0.0 0.0 0.000 318s demand_17 0.0 0.0 0.000 318s demand_18 0.0 0.0 0.000 318s demand_19 0.0 0.0 0.000 318s demand_20 0.0 0.0 0.000 318s supply_1 -26.7 -26.3 -0.268 318s supply_2 -149.1 -140.5 -2.836 318s supply_3 168.7 161.1 4.876 318s supply_4 82.6 77.5 3.159 318s supply_5 141.9 159.3 7.190 318s supply_6 61.1 66.4 3.680 318s supply_7 124.1 128.5 8.520 318s supply_8 -436.1 -468.3 -34.122 318s supply_9 -185.0 -212.6 -17.602 318s supply_10 258.2 280.1 27.848 318s supply_11 21.5 18.8 2.558 318s supply_12 -141.0 -97.8 -17.107 318s supply_13 -95.5 -66.3 -12.152 318s supply_14 80.6 65.4 11.246 318s supply_15 281.7 295.2 43.286 318s supply_16 -334.7 -362.7 -55.267 318s supply_17 34.3 43.2 6.650 318s supply_18 -208.3 -190.7 -37.106 318s supply_19 275.4 231.8 49.327 318s supply_20 46.5 37.8 8.122 318s > round( colSums( estfun( fit2sls1s ) ), digits = 7 ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s 0 0 0 0 318s supply_price supply_farmPrice supply_trend 318s 0 0 0 318s > 318s > estfun( fit2sls1r ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s demand_1 0.6738 67.13 58.89 0.000 318s demand_2 -0.4897 -51.48 -47.80 0.000 318s demand_3 2.4440 253.65 236.33 0.000 318s demand_4 1.4958 156.35 146.88 0.000 318s demand_5 2.2975 226.65 229.29 0.000 318s demand_6 1.3235 131.89 133.02 0.000 318s demand_7 1.7917 182.70 184.90 0.000 318s demand_8 -3.6818 -376.41 -396.90 0.000 318s demand_9 -1.5729 -148.80 -151.94 0.000 318s demand_10 2.8552 264.73 253.83 0.000 318s demand_11 -0.2736 -25.29 -20.55 0.000 318s demand_12 -2.2634 -223.89 -174.06 0.000 318s demand_13 -1.7795 -181.80 -150.55 0.000 318s demand_14 0.0991 9.93 8.98 0.000 318s demand_15 2.5674 250.64 264.70 0.000 318s demand_16 -3.8102 -369.18 -400.45 0.000 318s demand_17 -0.0206 -1.81 -1.99 0.000 318s demand_18 -2.8715 -290.19 -299.78 0.000 318s demand_19 1.6632 176.41 184.12 0.000 318s demand_20 -0.4478 -51.23 -56.92 0.000 318s supply_1 0.0000 0.00 0.00 -0.268 318s supply_2 0.0000 0.00 0.00 -1.418 318s supply_3 0.0000 0.00 0.00 1.625 318s supply_4 0.0000 0.00 0.00 0.790 318s supply_5 0.0000 0.00 0.00 1.438 318s supply_6 0.0000 0.00 0.00 0.613 318s supply_7 0.0000 0.00 0.00 1.217 318s supply_8 0.0000 0.00 0.00 -4.265 318s supply_9 0.0000 0.00 0.00 -1.956 318s supply_10 0.0000 0.00 0.00 2.785 318s supply_11 0.0000 0.00 0.00 0.233 318s supply_12 0.0000 0.00 0.00 -1.426 318s supply_13 0.0000 0.00 0.00 -0.935 318s supply_14 0.0000 0.00 0.00 0.803 318s supply_15 0.0000 0.00 0.00 2.886 318s supply_16 0.0000 0.00 0.00 -3.454 318s supply_17 0.0000 0.00 0.00 0.391 318s supply_18 0.0000 0.00 0.00 -2.061 318s supply_19 0.0000 0.00 0.00 2.596 318s supply_20 0.0000 0.00 0.00 0.406 318s supply_price supply_farmPrice supply_trend 318s demand_1 0.0 0.0 0.000 318s demand_2 0.0 0.0 0.000 318s demand_3 0.0 0.0 0.000 318s demand_4 0.0 0.0 0.000 318s demand_5 0.0 0.0 0.000 318s demand_6 0.0 0.0 0.000 318s demand_7 0.0 0.0 0.000 318s demand_8 0.0 0.0 0.000 318s demand_9 0.0 0.0 0.000 318s demand_10 0.0 0.0 0.000 318s demand_11 0.0 0.0 0.000 318s demand_12 0.0 0.0 0.000 318s demand_13 0.0 0.0 0.000 318s demand_14 0.0 0.0 0.000 318s demand_15 0.0 0.0 0.000 318s demand_16 0.0 0.0 0.000 318s demand_17 0.0 0.0 0.000 318s demand_18 0.0 0.0 0.000 318s demand_19 0.0 0.0 0.000 318s demand_20 0.0 0.0 0.000 318s supply_1 -26.7 -26.3 -0.268 318s supply_2 -149.1 -140.5 -2.836 318s supply_3 168.7 161.1 4.876 318s supply_4 82.6 77.5 3.159 318s supply_5 141.9 159.3 7.190 318s supply_6 61.1 66.4 3.680 318s supply_7 124.1 128.5 8.520 318s supply_8 -436.1 -468.3 -34.122 318s supply_9 -185.0 -212.6 -17.602 318s supply_10 258.2 280.1 27.848 318s supply_11 21.5 18.8 2.558 318s supply_12 -141.0 -97.8 -17.107 318s supply_13 -95.5 -66.3 -12.152 318s supply_14 80.6 65.4 11.246 318s supply_15 281.7 295.2 43.286 318s supply_16 -334.7 -362.7 -55.267 318s supply_17 34.3 43.2 6.650 318s supply_18 -208.3 -190.7 -37.106 318s supply_19 275.4 231.8 49.327 318s supply_20 46.5 37.8 8.122 318s > round( colSums( estfun( fit2sls1r ) ), digits = 7 ) 318s demand_(Intercept) demand_price demand_income supply_(Intercept) 318s 0 0 0 0 318s supply_price supply_farmPrice supply_trend 318s 0 0 0 318s > 318s > 318s > ## **************** bread ************************ 318s > bread( fit2sls1 ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 649.07 -6.9669 0.5100 318s demand_price -6.97 0.0963 -0.0273 318s demand_income 0.51 -0.0273 0.0228 318s supply_(Intercept) 0.00 0.0000 0.0000 318s supply_price 0.00 0.0000 0.0000 318s supply_farmPrice 0.00 0.0000 0.0000 318s supply_trend 0.00 0.0000 0.0000 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) 0.00 0.00000 0.00000 318s demand_price 0.00 0.00000 0.00000 318s demand_income 0.00 0.00000 0.00000 318s supply_(Intercept) 955.38 -7.25488 -2.14464 318s supply_price -7.25 0.06614 0.00620 318s supply_farmPrice -2.14 0.00620 0.01479 318s supply_trend -1.96 0.00384 0.00912 318s supply_trend 318s demand_(Intercept) 0.00000 318s demand_price 0.00000 318s demand_income 0.00000 318s supply_(Intercept) -1.95529 318s supply_price 0.00384 318s supply_farmPrice 0.00912 318s supply_trend 0.06577 318s > 318s > bread( fit2sls1s ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 649.07 -6.9669 0.5100 318s demand_price -6.97 0.0963 -0.0273 318s demand_income 0.51 -0.0273 0.0228 318s supply_(Intercept) 0.00 0.0000 0.0000 318s supply_price 0.00 0.0000 0.0000 318s supply_farmPrice 0.00 0.0000 0.0000 318s supply_trend 0.00 0.0000 0.0000 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) 0.00 0.00000 0.00000 318s demand_price 0.00 0.00000 0.00000 318s demand_income 0.00 0.00000 0.00000 318s supply_(Intercept) 955.38 -7.25488 -2.14464 318s supply_price -7.25 0.06614 0.00620 318s supply_farmPrice -2.14 0.00620 0.01479 318s supply_trend -1.96 0.00384 0.00912 318s supply_trend 318s demand_(Intercept) 0.00000 318s demand_price 0.00000 318s demand_income 0.00000 318s supply_(Intercept) -1.95529 318s supply_price 0.00384 318s supply_farmPrice 0.00912 318s supply_trend 0.06577 318s > 318s > bread( fit2sls1r ) 318s demand_(Intercept) demand_price demand_income 318s demand_(Intercept) 649.07 -6.9669 0.5100 318s demand_price -6.97 0.0963 -0.0273 318s demand_income 0.51 -0.0273 0.0228 318s supply_(Intercept) 0.00 0.0000 0.0000 318s supply_price 0.00 0.0000 0.0000 318s supply_farmPrice 0.00 0.0000 0.0000 318s supply_trend 0.00 0.0000 0.0000 318s supply_(Intercept) supply_price supply_farmPrice 318s demand_(Intercept) 0.00 0.00000 0.00000 318s demand_price 0.00 0.00000 0.00000 318s demand_income 0.00 0.00000 0.00000 318s supply_(Intercept) 955.38 -7.25488 -2.14464 318s supply_price -7.25 0.06614 0.00620 318s supply_farmPrice -2.14 0.00620 0.01479 318s supply_trend -1.96 0.00384 0.00912 318s supply_trend 318s demand_(Intercept) 0.00000 318s demand_price 0.00000 318s demand_income 0.00000 318s supply_(Intercept) -1.95529 318s supply_price 0.00384 318s supply_farmPrice 0.00912 318s supply_trend 0.06577 318s > 318s BEGIN TEST test_3sls.R 319s 319s R version 4.3.2 (2023-10-31) -- "Eye Holes" 319s Copyright (C) 2023 The R Foundation for Statistical Computing 319s Platform: x86_64-pc-linux-gnu (64-bit) 319s 319s R is free software and comes with ABSOLUTELY NO WARRANTY. 319s You are welcome to redistribute it under certain conditions. 319s Type 'license()' or 'licence()' for distribution details. 319s 319s R is a collaborative project with many contributors. 319s Type 'contributors()' for more information and 319s 'citation()' on how to cite R or R packages in publications. 319s 319s Type 'demo()' for some demos, 'help()' for on-line help, or 319s 'help.start()' for an HTML browser interface to help. 319s Type 'q()' to quit R. 319s 319s > library( systemfit ) 319s Loading required package: Matrix 320s Loading required package: car 320s Loading required package: carData 320s Loading required package: lmtest 320s Loading required package: zoo 320s 320s Attaching package: ‘zoo’ 320s 320s The following objects are masked from ‘package:base’: 320s 320s as.Date, as.Date.numeric 320s 320s 320s Please cite the 'systemfit' package as: 320s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 320s 320s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 320s https://r-forge.r-project.org/projects/systemfit/ 320s > options( digits = 3 ) 320s > 320s > data( "Kmenta" ) 320s > useMatrix <- FALSE 320s > 320s > demand <- consump ~ price + income 320s > supply <- consump ~ price + farmPrice + trend 320s > inst <- ~ income + farmPrice + trend 320s > inst1 <- ~ income + farmPrice 320s > instlist <- list( inst1, inst ) 320s > system <- list( demand = demand, supply = supply ) 320s > restrm <- matrix(0,1,7) # restriction matrix "R" 320s > restrm[1,3] <- 1 320s > restrm[1,7] <- -1 320s > restrict <- "demand_income - supply_trend = 0" 320s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 320s > restr2m[1,3] <- 1 320s > restr2m[1,7] <- -1 320s > restr2m[2,2] <- -1 320s > restr2m[2,5] <- 1 320s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 320s > restrict2 <- c( "demand_income - supply_trend = 0", 320s + "- demand_price + supply_price = 0.5" ) 320s > tc <- matrix(0,7,6) 320s > tc[1,1] <- 1 320s > tc[2,2] <- 1 320s > tc[3,3] <- 1 320s > tc[4,4] <- 1 320s > tc[5,5] <- 1 320s > tc[6,6] <- 1 320s > tc[7,3] <- 1 320s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 320s > restr3m[1,2] <- -1 320s > restr3m[1,5] <- 1 320s > restr3q <- c( 0.5 ) # restriction vector "q" 2 320s > restrict3 <- "- C2 + C5 = 0.5" 320s > 320s > 320s > ## *************** 3SLS estimation ************************ 320s > fit3sls <- list() 320s > formulas <- c( "GLS", "IV", "Schmidt", "GMM", "EViews" ) 320s > for( i in seq( along = formulas ) ) { 320s + fit3sls[[ i ]] <- list() 320s + 320s + print( "***************************************************" ) 320s + print( paste( "3SLS formula:", formulas[ i ] ) ) 320s + print( "************* 3SLS *********************************" ) 320s + fit3sls[[ i ]]$e1 <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, method3sls = formulas[ i ], useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e1 ) ) 320s + 320s + print( "********************* 3SLS EViews-like *****************" ) 320s + fit3sls[[ i ]]$e1e <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, methodResidCov = "noDfCor", method3sls = formulas[ i ], 320s + useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e1e, useDfSys = TRUE ) ) 320s + 320s + print( "********************* 3SLS with methodResidCov = Theil *****************" ) 320s + fit3sls[[ i ]]$e1c <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, methodResidCov = "Theil", method3sls = formulas[ i ], 320s + x = TRUE, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e1c, useDfSys = TRUE ) ) 320s + 320s + print( "*************** W3SLS with methodResidCov = Theil *****************" ) 320s + fit3sls[[ i ]]$e1wc <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, methodResidCov = "Theil", method3sls = formulas[ i ], 320s + residCovWeighted = TRUE, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e1wc, useDfSys = TRUE ) ) 320s + 320s + 320s + print( "*************** 3SLS with restriction *****************" ) 320s + fit3sls[[ i ]]$e2 <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.matrix = restrm, method3sls = formulas[ i ], 320s + x = TRUE, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e2 ) ) 320s + # the same with symbolically specified restrictions 320s + fit3sls[[ i ]]$e2Sym <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.matrix = restrict, method3sls = formulas[ i ], 320s + x = TRUE, useMatrix = useMatrix ) 320s + print( all.equal( fit3sls[[ i ]]$e2, fit3sls[[ i ]]$e2Sym ) ) 320s + 320s + print( "************** 3SLS with restriction (EViews-like) *****************" ) 320s + fit3sls[[ i ]]$e2e <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restrm, 320s + method3sls = formulas[ i ], useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e2e, useDfSys = TRUE ) ) 320s + print( nobs( fit3sls[[i]]$e2e )) 320s + 320s + print( "*************** W3SLS with restriction *****************" ) 320s + fit3sls[[ i ]]$e2w <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.matrix = restrm, method3sls = formulas[ i ], 320s + residCovWeighted = TRUE, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e2w ) ) 320s + 320s + 320s + print( "*************** 3SLS with restriction via restrict.regMat ********************" ) 320s + fit3sls[[ i ]]$e3 <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.regMat = tc, method3sls = formulas[ i ], 320s + useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e3 ) ) 320s + 320s + print( "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" ) 320s + fit3sls[[ i ]]$e3e <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, methodResidCov = "noDfCor", restrict.regMat = tc, 320s + method3sls = formulas[ i ], x = TRUE, 320s + useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e3e, useDfSys = TRUE ) ) 320s + 320s + print( "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" ) 320s + fit3sls[[ i ]]$e3we <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, methodResidCov = "noDfCor", restrict.regMat = tc, 320s + method3sls = formulas[ i ], residCovWeighted = TRUE, 320s + useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e3we, useDfSys = TRUE ) ) 320s + 320s + 320s + print( "*************** 3SLS with 2 restrictions **********************" ) 320s + fit3sls[[ i ]]$e4 <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.matrix = restr2m, restrict.rhs = restr2q, 320s + method3sls = formulas[ i ], x = TRUE, 320s + useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e4 ) ) 320s + # the same with symbolically specified restrictions 320s + fit3sls[[ i ]]$e4Sym <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.matrix = restrict2, method3sls = formulas[ i ], 320s + x = TRUE, useMatrix = useMatrix ) 320s + print( all.equal( fit3sls[[ i ]]$e4, fit3sls[[ i ]]$e4Sym ) ) 320s + 320s + print( "*************** 3SLS with 2 restrictions (EViews-like) ************" ) 320s + fit3sls[[ i ]]$e4e <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restr2m, 320s + restrict.rhs = restr2q, method3sls = formulas[ i ], 320s + useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e4e, useDfSys = TRUE ) ) 320s + 320s + print( "********** W3SLS with 2 (symbolic) restrictions ***************" ) 320s + fit3sls[[ i ]]$e4wSym <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.matrix = restrict2, method3sls = formulas[ i ], 320s + residCovWeighted = TRUE, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e4wSym ) ) 320s + 320s + 320s + print( "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" ) 320s + fit3sls[[ i ]]$e5 <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.regMat = tc, restrict.matrix = restr3m, 320s + restrict.rhs = restr3q, method3sls = formulas[ i ], 320s + useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e5 ) ) 320s + # the same with symbolically specified restrictions 320s + fit3sls[[ i ]]$e5Sym <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.regMat = tc, restrict.matrix = restrict3, 320s + method3sls = formulas[ i ], useMatrix = useMatrix ) 320s + print( all.equal( fit3sls[[ i ]]$e5, fit3sls[[ i ]]$e5Sym ) ) 320s + 320s + print( "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" ) 320s + fit3sls[[ i ]]$e5e <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.regMat = tc, methodResidCov = "noDfCor", 320s + restrict.matrix = restr3m, restrict.rhs = restr3q, 320s + method3sls = formulas[ i ], x = TRUE, 320s + useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e5e, useDfSys = TRUE ) ) 320s + 320s + print( "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" ) 320s + fit3sls[[ i ]]$e5we <- systemfit( system, "3SLS", data = Kmenta, 320s + inst = inst, restrict.regMat = tc, methodResidCov = "noDfCor", 320s + restrict.matrix = restr3m, restrict.rhs = restr3q, method3sls = formulas[ i ], 320s + residCovWeighted = TRUE, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$e5we, useDfSys = TRUE ) ) 320s + 320s + ## *********** estimations with a single regressor ************ 320s + fit3sls[[ i ]]$S1 <- systemfit( 320s + list( farmPrice ~ consump - 1, price ~ consump + trend ), "3SLS", 320s + data = Kmenta, inst = ~ trend + income, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$S1 ) ) 320s + fit3sls[[ i ]]$S2 <- systemfit( 320s + list( consump ~ farmPrice - 1, consump ~ trend - 1 ), "3SLS", 320s + data = Kmenta, inst = ~ price + income, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$S2 ) ) 320s + fit3sls[[ i ]]$S3 <- systemfit( 320s + list( consump ~ trend - 1, farmPrice ~ trend - 1 ), "3SLS", 320s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$S3 ) ) 320s + fit3sls[[ i ]]$S4 <- systemfit( 320s + list( consump ~ farmPrice - 1, price ~ trend - 1 ), "3SLS", 320s + data = Kmenta, inst = ~ farmPrice + trend + income, 320s + restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$S4 ) ) 320s + fit3sls[[ i ]]$S5 <- systemfit( 320s + list( consump ~ 1, price ~ 1 ), "3SLS", 320s + data = Kmenta, inst = ~ income, useMatrix = useMatrix ) 320s + print( summary( fit3sls[[ i ]]$S5 ) ) 320s + } 320s [1] "***************************************************" 320s [1] "3SLS formula: GLS" 320s [1] "************* 3SLS *********************************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 33 174 1.03 0.676 0.786 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.7 3.87 1.97 0.755 0.726 320s supply 20 16 107.9 6.75 2.60 0.598 0.522 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.87 4.36 320s supply 4.36 6.04 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 5.00 320s supply 5.00 6.74 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.00 0.98 320s supply 0.98 1.00 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 320s price -0.2436 0.0965 -2.52 0.022 * 320s income 0.3140 0.0469 6.69 3.8e-06 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.966 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 320s price 0.2286 0.0997 2.29 0.03571 * 320s farmPrice 0.2282 0.0440 5.19 9e-05 *** 320s trend 0.3611 0.0729 4.95 0.00014 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.597 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 320s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 320s 320s [1] "********************* 3SLS EViews-like *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 33 173 0.719 0.677 0.748 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.7 3.87 1.97 0.755 0.726 320s supply 20 16 107.2 6.70 2.59 0.600 0.525 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.29 3.59 320s supply 3.59 4.83 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.29 4.11 320s supply 4.11 5.36 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.979 320s supply 0.979 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 320s price -0.2436 0.0890 -2.74 0.0099 ** 320s income 0.3140 0.0433 7.25 2.5e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.966 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 320s price 0.2289 0.0892 2.57 0.015 * 320s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 320s trend 0.3579 0.0652 5.49 4.3e-06 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.589 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 320s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 320s 320s [1] "********************* 3SLS with methodResidCov = Theil *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 33 174 -0.718 0.675 0.922 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.7 3.87 1.97 0.755 0.726 320s supply 20 16 108.7 6.79 2.61 0.594 0.518 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.87 4.50 320s supply 4.50 6.04 320s 320s warning: this covariance matrix is NOT positive semidefinit! 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 5.2 320s supply 5.20 6.8 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.981 320s supply 0.981 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 320s price -0.2436 0.0965 -2.52 0.017 * 320s income 0.3140 0.0469 6.69 1.3e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.966 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 320s price 0.2282 0.0997 2.29 0.02855 * 320s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 320s trend 0.3648 0.0707 5.16 1.1e-05 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.607 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 320s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 320s 320s [1] "*************** W3SLS with methodResidCov = Theil *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 33 174 -0.718 0.675 0.922 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.7 3.87 1.97 0.755 0.726 320s supply 20 16 108.7 6.79 2.61 0.594 0.518 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.87 4.50 320s supply 4.50 6.04 320s 320s warning: this covariance matrix is NOT positive semidefinit! 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 5.2 320s supply 5.20 6.8 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.981 320s supply 0.981 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 320s price -0.2436 0.0965 -2.52 0.017 * 320s income 0.3140 0.0469 6.69 1.3e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.966 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 320s price 0.2282 0.0997 2.29 0.02855 * 320s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 320s trend 0.3648 0.0707 5.16 1.1e-05 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.607 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 320s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 320s 320s [1] "*************** 3SLS with restriction *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 173 1.27 0.678 0.722 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.8 3.99 2.00 0.747 0.717 320s supply 20 16 104.8 6.55 2.56 0.609 0.536 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.97 4.55 320s supply 4.55 6.13 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.99 4.98 320s supply 4.98 6.55 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.975 320s supply 0.975 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 320s price -0.222 0.096 -2.31 0.027 * 320s income 0.296 0.045 6.57 1.6e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.997 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 320s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 320s price 0.2193 0.1002 2.19 0.036 * 320s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 320s trend 0.2956 0.0450 6.57 1.6e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.559 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 320s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 320s 320s [1] "Component “call”: target, current do not match when deparsed" 320s [1] "************** 3SLS with restriction (EViews-like) *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 171 0.887 0.68 0.678 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.5 3.97 1.99 0.748 0.719 320s supply 20 16 104.0 6.50 2.55 0.612 0.539 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.37 3.75 320s supply 3.75 4.91 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.37 4.08 320s supply 4.08 5.20 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.974 320s supply 0.974 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 320s price -0.2243 0.0888 -2.53 0.016 * 320s income 0.2979 0.0420 7.10 3.4e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.992 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 320s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 320s price 0.2207 0.0896 2.46 0.019 * 320s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 320s trend 0.2979 0.0420 7.10 3.4e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.55 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 320s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 320s 320s [1] 40 320s [1] "*************** W3SLS with restriction *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 173 1.24 0.677 0.725 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 68.1 4.00 2.00 0.746 0.716 320s supply 20 16 105.2 6.57 2.56 0.608 0.534 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.93 4.56 320s supply 4.56 6.15 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 4.00 5.01 320s supply 5.01 6.57 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.976 320s supply 0.976 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 320s price -0.2194 0.0954 -2.3 0.028 * 320s income 0.2938 0.0445 6.6 1.4e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.001 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 320s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 320s price 0.2184 0.1003 2.18 0.036 * 320s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 320s trend 0.2938 0.0445 6.60 1.4e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.564 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 320s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 320s 320s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 173 1.27 0.678 0.722 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.8 3.99 2.00 0.747 0.717 320s supply 20 16 104.8 6.55 2.56 0.609 0.536 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.97 4.55 320s supply 4.55 6.13 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.99 4.98 320s supply 4.98 6.55 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.975 320s supply 0.975 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 320s price -0.222 0.096 -2.31 0.027 * 320s income 0.296 0.045 6.57 1.6e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.997 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 320s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 320s price 0.2193 0.1002 2.19 0.036 * 320s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 320s trend 0.2956 0.0450 6.57 1.6e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.559 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 320s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 320s 320s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 171 0.887 0.68 0.678 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.5 3.97 1.99 0.748 0.719 320s supply 20 16 104.0 6.50 2.55 0.612 0.539 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.37 3.75 320s supply 3.75 4.91 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.37 4.08 320s supply 4.08 5.20 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.974 320s supply 0.974 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 320s price -0.2243 0.0888 -2.53 0.016 * 320s income 0.2979 0.0420 7.10 3.4e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.992 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 320s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 320s price 0.2207 0.0896 2.46 0.019 * 320s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 320s trend 0.2979 0.0420 7.10 3.4e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.55 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 320s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 320s 320s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 172 0.873 0.679 0.681 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.7 3.98 2.00 0.748 0.718 320s supply 20 16 104.3 6.52 2.55 0.611 0.538 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.35 3.76 320s supply 3.76 4.92 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.38 4.10 320s supply 4.10 5.22 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.975 320s supply 0.975 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 320s price -0.2225 0.0883 -2.52 0.017 * 320s income 0.2964 0.0416 7.13 3.1e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.995 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 320s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 320s price 0.2201 0.0897 2.45 0.019 * 320s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 320s trend 0.2964 0.0416 7.13 3.1e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.553 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 320s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 320s 320s [1] "*************** 3SLS with 2 restrictions **********************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 171 1.74 0.681 0.696 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.8 3.87 1.97 0.755 0.726 320s supply 20 16 105.4 6.59 2.57 0.607 0.533 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.89 4.53 320s supply 4.53 6.25 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 4.87 320s supply 4.87 6.59 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 320s price -0.2457 0.0891 -2.76 0.0092 ** 320s income 0.3236 0.0233 13.91 8.9e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.967 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 320s price 0.2543 0.0891 2.85 0.0072 ** 320s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 320s trend 0.3236 0.0233 13.91 8.9e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.566 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 320s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 320s 320s [1] "Component “call”: target, current do not match when deparsed" 320s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 170 1.19 0.683 0.658 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.6 3.86 1.96 0.755 0.727 320s supply 20 16 104.6 6.54 2.56 0.610 0.537 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.30 3.73 320s supply 3.73 5.00 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.28 4.00 320s supply 4.00 5.23 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 320s price -0.2494 0.0812 -3.07 0.0041 ** 320s income 0.3248 0.0209 15.57 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.964 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 320s price 0.2506 0.0812 3.09 0.0039 ** 320s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 320s trend 0.3248 0.0209 15.57 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.557 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 320s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 320s 320s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 172 1.74 0.68 0.697 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.9 3.88 1.97 0.754 0.725 320s supply 20 16 105.7 6.60 2.57 0.606 0.532 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.88 4.55 320s supply 4.55 6.27 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.88 4.88 320s supply 4.88 6.60 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 320s price -0.2443 0.0892 -2.74 0.0096 ** 320s income 0.3234 0.0229 14.14 4.4e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.969 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 320s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 320s price 0.2557 0.0892 2.87 0.0069 ** 320s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 320s trend 0.3234 0.0229 14.14 4.4e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.57 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 320s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 320s 320s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 171 1.74 0.681 0.696 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.8 3.87 1.97 0.755 0.726 320s supply 20 16 105.4 6.59 2.57 0.607 0.533 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.89 4.53 320s supply 4.53 6.25 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 4.87 320s supply 4.87 6.59 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 320s price -0.2457 0.0891 -2.76 0.0092 ** 320s income 0.3236 0.0233 13.91 8.9e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.967 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 320s price 0.2543 0.0891 2.85 0.0072 ** 320s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 320s trend 0.3236 0.0233 13.91 8.9e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.566 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 320s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 320s 320s [1] "Component “call”: target, current do not match when deparsed" 320s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 170 1.19 0.683 0.658 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.6 3.86 1.96 0.755 0.727 320s supply 20 16 104.6 6.54 2.56 0.610 0.537 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.30 3.73 320s supply 3.73 5.00 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.28 4.00 320s supply 4.00 5.23 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 320s price -0.2494 0.0812 -3.07 0.0041 ** 320s income 0.3248 0.0209 15.57 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.964 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 320s price 0.2506 0.0812 3.09 0.0039 ** 320s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 320s trend 0.3248 0.0209 15.57 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.557 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 320s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 320s 320s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 170 1.19 0.682 0.659 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.6 3.86 1.97 0.755 0.726 320s supply 20 16 104.8 6.55 2.56 0.609 0.536 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.30 3.75 320s supply 3.75 5.01 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.28 4.00 320s supply 4.00 5.24 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 320s price -0.2484 0.0812 -3.06 0.0042 ** 320s income 0.3246 0.0205 15.81 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.965 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 320s price 0.2516 0.0812 3.10 0.0038 ** 320s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 320s trend 0.3246 0.0205 15.81 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.559 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 320s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 320s 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 36 3690 5613 0.012 0.368 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s eq1 20 19 2132 112.2 10.59 0.305 0.305 320s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 320s 320s The covariance matrix of the residuals used for estimation 320s eq1 eq2 320s eq1 112.2 -44.8 320s eq2 -44.8 56.8 320s 320s The covariance matrix of the residuals 320s eq1 eq2 320s eq1 112.2 -68.3 320s eq2 -68.3 91.7 320s 320s The correlations of the residuals 320s eq1 eq2 320s eq1 1.000 -0.674 320s eq2 -0.674 1.000 320s 320s 320s 3SLS estimates for 'eq1' (equation 1) 320s Model Formula: farmPrice ~ consump - 1 320s Instruments: ~trend + income 320s 320s Estimate Std. Error t value Pr(>|t|) 320s consump 0.9588 0.0235 40.9 <2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 10.592 on 19 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 19 320s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 320s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 320s 320s 320s 3SLS estimates for 'eq2' (equation 2) 320s Model Formula: price ~ consump + trend 320s Instruments: ~trend + income 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) -92.192 49.896 -1.85 0.0821 . 320s consump 1.953 0.499 3.92 0.0011 ** 320s trend -0.469 0.247 -1.90 0.0743 . 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 9.574 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 320s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 320s 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 38 56326 283068 -104 -10.6 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s eq1 20 19 2313 122 11.0 -7.63 -7.63 320s eq2 20 19 54013 2843 53.3 -200.46 -200.46 320s 320s The covariance matrix of the residuals used for estimation 320s eq1 eq2 320s eq1 121 -255 320s eq2 -255 2953 320s 320s The covariance matrix of the residuals 320s eq1 eq2 320s eq1 122 -251 320s eq2 -251 2843 320s 320s The correlations of the residuals 320s eq1 eq2 320s eq1 1.000 -0.433 320s eq2 -0.433 1.000 320s 320s 320s 3SLS estimates for 'eq1' (equation 1) 320s Model Formula: consump ~ farmPrice - 1 320s Instruments: ~price + income 320s 320s Estimate Std. Error t value Pr(>|t|) 320s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 11.034 on 19 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 19 320s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 320s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 320s 320s 320s 3SLS estimates for 'eq2' (equation 2) 320s Model Formula: consump ~ trend - 1 320s Instruments: ~price + income 320s 320s Estimate Std. Error t value Pr(>|t|) 320s trend 9.02 1.13 8 1.7e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 53.318 on 19 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 19 320s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 320s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 320s 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 38 167069 397886 -49.1 -0.82 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s eq1 20 19 76692 4036 63.5 -285.0 -285.0 320s eq2 20 19 90377 4757 69.0 -28.5 -28.5 320s 320s The covariance matrix of the residuals used for estimation 320s eq1 eq2 320s eq1 2682 2547 320s eq2 2547 2741 320s 320s The covariance matrix of the residuals 320s eq1 eq2 320s eq1 4036 4336 320s eq2 4336 4757 320s 320s The correlations of the residuals 320s eq1 eq2 320s eq1 1.000 0.928 320s eq2 0.928 1.000 320s 320s 320s 3SLS estimates for 'eq1' (equation 1) 320s Model Formula: consump ~ trend - 1 320s Instruments: ~income + farmPrice 320s 320s Estimate Std. Error t value Pr(>|t|) 320s trend 4.162 0.723 5.75 1.5e-05 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 63.533 on 19 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 19 320s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 320s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 320s 320s 320s 3SLS estimates for 'eq2' (equation 2) 320s Model Formula: farmPrice ~ trend - 1 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s trend 3.274 0.676 4.84 0.00011 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 68.969 on 19 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 19 320s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 320s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 320s 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 39 161126 1162329 -171 -17.4 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s eq1 20 19 3553 187 13.7 -12.3 -12.3 320s eq2 20 19 157573 8293 91.1 -235.2 -235.2 320s 320s The covariance matrix of the residuals used for estimation 320s eq1 eq2 320s eq1 208 -731 320s eq2 -731 8271 320s 320s The covariance matrix of the residuals 320s eq1 eq2 320s eq1 187 -623 320s eq2 -623 8293 320s 320s The correlations of the residuals 320s eq1 eq2 320s eq1 1.000 -0.121 320s eq2 -0.121 1.000 320s 320s 320s 3SLS estimates for 'eq1' (equation 1) 320s Model Formula: consump ~ farmPrice - 1 320s Instruments: ~farmPrice + trend + income 320s 320s Estimate Std. Error t value Pr(>|t|) 320s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 13.675 on 19 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 19 320s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 320s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 320s 320s 320s 3SLS estimates for 'eq2' (equation 2) 320s Model Formula: price ~ trend - 1 320s Instruments: ~farmPrice + trend + income 320s 320s Estimate Std. Error t value Pr(>|t|) 320s trend 1.1122 0.0272 40.8 <2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 91.068 on 19 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 19 320s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 320s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 320s 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 38 935 491 0 0 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s eq1 20 19 268 14.1 3.76 0 0 320s eq2 20 19 667 35.1 5.93 0 0 320s 320s The covariance matrix of the residuals used for estimation 320s eq1 eq2 320s eq1 14.11 2.18 320s eq2 2.18 35.12 320s 320s The covariance matrix of the residuals 320s eq1 eq2 320s eq1 14.11 2.18 320s eq2 2.18 35.12 320s 320s The correlations of the residuals 320s eq1 eq2 320s eq1 1.0000 0.0981 320s eq2 0.0981 1.0000 320s 320s 320s 3SLS estimates for 'eq1' (equation 1) 320s Model Formula: consump ~ 1 320s Instruments: ~income 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 100.90 0.84 120 <2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 3.756 on 19 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 19 320s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 320s Multiple R-Squared: 0 Adjusted R-Squared: 0 320s 320s 320s 3SLS estimates for 'eq2' (equation 2) 320s Model Formula: price ~ 1 320s Instruments: ~income 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 100.02 1.33 75.5 <2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 5.926 on 19 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 19 320s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 320s Multiple R-Squared: 0 Adjusted R-Squared: 0 320s 320s [1] "***************************************************" 320s [1] "3SLS formula: IV" 320s [1] "************* 3SLS *********************************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 33 174 1.03 0.676 0.786 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.7 3.87 1.97 0.755 0.726 320s supply 20 16 107.9 6.75 2.60 0.598 0.522 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.87 4.36 320s supply 4.36 6.04 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 5.00 320s supply 5.00 6.74 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.00 0.98 320s supply 0.98 1.00 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 320s price -0.2436 0.0965 -2.52 0.022 * 320s income 0.3140 0.0469 6.69 3.8e-06 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.966 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 320s price 0.2286 0.0997 2.29 0.03571 * 320s farmPrice 0.2282 0.0440 5.19 9e-05 *** 320s trend 0.3611 0.0729 4.95 0.00014 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.597 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 320s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 320s 320s [1] "********************* 3SLS EViews-like *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 33 173 0.719 0.677 0.748 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.7 3.87 1.97 0.755 0.726 320s supply 20 16 107.2 6.70 2.59 0.600 0.525 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.29 3.59 320s supply 3.59 4.83 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.29 4.11 320s supply 4.11 5.36 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.979 320s supply 0.979 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 320s price -0.2436 0.0890 -2.74 0.0099 ** 320s income 0.3140 0.0433 7.25 2.5e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.966 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 320s price 0.2289 0.0892 2.57 0.015 * 320s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 320s trend 0.3579 0.0652 5.49 4.3e-06 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.589 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 320s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 320s 320s [1] "********************* 3SLS with methodResidCov = Theil *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 33 174 -0.718 0.675 0.922 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.7 3.87 1.97 0.755 0.726 320s supply 20 16 108.7 6.79 2.61 0.594 0.518 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.87 4.50 320s supply 4.50 6.04 320s 320s warning: this covariance matrix is NOT positive semidefinit! 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 5.2 320s supply 5.20 6.8 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.981 320s supply 0.981 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 320s price -0.2436 0.0965 -2.52 0.017 * 320s income 0.3140 0.0469 6.69 1.3e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.966 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 320s price 0.2282 0.0997 2.29 0.02855 * 320s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 320s trend 0.3648 0.0707 5.16 1.1e-05 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.607 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 320s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 320s 320s [1] "*************** W3SLS with methodResidCov = Theil *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 33 174 -0.718 0.675 0.922 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.7 3.87 1.97 0.755 0.726 320s supply 20 16 108.7 6.79 2.61 0.594 0.518 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.87 4.50 320s supply 4.50 6.04 320s 320s warning: this covariance matrix is NOT positive semidefinit! 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 5.2 320s supply 5.20 6.8 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.981 320s supply 0.981 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 320s price -0.2436 0.0965 -2.52 0.017 * 320s income 0.3140 0.0469 6.69 1.3e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.966 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 320s price 0.2282 0.0997 2.29 0.02855 * 320s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 320s trend 0.3648 0.0707 5.16 1.1e-05 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.607 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 320s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 320s 320s [1] "*************** 3SLS with restriction *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 173 1.27 0.678 0.722 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.8 3.99 2.00 0.747 0.717 320s supply 20 16 104.8 6.55 2.56 0.609 0.536 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.97 4.55 320s supply 4.55 6.13 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.99 4.98 320s supply 4.98 6.55 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.975 320s supply 0.975 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 320s price -0.222 0.096 -2.31 0.027 * 320s income 0.296 0.045 6.57 1.6e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.997 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 320s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 320s price 0.2193 0.1002 2.19 0.036 * 320s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 320s trend 0.2956 0.0450 6.57 1.6e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.559 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 320s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 320s 320s [1] "Component “call”: target, current do not match when deparsed" 320s [1] "************** 3SLS with restriction (EViews-like) *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 171 0.887 0.68 0.678 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.5 3.97 1.99 0.748 0.719 320s supply 20 16 104.0 6.50 2.55 0.612 0.539 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.37 3.75 320s supply 3.75 4.91 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.37 4.08 320s supply 4.08 5.20 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.974 320s supply 0.974 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 320s price -0.2243 0.0888 -2.53 0.016 * 320s income 0.2979 0.0420 7.10 3.4e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.992 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 320s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 320s price 0.2207 0.0896 2.46 0.019 * 320s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 320s trend 0.2979 0.0420 7.10 3.4e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.55 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 320s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 320s 320s [1] 40 320s [1] "*************** W3SLS with restriction *****************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 173 1.24 0.677 0.725 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 68.1 4.00 2.00 0.746 0.716 320s supply 20 16 105.2 6.57 2.56 0.608 0.534 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.93 4.56 320s supply 4.56 6.15 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 4.00 5.01 320s supply 5.01 6.57 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.976 320s supply 0.976 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 320s price -0.2194 0.0954 -2.3 0.028 * 320s income 0.2938 0.0445 6.6 1.4e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.001 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 320s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 320s price 0.2184 0.1003 2.18 0.036 * 320s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 320s trend 0.2938 0.0445 6.60 1.4e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.564 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 320s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 320s 320s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 173 1.27 0.678 0.722 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.8 3.99 2.00 0.747 0.717 320s supply 20 16 104.8 6.55 2.56 0.609 0.536 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.97 4.55 320s supply 4.55 6.13 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.99 4.98 320s supply 4.98 6.55 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.975 320s supply 0.975 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 320s price -0.222 0.096 -2.31 0.027 * 320s income 0.296 0.045 6.57 1.6e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.997 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 320s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 320s price 0.2193 0.1002 2.19 0.036 * 320s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 320s trend 0.2956 0.0450 6.57 1.6e-07 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.559 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 320s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 320s 320s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 171 0.887 0.68 0.678 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.5 3.97 1.99 0.748 0.719 320s supply 20 16 104.0 6.50 2.55 0.612 0.539 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.37 3.75 320s supply 3.75 4.91 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.37 4.08 320s supply 4.08 5.20 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.974 320s supply 0.974 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 320s price -0.2243 0.0888 -2.53 0.016 * 320s income 0.2979 0.0420 7.10 3.4e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.992 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 320s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 320s price 0.2207 0.0896 2.46 0.019 * 320s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 320s trend 0.2979 0.0420 7.10 3.4e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.55 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 320s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 320s 320s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 34 172 0.873 0.679 0.681 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 67.7 3.98 2.00 0.748 0.718 320s supply 20 16 104.3 6.52 2.55 0.611 0.538 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.35 3.76 320s supply 3.76 4.92 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.38 4.10 320s supply 4.10 5.22 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.975 320s supply 0.975 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 320s price -0.2225 0.0883 -2.52 0.017 * 320s income 0.2964 0.0416 7.13 3.1e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.995 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 320s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 320s price 0.2201 0.0897 2.45 0.019 * 320s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 320s trend 0.2964 0.0416 7.13 3.1e-08 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.553 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 320s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 320s 320s [1] "*************** 3SLS with 2 restrictions **********************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 171 1.74 0.681 0.696 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.8 3.87 1.97 0.755 0.726 320s supply 20 16 105.4 6.59 2.57 0.607 0.533 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.89 4.53 320s supply 4.53 6.25 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 4.87 320s supply 4.87 6.59 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 320s price -0.2457 0.0891 -2.76 0.0092 ** 320s income 0.3236 0.0233 13.91 8.9e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.967 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 320s price 0.2543 0.0891 2.85 0.0072 ** 320s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 320s trend 0.3236 0.0233 13.91 8.9e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.566 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 320s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 320s 320s [1] "Component “call”: target, current do not match when deparsed" 320s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 170 1.19 0.683 0.658 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.6 3.86 1.96 0.755 0.727 320s supply 20 16 104.6 6.54 2.56 0.610 0.537 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.30 3.73 320s supply 3.73 5.00 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.28 4.00 320s supply 4.00 5.23 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 320s price -0.2494 0.0812 -3.07 0.0041 ** 320s income 0.3248 0.0209 15.57 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.964 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 320s price 0.2506 0.0812 3.09 0.0039 ** 320s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 320s trend 0.3248 0.0209 15.57 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.557 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 320s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 320s 320s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 172 1.74 0.68 0.697 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.9 3.88 1.97 0.754 0.725 320s supply 20 16 105.7 6.60 2.57 0.606 0.532 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.88 4.55 320s supply 4.55 6.27 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.88 4.88 320s supply 4.88 6.60 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 320s price -0.2443 0.0892 -2.74 0.0096 ** 320s income 0.3234 0.0229 14.14 4.4e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.969 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 320s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 320s price 0.2557 0.0892 2.87 0.0069 ** 320s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 320s trend 0.3234 0.0229 14.14 4.4e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.57 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 320s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 320s 320s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 171 1.74 0.681 0.696 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.8 3.87 1.97 0.755 0.726 320s supply 20 16 105.4 6.59 2.57 0.607 0.533 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.89 4.53 320s supply 4.53 6.25 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.87 4.87 320s supply 4.87 6.59 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 320s price -0.2457 0.0891 -2.76 0.0092 ** 320s income 0.3236 0.0233 13.91 8.9e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.967 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 320s price 0.2543 0.0891 2.85 0.0072 ** 320s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 320s trend 0.3236 0.0233 13.91 8.9e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.566 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 320s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 320s 320s [1] "Component “call”: target, current do not match when deparsed" 320s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 320s 320s systemfit results 320s method: 3SLS 320s 320s N DF SSR detRCov OLS-R2 McElroy-R2 320s system 40 35 170 1.19 0.683 0.658 320s 320s N DF SSR MSE RMSE R2 Adj R2 320s demand 20 17 65.6 3.86 1.96 0.755 0.727 320s supply 20 16 104.6 6.54 2.56 0.610 0.537 320s 320s The covariance matrix of the residuals used for estimation 320s demand supply 320s demand 3.30 3.73 320s supply 3.73 5.00 320s 320s The covariance matrix of the residuals 320s demand supply 320s demand 3.28 4.00 320s supply 4.00 5.23 320s 320s The correlations of the residuals 320s demand supply 320s demand 1.000 0.965 320s supply 0.965 1.000 320s 320s 320s 3SLS estimates for 'demand' (equation 1) 320s Model Formula: consump ~ price + income 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 320s price -0.2494 0.0812 -3.07 0.0041 ** 320s income 0.3248 0.0209 15.57 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 1.964 on 17 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 17 320s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 320s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 320s 320s 320s 3SLS estimates for 'supply' (equation 2) 320s Model Formula: consump ~ price + farmPrice + trend 320s Instruments: ~income + farmPrice + trend 320s 320s Estimate Std. Error t value Pr(>|t|) 320s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 320s price 0.2506 0.0812 3.09 0.0039 ** 320s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 320s trend 0.3248 0.0209 15.57 < 2e-16 *** 320s --- 320s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 320s 320s Residual standard error: 2.557 on 16 degrees of freedom 320s Number of observations: 20 Degrees of Freedom: 16 320s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 320s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 320s 320s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 170 1.19 0.682 0.659 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.6 3.86 1.97 0.755 0.726 321s supply 20 16 104.8 6.55 2.56 0.609 0.536 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.75 321s supply 3.75 5.01 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.28 4.00 321s supply 4.00 5.24 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 321s price -0.2484 0.0812 -3.06 0.0042 ** 321s income 0.3246 0.0205 15.81 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.965 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 321s price 0.2516 0.0812 3.10 0.0038 ** 321s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 321s trend 0.3246 0.0205 15.81 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.559 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 321s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 36 3690 5613 0.012 0.368 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 2132 112.2 10.59 0.305 0.305 321s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 112.2 -44.8 321s eq2 -44.8 56.8 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 112.2 -68.3 321s eq2 -68.3 91.7 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.674 321s eq2 -0.674 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: farmPrice ~ consump - 1 321s Instruments: ~trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s consump 0.9588 0.0235 40.9 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 10.592 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 321s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ consump + trend 321s Instruments: ~trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) -92.192 49.896 -1.85 0.0821 . 321s consump 1.953 0.499 3.92 0.0011 ** 321s trend -0.469 0.247 -1.90 0.0743 . 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 9.574 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 321s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 56326 283068 -104 -10.6 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 2313 122 11.0 -7.63 -7.63 321s eq2 20 19 54013 2843 53.3 -200.46 -200.46 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 121 -255 321s eq2 -255 2953 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 122 -251 321s eq2 -251 2843 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.433 321s eq2 -0.433 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ farmPrice - 1 321s Instruments: ~price + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 11.034 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 321s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: consump ~ trend - 1 321s Instruments: ~price + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 9.02 1.13 8 1.7e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 53.318 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 321s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 167069 397886 -49.1 -0.82 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 76692 4036 63.5 -285.0 -285.0 321s eq2 20 19 90377 4757 69.0 -28.5 -28.5 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 2682 2547 321s eq2 2547 2741 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 4036 4336 321s eq2 4336 4757 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 0.928 321s eq2 0.928 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ trend - 1 321s Instruments: ~income + farmPrice 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 4.162 0.723 5.75 1.5e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 63.533 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 321s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: farmPrice ~ trend - 1 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 3.274 0.676 4.84 0.00011 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 68.969 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 321s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 39 161126 1162329 -171 -17.4 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 3553 187 13.7 -12.3 -12.3 321s eq2 20 19 157573 8293 91.1 -235.2 -235.2 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 208 -731 321s eq2 -731 8271 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 187 -623 321s eq2 -623 8293 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.121 321s eq2 -0.121 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ farmPrice - 1 321s Instruments: ~farmPrice + trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 13.675 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 321s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ trend - 1 321s Instruments: ~farmPrice + trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 1.1122 0.0272 40.8 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 91.068 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 321s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 935 491 0 0 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 268 14.1 3.76 0 0 321s eq2 20 19 667 35.1 5.93 0 0 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 14.11 2.18 321s eq2 2.18 35.12 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 14.11 2.18 321s eq2 2.18 35.12 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.0000 0.0981 321s eq2 0.0981 1.0000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ 1 321s Instruments: ~income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 100.90 0.84 120 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.756 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 321s Multiple R-Squared: 0 Adjusted R-Squared: 0 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ 1 321s Instruments: ~income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 100.02 1.33 75.5 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 5.926 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 321s Multiple R-Squared: 0 Adjusted R-Squared: 0 321s 321s [1] "***************************************************" 321s [1] "3SLS formula: Schmidt" 321s [1] "************* 3SLS *********************************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 174 1.03 0.676 0.786 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 107.9 6.75 2.60 0.598 0.522 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 4.36 321s supply 4.36 6.04 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.00 321s supply 5.00 6.74 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.00 0.98 321s supply 0.98 1.00 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 321s price -0.2436 0.0965 -2.52 0.022 * 321s income 0.3140 0.0469 6.69 3.8e-06 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 321s price 0.2286 0.0997 2.29 0.03571 * 321s farmPrice 0.2282 0.0440 5.19 9e-05 *** 321s trend 0.3611 0.0729 4.95 0.00014 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.597 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 321s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 321s 321s [1] "********************* 3SLS EViews-like *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 173 0.719 0.677 0.748 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 107.2 6.70 2.59 0.600 0.525 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.29 3.59 321s supply 3.59 4.83 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.29 4.11 321s supply 4.11 5.36 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.979 321s supply 0.979 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 321s price -0.2436 0.0890 -2.74 0.0099 ** 321s income 0.3140 0.0433 7.25 2.5e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 321s price 0.2289 0.0892 2.57 0.015 * 321s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 321s trend 0.3579 0.0652 5.49 4.3e-06 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.589 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 321s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 321s 321s [1] "********************* 3SLS with methodResidCov = Theil *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 174 -0.718 0.675 0.922 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 108.7 6.79 2.61 0.594 0.518 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 4.50 321s supply 4.50 6.04 321s 321s warning: this covariance matrix is NOT positive semidefinit! 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.2 321s supply 5.20 6.8 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.981 321s supply 0.981 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 321s price -0.2436 0.0965 -2.52 0.017 * 321s income 0.3140 0.0469 6.69 1.3e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 321s price 0.2282 0.0997 2.29 0.02855 * 321s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 321s trend 0.3648 0.0707 5.16 1.1e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.607 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 321s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 321s 321s [1] "*************** W3SLS with methodResidCov = Theil *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 174 -0.718 0.675 0.922 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 108.7 6.79 2.61 0.594 0.518 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 4.50 321s supply 4.50 6.04 321s 321s warning: this covariance matrix is NOT positive semidefinit! 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.2 321s supply 5.20 6.8 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.981 321s supply 0.981 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 321s price -0.2436 0.0965 -2.52 0.017 * 321s income 0.3140 0.0469 6.69 1.3e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 321s price 0.2282 0.0997 2.29 0.02855 * 321s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 321s trend 0.3648 0.0707 5.16 1.1e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.607 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 321s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 321s 321s [1] "*************** 3SLS with restriction *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 173 1.27 0.678 0.722 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.8 3.99 2.00 0.747 0.717 321s supply 20 16 104.8 6.55 2.56 0.609 0.536 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.97 4.55 321s supply 4.55 6.13 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.99 4.98 321s supply 4.98 6.55 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.975 321s supply 0.975 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 321s price -0.222 0.096 -2.31 0.027 * 321s income 0.296 0.045 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.997 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 321s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 321s price 0.2193 0.1002 2.19 0.036 * 321s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 321s trend 0.2956 0.0450 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.559 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 321s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 321s 321s [1] "Component “call”: target, current do not match when deparsed" 321s [1] "************** 3SLS with restriction (EViews-like) *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 171 0.887 0.68 0.678 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.5 3.97 1.99 0.748 0.719 321s supply 20 16 104.0 6.50 2.55 0.612 0.539 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.37 3.75 321s supply 3.75 4.91 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.37 4.08 321s supply 4.08 5.20 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.974 321s supply 0.974 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 321s price -0.2243 0.0888 -2.53 0.016 * 321s income 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.992 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 321s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 321s price 0.2207 0.0896 2.46 0.019 * 321s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 321s trend 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.55 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 321s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 321s 321s [1] 40 321s [1] "*************** W3SLS with restriction *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 173 1.24 0.677 0.725 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 68.1 4.00 2.00 0.746 0.716 321s supply 20 16 105.2 6.57 2.56 0.608 0.534 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.93 4.56 321s supply 4.56 6.15 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 4.00 5.01 321s supply 5.01 6.57 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.976 321s supply 0.976 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 321s price -0.2194 0.0954 -2.3 0.028 * 321s income 0.2938 0.0445 6.6 1.4e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.001 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 321s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 321s price 0.2184 0.1003 2.18 0.036 * 321s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 321s trend 0.2938 0.0445 6.60 1.4e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.564 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 321s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 321s 321s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 173 1.27 0.678 0.722 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.8 3.99 2.00 0.747 0.717 321s supply 20 16 104.8 6.55 2.56 0.609 0.536 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.97 4.55 321s supply 4.55 6.13 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.99 4.98 321s supply 4.98 6.55 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.975 321s supply 0.975 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 321s price -0.222 0.096 -2.31 0.027 * 321s income 0.296 0.045 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.997 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 321s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 321s price 0.2193 0.1002 2.19 0.036 * 321s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 321s trend 0.2956 0.0450 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.559 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 321s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 321s 321s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 171 0.887 0.68 0.678 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.5 3.97 1.99 0.748 0.719 321s supply 20 16 104.0 6.50 2.55 0.612 0.539 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.37 3.75 321s supply 3.75 4.91 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.37 4.08 321s supply 4.08 5.20 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.974 321s supply 0.974 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 321s price -0.2243 0.0888 -2.53 0.016 * 321s income 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.992 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 321s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 321s price 0.2207 0.0896 2.46 0.019 * 321s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 321s trend 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.55 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 321s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 321s 321s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 172 0.873 0.679 0.681 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.7 3.98 2.00 0.748 0.718 321s supply 20 16 104.3 6.52 2.55 0.611 0.538 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.35 3.76 321s supply 3.76 4.92 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.38 4.10 321s supply 4.10 5.22 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.975 321s supply 0.975 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 321s price -0.2225 0.0883 -2.52 0.017 * 321s income 0.2964 0.0416 7.13 3.1e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.995 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 321s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 321s price 0.2201 0.0897 2.45 0.019 * 321s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 321s trend 0.2964 0.0416 7.13 3.1e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.553 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 321s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 321s 321s [1] "*************** 3SLS with 2 restrictions **********************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 171 1.74 0.681 0.696 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.8 3.87 1.97 0.755 0.726 321s supply 20 16 105.4 6.59 2.57 0.607 0.533 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.89 4.53 321s supply 4.53 6.25 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 4.87 321s supply 4.87 6.59 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 321s price -0.2457 0.0891 -2.76 0.0092 ** 321s income 0.3236 0.0233 13.91 8.9e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.967 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 321s price 0.2543 0.0891 2.85 0.0072 ** 321s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 321s trend 0.3236 0.0233 13.91 8.9e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.566 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 321s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 321s 321s [1] "Component “call”: target, current do not match when deparsed" 321s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 170 1.19 0.683 0.658 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.6 3.86 1.96 0.755 0.727 321s supply 20 16 104.6 6.54 2.56 0.610 0.537 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.73 321s supply 3.73 5.00 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.28 4.00 321s supply 4.00 5.23 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 321s price -0.2494 0.0812 -3.07 0.0041 ** 321s income 0.3248 0.0209 15.57 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.964 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 321s price 0.2506 0.0812 3.09 0.0039 ** 321s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 321s trend 0.3248 0.0209 15.57 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.557 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 321s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 321s 321s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 172 1.74 0.68 0.697 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.9 3.88 1.97 0.754 0.725 321s supply 20 16 105.7 6.60 2.57 0.606 0.532 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.88 4.55 321s supply 4.55 6.27 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.88 4.88 321s supply 4.88 6.60 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 321s price -0.2443 0.0892 -2.74 0.0096 ** 321s income 0.3234 0.0229 14.14 4.4e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.969 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 321s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 321s price 0.2557 0.0892 2.87 0.0069 ** 321s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 321s trend 0.3234 0.0229 14.14 4.4e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.57 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 321s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 321s 321s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 171 1.74 0.681 0.696 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.8 3.87 1.97 0.755 0.726 321s supply 20 16 105.4 6.59 2.57 0.607 0.533 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.89 4.53 321s supply 4.53 6.25 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 4.87 321s supply 4.87 6.59 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 321s price -0.2457 0.0891 -2.76 0.0092 ** 321s income 0.3236 0.0233 13.91 8.9e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.967 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 321s price 0.2543 0.0891 2.85 0.0072 ** 321s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 321s trend 0.3236 0.0233 13.91 8.9e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.566 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 321s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 321s 321s [1] "Component “call”: target, current do not match when deparsed" 321s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 170 1.19 0.683 0.658 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.6 3.86 1.96 0.755 0.727 321s supply 20 16 104.6 6.54 2.56 0.610 0.537 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.73 321s supply 3.73 5.00 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.28 4.00 321s supply 4.00 5.23 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 321s price -0.2494 0.0812 -3.07 0.0041 ** 321s income 0.3248 0.0209 15.57 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.964 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 321s price 0.2506 0.0812 3.09 0.0039 ** 321s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 321s trend 0.3248 0.0209 15.57 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.557 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 321s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 321s 321s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 170 1.19 0.682 0.659 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.6 3.86 1.97 0.755 0.726 321s supply 20 16 104.8 6.55 2.56 0.609 0.536 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.75 321s supply 3.75 5.01 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.28 4.00 321s supply 4.00 5.24 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 321s price -0.2484 0.0812 -3.06 0.0042 ** 321s income 0.3246 0.0205 15.81 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.965 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 321s price 0.2516 0.0812 3.10 0.0038 ** 321s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 321s trend 0.3246 0.0205 15.81 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.559 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 321s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 36 3690 5613 0.012 0.368 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 2132 112.2 10.59 0.305 0.305 321s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 112.2 -44.8 321s eq2 -44.8 56.8 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 112.2 -68.3 321s eq2 -68.3 91.7 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.674 321s eq2 -0.674 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: farmPrice ~ consump - 1 321s Instruments: ~trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s consump 0.9588 0.0235 40.9 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 10.592 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 321s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ consump + trend 321s Instruments: ~trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) -92.192 49.896 -1.85 0.0821 . 321s consump 1.953 0.499 3.92 0.0011 ** 321s trend -0.469 0.247 -1.90 0.0743 . 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 9.574 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 321s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 56326 283068 -104 -10.6 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 2313 122 11.0 -7.63 -7.63 321s eq2 20 19 54013 2843 53.3 -200.46 -200.46 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 121 -255 321s eq2 -255 2953 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 122 -251 321s eq2 -251 2843 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.433 321s eq2 -0.433 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ farmPrice - 1 321s Instruments: ~price + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 11.034 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 321s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: consump ~ trend - 1 321s Instruments: ~price + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 9.02 1.13 8 1.7e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 53.318 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 321s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 167069 397886 -49.1 -0.82 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 76692 4036 63.5 -285.0 -285.0 321s eq2 20 19 90377 4757 69.0 -28.5 -28.5 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 2682 2547 321s eq2 2547 2741 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 4036 4336 321s eq2 4336 4757 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 0.928 321s eq2 0.928 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ trend - 1 321s Instruments: ~income + farmPrice 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 4.162 0.723 5.75 1.5e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 63.533 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 321s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: farmPrice ~ trend - 1 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 3.274 0.676 4.84 0.00011 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 68.969 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 321s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 39 161126 1162329 -171 -17.4 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 3553 187 13.7 -12.3 -12.3 321s eq2 20 19 157573 8293 91.1 -235.2 -235.2 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 208 -731 321s eq2 -731 8271 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 187 -623 321s eq2 -623 8293 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.121 321s eq2 -0.121 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ farmPrice - 1 321s Instruments: ~farmPrice + trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 13.675 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 321s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ trend - 1 321s Instruments: ~farmPrice + trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 1.1122 0.0272 40.8 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 91.068 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 321s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 935 491 0 0 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 268 14.1 3.76 0 0 321s eq2 20 19 667 35.1 5.93 0 0 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 14.11 2.18 321s eq2 2.18 35.12 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 14.11 2.18 321s eq2 2.18 35.12 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.0000 0.0981 321s eq2 0.0981 1.0000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ 1 321s Instruments: ~income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 100.90 0.84 120 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.756 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 321s Multiple R-Squared: 0 Adjusted R-Squared: 0 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ 1 321s Instruments: ~income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 100.02 1.33 75.5 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 5.926 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 321s Multiple R-Squared: 0 Adjusted R-Squared: 0 321s 321s [1] "***************************************************" 321s [1] "3SLS formula: GMM" 321s [1] "************* 3SLS *********************************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 174 1.03 0.676 0.786 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 107.9 6.75 2.60 0.598 0.522 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 4.36 321s supply 4.36 6.04 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.00 321s supply 5.00 6.74 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.00 0.98 321s supply 0.98 1.00 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 321s price -0.2436 0.0965 -2.52 0.022 * 321s income 0.3140 0.0469 6.69 3.8e-06 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 321s price 0.2286 0.0997 2.29 0.03571 * 321s farmPrice 0.2282 0.0440 5.19 9e-05 *** 321s trend 0.3611 0.0729 4.95 0.00014 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.597 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 321s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 321s 321s [1] "********************* 3SLS EViews-like *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 173 0.719 0.677 0.748 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 107.2 6.70 2.59 0.600 0.525 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.29 3.59 321s supply 3.59 4.83 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.29 4.11 321s supply 4.11 5.36 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.979 321s supply 0.979 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 321s price -0.2436 0.0890 -2.74 0.0099 ** 321s income 0.3140 0.0433 7.25 2.5e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 321s price 0.2289 0.0892 2.57 0.015 * 321s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 321s trend 0.3579 0.0652 5.49 4.3e-06 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.589 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 321s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 321s 321s [1] "********************* 3SLS with methodResidCov = Theil *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 174 -0.718 0.675 0.922 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 108.7 6.79 2.61 0.594 0.518 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 4.50 321s supply 4.50 6.04 321s 321s warning: this covariance matrix is NOT positive semidefinit! 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.2 321s supply 5.20 6.8 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.981 321s supply 0.981 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 321s price -0.2436 0.0965 -2.52 0.017 * 321s income 0.3140 0.0469 6.69 1.3e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 321s price 0.2282 0.0997 2.29 0.02855 * 321s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 321s trend 0.3648 0.0707 5.16 1.1e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.607 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 321s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 321s 321s [1] "*************** W3SLS with methodResidCov = Theil *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 174 -0.718 0.675 0.922 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 108.7 6.79 2.61 0.594 0.518 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 4.50 321s supply 4.50 6.04 321s 321s warning: this covariance matrix is NOT positive semidefinit! 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.2 321s supply 5.20 6.8 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.981 321s supply 0.981 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 321s price -0.2436 0.0965 -2.52 0.017 * 321s income 0.3140 0.0469 6.69 1.3e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 321s price 0.2282 0.0997 2.29 0.02855 * 321s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 321s trend 0.3648 0.0707 5.16 1.1e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.607 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 321s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 321s 321s [1] "*************** 3SLS with restriction *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 173 1.27 0.678 0.722 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.8 3.99 2.00 0.747 0.717 321s supply 20 16 104.8 6.55 2.56 0.609 0.536 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.97 4.55 321s supply 4.55 6.13 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.99 4.98 321s supply 4.98 6.55 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.975 321s supply 0.975 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 321s price -0.222 0.096 -2.31 0.027 * 321s income 0.296 0.045 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.997 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 321s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 321s price 0.2193 0.1002 2.19 0.036 * 321s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 321s trend 0.2956 0.0450 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.559 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 321s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 321s 321s [1] "Component “call”: target, current do not match when deparsed" 321s [1] "************** 3SLS with restriction (EViews-like) *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 171 0.887 0.68 0.678 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.5 3.97 1.99 0.748 0.719 321s supply 20 16 104.0 6.50 2.55 0.612 0.539 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.37 3.75 321s supply 3.75 4.91 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.37 4.08 321s supply 4.08 5.20 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.974 321s supply 0.974 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 321s price -0.2243 0.0888 -2.53 0.016 * 321s income 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.992 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 321s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 321s price 0.2207 0.0896 2.46 0.019 * 321s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 321s trend 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.55 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 321s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 321s 321s [1] 40 321s [1] "*************** W3SLS with restriction *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 173 1.24 0.677 0.725 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 68.1 4.00 2.00 0.746 0.716 321s supply 20 16 105.2 6.57 2.56 0.608 0.534 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.93 4.56 321s supply 4.56 6.15 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 4.00 5.01 321s supply 5.01 6.57 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.976 321s supply 0.976 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 321s price -0.2194 0.0954 -2.3 0.028 * 321s income 0.2938 0.0445 6.6 1.4e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.001 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 321s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 321s price 0.2184 0.1003 2.18 0.036 * 321s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 321s trend 0.2938 0.0445 6.60 1.4e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.564 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 321s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 321s 321s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 173 1.27 0.678 0.722 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.8 3.99 2.00 0.747 0.717 321s supply 20 16 104.8 6.55 2.56 0.609 0.536 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.97 4.55 321s supply 4.55 6.13 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.99 4.98 321s supply 4.98 6.55 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.975 321s supply 0.975 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 321s price -0.222 0.096 -2.31 0.027 * 321s income 0.296 0.045 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.997 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 321s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 321s price 0.2193 0.1002 2.19 0.036 * 321s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 321s trend 0.2956 0.0450 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.559 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 321s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 321s 321s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 171 0.887 0.68 0.678 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.5 3.97 1.99 0.748 0.719 321s supply 20 16 104.0 6.50 2.55 0.612 0.539 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.37 3.75 321s supply 3.75 4.91 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.37 4.08 321s supply 4.08 5.20 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.974 321s supply 0.974 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 321s price -0.2243 0.0888 -2.53 0.016 * 321s income 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.992 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 321s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 321s price 0.2207 0.0896 2.46 0.019 * 321s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 321s trend 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.55 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 321s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 321s 321s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 172 0.873 0.679 0.681 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.7 3.98 2.00 0.748 0.718 321s supply 20 16 104.3 6.52 2.55 0.611 0.538 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.35 3.76 321s supply 3.76 4.92 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.38 4.10 321s supply 4.10 5.22 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.975 321s supply 0.975 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 321s price -0.2225 0.0883 -2.52 0.017 * 321s income 0.2964 0.0416 7.13 3.1e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.995 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 321s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 321s price 0.2201 0.0897 2.45 0.019 * 321s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 321s trend 0.2964 0.0416 7.13 3.1e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.553 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 321s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 321s 321s [1] "*************** 3SLS with 2 restrictions **********************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 171 1.74 0.681 0.696 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.8 3.87 1.97 0.755 0.726 321s supply 20 16 105.4 6.59 2.57 0.607 0.533 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.89 4.53 321s supply 4.53 6.25 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 4.87 321s supply 4.87 6.59 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 321s price -0.2457 0.0891 -2.76 0.0092 ** 321s income 0.3236 0.0233 13.91 8.9e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.967 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 321s price 0.2543 0.0891 2.85 0.0072 ** 321s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 321s trend 0.3236 0.0233 13.91 8.9e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.566 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 321s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 321s 321s [1] "Component “call”: target, current do not match when deparsed" 321s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 170 1.19 0.683 0.658 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.6 3.86 1.96 0.755 0.727 321s supply 20 16 104.6 6.54 2.56 0.610 0.537 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.73 321s supply 3.73 5.00 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.28 4.00 321s supply 4.00 5.23 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 321s price -0.2494 0.0812 -3.07 0.0041 ** 321s income 0.3248 0.0209 15.57 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.964 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 321s price 0.2506 0.0812 3.09 0.0039 ** 321s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 321s trend 0.3248 0.0209 15.57 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.557 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 321s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 321s 321s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 172 1.74 0.68 0.697 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.9 3.88 1.97 0.754 0.725 321s supply 20 16 105.7 6.60 2.57 0.606 0.532 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.88 4.55 321s supply 4.55 6.27 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.88 4.88 321s supply 4.88 6.60 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 321s price -0.2443 0.0892 -2.74 0.0096 ** 321s income 0.3234 0.0229 14.14 4.4e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.969 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 321s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 321s price 0.2557 0.0892 2.87 0.0069 ** 321s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 321s trend 0.3234 0.0229 14.14 4.4e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.57 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 321s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 321s 321s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 171 1.74 0.681 0.696 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.8 3.87 1.97 0.755 0.726 321s supply 20 16 105.4 6.59 2.57 0.607 0.533 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.89 4.53 321s supply 4.53 6.25 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 4.87 321s supply 4.87 6.59 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 321s price -0.2457 0.0891 -2.76 0.0092 ** 321s income 0.3236 0.0233 13.91 8.9e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.967 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 321s price 0.2543 0.0891 2.85 0.0072 ** 321s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 321s trend 0.3236 0.0233 13.91 8.9e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.566 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 321s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 321s 321s [1] "Component “call”: target, current do not match when deparsed" 321s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 170 1.19 0.683 0.658 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.6 3.86 1.96 0.755 0.727 321s supply 20 16 104.6 6.54 2.56 0.610 0.537 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.73 321s supply 3.73 5.00 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.28 4.00 321s supply 4.00 5.23 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 321s price -0.2494 0.0812 -3.07 0.0041 ** 321s income 0.3248 0.0209 15.57 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.964 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 321s price 0.2506 0.0812 3.09 0.0039 ** 321s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 321s trend 0.3248 0.0209 15.57 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.557 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 321s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 321s 321s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 170 1.19 0.682 0.659 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.6 3.86 1.97 0.755 0.726 321s supply 20 16 104.8 6.55 2.56 0.609 0.536 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.75 321s supply 3.75 5.01 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.28 4.00 321s supply 4.00 5.24 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.965 321s supply 0.965 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 321s price -0.2484 0.0812 -3.06 0.0042 ** 321s income 0.3246 0.0205 15.81 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.965 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 321s price 0.2516 0.0812 3.10 0.0038 ** 321s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 321s trend 0.3246 0.0205 15.81 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.559 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 321s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 36 3690 5613 0.012 0.368 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 2132 112.2 10.59 0.305 0.305 321s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 112.2 -44.8 321s eq2 -44.8 56.8 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 112.2 -68.3 321s eq2 -68.3 91.7 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.674 321s eq2 -0.674 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: farmPrice ~ consump - 1 321s Instruments: ~trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s consump 0.9588 0.0235 40.9 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 10.592 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 321s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ consump + trend 321s Instruments: ~trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) -92.192 49.896 -1.85 0.0821 . 321s consump 1.953 0.499 3.92 0.0011 ** 321s trend -0.469 0.247 -1.90 0.0743 . 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 9.574 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 321s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 56326 283068 -104 -10.6 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 2313 122 11.0 -7.63 -7.63 321s eq2 20 19 54013 2843 53.3 -200.46 -200.46 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 121 -255 321s eq2 -255 2953 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 122 -251 321s eq2 -251 2843 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.433 321s eq2 -0.433 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ farmPrice - 1 321s Instruments: ~price + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 11.034 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 321s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: consump ~ trend - 1 321s Instruments: ~price + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 9.02 1.13 8 1.7e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 53.318 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 321s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 167069 397886 -49.1 -0.82 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 76692 4036 63.5 -285.0 -285.0 321s eq2 20 19 90377 4757 69.0 -28.5 -28.5 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 2682 2547 321s eq2 2547 2741 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 4036 4336 321s eq2 4336 4757 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 0.928 321s eq2 0.928 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ trend - 1 321s Instruments: ~income + farmPrice 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 4.162 0.723 5.75 1.5e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 63.533 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 321s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: farmPrice ~ trend - 1 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 3.274 0.676 4.84 0.00011 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 68.969 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 321s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 39 161126 1162329 -171 -17.4 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 3553 187 13.7 -12.3 -12.3 321s eq2 20 19 157573 8293 91.1 -235.2 -235.2 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 208 -731 321s eq2 -731 8271 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 187 -623 321s eq2 -623 8293 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.121 321s eq2 -0.121 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ farmPrice - 1 321s Instruments: ~farmPrice + trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 13.675 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 321s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ trend - 1 321s Instruments: ~farmPrice + trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 1.1122 0.0272 40.8 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 91.068 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 321s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 935 491 0 0 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 268 14.1 3.76 0 0 321s eq2 20 19 667 35.1 5.93 0 0 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 14.11 2.18 321s eq2 2.18 35.12 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 14.11 2.18 321s eq2 2.18 35.12 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.0000 0.0981 321s eq2 0.0981 1.0000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ 1 321s Instruments: ~income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 100.90 0.84 120 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.756 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 321s Multiple R-Squared: 0 Adjusted R-Squared: 0 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ 1 321s Instruments: ~income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 100.02 1.33 75.5 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 5.926 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 321s Multiple R-Squared: 0 Adjusted R-Squared: 0 321s 321s [1] "***************************************************" 321s [1] "3SLS formula: EViews" 321s [1] "************* 3SLS *********************************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 174 1.03 0.676 0.786 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 107.9 6.75 2.60 0.598 0.522 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 4.36 321s supply 4.36 6.04 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.00 321s supply 5.00 6.74 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.00 0.98 321s supply 0.98 1.00 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 321s price -0.2436 0.0965 -2.52 0.022 * 321s income 0.3140 0.0469 6.69 3.8e-06 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 321s price 0.2286 0.0997 2.29 0.03571 * 321s farmPrice 0.2282 0.0440 5.19 9e-05 *** 321s trend 0.3611 0.0729 4.95 0.00014 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.597 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 321s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 321s 321s [1] "********************* 3SLS EViews-like *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 173 0.719 0.677 0.748 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 107.2 6.70 2.59 0.600 0.525 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.29 3.59 321s supply 3.59 4.83 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.29 4.11 321s supply 4.11 5.36 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.979 321s supply 0.979 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 321s price -0.2436 0.0890 -2.74 0.0099 ** 321s income 0.3140 0.0433 7.25 2.5e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 321s price 0.2289 0.0892 2.57 0.015 * 321s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 321s trend 0.3579 0.0652 5.49 4.3e-06 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.589 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 321s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 321s 321s [1] "********************* 3SLS with methodResidCov = Theil *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 174 -0.718 0.675 0.922 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 108.7 6.79 2.61 0.594 0.518 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 4.50 321s supply 4.50 6.04 321s 321s warning: this covariance matrix is NOT positive semidefinit! 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.2 321s supply 5.20 6.8 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.981 321s supply 0.981 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 321s price -0.2436 0.0965 -2.52 0.017 * 321s income 0.3140 0.0469 6.69 1.3e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 321s price 0.2282 0.0997 2.29 0.02855 * 321s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 321s trend 0.3648 0.0707 5.16 1.1e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.607 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 321s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 321s 321s [1] "*************** W3SLS with methodResidCov = Theil *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 174 -0.718 0.675 0.922 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 108.7 6.79 2.61 0.594 0.518 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 4.50 321s supply 4.50 6.04 321s 321s warning: this covariance matrix is NOT positive semidefinit! 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.2 321s supply 5.20 6.8 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.981 321s supply 0.981 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 321s price -0.2436 0.0965 -2.52 0.017 * 321s income 0.3140 0.0469 6.69 1.3e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 321s price 0.2282 0.0997 2.29 0.02855 * 321s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 321s trend 0.3648 0.0707 5.16 1.1e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.607 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 321s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 321s 321s [1] "*************** 3SLS with restriction *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 173 1.27 0.678 0.722 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.8 3.99 2.00 0.747 0.717 321s supply 20 16 104.8 6.55 2.56 0.609 0.536 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.97 4.55 321s supply 4.55 6.13 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.99 4.98 321s supply 4.98 6.55 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.975 321s supply 0.975 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 321s price -0.222 0.096 -2.31 0.027 * 321s income 0.296 0.045 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.997 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 321s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 321s price 0.2193 0.1002 2.19 0.036 * 321s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 321s trend 0.2956 0.0450 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.559 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 321s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 321s 321s [1] "Component “call”: target, current do not match when deparsed" 321s [1] "************** 3SLS with restriction (EViews-like) *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 171 0.887 0.68 0.678 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.5 3.97 1.99 0.748 0.719 321s supply 20 16 104.0 6.50 2.55 0.612 0.539 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.37 3.75 321s supply 3.75 4.91 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.37 4.08 321s supply 4.08 5.20 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.974 321s supply 0.974 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 321s price -0.2243 0.0888 -2.53 0.016 * 321s income 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.992 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 321s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 321s price 0.2207 0.0896 2.46 0.019 * 321s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 321s trend 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.55 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 321s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 321s 321s [1] 40 321s [1] "*************** W3SLS with restriction *****************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 173 1.24 0.677 0.725 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 68.1 4.00 2.00 0.746 0.716 321s supply 20 16 105.2 6.57 2.56 0.608 0.534 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.93 4.56 321s supply 4.56 6.15 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 4.00 5.01 321s supply 5.01 6.57 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.976 321s supply 0.976 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 321s price -0.2194 0.0954 -2.3 0.028 * 321s income 0.2938 0.0445 6.6 1.4e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.001 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 321s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 321s price 0.2184 0.1003 2.18 0.036 * 321s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 321s trend 0.2938 0.0445 6.60 1.4e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.564 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 321s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 321s 321s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 173 1.27 0.678 0.722 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.8 3.99 2.00 0.747 0.717 321s supply 20 16 104.8 6.55 2.56 0.609 0.536 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.97 4.55 321s supply 4.55 6.13 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.99 4.98 321s supply 4.98 6.55 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.975 321s supply 0.975 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 321s price -0.222 0.096 -2.31 0.027 * 321s income 0.296 0.045 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.997 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 321s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 321s price 0.2193 0.1002 2.19 0.036 * 321s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 321s trend 0.2956 0.0450 6.57 1.6e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.559 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 321s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 321s 321s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 171 0.887 0.68 0.678 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.5 3.97 1.99 0.748 0.719 321s supply 20 16 104.0 6.50 2.55 0.612 0.539 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.37 3.75 321s supply 3.75 4.91 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.37 4.08 321s supply 4.08 5.20 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.974 321s supply 0.974 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 321s price -0.2243 0.0888 -2.53 0.016 * 321s income 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.992 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 321s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 321s price 0.2207 0.0896 2.46 0.019 * 321s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 321s trend 0.2979 0.0420 7.10 3.4e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.55 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 321s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 321s 321s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 34 172 0.873 0.679 0.681 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 67.7 3.98 2.00 0.748 0.718 321s supply 20 16 104.3 6.52 2.55 0.611 0.538 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.35 3.76 321s supply 3.76 4.92 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.38 4.10 321s supply 4.10 5.22 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.975 321s supply 0.975 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 321s price -0.2225 0.0883 -2.52 0.017 * 321s income 0.2964 0.0416 7.13 3.1e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.995 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 321s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 321s price 0.2201 0.0897 2.45 0.019 * 321s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 321s trend 0.2964 0.0416 7.13 3.1e-08 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.553 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 321s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 321s 321s [1] "*************** 3SLS with 2 restrictions **********************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 442 31.1 0.176 -0.052 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 164 9.66 3.11 0.388 0.316 321s supply 20 16 278 17.36 4.17 -0.036 -0.230 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.89 4.53 321s supply 4.53 6.25 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 9.66 11.7 321s supply 11.69 17.4 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.903 321s supply 0.903 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 91.2986 7.9234 11.52 1.8e-13 *** 321s price -0.4494 0.0891 -5.04 1.4e-05 *** 321s income 0.5592 0.0233 24.04 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.108 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 164.177 MSE: 9.657 Root MSE: 3.108 321s Multiple R-Squared: 0.388 Adjusted R-Squared: 0.316 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) -1.8394 8.1797 -0.22 0.82 321s price 0.5506 0.0891 6.18 4.5e-07 *** 321s farmPrice 0.4325 0.0241 17.95 < 2e-16 *** 321s trend 0.5592 0.0233 24.04 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 4.167 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 277.77 MSE: 17.361 Root MSE: 4.167 321s Multiple R-Squared: -0.036 Adjusted R-Squared: -0.23 321s 321s [1] "Component “call”: target, current do not match when deparsed" 321s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 439 21.3 0.18 -0.18 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 169 9.93 3.15 0.370 0.296 321s supply 20 16 271 16.91 4.11 -0.009 -0.198 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.73 321s supply 3.73 5.00 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 8.44 9.64 321s supply 9.64 13.53 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.902 321s supply 0.902 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 93.2926 7.3154 12.75 1.0e-14 *** 321s price -0.4781 0.0812 -5.89 1.1e-06 *** 321s income 0.5683 0.0209 27.24 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.152 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 168.882 MSE: 9.934 Root MSE: 3.152 321s Multiple R-Squared: 0.37 Adjusted R-Squared: 0.296 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 0.6559 7.5503 0.09 0.93 321s price 0.5219 0.0812 6.43 2.1e-07 *** 321s farmPrice 0.4355 0.0212 20.49 < 2e-16 *** 321s trend 0.5683 0.0209 27.24 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 4.112 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 270.595 MSE: 16.912 Root MSE: 4.112 321s Multiple R-Squared: -0.009 Adjusted R-Squared: -0.198 321s 321s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 448 31.2 0.165 -0.057 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 166 9.77 3.13 0.38 0.307 321s supply 20 16 281 17.59 4.19 -0.05 -0.246 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.88 4.55 321s supply 4.55 6.27 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 9.77 11.9 321s supply 11.86 17.6 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.905 321s supply 0.905 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 90.6391 7.9088 11.46 2.1e-13 *** 321s price -0.4438 0.0892 -4.98 1.7e-05 *** 321s income 0.5603 0.0229 24.50 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.126 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 166.148 MSE: 9.773 Root MSE: 3.126 321s Multiple R-Squared: 0.38 Adjusted R-Squared: 0.307 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) -2.5480 8.1522 -0.31 0.76 321s price 0.5562 0.0892 6.24 3.7e-07 *** 321s farmPrice 0.4340 0.0237 18.33 < 2e-16 *** 321s trend 0.5603 0.0229 24.50 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 4.194 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 281.4 MSE: 17.587 Root MSE: 4.194 321s Multiple R-Squared: -0.05 Adjusted R-Squared: -0.246 321s 321s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 442 31.1 0.176 -0.052 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 164 9.66 3.11 0.388 0.316 321s supply 20 16 278 17.36 4.17 -0.036 -0.230 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.89 4.53 321s supply 4.53 6.25 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 9.66 11.7 321s supply 11.69 17.4 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.903 321s supply 0.903 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 91.2986 7.9234 11.52 1.8e-13 *** 321s price -0.4494 0.0891 -5.04 1.4e-05 *** 321s income 0.5592 0.0233 24.04 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.108 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 164.177 MSE: 9.657 Root MSE: 3.108 321s Multiple R-Squared: 0.388 Adjusted R-Squared: 0.316 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) -1.8394 8.1797 -0.22 0.82 321s price 0.5506 0.0891 6.18 4.5e-07 *** 321s farmPrice 0.4325 0.0241 17.95 < 2e-16 *** 321s trend 0.5592 0.0233 24.04 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 4.167 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 277.77 MSE: 17.361 Root MSE: 4.167 321s Multiple R-Squared: -0.036 Adjusted R-Squared: -0.23 321s 321s [1] "Component “call”: target, current do not match when deparsed" 321s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 439 21.3 0.18 -0.18 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 169 9.93 3.15 0.370 0.296 321s supply 20 16 271 16.91 4.11 -0.009 -0.198 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.73 321s supply 3.73 5.00 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 8.44 9.64 321s supply 9.64 13.53 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.902 321s supply 0.902 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 93.2926 7.3154 12.75 1.0e-14 *** 321s price -0.4781 0.0812 -5.89 1.1e-06 *** 321s income 0.5683 0.0209 27.24 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.152 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 168.882 MSE: 9.934 Root MSE: 3.152 321s Multiple R-Squared: 0.37 Adjusted R-Squared: 0.296 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 0.6559 7.5503 0.09 0.93 321s price 0.5219 0.0812 6.43 2.1e-07 *** 321s farmPrice 0.4355 0.0212 20.49 < 2e-16 *** 321s trend 0.5683 0.0209 27.24 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 4.112 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 270.595 MSE: 16.912 Root MSE: 4.112 321s Multiple R-Squared: -0.009 Adjusted R-Squared: -0.198 321s 321s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 35 444 21.3 0.172 -0.188 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 171 10.0 3.17 0.363 0.289 321s supply 20 16 274 17.1 4.13 -0.020 -0.212 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.30 3.75 321s supply 3.75 5.01 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 8.53 9.77 321s supply 9.77 13.68 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.904 321s supply 0.904 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 92.7628 7.3058 12.70 1.2e-14 *** 321s price -0.4740 0.0812 -5.84 1.3e-06 *** 321s income 0.5694 0.0205 27.74 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.168 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 170.659 MSE: 10.039 Root MSE: 3.168 321s Multiple R-Squared: 0.363 Adjusted R-Squared: 0.289 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 0.0845 7.5314 0.01 0.99 321s price 0.5260 0.0812 6.48 1.8e-07 *** 321s farmPrice 0.4370 0.0209 20.91 < 2e-16 *** 321s trend 0.5694 0.0205 27.74 < 2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 4.135 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 273.568 MSE: 17.098 Root MSE: 4.135 321s Multiple R-Squared: -0.02 Adjusted R-Squared: -0.212 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 36 3690 5613 0.012 0.368 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 2132 112.2 10.59 0.305 0.305 321s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 112.2 -44.8 321s eq2 -44.8 56.8 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 112.2 -68.3 321s eq2 -68.3 91.7 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.674 321s eq2 -0.674 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: farmPrice ~ consump - 1 321s Instruments: ~trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s consump 0.9588 0.0235 40.9 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 10.592 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 321s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ consump + trend 321s Instruments: ~trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) -92.192 49.896 -1.85 0.0821 . 321s consump 1.953 0.499 3.92 0.0011 ** 321s trend -0.469 0.247 -1.90 0.0743 . 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 9.574 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 321s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 56326 283068 -104 -10.6 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 2313 122 11.0 -7.63 -7.63 321s eq2 20 19 54013 2843 53.3 -200.46 -200.46 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 121 -255 321s eq2 -255 2953 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 122 -251 321s eq2 -251 2843 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.433 321s eq2 -0.433 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ farmPrice - 1 321s Instruments: ~price + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 11.034 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 321s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: consump ~ trend - 1 321s Instruments: ~price + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 9.02 1.13 8 1.7e-07 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 53.318 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 321s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 167069 397886 -49.1 -0.82 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 76692 4036 63.5 -285.0 -285.0 321s eq2 20 19 90377 4757 69.0 -28.5 -28.5 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 2682 2547 321s eq2 2547 2741 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 4036 4336 321s eq2 4336 4757 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 0.928 321s eq2 0.928 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ trend - 1 321s Instruments: ~income + farmPrice 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 4.162 0.723 5.75 1.5e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 63.533 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 321s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: farmPrice ~ trend - 1 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 3.274 0.676 4.84 0.00011 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 68.969 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 321s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 39 161126 1162329 -171 -17.4 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 3553 187 13.7 -12.3 -12.3 321s eq2 20 19 157573 8293 91.1 -235.2 -235.2 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 208 -731 321s eq2 -731 8271 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 187 -623 321s eq2 -623 8293 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.000 -0.121 321s eq2 -0.121 1.000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ farmPrice - 1 321s Instruments: ~farmPrice + trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 13.675 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 321s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ trend - 1 321s Instruments: ~farmPrice + trend + income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s trend 1.1122 0.0272 40.8 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 91.068 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 321s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 321s 321s 321s systemfit results 321s method: 3SLS 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 38 935 491 0 0 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s eq1 20 19 268 14.1 3.76 0 0 321s eq2 20 19 667 35.1 5.93 0 0 321s 321s The covariance matrix of the residuals used for estimation 321s eq1 eq2 321s eq1 14.11 2.18 321s eq2 2.18 35.12 321s 321s The covariance matrix of the residuals 321s eq1 eq2 321s eq1 14.11 2.18 321s eq2 2.18 35.12 321s 321s The correlations of the residuals 321s eq1 eq2 321s eq1 1.0000 0.0981 321s eq2 0.0981 1.0000 321s 321s 321s 3SLS estimates for 'eq1' (equation 1) 321s Model Formula: consump ~ 1 321s Instruments: ~income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 100.90 0.84 120 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 3.756 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 321s Multiple R-Squared: 0 Adjusted R-Squared: 0 321s 321s 321s 3SLS estimates for 'eq2' (equation 2) 321s Model Formula: price ~ 1 321s Instruments: ~income 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 100.02 1.33 75.5 <2e-16 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 5.926 on 19 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 19 321s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 321s Multiple R-Squared: 0 Adjusted R-Squared: 0 321s 321s > 321s > ## ******************** iterated 3SLS ********************** 321s > fit3slsi <- list() 321s > formulas <- c( "GLS", "IV", "Schmidt", "GMM", "EViews" ) 321s > for( i in seq( along = formulas ) ) { 321s + fit3slsi[[ i ]] <- list() 321s + 321s + print( "***************************************************" ) 321s + print( paste( "3SLS formula:", formulas[ i ] ) ) 321s + print( "************* 3SLS *********************************" ) 321s + fit3slsi[[ i ]]$e1 <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, method3sls = formulas[ i ], maxiter = 100, 321s + useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e1 ) ) 321s + 321s + print( "********************* iterated 3SLS EViews-like ****************" ) 321s + fit3slsi[[ i ]]$e1e <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, methodResidCov = "noDfCor", method3sls = formulas[ i ], 321s + maxiter = 100, useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e1e, useDfSys = TRUE ) ) 321s + 321s + print( "************** iterated 3SLS with methodResidCov = Theil **************" ) 321s + fit3slsi[[ i ]]$e1c <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, methodResidCov = "Theil", method3sls = formulas[ i ], 321s + maxiter = 100, x = TRUE, useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e1c, useDfSys = TRUE ) ) 321s + 321s + print( "**************** iterated W3SLS EViews-like ****************" ) 321s + fit3slsi[[ i ]]$e1we <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, methodResidCov = "noDfCor", method3sls = formulas[ i ], 321s + maxiter = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e1we, useDfSys = TRUE ) ) 321s + 321s + 321s + print( "******* iterated 3SLS with restriction *****************" ) 321s + fit3slsi[[ i ]]$e2 <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, restrict.matrix = restrm, method3sls = formulas[ i ], 321s + maxiter = 100, x = TRUE, useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e2 ) ) 321s + 321s + print( "********* iterated 3SLS with restriction (EViews-like) *********" ) 321s + fit3slsi[[ i ]]$e2e <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restrm, 321s + method3sls = formulas[ i ], maxiter = 100, useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e2e, useDfSys = TRUE ) ) 321s + 321s + print( "******** iterated W3SLS with restriction (EViews-like) *********" ) 321s + fit3slsi[[ i ]]$e2we <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restrm, 321s + method3sls = formulas[ i ], maxiter = 100, residCovWeighted = TRUE, 321s + useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e2we, useDfSys = TRUE ) ) 321s + 321s + 321s + print( "********* iterated 3SLS with restriction via restrict.regMat *****************" ) 321s + fit3slsi[[ i ]]$e3 <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, restrict.regMat = tc, method3sls = formulas[ i ], 321s + maxiter = 100, useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e3 ) ) 321s + 321s + print( "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" ) 321s + fit3slsi[[ i ]]$e3e <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, methodResidCov = "noDfCor", restrict.regMat = tc, 321s + method3sls = formulas[ i ], maxiter = 100, x = TRUE, 321s + useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e3e, useDfSys = TRUE ) ) 321s + 321s + print( "***** iterated W3SLS with restriction via restrict.regMat ********" ) 321s + fit3slsi[[ i ]]$e3w <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, restrict.regMat = tc, method3sls = formulas[ i ], maxiter = 100, 321s + residCovWeighted = TRUE, x = TRUE, useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e3w ) ) 321s + 321s + 321s + print( "******** iterated 3SLS with 2 restrictions *********************" ) 321s + fit3slsi[[ i ]]$e4 <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, restrict.matrix = restr2m, restrict.rhs = restr2q, 321s + method3sls = formulas[ i ], maxiter = 100, x = TRUE, 321s + useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e4 ) ) 321s + 321s + print( "********* iterated 3SLS with 2 restrictions (EViews-like) *******" ) 321s + fit3slsi[[ i ]]$e4e <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restr2m, 321s + restrict.rhs = restr2q, method3sls = formulas[ i ], maxiter = 100, 321s + useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e4e, useDfSys = TRUE ) ) 321s + 321s + print( "******** iterated W3SLS with 2 restrictions (EViews-like) *******" ) 321s + fit3slsi[[ i ]]$e4we <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restr2m, 321s + restrict.rhs = restr2q, method3sls = formulas[ i ], maxiter = 100, 321s + residCovWeighted = TRUE, useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e4we, useDfSys = TRUE ) ) 321s + 321s + 321s + print( "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" ) 321s + fit3slsi[[ i ]]$e5 <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, restrict.regMat = tc, restrict.matrix = restr3m, 321s + restrict.rhs = restr3q, method3sls = formulas[ i ], maxiter = 100, 321s + useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e5 ) ) 321s + 321s + print( "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" ) 321s + fit3slsi[[ i ]]$e5e <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, restrict.regMat = tc, methodResidCov = "noDfCor", 321s + restrict.matrix = restr3m, restrict.rhs = restr3q, 321s + method3sls = formulas[ i ], maxiter = 100, useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e5e, useDfSys = TRUE ) ) 321s + 321s + print( "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" ) 321s + fit3slsi[[ i ]]$e5w <- systemfit( system, "3SLS", data = Kmenta, 321s + inst = inst, restrict.regMat = tc, restrict.matrix = restr3m, 321s + restrict.rhs = restr3q, method3sls = formulas[ i ], maxiter = 100, 321s + residCovWeighted = TRUE, x = TRUE, 321s + useMatrix = useMatrix ) 321s + print( summary( fit3slsi[[ i ]]$e5w ) ) 321s + } 321s [1] "***************************************************" 321s [1] "3SLS formula: GLS" 321s [1] "************* 3SLS *********************************" 321s 321s systemfit results 321s method: iterated 3SLS 321s 321s convergence achieved after 6 iterations 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 321s system 40 33 178 0.983 0.668 0.814 321s 321s N DF SSR MSE RMSE R2 Adj R2 321s demand 20 17 65.7 3.87 1.97 0.755 0.726 321s supply 20 16 112.4 7.03 2.65 0.581 0.502 321s 321s The covariance matrix of the residuals used for estimation 321s demand supply 321s demand 3.87 5.12 321s supply 5.12 7.03 321s 321s The covariance matrix of the residuals 321s demand supply 321s demand 3.87 5.12 321s supply 5.12 7.03 321s 321s The correlations of the residuals 321s demand supply 321s demand 1.000 0.982 321s supply 0.982 1.000 321s 321s 321s 3SLS estimates for 'demand' (equation 1) 321s Model Formula: consump ~ price + income 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 321s price -0.2436 0.0965 -2.52 0.022 * 321s income 0.3140 0.0469 6.69 3.8e-06 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 1.966 on 17 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 17 321s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 321s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 321s 321s 321s 3SLS estimates for 'supply' (equation 2) 321s Model Formula: consump ~ price + farmPrice + trend 321s Instruments: ~income + farmPrice + trend 321s 321s Estimate Std. Error t value Pr(>|t|) 321s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 321s price 0.2266 0.1075 2.11 0.05110 . 321s farmPrice 0.2234 0.0468 4.78 0.00021 *** 321s trend 0.3800 0.0720 5.28 7.5e-05 *** 321s --- 321s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 321s 321s Residual standard error: 2.651 on 16 degrees of freedom 321s Number of observations: 20 Degrees of Freedom: 16 321s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 321s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 321s 321s [1] "********************* iterated 3SLS EViews-like ****************" 321s 321s systemfit results 321s method: iterated 3SLS 321s 321s convergence achieved after 6 iterations 321s 321s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 179 -0.818 0.665 0.957 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 113.8 7.11 2.67 0.576 0.496 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s warning: this covariance matrix is NOT positive semidefinit! 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 322s price -0.2436 0.0965 -2.52 0.017 * 322s income 0.3140 0.0469 6.69 1.3e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 322s price 0.2261 0.1081 2.09 0.04425 * 322s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 322s trend 0.3851 0.0693 5.55 3.6e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.667 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 322s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 322s 322s [1] "**************** iterated W3SLS EViews-like ****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "******* iterated 3SLS with restriction *****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "******** iterated 3SLS with 2 restrictions *********************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "***************************************************" 322s [1] "3SLS formula: IV" 322s [1] "************* 3SLS *********************************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 178 0.983 0.668 0.814 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 112.4 7.03 2.65 0.581 0.502 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.87 5.12 322s supply 5.12 7.03 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.87 5.12 322s supply 5.12 7.03 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 322s price -0.2436 0.0965 -2.52 0.022 * 322s income 0.3140 0.0469 6.69 3.8e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 322s price 0.2266 0.1075 2.11 0.05110 . 322s farmPrice 0.2234 0.0468 4.78 0.00021 *** 322s trend 0.3800 0.0720 5.28 7.5e-05 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.651 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 322s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 322s 322s [1] "********************* iterated 3SLS EViews-like ****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 179 -0.818 0.665 0.957 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 113.8 7.11 2.67 0.576 0.496 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s warning: this covariance matrix is NOT positive semidefinit! 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 322s price -0.2436 0.0965 -2.52 0.017 * 322s income 0.3140 0.0469 6.69 1.3e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 322s price 0.2261 0.1081 2.09 0.04425 * 322s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 322s trend 0.3851 0.0693 5.55 3.6e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.667 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 322s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 322s 322s [1] "**************** iterated W3SLS EViews-like ****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "******* iterated 3SLS with restriction *****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "******** iterated 3SLS with 2 restrictions *********************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "***************************************************" 322s [1] "3SLS formula: Schmidt" 322s [1] "************* 3SLS *********************************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 178 0.983 0.668 0.814 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 112.4 7.03 2.65 0.581 0.502 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.87 5.12 322s supply 5.12 7.03 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.87 5.12 322s supply 5.12 7.03 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 322s price -0.2436 0.0965 -2.52 0.022 * 322s income 0.3140 0.0469 6.69 3.8e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 322s price 0.2266 0.1075 2.11 0.05110 . 322s farmPrice 0.2234 0.0468 4.78 0.00021 *** 322s trend 0.3800 0.0720 5.28 7.5e-05 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.651 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 322s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 322s 322s [1] "********************* iterated 3SLS EViews-like ****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 179 -0.818 0.665 0.957 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 113.8 7.11 2.67 0.576 0.496 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s warning: this covariance matrix is NOT positive semidefinit! 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 322s price -0.2436 0.0965 -2.52 0.017 * 322s income 0.3140 0.0469 6.69 1.3e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 322s price 0.2261 0.1081 2.09 0.04425 * 322s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 322s trend 0.3851 0.0693 5.55 3.6e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.667 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 322s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 322s 322s [1] "**************** iterated W3SLS EViews-like ****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "******* iterated 3SLS with restriction *****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "******** iterated 3SLS with 2 restrictions *********************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "***************************************************" 322s [1] "3SLS formula: GMM" 322s [1] "************* 3SLS *********************************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 178 0.983 0.668 0.814 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 112.4 7.03 2.65 0.581 0.502 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.87 5.12 322s supply 5.12 7.03 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.87 5.12 322s supply 5.12 7.03 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 322s price -0.2436 0.0965 -2.52 0.022 * 322s income 0.3140 0.0469 6.69 3.8e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 322s price 0.2266 0.1075 2.11 0.05110 . 322s farmPrice 0.2234 0.0468 4.78 0.00021 *** 322s trend 0.3800 0.0720 5.28 7.5e-05 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.651 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 322s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 322s 322s [1] "********************* iterated 3SLS EViews-like ****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 179 -0.818 0.665 0.957 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 113.8 7.11 2.67 0.576 0.496 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s warning: this covariance matrix is NOT positive semidefinit! 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 322s price -0.2436 0.0965 -2.52 0.017 * 322s income 0.3140 0.0469 6.69 1.3e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 322s price 0.2261 0.1081 2.09 0.04425 * 322s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 322s trend 0.3851 0.0693 5.55 3.6e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.667 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 322s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 322s 322s [1] "**************** iterated W3SLS EViews-like ****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "******* iterated 3SLS with restriction *****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 322s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 322s price 0.1851 0.1053 1.76 0.088 . 322s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 322s trend 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.938 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 322s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 322s 322s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "******** iterated 3SLS with 2 restrictions *********************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 8 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 179 1.19 0.666 0.668 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 68.3 4.02 2.00 0.745 0.715 322s supply 20 16 110.8 6.92 2.63 0.587 0.509 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.41 4.21 322s supply 4.21 5.54 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.968 322s supply 0.968 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 322s price -0.2168 0.0835 -2.6 0.014 * 322s income 0.3199 0.0168 19.1 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.004 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 322s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 322s price 0.2832 0.0835 3.39 0.0017 ** 322s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 322s trend 0.3199 0.0168 19.07 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.631 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 322s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 322s 322s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 9 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 35 185 1.76 0.655 0.71 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 69.9 4.11 2.03 0.739 0.709 322s supply 20 16 114.8 7.18 2.68 0.572 0.491 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.11 5.27 322s supply 5.27 7.18 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.00 0.97 322s supply 0.97 1.00 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 322s price -0.2007 0.0920 -2.18 0.036 * 322s income 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.028 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 322s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 322s price 0.2993 0.0920 3.25 0.0025 ** 322s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 322s trend 0.3159 0.0192 16.42 < 2e-16 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.679 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 322s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 322s 322s [1] "***************************************************" 322s [1] "3SLS formula: EViews" 322s [1] "************* 3SLS *********************************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 178 0.983 0.668 0.814 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 112.4 7.03 2.65 0.581 0.502 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.87 5.12 322s supply 5.12 7.03 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.87 5.12 322s supply 5.12 7.03 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 322s price -0.2436 0.0965 -2.52 0.022 * 322s income 0.3140 0.0469 6.69 3.8e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 322s price 0.2266 0.1075 2.11 0.05110 . 322s farmPrice 0.2234 0.0468 4.78 0.00021 *** 322s trend 0.3800 0.0720 5.28 7.5e-05 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.651 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 322s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 322s 322s [1] "********************* iterated 3SLS EViews-like ****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 179 -0.818 0.665 0.957 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 113.8 7.11 2.67 0.576 0.496 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s warning: this covariance matrix is NOT positive semidefinit! 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.87 5.32 322s supply 5.32 7.11 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 322s price -0.2436 0.0965 -2.52 0.017 * 322s income 0.3140 0.0469 6.69 1.3e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 322s price 0.2261 0.1081 2.09 0.04425 * 322s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 322s trend 0.3851 0.0693 5.55 3.6e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.667 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 322s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 322s 322s [1] "**************** iterated W3SLS EViews-like ****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 6 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 33 177 0.667 0.67 0.782 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 65.7 3.87 1.97 0.755 0.726 322s supply 20 16 111.3 6.96 2.64 0.585 0.507 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 3.29 4.20 322s supply 4.20 5.57 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.982 322s supply 0.982 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 322s price -0.2436 0.0890 -2.74 0.0099 ** 322s income 0.3140 0.0433 7.25 2.5e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 1.966 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 322s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 322s price 0.2271 0.0956 2.37 0.024 * 322s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 322s trend 0.3756 0.0641 5.86 1.5e-06 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.637 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 322s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 322s 322s [1] "******* iterated 3SLS with restriction *****************" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 17 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 240 0.56 0.553 0.819 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 98.4 5.79 2.41 0.633 0.590 322s supply 20 16 141.1 8.82 2.97 0.474 0.375 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 5.79 7.11 322s supply 7.11 8.82 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 322s price -0.1064 0.1023 -1.04 0.31 322s income 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.406 on 17 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 17 322s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 322s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 322s 322s 322s 3SLS estimates for 'supply' (equation 2) 322s Model Formula: consump ~ price + farmPrice + trend 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 322s price 0.1833 0.1189 1.54 0.13 322s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 322s trend 0.1996 0.0297 6.73 9.9e-08 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.97 on 16 degrees of freedom 322s Number of observations: 20 Degrees of Freedom: 16 322s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 322s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 322s 322s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 322s 322s systemfit results 322s method: iterated 3SLS 322s 322s convergence achieved after 20 iterations 322s 322s N DF SSR detRCov OLS-R2 McElroy-R2 322s system 40 34 237 0.364 0.557 0.755 322s 322s N DF SSR MSE RMSE R2 Adj R2 322s demand 20 17 99.3 5.84 2.42 0.630 0.586 322s supply 20 16 138.1 8.63 2.94 0.485 0.388 322s 322s The covariance matrix of the residuals used for estimation 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The covariance matrix of the residuals 322s demand supply 322s demand 4.96 5.82 322s supply 5.82 6.90 322s 322s The correlations of the residuals 322s demand supply 322s demand 1.000 0.995 322s supply 0.995 1.000 322s 322s 322s 3SLS estimates for 'demand' (equation 1) 322s Model Formula: consump ~ price + income 322s Instruments: ~income + farmPrice + trend 322s 322s Estimate Std. Error t value Pr(>|t|) 322s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 322s price -0.1043 0.0958 -1.09 0.28 322s income 0.1979 0.0299 6.61 1.4e-07 *** 322s --- 322s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 322s 322s Residual standard error: 2.417 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 323s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 323s price 0.1851 0.1053 1.76 0.088 . 323s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 323s trend 0.1979 0.0299 6.61 1.4e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.938 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 323s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 323s 323s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s convergence achieved after 20 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 237 0.364 0.557 0.755 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 99.3 5.84 2.42 0.630 0.586 323s supply 20 16 138.1 8.63 2.94 0.485 0.388 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 4.96 5.82 323s supply 5.82 6.90 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 4.96 5.82 323s supply 5.82 6.90 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.995 323s supply 0.995 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 323s price -0.1043 0.0958 -1.09 0.28 323s income 0.1979 0.0299 6.61 1.4e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.417 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 323s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 323s price 0.1851 0.1053 1.76 0.088 . 323s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 323s trend 0.1979 0.0299 6.61 1.4e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.938 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 323s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 323s 323s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s convergence achieved after 17 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 240 0.56 0.553 0.819 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 98.4 5.79 2.41 0.633 0.590 323s supply 20 16 141.1 8.82 2.97 0.474 0.375 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 5.79 7.11 323s supply 7.11 8.82 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 5.79 7.11 323s supply 7.11 8.82 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.995 323s supply 0.995 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 323s price -0.1064 0.1023 -1.04 0.31 323s income 0.1996 0.0297 6.73 9.9e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.406 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 323s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 323s price 0.1833 0.1189 1.54 0.13 323s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 323s trend 0.1996 0.0297 6.73 9.9e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.97 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 323s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 323s 323s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s convergence achieved after 20 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 237 0.364 0.557 0.755 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 99.3 5.84 2.42 0.630 0.586 323s supply 20 16 138.1 8.63 2.94 0.485 0.388 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 4.96 5.82 323s supply 5.82 6.90 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 4.96 5.82 323s supply 5.82 6.90 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.995 323s supply 0.995 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 323s price -0.1043 0.0958 -1.09 0.28 323s income 0.1979 0.0299 6.61 1.4e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.417 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 323s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 323s price 0.1851 0.1053 1.76 0.088 . 323s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 323s trend 0.1979 0.0299 6.61 1.4e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.938 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 323s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 323s 323s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s convergence achieved after 17 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 240 0.56 0.553 0.819 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 98.4 5.79 2.41 0.633 0.590 323s supply 20 16 141.1 8.82 2.97 0.474 0.375 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 5.79 7.11 323s supply 7.11 8.82 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 5.79 7.11 323s supply 7.11 8.82 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.995 323s supply 0.995 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 323s price -0.1064 0.1023 -1.04 0.31 323s income 0.1996 0.0297 6.73 9.9e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.406 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 323s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 323s price 0.1833 0.1189 1.54 0.13 323s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 323s trend 0.1996 0.0297 6.73 9.9e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.97 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 323s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 323s 323s [1] "******** iterated 3SLS with 2 restrictions *********************" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s warning: convergence not achieved after 100 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 1194 34.7 -1.23 0.688 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 274 16.1 4.02 -0.024 -0.144 323s supply 20 16 920 57.5 7.58 -2.431 -3.074 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 16.1 29.9 323s supply 29.9 57.5 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 16.1 29.9 323s supply 29.9 57.5 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.981 323s supply 0.981 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 43.5261 10.3602 4.20 0.00017 *** 323s price 0.2553 0.1380 1.85 0.07275 . 323s income 0.3264 0.0424 7.71 4.8e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 4.018 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 274.43 MSE: 16.143 Root MSE: 4.018 323s Multiple R-Squared: -0.024 Adjusted R-Squared: -0.144 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) -49.0143 9.6115 -5.10 1.2e-05 *** 323s price 1.2553 0.1380 9.10 9.5e-11 *** 323s farmPrice 0.2166 0.0573 3.78 0.00058 *** 323s trend 0.3264 0.0424 7.71 4.8e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 7.582 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 919.812 MSE: 57.488 Root MSE: 7.582 323s Multiple R-Squared: -2.431 Adjusted R-Squared: -3.074 323s 323s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s convergence achieved after 66 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 615 20.5 -0.147 0.48 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 151 8.87 2.98 0.437 0.371 323s supply 20 16 464 29.00 5.38 -0.731 -1.055 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 7.54 12.4 323s supply 12.43 23.2 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 7.54 12.4 323s supply 12.43 23.2 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.939 323s supply 0.939 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 68.3925 9.6792 7.07 3.1e-08 *** 323s price -0.0907 0.1236 -0.73 0.47 323s income 0.4263 0.0385 11.08 5.4e-13 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.979 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 150.821 MSE: 8.872 Root MSE: 2.979 323s Multiple R-Squared: 0.437 Adjusted R-Squared: 0.371 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) -27.3424 9.5498 -2.86 0.007 ** 323s price 0.9093 0.1236 7.36 1.3e-08 *** 323s farmPrice 0.3396 0.0498 6.82 6.5e-08 *** 323s trend 0.4263 0.0385 11.08 5.4e-13 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 5.385 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 464.036 MSE: 29.002 Root MSE: 5.385 323s Multiple R-Squared: -0.731 Adjusted R-Squared: -1.055 323s 323s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s convergence achieved after 66 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 615 20.5 -0.147 0.48 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 151 8.87 2.98 0.437 0.371 323s supply 20 16 464 29.00 5.38 -0.731 -1.055 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 7.54 12.4 323s supply 12.43 23.2 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 7.54 12.4 323s supply 12.43 23.2 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.939 323s supply 0.939 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 68.3925 9.6792 7.07 3.1e-08 *** 323s price -0.0907 0.1236 -0.73 0.47 323s income 0.4263 0.0385 11.08 5.4e-13 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.979 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 150.821 MSE: 8.872 Root MSE: 2.979 323s Multiple R-Squared: 0.437 Adjusted R-Squared: 0.371 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) -27.3423 9.5498 -2.86 0.007 ** 323s price 0.9093 0.1236 7.36 1.3e-08 *** 323s farmPrice 0.3396 0.0498 6.82 6.5e-08 *** 323s trend 0.4263 0.0385 11.08 5.4e-13 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 5.385 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 464.036 MSE: 29.002 Root MSE: 5.385 323s Multiple R-Squared: -0.731 Adjusted R-Squared: -1.055 323s 323s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s warning: convergence not achieved after 100 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 1194 34.7 -1.23 0.688 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 274 16.1 4.02 -0.024 -0.144 323s supply 20 16 920 57.5 7.58 -2.431 -3.074 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 16.1 29.9 323s supply 29.9 57.5 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 16.1 29.9 323s supply 29.9 57.5 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.981 323s supply 0.981 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 43.5261 10.3602 4.20 0.00017 *** 323s price 0.2553 0.1380 1.85 0.07275 . 323s income 0.3264 0.0424 7.71 4.8e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 4.018 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 274.43 MSE: 16.143 Root MSE: 4.018 323s Multiple R-Squared: -0.024 Adjusted R-Squared: -0.144 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) -49.0143 9.6115 -5.10 1.2e-05 *** 323s price 1.2553 0.1380 9.10 9.5e-11 *** 323s farmPrice 0.2166 0.0573 3.78 0.00058 *** 323s trend 0.3264 0.0424 7.71 4.8e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 7.582 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 919.812 MSE: 57.488 Root MSE: 7.582 323s Multiple R-Squared: -2.431 Adjusted R-Squared: -3.074 323s 323s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s convergence achieved after 66 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 615 20.5 -0.147 0.48 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 151 8.87 2.98 0.437 0.371 323s supply 20 16 464 29.00 5.38 -0.731 -1.055 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 7.54 12.4 323s supply 12.43 23.2 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 7.54 12.4 323s supply 12.43 23.2 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.939 323s supply 0.939 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 68.3925 9.6792 7.07 3.1e-08 *** 323s price -0.0907 0.1236 -0.73 0.47 323s income 0.4263 0.0385 11.08 5.4e-13 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.979 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 150.821 MSE: 8.872 Root MSE: 2.979 323s Multiple R-Squared: 0.437 Adjusted R-Squared: 0.371 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) -27.3424 9.5498 -2.86 0.007 ** 323s price 0.9093 0.1236 7.36 1.3e-08 *** 323s farmPrice 0.3396 0.0498 6.82 6.5e-08 *** 323s trend 0.4263 0.0385 11.08 5.4e-13 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 5.385 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 464.036 MSE: 29.002 Root MSE: 5.385 323s Multiple R-Squared: -0.731 Adjusted R-Squared: -1.055 323s 323s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 323s 323s systemfit results 323s method: iterated 3SLS 323s 323s warning: convergence not achieved after 100 iterations 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 1194 34.7 -1.23 0.688 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 274 16.1 4.02 -0.024 -0.144 323s supply 20 16 920 57.5 7.58 -2.431 -3.074 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 16.1 29.9 323s supply 29.9 57.5 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 16.1 29.9 323s supply 29.9 57.5 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.981 323s supply 0.981 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 43.5261 10.3602 4.20 0.00017 *** 323s price 0.2553 0.1380 1.85 0.07275 . 323s income 0.3264 0.0424 7.71 4.8e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 4.018 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 274.43 MSE: 16.143 Root MSE: 4.018 323s Multiple R-Squared: -0.024 Adjusted R-Squared: -0.144 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) -49.0142 9.6115 -5.10 1.2e-05 *** 323s price 1.2553 0.1380 9.10 9.5e-11 *** 323s farmPrice 0.2166 0.0573 3.78 0.00058 *** 323s trend 0.3264 0.0424 7.71 4.8e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 7.582 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 919.811 MSE: 57.488 Root MSE: 7.582 323s Multiple R-Squared: -2.431 Adjusted R-Squared: -3.074 323s 323s > 323s > ## **************** 3SLS with different instruments ************* 323s > fit3slsd <- list() 323s > formulas <- c( "GLS", "IV", "Schmidt", "GMM", "EViews" ) 323s > for( i in seq( along = formulas ) ) { 323s + fit3slsd[[ i ]] <- list() 323s + 323s + print( "***************************************************" ) 323s + print( paste( "3SLS formula:", formulas[ i ] ) ) 323s + print( "************* 3SLS with different instruments **************" ) 323s + fit3slsd[[ i ]]$e1 <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, method3sls = formulas[ i ], useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e1 ) ) 323s + 323s + print( "******* 3SLS with different instruments (EViews-like) **********" ) 323s + fit3slsd[[ i ]]$e1e <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, methodResidCov = "noDfCor", method3sls = formulas[ i ], 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e1e, useDfSys = TRUE ) ) 323s + 323s + print( "**** 3SLS with different instruments and methodResidCov = Theil ***" ) 323s + fit3slsd[[ i ]]$e1c <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, methodResidCov = "Theil", method3sls = formulas[ i ], 323s + x = TRUE, useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e1c, useDfSys = TRUE ) ) 323s + 323s + print( "************* W3SLS with different instruments **************" ) 323s + fit3slsd[[ i ]]$e1w <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, method3sls = formulas[ i ], residCovWeighted = TRUE, 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e1w ) ) 323s + 323s + 323s + print( "******* 3SLS with different instruments and restriction ********" ) 323s + fit3slsd[[ i ]]$e2 <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, restrict.matrix = restrm, method3sls = formulas[ i ], 323s + x = TRUE, useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e2 ) ) 323s + 323s + print( "** 3SLS with different instruments and restriction (EViews-like) *" ) 323s + fit3slsd[[ i ]]$e2e <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, methodResidCov = "noDfCor", restrict.matrix = restrm, 323s + method3sls = formulas[ i ], useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e2e, useDfSys = TRUE ) ) 323s + 323s + print( "** W3SLS with different instruments and restriction (EViews-like) *" ) 323s + fit3slsd[[ i ]]$e2we <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, methodResidCov = "noDfCor", restrict.matrix = restrm, 323s + method3sls = formulas[ i ], residCovWeighted = TRUE, 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e2we, useDfSys = TRUE ) ) 323s + 323s + 323s + print( "** 3SLS with different instruments and restriction via restrict.regMat *******" ) 323s + fit3slsd[[ i ]]$e3 <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, restrict.regMat = tc, method3sls = formulas[ i ], 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e3 ) ) 323s + 323s + print( "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" ) 323s + fit3slsd[[ i ]]$e3e <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, methodResidCov = "noDfCor", restrict.regMat = tc, 323s + method3sls = formulas[ i ], x = TRUE, 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e3e, useDfSys = TRUE ) ) 323s + 323s + print( "** W3SLS with different instr. and restr. via restrict.regMat ****" ) 323s + fit3slsd[[ i ]]$e3w <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, restrict.regMat = tc, method3sls = formulas[ i ], 323s + residCovWeighted = TRUE, x = TRUE, 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e3w ) ) 323s + 323s + 323s + print( "****** 3SLS with different instruments and 2 restrictions *********" ) 323s + fit3slsd[[ i ]]$e4 <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, restrict.matrix = restr2m, restrict.rhs = restr2q, 323s + method3sls = formulas[ i ], x = TRUE, 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e4 ) ) 323s + 323s + print( "** 3SLS with different instruments and 2 restrictions (EViews-like) *" ) 323s + fit3slsd[[ i ]]$e4e <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, methodResidCov = "noDfCor", restrict.matrix = restr2m, 323s + restrict.rhs = restr2q, method3sls = formulas[ i ], 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e4e, useDfSys = TRUE ) ) 323s + 323s + print( "**** W3SLS with different instruments and 2 restrictions *********" ) 323s + fit3slsd[[ i ]]$e4w <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, restrict.matrix = restr2m, restrict.rhs = restr2q, 323s + method3sls = formulas[ i ], residCovWeighted = TRUE, 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e4w ) ) 323s + 323s + 323s + print( " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" ) 323s + fit3slsd[[ i ]]$e5 <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, restrict.regMat = tc, restrict.matrix = restr3m, 323s + restrict.rhs = restr3q, method3sls = formulas[ i ], 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e5 ) ) 323s + 323s + print( "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" ) 323s + fit3slsd[[ i ]]$e5e <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, restrict.regMat = tc, methodResidCov = "noDfCor", 323s + restrict.matrix = restr3m, restrict.rhs = restr3q, 323s + method3sls = formulas[ i ], x = TRUE, 323s + useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e5e, useDfSys = TRUE ) ) 323s + 323s + print( "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" ) 323s + fit3slsd[[ i ]]$e5we <- systemfit( system, "3SLS", data = Kmenta, 323s + inst = instlist, restrict.regMat = tc, methodResidCov = "noDfCor", 323s + restrict.matrix = restr3m, restrict.rhs = restr3q, method3sls = formulas[ i ], 323s + residCovWeighted = TRUE, useMatrix = useMatrix ) 323s + print( summary( fit3slsd[[ i ]]$e5we, useDfSys = TRUE ) ) 323s + } 323s [1] "***************************************************" 323s [1] "3SLS formula: GLS" 323s [1] "************* 3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 170 13.4 0.683 0.52 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 102.4 6.40 2.53 0.618 0.546 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 3.47 323s supply 3.47 6.40 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.688 323s supply 0.688 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 46.9385 11.5390 4.07 0.0009 *** 323s price 0.2744 0.0897 3.06 0.0075 ** 323s farmPrice 0.2521 0.0470 5.36 6.4e-05 *** 323s trend 0.2048 0.0781 2.62 0.0185 * 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.53 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.443 MSE: 6.403 Root MSE: 2.53 323s Multiple R-Squared: 0.618 Adjusted R-Squared: 0.546 323s 323s [1] "******* 3SLS with different instruments (EViews-like) **********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 170 9 0.684 0.511 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 102.2 6.39 2.53 0.619 0.547 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.37 3.16 323s supply 3.16 4.83 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.37 2.87 323s supply 2.87 5.11 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.691 323s supply 0.691 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 323s price -0.412 0.134 -3.08 0.0041 ** 323s income 0.362 0.052 6.95 6.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 47.0160 10.3208 4.56 6.8e-05 *** 323s price 0.2734 0.0802 3.41 0.0017 ** 323s farmPrice 0.2522 0.0421 6.00 9.8e-07 *** 323s trend 0.2062 0.0699 2.95 0.0058 ** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.527 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.203 MSE: 6.388 Root MSE: 2.527 323s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 323s 323s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 170 12.7 0.683 0.502 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 102.7 6.42 2.53 0.617 0.545 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.96 323s supply 3.96 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 3.57 323s supply 3.57 6.42 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.685 323s supply 0.685 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 323s price -0.4116 0.1448 -2.84 0.0076 ** 323s income 0.3617 0.0564 6.41 2.9e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 46.8512 11.5060 4.07 0.00027 *** 323s price 0.2756 0.0889 3.10 0.00395 ** 323s farmPrice 0.2520 0.0470 5.36 6.4e-06 *** 323s trend 0.2032 0.0765 2.66 0.01204 * 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.534 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.718 MSE: 6.42 Root MSE: 2.534 323s Multiple R-Squared: 0.617 Adjusted R-Squared: 0.545 323s 323s [1] "************* W3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 170 13.4 0.683 0.52 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 102.4 6.40 2.53 0.618 0.546 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 3.47 323s supply 3.47 6.40 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.688 323s supply 0.688 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 46.9385 11.5390 4.07 0.0009 *** 323s price 0.2744 0.0897 3.06 0.0075 ** 323s farmPrice 0.2521 0.0470 5.36 6.4e-05 *** 323s trend 0.2048 0.0781 2.62 0.0185 * 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.53 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.443 MSE: 6.403 Root MSE: 2.53 323s Multiple R-Squared: 0.618 Adjusted R-Squared: 0.546 323s 323s [1] "******* 3SLS with different instruments and restriction ********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 201 2.72 0.626 0.685 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 72.3 4.25 2.06 0.730 0.699 323s supply 20 16 128.3 8.02 2.83 0.521 0.432 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.35 323s supply 4.35 6.27 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 4.25 5.60 323s supply 5.60 8.02 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.959 323s supply 0.959 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 88.9456 6.3475 14.01 1.1e-15 *** 323s price -0.1778 0.0812 -2.19 0.036 * 323s income 0.3049 0.0474 6.43 2.4e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.062 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 72.262 MSE: 4.251 Root MSE: 2.062 323s Multiple R-Squared: 0.73 Adjusted R-Squared: 0.699 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 40.2918 11.2022 3.60 0.001 ** 323s price 0.3613 0.0785 4.60 5.6e-05 *** 323s farmPrice 0.2201 0.0453 4.86 2.6e-05 *** 323s trend 0.3049 0.0474 6.43 2.4e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.832 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 128.304 MSE: 8.019 Root MSE: 2.832 323s Multiple R-Squared: 0.521 Adjusted R-Squared: 0.432 323s 323s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 200 1.75 0.627 0.651 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 72.7 4.28 2.07 0.729 0.697 323s supply 20 16 127.0 7.94 2.82 0.526 0.437 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.58 323s supply 3.58 5.02 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.64 4.62 323s supply 4.62 6.35 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.961 323s supply 0.961 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 88.7634 5.8428 15.19 < 2e-16 *** 323s price -0.1738 0.0737 -2.36 0.024 * 323s income 0.3027 0.0432 7.00 4.5e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.068 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 72.717 MSE: 4.277 Root MSE: 2.068 323s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 40.8177 10.0564 4.06 0.00027 *** 323s price 0.3569 0.0705 5.06 1.4e-05 *** 323s farmPrice 0.2195 0.0403 5.45 4.4e-06 *** 323s trend 0.3027 0.0432 7.00 4.5e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.818 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 127.044 MSE: 7.94 Root MSE: 2.818 323s Multiple R-Squared: 0.526 Adjusted R-Squared: 0.437 323s 323s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 199 1.77 0.629 0.65 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 72.4 4.26 2.06 0.730 0.698 323s supply 20 16 126.7 7.92 2.81 0.527 0.439 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.24 3.60 323s supply 3.60 5.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.62 4.60 323s supply 4.60 6.34 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.961 323s supply 0.961 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 88.9298 5.9083 15.05 < 2e-16 *** 323s price -0.1760 0.0746 -2.36 0.024 * 323s income 0.3032 0.0434 6.99 4.6e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.064 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 72.435 MSE: 4.261 Root MSE: 2.064 323s Multiple R-Squared: 0.73 Adjusted R-Squared: 0.698 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 40.8325 10.1094 4.04 0.00029 *** 323s price 0.3562 0.0711 5.01 1.7e-05 *** 323s farmPrice 0.2200 0.0405 5.43 4.8e-06 *** 323s trend 0.3032 0.0434 6.99 4.6e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.814 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 126.74 MSE: 7.921 Root MSE: 2.814 323s Multiple R-Squared: 0.527 Adjusted R-Squared: 0.439 323s 323s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 201 2.72 0.626 0.685 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 72.3 4.25 2.06 0.730 0.699 323s supply 20 16 128.3 8.02 2.83 0.521 0.432 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.35 323s supply 4.35 6.27 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 4.25 5.60 323s supply 5.60 8.02 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.959 323s supply 0.959 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 88.9456 6.3475 14.01 1.1e-15 *** 323s price -0.1778 0.0812 -2.19 0.036 * 323s income 0.3049 0.0474 6.43 2.4e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.062 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 72.262 MSE: 4.251 Root MSE: 2.062 323s Multiple R-Squared: 0.73 Adjusted R-Squared: 0.699 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 40.2918 11.2022 3.60 0.001 ** 323s price 0.3613 0.0785 4.60 5.6e-05 *** 323s farmPrice 0.2201 0.0453 4.86 2.6e-05 *** 323s trend 0.3049 0.0474 6.43 2.4e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.832 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 128.304 MSE: 8.019 Root MSE: 2.832 323s Multiple R-Squared: 0.521 Adjusted R-Squared: 0.432 323s 323s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 200 1.75 0.627 0.651 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 72.7 4.28 2.07 0.729 0.697 323s supply 20 16 127.0 7.94 2.82 0.526 0.437 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.58 323s supply 3.58 5.02 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.64 4.62 323s supply 4.62 6.35 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.961 323s supply 0.961 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 88.7634 5.8428 15.19 < 2e-16 *** 323s price -0.1738 0.0737 -2.36 0.024 * 323s income 0.3027 0.0432 7.00 4.5e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.068 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 72.717 MSE: 4.277 Root MSE: 2.068 323s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 40.8177 10.0564 4.06 0.00027 *** 323s price 0.3569 0.0705 5.06 1.4e-05 *** 323s farmPrice 0.2195 0.0403 5.45 4.4e-06 *** 323s trend 0.3027 0.0432 7.00 4.5e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.818 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 127.044 MSE: 7.94 Root MSE: 2.818 323s Multiple R-Squared: 0.526 Adjusted R-Squared: 0.437 323s 323s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 200 2.75 0.627 0.684 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 71.9 4.23 2.06 0.732 0.700 323s supply 20 16 127.9 8.00 2.83 0.523 0.433 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.81 4.36 323s supply 4.36 6.34 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 4.23 5.58 323s supply 5.58 7.99 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.958 323s supply 0.958 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 89.1391 6.4318 13.86 1.6e-15 *** 323s price -0.1803 0.0823 -2.19 0.035 * 323s income 0.3055 0.0476 6.42 2.5e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.057 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 71.945 MSE: 4.232 Root MSE: 2.057 323s Multiple R-Squared: 0.732 Adjusted R-Squared: 0.7 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 40.3187 11.2699 3.58 0.0011 ** 323s price 0.3604 0.0792 4.55 6.5e-05 *** 323s farmPrice 0.2207 0.0456 4.84 2.8e-05 *** 323s trend 0.3055 0.0476 6.42 2.5e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.828 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 127.918 MSE: 7.995 Root MSE: 2.828 323s Multiple R-Squared: 0.523 Adjusted R-Squared: 0.433 323s 323s [1] "****** 3SLS with different instruments and 2 restrictions *********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 211 2.1 0.606 0.71 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 77.9 4.58 2.14 0.709 0.675 323s supply 20 16 133.2 8.32 2.88 0.503 0.410 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.45 323s supply 4.45 6.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 4.58 6.01 323s supply 6.01 8.32 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.972 323s supply 0.972 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 86.4443 5.3770 16.08 <2e-16 *** 323s price -0.1371 0.0504 -2.72 0.01 * 323s income 0.2888 0.0182 15.89 <2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.141 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 77.945 MSE: 4.585 Root MSE: 2.141 323s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 41.8618 5.4316 7.71 4.8e-09 *** 323s price 0.3629 0.0504 7.20 2.1e-08 *** 323s farmPrice 0.2040 0.0205 9.96 9.4e-12 *** 323s trend 0.2888 0.0182 15.89 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.885 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 133.177 MSE: 8.324 Root MSE: 2.885 323s Multiple R-Squared: 0.503 Adjusted R-Squared: 0.41 323s 323s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 210 1.42 0.609 0.668 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 77.9 4.58 2.14 0.709 0.675 323s supply 20 16 132.0 8.25 2.87 0.508 0.415 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.67 323s supply 3.67 4.85 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.90 4.93 323s supply 4.93 6.60 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.972 323s supply 0.972 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 86.3521 4.9704 17.4 <2e-16 *** 323s price -0.1376 0.0458 -3.0 0.0049 ** 323s income 0.2902 0.0168 17.3 <2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.141 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 77.912 MSE: 4.583 Root MSE: 2.141 323s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 41.6089 4.9950 8.33 8.0e-10 *** 323s price 0.3624 0.0458 7.91 2.6e-09 *** 323s farmPrice 0.2069 0.0184 11.27 3.4e-13 *** 323s trend 0.2902 0.0168 17.27 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.872 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 131.997 MSE: 8.25 Root MSE: 2.872 323s Multiple R-Squared: 0.508 Adjusted R-Squared: 0.415 323s 323s [1] "**** W3SLS with different instruments and 2 restrictions *********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 214 2.1 0.601 0.713 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 78.9 4.64 2.15 0.706 0.671 323s supply 20 16 135.2 8.45 2.91 0.496 0.401 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.75 4.46 323s supply 4.46 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 4.64 6.09 323s supply 6.09 8.45 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.973 323s supply 0.973 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 85.9516 5.1136 16.81 <2e-16 *** 323s price -0.1318 0.0479 -2.75 0.0093 ** 323s income 0.2884 0.0171 16.86 <2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.154 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 78.853 MSE: 4.638 Root MSE: 2.154 323s Multiple R-Squared: 0.706 Adjusted R-Squared: 0.671 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 41.4498 5.1591 8.03 1.9e-09 *** 323s price 0.3682 0.0479 7.69 5.0e-09 *** 323s farmPrice 0.2028 0.0193 10.50 2.3e-12 *** 323s trend 0.2884 0.0171 16.86 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.907 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 135.215 MSE: 8.451 Root MSE: 2.907 323s Multiple R-Squared: 0.496 Adjusted R-Squared: 0.401 323s 323s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 211 2.1 0.606 0.71 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 77.9 4.58 2.14 0.709 0.675 323s supply 20 16 133.2 8.32 2.88 0.503 0.410 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.45 323s supply 4.45 6.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 4.58 6.01 323s supply 6.01 8.32 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.972 323s supply 0.972 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 86.4443 5.3770 16.08 <2e-16 *** 323s price -0.1371 0.0504 -2.72 0.01 * 323s income 0.2888 0.0182 15.89 <2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.141 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 77.945 MSE: 4.585 Root MSE: 2.141 323s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 41.8618 5.4316 7.71 4.8e-09 *** 323s price 0.3629 0.0504 7.20 2.1e-08 *** 323s farmPrice 0.2040 0.0205 9.96 9.4e-12 *** 323s trend 0.2888 0.0182 15.89 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.885 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 133.177 MSE: 8.324 Root MSE: 2.885 323s Multiple R-Squared: 0.503 Adjusted R-Squared: 0.41 323s 323s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 210 1.42 0.609 0.668 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 77.9 4.58 2.14 0.709 0.675 323s supply 20 16 132.0 8.25 2.87 0.508 0.415 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.67 323s supply 3.67 4.85 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.90 4.93 323s supply 4.93 6.60 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.972 323s supply 0.972 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 86.3521 4.9704 17.4 <2e-16 *** 323s price -0.1376 0.0458 -3.0 0.0049 ** 323s income 0.2902 0.0168 17.3 <2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.141 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 77.912 MSE: 4.583 Root MSE: 2.141 323s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 41.6089 4.9950 8.33 8.0e-10 *** 323s price 0.3624 0.0458 7.91 2.6e-09 *** 323s farmPrice 0.2069 0.0184 11.27 3.4e-13 *** 323s trend 0.2902 0.0168 17.27 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.872 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 131.997 MSE: 8.25 Root MSE: 2.872 323s Multiple R-Squared: 0.508 Adjusted R-Squared: 0.415 323s 323s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 212 1.42 0.604 0.671 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 78.7 4.63 2.15 0.706 0.672 323s supply 20 16 133.7 8.36 2.89 0.501 0.408 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.19 3.68 323s supply 3.68 4.83 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.94 4.99 323s supply 4.99 6.69 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.973 323s supply 0.973 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 85.9108 4.7598 18.05 <2e-16 *** 323s price -0.1329 0.0438 -3.03 0.0045 ** 323s income 0.2900 0.0159 18.18 <2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.152 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 78.713 MSE: 4.63 Root MSE: 2.152 323s Multiple R-Squared: 0.706 Adjusted R-Squared: 0.672 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 41.2362 4.7784 8.63 3.5e-10 *** 323s price 0.3671 0.0438 8.38 7.0e-10 *** 323s farmPrice 0.2060 0.0174 11.81 9.1e-14 *** 323s trend 0.2900 0.0159 18.18 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.891 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 133.715 MSE: 8.357 Root MSE: 2.891 323s Multiple R-Squared: 0.501 Adjusted R-Squared: 0.408 323s 323s [1] "***************************************************" 323s [1] "3SLS formula: IV" 323s [1] "************* 3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 174 2.12 0.675 0.659 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 106.6 6.66 2.58 0.602 0.528 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 4.93 323s supply 4.93 6.66 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.959 323s supply 0.959 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 57.2953 11.7078 4.89 0.00016 *** 323s price 0.1373 0.0979 1.40 0.17978 323s farmPrice 0.2660 0.0483 5.51 4.8e-05 *** 323s trend 0.3970 0.0672 5.91 2.2e-05 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.582 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 323s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 323s 323s [1] "******* 3SLS with different instruments (EViews-like) **********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 173 1.51 0.677 0.612 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 105.7 6.61 2.57 0.606 0.532 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.37 3.16 323s supply 3.16 4.83 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.37 4.04 323s supply 4.04 5.29 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.957 323s supply 0.957 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 323s price -0.412 0.134 -3.08 0.0041 ** 323s income 0.362 0.052 6.95 6.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 57.0636 10.4717 5.45 4.9e-06 *** 323s price 0.1403 0.0875 1.60 0.12 323s farmPrice 0.2657 0.0432 6.15 6.2e-07 *** 323s trend 0.3927 0.0601 6.53 2.0e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.571 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 105.735 MSE: 6.608 Root MSE: 2.571 323s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 323s 323s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 175 0.321 0.673 0.655 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 107.7 6.73 2.59 0.598 0.523 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.96 323s supply 3.96 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 5.14 323s supply 5.14 6.73 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.962 323s supply 0.962 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 323s price -0.4116 0.1448 -2.84 0.0076 ** 323s income 0.3617 0.0564 6.41 2.9e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 57.5567 11.6867 4.92 2.3e-05 *** 323s price 0.1338 0.0977 1.37 0.18 323s farmPrice 0.2664 0.0484 5.51 4.1e-06 *** 323s trend 0.4018 0.0644 6.24 4.8e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.594 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 107.679 MSE: 6.73 Root MSE: 2.594 323s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 323s 323s [1] "************* W3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 174 2.12 0.675 0.659 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 106.6 6.66 2.58 0.602 0.528 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 4.93 323s supply 4.93 6.66 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.959 323s supply 0.959 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 57.2953 11.7078 4.89 0.00016 *** 323s price 0.1373 0.0979 1.40 0.17978 323s farmPrice 0.2660 0.0483 5.51 4.8e-05 *** 323s trend 0.3970 0.0672 5.91 2.2e-05 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.582 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 323s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 323s 323s [1] "******* 3SLS with different instruments and restriction ********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 397 11.4 0.26 -0.128 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 175 10.3 3.20 0.349 0.273 323s supply 20 16 223 13.9 3.73 0.170 0.014 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.35 323s supply 4.35 6.27 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 10.3 11.5 323s supply 11.5 13.9 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.959 323s supply 0.959 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 137.2061 12.4591 11.01 9.3e-13 *** 323s price -0.8101 0.1734 -4.67 4.5e-05 *** 323s income 0.4585 0.0659 6.96 5.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.204 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 174.513 MSE: 10.265 Root MSE: 3.204 323s Multiple R-Squared: 0.349 Adjusted R-Squared: 0.273 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 81.1339 9.1968 8.82 2.6e-10 *** 323s price -0.1765 0.0892 -1.98 0.056 . 323s farmPrice 0.3374 0.0591 5.71 2.1e-06 *** 323s trend 0.4585 0.0659 6.96 5.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.73 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 222.562 MSE: 13.91 Root MSE: 3.73 323s Multiple R-Squared: 0.17 Adjusted R-Squared: 0.014 323s 323s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 365 7.14 0.319 -0.166 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 163 9.57 3.09 0.393 0.322 323s supply 20 16 202 12.65 3.56 0.245 0.104 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.58 323s supply 3.58 5.02 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 8.13 8.67 323s supply 8.67 10.12 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.956 323s supply 0.956 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 134.9751 11.3086 11.94 1.0e-13 *** 323s price -0.7834 0.1565 -5.01 1.7e-05 *** 323s income 0.4539 0.0598 7.60 8.0e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.093 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 162.635 MSE: 9.567 Root MSE: 3.093 323s Multiple R-Squared: 0.393 Adjusted R-Squared: 0.322 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 78.1824 8.5029 9.19 9.6e-11 *** 323s price -0.1415 0.0807 -1.75 0.089 . 323s farmPrice 0.3322 0.0524 6.34 3.1e-07 *** 323s trend 0.4539 0.0598 7.60 8.0e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.557 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 202.39 MSE: 12.649 Root MSE: 3.557 323s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.104 323s 323s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 351 6.72 0.345 -0.118 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 156 9.18 3.03 0.418 0.349 323s supply 20 16 195 12.20 3.49 0.272 0.135 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.24 3.60 323s supply 3.60 5.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 7.81 8.34 323s supply 8.34 9.76 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.955 323s supply 0.955 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 133.7954 11.2810 11.86 1.2e-13 *** 323s price -0.7678 0.1558 -4.93 2.1e-05 *** 323s income 0.4501 0.0595 7.56 8.8e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.031 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 156.133 MSE: 9.184 Root MSE: 3.031 323s Multiple R-Squared: 0.418 Adjusted R-Squared: 0.349 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 77.4097 8.6219 8.98 1.7e-10 *** 323s price -0.1304 0.0814 -1.60 0.12 323s farmPrice 0.3292 0.0523 6.29 3.6e-07 *** 323s trend 0.4501 0.0595 7.56 8.8e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.493 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 195.256 MSE: 12.204 Root MSE: 3.493 323s Multiple R-Squared: 0.272 Adjusted R-Squared: 0.135 323s 323s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 397 11.4 0.26 -0.128 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 175 10.3 3.20 0.349 0.273 323s supply 20 16 223 13.9 3.73 0.170 0.014 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.35 323s supply 4.35 6.27 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 10.3 11.5 323s supply 11.5 13.9 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.959 323s supply 0.959 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 137.2061 12.4591 11.01 9.3e-13 *** 323s price -0.8101 0.1734 -4.67 4.5e-05 *** 323s income 0.4585 0.0659 6.96 5.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.204 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 174.513 MSE: 10.265 Root MSE: 3.204 323s Multiple R-Squared: 0.349 Adjusted R-Squared: 0.273 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 81.1339 9.1968 8.82 2.6e-10 *** 323s price -0.1765 0.0892 -1.98 0.056 . 323s farmPrice 0.3374 0.0591 5.71 2.1e-06 *** 323s trend 0.4585 0.0659 6.96 5.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.73 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 222.562 MSE: 13.91 Root MSE: 3.73 323s Multiple R-Squared: 0.17 Adjusted R-Squared: 0.014 323s 323s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 365 7.14 0.319 -0.166 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 163 9.57 3.09 0.393 0.322 323s supply 20 16 202 12.65 3.56 0.245 0.104 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.58 323s supply 3.58 5.02 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 8.13 8.67 323s supply 8.67 10.12 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.956 323s supply 0.956 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 134.9751 11.3086 11.94 1.0e-13 *** 323s price -0.7834 0.1565 -5.01 1.7e-05 *** 323s income 0.4539 0.0598 7.60 8.0e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.093 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 162.635 MSE: 9.567 Root MSE: 3.093 323s Multiple R-Squared: 0.393 Adjusted R-Squared: 0.322 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 78.1824 8.5029 9.19 9.6e-11 *** 323s price -0.1415 0.0807 -1.75 0.089 . 323s farmPrice 0.3322 0.0524 6.34 3.1e-07 *** 323s trend 0.4539 0.0598 7.60 8.0e-09 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.557 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 202.39 MSE: 12.649 Root MSE: 3.557 323s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.104 323s 323s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 378 10.5 0.295 -0.071 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 166 9.74 3.12 0.382 0.309 323s supply 20 16 212 13.26 3.64 0.209 0.060 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.81 4.36 323s supply 4.36 6.34 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 9.75 10.9 323s supply 10.89 13.3 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.958 323s supply 0.958 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 135.6740 12.4146 10.93 1.1e-12 *** 323s price -0.7901 0.1723 -4.59 5.9e-05 *** 323s income 0.4537 0.0655 6.92 5.6e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.122 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 165.668 MSE: 9.745 Root MSE: 3.122 323s Multiple R-Squared: 0.382 Adjusted R-Squared: 0.309 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 80.0613 9.3724 8.54 5.6e-10 *** 323s price -0.1614 0.0902 -1.79 0.082 . 323s farmPrice 0.3335 0.0590 5.65 2.4e-06 *** 323s trend 0.4537 0.0655 6.92 5.6e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.642 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 212.177 MSE: 13.261 Root MSE: 3.642 323s Multiple R-Squared: 0.209 Adjusted R-Squared: 0.06 323s 323s [1] "****** 3SLS with different instruments and 2 restrictions *********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 362 6.33 0.325 0.259 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 149 8.79 2.96 0.443 0.377 323s supply 20 16 213 13.30 3.65 0.206 0.058 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.45 323s supply 4.45 6.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 8.79 10.5 323s supply 10.51 13.3 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.973 323s supply 0.973 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 135.467 10.955 12.37 2.5e-14 *** 323s price -0.727 0.116 -6.27 3.4e-07 *** 323s income 0.391 0.018 21.77 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.964 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 149.387 MSE: 8.787 Root MSE: 2.964 323s Multiple R-Squared: 0.443 Adjusted R-Squared: 0.377 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 92.2897 11.0352 8.36 7.3e-10 *** 323s price -0.2272 0.1160 -1.96 0.058 . 323s farmPrice 0.2817 0.0209 13.47 2.0e-15 *** 323s trend 0.3913 0.0180 21.77 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.647 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 212.786 MSE: 13.299 Root MSE: 3.647 323s Multiple R-Squared: 0.206 Adjusted R-Squared: 0.058 323s 323s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 306 3.37 0.43 0.248 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 127 7.5 2.74 0.525 0.469 323s supply 20 16 178 11.2 3.34 0.334 0.210 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.67 323s supply 3.67 4.85 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 6.37 7.31 323s supply 7.31 8.92 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.97 323s supply 0.97 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 130.7296 9.6847 13.50 2.0e-15 *** 323s price -0.6671 0.1009 -6.61 1.2e-07 *** 323s income 0.3782 0.0159 23.74 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.738 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 127.413 MSE: 7.495 Root MSE: 2.738 323s Multiple R-Squared: 0.525 Adjusted R-Squared: 0.469 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 87.4510 9.7547 8.96 1.4e-10 *** 323s price -0.1671 0.1009 -1.66 0.11 323s farmPrice 0.2710 0.0183 14.81 < 2e-16 *** 323s trend 0.3782 0.0159 23.74 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.34 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 178.456 MSE: 11.154 Root MSE: 3.34 323s Multiple R-Squared: 0.334 Adjusted R-Squared: 0.21 323s 323s [1] "**** W3SLS with different instruments and 2 restrictions *********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 467 8.98 0.128 0.113 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 193 11.3 3.37 0.282 0.197 323s supply 20 16 275 17.2 4.14 -0.025 -0.217 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.75 4.46 323s supply 4.46 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 11.3 13.6 323s supply 13.6 17.2 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.977 323s supply 0.977 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 143.4678 11.2566 12.75 1.0e-14 *** 323s price -0.8203 0.1194 -6.87 5.6e-08 *** 323s income 0.4047 0.0168 24.13 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.366 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 192.561 MSE: 11.327 Root MSE: 3.366 323s Multiple R-Squared: 0.282 Adjusted R-Squared: 0.197 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 100.3734 11.3093 8.88 1.7e-10 *** 323s price -0.3203 0.1194 -2.68 0.011 * 323s farmPrice 0.2930 0.0198 14.79 < 2e-16 *** 323s trend 0.4047 0.0168 24.13 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 4.144 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 274.775 MSE: 17.173 Root MSE: 4.144 323s Multiple R-Squared: -0.025 Adjusted R-Squared: -0.217 323s 323s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 362 6.33 0.325 0.259 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 149 8.79 2.96 0.443 0.377 323s supply 20 16 213 13.30 3.65 0.206 0.058 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.45 323s supply 4.45 6.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 8.79 10.5 323s supply 10.51 13.3 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.973 323s supply 0.973 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 135.467 10.955 12.37 2.5e-14 *** 323s price -0.727 0.116 -6.27 3.4e-07 *** 323s income 0.391 0.018 21.77 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.964 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 149.387 MSE: 8.787 Root MSE: 2.964 323s Multiple R-Squared: 0.443 Adjusted R-Squared: 0.377 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 92.2897 11.0352 8.36 7.3e-10 *** 323s price -0.2272 0.1160 -1.96 0.058 . 323s farmPrice 0.2817 0.0209 13.47 2.0e-15 *** 323s trend 0.3913 0.0180 21.77 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.647 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 212.786 MSE: 13.299 Root MSE: 3.647 323s Multiple R-Squared: 0.206 Adjusted R-Squared: 0.058 323s 323s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 306 3.37 0.43 0.248 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 127 7.5 2.74 0.525 0.469 323s supply 20 16 178 11.2 3.34 0.334 0.210 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.67 323s supply 3.67 4.85 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 6.37 7.31 323s supply 7.31 8.92 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.97 323s supply 0.97 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 130.7296 9.6847 13.50 2.0e-15 *** 323s price -0.6671 0.1009 -6.61 1.2e-07 *** 323s income 0.3782 0.0159 23.74 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.738 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 127.413 MSE: 7.495 Root MSE: 2.738 323s Multiple R-Squared: 0.525 Adjusted R-Squared: 0.469 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 87.4510 9.7547 8.96 1.4e-10 *** 323s price -0.1671 0.1009 -1.66 0.11 323s farmPrice 0.2710 0.0183 14.81 < 2e-16 *** 323s trend 0.3782 0.0159 23.74 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.34 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 178.456 MSE: 11.154 Root MSE: 3.34 323s Multiple R-Squared: 0.334 Adjusted R-Squared: 0.21 323s 323s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 365 4.27 0.319 0.127 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 153 8.97 3.00 0.431 0.364 323s supply 20 16 213 13.29 3.65 0.207 0.058 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.19 3.68 323s supply 3.68 4.83 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 7.63 8.77 323s supply 8.77 10.64 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.973 323s supply 0.973 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 136.2729 9.8523 13.83 8.9e-16 *** 323s price -0.7306 0.1027 -7.11 2.7e-08 *** 323s income 0.3865 0.0149 25.95 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.996 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 152.579 MSE: 8.975 Root MSE: 2.996 323s Multiple R-Squared: 0.431 Adjusted R-Squared: 0.364 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 93.0701 9.9030 9.40 4.2e-11 *** 323s price -0.2306 0.1027 -2.24 0.031 * 323s farmPrice 0.2777 0.0174 15.99 < 2e-16 *** 323s trend 0.3865 0.0149 25.95 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 3.646 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 212.723 MSE: 13.295 Root MSE: 3.646 323s Multiple R-Squared: 0.207 Adjusted R-Squared: 0.058 323s 323s [1] "***************************************************" 323s [1] "3SLS formula: Schmidt" 323s [1] "************* 3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 164 9.25 0.694 0.512 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 96.6 6.04 2.46 0.640 0.572 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.784 323s supply 0.784 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 323s price 0.2401 0.0999 2.40 0.0288 * 323s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 323s trend 0.2529 0.0997 2.54 0.0219 * 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.458 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 323s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 323s 323s [1] "******* 3SLS with different instruments (EViews-like) **********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 164 6.29 0.694 0.5 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 96.6 6.04 2.46 0.640 0.572 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.37 3.16 323s supply 3.16 4.83 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.37 3.16 323s supply 3.16 4.83 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.784 323s supply 0.784 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 323s price -0.412 0.134 -3.08 0.0041 ** 323s income 0.362 0.052 6.95 6.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 323s price 0.2401 0.0894 2.69 0.0112 * 323s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 323s trend 0.2529 0.0891 2.84 0.0077 ** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.458 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 323s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 323s 323s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 164 8.24 0.694 0.481 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 96.6 6.04 2.46 0.640 0.572 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.96 323s supply 3.96 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 3.96 323s supply 3.96 6.04 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.784 323s supply 0.784 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 323s price -0.4116 0.1448 -2.84 0.0076 ** 323s income 0.3617 0.0564 6.41 2.9e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 323s price 0.2401 0.0999 2.40 0.02208 * 323s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 323s trend 0.2529 0.0997 2.54 0.01605 * 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.458 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 323s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 323s 323s [1] "************* W3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 164 9.25 0.694 0.512 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 96.6 6.04 2.46 0.640 0.572 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.784 323s supply 0.784 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 323s price 0.2401 0.0999 2.40 0.0288 * 323s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 323s trend 0.2529 0.0997 2.54 0.0219 * 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.458 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 323s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 323s 323s [1] "******* 3SLS with different instruments and restriction ********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 175 2.68 0.673 0.665 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 65 3.82 1.96 0.758 0.729 323s supply 20 16 110 6.90 2.63 0.588 0.511 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.35 323s supply 4.35 6.27 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.82 4.87 323s supply 4.87 6.90 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.948 323s supply 0.948 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 95.0869 9.9882 9.52 4.0e-11 *** 323s price -0.2583 0.1296 -1.99 0.054 . 323s income 0.3244 0.0534 6.08 6.8e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.955 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 64.961 MSE: 3.821 Root MSE: 1.955 323s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.729 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 45.4891 12.9647 3.51 0.0013 ** 323s price 0.2929 0.1164 2.52 0.0167 * 323s farmPrice 0.2350 0.0490 4.80 3.1e-05 *** 323s trend 0.3244 0.0534 6.08 6.8e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.627 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 110.382 MSE: 6.899 Root MSE: 2.627 323s Multiple R-Squared: 0.588 Adjusted R-Squared: 0.511 323s 323s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 175 1.75 0.673 0.636 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 65.2 3.83 1.96 0.757 0.728 323s supply 20 16 110.0 6.88 2.62 0.590 0.513 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.58 323s supply 3.58 5.02 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.26 4.02 323s supply 4.02 5.50 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.95 323s supply 0.95 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 94.845 9.149 10.37 4.6e-12 *** 323s price -0.254 0.119 -2.14 0.039 * 323s income 0.323 0.049 6.58 1.5e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.958 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 65.171 MSE: 3.834 Root MSE: 1.958 323s Multiple R-Squared: 0.757 Adjusted R-Squared: 0.728 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 45.7348 11.5558 3.96 0.00037 *** 323s price 0.2913 0.1036 2.81 0.00814 ** 323s farmPrice 0.2343 0.0438 5.35 6.0e-06 *** 323s trend 0.3226 0.0490 6.58 1.5e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.622 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 110.035 MSE: 6.877 Root MSE: 2.622 323s Multiple R-Squared: 0.59 Adjusted R-Squared: 0.513 323s 323s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 175 1.76 0.674 0.635 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 65.1 3.83 1.96 0.757 0.729 323s supply 20 16 109.9 6.87 2.62 0.590 0.513 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.24 3.60 323s supply 3.60 5.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.25 4.02 323s supply 4.02 5.50 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.949 323s supply 0.949 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 94.9533 9.1511 10.38 4.5e-12 *** 323s price -0.2555 0.1186 -2.15 0.038 * 323s income 0.3229 0.0491 6.58 1.5e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.957 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 65.09 MSE: 3.829 Root MSE: 1.957 323s Multiple R-Squared: 0.757 Adjusted R-Squared: 0.729 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 45.7433 11.6043 3.94 0.00038 *** 323s price 0.2908 0.1039 2.80 0.00839 ** 323s farmPrice 0.2347 0.0440 5.34 6.2e-06 *** 323s trend 0.3229 0.0491 6.58 1.5e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.621 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 109.922 MSE: 6.87 Root MSE: 2.621 323s Multiple R-Squared: 0.59 Adjusted R-Squared: 0.513 323s 323s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 175 2.68 0.673 0.665 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 65 3.82 1.96 0.758 0.729 323s supply 20 16 110 6.90 2.63 0.588 0.511 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.35 323s supply 4.35 6.27 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.82 4.87 323s supply 4.87 6.90 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.948 323s supply 0.948 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 95.0869 9.9882 9.52 4.0e-11 *** 323s price -0.2583 0.1296 -1.99 0.054 . 323s income 0.3244 0.0534 6.08 6.8e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.955 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 64.961 MSE: 3.821 Root MSE: 1.955 323s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.729 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 45.4891 12.9647 3.51 0.0013 ** 323s price 0.2929 0.1164 2.52 0.0167 * 323s farmPrice 0.2350 0.0490 4.80 3.1e-05 *** 323s trend 0.3244 0.0534 6.08 6.8e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.627 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 110.382 MSE: 6.899 Root MSE: 2.627 323s Multiple R-Squared: 0.588 Adjusted R-Squared: 0.511 323s 323s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 175 1.75 0.673 0.636 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 65.2 3.83 1.96 0.757 0.728 323s supply 20 16 110.0 6.88 2.62 0.590 0.513 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.58 323s supply 3.58 5.02 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.26 4.02 323s supply 4.02 5.50 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.95 323s supply 0.95 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 94.845 9.149 10.37 4.6e-12 *** 323s price -0.254 0.119 -2.14 0.039 * 323s income 0.323 0.049 6.58 1.5e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.958 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 65.171 MSE: 3.834 Root MSE: 1.958 323s Multiple R-Squared: 0.757 Adjusted R-Squared: 0.728 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 45.7348 11.5558 3.96 0.00037 *** 323s price 0.2913 0.1036 2.81 0.00814 ** 323s farmPrice 0.2343 0.0438 5.35 6.0e-06 *** 323s trend 0.3226 0.0490 6.58 1.5e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.622 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 110.035 MSE: 6.877 Root MSE: 2.622 323s Multiple R-Squared: 0.59 Adjusted R-Squared: 0.513 323s 323s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 175 2.7 0.673 0.664 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 64.9 3.82 1.95 0.758 0.730 323s supply 20 16 110.2 6.89 2.62 0.589 0.512 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.81 4.36 323s supply 4.36 6.34 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.82 4.86 323s supply 4.86 6.89 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.947 323s supply 0.947 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 95.2108 9.9899 9.53 3.9e-11 *** 323s price -0.2599 0.1296 -2.00 0.053 . 323s income 0.3248 0.0535 6.08 6.9e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.954 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 64.876 MSE: 3.816 Root MSE: 1.954 323s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.73 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 45.5042 13.0242 3.49 0.0013 ** 323s price 0.2923 0.1167 2.50 0.0172 * 323s farmPrice 0.2354 0.0492 4.78 3.3e-05 *** 323s trend 0.3248 0.0535 6.08 6.9e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.625 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 110.241 MSE: 6.89 Root MSE: 2.625 323s Multiple R-Squared: 0.589 Adjusted R-Squared: 0.512 323s 323s [1] "****** 3SLS with different instruments and 2 restrictions *********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 178 1.92 0.667 0.696 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.5 3.97 1.99 0.748 0.719 323s supply 20 16 110.9 6.93 2.63 0.586 0.509 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.45 323s supply 4.45 6.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 5.06 323s supply 5.06 6.93 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.964 323s supply 0.964 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 93.3937 10.2477 9.11 9.1e-11 *** 323s price -0.2208 0.1165 -1.90 0.066 . 323s income 0.3033 0.0257 11.78 9.9e-14 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.993 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.513 MSE: 3.971 Root MSE: 1.993 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.0104 10.4895 4.67 4.3e-05 *** 323s price 0.2792 0.1165 2.40 0.022 * 323s farmPrice 0.2150 0.0247 8.70 2.8e-10 *** 323s trend 0.3033 0.0257 11.78 9.9e-14 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.633 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 110.934 MSE: 6.933 Root MSE: 2.633 323s Multiple R-Squared: 0.586 Adjusted R-Squared: 0.509 323s 323s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 178 1.3 0.668 0.659 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.6 3.98 1.99 0.748 0.718 323s supply 20 16 110.7 6.92 2.63 0.587 0.510 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.67 323s supply 3.67 4.85 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.38 4.17 323s supply 4.17 5.53 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.965 323s supply 0.965 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 93.210 9.365 9.95 9.6e-12 *** 323s price -0.219 0.105 -2.09 0.044 * 323s income 0.304 0.023 13.19 3.8e-15 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.994 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.616 MSE: 3.977 Root MSE: 1.994 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 48.6930 9.6005 5.07 1.3e-05 *** 323s price 0.2806 0.1052 2.67 0.011 * 323s farmPrice 0.2168 0.0216 10.02 8.1e-12 *** 323s trend 0.3038 0.0230 13.19 3.8e-15 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.63 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 110.672 MSE: 6.917 Root MSE: 2.63 323s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.51 323s 323s [1] "**** W3SLS with different instruments and 2 restrictions *********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 179 1.92 0.666 0.698 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.7 3.98 2.00 0.747 0.718 323s supply 20 16 111.6 6.98 2.64 0.584 0.506 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.75 4.46 323s supply 4.46 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.98 5.09 323s supply 5.09 6.98 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.965 323s supply 0.965 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 93.180 10.378 8.98 1.3e-10 *** 323s price -0.218 0.118 -1.85 0.073 . 323s income 0.303 0.025 12.11 4.5e-14 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.996 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.719 MSE: 3.983 Root MSE: 1.996 323s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.718 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 48.8549 10.5929 4.61 5.1e-05 *** 323s price 0.2817 0.1182 2.38 0.023 * 323s farmPrice 0.2141 0.0239 8.94 1.5e-10 *** 323s trend 0.3030 0.0250 12.11 4.5e-14 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.641 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 111.614 MSE: 6.976 Root MSE: 2.641 323s Multiple R-Squared: 0.584 Adjusted R-Squared: 0.506 323s 323s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 178 1.92 0.667 0.696 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.5 3.97 1.99 0.748 0.719 323s supply 20 16 110.9 6.93 2.63 0.586 0.509 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.45 323s supply 4.45 6.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 5.06 323s supply 5.06 6.93 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.964 323s supply 0.964 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 93.3937 10.2477 9.11 9.1e-11 *** 323s price -0.2208 0.1165 -1.90 0.066 . 323s income 0.3033 0.0257 11.78 9.9e-14 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.993 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.513 MSE: 3.971 Root MSE: 1.993 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.0104 10.4895 4.67 4.3e-05 *** 323s price 0.2792 0.1165 2.40 0.022 * 323s farmPrice 0.2150 0.0247 8.70 2.8e-10 *** 323s trend 0.3033 0.0257 11.78 9.9e-14 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.633 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 110.934 MSE: 6.933 Root MSE: 2.633 323s Multiple R-Squared: 0.586 Adjusted R-Squared: 0.509 323s 323s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 178 1.3 0.668 0.659 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.6 3.98 1.99 0.748 0.718 323s supply 20 16 110.7 6.92 2.63 0.587 0.510 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.67 323s supply 3.67 4.85 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.38 4.17 323s supply 4.17 5.53 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.965 323s supply 0.965 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 93.210 9.365 9.95 9.6e-12 *** 323s price -0.219 0.105 -2.09 0.044 * 323s income 0.304 0.023 13.19 3.8e-15 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.994 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.616 MSE: 3.977 Root MSE: 1.994 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 48.6930 9.6005 5.07 1.3e-05 *** 323s price 0.2806 0.1052 2.67 0.011 * 323s farmPrice 0.2168 0.0216 10.02 8.1e-12 *** 323s trend 0.3038 0.0230 13.19 3.8e-15 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.63 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 110.672 MSE: 6.917 Root MSE: 2.63 323s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.51 323s 323s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 179 1.3 0.666 0.661 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.8 3.99 2.00 0.747 0.717 323s supply 20 16 111.2 6.95 2.64 0.585 0.507 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.19 3.68 323s supply 3.68 4.83 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.39 4.19 323s supply 4.19 5.56 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.965 323s supply 0.965 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 93.0165 9.4718 9.82 1.4e-11 *** 323s price -0.2172 0.1066 -2.04 0.049 * 323s income 0.3036 0.0224 13.56 1.8e-15 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.997 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.8 MSE: 3.988 Root MSE: 1.997 323s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 48.5496 9.6886 5.01 1.6e-05 *** 323s price 0.2828 0.1066 2.65 0.012 * 323s farmPrice 0.2161 0.0210 10.30 3.9e-12 *** 323s trend 0.3036 0.0224 13.56 1.8e-15 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.637 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 111.249 MSE: 6.953 Root MSE: 2.637 323s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 323s 323s [1] "***************************************************" 323s [1] "3SLS formula: GMM" 323s [1] "************* 3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 164 9.25 0.694 0.512 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 96.6 6.04 2.46 0.640 0.572 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.784 323s supply 0.784 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 323s price 0.2401 0.0999 2.40 0.0288 * 323s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 323s trend 0.2529 0.0997 2.54 0.0219 * 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.458 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 323s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 323s 323s [1] "******* 3SLS with different instruments (EViews-like) **********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 164 6.29 0.694 0.5 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 96.6 6.04 2.46 0.640 0.572 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.37 3.16 323s supply 3.16 4.83 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.37 3.16 323s supply 3.16 4.83 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.784 323s supply 0.784 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 323s price -0.412 0.134 -3.08 0.0041 ** 323s income 0.362 0.052 6.95 6.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 323s price 0.2401 0.0894 2.69 0.0112 * 323s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 323s trend 0.2529 0.0891 2.84 0.0077 ** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.458 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 323s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 323s 323s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 164 8.24 0.694 0.481 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 96.6 6.04 2.46 0.640 0.572 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.96 323s supply 3.96 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 3.96 323s supply 3.96 6.04 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.784 323s supply 0.784 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 323s price -0.4116 0.1448 -2.84 0.0076 ** 323s income 0.3617 0.0564 6.41 2.9e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 323s price 0.2401 0.0999 2.40 0.02208 * 323s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 323s trend 0.2529 0.0997 2.54 0.01605 * 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.458 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 323s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 323s 323s [1] "************* W3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 164 9.25 0.694 0.512 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 96.6 6.04 2.46 0.640 0.572 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.784 323s supply 0.784 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 323s price 0.2401 0.0999 2.40 0.0288 * 323s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 323s trend 0.2529 0.0997 2.54 0.0219 * 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.458 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 323s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 323s 323s [1] "******* 3SLS with different instruments and restriction ********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 166 2.78 0.691 0.636 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 63.4 3.73 1.93 0.764 0.736 323s supply 20 16 102.2 6.39 2.53 0.619 0.547 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.35 323s supply 4.35 6.27 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.73 4.59 323s supply 4.59 6.39 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.94 323s supply 0.94 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 100.1363 8.6083 11.63 2.1e-13 *** 323s price -0.3244 0.1114 -2.91 0.0063 ** 323s income 0.3405 0.0509 6.69 1.1e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.931 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 63.395 MSE: 3.729 Root MSE: 1.931 323s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.7623 12.2354 4.07 0.00027 *** 323s price 0.2366 0.1018 2.33 0.02617 * 323s farmPrice 0.2473 0.0474 5.22 9.0e-06 *** 323s trend 0.3405 0.0509 6.69 1.1e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.527 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.181 MSE: 6.386 Root MSE: 2.527 323s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 323s 323s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 165 1.84 0.691 0.608 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 63.4 3.73 1.93 0.764 0.736 323s supply 20 16 102.1 6.38 2.53 0.619 0.548 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.58 323s supply 3.58 5.02 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.17 3.79 323s supply 3.79 5.10 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.941 323s supply 0.941 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 99.9363 7.9106 12.63 2.1e-14 *** 323s price -0.3212 0.1019 -3.15 0.0034 ** 323s income 0.3393 0.0466 7.28 2.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.931 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 63.37 MSE: 3.728 Root MSE: 1.931 323s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.8516 10.9418 4.56 6.4e-05 *** 323s price 0.2364 0.0910 2.60 0.014 * 323s farmPrice 0.2467 0.0423 5.83 1.4e-06 *** 323s trend 0.3393 0.0466 7.28 2.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.526 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.07 MSE: 6.379 Root MSE: 2.526 323s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 323s 323s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 165 1.85 0.691 0.608 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 63.4 3.73 1.93 0.764 0.736 323s supply 20 16 102.1 6.38 2.53 0.619 0.548 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.24 3.60 323s supply 3.60 5.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.17 3.78 323s supply 3.78 5.10 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.941 323s supply 0.941 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 99.9706 7.9399 12.59 2.4e-14 *** 323s price -0.3217 0.1023 -3.15 0.0034 ** 323s income 0.3394 0.0467 7.26 2.1e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.931 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 63.372 MSE: 3.728 Root MSE: 1.931 323s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.8336 10.9955 4.53 6.9e-05 *** 323s price 0.2364 0.0915 2.59 0.014 * 323s farmPrice 0.2469 0.0425 5.80 1.6e-06 *** 323s trend 0.3394 0.0467 7.26 2.1e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.526 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.073 MSE: 6.38 Root MSE: 2.526 323s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 323s 323s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 166 2.78 0.691 0.636 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 63.4 3.73 1.93 0.764 0.736 323s supply 20 16 102.2 6.39 2.53 0.619 0.547 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.35 323s supply 4.35 6.27 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.73 4.59 323s supply 4.59 6.39 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.94 323s supply 0.94 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 100.1363 8.6083 11.63 2.1e-13 *** 323s price -0.3244 0.1114 -2.91 0.0063 ** 323s income 0.3405 0.0509 6.69 1.1e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.931 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 63.395 MSE: 3.729 Root MSE: 1.931 323s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.7623 12.2354 4.07 0.00027 *** 323s price 0.2366 0.1018 2.33 0.02617 * 323s farmPrice 0.2473 0.0474 5.22 9.0e-06 *** 323s trend 0.3405 0.0509 6.69 1.1e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.527 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.181 MSE: 6.386 Root MSE: 2.527 323s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 323s 323s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 165 1.84 0.691 0.608 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 63.4 3.73 1.93 0.764 0.736 323s supply 20 16 102.1 6.38 2.53 0.619 0.548 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.58 323s supply 3.58 5.02 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.17 3.79 323s supply 3.79 5.10 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.941 323s supply 0.941 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 99.9363 7.9106 12.63 2.1e-14 *** 323s price -0.3212 0.1019 -3.15 0.0034 ** 323s income 0.3393 0.0466 7.28 2.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.931 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 63.37 MSE: 3.728 Root MSE: 1.931 323s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.8516 10.9418 4.56 6.4e-05 *** 323s price 0.2364 0.0910 2.60 0.014 * 323s farmPrice 0.2467 0.0423 5.83 1.4e-06 *** 323s trend 0.3393 0.0466 7.28 2.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.526 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.07 MSE: 6.379 Root MSE: 2.526 323s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 323s 323s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 34 166 2.79 0.691 0.635 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 63.4 3.73 1.93 0.764 0.736 323s supply 20 16 102.2 6.39 2.53 0.619 0.547 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.81 4.36 323s supply 4.36 6.34 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.73 4.59 323s supply 4.59 6.39 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.94 323s supply 0.94 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 100.174 8.646 11.59 2.4e-13 *** 323s price -0.325 0.112 -2.91 0.0064 ** 323s income 0.341 0.051 6.67 1.2e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.931 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 63.398 MSE: 3.729 Root MSE: 1.931 323s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 49.7425 12.3029 4.04 0.00029 *** 323s price 0.2367 0.1023 2.31 0.02691 * 323s farmPrice 0.2474 0.0477 5.19 9.8e-06 *** 323s trend 0.3406 0.0510 6.67 1.2e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.527 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 102.183 MSE: 6.386 Root MSE: 2.527 323s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 323s 323s [1] "****** 3SLS with different instruments and 2 restrictions *********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 165 1.89 0.692 0.677 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 64.1 3.77 1.94 0.761 0.733 323s supply 20 16 101.2 6.32 2.52 0.623 0.552 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.45 323s supply 4.45 6.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.77 4.68 323s supply 4.68 6.32 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.96 323s supply 0.96 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 98.8949 8.2696 11.96 6.4e-14 *** 323s price -0.2870 0.0909 -3.16 0.0033 ** 323s income 0.3148 0.0224 14.04 4.4e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.941 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 64.072 MSE: 3.769 Root MSE: 1.941 323s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 54.6693 8.4422 6.48 1.8e-07 *** 323s price 0.2130 0.0909 2.34 0.025 * 323s farmPrice 0.2237 0.0228 9.82 1.3e-11 *** 323s trend 0.3148 0.0224 14.04 4.4e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.515 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 101.181 MSE: 6.324 Root MSE: 2.515 323s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 323s 323s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 165 1.28 0.692 0.642 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 64.1 3.77 1.94 0.761 0.733 323s supply 20 16 101.1 6.32 2.51 0.623 0.552 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.67 323s supply 3.67 4.85 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.21 3.86 323s supply 3.86 5.06 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.96 323s supply 0.96 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 98.6650 7.5755 13.02 5.6e-15 *** 323s price -0.2845 0.0822 -3.46 0.0014 ** 323s income 0.3146 0.0203 15.52 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.942 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 64.111 MSE: 3.771 Root MSE: 1.942 323s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 54.3281 7.7347 7.02 3.6e-08 *** 323s price 0.2155 0.0822 2.62 0.013 * 323s farmPrice 0.2247 0.0201 11.16 4.4e-13 *** 323s trend 0.3146 0.0203 15.52 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.514 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 101.149 MSE: 6.322 Root MSE: 2.514 323s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 323s 323s [1] "**** W3SLS with different instruments and 2 restrictions *********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 165 1.89 0.692 0.677 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 64.1 3.77 1.94 0.761 0.733 323s supply 20 16 101.3 6.33 2.52 0.622 0.551 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.75 4.46 323s supply 4.46 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.77 4.69 323s supply 4.69 6.33 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.96 323s supply 0.96 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 98.9360 8.2215 12.03 5.4e-14 *** 323s price -0.2872 0.0907 -3.17 0.0032 ** 323s income 0.3147 0.0215 14.64 2.2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.941 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 64.08 MSE: 3.769 Root MSE: 1.941 323s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 54.7520 8.3733 6.54 1.5e-07 *** 323s price 0.2128 0.0907 2.35 0.025 * 323s farmPrice 0.2231 0.0218 10.24 4.5e-12 *** 323s trend 0.3147 0.0215 14.64 2.2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.516 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 101.278 MSE: 6.33 Root MSE: 2.516 323s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 323s 323s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 165 1.89 0.692 0.677 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 64.1 3.77 1.94 0.761 0.733 323s supply 20 16 101.2 6.32 2.52 0.623 0.552 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.79 4.45 323s supply 4.45 6.06 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.77 4.68 323s supply 4.68 6.32 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.96 323s supply 0.96 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 98.8949 8.2696 11.96 6.4e-14 *** 323s price -0.2870 0.0909 -3.16 0.0033 ** 323s income 0.3148 0.0224 14.04 4.4e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.941 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 64.072 MSE: 3.769 Root MSE: 1.941 323s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 54.6693 8.4422 6.48 1.8e-07 *** 323s price 0.2130 0.0909 2.34 0.025 * 323s farmPrice 0.2237 0.0228 9.82 1.3e-11 *** 323s trend 0.3148 0.0224 14.04 4.4e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.515 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 101.181 MSE: 6.324 Root MSE: 2.515 323s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 323s 323s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 165 1.28 0.692 0.642 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 64.1 3.77 1.94 0.761 0.733 323s supply 20 16 101.1 6.32 2.51 0.623 0.552 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.22 3.67 323s supply 3.67 4.85 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.21 3.86 323s supply 3.86 5.06 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.96 323s supply 0.96 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 98.6650 7.5755 13.02 5.6e-15 *** 323s price -0.2845 0.0822 -3.46 0.0014 ** 323s income 0.3146 0.0203 15.52 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.942 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 64.111 MSE: 3.771 Root MSE: 1.942 323s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 54.3281 7.7347 7.02 3.6e-08 *** 323s price 0.2155 0.0822 2.62 0.013 * 323s farmPrice 0.2247 0.0201 11.16 4.4e-13 *** 323s trend 0.3146 0.0203 15.52 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.514 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 101.149 MSE: 6.322 Root MSE: 2.514 323s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 323s 323s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 35 165 1.28 0.692 0.643 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 64.1 3.77 1.94 0.761 0.733 323s supply 20 16 101.2 6.33 2.52 0.622 0.552 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.19 3.68 323s supply 3.68 4.83 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.21 3.87 323s supply 3.87 5.06 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.00 0.96 323s supply 0.96 1.00 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 98.6980 7.5376 13.09 4.9e-15 *** 323s price -0.2847 0.0820 -3.47 0.0014 ** 323s income 0.3145 0.0195 16.13 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.942 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 64.117 MSE: 3.772 Root MSE: 1.942 323s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 54.3972 7.6824 7.08 3.0e-08 *** 323s price 0.2153 0.0820 2.62 0.013 * 323s farmPrice 0.2242 0.0193 11.60 1.5e-13 *** 323s trend 0.3145 0.0195 16.13 < 2e-16 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.515 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 101.231 MSE: 6.327 Root MSE: 2.515 323s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.552 323s 323s [1] "***************************************************" 323s [1] "3SLS formula: EViews" 323s [1] "************* 3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 174 2.12 0.675 0.659 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 106.6 6.66 2.58 0.602 0.528 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 4.93 323s supply 4.93 6.66 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.959 323s supply 0.959 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 57.2953 11.5390 4.97 0.00014 *** 323s price 0.1373 0.0897 1.53 0.14529 323s farmPrice 0.2660 0.0470 5.66 3.6e-05 *** 323s trend 0.3970 0.0781 5.08 0.00011 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.582 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 323s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 323s 323s [1] "******* 3SLS with different instruments (EViews-like) **********" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 173 1.51 0.677 0.612 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 105.7 6.61 2.57 0.606 0.532 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.37 3.16 323s supply 3.16 4.83 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.37 4.04 323s supply 4.04 5.29 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.957 323s supply 0.957 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 323s price -0.412 0.134 -3.08 0.0041 ** 323s income 0.362 0.052 6.95 6.0e-08 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 57.0636 10.3208 5.53 3.9e-06 *** 323s price 0.1403 0.0802 1.75 0.089 . 323s farmPrice 0.2657 0.0421 6.32 3.8e-07 *** 323s trend 0.3927 0.0699 5.62 3.0e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.571 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 105.735 MSE: 6.608 Root MSE: 2.571 323s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 323s 323s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 175 0.321 0.673 0.655 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 107.7 6.73 2.59 0.598 0.523 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.96 323s supply 3.96 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 5.14 323s supply 5.14 6.73 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.962 323s supply 0.962 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 323s price -0.4116 0.1448 -2.84 0.0076 ** 323s income 0.3617 0.0564 6.41 2.9e-07 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 57.5567 11.5060 5.00 1.8e-05 *** 323s price 0.1338 0.0889 1.50 0.14 323s farmPrice 0.2664 0.0470 5.66 2.6e-06 *** 323s trend 0.4018 0.0765 5.26 8.7e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.594 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 107.679 MSE: 6.73 Root MSE: 2.594 323s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 323s 323s [1] "************* W3SLS with different instruments **************" 323s 323s systemfit results 323s method: 3SLS 323s 323s N DF SSR detRCov OLS-R2 McElroy-R2 323s system 40 33 174 2.12 0.675 0.659 323s 323s N DF SSR MSE RMSE R2 Adj R2 323s demand 20 17 67.4 3.97 1.99 0.748 0.719 323s supply 20 16 106.6 6.66 2.58 0.602 0.528 323s 323s The covariance matrix of the residuals used for estimation 323s demand supply 323s demand 3.97 3.84 323s supply 3.84 6.04 323s 323s The covariance matrix of the residuals 323s demand supply 323s demand 3.97 4.93 323s supply 4.93 6.66 323s 323s The correlations of the residuals 323s demand supply 323s demand 1.000 0.959 323s supply 0.959 1.000 323s 323s 323s 3SLS estimates for 'demand' (equation 1) 323s Model Formula: consump ~ price + income 323s Instruments: ~income + farmPrice 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 323s price -0.4116 0.1448 -2.84 0.011 * 323s income 0.3617 0.0564 6.41 6.4e-06 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 1.992 on 17 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 17 323s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 323s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 323s 323s 323s 3SLS estimates for 'supply' (equation 2) 323s Model Formula: consump ~ price + farmPrice + trend 323s Instruments: ~income + farmPrice + trend 323s 323s Estimate Std. Error t value Pr(>|t|) 323s (Intercept) 57.2953 11.5390 4.97 0.00014 *** 323s price 0.1373 0.0897 1.53 0.14529 323s farmPrice 0.2660 0.0470 5.66 3.6e-05 *** 323s trend 0.3970 0.0781 5.08 0.00011 *** 323s --- 323s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 323s 323s Residual standard error: 2.582 on 16 degrees of freedom 323s Number of observations: 20 Degrees of Freedom: 16 323s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 323s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 323s 323s [1] "******* 3SLS with different instruments and restriction ********" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 174 3.39 0.676 0.542 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 71.1 4.18 2.04 0.735 0.704 324s supply 20 16 102.6 6.41 2.53 0.617 0.546 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.79 4.35 324s supply 4.35 6.27 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 4.18 4.84 324s supply 4.84 6.41 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.935 324s supply 0.935 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 109.4916 6.3475 17.25 < 2e-16 *** 324s price -0.4470 0.0812 -5.50 3.8e-06 *** 324s income 0.3703 0.0474 7.81 4.3e-09 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.045 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 71.077 MSE: 4.181 Root MSE: 2.045 324s Multiple R-Squared: 0.735 Adjusted R-Squared: 0.704 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 57.6795 11.2022 5.15 1.1e-05 *** 324s price 0.1324 0.0785 1.69 0.1 324s farmPrice 0.2700 0.0453 5.97 9.5e-07 *** 324s trend 0.3703 0.0474 7.81 4.3e-09 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.532 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 102.574 MSE: 6.411 Root MSE: 2.532 324s Multiple R-Squared: 0.617 Adjusted R-Squared: 0.546 324s 324s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 173 2.29 0.678 0.515 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 70.5 4.15 2.04 0.737 0.706 324s supply 20 16 102.2 6.38 2.53 0.619 0.548 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.22 3.58 324s supply 3.58 5.02 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 3.53 3.96 324s supply 3.96 5.11 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.934 324s supply 0.934 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 109.1085 5.8428 18.67 < 2e-16 *** 324s price -0.4422 0.0737 -6.00 8.6e-07 *** 324s income 0.3693 0.0432 8.54 5.6e-10 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.037 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 70.515 MSE: 4.148 Root MSE: 2.037 324s Multiple R-Squared: 0.737 Adjusted R-Squared: 0.706 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 57.2679 10.0564 5.69 2.1e-06 *** 324s price 0.1375 0.0705 1.95 0.06 . 324s farmPrice 0.2691 0.0403 6.68 1.1e-07 *** 324s trend 0.3693 0.0432 8.54 5.6e-10 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.527 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 102.156 MSE: 6.385 Root MSE: 2.527 324s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 324s 324s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 173 2.29 0.678 0.515 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 70.5 4.15 2.04 0.737 0.706 324s supply 20 16 102.1 6.38 2.53 0.619 0.548 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.24 3.60 324s supply 3.60 5.06 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 3.52 3.96 324s supply 3.96 5.11 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.934 324s supply 0.934 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 109.0818 5.9083 18.46 < 2e-16 *** 324s price -0.4418 0.0746 -5.92 1.1e-06 *** 324s income 0.3692 0.0434 8.51 6.2e-10 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.036 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 70.475 MSE: 4.146 Root MSE: 2.036 324s Multiple R-Squared: 0.737 Adjusted R-Squared: 0.706 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 57.2616 10.1094 5.66 2.4e-06 *** 324s price 0.1376 0.0711 1.94 0.061 . 324s farmPrice 0.2690 0.0405 6.64 1.3e-07 *** 324s trend 0.3692 0.0434 8.51 6.2e-10 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.527 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 102.135 MSE: 6.383 Root MSE: 2.527 324s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 324s 324s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 174 3.39 0.676 0.542 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 71.1 4.18 2.04 0.735 0.704 324s supply 20 16 102.6 6.41 2.53 0.617 0.546 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.79 4.35 324s supply 4.35 6.27 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 4.18 4.84 324s supply 4.84 6.41 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.935 324s supply 0.935 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 109.4916 6.3475 17.25 < 2e-16 *** 324s price -0.4470 0.0812 -5.50 3.8e-06 *** 324s income 0.3703 0.0474 7.81 4.3e-09 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.045 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 71.077 MSE: 4.181 Root MSE: 2.045 324s Multiple R-Squared: 0.735 Adjusted R-Squared: 0.704 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 57.6795 11.2022 5.15 1.1e-05 *** 324s price 0.1324 0.0785 1.69 0.1 324s farmPrice 0.2700 0.0453 5.97 9.5e-07 *** 324s trend 0.3703 0.0474 7.81 4.3e-09 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.532 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 102.574 MSE: 6.411 Root MSE: 2.532 324s Multiple R-Squared: 0.617 Adjusted R-Squared: 0.546 324s 324s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 173 2.29 0.678 0.515 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 70.5 4.15 2.04 0.737 0.706 324s supply 20 16 102.2 6.38 2.53 0.619 0.548 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.22 3.58 324s supply 3.58 5.02 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 3.53 3.96 324s supply 3.96 5.11 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.934 324s supply 0.934 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 109.1085 5.8428 18.67 < 2e-16 *** 324s price -0.4422 0.0737 -6.00 8.6e-07 *** 324s income 0.3693 0.0432 8.54 5.6e-10 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.037 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 70.515 MSE: 4.148 Root MSE: 2.037 324s Multiple R-Squared: 0.737 Adjusted R-Squared: 0.706 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 57.2679 10.0564 5.69 2.1e-06 *** 324s price 0.1375 0.0705 1.95 0.06 . 324s farmPrice 0.2691 0.0403 6.68 1.1e-07 *** 324s trend 0.3693 0.0432 8.54 5.6e-10 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.527 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 102.156 MSE: 6.385 Root MSE: 2.527 324s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 324s 324s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 174 3.38 0.676 0.543 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 71 4.18 2.04 0.735 0.704 324s supply 20 16 103 6.41 2.53 0.618 0.546 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.81 4.36 324s supply 4.36 6.34 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 4.18 4.84 324s supply 4.84 6.41 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.935 324s supply 0.935 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 109.4522 6.4318 17.02 < 2e-16 *** 324s price -0.4465 0.0823 -5.42 4.8e-06 *** 324s income 0.3702 0.0476 7.78 4.8e-09 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.044 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 71.017 MSE: 4.177 Root MSE: 2.044 324s Multiple R-Squared: 0.735 Adjusted R-Squared: 0.704 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 57.6669 11.2699 5.12 1.2e-05 *** 324s price 0.1326 0.0792 1.67 0.1 324s farmPrice 0.2699 0.0456 5.92 1.1e-06 *** 324s trend 0.3702 0.0476 7.78 4.8e-09 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.532 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 102.539 MSE: 6.409 Root MSE: 2.532 324s Multiple R-Squared: 0.618 Adjusted R-Squared: 0.546 324s 324s [1] "****** 3SLS with different instruments and 2 restrictions *********" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 358 32.4 0.333 -0.013 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 141 8.32 2.88 0.472 0.410 324s supply 20 16 216 13.53 3.68 0.193 0.042 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.79 4.45 324s supply 4.45 6.06 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 8.32 8.95 324s supply 8.95 13.53 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.844 324s supply 0.844 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 108.5837 5.3770 20.2 < 2e-16 *** 324s price -0.6034 0.0504 -12.0 6.2e-14 *** 324s income 0.5399 0.0182 29.7 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.884 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 141.436 MSE: 8.32 Root MSE: 2.884 324s Multiple R-Squared: 0.472 Adjusted R-Squared: 0.41 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 14.7043 5.4316 2.71 0.01 * 324s price 0.3966 0.0504 7.87 3e-09 *** 324s farmPrice 0.4228 0.0205 20.65 <2e-16 *** 324s trend 0.5399 0.0182 29.71 <2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 3.678 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 216.4 MSE: 13.525 Root MSE: 3.678 324s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 324s 324s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 359 21.9 0.331 -0.059 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 143 8.38 2.90 0.468 0.406 324s supply 20 16 216 13.52 3.68 0.193 0.042 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.22 3.67 324s supply 3.67 4.85 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 7.13 7.43 324s supply 7.43 10.82 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.846 324s supply 0.846 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 107.9852 4.9704 21.7 < 2e-16 *** 324s price -0.5994 0.0458 -13.1 4.9e-15 *** 324s income 0.5420 0.0168 32.2 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.896 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 142.542 MSE: 8.385 Root MSE: 2.896 324s Multiple R-Squared: 0.468 Adjusted R-Squared: 0.406 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 14.4922 4.9950 2.90 0.0064 ** 324s price 0.4006 0.0458 8.75 2.5e-10 *** 324s farmPrice 0.4207 0.0184 22.92 < 2e-16 *** 324s trend 0.5420 0.0168 32.25 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 3.677 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 216.315 MSE: 13.52 Root MSE: 3.677 324s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 324s 324s [1] "**** W3SLS with different instruments and 2 restrictions *********" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 364 32.3 0.322 -0.022 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 143 8.43 2.90 0.466 0.403 324s supply 20 16 220 13.78 3.71 0.178 0.024 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.75 4.46 324s supply 4.46 6.04 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 8.43 9.15 324s supply 9.15 13.78 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.00 0.85 324s supply 0.85 1.00 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 107.9125 5.1136 21.1 < 2e-16 *** 324s price -0.5996 0.0479 -12.5 1.7e-14 *** 324s income 0.5430 0.0171 31.7 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.903 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 143.236 MSE: 8.426 Root MSE: 2.903 324s Multiple R-Squared: 0.466 Adjusted R-Squared: 0.403 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 13.9658 5.1591 2.71 0.01 * 324s price 0.4004 0.0479 8.36 7.3e-10 *** 324s farmPrice 0.4263 0.0193 22.08 < 2e-16 *** 324s trend 0.5430 0.0171 31.74 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 3.712 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 220.468 MSE: 13.779 Root MSE: 3.712 324s Multiple R-Squared: 0.178 Adjusted R-Squared: 0.024 324s 324s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 358 32.4 0.333 -0.013 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 141 8.32 2.88 0.472 0.410 324s supply 20 16 216 13.53 3.68 0.193 0.042 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.79 4.45 324s supply 4.45 6.06 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 8.32 8.95 324s supply 8.95 13.53 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.844 324s supply 0.844 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 108.5837 5.3770 20.2 < 2e-16 *** 324s price -0.6034 0.0504 -12.0 6.2e-14 *** 324s income 0.5399 0.0182 29.7 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.884 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 141.436 MSE: 8.32 Root MSE: 2.884 324s Multiple R-Squared: 0.472 Adjusted R-Squared: 0.41 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 14.7043 5.4316 2.71 0.01 * 324s price 0.3966 0.0504 7.87 3e-09 *** 324s farmPrice 0.4228 0.0205 20.65 <2e-16 *** 324s trend 0.5399 0.0182 29.71 <2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 3.678 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 216.4 MSE: 13.525 Root MSE: 3.678 324s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 324s 324s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 359 21.9 0.331 -0.059 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 143 8.38 2.90 0.468 0.406 324s supply 20 16 216 13.52 3.68 0.193 0.042 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.22 3.67 324s supply 3.67 4.85 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 7.13 7.43 324s supply 7.43 10.82 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.846 324s supply 0.846 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 107.9852 4.9704 21.7 < 2e-16 *** 324s price -0.5994 0.0458 -13.1 4.9e-15 *** 324s income 0.5420 0.0168 32.2 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.896 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 142.542 MSE: 8.385 Root MSE: 2.896 324s Multiple R-Squared: 0.468 Adjusted R-Squared: 0.406 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 14.4922 4.9950 2.90 0.0064 ** 324s price 0.4006 0.0458 8.75 2.5e-10 *** 324s farmPrice 0.4207 0.0184 22.92 < 2e-16 *** 324s trend 0.5420 0.0168 32.25 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 3.677 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 216.315 MSE: 13.52 Root MSE: 3.677 324s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 324s 324s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 364 21.8 0.321 -0.069 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 144 8.49 2.91 0.462 0.399 324s supply 20 16 220 13.76 3.71 0.179 0.025 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.19 3.68 324s supply 3.68 4.83 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 7.21 7.59 324s supply 7.59 11.00 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.852 324s supply 0.852 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 107.3179 4.7598 22.6 < 2e-16 *** 324s price -0.5955 0.0438 -13.6 1.6e-15 *** 324s income 0.5449 0.0159 34.2 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.913 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 144.274 MSE: 8.487 Root MSE: 2.913 324s Multiple R-Squared: 0.462 Adjusted R-Squared: 0.399 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 13.7761 4.7784 2.88 0.0067 ** 324s price 0.4045 0.0438 9.23 6.6e-11 *** 324s farmPrice 0.4237 0.0174 24.30 < 2e-16 *** 324s trend 0.5449 0.0159 34.17 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 3.709 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 220.081 MSE: 13.755 Root MSE: 3.709 324s Multiple R-Squared: 0.179 Adjusted R-Squared: 0.025 324s 324s > 324s > 324s > ## **************** shorter summaries ********************** 324s > print( summary( fit3sls[[ 2 ]]$e1c, equations = FALSE ) ) 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 33 174 -0.718 0.675 0.922 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 65.7 3.87 1.97 0.755 0.726 324s supply 20 16 108.7 6.79 2.61 0.594 0.518 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.87 4.50 324s supply 4.50 6.04 324s 324s warning: this covariance matrix is NOT positive semidefinit! 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 3.87 5.2 324s supply 5.20 6.8 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.981 324s supply 0.981 1.000 324s 324s 324s Coefficients: 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 324s demand_price -0.2436 0.0965 -2.52 0.02183 * 324s demand_income 0.3140 0.0469 6.69 3.8e-06 *** 324s supply_(Intercept) 52.2869 11.8853 4.40 0.00045 *** 324s supply_price 0.2282 0.0997 2.29 0.03595 * 324s supply_farmPrice 0.2272 0.0438 5.19 8.9e-05 *** 324s supply_trend 0.3648 0.0707 5.16 9.5e-05 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( summary( fit3sls[[ 3 ]]$e2e ), residCov = FALSE ) 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 171 0.887 0.68 0.678 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 67.5 3.97 1.99 0.748 0.719 324s supply 20 16 104.0 6.50 2.55 0.612 0.539 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 324s price -0.2243 0.0888 -2.53 0.016 * 324s income 0.2979 0.0420 7.10 3.4e-08 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 1.992 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 324s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 324s price 0.2207 0.0896 2.46 0.019 * 324s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 324s trend 0.2979 0.0420 7.10 3.4e-08 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.55 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 324s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 324s 324s > 324s > print( summary( fit3sls[[ 4 ]]$e3, useDfSys = FALSE ), residCov = FALSE ) 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 173 1.27 0.678 0.722 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 67.8 3.99 2.00 0.747 0.717 324s supply 20 16 104.8 6.55 2.56 0.609 0.536 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 94.222 8.015 11.76 1.4e-09 *** 324s price -0.222 0.096 -2.31 0.034 * 324s income 0.296 0.045 6.57 4.8e-06 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 1.997 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 324s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 55.9604 11.5777 4.83 0.00018 *** 324s price 0.2193 0.1002 2.19 0.04374 * 324s farmPrice 0.2060 0.0403 5.11 0.00011 *** 324s trend 0.2956 0.0450 6.57 6.5e-06 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.559 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 324s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 324s 324s > 324s > print( summary( fit3sls[[ 5 ]]$e4e, equations = FALSE ), 324s + equations = FALSE ) 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 439 21.3 0.18 -0.18 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 169 9.93 3.15 0.370 0.296 324s supply 20 16 271 16.91 4.11 -0.009 -0.198 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.30 3.73 324s supply 3.73 5.00 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 8.44 9.64 324s supply 9.64 13.53 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.902 324s supply 0.902 1.000 324s 324s 324s Coefficients: 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 93.2926 7.3154 12.75 1.0e-14 *** 324s demand_price -0.4781 0.0812 -5.89 1.1e-06 *** 324s demand_income 0.5683 0.0209 27.24 < 2e-16 *** 324s supply_(Intercept) 0.6559 7.5503 0.09 0.93 324s supply_price 0.5219 0.0812 6.43 2.1e-07 *** 324s supply_farmPrice 0.4355 0.0212 20.49 < 2e-16 *** 324s supply_trend 0.5683 0.0209 27.24 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( summary( fit3sls[[ 1 ]]$e4wSym, residCov = FALSE ), 324s + equations = FALSE ) 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 172 1.74 0.68 0.697 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 65.9 3.88 1.97 0.754 0.725 324s supply 20 16 105.7 6.60 2.57 0.606 0.532 324s 324s 324s Coefficients: 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 324s demand_price -0.2443 0.0892 -2.74 0.0096 ** 324s demand_income 0.3234 0.0229 14.14 4.4e-16 *** 324s supply_(Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 324s supply_price 0.2557 0.0892 2.87 0.0069 ** 324s supply_farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 324s supply_trend 0.3234 0.0229 14.14 4.4e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( summary( fit3sls[[ 2 ]]$e5, residCov = FALSE ), residCov = TRUE ) 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 171 1.74 0.681 0.696 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 65.8 3.87 1.97 0.755 0.726 324s supply 20 16 105.4 6.59 2.57 0.607 0.533 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.89 4.53 324s supply 4.53 6.25 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 3.87 4.87 324s supply 4.87 6.59 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.965 324s supply 0.965 1.000 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 324s price -0.2457 0.0891 -2.76 0.0092 ** 324s income 0.3236 0.0233 13.91 8.9e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 1.967 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 324s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 324s price 0.2543 0.0891 2.85 0.0072 ** 324s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 324s trend 0.3236 0.0233 13.91 8.9e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.566 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 324s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 324s 324s > 324s > print( summary( fit3slsi[[ 3 ]]$e3e, residCov = FALSE, 324s + equations = FALSE ) ) 324s 324s systemfit results 324s method: iterated 3SLS 324s 324s convergence achieved after 20 iterations 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 237 0.364 0.557 0.755 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 99.3 5.84 2.42 0.630 0.586 324s supply 20 16 138.1 8.63 2.94 0.485 0.388 324s 324s 324s Coefficients: 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 324s demand_price -0.1043 0.0958 -1.09 0.284 324s demand_income 0.1979 0.0299 6.61 1.4e-07 *** 324s supply_(Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 324s supply_price 0.1851 0.1053 1.76 0.088 . 324s supply_farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 324s supply_trend 0.1979 0.0299 6.61 1.4e-07 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( summary( fit3slsi[[ 4 ]]$e1we ), equations = FALSE, residCov = FALSE ) 324s 324s systemfit results 324s method: iterated 3SLS 324s 324s convergence achieved after 6 iterations 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 33 177 0.667 0.67 0.782 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 65.7 3.87 1.97 0.755 0.726 324s supply 20 16 111.3 6.96 2.64 0.585 0.507 324s 324s 324s Coefficients: 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 94.6333 7.3027 12.96 3.1e-10 *** 324s demand_price -0.2436 0.0890 -2.74 0.01402 * 324s demand_income 0.3140 0.0433 7.25 1.3e-06 *** 324s supply_(Intercept) 52.5527 11.3956 4.61 0.00029 *** 324s supply_price 0.2271 0.0956 2.37 0.03043 * 324s supply_farmPrice 0.2245 0.0416 5.39 6.0e-05 *** 324s supply_trend 0.3756 0.0641 5.86 2.4e-05 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( summary( fit3slsd[[ 5 ]]$e4, residCov = FALSE ) ) 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 35 358 32.4 0.333 -0.013 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 141 8.32 2.88 0.472 0.410 324s supply 20 16 216 13.53 3.68 0.193 0.042 324s 324s 324s 3SLS estimates for 'demand' (equation 1) 324s Model Formula: consump ~ price + income 324s Instruments: ~income + farmPrice 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 108.5837 5.3770 20.2 < 2e-16 *** 324s price -0.6034 0.0504 -12.0 6.2e-14 *** 324s income 0.5399 0.0182 29.7 < 2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 2.884 on 17 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 17 324s SSR: 141.436 MSE: 8.32 Root MSE: 2.884 324s Multiple R-Squared: 0.472 Adjusted R-Squared: 0.41 324s 324s 324s 3SLS estimates for 'supply' (equation 2) 324s Model Formula: consump ~ price + farmPrice + trend 324s Instruments: ~income + farmPrice + trend 324s 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 14.7043 5.4316 2.71 0.01 * 324s price 0.3966 0.0504 7.87 3e-09 *** 324s farmPrice 0.4228 0.0205 20.65 <2e-16 *** 324s trend 0.5399 0.0182 29.71 <2e-16 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s 324s Residual standard error: 3.678 on 16 degrees of freedom 324s Number of observations: 20 Degrees of Freedom: 16 324s SSR: 216.4 MSE: 13.525 Root MSE: 3.678 324s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 324s 324s > 324s > print( summary( fit3slsd[[ 1 ]]$e2we, equations = FALSE ) ) 324s 324s systemfit results 324s method: 3SLS 324s 324s N DF SSR detRCov OLS-R2 McElroy-R2 324s system 40 34 199 1.77 0.629 0.65 324s 324s N DF SSR MSE RMSE R2 Adj R2 324s demand 20 17 72.4 4.26 2.06 0.730 0.698 324s supply 20 16 126.7 7.92 2.81 0.527 0.439 324s 324s The covariance matrix of the residuals used for estimation 324s demand supply 324s demand 3.24 3.60 324s supply 3.60 5.06 324s 324s The covariance matrix of the residuals 324s demand supply 324s demand 3.62 4.60 324s supply 4.60 6.34 324s 324s The correlations of the residuals 324s demand supply 324s demand 1.000 0.961 324s supply 0.961 1.000 324s 324s 324s Coefficients: 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 88.9298 5.9083 15.05 < 2e-16 *** 324s demand_price -0.1760 0.0746 -2.36 0.02415 * 324s demand_income 0.3032 0.0434 6.99 4.6e-08 *** 324s supply_(Intercept) 40.8325 10.1094 4.04 0.00029 *** 324s supply_price 0.3562 0.0711 5.01 1.7e-05 *** 324s supply_farmPrice 0.2200 0.0405 5.43 4.8e-06 *** 324s supply_trend 0.3032 0.0434 6.99 4.6e-08 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > 324s > ## ****************** residuals ************************** 324s > print( residuals( fit3sls[[ 1 ]]$e1c ) ) 324s demand supply 324s 1 0.843 0.670 324s 2 -0.698 -0.142 324s 3 2.359 2.659 324s 4 1.490 1.618 324s 5 2.139 2.588 324s 6 1.277 1.485 324s 7 1.571 2.093 324s 8 -3.066 -4.163 324s 9 -1.125 -1.929 324s 10 2.492 3.207 324s 11 -0.108 -0.513 324s 12 -2.292 -2.375 324s 13 -1.598 -2.089 324s 14 -0.271 0.330 324s 15 1.958 3.086 324s 16 -3.430 -4.225 324s 17 -0.313 0.185 324s 18 -2.151 -3.680 324s 19 1.592 1.576 324s 20 -0.668 -0.382 324s > print( residuals( fit3sls[[ 1 ]]$e1c$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 324s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 324s 12 13 14 15 16 17 18 19 20 324s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 324s > 324s > print( residuals( fit3sls[[ 4 ]]$e1wc ) ) 324s demand supply 324s 1 0.843 0.670 324s 2 -0.698 -0.142 324s 3 2.359 2.659 324s 4 1.490 1.618 324s 5 2.139 2.588 324s 6 1.277 1.485 324s 7 1.571 2.093 324s 8 -3.066 -4.163 324s 9 -1.125 -1.929 324s 10 2.492 3.207 324s 11 -0.108 -0.513 324s 12 -2.292 -2.375 324s 13 -1.598 -2.089 324s 14 -0.271 0.330 324s 15 1.958 3.086 324s 16 -3.430 -4.225 324s 17 -0.313 0.185 324s 18 -2.151 -3.680 324s 19 1.592 1.576 324s 20 -0.668 -0.382 324s > print( residuals( fit3sls[[ 4 ]]$e1wc$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 324s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 324s 12 13 14 15 16 17 18 19 20 324s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 324s > 324s > print( residuals( fit3sls[[ 2 ]]$e2e ) ) 324s demand supply 324s 1 0.6744 0.0619 324s 2 -0.7785 -0.6344 324s 3 2.2797 2.2267 324s 4 1.4140 1.2428 324s 5 2.2144 2.4566 324s 6 1.3352 1.3851 324s 7 1.6419 2.0264 324s 8 -2.9923 -4.0603 324s 9 -1.0710 -1.8419 324s 10 2.5226 3.1787 324s 11 -0.3346 -0.8086 324s 12 -2.5999 -2.7819 324s 13 -1.8617 -2.3572 324s 14 -0.3584 0.2840 324s 15 2.1419 3.4511 324s 16 -3.2786 -3.7199 324s 17 -0.0706 0.7656 324s 18 -2.1179 -3.2218 324s 19 1.6924 2.0576 324s 20 -0.4528 0.2893 324s > print( residuals( fit3sls[[ 2 ]]$e2e$eq[[ 2 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 324s 0.0619 -0.6344 2.2267 1.2428 2.4566 1.3851 2.0264 -4.0603 -1.8419 3.1787 324s 11 12 13 14 15 16 17 18 19 20 324s -0.8086 -2.7819 -2.3572 0.2840 3.4511 -3.7199 0.7656 -3.2218 2.0576 0.2893 324s > 324s > print( residuals( fit3sls[[ 3 ]]$e3 ) ) 324s demand supply 324s 1 0.6499 0.045 324s 2 -0.7902 -0.639 324s 3 2.2682 2.223 324s 4 1.4031 1.239 324s 5 2.2253 2.490 324s 6 1.3437 1.414 324s 7 1.6522 2.051 324s 8 -2.9817 -4.013 324s 9 -1.0632 -1.808 324s 10 2.5270 3.179 324s 11 -0.3675 -0.872 324s 12 -2.6445 -2.878 324s 13 -1.8999 -2.437 324s 14 -0.3711 0.237 324s 15 2.1685 3.474 324s 16 -3.2566 -3.680 324s 17 -0.0355 0.809 324s 18 -2.1131 -3.213 324s 19 1.7070 2.060 324s 20 -0.4215 0.319 324s > print( residuals( fit3sls[[ 3 ]]$e3$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 324s 0.6499 -0.7902 2.2682 1.4031 2.2253 1.3437 1.6522 -2.9817 -1.0632 2.5270 324s 11 12 13 14 15 16 17 18 19 20 324s -0.3675 -2.6445 -1.8999 -0.3711 2.1685 -3.2566 -0.0355 -2.1131 1.7070 -0.4215 324s > 324s > print( residuals( fit3sls[[ 4 ]]$e4e ) ) 324s demand supply 324s 1 0.9543 0.278 324s 2 -0.6734 -0.586 324s 3 2.3881 2.272 324s 4 1.5091 1.252 324s 5 2.1028 2.356 324s 6 1.2414 1.271 324s 7 1.5161 1.894 324s 8 -3.1487 -4.421 324s 9 -1.1358 -1.958 324s 10 2.5334 3.368 324s 11 0.0936 -0.275 324s 12 -2.0762 -2.176 324s 13 -1.4415 -1.951 324s 14 -0.2039 0.559 324s 15 1.8691 3.353 324s 16 -3.5213 -4.003 324s 17 -0.3804 0.692 324s 18 -2.2018 -3.453 324s 19 1.4834 1.817 324s 20 -0.9080 -0.289 324s > print( residuals( fit3sls[[ 4 ]]$e4e$eq[[ 2 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 324s 0.278 -0.586 2.272 1.252 2.356 1.271 1.894 -4.421 -1.958 3.368 -0.275 324s 12 13 14 15 16 17 18 19 20 324s -2.176 -1.951 0.559 3.353 -4.003 0.692 -3.453 1.817 -0.289 324s > 324s > print( residuals( fit3sls[[ 5 ]]$e5 ) ) 324s demand supply 324s 1 3.391 2.137 324s 2 0.160 -0.366 324s 3 3.267 2.508 324s 4 2.250 1.132 324s 5 1.168 1.398 324s 6 0.434 0.165 324s 7 0.397 0.594 324s 8 -4.607 -7.911 324s 9 -1.631 -2.964 324s 10 2.800 5.323 324s 11 3.967 4.833 324s 12 2.518 3.479 324s 13 2.169 1.774 324s 14 1.169 3.182 324s 15 -0.415 2.626 324s 16 -5.608 -6.508 324s 17 -2.817 0.433 324s 18 -3.012 -5.580 324s 19 -0.454 -0.427 324s 20 -5.146 -5.829 324s > print( residuals( fit3sls[[ 5 ]]$e5$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 324s 3.391 0.160 3.267 2.250 1.168 0.434 0.397 -4.607 -1.631 2.800 3.967 324s 12 13 14 15 16 17 18 19 20 324s 2.518 2.169 1.169 -0.415 -5.608 -2.817 -3.012 -0.454 -5.146 324s > 324s > print( residuals( fit3slsi[[ 2 ]]$e3e ) ) 324s demand supply 324s 1 -0.376 -0.761 324s 2 -1.281 -1.123 324s 3 1.786 1.809 324s 4 0.942 0.878 324s 5 2.683 3.039 324s 6 1.699 1.899 324s 7 2.083 2.477 324s 8 -2.534 -3.021 324s 9 -0.736 -1.093 324s 10 2.713 3.153 324s 11 -1.748 -2.334 324s 12 -4.518 -5.058 324s 13 -3.502 -4.191 324s 14 -0.901 -0.705 324s 15 3.286 4.209 324s 16 -2.334 -2.514 324s 17 1.438 2.113 324s 18 -1.911 -2.680 324s 19 2.320 2.490 324s 20 0.889 1.412 324s > print( residuals( fit3slsi[[ 2 ]]$e3e$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 324s -0.376 -1.281 1.786 0.942 2.683 1.699 2.083 -2.534 -0.736 2.713 -1.748 324s 12 13 14 15 16 17 18 19 20 324s -4.518 -3.502 -0.901 3.286 -2.334 1.438 -1.911 2.320 0.889 324s > 324s > print( residuals( fit3slsi[[ 1 ]]$e2we ) ) 324s demand supply 324s 1 -0.376 -0.761 324s 2 -1.281 -1.123 324s 3 1.786 1.809 324s 4 0.942 0.878 324s 5 2.683 3.039 324s 6 1.699 1.899 324s 7 2.083 2.477 324s 8 -2.534 -3.021 324s 9 -0.736 -1.093 324s 10 2.713 3.153 324s 11 -1.748 -2.334 324s 12 -4.518 -5.058 324s 13 -3.502 -4.191 324s 14 -0.901 -0.705 324s 15 3.286 4.209 324s 16 -2.334 -2.514 324s 17 1.438 2.113 324s 18 -1.911 -2.680 324s 19 2.320 2.490 324s 20 0.889 1.412 324s > print( residuals( fit3slsi[[ 1 ]]$e2we$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 324s -0.376 -1.281 1.786 0.942 2.683 1.699 2.083 -2.534 -0.736 2.713 -1.748 324s 12 13 14 15 16 17 18 19 20 324s -4.518 -3.502 -0.901 3.286 -2.334 1.438 -1.911 2.320 0.889 324s > 324s > print( residuals( fit3slsd[[ 3 ]]$e4 ) ) 324s demand supply 324s 1 0.7282 0.088 324s 2 -0.7938 -0.850 324s 3 2.2722 2.054 324s 4 1.3947 1.007 324s 5 2.2092 2.526 324s 6 1.3211 1.378 324s 7 1.6076 1.935 324s 8 -3.0646 -4.397 324s 9 -1.0534 -1.692 324s 10 2.6003 3.674 324s 11 -0.1888 -0.319 324s 12 -2.4839 -2.564 324s 13 -1.8018 -2.397 324s 14 -0.3164 0.423 324s 15 2.1290 3.682 324s 16 -3.3141 -3.704 324s 17 -0.0169 1.445 324s 18 -2.1692 -3.473 324s 19 1.6008 1.716 324s 20 -0.6603 -0.530 324s > print( residuals( fit3slsd[[ 3 ]]$e4$eq[[ 2 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 324s 0.088 -0.850 2.054 1.007 2.526 1.378 1.935 -4.397 -1.692 3.674 -0.319 324s 12 13 14 15 16 17 18 19 20 324s -2.564 -2.397 0.423 3.682 -3.704 1.445 -3.473 1.716 -0.530 324s > 324s > print( residuals( fit3slsd[[ 5 ]]$e5we ) ) 324s demand supply 324s 1 3.290 2.057 324s 2 0.781 0.154 324s 3 3.754 2.921 324s 4 2.915 1.707 324s 5 0.906 1.148 324s 6 0.394 0.120 324s 7 0.632 0.775 324s 8 -3.766 -7.138 324s 9 -2.167 -3.402 324s 10 1.391 4.066 324s 11 2.631 3.690 324s 12 2.043 3.077 324s 13 2.405 2.007 324s 14 0.885 2.914 324s 15 -1.051 2.024 324s 16 -5.729 -6.584 324s 17 -4.810 -1.328 324s 18 -2.329 -4.924 324s 19 0.576 0.472 324s 20 -2.753 -3.755 324s > print( residuals( fit3slsd[[ 5 ]]$e5we$eq[[ 2 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 324s 2.057 0.154 2.921 1.707 1.148 0.120 0.775 -7.138 -3.402 4.066 3.690 324s 12 13 14 15 16 17 18 19 20 324s 3.077 2.007 2.914 2.024 -6.584 -1.328 -4.924 0.472 -3.755 324s > 324s > 324s > ## *************** coefficients ********************* 324s > print( round( coef( fit3sls[[ 3 ]]$e1c ), digits = 6 ) ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 94.633 -0.244 0.314 52.287 324s supply_price supply_farmPrice supply_trend 324s 0.228 0.227 0.365 324s > print( round( coef( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]] ), digits = 6 ) ) 324s (Intercept) price farmPrice trend 324s 52.287 0.228 0.227 0.365 324s > 324s > print( round( coef( fit3slsi[[ 4 ]]$e2 ), digits = 6 ) ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 92.074 -0.106 0.200 68.855 324s supply_price supply_farmPrice supply_trend 324s 0.183 0.120 0.200 324s > print( round( coef( fit3slsi[[ 5 ]]$e2$eq[[ 1 ]] ), digits = 6 ) ) 324s (Intercept) price income 324s 92.074 -0.106 0.200 324s > 324s > print( round( coef( fit3sls[[ 2 ]]$e2w ), digits = 6 ) ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 94.182 -0.219 0.294 56.254 324s supply_price supply_farmPrice supply_trend 324s 0.218 0.204 0.294 324s > print( round( coef( fit3sls[[ 3 ]]$e2w$eq[[ 1 ]] ), digits = 6 ) ) 324s (Intercept) price income 324s 94.182 -0.219 0.294 324s > 324s > print( round( coef( fit3slsd[[ 5 ]]$e3e ), digits = 6 ) ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 109.109 -0.442 0.369 57.268 324s supply_price supply_farmPrice supply_trend 324s 0.137 0.269 0.369 324s > print( round( coef( fit3slsd[[ 5 ]]$e3e, modified.regMat = TRUE ), digits = 6 ) ) 324s C1 C2 C3 C4 C5 C6 324s 109.109 -0.442 0.369 57.268 0.137 0.269 324s > print( round( coef( fit3slsd[[ 1 ]]$e3e$eq[[ 2 ]] ), digits = 6 ) ) 324s (Intercept) price farmPrice trend 324s 40.818 0.357 0.219 0.303 324s > 324s > print( round( coef( fit3slsd[[ 4 ]]$e3w ), digits = 6 ) ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 100.174 -0.325 0.341 49.743 324s supply_price supply_farmPrice supply_trend 324s 0.237 0.247 0.341 324s > print( round( coef( fit3slsd[[ 4 ]]$e3w, modified.regMat = TRUE ), digits = 6 ) ) 324s C1 C2 C3 C4 C5 C6 324s 100.174 -0.325 0.341 49.743 0.237 0.247 324s > print( round( coef( fit3slsd[[ 5 ]]$e3w$eq[[ 2 ]] ), digits = 6 ) ) 324s (Intercept) price farmPrice trend 324s 57.667 0.133 0.270 0.370 324s > 324s > print( round( coef( fit3sls[[ 1 ]]$e4 ), digits = 6 ) ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 93.907 -0.246 0.324 49.905 324s supply_price supply_farmPrice supply_trend 324s 0.254 0.229 0.324 324s > print( round( coef( fit3sls[[ 2 ]]$e4$eq[[ 1 ]] ), digits = 6 ) ) 324s (Intercept) price income 324s 93.907 -0.246 0.324 324s > 324s > print( round( coef( fit3slsi[[ 2 ]]$e4we ), digits = 6 ) ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 91.390 -0.217 0.320 47.579 324s supply_price supply_farmPrice supply_trend 324s 0.283 0.224 0.320 324s > print( round( coef( fit3slsi[[ 1 ]]$e4we$eq[[ 1 ]] ), digits = 6 ) ) 324s (Intercept) price income 324s 91.390 -0.217 0.320 324s > 324s > print( round( coef( fit3slsi[[ 2 ]]$e5e ), digits = 6 ) ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 91.390 -0.217 0.320 47.579 324s supply_price supply_farmPrice supply_trend 324s 0.283 0.224 0.320 324s > print( round( coef( fit3slsi[[ 2 ]]$e5e, modified.regMat = TRUE ), digits = 6 ) ) 324s C1 C2 C3 C4 C5 C6 324s 91.390 -0.217 0.320 47.579 0.283 0.224 324s > print( round( coef( fit3slsi[[ 3 ]]$e5e$eq[[ 2 ]] ), digits = 6 ) ) 324s (Intercept) price farmPrice trend 324s 47.579 0.283 0.224 0.320 324s > 324s > 324s > ## *************** coefficients with stats ********************* 324s > print( round( coef( summary( fit3sls[[ 3 ]]$e1c, useDfSys = FALSE ) ), 324s + digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 94.633 7.9208 11.95 0.000000 324s demand_price -0.244 0.0965 -2.52 0.021832 324s demand_income 0.314 0.0469 6.69 0.000004 324s supply_(Intercept) 52.287 11.8853 4.40 0.000448 324s supply_price 0.228 0.0997 2.29 0.035951 324s supply_farmPrice 0.227 0.0438 5.19 0.000089 324s supply_trend 0.365 0.0707 5.16 0.000095 324s > print( round( coef( summary( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]], useDfSys = FALSE ) ), 324s + digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 52.287 11.8853 4.40 0.000448 324s price 0.228 0.0997 2.29 0.035951 324s farmPrice 0.227 0.0438 5.19 0.000089 324s trend 0.365 0.0707 5.16 0.000095 324s > 324s > print( round( coef( summary( fit3slsd[[ 2 ]]$e1w, useDfSys = FALSE ) ), 324s + digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 106.789 11.1435 9.58 0.000000 324s demand_price -0.412 0.1448 -2.84 0.011271 324s demand_income 0.362 0.0564 6.41 0.000006 324s supply_(Intercept) 57.295 11.7078 4.89 0.000162 324s supply_price 0.137 0.0979 1.40 0.179781 324s supply_farmPrice 0.266 0.0483 5.51 0.000048 324s supply_trend 0.397 0.0672 5.91 0.000022 324s > print( round( coef( summary( fit3slsd[[ 3 ]]$e1w$eq[[ 2 ]], useDfSys = FALSE ) ), 324s + digits = 3 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 49.532 12.011 4.12 0.001 324s price 0.240 0.100 2.40 0.029 324s farmPrice 0.256 0.047 5.41 0.000 324s trend 0.253 0.100 2.54 0.022 324s > 324s > print( round( coef( summary( fit3slsi[[ 4 ]]$e2 ) ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 92.074 9.6303 9.56 0.000000 324s demand_price -0.106 0.1023 -1.04 0.305469 324s demand_income 0.200 0.0297 6.73 0.000000 324s supply_(Intercept) 68.855 12.4839 5.52 0.000004 324s supply_price 0.183 0.1189 1.54 0.132354 324s supply_farmPrice 0.120 0.0260 4.63 0.000051 324s supply_trend 0.200 0.0297 6.73 0.000000 324s > print( round( coef( summary( fit3slsi[[ 5 ]]$e2$eq[[ 1 ]] ) ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 92.074 9.6303 9.56 0.000 324s price -0.106 0.1023 -1.04 0.305 324s income 0.200 0.0297 6.73 0.000 324s > 324s > print( round( coef( summary( fit3slsd[[ 5 ]]$e3e, useDfSys = FALSE ) ), 324s + digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 109.109 5.8428 18.67 0.000000 324s demand_price -0.442 0.0737 -6.00 0.000014 324s demand_income 0.369 0.0432 8.54 0.000000 324s supply_(Intercept) 57.268 10.0564 5.69 0.000033 324s supply_price 0.137 0.0705 1.95 0.069081 324s supply_farmPrice 0.269 0.0403 6.68 0.000005 324s supply_trend 0.369 0.0432 8.54 0.000000 324s > print( round( coef( summary( fit3slsd[[ 5 ]]$e3e, useDfSys = FALSE ), 324s + modified.regMat = TRUE ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s C1 109.109 5.8428 18.67 NA 324s C2 -0.442 0.0737 -6.00 NA 324s C3 0.369 0.0432 8.54 NA 324s C4 57.268 10.0564 5.69 NA 324s C5 0.137 0.0705 1.95 NA 324s C6 0.269 0.0403 6.68 NA 324s > print( round( coef( summary( fit3slsd[[ 1 ]]$e3e$eq[[ 2 ]], useDfSys = FALSE ) ), 324s + digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 40.818 10.0564 4.06 0.000912 324s price 0.357 0.0705 5.06 0.000116 324s farmPrice 0.219 0.0403 5.45 0.000053 324s trend 0.303 0.0432 7.00 0.000003 324s > 324s > print( round( coef( summary( fit3slsi[[ 4 ]]$e3w, useDfSys = FALSE ) ), 324s + digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 92.074 9.6303 9.56 0.000000 324s demand_price -0.106 0.1023 -1.04 0.312700 324s demand_income 0.200 0.0297 6.73 0.000004 324s supply_(Intercept) 68.855 12.4839 5.52 0.000047 324s supply_price 0.183 0.1189 1.54 0.142642 324s supply_farmPrice 0.120 0.0260 4.63 0.000278 324s supply_trend 0.200 0.0297 6.73 0.000005 324s > print( round( coef( summary( fit3slsi[[ 4 ]]$e3w, useDfSys = FALSE ), 324s + modified.regMat = TRUE ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s C1 92.074 9.6303 9.56 NA 324s C2 -0.106 0.1023 -1.04 NA 324s C3 0.200 0.0297 6.73 NA 324s C4 68.855 12.4839 5.52 NA 324s C5 0.183 0.1189 1.54 NA 324s C6 0.120 0.0260 4.63 NA 324s > print( round( coef( summary( fit3slsi[[ 5 ]]$e3w$eq[[ 2 ]], useDfSys = FALSE ) ), 324s + digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 68.855 12.4839 5.52 0.000047 324s price 0.183 0.1189 1.54 0.142642 324s farmPrice 0.120 0.0260 4.63 0.000278 324s trend 0.200 0.0297 6.73 0.000005 324s > 324s > print( round( coef( summary( fit3sls[[ 1 ]]$e4 ) ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 93.907 7.9234 11.85 0.000000 324s demand_price -0.246 0.0891 -2.76 0.009212 324s demand_income 0.324 0.0233 13.91 0.000000 324s supply_(Intercept) 49.905 8.1797 6.10 0.000001 324s supply_price 0.254 0.0891 2.85 0.007217 324s supply_farmPrice 0.229 0.0241 9.52 0.000000 324s supply_trend 0.324 0.0233 13.91 0.000000 324s > print( round( coef( summary( fit3sls[[ 2 ]]$e4$eq[[ 1 ]] ) ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 93.907 7.9234 11.85 0.00000 324s price -0.246 0.0891 -2.76 0.00921 324s income 0.324 0.0233 13.91 0.00000 324s > 324s > print( round( coef( summary( fit3slsi[[ 2 ]]$e5e ) ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 91.390 7.3161 12.49 0.00000 324s demand_price -0.217 0.0835 -2.60 0.01365 324s demand_income 0.320 0.0168 19.07 0.00000 324s supply_(Intercept) 47.579 7.4268 6.41 0.00000 324s supply_price 0.283 0.0835 3.39 0.00174 324s supply_farmPrice 0.224 0.0168 13.36 0.00000 324s supply_trend 0.320 0.0168 19.07 0.00000 324s > print( round( coef( summary( fit3slsi[[ 2 ]]$e5e ), modified.regMat = TRUE ), 324s + digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s C1 91.390 7.3161 12.49 0.00000 324s C2 -0.217 0.0835 -2.60 0.01365 324s C3 0.320 0.0168 19.07 0.00000 324s C4 47.579 7.4268 6.41 0.00000 324s C5 0.283 0.0835 3.39 0.00174 324s C6 0.224 0.0168 13.36 0.00000 324s > print( round( coef( summary( fit3slsi[[ 3 ]]$e5e$eq[[ 2 ]] ) ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 47.579 7.4268 6.41 0.00000 324s price 0.283 0.0835 3.39 0.00174 324s farmPrice 0.224 0.0168 13.36 0.00000 324s trend 0.320 0.0168 19.07 0.00000 324s > 324s > print( round( coef( summary( fit3sls[[ 2 ]]$e5we ) ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s demand_(Intercept) 94.083 7.3058 12.88 0.00000 324s demand_price -0.248 0.0812 -3.06 0.00424 324s demand_income 0.325 0.0205 15.81 0.00000 324s supply_(Intercept) 50.019 7.5314 6.64 0.00000 324s supply_price 0.252 0.0812 3.10 0.00383 324s supply_farmPrice 0.231 0.0209 11.05 0.00000 324s supply_trend 0.325 0.0205 15.81 0.00000 324s > print( round( coef( summary( fit3sls[[ 2 ]]$e5we ), modified.regMat = TRUE ), 324s + digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s C1 94.083 7.3058 12.88 0.00000 324s C2 -0.248 0.0812 -3.06 0.00424 324s C3 0.325 0.0205 15.81 0.00000 324s C4 50.019 7.5314 6.64 0.00000 324s C5 0.252 0.0812 3.10 0.00383 324s C6 0.231 0.0209 11.05 0.00000 324s > print( round( coef( summary( fit3sls[[ 3 ]]$e5we$eq[[ 2 ]] ) ), digits = 6 ) ) 324s Estimate Std. Error t value Pr(>|t|) 324s (Intercept) 50.019 7.5314 6.64 0.00000 324s price 0.252 0.0812 3.10 0.00383 324s farmPrice 0.231 0.0209 11.05 0.00000 324s trend 0.325 0.0205 15.81 0.00000 324s > 324s > 324s > ## *********** variance covariance matrix of the coefficients ******* 324s > print( round( vcov( fit3sls[[ 3 ]]$e1c ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 62.7397 -0.67342 0.04930 324s demand_price -0.6734 0.00931 -0.00264 324s demand_income 0.0493 -0.00264 0.00220 324s supply_(Intercept) 65.2708 -0.36561 -0.29198 324s supply_price -0.6979 0.00620 0.00079 324s supply_farmPrice 0.0423 -0.00227 0.00189 324s supply_trend 0.0638 -0.00342 0.00285 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 65.271 -0.69790 0.04230 324s demand_price -0.366 0.00620 -0.00227 324s demand_income -0.292 0.00079 0.00189 324s supply_(Intercept) 141.261 -1.08251 -0.29300 324s supply_price -1.083 0.00993 0.00080 324s supply_farmPrice -0.293 0.00080 0.00192 324s supply_trend -0.417 0.00110 0.00263 324s supply_trend 324s demand_(Intercept) 0.06383 324s demand_price -0.00342 324s demand_income 0.00285 324s supply_(Intercept) -0.41674 324s supply_price 0.00110 324s supply_farmPrice 0.00263 324s supply_trend 0.00500 324s > print( round( vcov( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]] ), digits = 5 ) ) 324s (Intercept) price farmPrice trend 324s (Intercept) 141.261 -1.08251 -0.29300 -0.41674 324s price -1.083 0.00993 0.00080 0.00110 324s farmPrice -0.293 0.00080 0.00192 0.00263 324s trend -0.417 0.00110 0.00263 0.00500 324s > 324s > print( round( vcov( fit3sls[[ 4 ]]$e2 ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 64.2351 -0.68447 0.04535 324s demand_price -0.6845 0.00921 -0.00243 324s demand_income 0.0454 -0.00243 0.00203 324s supply_(Intercept) 67.0281 -0.42600 -0.24804 324s supply_price -0.7080 0.00641 0.00069 324s supply_farmPrice 0.0366 -0.00196 0.00164 324s supply_trend 0.0454 -0.00243 0.00203 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 67.028 -0.70800 0.03661 324s demand_price -0.426 0.00641 -0.00196 324s demand_income -0.248 0.00069 0.00164 324s supply_(Intercept) 134.043 -1.07653 -0.24277 324s supply_price -1.077 0.01003 0.00068 324s supply_farmPrice -0.243 0.00068 0.00163 324s supply_trend -0.248 0.00069 0.00164 324s supply_trend 324s demand_(Intercept) 0.04535 324s demand_price -0.00243 324s demand_income 0.00203 324s supply_(Intercept) -0.24804 324s supply_price 0.00069 324s supply_farmPrice 0.00164 324s supply_trend 0.00203 324s > print( round( vcov( fit3sls[[ 5 ]]$e2$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 64.2351 -0.68447 0.04535 324s price -0.6845 0.00921 -0.00243 324s income 0.0454 -0.00243 0.00203 324s > 324s > print( round( vcov( fit3sls[[ 5 ]]$e3e ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 54.6190 -0.58283 0.03940 324s demand_price -0.5828 0.00789 -0.00211 324s demand_income 0.0394 -0.00211 0.00176 324s supply_(Intercept) 55.1360 -0.34396 -0.21065 324s supply_price -0.5835 0.00527 0.00058 324s supply_farmPrice 0.0310 -0.00166 0.00139 324s supply_trend 0.0394 -0.00211 0.00176 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 55.136 -0.58348 0.03102 324s demand_price -0.344 0.00527 -0.00166 324s demand_income -0.211 0.00058 0.00139 324s supply_(Intercept) 108.147 -0.86360 -0.19987 324s supply_price -0.864 0.00803 0.00056 324s supply_farmPrice -0.200 0.00056 0.00134 324s supply_trend -0.211 0.00058 0.00139 324s supply_trend 324s demand_(Intercept) 0.03940 324s demand_price -0.00211 324s demand_income 0.00176 324s supply_(Intercept) -0.21065 324s supply_price 0.00058 324s supply_farmPrice 0.00139 324s supply_trend 0.00176 324s > print( round( vcov( fit3sls[[ 5 ]]$e3e, modified.regMat = TRUE ), digits = 5 ) ) 324s C1 C2 C3 C4 C5 C6 324s C1 54.6190 -0.58283 0.03940 55.136 -0.58348 0.03102 324s C2 -0.5828 0.00789 -0.00211 -0.344 0.00527 -0.00166 324s C3 0.0394 -0.00211 0.00176 -0.211 0.00058 0.00139 324s C4 55.1360 -0.34396 -0.21065 108.147 -0.86360 -0.19987 324s C5 -0.5835 0.00527 0.00058 -0.864 0.00803 0.00056 324s C6 0.0310 -0.00166 0.00139 -0.200 0.00056 0.00134 324s > print( round( vcov( fit3sls[[ 1 ]]$e3e$eq[[ 2 ]] ), digits = 5 ) ) 324s (Intercept) price farmPrice trend 324s (Intercept) 108.147 -0.86360 -0.19987 -0.21065 324s price -0.864 0.00803 0.00056 0.00058 324s farmPrice -0.200 0.00056 0.00134 0.00139 324s trend -0.211 0.00058 0.00139 0.00176 324s > 324s > print( round( vcov( fit3sls[[ 1 ]]$e4 ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 62.7805 -0.68439 0.06014 324s demand_price -0.6844 0.00794 -0.00113 324s demand_income 0.0601 -0.00113 0.00054 324s supply_(Intercept) 63.2287 -0.69892 0.07078 324s supply_price -0.6844 0.00794 -0.00113 324s supply_farmPrice 0.0499 -0.00087 0.00038 324s supply_trend 0.0601 -0.00113 0.00054 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 63.2287 -0.68439 0.04986 324s demand_price -0.6989 0.00794 -0.00087 324s demand_income 0.0708 -0.00113 0.00038 324s supply_(Intercept) 66.9073 -0.69892 0.02657 324s supply_price -0.6989 0.00794 -0.00087 324s supply_farmPrice 0.0266 -0.00087 0.00058 324s supply_trend 0.0708 -0.00113 0.00038 324s supply_trend 324s demand_(Intercept) 0.06014 324s demand_price -0.00113 324s demand_income 0.00054 324s supply_(Intercept) 0.07078 324s supply_price -0.00113 324s supply_farmPrice 0.00038 324s supply_trend 0.00054 324s > print( round( vcov( fit3sls[[ 2 ]]$e4$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 62.7805 -0.68439 0.06014 324s price -0.6844 0.00794 -0.00113 324s income 0.0601 -0.00113 0.00054 324s > 324s > print( round( vcov( fit3sls[[ 3 ]]$e4wSym ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 62.5490 -0.68436 0.06248 324s demand_price -0.6844 0.00795 -0.00113 324s demand_income 0.0625 -0.00113 0.00052 324s supply_(Intercept) 62.9766 -0.69799 0.07241 324s supply_price -0.6844 0.00795 -0.00113 324s supply_farmPrice 0.0522 -0.00088 0.00037 324s supply_trend 0.0625 -0.00113 0.00052 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 62.9766 -0.68436 0.05220 324s demand_price -0.6980 0.00795 -0.00088 324s demand_income 0.0724 -0.00113 0.00037 324s supply_(Intercept) 66.4588 -0.69799 0.03007 324s supply_price -0.6980 0.00795 -0.00088 324s supply_farmPrice 0.0301 -0.00088 0.00056 324s supply_trend 0.0724 -0.00113 0.00037 324s supply_trend 324s demand_(Intercept) 0.06248 324s demand_price -0.00113 324s demand_income 0.00052 324s supply_(Intercept) 0.07241 324s supply_price -0.00113 324s supply_farmPrice 0.00037 324s supply_trend 0.00052 324s > print( round( vcov( fit3sls[[ 4 ]]$e4wSym$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 62.5490 -0.68436 0.06248 324s price -0.6844 0.00795 -0.00113 324s income 0.0625 -0.00113 0.00052 324s > 324s > print( round( vcov( fit3sls[[ 2 ]]$e5e ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 53.5147 -0.57537 0.04304 324s demand_price -0.5754 0.00659 -0.00085 324s demand_income 0.0430 -0.00085 0.00044 324s supply_(Intercept) 53.9493 -0.58881 0.05259 324s supply_price -0.5754 0.00659 -0.00085 324s supply_farmPrice 0.0345 -0.00063 0.00029 324s supply_trend 0.0430 -0.00085 0.00044 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 53.9493 -0.57537 0.03449 324s demand_price -0.5888 0.00659 -0.00063 324s demand_income 0.0526 -0.00085 0.00029 324s supply_(Intercept) 57.0063 -0.58881 0.01639 324s supply_price -0.5888 0.00659 -0.00063 324s supply_farmPrice 0.0164 -0.00063 0.00045 324s supply_trend 0.0526 -0.00085 0.00029 324s supply_trend 324s demand_(Intercept) 0.04304 324s demand_price -0.00085 324s demand_income 0.00044 324s supply_(Intercept) 0.05259 324s supply_price -0.00085 324s supply_farmPrice 0.00029 324s supply_trend 0.00044 324s > print( round( vcov( fit3sls[[ 2 ]]$e5e, modified.regMat = TRUE ), digits = 5 ) ) 324s C1 C2 C3 C4 C5 C6 324s C1 53.5147 -0.57537 0.04304 53.9493 -0.57537 0.03449 324s C2 -0.5754 0.00659 -0.00085 -0.5888 0.00659 -0.00063 324s C3 0.0430 -0.00085 0.00044 0.0526 -0.00085 0.00029 324s C4 53.9493 -0.58881 0.05259 57.0063 -0.58881 0.01639 324s C5 -0.5754 0.00659 -0.00085 -0.5888 0.00659 -0.00063 324s C6 0.0345 -0.00063 0.00029 0.0164 -0.00063 0.00045 324s > print( round( vcov( fit3sls[[ 3 ]]$e5e$eq[[ 2 ]] ), digits = 5 ) ) 324s (Intercept) price farmPrice trend 324s (Intercept) 57.0063 -0.58881 0.01639 0.05259 324s price -0.5888 0.00659 -0.00063 -0.00085 324s farmPrice 0.0164 -0.00063 0.00045 0.00029 324s trend 0.0526 -0.00085 0.00029 0.00044 324s > 324s > print( round( vcov( fit3slsi[[ 4 ]]$e1e ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 53.3287 -0.57241 0.04191 324s demand_price -0.5724 0.00791 -0.00225 324s demand_income 0.0419 -0.00225 0.00187 324s supply_(Intercept) 60.8329 -0.34075 -0.27213 324s supply_price -0.6504 0.00578 0.00074 324s supply_farmPrice 0.0394 -0.00211 0.00176 324s supply_trend 0.0595 -0.00319 0.00266 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 60.833 -0.65044 0.03942 324s demand_price -0.341 0.00578 -0.00211 324s demand_income -0.272 0.00074 0.00176 324s supply_(Intercept) 129.860 -0.99616 -0.26688 324s supply_price -0.996 0.00915 0.00073 324s supply_farmPrice -0.267 0.00073 0.00173 324s supply_trend -0.396 0.00107 0.00255 324s supply_trend 324s demand_(Intercept) 0.05949 324s demand_price -0.00319 324s demand_income 0.00266 324s supply_(Intercept) -0.39621 324s supply_price 0.00107 324s supply_farmPrice 0.00255 324s supply_trend 0.00411 324s > print( round( vcov( fit3slsi[[ 3 ]]$e1e$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 53.3287 -0.57241 0.04191 324s price -0.5724 0.00791 -0.00225 324s income 0.0419 -0.00225 0.00187 324s > 324s > print( round( vcov( fit3slsi[[ 5 ]]$e1we ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 53.3287 -0.57241 0.04191 324s demand_price -0.5724 0.00791 -0.00225 324s demand_income 0.0419 -0.00225 0.00187 324s supply_(Intercept) 60.8329 -0.34075 -0.27213 324s supply_price -0.6504 0.00578 0.00074 324s supply_farmPrice 0.0394 -0.00211 0.00176 324s supply_trend 0.0595 -0.00319 0.00266 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 60.833 -0.65044 0.03942 324s demand_price -0.341 0.00578 -0.00211 324s demand_income -0.272 0.00074 0.00176 324s supply_(Intercept) 129.860 -0.99616 -0.26688 324s supply_price -0.996 0.00915 0.00073 324s supply_farmPrice -0.267 0.00073 0.00173 324s supply_trend -0.396 0.00107 0.00255 324s supply_trend 324s demand_(Intercept) 0.05949 324s demand_price -0.00319 324s demand_income 0.00266 324s supply_(Intercept) -0.39621 324s supply_price 0.00107 324s supply_farmPrice 0.00255 324s supply_trend 0.00411 324s > print( round( vcov( fit3slsi[[ 1 ]]$e1we$eq[[ 2 ]] ), digits = 5 ) ) 324s (Intercept) price farmPrice trend 324s (Intercept) 129.860 -0.99616 -0.26688 -0.39621 324s price -0.996 0.00915 0.00073 0.00107 324s farmPrice -0.267 0.00073 0.00173 0.00255 324s trend -0.396 0.00107 0.00255 0.00411 324s > 324s > print( round( vcov( fit3slsi[[ 5 ]]$e2e ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 79.5917 -0.81281 0.02003 324s demand_price -0.8128 0.00917 -0.00107 324s demand_income 0.0200 -0.00107 0.00090 324s supply_(Intercept) 90.3437 -0.79178 -0.11134 324s supply_price -0.9184 0.00888 0.00031 324s supply_farmPrice 0.0165 -0.00088 0.00074 324s supply_trend 0.0200 -0.00107 0.00090 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 90.3437 -0.91836 0.01646 324s demand_price -0.7918 0.00888 -0.00088 324s demand_income -0.1113 0.00031 0.00074 324s supply_(Intercept) 124.3894 -1.13680 -0.09494 324s supply_price -1.1368 0.01108 0.00026 324s supply_farmPrice -0.0949 0.00026 0.00063 324s supply_trend -0.1113 0.00031 0.00074 324s supply_trend 324s demand_(Intercept) 0.02003 324s demand_price -0.00107 324s demand_income 0.00090 324s supply_(Intercept) -0.11134 324s supply_price 0.00031 324s supply_farmPrice 0.00074 324s supply_trend 0.00090 324s > print( round( vcov( fit3slsi[[ 4 ]]$e2e$eq[[ 2 ]] ), digits = 5 ) ) 324s (Intercept) price farmPrice trend 324s (Intercept) 124.3894 -1.13680 -0.09494 -0.11134 324s price -1.1368 0.01108 0.00026 0.00031 324s farmPrice -0.0949 0.00026 0.00063 0.00074 324s trend -0.1113 0.00031 0.00074 0.00090 324s > 324s > print( round( vcov( fit3slsi[[ 1 ]]$e3 ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 92.7431 -0.94355 0.01968 324s demand_price -0.9435 0.01046 -0.00105 324s demand_income 0.0197 -0.00105 0.00088 324s supply_(Intercept) 110.7701 -0.99345 -0.11331 324s supply_price -1.1222 0.01091 0.00031 324s supply_farmPrice 0.0168 -0.00090 0.00075 324s supply_trend 0.0197 -0.00105 0.00088 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 110.770 -1.12223 0.01680 324s demand_price -0.993 0.01091 -0.00090 324s demand_income -0.113 0.00031 0.00075 324s supply_(Intercept) 155.849 -1.44407 -0.10125 324s supply_price -1.444 0.01413 0.00028 324s supply_farmPrice -0.101 0.00028 0.00067 324s supply_trend -0.113 0.00031 0.00075 324s supply_trend 324s demand_(Intercept) 0.01968 324s demand_price -0.00105 324s demand_income 0.00088 324s supply_(Intercept) -0.11331 324s supply_price 0.00031 324s supply_farmPrice 0.00075 324s supply_trend 0.00088 324s > print( round( vcov( fit3slsi[[ 1 ]]$e3, modified.regMat = TRUE ), digits = 5 ) ) 324s C1 C2 C3 C4 C5 C6 324s C1 92.7431 -0.94355 0.01968 110.770 -1.12223 0.01680 324s C2 -0.9435 0.01046 -0.00105 -0.993 0.01091 -0.00090 324s C3 0.0197 -0.00105 0.00088 -0.113 0.00031 0.00075 324s C4 110.7701 -0.99345 -0.11331 155.849 -1.44407 -0.10125 324s C5 -1.1222 0.01091 0.00031 -1.444 0.01413 0.00028 324s C6 0.0168 -0.00090 0.00075 -0.101 0.00028 0.00067 324s > print( round( vcov( fit3slsi[[ 5 ]]$e3$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 92.7431 -0.94355 0.01968 324s price -0.9435 0.01046 -0.00105 324s income 0.0197 -0.00105 0.00088 324s > 324s > print( round( vcov( fit3slsi[[ 2 ]]$e4e ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 53.5249 -0.60193 0.07023 324s demand_price -0.6019 0.00697 -0.00098 324s demand_income 0.0702 -0.00098 0.00028 324s supply_(Intercept) 53.7695 -0.60749 0.07383 324s supply_price -0.6019 0.00697 -0.00098 324s supply_farmPrice 0.0611 -0.00082 0.00022 324s supply_trend 0.0702 -0.00098 0.00028 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 53.7695 -0.60193 0.06114 324s demand_price -0.6075 0.00697 -0.00082 324s demand_income 0.0738 -0.00098 0.00022 324s supply_(Intercept) 55.1575 -0.60749 0.05283 324s supply_price -0.6075 0.00697 -0.00082 324s supply_farmPrice 0.0528 -0.00082 0.00028 324s supply_trend 0.0738 -0.00098 0.00022 324s supply_trend 324s demand_(Intercept) 0.07023 324s demand_price -0.00098 324s demand_income 0.00028 324s supply_(Intercept) 0.07383 324s supply_price -0.00098 324s supply_farmPrice 0.00022 324s supply_trend 0.00028 324s > print( round( vcov( fit3slsi[[ 1 ]]$e4e$eq[[ 2 ]] ), digits = 5 ) ) 324s (Intercept) price farmPrice trend 324s (Intercept) 55.1575 -0.60749 0.05283 0.07383 324s price -0.6075 0.00697 -0.00082 -0.00098 324s farmPrice 0.0528 -0.00082 0.00028 0.00022 324s trend 0.0738 -0.00098 0.00022 0.00028 324s > 324s > print( round( vcov( fit3slsi[[ 3 ]]$e5 ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 62.6857 -0.71803 0.09573 324s demand_price -0.7180 0.00846 -0.00132 324s demand_income 0.0957 -0.00132 0.00037 324s supply_(Intercept) 62.7317 -0.72119 0.09909 324s supply_price -0.7180 0.00846 -0.00132 324s supply_farmPrice 0.0863 -0.00115 0.00030 324s supply_trend 0.0957 -0.00132 0.00037 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 62.7317 -0.71803 0.08635 324s demand_price -0.7212 0.00846 -0.00115 324s demand_income 0.0991 -0.00132 0.00030 324s supply_(Intercept) 64.1668 -0.72119 0.07539 324s supply_price -0.7212 0.00846 -0.00115 324s supply_farmPrice 0.0754 -0.00115 0.00038 324s supply_trend 0.0991 -0.00132 0.00030 324s supply_trend 324s demand_(Intercept) 0.09573 324s demand_price -0.00132 324s demand_income 0.00037 324s supply_(Intercept) 0.09909 324s supply_price -0.00132 324s supply_farmPrice 0.00030 324s supply_trend 0.00037 324s > print( round( vcov( fit3slsi[[ 3 ]]$e5, modified.regMat = TRUE ), digits = 5 ) ) 324s C1 C2 C3 C4 C5 C6 324s C1 62.6857 -0.71803 0.09573 62.7317 -0.71803 0.08635 324s C2 -0.7180 0.00846 -0.00132 -0.7212 0.00846 -0.00115 324s C3 0.0957 -0.00132 0.00037 0.0991 -0.00132 0.00030 324s C4 62.7317 -0.72119 0.09909 64.1668 -0.72119 0.07539 324s C5 -0.7180 0.00846 -0.00132 -0.7212 0.00846 -0.00115 324s C6 0.0863 -0.00115 0.00030 0.0754 -0.00115 0.00038 324s > print( round( vcov( fit3slsi[[ 2 ]]$e5$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 62.6857 -0.71803 0.09573 324s price -0.7180 0.00846 -0.00132 324s income 0.0957 -0.00132 0.00037 324s > 324s > print( round( vcov( fit3slsi[[ 5 ]]$e5w ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 107.334 -1.39936 0.34281 324s demand_price -1.399 0.01904 -0.00518 324s demand_income 0.343 -0.00518 0.00179 324s supply_(Intercept) 95.422 -1.22389 0.29205 324s supply_price -1.399 0.01904 -0.00518 324s supply_farmPrice 0.439 -0.00648 0.00214 324s supply_trend 0.343 -0.00518 0.00179 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 95.422 -1.39936 0.43918 324s demand_price -1.224 0.01904 -0.00648 324s demand_income 0.292 -0.00518 0.00214 324s supply_(Intercept) 92.381 -1.22389 0.30881 324s supply_price -1.224 0.01904 -0.00648 324s supply_farmPrice 0.309 -0.00648 0.00328 324s supply_trend 0.292 -0.00518 0.00214 324s supply_trend 324s demand_(Intercept) 0.34281 324s demand_price -0.00518 324s demand_income 0.00179 324s supply_(Intercept) 0.29205 324s supply_price -0.00518 324s supply_farmPrice 0.00214 324s supply_trend 0.00179 324s > print( round( vcov( fit3slsi[[ 5 ]]$e5w, modified.regMat = TRUE ), digits = 5 ) ) 324s C1 C2 C3 C4 C5 C6 324s C1 107.334 -1.39936 0.34281 95.422 -1.39936 0.43918 324s C2 -1.399 0.01904 -0.00518 -1.224 0.01904 -0.00648 324s C3 0.343 -0.00518 0.00179 0.292 -0.00518 0.00214 324s C4 95.422 -1.22389 0.29205 92.381 -1.22389 0.30881 324s C5 -1.399 0.01904 -0.00518 -1.224 0.01904 -0.00648 324s C6 0.439 -0.00648 0.00214 0.309 -0.00648 0.00328 324s > print( round( vcov( fit3slsi[[ 4 ]]$e5w$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 62.6858 -0.71803 0.09573 324s price -0.7180 0.00846 -0.00132 324s income 0.0957 -0.00132 0.00037 324s > 324s > print( round( vcov( fit3slsd[[ 5 ]]$e1c ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 124.179 -1.51767 0.28519 324s demand_price -1.518 0.02098 -0.00595 324s demand_income 0.285 -0.00595 0.00318 324s supply_(Intercept) 45.831 -0.16114 -0.30261 324s supply_price -0.564 0.00477 0.00089 324s supply_farmPrice 0.157 -0.00365 0.00213 324s supply_trend -0.416 0.00351 0.00066 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 45.831 -0.56422 0.15696 324s demand_price -0.161 0.00477 -0.00365 324s demand_income -0.303 0.00089 0.00213 324s supply_(Intercept) 132.389 -0.93831 -0.33973 324s supply_price -0.938 0.00791 0.00115 324s supply_farmPrice -0.340 0.00115 0.00221 324s supply_trend -0.515 0.00349 0.00108 324s supply_trend 324s demand_(Intercept) -0.41585 324s demand_price 0.00351 324s demand_income 0.00066 324s supply_(Intercept) -0.51541 324s supply_price 0.00349 324s supply_farmPrice 0.00108 324s supply_trend 0.00585 324s > print( round( vcov( fit3slsd[[ 2 ]]$e1c$eq[[ 2 ]] ), digits = 5 ) ) 324s (Intercept) price farmPrice trend 324s (Intercept) 136.580 -1.06234 -0.24479 -0.60682 324s price -0.994 0.00955 -0.00011 0.00471 324s farmPrice -0.334 0.00098 0.00234 0.00096 324s trend -0.438 0.00119 0.00284 0.00415 324s > 324s > print( round( vcov( fit3slsd[[ 1 ]]$e2 ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 40.2908 -0.42351 0.02315 324s demand_price -0.4235 0.00660 -0.00242 324s demand_income 0.0232 -0.00242 0.00225 324s supply_(Intercept) 23.1539 0.17811 -0.41781 324s supply_price -0.2648 0.00059 0.00211 324s supply_farmPrice 0.0342 -0.00220 0.00190 324s supply_trend 0.0232 -0.00242 0.00225 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 23.154 -0.26482 0.03423 324s demand_price 0.178 0.00059 -0.00220 324s demand_income -0.418 0.00211 0.00190 324s supply_(Intercept) 125.488 -0.81757 -0.40378 324s supply_price -0.818 0.00616 0.00186 324s supply_farmPrice -0.404 0.00186 0.00205 324s supply_trend -0.418 0.00211 0.00190 324s supply_trend 324s demand_(Intercept) 0.02315 324s demand_price -0.00242 324s demand_income 0.00225 324s supply_(Intercept) -0.41781 324s supply_price 0.00211 324s supply_farmPrice 0.00190 324s supply_trend 0.00225 324s > print( round( vcov( fit3slsd[[ 3 ]]$e2$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 99.763 -1.2027 0.21239 324s price -1.203 0.0168 -0.00490 324s income 0.212 -0.0049 0.00285 324s > 324s > print( round( vcov( fit3slsd[[ 5 ]]$e2we ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 34.9080 -0.36232 0.01530 324s demand_price -0.3623 0.00556 -0.00199 324s demand_income 0.0153 -0.00199 0.00188 324s supply_(Intercept) 20.3293 0.13409 -0.34409 324s supply_price -0.2272 0.00057 0.00174 324s supply_farmPrice 0.0249 -0.00176 0.00155 324s supply_trend 0.0153 -0.00199 0.00188 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 20.329 -0.22716 0.02494 324s demand_price 0.134 0.00057 -0.00176 324s demand_income -0.344 0.00174 0.00155 324s supply_(Intercept) 102.201 -0.66897 -0.32522 324s supply_price -0.669 0.00505 0.00150 324s supply_farmPrice -0.325 0.00150 0.00164 324s supply_trend -0.344 0.00174 0.00155 324s supply_trend 324s demand_(Intercept) 0.01530 324s demand_price -0.00199 324s demand_income 0.00188 324s supply_(Intercept) -0.34409 324s supply_price 0.00174 324s supply_farmPrice 0.00155 324s supply_trend 0.00188 324s > print( round( vcov( fit3slsd[[ 3 ]]$e2we$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 83.743 -1.0065 0.17519 324s price -1.006 0.0141 -0.00410 324s income 0.175 -0.0041 0.00241 324s > 324s > print( round( vcov( fit3slsd[[ 2 ]]$e3 ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 155.228 -2.21373 0.68055 324s demand_price -1.929 0.03005 -0.01103 324s demand_income 0.389 -0.00812 0.00434 324s supply_(Intercept) 120.424 -1.33693 0.13854 324s supply_price -1.546 0.02054 -0.00522 324s supply_farmPrice 0.314 -0.00655 0.00350 324s supply_trend 0.389 -0.00812 0.00434 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) -25.183 -0.42614 0.63002 324s demand_price 0.811 0.00271 -0.01000 324s demand_income -0.572 0.00159 0.00380 324s supply_(Intercept) 84.582 -0.95409 0.10043 324s supply_price -0.279 0.00796 -0.00478 324s supply_farmPrice -0.521 0.00147 0.00350 324s supply_trend -0.572 0.00159 0.00380 324s supply_trend 324s demand_(Intercept) 0.68055 324s demand_price -0.01103 324s demand_income 0.00434 324s supply_(Intercept) 0.13854 324s supply_price -0.00522 324s supply_farmPrice 0.00350 324s supply_trend 0.00434 324s > print( round( vcov( fit3slsd[[ 2 ]]$e3, modified.regMat = TRUE ), digits = 5 ) ) 324s C1 C2 C3 C4 C5 C6 324s C1 155.228 -2.21373 0.68055 -25.183 -0.42614 0.63002 324s C2 -1.929 0.03005 -0.01103 0.811 0.00271 -0.01000 324s C3 0.389 -0.00812 0.00434 -0.572 0.00159 0.00380 324s C4 120.424 -1.33693 0.13854 84.582 -0.95409 0.10043 324s C5 -1.546 0.02054 -0.00522 -0.279 0.00796 -0.00478 324s C6 0.314 -0.00655 0.00350 -0.521 0.00147 0.00350 324s > print( round( vcov( fit3slsd[[ 4 ]]$e3$eq[[ 2 ]] ), digits = 5 ) ) 324s (Intercept) price farmPrice trend 324s (Intercept) 149.704 -1.13641 -0.33425 -0.32676 324s price -1.136 0.01036 0.00094 0.00091 324s farmPrice -0.334 0.00094 0.00225 0.00216 324s trend -0.327 0.00091 0.00216 0.00259 324s > 324s > print( round( vcov( fit3slsd[[ 3 ]]$e4 ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 105.016 -1.17085 0.12591 324s demand_price -1.171 0.01356 -0.00191 324s demand_income 0.126 -0.00191 0.00066 324s supply_(Intercept) 106.127 -1.19320 0.13778 324s supply_price -1.171 0.01356 -0.00191 324s supply_farmPrice 0.102 -0.00148 0.00047 324s supply_trend 0.126 -0.00191 0.00066 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 106.1266 -1.17085 0.10227 324s demand_price -1.1932 0.01356 -0.00148 324s demand_income 0.1378 -0.00191 0.00047 324s supply_(Intercept) 110.0305 -1.19320 0.08453 324s supply_price -1.1932 0.01356 -0.00148 324s supply_farmPrice 0.0845 -0.00148 0.00061 324s supply_trend 0.1378 -0.00191 0.00047 324s supply_trend 324s demand_(Intercept) 0.12591 324s demand_price -0.00191 324s demand_income 0.00066 324s supply_(Intercept) 0.13778 324s supply_price -0.00191 324s supply_farmPrice 0.00047 324s supply_trend 0.00066 324s > print( round( vcov( fit3slsd[[ 5 ]]$e4$eq[[ 1 ]] ), digits = 5 ) ) 324s (Intercept) price income 324s (Intercept) 28.9118 -0.25481 -0.03319 324s price -0.2548 0.00254 0.00001 324s income -0.0332 0.00001 0.00033 324s > 324s > print( round( vcov( fit3slsd[[ 4 ]]$e5e ), digits = 5 ) ) 324s demand_(Intercept) demand_price demand_income 324s demand_(Intercept) 57.3878 -0.60414 0.03280 324s demand_price -0.6041 0.00675 -0.00073 324s demand_income 0.0328 -0.00073 0.00041 324s supply_(Intercept) 57.4828 -0.61352 0.04167 324s supply_price -0.6041 0.00675 -0.00073 324s supply_farmPrice 0.0288 -0.00056 0.00028 324s supply_trend 0.0328 -0.00073 0.00041 324s supply_(Intercept) supply_price supply_farmPrice 324s demand_(Intercept) 57.4828 -0.60414 0.02879 324s demand_price -0.6135 0.00675 -0.00056 324s demand_income 0.0417 -0.00073 0.00028 324s supply_(Intercept) 59.8263 -0.61352 0.01389 324s supply_price -0.6135 0.00675 -0.00056 324s supply_farmPrice 0.0139 -0.00056 0.00041 324s supply_trend 0.0417 -0.00073 0.00028 324s supply_trend 324s demand_(Intercept) 0.03280 324s demand_price -0.00073 324s demand_income 0.00041 324s supply_(Intercept) 0.04167 324s supply_price -0.00073 324s supply_farmPrice 0.00028 324s supply_trend 0.00041 324s > print( round( vcov( fit3slsd[[ 4 ]]$e5e, modified.regMat = TRUE ), digits = 5 ) ) 324s C1 C2 C3 C4 C5 C6 324s C1 57.3878 -0.60414 0.03280 57.4828 -0.60414 0.02879 324s C2 -0.6041 0.00675 -0.00073 -0.6135 0.00675 -0.00056 324s C3 0.0328 -0.00073 0.00041 0.0417 -0.00073 0.00028 324s C4 57.4828 -0.61352 0.04167 59.8263 -0.61352 0.01389 324s C5 -0.6041 0.00675 -0.00073 -0.6135 0.00675 -0.00056 324s C6 0.0288 -0.00056 0.00028 0.0139 -0.00056 0.00041 324s > print( round( vcov( fit3slsd[[ 1 ]]$e5e$eq[[ 2 ]] ), digits = 5 ) ) 324s (Intercept) price farmPrice trend 324s (Intercept) 24.9502 -0.21066 -0.03490 -0.02530 324s price -0.2107 0.00210 0.00000 0.00004 324s farmPrice -0.0349 0.00000 0.00034 0.00018 324s trend -0.0253 0.00004 0.00018 0.00028 324s > 324s > 324s > ## *********** confidence intervals of coefficients ************* 324s > print( confint( fit3sls[[ 1 ]]$e1c, useDfSys = TRUE ) ) 324s 2.5 % 97.5 % 324s demand_(Intercept) 78.518 110.748 324s demand_price -0.440 -0.047 324s demand_income 0.218 0.409 324s supply_(Intercept) 28.106 76.468 324s supply_price 0.025 0.431 324s supply_farmPrice 0.138 0.316 324s supply_trend 0.221 0.509 324s > print( confint( fit3sls[[ 1 ]]$e1c$eq[[ 1 ]], level = 0.9, useDfSys = TRUE ) ) 324s 5 % 95 % 324s (Intercept) 81.228 108.038 324s price -0.407 -0.080 324s income 0.235 0.393 324s > 324s > print( confint( fit3sls[[ 2 ]]$e2e, level = 0.9, useDfSys = TRUE ) ) 324s 5 % 95 % 324s demand_(Intercept) 79.254 109.293 324s demand_price -0.405 -0.044 324s demand_income 0.213 0.383 324s supply_(Intercept) 34.318 76.586 324s supply_price 0.039 0.403 324s supply_farmPrice 0.135 0.284 324s supply_trend 0.213 0.383 324s > print( confint( fit3sls[[ 2 ]]$e2e$eq[[ 2 ]], level = 0.99, useDfSys = TRUE ) ) 324s 0.5 % 99.5 % 324s (Intercept) 27.079 83.826 324s price -0.024 0.465 324s farmPrice 0.110 0.309 324s trend 0.183 0.412 324s > 324s > print( confint( fit3sls[[ 3 ]]$e3, level = 0.99 ) ) 324s 0.5 % 99.5 % 324s demand_(Intercept) 77.934 110.509 324s demand_price -0.417 -0.026 324s demand_income 0.204 0.387 324s supply_(Intercept) 32.432 79.489 324s supply_price 0.016 0.423 324s supply_farmPrice 0.124 0.288 324s supply_trend 0.204 0.387 324s > print( confint( fit3sls[[ 3 ]]$e3$eq[[ 1 ]], level = 0.5 ) ) 324s 25 % 75 % 324s (Intercept) 88.757 99.686 324s price -0.287 -0.156 324s income 0.265 0.326 324s > 324s > print( confint( fit3sls[[ 5 ]]$e3we, level = 0.99 ) ) 324s 0.5 % 99.5 % 324s demand_(Intercept) 79.280 109.202 324s demand_price -0.402 -0.043 324s demand_income 0.212 0.381 324s supply_(Intercept) 34.570 76.815 324s supply_price 0.038 0.402 324s supply_farmPrice 0.134 0.282 324s supply_trend 0.212 0.381 324s > print( confint( fit3sls[[ 5 ]]$e3we$eq[[ 1 ]], level = 0.5 ) ) 324s 25 % 75 % 324s (Intercept) 89.222 99.260 324s price -0.283 -0.162 324s income 0.268 0.325 324s > 324s > print( confint( fit3sls[[ 4 ]]$e4e, level = 0.5, useDfSys = TRUE ) ) 324s 25 % 75 % 324s demand_(Intercept) 79.319 109.021 324s demand_price -0.414 -0.085 324s demand_income 0.282 0.367 324s supply_(Intercept) 34.758 65.413 324s supply_price 0.086 0.415 324s supply_farmPrice 0.188 0.274 324s supply_trend 0.282 0.367 324s > print( confint( fit3sls[[ 4 ]]$e4e$eq[[ 2 ]], level = 0.25, useDfSys = TRUE ) ) 324s 37.5 % 62.5 % 324s (Intercept) 47.661 52.510 324s price 0.224 0.277 324s farmPrice 0.224 0.238 324s trend 0.318 0.331 324s > 324s > print( confint( fit3sls[[ 5 ]]$e5, level = 0.25 ) ) 324s 37.5 % 62.5 % 324s demand_(Intercept) 75.213 107.384 324s demand_price -0.630 -0.268 324s demand_income 0.512 0.606 324s supply_(Intercept) -18.445 14.766 324s supply_price 0.370 0.732 324s supply_farmPrice 0.384 0.481 324s supply_trend 0.512 0.606 324s > print( confint( fit3sls[[ 5 ]]$e5$eq[[ 1 ]], level = 0.975 ) ) 324s 1.3 % 98.8 % 324s (Intercept) 72.742 109.855 324s price -0.658 -0.241 324s income 0.505 0.614 324s > 324s > print( confint( fit3slsi[[ 2 ]]$e3e, level = 0.975, useDfSys = TRUE ) ) 324s 1.3 % 98.8 % 324s demand_(Intercept) 73.905 110.166 324s demand_price -0.299 0.090 324s demand_income 0.137 0.259 324s supply_(Intercept) 45.617 90.949 324s supply_price -0.029 0.399 324s supply_farmPrice 0.073 0.175 324s supply_trend 0.137 0.259 324s > print( confint( fit3slsi[[ 2 ]]$e3e$eq[[ 1 ]], level = 0.999, useDfSys = TRUE ) ) 324s 0.1 % 100 % 324s (Intercept) 59.912 124.159 324s price -0.449 0.241 324s income 0.090 0.306 324s > 324s > print( confint( fit3slsi[[ 1 ]]$e5w, level = 0.975, useDfSys = TRUE ) ) 324s 1.3 % 98.8 % 324s demand_(Intercept) 74.084 106.230 324s demand_price -0.387 -0.014 324s demand_income 0.277 0.355 324s supply_(Intercept) 30.219 62.743 324s supply_price 0.113 0.486 324s supply_farmPrice 0.179 0.259 324s supply_trend 0.277 0.355 324s > print( confint( fit3slsi[[ 1 ]]$e5w$eq[[ 1 ]], level = 0.999, useDfSys = TRUE ) ) 324s 0.1 % 100 % 324s (Intercept) 61.724 118.590 324s price -0.531 0.130 324s income 0.247 0.385 324s > 324s > print( confint( fit3slsd[[ 3 ]]$e4, level = 0.999 ) ) 324s 0.1 % 100 % 324s demand_(Intercept) 72.590 114.198 324s demand_price -0.457 0.016 324s demand_income 0.251 0.356 324s supply_(Intercept) 27.716 70.305 324s supply_price 0.043 0.516 324s supply_farmPrice 0.165 0.265 324s supply_trend 0.251 0.356 324s > print( confint( fit3slsd[[ 3 ]]$e4$eq[[ 2 ]] ) ) 324s 2.5 % 97.5 % 324s (Intercept) 27.716 70.305 324s price 0.043 0.516 324s farmPrice 0.165 0.265 324s trend 0.251 0.356 324s > 324s > print( confint( fit3slsd[[ 2 ]]$e4w, level = 0.999 ) ) 324s 0.1 % 100 % 324s demand_(Intercept) 120.616 166.320 324s demand_price -1.063 -0.578 324s demand_income 0.371 0.439 324s supply_(Intercept) 77.414 123.333 324s supply_price -0.563 -0.078 324s supply_farmPrice 0.253 0.333 324s supply_trend 0.371 0.439 324s > print( confint( fit3slsd[[ 2 ]]$e4w$eq[[ 2 ]] ) ) 324s 2.5 % 97.5 % 324s (Intercept) 77.414 123.333 324s price -0.563 -0.078 324s farmPrice 0.253 0.333 324s trend 0.371 0.439 324s > 324s > 324s > ## *********** fitted values ************* 324s > print( fitted( fit3sls[[ 2 ]]$e1c ) ) 324s demand supply 324s 1 97.6 97.8 324s 2 99.9 99.3 324s 3 99.8 99.5 324s 4 100.0 99.9 324s 5 102.1 101.7 324s 6 102.0 101.8 324s 7 102.4 101.9 324s 8 103.0 104.1 324s 9 101.5 102.3 324s 10 100.3 99.6 324s 11 95.5 95.9 324s 12 94.7 94.8 324s 13 96.1 96.6 324s 14 99.0 98.4 324s 15 103.8 102.7 324s 16 103.7 104.4 324s 17 103.8 103.3 324s 18 102.1 103.6 324s 19 103.6 103.6 324s 20 106.9 106.6 324s > print( fitted( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 12 13 324s 97.6 99.9 99.8 100.0 102.1 102.0 102.4 103.0 101.5 100.3 95.5 94.7 96.1 324s 14 15 16 17 18 19 20 324s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 324s > 324s > print( fitted( fit3sls[[ 1 ]]$e1wc ) ) 324s demand supply 324s 1 97.6 97.8 324s 2 99.9 99.3 324s 3 99.8 99.5 324s 4 100.0 99.9 324s 5 102.1 101.7 324s 6 102.0 101.8 324s 7 102.4 101.9 324s 8 103.0 104.1 324s 9 101.5 102.3 324s 10 100.3 99.6 324s 11 95.5 95.9 324s 12 94.7 94.8 324s 13 96.1 96.6 324s 14 99.0 98.4 324s 15 103.8 102.7 324s 16 103.7 104.4 324s 17 103.8 103.3 324s 18 102.1 103.6 324s 19 103.6 103.6 324s 20 106.9 106.6 324s > print( fitted( fit3sls[[ 1 ]]$e1wc$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 12 13 324s 97.6 99.9 99.8 100.0 102.1 102.0 102.4 103.0 101.5 100.3 95.5 94.7 96.1 324s 14 15 16 17 18 19 20 324s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 324s > 324s > print( fitted( fit3sls[[ 3 ]]$e2e ) ) 324s demand supply 324s 1 97.8 98.4 324s 2 100.0 99.8 324s 3 99.9 99.9 324s 4 100.1 100.3 324s 5 102.0 101.8 324s 6 101.9 101.9 324s 7 102.4 102.0 324s 8 102.9 104.0 324s 9 101.4 102.2 324s 10 100.3 99.6 324s 11 95.8 96.2 324s 12 95.0 95.2 324s 13 96.4 96.9 324s 14 99.1 98.5 324s 15 103.7 102.3 324s 16 103.5 103.9 324s 17 103.6 102.8 324s 18 102.0 103.2 324s 19 103.5 103.2 324s 20 106.7 105.9 324s > print( fitted( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 12 13 324s 98.4 99.8 99.9 100.3 101.8 101.9 102.0 104.0 102.2 99.6 96.2 95.2 96.9 324s 14 15 16 17 18 19 20 324s 98.5 102.3 103.9 102.8 103.2 103.2 105.9 324s > 324s > print( fitted( fit3sls[[ 4 ]]$e3 ) ) 324s demand supply 324s 1 97.8 98.4 324s 2 100.0 99.8 324s 3 99.9 99.9 324s 4 100.1 100.3 324s 5 102.0 101.7 324s 6 101.9 101.8 324s 7 102.3 101.9 324s 8 102.9 103.9 324s 9 101.4 102.2 324s 10 100.3 99.6 324s 11 95.8 96.3 324s 12 95.1 95.3 324s 13 96.4 97.0 324s 14 99.1 98.5 324s 15 103.6 102.3 324s 16 103.5 103.9 324s 17 103.6 102.7 324s 18 102.0 103.1 324s 19 103.5 103.2 324s 20 106.7 105.9 324s > print( fitted( fit3sls[[ 4 ]]$e3$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 12 13 324s 97.8 100.0 99.9 100.1 102.0 101.9 102.3 102.9 101.4 100.3 95.8 95.1 96.4 324s 14 15 16 17 18 19 20 324s 99.1 103.6 103.5 103.6 102.0 103.5 106.7 324s > 324s > print( fitted( fit3sls[[ 5 ]]$e4e ) ) 324s demand supply 324s 1 95.0 96.3 324s 2 98.9 99.4 324s 3 98.8 99.5 324s 4 99.1 100.2 324s 5 103.2 102.9 324s 6 102.9 103.1 324s 7 103.6 103.4 324s 8 104.5 107.7 324s 9 102.1 103.4 324s 10 100.2 97.8 324s 11 91.5 90.8 324s 12 89.8 88.9 324s 13 92.2 92.6 324s 14 97.6 95.6 324s 15 106.4 103.4 324s 16 105.9 106.9 324s 17 106.7 103.6 324s 18 102.9 105.4 324s 19 105.6 105.5 324s 20 111.3 111.7 324s > print( fitted( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 12 13 324s 96.3 99.4 99.5 100.2 102.9 103.1 103.4 107.7 103.4 97.8 90.8 88.9 92.6 324s 14 15 16 17 18 19 20 324s 95.6 103.4 106.9 103.6 105.4 105.5 111.7 324s > 324s > print( fitted( fit3sls[[ 1 ]]$e5 ) ) 324s demand supply 324s 1 97.5 98.2 324s 2 99.9 99.8 324s 3 99.8 99.9 324s 4 100.0 100.3 324s 5 102.1 101.9 324s 6 102.0 102.0 324s 7 102.5 102.1 324s 8 103.1 104.3 324s 9 101.5 102.3 324s 10 100.3 99.4 324s 11 95.3 95.7 324s 12 94.5 94.6 324s 13 96.0 96.5 324s 14 99.0 98.2 324s 15 103.9 102.4 324s 16 103.7 104.2 324s 17 103.9 102.7 324s 18 102.1 103.4 324s 19 103.7 103.4 324s 20 107.2 106.6 324s > print( fitted( fit3sls[[ 1 ]]$e5$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 12 13 324s 97.5 99.9 99.8 100.0 102.1 102.0 102.5 103.1 101.5 100.3 95.3 94.5 96.0 324s 14 15 16 17 18 19 20 324s 99.0 103.9 103.7 103.9 102.1 103.7 107.2 324s > 324s > print( fitted( fit3slsi[[ 3 ]]$e3e ) ) 324s demand supply 324s 1 98.9 99.2 324s 2 100.5 100.3 324s 3 100.4 100.4 324s 4 100.6 100.6 324s 5 101.6 101.2 324s 6 101.5 101.3 324s 7 101.9 101.5 324s 8 102.4 102.9 324s 9 101.1 101.4 324s 10 100.1 99.7 324s 11 97.2 97.8 324s 12 96.9 97.5 324s 13 98.0 98.7 324s 14 99.7 99.5 324s 15 102.5 101.6 324s 16 102.6 102.7 324s 17 102.1 101.4 324s 18 101.8 102.6 324s 19 102.9 102.7 324s 20 105.3 104.8 324s > print( fitted( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 12 13 324s 98.9 100.5 100.4 100.6 101.6 101.5 101.9 102.4 101.1 100.1 97.2 96.9 98.0 324s 14 15 16 17 18 19 20 324s 99.7 102.5 102.6 102.1 101.8 102.9 105.3 324s > 324s > print( fitted( fit3slsd[[ 4 ]]$e4 ) ) 324s demand supply 324s 1 97.6 98.3 324s 2 99.7 99.7 324s 3 99.7 99.8 324s 4 99.8 100.1 324s 5 102.2 101.9 324s 6 102.0 102.0 324s 7 102.4 102.0 324s 8 102.8 104.1 324s 9 101.6 102.4 324s 10 100.7 99.8 324s 11 95.8 96.1 324s 12 94.8 94.8 324s 13 96.0 96.5 324s 14 99.1 98.3 324s 15 104.1 102.5 324s 16 103.7 104.2 324s 17 104.4 103.2 324s 18 101.9 103.2 324s 19 103.4 103.2 324s 20 106.3 105.9 324s > print( fitted( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 12 13 324s 98.3 99.7 99.8 100.1 101.9 102.0 102.0 104.1 102.4 99.8 96.1 94.8 96.5 324s 14 15 16 17 18 19 20 324s 98.3 102.5 104.2 103.2 103.2 103.2 105.9 324s > 324s > print( fitted( fit3slsd[[ 2 ]]$e3w ) ) 324s demand supply 324s 1 96.1 97.0 324s 2 97.6 97.2 324s 3 97.8 97.8 324s 4 97.7 97.7 324s 5 103.5 103.5 324s 6 102.7 102.8 324s 7 102.6 102.1 324s 8 101.8 103.4 324s 9 103.3 104.8 324s 10 103.9 103.4 324s 11 96.2 97.0 324s 12 92.5 92.4 324s 13 92.7 93.0 324s 14 98.8 97.6 324s 15 107.3 105.6 324s 16 105.6 106.4 324s 17 111.1 110.7 324s 18 100.9 102.3 324s 19 102.3 101.4 324s 20 103.7 101.8 324s > print( fitted( fit3slsd[[ 2 ]]$e3w$eq[[ 2 ]] ) ) 324s 1 2 3 4 5 6 7 8 9 10 11 12 13 324s 97.0 97.2 97.8 97.7 103.5 102.8 102.1 103.4 104.8 103.4 97.0 92.4 93.0 324s 14 15 16 17 18 19 20 324s 97.6 105.6 106.4 110.7 102.3 101.4 101.8 324s > 324s > 324s > ## *********** predicted values ************* 324s > predictData <- Kmenta 324s > predictData$consump <- NULL 324s > predictData$price <- Kmenta$price * 0.9 324s > predictData$income <- Kmenta$income * 1.1 324s > 324s > print( predict( fit3sls[[ 2 ]]$e1c, se.fit = TRUE, interval = "prediction", 324s + useDfSys = TRUE ) ) 324s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 324s 1 97.6 0.661 93.4 101.9 97.8 0.826 324s 2 99.9 0.600 95.7 104.1 99.3 0.825 324s 3 99.8 0.564 95.6 104.0 99.5 0.755 324s 4 100.0 0.605 95.8 104.2 99.9 0.783 324s 5 102.1 0.516 98.0 106.2 101.7 0.669 324s 6 102.0 0.474 97.9 106.1 101.8 0.620 324s 7 102.4 0.493 98.3 106.5 101.9 0.608 324s 8 103.0 0.615 98.8 107.2 104.1 0.889 324s 9 101.5 0.544 97.3 105.6 102.3 0.753 324s 10 100.3 0.822 96.0 104.7 99.6 1.022 324s 11 95.5 0.963 91.1 100.0 95.9 1.172 324s 12 94.7 1.006 90.2 99.2 94.8 1.289 324s 13 96.1 0.915 91.7 100.5 96.6 1.114 324s 14 99.0 0.518 94.9 103.2 98.4 0.751 324s 15 103.8 0.793 99.5 108.2 102.7 0.863 324s 16 103.7 0.636 99.5 107.9 104.4 0.902 324s 17 103.8 1.348 99.0 108.7 103.3 1.636 324s 18 102.1 0.549 97.9 106.2 103.6 0.807 324s 19 103.6 0.695 99.4 107.9 103.6 0.898 324s 20 106.9 1.306 102.1 111.7 106.6 1.613 324s supply.lwr supply.upr 324s 1 92.3 103 324s 2 93.8 105 324s 3 94.0 105 324s 4 94.3 105 324s 5 96.2 107 324s 6 96.3 107 324s 7 96.5 107 324s 8 98.5 110 324s 9 96.8 108 324s 10 93.9 105 324s 11 90.1 102 324s 12 88.9 101 324s 13 90.9 102 324s 14 92.9 104 324s 15 97.1 108 324s 16 98.8 110 324s 17 97.1 110 324s 18 98.1 109 324s 19 98.0 109 324s 20 100.4 113 324s > print( predict( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 324s + useDfSys = TRUE ) ) 324s fit se.fit lwr upr 324s 1 97.6 0.661 93.4 101.9 324s 2 99.9 0.600 95.7 104.1 324s 3 99.8 0.564 95.6 104.0 324s 4 100.0 0.605 95.8 104.2 324s 5 102.1 0.516 98.0 106.2 324s 6 102.0 0.474 97.9 106.1 324s 7 102.4 0.493 98.3 106.5 324s 8 103.0 0.615 98.8 107.2 324s 9 101.5 0.544 97.3 105.6 324s 10 100.3 0.822 96.0 104.7 324s 11 95.5 0.963 91.1 100.0 324s 12 94.7 1.006 90.2 99.2 324s 13 96.1 0.915 91.7 100.5 324s 14 99.0 0.518 94.9 103.2 324s 15 103.8 0.793 99.5 108.2 324s 16 103.7 0.636 99.5 107.9 324s 17 103.8 1.348 99.0 108.7 324s 18 102.1 0.549 97.9 106.2 324s 19 103.6 0.695 99.4 107.9 324s 20 106.9 1.306 102.1 111.7 324s > 324s > print( predict( fit3sls[[ 3 ]]$e2e, se.pred = TRUE, interval = "confidence", 324s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 324s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 324s 1 102.7 2.20 99.3 106 96.2 2.78 324s 2 105.2 2.21 101.8 109 97.5 2.68 324s 3 105.1 2.22 101.6 109 97.7 2.69 324s 4 105.4 2.21 101.9 109 98.0 2.67 324s 5 107.2 2.47 101.9 112 99.6 2.80 324s 6 107.1 2.43 102.1 112 99.7 2.76 324s 7 107.7 2.42 102.8 113 99.7 2.72 324s 8 108.5 2.38 103.7 113 101.6 2.66 324s 9 106.5 2.48 101.2 112 100.1 2.85 324s 10 105.0 2.59 99.1 111 97.6 3.04 324s 11 100.1 2.36 95.5 105 94.2 3.07 324s 12 99.5 2.19 96.3 103 93.0 3.00 324s 13 101.2 2.11 98.7 104 94.6 2.85 324s 14 104.0 2.29 100.0 108 96.3 2.84 324s 15 108.9 2.68 102.4 115 100.2 2.90 324s 16 108.8 2.57 103.0 115 101.8 2.81 324s 17 108.4 2.99 100.4 116 100.8 3.28 324s 18 107.5 2.34 103.1 112 100.9 2.66 324s 19 109.2 2.42 104.3 114 100.8 2.64 324s 20 113.0 2.63 106.8 119 103.4 2.62 324s supply.lwr supply.upr 324s 1 92.2 100.2 324s 2 94.6 100.5 324s 3 94.6 100.7 324s 4 95.1 100.8 324s 5 95.4 103.8 324s 6 95.8 103.5 324s 7 96.3 103.1 324s 8 98.9 104.4 324s 9 95.4 104.7 324s 10 91.6 103.6 324s 11 88.0 100.4 324s 12 87.3 98.7 324s 13 90.1 99.2 324s 14 91.8 100.8 324s 15 95.3 105.2 324s 16 97.5 106.0 324s 17 93.4 108.3 324s 18 98.1 103.6 324s 19 98.4 103.2 324s 20 101.2 105.6 324s > print( predict( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 324s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 324s fit se.pred lwr upr 324s 1 96.2 2.78 92.2 100.2 324s 2 97.5 2.68 94.6 100.5 324s 3 97.7 2.69 94.6 100.7 324s 4 98.0 2.67 95.1 100.8 324s 5 99.6 2.80 95.4 103.8 324s 6 99.7 2.76 95.8 103.5 324s 7 99.7 2.72 96.3 103.1 324s 8 101.6 2.66 98.9 104.4 324s 9 100.1 2.85 95.4 104.7 324s 10 97.6 3.04 91.6 103.6 324s 11 94.2 3.07 88.0 100.4 324s 12 93.0 3.00 87.3 98.7 324s 13 94.6 2.85 90.1 99.2 324s 14 96.3 2.84 91.8 100.8 324s 15 100.2 2.90 95.3 105.2 324s 16 101.8 2.81 97.5 106.0 324s 17 100.8 3.28 93.4 108.3 324s 18 100.9 2.66 98.1 103.6 324s 19 100.8 2.64 98.4 103.2 324s 20 103.4 2.62 101.2 105.6 324s > 324s > print( predict( fit3sls[[ 5 ]]$e2w, se.pred = TRUE, interval = "confidence", 324s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 324s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 324s 1 102.6 2.24 99.0 106 96.3 2.84 324s 2 105.1 2.24 101.5 109 97.6 2.72 324s 3 105.0 2.25 101.3 109 97.7 2.73 324s 4 105.3 2.24 101.6 109 98.0 2.71 324s 5 107.1 2.54 101.5 113 99.6 2.88 324s 6 107.0 2.49 101.7 112 99.6 2.82 324s 7 107.6 2.48 102.3 113 99.7 2.77 324s 8 108.3 2.44 103.3 113 101.6 2.70 324s 9 106.4 2.55 100.7 112 100.0 2.94 324s 10 104.9 2.67 98.5 111 97.6 3.17 324s 11 100.1 2.43 95.1 105 94.3 3.20 324s 12 99.5 2.23 96.0 103 93.2 3.11 324s 13 101.2 2.14 98.5 104 94.8 2.92 324s 14 104.0 2.33 99.6 108 96.4 2.92 324s 15 108.7 2.77 101.8 116 100.2 2.99 324s 16 108.7 2.65 102.5 115 101.7 2.88 324s 17 108.3 3.12 99.7 117 100.8 3.45 324s 18 107.4 2.39 102.7 112 100.9 2.70 324s 19 109.1 2.48 103.8 114 100.8 2.67 324s 20 112.9 2.71 106.3 119 103.4 2.65 324s supply.lwr supply.upr 324s 1 91.8 100.7 324s 2 94.3 100.8 324s 3 94.3 101.1 324s 4 94.8 101.1 324s 5 94.9 104.3 324s 6 95.4 103.9 324s 7 95.9 103.5 324s 8 98.5 104.7 324s 9 94.9 105.2 324s 10 90.9 104.4 324s 11 87.4 101.2 324s 12 86.9 99.5 324s 13 89.7 99.8 324s 14 91.4 101.4 324s 15 94.7 105.8 324s 16 97.0 106.5 324s 17 92.5 109.1 324s 18 97.8 103.9 324s 19 98.1 103.5 324s 20 101.0 105.9 324s > print( predict( fit3sls[[ 5 ]]$e2w$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 324s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 324s fit se.pred lwr upr 324s 1 96.3 2.84 91.8 100.7 324s 2 97.6 2.72 94.3 100.8 324s 3 97.7 2.73 94.3 101.1 324s 4 98.0 2.71 94.8 101.1 324s 5 99.6 2.88 94.9 104.3 324s 6 99.6 2.82 95.4 103.9 324s 7 99.7 2.77 95.9 103.5 324s 8 101.6 2.70 98.5 104.7 324s 9 100.0 2.94 94.9 105.2 324s 10 97.6 3.17 90.9 104.4 324s 11 94.3 3.20 87.4 101.2 324s 12 93.2 3.11 86.9 99.5 324s 13 94.8 2.92 89.7 99.8 324s 14 96.4 2.92 91.4 101.4 324s 15 100.2 2.99 94.7 105.8 324s 16 101.7 2.88 97.0 106.5 324s 17 100.8 3.45 92.5 109.1 324s 18 100.9 2.70 97.8 103.9 324s 19 100.8 2.67 98.1 103.5 324s 20 103.4 2.65 101.0 105.9 324s > 324s > print( predict( fit3sls[[ 4 ]]$e3, se.pred = TRUE, interval = "prediction", 324s + level = 0.975 ) ) 324s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 324s 1 97.8 2.10 92.9 103 98.4 2.64 324s 2 100.0 2.09 95.1 105 99.8 2.66 324s 3 99.9 2.08 95.0 105 99.9 2.65 324s 4 100.1 2.09 95.2 105 100.3 2.66 324s 5 102.0 2.06 97.2 107 101.7 2.65 324s 6 101.9 2.05 97.1 107 101.8 2.63 324s 7 102.3 2.06 97.5 107 101.9 2.63 324s 8 102.9 2.09 98.0 108 103.9 2.71 324s 9 101.4 2.07 96.6 106 102.2 2.67 324s 10 100.3 2.16 95.2 105 99.6 2.76 324s 11 95.8 2.21 90.6 101 96.3 2.80 324s 12 95.1 2.22 89.9 100 95.3 2.84 324s 13 96.4 2.19 91.3 102 97.0 2.78 324s 14 99.1 2.06 94.3 104 98.5 2.67 324s 15 103.6 2.15 98.6 109 102.3 2.68 324s 16 103.5 2.09 98.6 108 103.9 2.68 324s 17 103.6 2.41 97.9 109 102.7 3.00 324s 18 102.0 2.07 97.2 107 103.1 2.66 324s 19 103.5 2.12 98.6 108 103.2 2.69 324s 20 106.7 2.39 101.1 112 105.9 2.98 324s supply.lwr supply.upr 324s 1 92.2 105 324s 2 93.6 106 324s 3 93.7 106 324s 4 94.0 107 324s 5 95.5 108 324s 6 95.7 108 324s 7 95.8 108 324s 8 97.6 110 324s 9 95.9 108 324s 10 93.2 106 324s 11 89.7 103 324s 12 88.6 102 324s 13 90.5 103 324s 14 92.3 105 324s 15 96.0 109 324s 16 97.6 110 324s 17 95.7 110 324s 18 96.9 109 324s 19 96.9 109 324s 20 98.9 113 324s > print( predict( fit3sls[[ 4 ]]$e3$eq[[ 1 ]], se.pred = TRUE, interval = "prediction", 324s + level = 0.975 ) ) 324s fit se.pred lwr upr 324s 1 97.8 2.10 92.9 103 324s 2 100.0 2.09 95.1 105 324s 3 99.9 2.08 95.0 105 324s 4 100.1 2.09 95.2 105 324s 5 102.0 2.06 97.2 107 324s 6 101.9 2.05 97.1 107 324s 7 102.3 2.06 97.5 107 324s 8 102.9 2.09 98.0 108 324s 9 101.4 2.07 96.6 106 324s 10 100.3 2.16 95.2 105 324s 11 95.8 2.21 90.6 101 324s 12 95.1 2.22 89.9 100 324s 13 96.4 2.19 91.3 102 324s 14 99.1 2.06 94.3 104 324s 15 103.6 2.15 98.6 109 324s 16 103.5 2.09 98.6 108 324s 17 103.6 2.41 97.9 109 324s 18 102.0 2.07 97.2 107 324s 19 103.5 2.12 98.6 108 324s 20 106.7 2.39 101.1 112 324s > 324s > print( predict( fit3sls[[ 5 ]]$e4e, se.fit = TRUE, interval = "confidence", 324s + level = 0.25, useDfSys = TRUE ) ) 324s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 324s 1 95.0 0.465 94.8 95.1 96.3 0.536 324s 2 98.9 0.532 98.7 99.1 99.4 0.663 324s 3 98.8 0.497 98.6 99.0 99.5 0.613 324s 4 99.1 0.541 99.0 99.3 100.2 0.662 324s 5 103.2 0.450 103.0 103.3 102.9 0.593 324s 6 102.9 0.417 102.7 103.0 103.1 0.543 324s 7 103.6 0.420 103.5 103.8 103.4 0.524 324s 8 104.5 0.525 104.3 104.6 107.7 0.634 324s 9 102.1 0.494 101.9 102.2 103.4 0.660 324s 10 100.2 0.760 100.0 100.4 97.8 0.895 324s 11 91.5 0.660 91.3 91.7 90.8 0.736 324s 12 89.8 0.563 89.6 89.9 88.9 0.742 324s 13 92.2 0.597 92.0 92.4 92.6 0.806 324s 14 97.6 0.426 97.4 97.7 95.6 0.568 324s 15 106.4 0.619 106.2 106.6 103.4 0.721 324s 16 105.9 0.476 105.8 106.1 106.9 0.608 324s 17 106.7 1.159 106.3 107.1 103.6 1.414 324s 18 102.9 0.494 102.7 103.0 105.4 0.582 324s 19 105.6 0.574 105.4 105.8 105.5 0.676 324s 20 111.3 1.030 110.9 111.6 111.7 1.146 324s supply.lwr supply.upr 324s 1 96.1 96.4 324s 2 99.1 99.6 324s 3 99.3 99.7 324s 4 100.0 100.4 324s 5 102.7 103.1 324s 6 102.9 103.3 324s 7 103.2 103.5 324s 8 107.5 107.9 324s 9 103.2 103.7 324s 10 97.5 98.0 324s 11 90.5 91.0 324s 12 88.7 89.1 324s 13 92.4 92.9 324s 14 95.4 95.8 324s 15 103.1 103.6 324s 16 106.7 107.0 324s 17 103.1 104.0 324s 18 105.3 105.6 324s 19 105.3 105.8 324s 20 111.4 112.1 324s > print( predict( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 324s + level = 0.25, useDfSys = TRUE ) ) 324s fit se.fit lwr upr 324s 1 96.3 0.536 96.1 96.4 324s 2 99.4 0.663 99.1 99.6 324s 3 99.5 0.613 99.3 99.7 324s 4 100.2 0.662 100.0 100.4 324s 5 102.9 0.593 102.7 103.1 324s 6 103.1 0.543 102.9 103.3 324s 7 103.4 0.524 103.2 103.5 324s 8 107.7 0.634 107.5 107.9 324s 9 103.4 0.660 103.2 103.7 324s 10 97.8 0.895 97.5 98.0 324s 11 90.8 0.736 90.5 91.0 324s 12 88.9 0.742 88.7 89.1 324s 13 92.6 0.806 92.4 92.9 324s 14 95.6 0.568 95.4 95.8 324s 15 103.4 0.721 103.1 103.6 324s 16 106.9 0.608 106.7 107.0 324s 17 103.6 1.414 103.1 104.0 324s 18 105.4 0.582 105.3 105.6 324s 19 105.5 0.676 105.3 105.8 324s 20 111.7 1.146 111.4 112.1 324s > 324s > print( predict( fit3sls[[ 1 ]]$e5, se.fit = TRUE, se.pred = TRUE, 324s + interval = "prediction", level = 0.5, newdata = predictData ) ) 324s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 324s 1 102.8 0.957 2.19 101.3 104 95.7 324s 2 105.6 0.829 2.13 104.1 107 97.1 324s 3 105.5 0.869 2.15 104.0 107 97.3 324s 4 105.8 0.823 2.13 104.3 107 97.6 324s 5 107.8 1.308 2.36 106.2 109 99.4 324s 6 107.7 1.213 2.31 106.1 109 99.4 324s 7 108.3 1.145 2.28 106.7 110 99.5 324s 8 109.1 0.984 2.20 107.6 111 101.7 324s 9 107.0 1.372 2.40 105.3 109 99.8 324s 10 105.4 1.659 2.57 103.6 107 97.1 324s 11 100.1 1.365 2.39 98.4 102 93.3 324s 12 99.4 0.969 2.19 97.9 101 92.1 324s 13 101.3 0.752 2.11 99.8 103 93.9 324s 14 104.3 1.112 2.26 102.8 106 95.7 324s 15 109.6 1.580 2.52 107.9 111 100.0 324s 16 109.6 1.368 2.40 107.9 111 101.7 324s 17 109.1 2.136 2.90 107.1 111 100.5 324s 18 108.1 0.966 2.19 106.6 110 100.8 324s 19 109.9 0.980 2.20 108.4 111 100.7 324s 20 114.1 0.997 2.21 112.6 116 103.7 324s supply.se.fit supply.se.pred supply.lwr supply.upr 324s 1 0.959 2.74 93.8 97.5 324s 2 0.742 2.67 95.3 99.0 324s 3 0.791 2.69 95.4 99.1 324s 4 0.735 2.67 95.8 99.4 324s 5 1.280 2.87 97.4 101.3 324s 6 1.159 2.82 97.5 101.3 324s 7 1.031 2.77 97.6 101.4 324s 8 0.867 2.71 99.8 103.5 324s 9 1.416 2.93 97.8 101.8 324s 10 1.724 3.09 95.0 99.2 324s 11 1.457 2.95 91.3 95.4 324s 12 1.102 2.79 90.2 94.0 324s 13 0.894 2.72 92.1 95.8 324s 14 1.092 2.79 93.8 97.6 324s 15 1.516 2.98 98.0 102.0 324s 16 1.321 2.89 99.7 103.7 324s 17 2.297 3.44 98.2 102.9 324s 18 0.847 2.70 98.9 102.6 324s 19 0.743 2.67 98.9 102.6 324s 20 0.589 2.63 101.9 105.5 324s > print( predict( fit3sls[[ 1 ]]$e5$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 324s + interval = "prediction", level = 0.5, newdata = predictData ) ) 324s fit se.fit se.pred lwr upr 324s 1 102.8 0.957 2.19 101.3 104 324s 2 105.6 0.829 2.13 104.1 107 324s 3 105.5 0.869 2.15 104.0 107 324s 4 105.8 0.823 2.13 104.3 107 324s 5 107.8 1.308 2.36 106.2 109 324s 6 107.7 1.213 2.31 106.1 109 324s 7 108.3 1.145 2.28 106.7 110 324s 8 109.1 0.984 2.20 107.6 111 324s 9 107.0 1.372 2.40 105.3 109 324s 10 105.4 1.659 2.57 103.6 107 324s 11 100.1 1.365 2.39 98.4 102 324s 12 99.4 0.969 2.19 97.9 101 324s 13 101.3 0.752 2.11 99.8 103 324s 14 104.3 1.112 2.26 102.8 106 324s 15 109.6 1.580 2.52 107.9 111 324s 16 109.6 1.368 2.40 107.9 111 324s 17 109.1 2.136 2.90 107.1 111 324s 18 108.1 0.966 2.19 106.6 110 324s 19 109.9 0.980 2.20 108.4 111 324s 20 114.1 0.997 2.21 112.6 116 324s > 324s > print( predict( fit3slsi[[ 3 ]]$e3e, se.fit = TRUE, se.pred = TRUE, 324s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 324s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 324s 1 98.9 0.590 2.49 97.3 100.5 99.2 324s 2 100.5 0.643 2.50 98.7 102.2 100.3 324s 3 100.4 0.602 2.49 98.7 102.0 100.4 324s 4 100.6 0.653 2.50 98.8 102.3 100.6 324s 5 101.6 0.548 2.48 100.1 103.1 101.2 324s 6 101.5 0.512 2.47 100.1 102.9 101.3 324s 7 101.9 0.524 2.47 100.5 103.3 101.5 324s 8 102.4 0.667 2.51 100.6 104.3 102.9 324s 9 101.1 0.599 2.49 99.5 102.7 101.4 324s 10 100.1 0.928 2.59 97.6 102.6 99.7 324s 11 97.2 0.898 2.58 94.7 99.6 97.8 324s 12 96.9 0.767 2.54 94.8 99.0 97.5 324s 13 98.0 0.745 2.53 96.0 100.1 98.7 324s 14 99.7 0.536 2.48 98.2 101.1 99.5 324s 15 102.5 0.745 2.53 100.5 104.5 101.6 324s 16 102.6 0.589 2.49 101.0 104.2 102.7 324s 17 102.1 1.376 2.78 98.3 105.8 101.4 324s 18 101.8 0.615 2.49 100.2 103.5 102.6 324s 19 102.9 0.738 2.53 100.9 104.9 102.7 324s 20 105.3 1.357 2.77 101.6 109.0 104.8 324s supply.se.fit supply.se.pred supply.lwr supply.upr 324s 1 0.638 3.01 97.5 101.0 324s 2 0.752 3.03 98.3 102.4 324s 3 0.700 3.02 98.4 102.3 324s 4 0.761 3.03 98.6 102.7 324s 5 0.649 3.01 99.4 103.0 324s 6 0.610 3.00 99.7 103.0 324s 7 0.613 3.00 99.8 103.2 324s 8 0.829 3.05 100.7 105.2 324s 9 0.731 3.03 99.4 103.4 324s 10 1.092 3.13 96.7 102.6 324s 11 1.037 3.12 94.9 100.6 324s 12 0.902 3.07 95.0 99.9 324s 13 0.855 3.06 96.4 101.1 324s 14 0.670 3.01 97.6 101.3 324s 15 0.812 3.05 99.4 103.8 324s 16 0.707 3.02 100.8 104.7 324s 17 1.584 3.34 97.1 105.7 324s 18 0.740 3.03 100.6 104.6 324s 19 0.852 3.06 100.4 105.1 324s 20 1.564 3.33 100.6 109.1 324s > print( predict( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 324s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 324s fit se.fit se.pred lwr upr 324s 1 98.9 0.590 2.49 97.3 100.5 324s 2 100.5 0.643 2.50 98.7 102.2 324s 3 100.4 0.602 2.49 98.7 102.0 324s 4 100.6 0.653 2.50 98.8 102.3 324s 5 101.6 0.548 2.48 100.1 103.1 324s 6 101.5 0.512 2.47 100.1 102.9 324s 7 101.9 0.524 2.47 100.5 103.3 324s 8 102.4 0.667 2.51 100.6 104.3 324s 9 101.1 0.599 2.49 99.5 102.7 324s 10 100.1 0.928 2.59 97.6 102.6 324s 11 97.2 0.898 2.58 94.7 99.6 324s 12 96.9 0.767 2.54 94.8 99.0 324s 13 98.0 0.745 2.53 96.0 100.1 324s 14 99.7 0.536 2.48 98.2 101.1 324s 15 102.5 0.745 2.53 100.5 104.5 324s 16 102.6 0.589 2.49 101.0 104.2 324s 17 102.1 1.376 2.78 98.3 105.8 324s 18 101.8 0.615 2.49 100.2 103.5 324s 19 102.9 0.738 2.53 100.9 104.9 324s 20 105.3 1.357 2.77 101.6 109.0 324s > 324s > print( predict( fit3slsi[[ 1 ]]$e5w, se.fit = TRUE, se.pred = TRUE, 324s + interval = "prediction", level = 0.5, newdata = predictData ) ) 324s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 324s 1 102.4 0.986 2.25 100.9 104 95.3 324s 2 105.2 0.851 2.20 103.7 107 96.9 324s 3 105.1 0.896 2.22 103.6 107 97.0 324s 4 105.4 0.844 2.20 103.9 107 97.4 324s 5 107.1 1.351 2.44 105.5 109 98.7 324s 6 107.1 1.250 2.38 105.5 109 98.9 324s 7 107.8 1.173 2.34 106.2 109 99.0 324s 8 108.7 0.983 2.25 107.2 110 101.3 324s 9 106.3 1.420 2.48 104.6 108 99.1 324s 10 104.6 1.713 2.65 102.8 106 96.2 324s 11 99.4 1.372 2.45 97.8 101 92.8 324s 12 99.0 0.965 2.25 97.5 101 91.9 324s 13 101.0 0.768 2.17 99.5 102 93.8 324s 14 103.8 1.149 2.33 102.2 105 95.3 324s 15 108.8 1.631 2.60 107.0 111 99.2 324s 16 108.9 1.405 2.47 107.2 111 101.1 324s 17 108.0 2.211 3.00 106.0 110 99.4 324s 18 107.7 0.978 2.25 106.1 109 100.4 324s 19 109.5 0.964 2.25 108.0 111 100.5 324s 20 113.8 0.818 2.19 112.3 115 103.7 324s supply.se.fit supply.se.pred supply.lwr supply.upr 324s 1 0.987 2.85 93.3 97.2 324s 2 0.772 2.79 95.0 98.8 324s 3 0.824 2.80 95.1 98.9 324s 4 0.767 2.79 95.5 99.3 324s 5 1.341 3.00 96.7 100.8 324s 6 1.215 2.94 96.9 100.9 324s 7 1.084 2.89 97.1 101.0 324s 8 0.907 2.83 99.4 103.2 324s 9 1.483 3.06 97.0 101.2 324s 10 1.795 3.22 94.1 98.4 324s 11 1.455 3.05 90.7 94.8 324s 12 1.002 2.86 90.0 93.9 324s 13 0.805 2.80 91.9 95.7 324s 14 1.087 2.89 93.4 97.3 324s 15 1.585 3.11 97.1 101.4 324s 16 1.383 3.01 99.0 103.1 324s 17 2.399 3.60 96.9 101.8 324s 18 0.883 2.82 98.5 102.4 324s 19 0.770 2.79 98.6 102.4 324s 20 0.616 2.75 101.9 105.6 324s > print( predict( fit3slsi[[ 1 ]]$e5w$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 324s + interval = "prediction", level = 0.5, newdata = predictData ) ) 324s fit se.fit se.pred lwr upr 324s 1 102.4 0.986 2.25 100.9 104 324s 2 105.2 0.851 2.20 103.7 107 324s 3 105.1 0.896 2.22 103.6 107 324s 4 105.4 0.844 2.20 103.9 107 324s 5 107.1 1.351 2.44 105.5 109 324s 6 107.1 1.250 2.38 105.5 109 324s 7 107.8 1.173 2.34 106.2 109 324s 8 108.7 0.983 2.25 107.2 110 324s 9 106.3 1.420 2.48 104.6 108 324s 10 104.6 1.713 2.65 102.8 106 324s 11 99.4 1.372 2.45 97.8 101 324s 12 99.0 0.965 2.25 97.5 101 324s 13 101.0 0.768 2.17 99.5 102 324s 14 103.8 1.149 2.33 102.2 105 324s 15 108.8 1.631 2.60 107.0 111 324s 16 108.9 1.405 2.47 107.2 111 324s 17 108.0 2.211 3.00 106.0 110 324s 18 107.7 0.978 2.25 106.1 109 324s 19 109.5 0.964 2.25 108.0 111 324s 20 113.8 0.818 2.19 112.3 115 324s > 324s > print( predict( fit3slsd[[ 4 ]]$e4, se.fit = TRUE, interval = "prediction", 324s + level = 0.9, newdata = predictData ) ) 324s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 324s 1 103 0.972 99.6 107 96.1 0.980 324s 2 106 0.820 102.2 109 97.5 0.751 324s 3 106 0.863 102.1 109 97.6 0.801 324s 4 106 0.813 102.4 109 97.9 0.741 324s 5 108 1.305 104.2 112 99.8 1.287 324s 6 108 1.206 104.1 112 99.8 1.164 324s 7 109 1.132 104.7 112 99.9 1.035 324s 8 109 0.960 105.5 113 101.8 0.857 324s 9 107 1.377 103.4 111 100.3 1.422 324s 10 106 1.688 101.8 110 97.8 1.748 324s 11 101 1.415 96.8 105 94.1 1.490 324s 12 100 1.004 96.3 104 92.7 1.115 324s 13 102 0.766 98.1 105 94.4 0.891 324s 14 105 1.124 101.0 109 96.2 1.107 324s 15 110 1.575 105.8 114 100.5 1.523 324s 16 110 1.355 105.9 114 102.1 1.318 324s 17 110 2.158 105.0 115 101.3 2.305 324s 18 108 0.947 104.5 112 101.0 0.843 324s 19 110 0.953 106.3 114 100.9 0.735 324s 20 114 0.974 109.9 117 103.5 0.583 324s supply.lwr supply.upr 324s 1 91.6 100.7 324s 2 93.0 101.9 324s 3 93.2 102.1 324s 4 93.5 102.3 324s 5 95.0 104.6 324s 6 95.2 104.5 324s 7 95.3 104.5 324s 8 97.3 106.3 324s 9 95.4 105.2 324s 10 92.6 103.0 324s 11 89.2 99.0 324s 12 88.1 97.4 324s 13 89.8 98.9 324s 14 91.6 100.9 324s 15 95.5 105.5 324s 16 97.3 106.9 324s 17 95.6 107.1 324s 18 96.5 105.5 324s 19 96.5 105.3 324s 20 99.2 107.9 324s > print( predict( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 324s + level = 0.9, newdata = predictData ) ) 324s fit se.fit lwr upr 324s 1 96.1 0.980 91.6 100.7 324s 2 97.5 0.751 93.0 101.9 324s 3 97.6 0.801 93.2 102.1 324s 4 97.9 0.741 93.5 102.3 324s 5 99.8 1.287 95.0 104.6 324s 6 99.8 1.164 95.2 104.5 324s 7 99.9 1.035 95.3 104.5 324s 8 101.8 0.857 97.3 106.3 324s 9 100.3 1.422 95.4 105.2 324s 10 97.8 1.748 92.6 103.0 324s 11 94.1 1.490 89.2 99.0 324s 12 92.7 1.115 88.1 97.4 324s 13 94.4 0.891 89.8 98.9 324s 14 96.2 1.107 91.6 100.9 324s 15 100.5 1.523 95.5 105.5 324s 16 102.1 1.318 97.3 106.9 324s 17 101.3 2.305 95.6 107.1 324s 18 101.0 0.843 96.5 105.5 324s 19 100.9 0.735 96.5 105.3 324s 20 103.5 0.583 99.2 107.9 324s > 324s > print( predict( fit3slsd[[ 2 ]]$e3w, se.fit = TRUE, se.pred = TRUE, 324s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 324s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 324s 1 96.1 0.832 3.23 93.8 98.3 97.0 324s 2 97.6 0.849 3.24 95.3 99.9 97.2 324s 3 97.8 0.771 3.22 95.7 99.9 97.8 324s 4 97.7 0.857 3.24 95.3 100.0 97.7 324s 5 103.5 0.648 3.19 101.8 105.3 103.5 324s 6 102.7 0.519 3.16 101.3 104.1 102.8 324s 7 102.6 0.499 3.16 101.3 104.0 102.1 324s 8 101.8 0.627 3.18 100.1 103.5 103.4 324s 9 103.3 0.714 3.20 101.3 105.2 104.8 324s 10 103.9 1.172 3.33 100.7 107.1 103.4 324s 11 96.2 0.920 3.25 93.7 98.7 97.0 324s 12 92.5 1.261 3.37 89.1 95.9 92.4 324s 13 92.7 1.364 3.41 89.0 96.5 93.0 324s 14 98.8 0.528 3.17 97.3 100.2 97.6 324s 15 107.3 1.245 3.36 103.9 110.7 105.6 324s 16 105.6 0.856 3.24 103.2 107.9 106.4 324s 17 111.1 2.310 3.88 104.8 117.4 110.7 324s 18 100.9 0.592 3.18 99.2 102.5 102.3 324s 19 102.3 0.700 3.20 100.4 104.2 101.4 324s 20 103.7 1.350 3.40 100.0 107.4 101.8 324s supply.se.fit supply.se.pred supply.lwr supply.upr 324s 1 0.791 3.73 94.8 99.2 324s 2 0.857 3.74 94.8 99.5 324s 3 0.776 3.72 95.7 99.9 324s 4 0.825 3.73 95.5 100.0 324s 5 0.817 3.73 101.2 105.7 324s 6 0.713 3.71 100.9 104.8 324s 7 0.644 3.70 100.4 103.9 324s 8 0.858 3.74 101.0 105.7 324s 9 0.962 3.77 102.2 107.4 324s 10 1.040 3.79 100.6 106.3 324s 11 1.083 3.80 94.1 100.0 324s 12 1.633 3.99 88.0 96.9 324s 13 1.568 3.96 88.7 97.3 324s 14 0.871 3.74 95.2 100.0 324s 15 1.029 3.78 102.8 108.4 324s 16 1.056 3.79 103.6 109.3 324s 17 2.050 4.18 105.1 116.2 324s 18 0.687 3.71 100.4 104.2 324s 19 0.773 3.72 99.3 103.5 324s 20 1.300 3.87 98.3 105.4 324s > print( predict( fit3slsd[[ 2 ]]$e3w$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 324s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 324s fit se.fit se.pred lwr upr 324s 1 96.1 0.832 3.23 93.8 98.3 324s 2 97.6 0.849 3.24 95.3 99.9 324s 3 97.8 0.771 3.22 95.7 99.9 324s 4 97.7 0.857 3.24 95.3 100.0 324s 5 103.5 0.648 3.19 101.8 105.3 324s 6 102.7 0.519 3.16 101.3 104.1 324s 7 102.6 0.499 3.16 101.3 104.0 324s 8 101.8 0.627 3.18 100.1 103.5 324s 9 103.3 0.714 3.20 101.3 105.2 324s 10 103.9 1.172 3.33 100.7 107.1 324s 11 96.2 0.920 3.25 93.7 98.7 324s 12 92.5 1.261 3.37 89.1 95.9 324s 13 92.7 1.364 3.41 89.0 96.5 324s 14 98.8 0.528 3.17 97.3 100.2 324s 15 107.3 1.245 3.36 103.9 110.7 324s 16 105.6 0.856 3.24 103.2 107.9 324s 17 111.1 2.310 3.88 104.8 117.4 324s 18 100.9 0.592 3.18 99.2 102.5 324s 19 102.3 0.700 3.20 100.4 104.2 324s 20 103.7 1.350 3.40 100.0 107.4 324s > 324s > 324s > # predict just one observation 324s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 324s + trend = 25 ) 324s > 324s > print( predict( fit3sls[[ 3 ]]$e1c, newdata = smallData ) ) 324s demand.pred supply.pred 324s 1 110 118 324s > print( predict( fit3sls[[ 3 ]]$e1c$eq[[ 1 ]], newdata = smallData ) ) 324s fit 324s 1 110 324s > 324s > print( predict( fit3sls[[ 4 ]]$e2e, se.fit = TRUE, level = 0.9, 324s + newdata = smallData ) ) 324s demand.pred demand.se.fit supply.pred supply.se.fit 324s 1 110 2.34 117 3.29 324s > print( predict( fit3sls[[ 5 ]]$e2e$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 324s + newdata = smallData ) ) 324s fit se.pred 324s 1 110 3.07 324s > 324s > print( predict( fit3sls[[ 1]]$e3, interval = "prediction", level = 0.975, 324s + newdata = smallData ) ) 324s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 324s 1 110 102 117 117 106 127 324s > print( predict( fit3sls[[ 1 ]]$e3$eq[[ 1 ]], interval = "confidence", level = 0.8, 324s + newdata = smallData ) ) 324s fit lwr upr 324s 1 110 106 113 324s > 324s > print( predict( fit3sls[[ 4]]$e3we, interval = "prediction", level = 0.975, 324s + newdata = smallData ) ) 324s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 324s 1 110 103 117 117 107 126 324s > print( predict( fit3sls[[ 4 ]]$e3we$eq[[ 1 ]], interval = "confidence", level = 0.8, 324s + newdata = smallData ) ) 324s fit lwr upr 324s 1 110 107 113 324s > 324s > print( predict( fit3sls[[ 2 ]]$e4e, se.fit = TRUE, interval = "confidence", 324s + level = 0.999, newdata = smallData ) ) 324s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 324s 1 110 2.14 103 118 119 2.25 324s supply.lwr supply.upr 324s 1 110 127 324s > print( predict( fit3sls[[ 2 ]]$e4e$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 324s + level = 0.75, newdata = smallData ) ) 324s fit se.pred lwr upr 324s 1 119 3.41 115 123 324s > 324s > print( predict( fit3sls[[ 3 ]]$e5, se.fit = TRUE, interval = "prediction", 324s + newdata = smallData ) ) 324s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 324s 1 111 2.3 104 117 119 2.44 324s supply.lwr supply.upr 324s 1 111 126 324s > print( predict( fit3sls[[ 3 ]]$e5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 324s + newdata = smallData ) ) 324s fit se.pred lwr upr 324s 1 111 3.02 106 115 324s > 324s > print( predict( fit3slsi[[ 4 ]]$e3e, se.fit = TRUE, se.pred = TRUE, 324s + interval = "prediction", level = 0.5, newdata = smallData ) ) 324s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 324s 1 108 2.75 3.66 106 111 112 324s supply.se.fit supply.se.pred supply.lwr supply.upr 324s 1 3.46 4.54 109 115 324s > print( predict( fit3slsd[[ 5 ]]$e4$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 324s + interval = "confidence", level = 0.25, newdata = smallData ) ) 324s fit se.fit se.pred lwr upr 324s 1 111 1.85 3.42 111 112 324s > 324s > print( predict( fit3slsd[[ 2 ]]$e2we, se.fit = TRUE, se.pred = TRUE, 324s + interval = "prediction", level = 0.5, newdata = smallData ) ) 324s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 324s 1 101 2.76 4.1 98.7 104 111 324s supply.se.fit supply.se.pred supply.lwr supply.upr 324s 1 2.79 4.47 108 114 324s > print( predict( fit3slsi[[ 3 ]]$e4we$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 324s + interval = "confidence", level = 0.25, newdata = smallData ) ) 324s fit se.fit se.pred lwr upr 324s 1 111 2.03 2.86 111 112 324s > 324s > 324s > ## ************ correlation of predicted values *************** 324s > print( correlation.systemfit( fit3sls[[ 1 ]]$e1c, 2, 1 ) ) 324s [,1] 324s [1,] 0.880 324s [2,] 0.881 324s [3,] 0.886 324s [4,] 0.901 324s [5,] 0.866 324s [6,] 0.881 324s [7,] 0.892 324s [8,] 0.887 324s [9,] 0.901 324s [10,] 0.924 324s [11,] 0.925 324s [12,] 0.916 324s [13,] 0.910 324s [14,] 0.885 324s [15,] 0.909 324s [16,] 0.921 324s [17,] 0.928 324s [18,] 0.845 324s [19,] 0.890 324s [20,] 0.920 324s > 324s > print( correlation.systemfit( fit3sls[[ 2 ]]$e2e, 1, 2 ) ) 324s [,1] 324s [1,] 0.935 324s [2,] 0.927 324s [3,] 0.923 324s [4,] 0.921 324s [5,] 0.876 324s [6,] 0.884 324s [7,] 0.894 324s [8,] 0.875 324s [9,] 0.890 324s [10,] 0.917 324s [11,] 0.911 324s [12,] 0.898 324s [13,] 0.892 324s [14,] 0.871 324s [15,] 0.905 324s [16,] 0.945 324s [17,] 0.926 324s [18,] 0.908 324s [19,] 0.915 324s [20,] 0.926 324s > 324s > print( correlation.systemfit( fit3sls[[ 5 ]]$e2w, 2, 1 ) ) 324s [,1] 324s [1,] 0.932 324s [2,] 0.928 324s [3,] 0.925 324s [4,] 0.923 324s [5,] 0.882 324s [6,] 0.890 324s [7,] 0.899 324s [8,] 0.880 324s [9,] 0.895 324s [10,] 0.921 324s [11,] 0.914 324s [12,] 0.900 324s [13,] 0.895 324s [14,] 0.876 324s [15,] 0.905 324s [16,] 0.947 324s [17,] 0.928 324s [18,] 0.915 324s [19,] 0.916 324s [20,] 0.928 324s > 324s > print( correlation.systemfit( fit3sls[[ 3 ]]$e3, 2, 1 ) ) 324s [,1] 324s [1,] 0.931 324s [2,] 0.925 324s [3,] 0.922 324s [4,] 0.920 324s [5,] 0.877 324s [6,] 0.884 324s [7,] 0.894 324s [8,] 0.875 324s [9,] 0.890 324s [10,] 0.917 324s [11,] 0.910 324s [12,] 0.896 324s [13,] 0.891 324s [14,] 0.871 324s [15,] 0.903 324s [16,] 0.944 324s [17,] 0.925 324s [18,] 0.911 324s [19,] 0.913 324s [20,] 0.925 324s > 324s > print( correlation.systemfit( fit3sls[[ 4 ]]$e4e, 1, 2 ) ) 324s [,1] 324s [1,] 0.924 324s [2,] 0.933 324s [3,] 0.933 324s [4,] 0.938 324s [5,] 0.862 324s [6,] 0.868 324s [7,] 0.874 324s [8,] 0.879 324s [9,] 0.883 324s [10,] 0.943 324s [11,] 0.830 324s [12,] 0.744 324s [13,] 0.826 324s [14,] 0.834 324s [15,] 0.952 324s [16,] 0.918 324s [17,] 0.954 324s [18,] 0.930 324s [19,] 0.890 324s [20,] 0.893 324s > 324s > print( correlation.systemfit( fit3sls[[ 5 ]]$e5, 2, 1 ) ) 324s [,1] 324s [1,] 0.922 324s [2,] 0.935 324s [3,] 0.934 324s [4,] 0.939 324s [5,] 0.863 324s [6,] 0.868 324s [7,] 0.874 324s [8,] 0.876 324s [9,] 0.884 324s [10,] 0.942 324s [11,] 0.824 324s [12,] 0.747 324s [13,] 0.830 324s [14,] 0.833 324s [15,] 0.952 324s [16,] 0.919 324s [17,] 0.955 324s [18,] 0.928 324s [19,] 0.886 324s [20,] 0.888 324s > 324s > print( correlation.systemfit( fit3slsi[[ 2 ]]$e3e, 1, 2 ) ) 324s [,1] 324s [1,] 0.982 324s [2,] 0.994 324s [3,] 0.993 324s [4,] 0.992 324s [5,] 0.990 324s [6,] 0.990 324s [7,] 0.991 324s [8,] 0.978 324s [9,] 0.984 324s [10,] 0.992 324s [11,] 0.991 324s [12,] 0.985 324s [13,] 0.986 324s [14,] 0.980 324s [15,] 0.976 324s [16,] 0.994 324s [17,] 0.992 324s [18,] 0.987 324s [19,] 0.990 324s [20,] 0.991 324s > 324s > print( correlation.systemfit( fit3slsi[[ 4 ]]$e5w, 1, 2 ) ) 324s [,1] 324s [1,] 0.962 324s [2,] 0.975 324s [3,] 0.974 324s [4,] 0.976 324s [5,] 0.946 324s [6,] 0.948 324s [7,] 0.951 324s [8,] 0.944 324s [9,] 0.952 324s [10,] 0.976 324s [11,] 0.912 324s [12,] 0.871 324s [13,] 0.926 324s [14,] 0.927 324s [15,] 0.979 324s [16,] 0.968 324s [17,] 0.981 324s [18,] 0.970 324s [19,] 0.947 324s [20,] 0.943 324s > 324s > print( correlation.systemfit( fit3slsd[[ 3 ]]$e4, 2, 1 ) ) 324s [,1] 324s [1,] 0.932 324s [2,] 0.954 324s [3,] 0.952 324s [4,] 0.957 324s [5,] 0.892 324s [6,] 0.887 324s [7,] 0.887 324s [8,] 0.905 324s [9,] 0.914 324s [10,] 0.963 324s [11,] 0.860 324s [12,] 0.779 324s [13,] 0.878 324s [14,] 0.852 324s [15,] 0.968 324s [16,] 0.938 324s [17,] 0.973 324s [18,] 0.946 324s [19,] 0.913 324s [20,] 0.921 324s > 324s > 324s > ## ************ Log-Likelihood values *************** 324s > print( logLik( fit3sls[[ 1 ]]$e1c ) ) 324s 'log Lik.' -53 (df=10) 324s > print( logLik( fit3sls[[ 1 ]]$e1c, residCovDiag = TRUE ) ) 324s 'log Lik.' -85.6 (df=10) 324s > 324s > print( logLik( fit3sls[[ 2 ]]$e2e ) ) 324s 'log Lik.' -55.6 (df=9) 324s > print( logLik( fit3sls[[ 2 ]]$e2e, residCovDiag = TRUE ) ) 324s 'log Lik.' -85.4 (df=9) 324s > 324s > print( logLik( fit3sls[[ 3 ]]$e3 ) ) 324s 'log Lik.' -55.3 (df=9) 324s > print( logLik( fit3sls[[ 3 ]]$e3, residCovDiag = TRUE ) ) 324s 'log Lik.' -85.5 (df=9) 324s > 324s > print( logLik( fit3sls[[ 4 ]]$e4e ) ) 324s 'log Lik.' -58.5 (df=8) 324s > print( logLik( fit3sls[[ 4 ]]$e4e, residCovDiag = TRUE ) ) 324s 'log Lik.' -85.2 (df=8) 324s > 324s > print( logLik( fit3sls[[ 2 ]]$e4wSym ) ) 324s 'log Lik.' -58.5 (df=8) 324s > print( logLik( fit3sls[[ 2 ]]$e4wSym, residCovDiag = TRUE ) ) 324s 'log Lik.' -85.3 (df=8) 324s > 324s > print( logLik( fit3sls[[ 5 ]]$e5 ) ) 324s 'log Lik.' -87.3 (df=8) 324s > print( logLik( fit3sls[[ 5 ]]$e5, residCovDiag = TRUE ) ) 324s 'log Lik.' -104 (df=8) 324s > 324s > print( logLik( fit3slsi[[ 2 ]]$e3e ) ) 324s 'log Lik.' -46.7 (df=9) 324s > print( logLik( fit3slsi[[ 2 ]]$e3e, residCovDiag = TRUE ) ) 324s 'log Lik.' -92.1 (df=9) 324s > 324s > print( logLik( fit3slsi[[ 1 ]]$e1we ) ) 324s 'log Lik.' -52.7 (df=10) 324s > print( logLik( fit3slsi[[ 1 ]]$e1we, residCovDiag = TRUE ) ) 324s 'log Lik.' -85.8 (df=10) 324s > 324s > print( logLik( fit3slsd[[ 3 ]]$e4 ) ) 324s 'log Lik.' -59.4 (df=8) 324s > print( logLik( fit3slsd[[ 3 ]]$e4, residCovDiag = TRUE ) ) 324s 'log Lik.' -86.1 (df=8) 324s > 324s > print( logLik( fit3slsd[[ 5 ]]$e2we ) ) 324s 'log Lik.' -65 (df=9) 324s > print( logLik( fit3slsd[[ 5 ]]$e2we, residCovDiag = TRUE ) ) 324s 'log Lik.' -85.7 (df=9) 324s > 324s > 324s > ## ************** F tests **************** 324s > # testing first restriction 324s > print( linearHypothesis( fit3sls[[ 1 ]]$e1, restrm ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[1]]$e1 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 1.69 0.2 324s > linearHypothesis( fit3sls[[ 1 ]]$e1, restrict ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[1]]$e1 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 1.69 0.2 324s > 324s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restrm ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[2]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 1.52 0.23 324s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[2]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 1.52 0.23 324s > 324s > print( linearHypothesis( fit3sls[[ 3 ]]$e1c, restrm ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[3]]$e1c 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 2.47 0.13 324s > linearHypothesis( fit3sls[[ 3 ]]$e1c, restrict ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[3]]$e1c 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 2.47 0.13 324s > 324s > print( linearHypothesis( fit3slsi[[ 4 ]]$e1, restrm ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[4]]$e1 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 4.75 0.037 * 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > linearHypothesis( fit3slsi[[ 4 ]]$e1, restrict ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[4]]$e1 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 4.75 0.037 * 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrm ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[5]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.18 0.68 324s > linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrict ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[5]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.18 0.68 324s > 324s > print( linearHypothesis( fit3slsd[[ 2 ]]$e1w, restrm ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[2]]$e1w 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.51 0.48 324s > linearHypothesis( fit3slsd[[ 2 ]]$e1w, restrict ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[2]]$e1w 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.51 0.48 324s > 324s > # testing second restriction 324s > restrOnly2m <- matrix(0,1,7) 324s > restrOnly2q <- 0.5 324s > restrOnly2m[1,2] <- -1 324s > restrOnly2m[1,5] <- 1 324s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 324s > # first restriction not imposed 324s > print( linearHypothesis( fit3sls[[ 5 ]]$e1c, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[5]]$e1c 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.17 0.69 324s > linearHypothesis( fit3sls[[ 5 ]]$e1c, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[5]]$e1c 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.17 0.69 324s > 324s > print( linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[1]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.13 0.72 324s > linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[1]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.13 0.72 324s > 324s > print( linearHypothesis( fit3slsi[[ 3 ]]$e1we, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[3]]$e1we 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.13 0.72 324s > linearHypothesis( fit3slsi[[ 3 ]]$e1we, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[3]]$e1we 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.13 0.72 324s > 324s > print( linearHypothesis( fit3slsd[[ 2 ]]$e1, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[2]]$e1 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.25 0.62 324s > linearHypothesis( fit3slsd[[ 2 ]]$e1, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[2]]$e1 324s 324s Res.Df Df F Pr(>F) 324s 1 34 324s 2 33 1 0.25 0.62 324s > 324s > # first restriction imposed 324s > print( linearHypothesis( fit3sls[[ 4 ]]$e2, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[4]]$e2 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.81 0.38 324s > linearHypothesis( fit3sls[[ 4 ]]$e2, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[4]]$e2 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.81 0.38 324s > 324s > print( linearHypothesis( fit3sls[[ 4 ]]$e3, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[4]]$e3 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.81 0.38 324s > linearHypothesis( fit3sls[[ 4 ]]$e3, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[4]]$e3 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.81 0.38 324s > 324s > print( linearHypothesis( fit3sls[[ 1 ]]$e2w, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[1]]$e2w 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.9 0.35 324s > linearHypothesis( fit3sls[[ 1 ]]$e2w, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[1]]$e2w 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.9 0.35 324s > 324s > print( linearHypothesis( fit3sls[[ 1 ]]$e3we, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[1]]$e3we 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.75 0.39 324s > linearHypothesis( fit3sls[[ 1 ]]$e3we, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[1]]$e3we 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.75 0.39 324s > 324s > print( linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[5]]$e2e 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 15.1 0.00044 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[5]]$e2e 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 15.1 0.00044 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[5]]$e3e 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 15.1 0.00044 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[5]]$e3e 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 15.1 0.00044 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( linearHypothesis( fit3slsd[[ 1 ]]$e2, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[1]]$e2 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.16 0.69 324s > linearHypothesis( fit3slsd[[ 1 ]]$e2, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[1]]$e2 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.16 0.69 324s > 324s > print( linearHypothesis( fit3slsd[[ 1 ]]$e3, restrOnly2m, restrOnly2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[1]]$e3 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.16 0.69 324s > linearHypothesis( fit3slsd[[ 1 ]]$e3, restrictOnly2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[1]]$e3 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 34 1 0.16 0.69 324s > 324s > # testing both of the restrictions 324s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restr2m, restr2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[2]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 33 2 1 0.38 324s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[2]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 33 2 1 0.38 324s > 324s > print( linearHypothesis( fit3slsi[[ 3 ]]$e1, restr2m, restr2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[3]]$e1 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 33 2 5.59 0.0081 ** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > linearHypothesis( fit3slsi[[ 3 ]]$e1, restrict2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[3]]$e1 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 33 2 5.59 0.0081 ** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( linearHypothesis( fit3slsd[[ 4 ]]$e1e, restr2m, restr2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[4]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 33 2 0.64 0.53 324s > linearHypothesis( fit3slsd[[ 4 ]]$e1e, restrict2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[4]]$e1e 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 33 2 0.64 0.53 324s > 324s > print( linearHypothesis( fit3slsd[[ 5 ]]$e1w, restr2m, restr2q ) ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[5]]$e1w 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 33 2 0.45 0.64 324s > linearHypothesis( fit3slsd[[ 5 ]]$e1w, restrict2 ) 324s Linear hypothesis test (Theil's F test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[5]]$e1w 324s 324s Res.Df Df F Pr(>F) 324s 1 35 324s 2 33 2 0.45 0.64 324s > 324s > 324s > ## ************** Wald tests **************** 324s > # testing first restriction 324s > print( linearHypothesis( fit3sls[[ 1 ]]$e1, restrm, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[1]]$e1 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 1.11 0.29 324s > linearHypothesis( fit3sls[[ 1 ]]$e1, restrict, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[1]]$e1 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 1.11 0.29 324s > 324s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restrm, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[2]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 1.23 0.27 324s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[2]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 1.23 0.27 324s > 324s > print( linearHypothesis( fit3sls[[ 3 ]]$e1c, restrm, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[3]]$e1c 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 1.73 0.19 324s > linearHypothesis( fit3sls[[ 3 ]]$e1c, restrict, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[3]]$e1c 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 1.73 0.19 324s > 324s > print( linearHypothesis( fit3slsi[[ 4 ]]$e1, restrm, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[4]]$e1 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 4.81 0.028 * 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > linearHypothesis( fit3slsi[[ 4 ]]$e1, restrict, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[4]]$e1 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 4.81 0.028 * 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( linearHypothesis( fit3slsi[[ 2 ]]$e1we, restrm, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[2]]$e1we 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 5.72 0.017 * 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > linearHypothesis( fit3slsi[[ 2 ]]$e1we, restrict, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[2]]$e1we 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 5.72 0.017 * 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrm, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[5]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.15 0.7 324s > linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrict, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[5]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.15 0.7 324s > 324s > # testing second restriction 324s > # first restriction not imposed 324s > print( linearHypothesis( fit3sls[[ 5 ]]$e1c, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[5]]$e1c 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.12 0.73 324s > linearHypothesis( fit3sls[[ 5 ]]$e1c, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[5]]$e1c 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.12 0.73 324s > 324s > print( linearHypothesis( fit3sls[[ 3 ]]$e1wc, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[3]]$e1wc 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.12 0.73 324s > linearHypothesis( fit3sls[[ 3 ]]$e1wc, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[3]]$e1wc 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.12 0.73 324s > 324s > print( linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[1]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.16 0.69 324s > linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[1]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.16 0.69 324s > 324s > print( linearHypothesis( fit3slsd[[ 2 ]]$e1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[2]]$e1 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.17 0.68 324s > linearHypothesis( fit3slsd[[ 2 ]]$e1, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[2]]$e1 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 34 324s 2 33 1 0.17 0.68 324s > 324s > # first restriction imposed 324s > print( linearHypothesis( fit3sls[[ 4 ]]$e2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[4]]$e2 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.55 0.46 324s > linearHypothesis( fit3sls[[ 4 ]]$e2, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[4]]$e2 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.55 0.46 324s > 324s > print( linearHypothesis( fit3sls[[ 4 ]]$e3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[4]]$e3 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.55 0.46 324s > linearHypothesis( fit3sls[[ 4 ]]$e3, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[4]]$e3 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.55 0.46 324s > 324s > print( linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[5]]$e2e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 17.8 2.4e-05 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[5]]$e2e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 17.8 2.4e-05 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[5]]$e3e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 17.8 2.4e-05 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[5]]$e3e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 17.8 2.4e-05 *** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( linearHypothesis( fit3slsd[[ 1 ]]$e2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[1]]$e2 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.13 0.72 324s > linearHypothesis( fit3slsd[[ 1 ]]$e2, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[1]]$e2 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.13 0.72 324s > 324s > print( linearHypothesis( fit3slsd[[ 1 ]]$e3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[1]]$e3 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.13 0.72 324s > linearHypothesis( fit3slsd[[ 1 ]]$e3, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[1]]$e3 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.13 0.72 324s > 324s > print( linearHypothesis( fit3slsd[[ 2 ]]$e2we, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[2]]$e2we 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 1.52 0.22 324s > linearHypothesis( fit3slsd[[ 2 ]]$e2we, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[2]]$e2we 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 1.52 0.22 324s > 324s > print( linearHypothesis( fit3slsd[[ 3 ]]$e3w, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[3]]$e3w 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.23 0.63 324s > linearHypothesis( fit3slsd[[ 3 ]]$e3w, restrictOnly2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[3]]$e3w 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 34 1 0.23 0.63 324s > 324s > # testing both of the restrictions 324s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restr2m, restr2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[2]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 33 2 1.62 0.44 324s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[2]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 33 2 1.62 0.44 324s > 324s > print( linearHypothesis( fit3sls[[ 5 ]]$e1wc, restr2m, restr2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[5]]$e1wc 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 33 2 2.43 0.3 324s > linearHypothesis( fit3sls[[ 5 ]]$e1wc, restrict2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3sls[[5]]$e1wc 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 33 2 2.43 0.3 324s > 324s > print( linearHypothesis( fit3slsi[[ 3 ]]$e1, restr2m, restr2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[3]]$e1 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 33 2 11.3 0.0035 ** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > linearHypothesis( fit3slsi[[ 3 ]]$e1, restrict2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsi[[3]]$e1 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 33 2 11.3 0.0035 ** 324s --- 324s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 324s > 324s > print( linearHypothesis( fit3slsd[[ 4 ]]$e1e, restr2m, restr2q, test = "Chisq" ) ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[4]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 33 2 1.55 0.46 324s > linearHypothesis( fit3slsd[[ 4 ]]$e1e, restrict2, test = "Chisq" ) 324s Linear hypothesis test (Chi^2 statistic of a Wald test) 324s 324s Hypothesis: 324s demand_income - supply_trend = 0 324s - demand_price + supply_price = 0.5 324s 324s Model 1: restricted model 324s Model 2: fit3slsd[[4]]$e1e 324s 324s Res.Df Df Chisq Pr(>Chisq) 324s 1 35 324s 2 33 2 1.55 0.46 324s > 324s > 324s > ## *********** model frame ************* 324s > print( mf <- model.frame( fit3sls[[ 3 ]]$e1c ) ) 324s consump price income farmPrice trend 324s 1 98.5 100.3 87.4 98.0 1 324s 2 99.2 104.3 97.6 99.1 2 324s 3 102.2 103.4 96.7 99.1 3 324s 4 101.5 104.5 98.2 98.1 4 324s 5 104.2 98.0 99.8 110.8 5 324s 6 103.2 99.5 100.5 108.2 6 324s 7 104.0 101.1 103.2 105.6 7 324s 8 99.9 104.8 107.8 109.8 8 324s 9 100.3 96.4 96.6 108.7 9 324s 10 102.8 91.2 88.9 100.6 10 324s 11 95.4 93.1 75.1 81.0 11 324s 12 92.4 98.8 76.9 68.6 12 324s 13 94.5 102.9 84.6 70.9 13 324s 14 98.8 98.8 90.6 81.4 14 324s 15 105.8 95.1 103.1 102.3 15 324s 16 100.2 98.5 105.1 105.0 16 324s 17 103.5 86.5 96.4 110.5 17 324s 18 99.9 104.0 104.4 92.5 18 324s 19 105.2 105.8 110.7 89.3 19 324s 20 106.2 113.5 127.1 93.0 20 324s > print( mf1 <- model.frame( fit3sls[[ 3 ]]$e1c$eq[[ 1 ]] ) ) 324s consump price income 324s 1 98.5 100.3 87.4 324s 2 99.2 104.3 97.6 324s 3 102.2 103.4 96.7 324s 4 101.5 104.5 98.2 324s 5 104.2 98.0 99.8 324s 6 103.2 99.5 100.5 324s 7 104.0 101.1 103.2 324s 8 99.9 104.8 107.8 324s 9 100.3 96.4 96.6 324s 10 102.8 91.2 88.9 324s 11 95.4 93.1 75.1 324s 12 92.4 98.8 76.9 324s 13 94.5 102.9 84.6 324s 14 98.8 98.8 90.6 324s 15 105.8 95.1 103.1 324s 16 100.2 98.5 105.1 324s 17 103.5 86.5 96.4 324s 18 99.9 104.0 104.4 324s 19 105.2 105.8 110.7 324s 20 106.2 113.5 127.1 324s > print( attributes( mf1 )$terms ) 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s > print( mf2 <- model.frame( fit3sls[[ 3 ]]$e1c$eq[[ 2 ]] ) ) 324s consump price farmPrice trend 324s 1 98.5 100.3 98.0 1 324s 2 99.2 104.3 99.1 2 324s 3 102.2 103.4 99.1 3 324s 4 101.5 104.5 98.1 4 324s 5 104.2 98.0 110.8 5 324s 6 103.2 99.5 108.2 6 324s 7 104.0 101.1 105.6 7 324s 8 99.9 104.8 109.8 8 324s 9 100.3 96.4 108.7 9 324s 10 102.8 91.2 100.6 10 324s 11 95.4 93.1 81.0 11 324s 12 92.4 98.8 68.6 12 324s 13 94.5 102.9 70.9 13 324s 14 98.8 98.8 81.4 14 324s 15 105.8 95.1 102.3 15 324s 16 100.2 98.5 105.0 16 324s 17 103.5 86.5 110.5 17 324s 18 99.9 104.0 92.5 18 324s 19 105.2 105.8 89.3 19 324s 20 106.2 113.5 93.0 20 324s > print( attributes( mf2 )$terms ) 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s > 324s > print( all.equal( mf, model.frame( fit3sls[[ 3 ]]$e1wc ) ) ) 324s [1] TRUE 324s > print( all.equal( mf2, model.frame( fit3sls[[ 3 ]]$e1wc$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > print( all.equal( mf, model.frame( fit3sls[[ 4 ]]$e2e ) ) ) 324s [1] TRUE 324s > print( all.equal( mf2, model.frame( fit3sls[[ 4 ]]$e2e$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > print( all.equal( mf, model.frame( fit3sls[[ 5 ]]$e3 ) ) ) 324s [1] TRUE 324s > print( all.equal( mf1, model.frame( fit3sls[[ 5 ]]$e3$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > 324s > print( all.equal( mf, model.frame( fit3sls[[ 1 ]]$e4e ) ) ) 324s [1] TRUE 324s > print( all.equal( mf2, model.frame( fit3sls[[ 1 ]]$e4e$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > print( all.equal( mf, model.frame( fit3sls[[ 2 ]]$e5 ) ) ) 324s [1] TRUE 324s > print( all.equal( mf1, model.frame( fit3sls[[ 3 ]]$e5$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > 324s > print( all.equal( mf, model.frame( fit3slsi[[ 4 ]]$e3e ) ) ) 324s [1] TRUE 324s > print( all.equal( mf1, model.frame( fit3slsi[[ 4 ]]$e3e$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > 324s > print( all.equal( mf, model.frame( fit3slsd[[ 5 ]]$e4 ) ) ) 324s [1] TRUE 324s > print( all.equal( mf2, model.frame( fit3slsd[[ 5 ]]$e4$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > fit3sls[[ 3 ]]$e1c$eq[[ 1 ]]$modelInst 324s income farmPrice trend 324s 1 87.4 98.0 1 324s 2 97.6 99.1 2 324s 3 96.7 99.1 3 324s 4 98.2 98.1 4 324s 5 99.8 110.8 5 324s 6 100.5 108.2 6 324s 7 103.2 105.6 7 324s 8 107.8 109.8 8 324s 9 96.6 108.7 9 324s 10 88.9 100.6 10 324s 11 75.1 81.0 11 324s 12 76.9 68.6 12 324s 13 84.6 70.9 13 324s 14 90.6 81.4 14 324s 15 103.1 102.3 15 324s 16 105.1 105.0 16 324s 17 96.4 110.5 17 324s 18 104.4 92.5 18 324s 19 110.7 89.3 19 324s 20 127.1 93.0 20 324s > fit3sls[[ 3 ]]$e1c$eq[[ 2 ]]$modelInst 324s income farmPrice trend 324s 1 87.4 98.0 1 324s 2 97.6 99.1 2 324s 3 96.7 99.1 3 324s 4 98.2 98.1 4 324s 5 99.8 110.8 5 324s 6 100.5 108.2 6 324s 7 103.2 105.6 7 324s 8 107.8 109.8 8 324s 9 96.6 108.7 9 324s 10 88.9 100.6 10 324s 11 75.1 81.0 11 324s 12 76.9 68.6 12 324s 13 84.6 70.9 13 324s 14 90.6 81.4 14 324s 15 103.1 102.3 15 324s 16 105.1 105.0 16 324s 17 96.4 110.5 17 324s 18 104.4 92.5 18 324s 19 110.7 89.3 19 324s 20 127.1 93.0 20 324s > 324s > fit3sls[[ 1 ]]$e3$eq[[ 1 ]]$modelInst 324s income farmPrice trend 324s 1 87.4 98.0 1 324s 2 97.6 99.1 2 324s 3 96.7 99.1 3 324s 4 98.2 98.1 4 324s 5 99.8 110.8 5 324s 6 100.5 108.2 6 324s 7 103.2 105.6 7 324s 8 107.8 109.8 8 324s 9 96.6 108.7 9 324s 10 88.9 100.6 10 324s 11 75.1 81.0 11 324s 12 76.9 68.6 12 324s 13 84.6 70.9 13 324s 14 90.6 81.4 14 324s 15 103.1 102.3 15 324s 16 105.1 105.0 16 324s 17 96.4 110.5 17 324s 18 104.4 92.5 18 324s 19 110.7 89.3 19 324s 20 127.1 93.0 20 324s > fit3sls[[ 1 ]]$e3$eq[[ 2 ]]$modelInst 324s income farmPrice trend 324s 1 87.4 98.0 1 324s 2 97.6 99.1 2 324s 3 96.7 99.1 3 324s 4 98.2 98.1 4 324s 5 99.8 110.8 5 324s 6 100.5 108.2 6 324s 7 103.2 105.6 7 324s 8 107.8 109.8 8 324s 9 96.6 108.7 9 324s 10 88.9 100.6 10 324s 11 75.1 81.0 11 324s 12 76.9 68.6 12 324s 13 84.6 70.9 13 324s 14 90.6 81.4 14 324s 15 103.1 102.3 15 324s 16 105.1 105.0 16 324s 17 96.4 110.5 17 324s 18 104.4 92.5 18 324s 19 110.7 89.3 19 324s 20 127.1 93.0 20 324s > 324s > fit3slsd[[ 5 ]]$e4$eq[[ 1 ]]$modelInst 324s income farmPrice 324s 1 87.4 98.0 324s 2 97.6 99.1 324s 3 96.7 99.1 324s 4 98.2 98.1 324s 5 99.8 110.8 324s 6 100.5 108.2 324s 7 103.2 105.6 324s 8 107.8 109.8 324s 9 96.6 108.7 324s 10 88.9 100.6 324s 11 75.1 81.0 324s 12 76.9 68.6 324s 13 84.6 70.9 324s 14 90.6 81.4 324s 15 103.1 102.3 324s 16 105.1 105.0 324s 17 96.4 110.5 324s 18 104.4 92.5 324s 19 110.7 89.3 324s 20 127.1 93.0 324s > fit3slsd[[ 5 ]]$e4$eq[[ 2 ]]$modelInst 324s income farmPrice trend 324s 1 87.4 98.0 1 324s 2 97.6 99.1 2 324s 3 96.7 99.1 3 324s 4 98.2 98.1 4 324s 5 99.8 110.8 5 324s 6 100.5 108.2 6 324s 7 103.2 105.6 7 324s 8 107.8 109.8 8 324s 9 96.6 108.7 9 324s 10 88.9 100.6 10 324s 11 75.1 81.0 11 324s 12 76.9 68.6 12 324s 13 84.6 70.9 13 324s 14 90.6 81.4 14 324s 15 103.1 102.3 15 324s 16 105.1 105.0 16 324s 17 96.4 110.5 17 324s 18 104.4 92.5 18 324s 19 110.7 89.3 19 324s 20 127.1 93.0 20 324s > 324s > 324s > ## **************** model matrix ************************ 324s > # with x (returnModelMatrix) = TRUE 324s > print( !is.null( fit3sls[[ 4 ]]$e1c$eq[[ 1 ]]$x ) ) 324s [1] TRUE 324s > print( mm <- model.matrix( fit3sls[[ 4 ]]$e1c ) ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s demand_1 1 100.3 87.4 0 324s demand_2 1 104.3 97.6 0 324s demand_3 1 103.4 96.7 0 324s demand_4 1 104.5 98.2 0 324s demand_5 1 98.0 99.8 0 324s demand_6 1 99.5 100.5 0 324s demand_7 1 101.1 103.2 0 324s demand_8 1 104.8 107.8 0 324s demand_9 1 96.4 96.6 0 324s demand_10 1 91.2 88.9 0 324s demand_11 1 93.1 75.1 0 324s demand_12 1 98.8 76.9 0 324s demand_13 1 102.9 84.6 0 324s demand_14 1 98.8 90.6 0 324s demand_15 1 95.1 103.1 0 324s demand_16 1 98.5 105.1 0 324s demand_17 1 86.5 96.4 0 324s demand_18 1 104.0 104.4 0 324s demand_19 1 105.8 110.7 0 324s demand_20 1 113.5 127.1 0 324s supply_1 0 0.0 0.0 1 324s supply_2 0 0.0 0.0 1 324s supply_3 0 0.0 0.0 1 324s supply_4 0 0.0 0.0 1 324s supply_5 0 0.0 0.0 1 324s supply_6 0 0.0 0.0 1 324s supply_7 0 0.0 0.0 1 324s supply_8 0 0.0 0.0 1 324s supply_9 0 0.0 0.0 1 324s supply_10 0 0.0 0.0 1 324s supply_11 0 0.0 0.0 1 324s supply_12 0 0.0 0.0 1 324s supply_13 0 0.0 0.0 1 324s supply_14 0 0.0 0.0 1 324s supply_15 0 0.0 0.0 1 324s supply_16 0 0.0 0.0 1 324s supply_17 0 0.0 0.0 1 324s supply_18 0 0.0 0.0 1 324s supply_19 0 0.0 0.0 1 324s supply_20 0 0.0 0.0 1 324s supply_price supply_farmPrice supply_trend 324s demand_1 0.0 0.0 0 324s demand_2 0.0 0.0 0 324s demand_3 0.0 0.0 0 324s demand_4 0.0 0.0 0 324s demand_5 0.0 0.0 0 324s demand_6 0.0 0.0 0 324s demand_7 0.0 0.0 0 324s demand_8 0.0 0.0 0 324s demand_9 0.0 0.0 0 324s demand_10 0.0 0.0 0 324s demand_11 0.0 0.0 0 324s demand_12 0.0 0.0 0 324s demand_13 0.0 0.0 0 324s demand_14 0.0 0.0 0 324s demand_15 0.0 0.0 0 324s demand_16 0.0 0.0 0 324s demand_17 0.0 0.0 0 324s demand_18 0.0 0.0 0 324s demand_19 0.0 0.0 0 324s demand_20 0.0 0.0 0 324s supply_1 100.3 98.0 1 324s supply_2 104.3 99.1 2 324s supply_3 103.4 99.1 3 324s supply_4 104.5 98.1 4 324s supply_5 98.0 110.8 5 324s supply_6 99.5 108.2 6 324s supply_7 101.1 105.6 7 324s supply_8 104.8 109.8 8 324s supply_9 96.4 108.7 9 324s supply_10 91.2 100.6 10 324s supply_11 93.1 81.0 11 324s supply_12 98.8 68.6 12 324s supply_13 102.9 70.9 13 324s supply_14 98.8 81.4 14 324s supply_15 95.1 102.3 15 324s supply_16 98.5 105.0 16 324s supply_17 86.5 110.5 17 324s supply_18 104.0 92.5 18 324s supply_19 105.8 89.3 19 324s supply_20 113.5 93.0 20 324s > print( mm1 <- model.matrix( fit3sls[[ 4 ]]$e1c$eq[[ 1 ]] ) ) 324s (Intercept) price income 324s 1 1 100.3 87.4 324s 2 1 104.3 97.6 324s 3 1 103.4 96.7 324s 4 1 104.5 98.2 324s 5 1 98.0 99.8 324s 6 1 99.5 100.5 324s 7 1 101.1 103.2 324s 8 1 104.8 107.8 324s 9 1 96.4 96.6 324s 10 1 91.2 88.9 324s 11 1 93.1 75.1 324s 12 1 98.8 76.9 324s 13 1 102.9 84.6 324s 14 1 98.8 90.6 324s 15 1 95.1 103.1 324s 16 1 98.5 105.1 324s 17 1 86.5 96.4 324s 18 1 104.0 104.4 324s 19 1 105.8 110.7 324s 20 1 113.5 127.1 324s attr(,"assign") 324s [1] 0 1 2 324s > print( mm2 <- model.matrix( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]] ) ) 324s (Intercept) price farmPrice trend 324s 1 1 100.3 98.0 1 324s 2 1 104.3 99.1 2 324s 3 1 103.4 99.1 3 324s 4 1 104.5 98.1 4 324s 5 1 98.0 110.8 5 324s 6 1 99.5 108.2 6 324s 7 1 101.1 105.6 7 324s 8 1 104.8 109.8 8 324s 9 1 96.4 108.7 9 324s 10 1 91.2 100.6 10 324s 11 1 93.1 81.0 11 324s 12 1 98.8 68.6 12 324s 13 1 102.9 70.9 13 324s 14 1 98.8 81.4 14 324s 15 1 95.1 102.3 15 324s 16 1 98.5 105.0 16 324s 17 1 86.5 110.5 17 324s 18 1 104.0 92.5 18 324s 19 1 105.8 89.3 19 324s 20 1 113.5 93.0 20 324s attr(,"assign") 324s [1] 0 1 2 3 324s > 324s > # with x (returnModelMatrix) = FALSE 324s > print( all.equal( mm, model.matrix( fit3sls[[ 4 ]]$e1wc ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3sls[[ 4 ]]$e1wc$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3sls[[ 4 ]]$e1wc$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > print( !is.null( fit3sls[[ 4 ]]$e1wc$eq[[ 1 ]]$x ) ) 324s [1] FALSE 324s > 324s > # with x (returnModelMatrix) = TRUE 324s > print( !is.null( fit3sls[[ 5 ]]$e2$eq[[ 1 ]]$x ) ) 324s [1] TRUE 324s > print( all.equal( mm, model.matrix( fit3sls[[ 5 ]]$e2 ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3sls[[ 5 ]]$e2$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3sls[[ 5 ]]$e2$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > # with x (returnModelMatrix) = FALSE 324s > print( all.equal( mm, model.matrix( fit3sls[[ 5 ]]$e2e ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3sls[[ 5 ]]$e2e$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3sls[[ 5 ]]$e2e$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > print( !is.null( fit3sls[[ 5 ]]$e1wc$e2e[[ 1 ]]$x ) ) 324s [1] FALSE 324s > 324s > # with x (returnModelMatrix) = TRUE 324s > print( !is.null( fit3sls[[ 1 ]]$e3e$eq[[ 1 ]]$x ) ) 324s [1] TRUE 324s > print( all.equal( mm, model.matrix( fit3sls[[ 1 ]]$e3e ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3sls[[ 1 ]]$e3e$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3sls[[ 1 ]]$e3e$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > # with x (returnModelMatrix) = FALSE 324s > print( all.equal( mm, model.matrix( fit3sls[[ 1 ]]$e3 ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3sls[[ 1 ]]$e3$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3sls[[ 1 ]]$e3$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > print( !is.null( fit3sls[[ 1 ]]$e3$eq[[ 1 ]]$x ) ) 324s [1] FALSE 324s > 324s > # with x (returnModelMatrix) = TRUE 324s > print( !is.null( fit3slsi[[ 2 ]]$e4$eq[[ 1 ]]$x ) ) 324s [1] TRUE 324s > print( all.equal( mm, model.matrix( fit3slsi[[ 2 ]]$e4 ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3slsi[[ 2 ]]$e4$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3slsi[[ 2 ]]$e4$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > # with x (returnModelMatrix) = FALSE 324s > print( all.equal( mm, model.matrix( fit3slsi[[ 2 ]]$e4we ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3slsi[[ 2 ]]$e4we$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3slsi[[ 2 ]]$e4we$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > print( !is.null( fit3slsi[[ 2 ]]$e1wc$e4we[[ 1 ]]$x ) ) 324s [1] FALSE 324s > 324s > # with x (returnModelMatrix) = TRUE 324s > print( !is.null( fit3slsi[[ 5 ]]$e5w$eq[[ 1 ]]$x ) ) 324s [1] TRUE 324s > print( all.equal( mm, model.matrix( fit3slsi[[ 5 ]]$e5w ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3slsi[[ 5 ]]$e5w$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3slsi[[ 5 ]]$e5w$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > # with x (returnModelMatrix) = FALSE 324s > print( all.equal( mm, model.matrix( fit3slsi[[ 5 ]]$e5 ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3slsi[[ 5 ]]$e5$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3slsi[[ 5 ]]$e5$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > print( !is.null( fit3slsi[[ 5 ]]$e5$eq[[ 1 ]]$x ) ) 324s [1] FALSE 324s > 324s > # with x (returnModelMatrix) = TRUE 324s > print( !is.null( fit3slsd[[ 3 ]]$e5e$eq[[ 1 ]]$x ) ) 324s [1] TRUE 324s > print( all.equal( mm, model.matrix( fit3slsd[[ 3 ]]$e5e ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3slsd[[ 3 ]]$e5e$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3slsd[[ 3 ]]$e5e$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > # with x (returnModelMatrix) = FALSE 324s > print( all.equal( mm, model.matrix( fit3slsd[[ 3 ]]$e5we ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3slsd[[ 3 ]]$e5we$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3slsd[[ 3 ]]$e5we$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > print( !is.null( fit3sls[[ 3 ]]$e5we$eq[[ 1 ]]$x ) ) 324s [1] FALSE 324s > 324s > # with x (returnModelMatrix) = TRUE 324s > print( !is.null( fit3slsd[[ 2 ]]$e3w$eq[[ 1 ]]$x ) ) 324s [1] TRUE 324s > print( all.equal( mm, model.matrix( fit3slsd[[ 2 ]]$e3w ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3slsd[[ 2 ]]$e3w$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3slsd[[ 2 ]]$e3w$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > 324s > # with x (returnModelMatrix) = FALSE 324s > print( all.equal( mm, model.matrix( fit3slsd[[ 2 ]]$e3 ) ) ) 324s [1] TRUE 324s > print( all.equal( mm1, model.matrix( fit3slsd[[ 2 ]]$e3$eq[[ 1 ]] ) ) ) 324s [1] TRUE 324s > print( all.equal( mm2, model.matrix( fit3slsd[[ 2 ]]$e3$eq[[ 2 ]] ) ) ) 324s [1] TRUE 324s > print( !is.null( fit3slsd[[ 2 ]]$e3$eq[[ 1 ]]$x ) ) 324s [1] FALSE 324s > 324s > # matrices of instrumental variables 324s > model.matrix( fit3sls[[ 1 ]]$e1c, which = "z" ) 324s demand_(Intercept) demand_income demand_farmPrice demand_trend 324s demand_1 1 87.4 98.0 1 324s demand_2 1 97.6 99.1 2 324s demand_3 1 96.7 99.1 3 324s demand_4 1 98.2 98.1 4 324s demand_5 1 99.8 110.8 5 324s demand_6 1 100.5 108.2 6 324s demand_7 1 103.2 105.6 7 324s demand_8 1 107.8 109.8 8 324s demand_9 1 96.6 108.7 9 324s demand_10 1 88.9 100.6 10 324s demand_11 1 75.1 81.0 11 324s demand_12 1 76.9 68.6 12 324s demand_13 1 84.6 70.9 13 324s demand_14 1 90.6 81.4 14 324s demand_15 1 103.1 102.3 15 324s demand_16 1 105.1 105.0 16 324s demand_17 1 96.4 110.5 17 324s demand_18 1 104.4 92.5 18 324s demand_19 1 110.7 89.3 19 324s demand_20 1 127.1 93.0 20 324s supply_1 0 0.0 0.0 0 324s supply_2 0 0.0 0.0 0 324s supply_3 0 0.0 0.0 0 324s supply_4 0 0.0 0.0 0 324s supply_5 0 0.0 0.0 0 324s supply_6 0 0.0 0.0 0 324s supply_7 0 0.0 0.0 0 324s supply_8 0 0.0 0.0 0 324s supply_9 0 0.0 0.0 0 324s supply_10 0 0.0 0.0 0 324s supply_11 0 0.0 0.0 0 324s supply_12 0 0.0 0.0 0 324s supply_13 0 0.0 0.0 0 324s supply_14 0 0.0 0.0 0 324s supply_15 0 0.0 0.0 0 324s supply_16 0 0.0 0.0 0 324s supply_17 0 0.0 0.0 0 324s supply_18 0 0.0 0.0 0 324s supply_19 0 0.0 0.0 0 324s supply_20 0 0.0 0.0 0 324s supply_(Intercept) supply_income supply_farmPrice supply_trend 324s demand_1 0 0.0 0.0 0 324s demand_2 0 0.0 0.0 0 324s demand_3 0 0.0 0.0 0 324s demand_4 0 0.0 0.0 0 324s demand_5 0 0.0 0.0 0 324s demand_6 0 0.0 0.0 0 324s demand_7 0 0.0 0.0 0 324s demand_8 0 0.0 0.0 0 324s demand_9 0 0.0 0.0 0 324s demand_10 0 0.0 0.0 0 324s demand_11 0 0.0 0.0 0 324s demand_12 0 0.0 0.0 0 324s demand_13 0 0.0 0.0 0 324s demand_14 0 0.0 0.0 0 324s demand_15 0 0.0 0.0 0 324s demand_16 0 0.0 0.0 0 324s demand_17 0 0.0 0.0 0 324s demand_18 0 0.0 0.0 0 324s demand_19 0 0.0 0.0 0 324s demand_20 0 0.0 0.0 0 324s supply_1 1 87.4 98.0 1 324s supply_2 1 97.6 99.1 2 324s supply_3 1 96.7 99.1 3 324s supply_4 1 98.2 98.1 4 324s supply_5 1 99.8 110.8 5 324s supply_6 1 100.5 108.2 6 324s supply_7 1 103.2 105.6 7 324s supply_8 1 107.8 109.8 8 324s supply_9 1 96.6 108.7 9 324s supply_10 1 88.9 100.6 10 324s supply_11 1 75.1 81.0 11 324s supply_12 1 76.9 68.6 12 324s supply_13 1 84.6 70.9 13 324s supply_14 1 90.6 81.4 14 324s supply_15 1 103.1 102.3 15 324s supply_16 1 105.1 105.0 16 324s supply_17 1 96.4 110.5 17 324s supply_18 1 104.4 92.5 18 324s supply_19 1 110.7 89.3 19 324s supply_20 1 127.1 93.0 20 324s > model.matrix( fit3sls[[ 3 ]]$e1c$eq[[ 1 ]], which = "z" ) 324s (Intercept) income farmPrice trend 324s 1 1 87.4 98.0 1 324s 2 1 97.6 99.1 2 324s 3 1 96.7 99.1 3 324s 4 1 98.2 98.1 4 324s 5 1 99.8 110.8 5 324s 6 1 100.5 108.2 6 324s 7 1 103.2 105.6 7 324s 8 1 107.8 109.8 8 324s 9 1 96.6 108.7 9 324s 10 1 88.9 100.6 10 324s 11 1 75.1 81.0 11 324s 12 1 76.9 68.6 12 324s 13 1 84.6 70.9 13 324s 14 1 90.6 81.4 14 324s 15 1 103.1 102.3 15 324s 16 1 105.1 105.0 16 324s 17 1 96.4 110.5 17 324s 18 1 104.4 92.5 18 324s 19 1 110.7 89.3 19 324s 20 1 127.1 93.0 20 324s attr(,"assign") 324s [1] 0 1 2 3 324s > model.matrix( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]], which = "z" ) 324s (Intercept) income farmPrice trend 324s 1 1 87.4 98.0 1 324s 2 1 97.6 99.1 2 324s 3 1 96.7 99.1 3 324s 4 1 98.2 98.1 4 324s 5 1 99.8 110.8 5 324s 6 1 100.5 108.2 6 324s 7 1 103.2 105.6 7 324s 8 1 107.8 109.8 8 324s 9 1 96.6 108.7 9 324s 10 1 88.9 100.6 10 324s 11 1 75.1 81.0 11 324s 12 1 76.9 68.6 12 324s 13 1 84.6 70.9 13 324s 14 1 90.6 81.4 14 324s 15 1 103.1 102.3 15 324s 16 1 105.1 105.0 16 324s 17 1 96.4 110.5 17 324s 18 1 104.4 92.5 18 324s 19 1 110.7 89.3 19 324s 20 1 127.1 93.0 20 324s attr(,"assign") 324s [1] 0 1 2 3 324s > 324s > # matrices of fitted regressors 324s > model.matrix( fit3slsd[[ 1 ]]$e3w, which = "xHat" ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s demand_1 1 95.2 87.4 0 324s demand_2 1 99.3 97.6 0 324s demand_3 1 99.0 96.7 0 324s demand_4 1 99.9 98.2 0 324s demand_5 1 97.0 99.8 0 324s demand_6 1 98.0 100.5 0 324s demand_7 1 99.9 103.2 0 324s demand_8 1 100.7 107.8 0 324s demand_9 1 96.2 96.6 0 324s demand_10 1 95.1 88.9 0 324s demand_11 1 94.7 75.1 0 324s demand_12 1 99.0 76.9 0 324s demand_13 1 101.7 84.6 0 324s demand_14 1 101.3 90.6 0 324s demand_15 1 100.8 103.1 0 324s demand_16 1 100.9 105.1 0 324s demand_17 1 95.6 96.4 0 324s demand_18 1 104.2 104.4 0 324s demand_19 1 107.8 110.7 0 324s demand_20 1 113.9 127.1 0 324s supply_1 0 0.0 0.0 1 324s supply_2 0 0.0 0.0 1 324s supply_3 0 0.0 0.0 1 324s supply_4 0 0.0 0.0 1 324s supply_5 0 0.0 0.0 1 324s supply_6 0 0.0 0.0 1 324s supply_7 0 0.0 0.0 1 324s supply_8 0 0.0 0.0 1 324s supply_9 0 0.0 0.0 1 324s supply_10 0 0.0 0.0 1 324s supply_11 0 0.0 0.0 1 324s supply_12 0 0.0 0.0 1 324s supply_13 0 0.0 0.0 1 324s supply_14 0 0.0 0.0 1 324s supply_15 0 0.0 0.0 1 324s supply_16 0 0.0 0.0 1 324s supply_17 0 0.0 0.0 1 324s supply_18 0 0.0 0.0 1 324s supply_19 0 0.0 0.0 1 324s supply_20 0 0.0 0.0 1 324s supply_price supply_farmPrice supply_trend 324s demand_1 0.0 0.0 0 324s demand_2 0.0 0.0 0 324s demand_3 0.0 0.0 0 324s demand_4 0.0 0.0 0 324s demand_5 0.0 0.0 0 324s demand_6 0.0 0.0 0 324s demand_7 0.0 0.0 0 324s demand_8 0.0 0.0 0 324s demand_9 0.0 0.0 0 324s demand_10 0.0 0.0 0 324s demand_11 0.0 0.0 0 324s demand_12 0.0 0.0 0 324s demand_13 0.0 0.0 0 324s demand_14 0.0 0.0 0 324s demand_15 0.0 0.0 0 324s demand_16 0.0 0.0 0 324s demand_17 0.0 0.0 0 324s demand_18 0.0 0.0 0 324s demand_19 0.0 0.0 0 324s demand_20 0.0 0.0 0 324s supply_1 99.6 98.0 1 324s supply_2 105.1 99.1 2 324s supply_3 103.8 99.1 3 324s supply_4 104.5 98.1 4 324s supply_5 98.7 110.8 5 324s supply_6 99.6 108.2 6 324s supply_7 102.0 105.6 7 324s supply_8 102.2 109.8 8 324s supply_9 94.6 108.7 9 324s supply_10 92.7 100.6 10 324s supply_11 92.4 81.0 11 324s supply_12 98.9 68.6 12 324s supply_13 102.2 70.9 13 324s supply_14 100.3 81.4 14 324s supply_15 97.6 102.3 15 324s supply_16 96.9 105.0 16 324s supply_17 87.7 110.5 17 324s supply_18 101.1 92.5 18 324s supply_19 106.1 89.3 19 324s supply_20 114.4 93.0 20 324s > model.matrix( fit3slsd[[ 3 ]]$e3w$eq[[ 1 ]], which = "xHat" ) 324s (Intercept) price income 324s 1 1 95.2 87.4 324s 2 1 99.3 97.6 324s 3 1 99.0 96.7 324s 4 1 99.9 98.2 324s 5 1 97.0 99.8 324s 6 1 98.0 100.5 324s 7 1 99.9 103.2 324s 8 1 100.7 107.8 324s 9 1 96.2 96.6 324s 10 1 95.1 88.9 324s 11 1 94.7 75.1 324s 12 1 99.0 76.9 324s 13 1 101.7 84.6 324s 14 1 101.3 90.6 324s 15 1 100.8 103.1 324s 16 1 100.9 105.1 324s 17 1 95.6 96.4 324s 18 1 104.2 104.4 324s 19 1 107.8 110.7 324s 20 1 113.9 127.1 324s > model.matrix( fit3slsd[[ 4 ]]$e3w$eq[[ 2 ]], which = "xHat" ) 324s (Intercept) price farmPrice trend 324s 1 1 99.6 98.0 1 324s 2 1 105.1 99.1 2 324s 3 1 103.8 99.1 3 324s 4 1 104.5 98.1 4 324s 5 1 98.7 110.8 5 324s 6 1 99.6 108.2 6 324s 7 1 102.0 105.6 7 324s 8 1 102.2 109.8 8 324s 9 1 94.6 108.7 9 324s 10 1 92.7 100.6 10 324s 11 1 92.4 81.0 11 324s 12 1 98.9 68.6 12 324s 13 1 102.2 70.9 13 324s 14 1 100.3 81.4 14 324s 15 1 97.6 102.3 15 324s 16 1 96.9 105.0 16 324s 17 1 87.7 110.5 17 324s 18 1 101.1 92.5 18 324s 19 1 106.1 89.3 19 324s 20 1 114.4 93.0 20 324s > 324s > 324s > ## **************** formulas ************************ 324s > formula( fit3sls[[ 2 ]]$e1c ) 324s $demand 324s consump ~ price + income 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s 324s > formula( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]] ) 324s consump ~ price + income 324s > 324s > formula( fit3sls[[ 3 ]]$e2e ) 324s $demand 324s consump ~ price + income 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s 324s > formula( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]] ) 324s consump ~ price + farmPrice + trend 324s > 324s > formula( fit3sls[[ 4 ]]$e3 ) 324s $demand 324s consump ~ price + income 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s 324s > formula( fit3sls[[ 4 ]]$e3$eq[[ 1 ]] ) 324s consump ~ price + income 324s > 324s > formula( fit3sls[[ 5 ]]$e4e ) 324s $demand 324s consump ~ price + income 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s 324s > formula( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]] ) 324s consump ~ price + farmPrice + trend 324s > 324s > formula( fit3sls[[ 1 ]]$e5 ) 324s $demand 324s consump ~ price + income 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s 324s > formula( fit3sls[[ 1 ]]$e5$eq[[ 1 ]] ) 324s consump ~ price + income 324s > 324s > formula( fit3slsi[[ 3 ]]$e3e ) 324s $demand 324s consump ~ price + income 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s 324s > formula( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]] ) 324s consump ~ price + income 324s > 324s > formula( fit3slsd[[ 4 ]]$e4 ) 324s $demand 324s consump ~ price + income 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s 324s > formula( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]] ) 324s consump ~ price + farmPrice + trend 324s > 324s > formula( fit3slsd[[ 2 ]]$e1w ) 324s $demand 324s consump ~ price + income 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s 324s > formula( fit3slsd[[ 2 ]]$e1w$eq[[ 1 ]] ) 324s consump ~ price + income 324s > 324s > 324s > ## **************** model terms ******************* 324s > terms( fit3sls[[ 2 ]]$e1c ) 324s $demand 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s 324s > terms( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]] ) 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s > 324s > terms( fit3sls[[ 3 ]]$e2e ) 324s $demand 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s 324s > terms( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]] ) 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s > 324s > terms( fit3sls[[ 4 ]]$e3 ) 324s $demand 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s 324s > terms( fit3sls[[ 4 ]]$e3$eq[[ 1 ]] ) 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s > 324s > terms( fit3sls[[ 5 ]]$e4e ) 324s $demand 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s 324s > terms( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]] ) 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s > 324s > terms( fit3sls[[ 1 ]]$e5 ) 324s $demand 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s 324s > terms( fit3sls[[ 1 ]]$e5$eq[[ 1 ]] ) 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s > 324s > terms( fit3sls[[ 2 ]]$e4wSym ) 324s $demand 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s 324s > terms( fit3sls[[ 2 ]]$e4wSym$eq[[ 1 ]] ) 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s > 324s > terms( fit3slsi[[ 3 ]]$e3e ) 324s $demand 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s 324s > terms( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]] ) 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s > 324s > terms( fit3slsd[[ 4 ]]$e4 ) 324s $demand 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s 324s > terms( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]] ) 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s > 324s > terms( fit3slsd[[ 5 ]]$e5we ) 324s $demand 324s consump ~ price + income 324s attr(,"variables") 324s list(consump, price, income) 324s attr(,"factors") 324s price income 324s consump 0 0 324s price 1 0 324s income 0 1 324s attr(,"term.labels") 324s [1] "price" "income" 324s attr(,"order") 324s [1] 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, income) 324s attr(,"dataClasses") 324s consump price income 324s "numeric" "numeric" "numeric" 324s 324s $supply 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s 324s > terms( fit3slsd[[ 5 ]]$e5we$eq[[ 2 ]] ) 324s consump ~ price + farmPrice + trend 324s attr(,"variables") 324s list(consump, price, farmPrice, trend) 324s attr(,"factors") 324s price farmPrice trend 324s consump 0 0 0 324s price 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "price" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 1 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(consump, price, farmPrice, trend) 324s attr(,"dataClasses") 324s consump price farmPrice trend 324s "numeric" "numeric" "numeric" "numeric" 324s > 324s > 324s > ## **************** terms of instruments ******************* 324s > fit3sls[[ 2 ]]$e1c$eq[[ 1 ]]$termsInst 324s ~income + farmPrice + trend 324s attr(,"variables") 324s list(income, farmPrice, trend) 324s attr(,"factors") 324s income farmPrice trend 324s income 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "income" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 0 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(income, farmPrice, trend) 324s attr(,"dataClasses") 324s income farmPrice trend 324s "numeric" "numeric" "numeric" 324s > 324s > fit3sls[[ 3 ]]$e2e$eq[[ 2 ]]$termsInst 324s ~income + farmPrice + trend 324s attr(,"variables") 324s list(income, farmPrice, trend) 324s attr(,"factors") 324s income farmPrice trend 324s income 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "income" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 0 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(income, farmPrice, trend) 324s attr(,"dataClasses") 324s income farmPrice trend 324s "numeric" "numeric" "numeric" 324s > 324s > fit3sls[[ 4 ]]$e3$eq[[ 1 ]]$termsInst 324s ~income + farmPrice + trend 324s attr(,"variables") 324s list(income, farmPrice, trend) 324s attr(,"factors") 324s income farmPrice trend 324s income 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "income" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 0 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(income, farmPrice, trend) 324s attr(,"dataClasses") 324s income farmPrice trend 324s "numeric" "numeric" "numeric" 324s > 324s > fit3sls[[ 5 ]]$e4e$eq[[ 2 ]]$termsInst 324s ~income + farmPrice + trend 324s attr(,"variables") 324s list(income, farmPrice, trend) 324s attr(,"factors") 324s income farmPrice trend 324s income 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "income" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 0 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(income, farmPrice, trend) 324s attr(,"dataClasses") 324s income farmPrice trend 324s "numeric" "numeric" "numeric" 324s > 324s > fit3sls[[ 1 ]]$e5$eq[[ 1 ]]$termsInst 324s ~income + farmPrice + trend 324s attr(,"variables") 324s list(income, farmPrice, trend) 324s attr(,"factors") 324s income farmPrice trend 324s income 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "income" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 0 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(income, farmPrice, trend) 324s attr(,"dataClasses") 324s income farmPrice trend 324s "numeric" "numeric" "numeric" 324s > 324s > fit3sls[[ 2 ]]$e4wSym$eq[[ 1 ]]$termsInst 324s ~income + farmPrice + trend 324s attr(,"variables") 324s list(income, farmPrice, trend) 324s attr(,"factors") 324s income farmPrice trend 324s income 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "income" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 0 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(income, farmPrice, trend) 324s attr(,"dataClasses") 324s income farmPrice trend 324s "numeric" "numeric" "numeric" 324s > 324s > fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]]$termsInst 324s ~income + farmPrice + trend 324s attr(,"variables") 324s list(income, farmPrice, trend) 324s attr(,"factors") 324s income farmPrice trend 324s income 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "income" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 0 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(income, farmPrice, trend) 324s attr(,"dataClasses") 324s income farmPrice trend 324s "numeric" "numeric" "numeric" 324s > 324s > fit3slsd[[ 4 ]]$e4$eq[[ 2 ]]$termsInst 324s ~income + farmPrice + trend 324s attr(,"variables") 324s list(income, farmPrice, trend) 324s attr(,"factors") 324s income farmPrice trend 324s income 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "income" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 0 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(income, farmPrice, trend) 324s attr(,"dataClasses") 324s income farmPrice trend 324s "numeric" "numeric" "numeric" 324s > 324s > fit3slsd[[ 5 ]]$e5we$eq[[ 2 ]]$termsInst 324s ~income + farmPrice + trend 324s attr(,"variables") 324s list(income, farmPrice, trend) 324s attr(,"factors") 324s income farmPrice trend 324s income 1 0 0 324s farmPrice 0 1 0 324s trend 0 0 1 324s attr(,"term.labels") 324s [1] "income" "farmPrice" "trend" 324s attr(,"order") 324s [1] 1 1 1 324s attr(,"intercept") 324s [1] 1 324s attr(,"response") 324s [1] 0 324s attr(,".Environment") 324s 324s attr(,"predvars") 324s list(income, farmPrice, trend) 324s attr(,"dataClasses") 324s income farmPrice trend 324s "numeric" "numeric" "numeric" 324s > 324s > 324s > ## **************** estfun ************************ 324s > library( "sandwich" ) 324s > 324s > estfun( fit3sls[[ 1 ]]$e1 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s demand_1 0.93243 92.895 81.494 -0.67273 324s demand_2 -0.67769 -71.238 -66.143 0.48894 324s demand_3 3.38220 351.019 327.058 -2.44019 324s demand_4 2.06995 216.373 203.269 -1.49343 324s demand_5 3.17940 313.652 317.304 -2.29388 324s demand_6 1.83161 182.517 184.077 -1.32147 324s demand_7 2.47947 252.837 255.881 -1.78889 324s demand_8 -5.09517 -520.901 -549.259 3.67607 324s demand_9 -2.17668 -205.928 -210.267 1.57043 324s demand_10 3.95122 366.354 351.263 -2.85073 324s demand_11 -0.37870 -34.993 -28.440 0.27322 324s demand_12 -3.13231 -309.838 -240.875 2.25990 324s demand_13 -2.46263 -251.590 -208.339 1.77674 324s demand_14 0.13711 13.748 12.422 -0.09892 324s demand_15 3.55301 346.849 366.315 -2.56343 324s demand_16 -5.27287 -510.898 -554.179 3.80428 324s demand_17 -0.02852 -2.502 -2.750 0.02058 324s demand_18 -3.97374 -401.582 -414.859 2.86698 324s demand_19 2.30169 244.124 254.797 -1.66062 324s demand_20 -0.61976 -70.898 -78.771 0.44714 324s supply_1 -0.79213 -78.918 -69.232 0.70287 324s supply_2 0.37122 39.022 36.231 -0.32939 324s supply_3 -2.54401 -264.028 -246.006 2.25734 324s supply_4 -1.58295 -165.467 -155.446 1.40458 324s supply_5 -2.40285 -237.044 -239.804 2.13208 324s supply_6 -1.41153 -140.656 -141.858 1.25247 324s supply_7 -1.86174 -189.846 -192.132 1.65195 324s supply_8 3.60208 368.256 388.304 -3.19618 324s supply_9 1.52187 143.979 147.013 -1.35038 324s supply_10 -2.85966 -265.145 -254.224 2.53741 324s supply_11 0.33741 31.177 25.339 -0.29938 324s supply_12 2.36613 234.051 181.956 -2.09950 324s supply_13 1.88385 192.460 159.374 -1.67157 324s supply_14 -0.00962 -0.965 -0.872 0.00854 324s supply_15 -2.52306 -246.304 -260.128 2.23875 324s supply_16 3.84942 372.977 404.574 -3.41564 324s supply_17 0.07279 6.384 7.017 -0.06459 324s supply_18 2.96969 300.114 310.035 -2.63504 324s supply_19 -1.54232 -163.584 -170.735 1.36853 324s supply_20 0.55542 63.538 70.594 -0.49283 324s supply_price supply_farmPrice supply_trend 324s demand_1 -67.022 -65.927 -0.673 324s demand_2 51.397 48.454 0.978 324s demand_3 -253.253 -241.823 -7.321 324s demand_4 -156.109 -146.505 -5.974 324s demand_5 -226.294 -254.162 -11.469 324s demand_6 -131.682 -142.983 -7.929 324s demand_7 -182.417 -188.907 -12.522 324s demand_8 375.820 403.632 29.409 324s demand_9 148.573 170.706 14.134 324s demand_10 -264.317 -286.783 -28.507 324s demand_11 25.247 22.131 3.005 324s demand_12 223.542 155.029 27.119 324s demand_13 181.517 125.971 23.098 324s demand_14 -9.919 -8.052 -1.385 324s demand_15 -250.245 -262.238 -38.451 324s demand_16 368.603 399.449 60.868 324s demand_17 1.805 2.274 0.350 324s demand_18 289.734 265.195 51.606 324s demand_19 -176.131 -148.294 -31.552 324s demand_20 51.151 41.584 8.943 324s supply_1 70.025 68.881 0.703 324s supply_2 -34.625 -32.642 -0.659 324s supply_3 234.276 223.702 6.772 324s supply_4 146.821 137.789 5.618 324s supply_5 210.332 236.235 10.660 324s supply_6 124.806 135.517 7.515 324s supply_7 168.453 174.446 11.564 324s supply_8 -326.759 -350.940 -25.569 324s supply_9 -127.755 -146.786 -12.153 324s supply_10 235.267 255.264 25.374 324s supply_11 -27.664 -24.250 -3.293 324s supply_12 -207.676 -144.026 -25.194 324s supply_13 -170.773 -118.514 -21.730 324s supply_14 0.856 0.695 0.120 324s supply_15 218.549 229.024 33.581 324s supply_16 -330.948 -358.642 -54.650 324s supply_17 -5.665 -7.137 -1.098 324s supply_18 -266.295 -243.742 -47.431 324s supply_19 145.150 122.209 26.002 324s supply_20 -56.378 -45.834 -9.857 324s > round( colSums( estfun( fit3sls[[ 1 ]]$e1 ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > estfun( fit3sls[[ 2 ]]$e1e ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s demand_1 1.0970 109.29 95.88 -0.8158 324s demand_2 -0.7973 -83.81 -77.82 0.5929 324s demand_3 3.9791 412.96 384.77 -2.9592 324s demand_4 2.4352 254.56 239.14 -1.8110 324s demand_5 3.7405 369.00 373.30 -2.7817 324s demand_6 2.1548 214.73 216.56 -1.6025 324s demand_7 2.9170 297.45 301.04 -2.1693 324s demand_8 -5.9943 -612.82 -646.19 4.4579 324s demand_9 -2.5608 -242.27 -247.37 1.9044 324s demand_10 4.6485 431.00 413.25 -3.4570 324s demand_11 -0.4455 -41.17 -33.46 0.3313 324s demand_12 -3.6851 -364.52 -283.38 2.7405 324s demand_13 -2.8972 -295.99 -245.10 2.1546 324s demand_14 0.1613 16.17 14.61 -0.1200 324s demand_15 4.1800 408.06 430.96 -3.1086 324s demand_16 -6.2034 -601.06 -651.98 4.6134 324s demand_17 -0.0336 -2.94 -3.24 0.0250 324s demand_18 -4.6750 -472.45 -488.07 3.4767 324s demand_19 2.7079 287.21 299.76 -2.0138 324s demand_20 -0.7291 -83.41 -92.67 0.5422 324s supply_1 -0.9222 -91.88 -80.60 0.8435 324s supply_2 0.4880 51.30 47.63 -0.4463 324s supply_3 -3.0517 -316.72 -295.10 2.7912 324s supply_4 -1.8908 -197.65 -185.68 1.7294 324s supply_5 -2.8789 -284.00 -287.31 2.6331 324s supply_6 -1.6828 -167.69 -169.12 1.5391 324s supply_7 -2.2343 -227.83 -230.58 2.0435 324s supply_8 4.3919 449.01 473.45 -4.0170 324s supply_9 1.8611 176.08 179.79 -1.7022 324s supply_10 -3.4650 -321.27 -308.04 3.1691 324s supply_11 0.3885 35.90 29.18 -0.3554 324s supply_12 2.8352 280.45 218.03 -2.5932 324s supply_13 2.2501 229.88 190.36 -2.0580 324s supply_14 -0.0404 -4.05 -3.66 0.0369 324s supply_15 -3.0726 -299.95 -316.79 2.8103 324s supply_16 4.6536 450.90 489.09 -4.2563 324s supply_17 0.0715 6.27 6.89 -0.0654 324s supply_18 3.5683 360.61 372.53 -3.2636 324s supply_19 -1.9084 -202.41 -211.25 1.7454 324s supply_20 0.6388 73.07 81.19 -0.5842 324s supply_price supply_farmPrice supply_trend 324s demand_1 -81.28 -79.95 -0.816 324s demand_2 62.33 58.76 1.186 324s demand_3 -307.11 -293.25 -8.877 324s demand_4 -189.31 -177.66 -7.244 324s demand_5 -274.42 -308.22 -13.909 324s demand_6 -159.69 -173.39 -9.615 324s demand_7 -221.21 -229.08 -15.185 324s demand_8 455.75 489.48 35.663 324s demand_9 180.17 207.01 17.140 324s demand_10 -320.53 -347.78 -34.570 324s demand_11 30.62 26.84 3.645 324s demand_12 271.08 188.00 32.886 324s demand_13 220.12 152.76 28.010 324s demand_14 -12.03 -9.76 -1.679 324s demand_15 -303.47 -318.01 -46.629 324s demand_16 447.00 484.40 73.814 324s demand_17 2.19 2.76 0.424 324s demand_18 351.35 321.60 62.581 324s demand_19 -213.59 -179.83 -38.262 324s demand_20 62.03 50.43 10.845 324s supply_1 84.04 82.66 0.843 324s supply_2 -46.92 -44.23 -0.893 324s supply_3 289.68 276.60 8.373 324s supply_4 180.78 169.66 6.918 324s supply_5 259.76 291.74 13.165 324s supply_6 153.37 166.53 9.235 324s supply_7 208.38 215.80 14.305 324s supply_8 -410.67 -441.06 -32.136 324s supply_9 -161.04 -185.03 -15.320 324s supply_10 293.84 318.82 31.691 324s supply_11 -32.84 -28.78 -3.909 324s supply_12 -256.51 -177.89 -31.118 324s supply_13 -210.25 -145.91 -26.754 324s supply_14 3.70 3.00 0.517 324s supply_15 274.34 287.49 42.154 324s supply_16 -412.40 -446.91 -68.101 324s supply_17 -5.73 -7.23 -1.112 324s supply_18 -329.82 -301.88 -58.745 324s supply_19 185.13 155.87 33.163 324s supply_20 -66.83 -54.33 -11.684 324s > round( colSums( estfun( fit3sls[[ 2 ]]$e1e ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > estfun( fit3sls[[ 3 ]]$e1c ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s demand_1 1.3280 132.31 116.07 -0.9904 324s demand_2 -0.9652 -101.46 -94.20 0.7198 324s demand_3 4.8171 499.94 465.81 -3.5924 324s demand_4 2.9481 308.17 289.50 -2.1986 324s demand_5 4.5282 446.72 451.92 -3.3770 324s demand_6 2.6087 259.95 262.17 -1.9455 324s demand_7 3.5314 360.10 364.44 -2.6336 324s demand_8 -7.2568 -741.89 -782.28 5.4119 324s demand_9 -3.1001 -293.29 -299.47 2.3120 324s demand_10 5.6275 521.78 500.28 -4.1968 324s demand_11 -0.5394 -49.84 -40.51 0.4022 324s demand_12 -4.4612 -441.28 -343.06 3.3270 324s demand_13 -3.5074 -358.33 -296.72 2.6157 324s demand_14 0.1953 19.58 17.69 -0.1456 324s demand_15 5.0603 494.00 521.72 -3.7739 324s demand_16 -7.5098 -727.64 -789.29 5.6006 324s demand_17 -0.0406 -3.56 -3.92 0.0303 324s demand_18 -5.6596 -571.95 -590.86 4.2207 324s demand_19 3.2782 347.69 362.89 -2.4448 324s demand_20 -0.8827 -100.98 -112.19 0.6583 324s supply_1 -1.2187 -121.42 -106.51 1.0461 324s supply_2 0.4947 52.00 48.29 -0.4247 324s supply_3 -3.7909 -393.44 -366.58 3.2542 324s supply_4 -2.3698 -247.71 -232.71 2.0343 324s supply_5 -3.5854 -353.70 -357.82 3.0777 324s supply_6 -2.1176 -211.02 -212.82 1.8178 324s supply_7 -2.7729 -282.76 -286.16 2.3803 324s supply_8 5.2704 538.82 568.15 -4.5242 324s supply_9 2.2191 209.94 214.37 -1.9049 324s supply_10 -4.2139 -390.71 -374.62 3.6173 324s supply_11 0.5250 48.51 39.42 -0.4506 324s supply_12 3.5301 349.19 271.47 -3.0303 324s supply_13 2.8205 288.15 238.61 -2.4212 324s supply_14 0.0251 2.52 2.28 -0.0216 324s supply_15 -3.6967 -360.87 -381.13 3.1733 324s supply_16 5.6869 551.02 597.70 -4.8817 324s supply_17 0.1301 11.41 12.54 -0.1117 324s supply_18 4.4171 446.39 461.15 -3.7917 324s supply_19 -2.2186 -235.31 -245.60 1.9044 324s supply_20 0.8653 98.99 109.98 -0.7428 324s supply_price supply_farmPrice supply_trend 324s demand_1 -98.67 -97.06 -0.990 324s demand_2 75.67 71.33 1.440 324s demand_3 -372.84 -356.01 -10.777 324s demand_4 -229.82 -215.68 -8.794 324s demand_5 -333.15 -374.17 -16.885 324s demand_6 -193.86 -210.50 -11.673 324s demand_7 -268.55 -278.11 -18.435 324s demand_8 553.28 594.22 43.295 324s demand_9 218.73 251.31 20.808 324s demand_10 -389.13 -422.20 -41.968 324s demand_11 37.17 32.58 4.425 324s demand_12 329.10 228.23 39.924 324s demand_13 267.23 185.45 34.004 324s demand_14 -14.60 -11.85 -2.039 324s demand_15 -368.41 -386.07 -56.608 324s demand_16 542.65 588.07 89.610 324s demand_17 2.66 3.35 0.515 324s demand_18 426.54 390.42 75.973 324s demand_19 -259.30 -218.32 -46.450 324s demand_20 75.30 61.22 13.166 324s supply_1 104.22 102.52 1.046 324s supply_2 -44.64 -42.09 -0.849 324s supply_3 337.73 322.49 9.763 324s supply_4 212.64 199.56 8.137 324s supply_5 303.62 341.01 15.389 324s supply_6 181.14 196.69 10.907 324s supply_7 242.72 251.36 16.662 324s supply_8 -462.53 -496.76 -36.194 324s supply_9 -180.22 -207.07 -17.144 324s supply_10 335.39 363.90 36.173 324s supply_11 -41.64 -36.50 -4.957 324s supply_12 -299.75 -207.88 -36.364 324s supply_13 -247.35 -171.66 -31.475 324s supply_14 -2.16 -1.75 -0.302 324s supply_15 309.78 324.63 47.599 324s supply_16 -473.00 -512.58 -78.108 324s supply_17 -9.80 -12.34 -1.899 324s supply_18 -383.19 -350.73 -68.251 324s supply_19 201.99 170.07 36.184 324s supply_20 -84.97 -69.08 -14.856 324s > round( colSums( estfun( fit3sls[[ 3 ]]$e1c ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > estfun( fit3sls[[ 4 ]]$e1wc ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s demand_1 1.3280 132.31 116.07 -0.9904 324s demand_2 -0.9652 -101.46 -94.20 0.7198 324s demand_3 4.8171 499.94 465.81 -3.5924 324s demand_4 2.9481 308.17 289.50 -2.1986 324s demand_5 4.5282 446.72 451.92 -3.3770 324s demand_6 2.6087 259.95 262.17 -1.9455 324s demand_7 3.5314 360.10 364.44 -2.6336 324s demand_8 -7.2568 -741.89 -782.28 5.4119 324s demand_9 -3.1001 -293.29 -299.47 2.3120 324s demand_10 5.6275 521.78 500.28 -4.1968 324s demand_11 -0.5394 -49.84 -40.51 0.4022 324s demand_12 -4.4612 -441.28 -343.06 3.3270 324s demand_13 -3.5074 -358.33 -296.72 2.6157 324s demand_14 0.1953 19.58 17.69 -0.1456 324s demand_15 5.0603 494.00 521.72 -3.7739 324s demand_16 -7.5098 -727.64 -789.29 5.6006 324s demand_17 -0.0406 -3.56 -3.92 0.0303 324s demand_18 -5.6596 -571.95 -590.86 4.2207 324s demand_19 3.2782 347.69 362.89 -2.4448 324s demand_20 -0.8827 -100.98 -112.19 0.6583 324s supply_1 -1.2187 -121.42 -106.51 1.0461 324s supply_2 0.4947 52.00 48.29 -0.4247 324s supply_3 -3.7909 -393.44 -366.58 3.2542 324s supply_4 -2.3698 -247.71 -232.71 2.0343 324s supply_5 -3.5854 -353.70 -357.82 3.0777 324s supply_6 -2.1176 -211.02 -212.82 1.8178 324s supply_7 -2.7729 -282.76 -286.16 2.3803 324s supply_8 5.2704 538.82 568.15 -4.5242 324s supply_9 2.2191 209.94 214.37 -1.9049 324s supply_10 -4.2139 -390.71 -374.62 3.6173 324s supply_11 0.5250 48.51 39.42 -0.4506 324s supply_12 3.5301 349.19 271.47 -3.0303 324s supply_13 2.8205 288.15 238.61 -2.4212 324s supply_14 0.0251 2.52 2.28 -0.0216 324s supply_15 -3.6967 -360.87 -381.13 3.1733 324s supply_16 5.6869 551.02 597.70 -4.8817 324s supply_17 0.1301 11.41 12.54 -0.1117 324s supply_18 4.4171 446.39 461.15 -3.7917 324s supply_19 -2.2186 -235.31 -245.60 1.9044 324s supply_20 0.8653 98.99 109.98 -0.7428 324s supply_price supply_farmPrice supply_trend 324s demand_1 -98.67 -97.06 -0.990 324s demand_2 75.67 71.33 1.440 324s demand_3 -372.84 -356.01 -10.777 324s demand_4 -229.82 -215.68 -8.794 324s demand_5 -333.15 -374.17 -16.885 324s demand_6 -193.86 -210.50 -11.673 324s demand_7 -268.55 -278.11 -18.435 324s demand_8 553.28 594.22 43.295 324s demand_9 218.73 251.31 20.808 324s demand_10 -389.13 -422.20 -41.968 324s demand_11 37.17 32.58 4.425 324s demand_12 329.10 228.23 39.924 324s demand_13 267.23 185.45 34.004 324s demand_14 -14.60 -11.85 -2.039 324s demand_15 -368.41 -386.07 -56.608 324s demand_16 542.65 588.07 89.610 324s demand_17 2.66 3.35 0.515 324s demand_18 426.54 390.42 75.973 324s demand_19 -259.30 -218.32 -46.450 324s demand_20 75.30 61.22 13.166 324s supply_1 104.22 102.52 1.046 324s supply_2 -44.64 -42.09 -0.849 324s supply_3 337.73 322.49 9.763 324s supply_4 212.64 199.56 8.137 324s supply_5 303.62 341.01 15.389 324s supply_6 181.14 196.69 10.907 324s supply_7 242.72 251.36 16.662 324s supply_8 -462.53 -496.76 -36.194 324s supply_9 -180.22 -207.07 -17.144 324s supply_10 335.39 363.90 36.173 324s supply_11 -41.64 -36.50 -4.957 324s supply_12 -299.75 -207.88 -36.364 324s supply_13 -247.35 -171.66 -31.475 324s supply_14 -2.16 -1.75 -0.302 324s supply_15 309.78 324.63 47.599 324s supply_16 -473.00 -512.58 -78.108 324s supply_17 -9.80 -12.34 -1.899 324s supply_18 -383.19 -350.73 -68.251 324s supply_19 201.99 170.07 36.184 324s supply_20 -84.97 -69.08 -14.856 324s > 324s > round( colSums( estfun( fit3sls[[ 5 ]]$e1wc ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > round( colSums( estfun( fit3sls[[ 5 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > round( colSums( estfun( fit3sls[[ 4 ]]$e1wc ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > round( colSums( estfun( fit3sls[[ 4 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > round( colSums( estfun( fit3sls[[ 3 ]]$e1wc ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > round( colSums( estfun( fit3sls[[ 3 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > round( colSums( estfun( fit3sls[[ 2 ]]$e1wc ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > round( colSums( estfun( fit3sls[[ 2 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > round( colSums( estfun( fit3sls[[ 1 ]]$e1wc ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > round( colSums( estfun( fit3sls[[ 1 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > estfun( fit3slsd[[ 5 ]]$e1w ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s demand_1 -0.471 -44.9 -41.2 0.299 324s demand_2 -1.315 -130.6 -128.3 0.835 324s demand_3 0.736 72.8 71.2 -0.467 324s demand_4 0.203 20.3 19.9 -0.129 324s demand_5 0.825 80.0 82.4 -0.524 324s demand_6 0.290 28.4 29.1 -0.184 324s demand_7 0.657 65.6 67.8 -0.417 324s demand_8 -2.887 -290.8 -311.2 1.833 324s demand_9 -1.172 -112.7 -113.2 0.744 324s demand_10 1.981 188.4 176.1 -1.258 324s demand_11 0.308 29.2 23.1 -0.196 324s demand_12 -0.922 -91.4 -70.9 0.586 324s demand_13 -0.639 -65.0 -54.1 0.406 324s demand_14 0.597 60.5 54.0 -0.379 324s demand_15 2.100 211.7 216.5 -1.333 324s demand_16 -1.984 -200.3 -208.6 1.260 324s demand_17 0.785 75.0 75.7 -0.499 324s demand_18 -1.136 -118.3 -118.6 0.721 324s demand_19 1.814 195.6 200.8 -1.152 324s demand_20 0.232 26.4 29.5 -0.147 324s supply_1 -0.434 -41.3 -37.9 0.449 324s supply_2 -0.126 -12.6 -12.3 0.131 324s supply_3 -1.272 -125.8 -123.0 1.316 324s supply_4 -0.902 -90.1 -88.6 0.933 324s supply_5 -0.805 -78.1 -80.4 0.833 324s supply_6 -0.457 -44.8 -46.0 0.473 324s supply_7 -0.758 -75.8 -78.3 0.784 324s supply_8 1.582 159.3 170.5 -1.636 324s supply_9 1.004 96.6 97.0 -1.039 324s supply_10 -0.856 -81.5 -76.1 0.886 324s supply_11 0.191 18.1 14.3 -0.197 324s supply_12 0.607 60.1 46.7 -0.628 324s supply_13 0.335 34.0 28.3 -0.346 324s supply_14 -0.201 -20.3 -18.2 0.208 324s supply_15 -0.801 -80.8 -82.6 0.829 324s supply_16 1.930 194.8 202.9 -1.997 324s supply_17 0.811 77.5 78.2 -0.839 324s supply_18 1.241 129.3 129.5 -1.283 324s supply_19 -0.858 -92.5 -95.0 0.888 324s supply_20 -0.229 -26.1 -29.1 0.237 324s supply_price supply_farmPrice supply_trend 324s demand_1 29.8 29.3 0.299 324s demand_2 87.8 82.7 1.670 324s demand_3 -48.5 -46.3 -1.402 324s demand_4 -13.5 -12.7 -0.516 324s demand_5 -51.7 -58.1 -2.620 324s demand_6 -18.3 -19.9 -1.105 324s demand_7 -42.5 -44.0 -2.919 324s demand_8 187.4 201.3 14.667 324s demand_9 70.4 80.9 6.698 324s demand_10 -116.6 -126.5 -12.579 324s demand_11 -18.1 -15.8 -2.152 324s demand_12 57.9 40.2 7.029 324s demand_13 41.5 28.8 5.278 324s demand_14 -38.0 -30.8 -5.304 324s demand_15 -130.2 -136.4 -20.000 324s demand_16 122.1 132.3 20.164 324s demand_17 -43.7 -55.1 -8.477 324s demand_18 72.9 66.7 12.986 324s demand_19 -122.2 -102.9 -21.890 324s demand_20 -16.9 -13.7 -2.947 324s supply_1 44.7 44.0 0.449 324s supply_2 13.7 13.0 0.262 324s supply_3 136.5 130.4 3.947 324s supply_4 97.5 91.5 3.731 324s supply_5 82.2 92.3 4.165 324s supply_6 47.1 51.2 2.839 324s supply_7 80.0 82.8 5.491 324s supply_8 -167.3 -179.7 -13.089 324s supply_9 -98.3 -112.9 -9.349 324s supply_10 82.1 89.1 8.857 324s supply_11 -18.2 -16.0 -2.169 324s supply_12 -62.1 -43.1 -7.532 324s supply_13 -35.4 -24.5 -4.499 324s supply_14 20.8 16.9 2.907 324s supply_15 80.9 84.8 12.430 324s supply_16 -193.5 -209.7 -31.948 324s supply_17 -73.6 -92.7 -14.264 324s supply_18 -129.7 -118.7 -23.101 324s supply_19 94.1 79.3 16.863 324s supply_20 27.1 22.1 4.744 324s Warning message: 324s In estfun.systemfit(fit3slsd[[5]]$e1w) : 324s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 324s > estfun( fit3slsd[[ 5 ]]$e1w, residFit = FALSE ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s demand_1 0.89947 85.649 78.613 -0.57123 324s demand_2 0.00817 0.811 0.797 -0.00519 324s demand_3 1.94109 192.071 187.703 -1.23275 324s demand_4 1.44439 144.277 141.839 -0.91731 324s demand_5 1.10477 107.119 110.256 -0.70162 324s demand_6 0.67950 66.596 68.290 -0.43154 324s demand_7 0.96428 96.352 99.513 -0.61239 324s demand_8 -1.80100 -181.402 -194.148 1.14378 324s demand_9 -1.09741 -105.536 -106.009 0.69694 324s demand_10 0.93145 88.611 82.806 -0.59155 324s demand_11 -0.13250 -12.551 -9.951 0.08415 324s demand_12 -0.98743 -97.798 -75.933 0.62710 324s demand_13 -0.32371 -32.932 -27.386 0.20558 324s demand_14 -0.09978 -10.112 -9.040 0.06337 324s demand_15 0.56754 57.219 58.513 -0.36043 324s demand_16 -2.64753 -267.185 -278.255 1.68140 324s demand_17 -1.65258 -157.934 -159.308 1.04952 324s demand_18 -1.17988 -122.919 -123.179 0.74932 324s demand_19 1.26015 135.883 139.499 -0.80030 324s demand_20 0.12101 13.783 15.380 -0.07685 324s supply_1 -0.39424 -37.540 -34.456 0.40779 324s supply_2 -0.17503 -17.388 -17.083 0.18104 324s supply_3 -1.29167 -127.811 -124.905 1.33607 324s supply_4 -0.90312 -90.210 -88.686 0.93416 324s supply_5 -0.84242 -81.682 -84.074 0.87137 324s supply_6 -0.46834 -45.901 -47.069 0.48444 324s supply_7 -0.80988 -80.925 -83.580 0.83772 324s supply_8 1.72577 173.825 186.038 -1.78508 324s supply_9 1.10899 106.650 107.128 -1.14710 324s supply_10 -0.94120 -89.538 -83.673 0.97355 324s supply_11 0.22943 21.733 17.231 -0.23732 324s supply_12 0.60019 59.445 46.155 -0.62082 324s supply_13 0.37695 38.348 31.890 -0.38990 324s supply_14 -0.28729 -29.116 -26.029 0.29717 324s supply_15 -0.94355 -95.128 -97.280 0.97597 324s supply_16 2.01917 203.771 212.215 -2.08856 324s supply_17 0.74286 70.994 71.612 -0.76839 324s supply_18 1.40908 146.797 147.108 -1.45750 324s supply_19 -0.87479 -94.329 -96.840 0.90486 324s supply_20 -0.28090 -31.995 -35.702 0.29055 324s supply_price supply_farmPrice supply_trend 324s demand_1 -56.911 -55.981 -0.5712 324s demand_2 -0.545 -0.514 -0.0104 324s demand_3 -127.940 -122.166 -3.6983 324s demand_4 -95.886 -89.988 -3.6692 324s demand_5 -69.215 -77.739 -3.5081 324s demand_6 -43.002 -46.692 -2.5892 324s demand_7 -62.447 -64.669 -4.2868 324s demand_8 116.934 125.587 9.1502 324s demand_9 65.935 75.758 6.2725 324s demand_10 -54.848 -59.510 -5.9155 324s demand_11 7.776 6.816 0.9257 324s demand_12 62.030 43.019 7.5252 324s demand_13 21.003 14.576 2.6726 324s demand_14 6.354 5.158 0.8871 324s demand_15 -35.186 -36.872 -5.4065 324s demand_16 162.914 176.547 26.9023 324s demand_17 92.041 115.972 17.8418 324s demand_18 75.726 69.312 13.4878 324s demand_19 -84.882 -71.467 -15.2057 324s demand_20 -8.791 -7.147 -1.5370 324s supply_1 40.627 39.963 0.4078 324s supply_2 19.031 17.941 0.3621 324s supply_3 138.662 132.404 4.0082 324s supply_4 97.648 91.641 3.7366 324s supply_5 85.962 96.548 4.3569 324s supply_6 48.274 52.416 2.9066 324s supply_7 85.424 88.463 5.8640 324s supply_8 -182.496 -196.002 -14.2806 324s supply_9 -108.523 -124.690 -10.3239 324s supply_10 90.266 97.939 9.7355 324s supply_11 -21.929 -19.223 -2.6105 324s supply_12 -61.410 -42.588 -7.4498 324s supply_13 -39.834 -27.644 -5.0687 324s supply_14 29.799 24.189 4.1603 324s supply_15 95.276 99.842 14.6396 324s supply_16 -202.365 -219.299 -33.4170 324s supply_17 -67.387 -84.908 -13.0627 324s supply_18 -147.294 -134.819 -26.2351 324s supply_19 95.972 80.804 17.1923 324s supply_20 33.238 27.021 5.8111 324s > 324s > round( colSums( estfun( fit3slsd[[ 5 ]]$e1w ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0.0 0.0 0.0 0.0 324s supply_price supply_farmPrice supply_trend 324s 38.6 0.0 -52.4 324s Warning message: 324s In estfun.systemfit(fit3slsd[[5]]$e1w) : 324s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 324s > round( colSums( estfun( fit3slsd[[ 5 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > round( colSums( estfun( fit3slsd[[ 4 ]]$e1w ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0.00 0.00 0.00 0.00 324s supply_price supply_farmPrice supply_trend 324s 9.67 0.00 -13.12 324s > round( colSums( estfun( fit3slsd[[ 4 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 324s Warning message: 324s In estfun.systemfit(fit3slsd[[4]]$e1w) : 324s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 324s Warning message: 324s In estfun.systemfit(fit3slsd[[4]]$e1w, residFit = FALSE) : 324s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 324s Warning message: 324s In estfun.systemfit(fit3slsd[[3]]$e1w) : 324s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0.0 0.0 0.0 0.0 324s supply_price supply_farmPrice supply_trend 324s -28.9 0.0 39.3 324s > 324s > round( colSums( estfun( fit3slsd[[ 3 ]]$e1w ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0.00 0.00 0.00 0.00 324s supply_price supply_farmPrice supply_trend 324s 9.67 0.00 -13.12 324s > round( colSums( estfun( fit3slsd[[ 3 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0.0 0.0 0.0 0.0 324s supply_price supply_farmPrice supply_trend 324s -28.9 0.0 39.3 324s > 324s > round( colSums( estfun( fit3slsd[[ 2 ]]$e1w ) ), digits = 7 ) 324s Warning message: 324s In estfun.systemfit(fit3slsd[[3]]$e1w, residFit = FALSE) : 324s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0.0 0.0 0.0 0.0 324s supply_price supply_farmPrice supply_trend 324s 38.6 0.0 -52.4 324s Warning message: 324s In estfun.systemfit(fit3slsd[[2]]$e1w) : 324s > round( colSums( estfun( fit3slsd[[ 2 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 324s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > 324s > round( colSums( estfun( fit3slsd[[ 1 ]]$e1w ) ), digits = 7 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0 0 0 0 324s supply_price supply_farmPrice supply_trend 324s 0 0 0 324s > round( colSums( estfun( fit3slsd[[ 1 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 324s Warning message: 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s 0.0 0.0 0.0 0.0 324s supply_price supply_farmPrice supply_trend 324s -38.6 0.0 52.4 324s In estfun.systemfit(fit3slsd[[1]]$e1w, residFit = FALSE) : 324s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 324s > 324s > 324s > ## **************** bread ************************ 324s > bread( fit3sls[[ 1 ]]$e1 ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s [1,] 2509.59 -26.9369 1.9721 2525.8 324s [2,] -26.94 0.3724 -0.1057 -14.1 324s [3,] 1.97 -0.1057 0.0881 -11.3 324s [4,] 2525.80 -14.1479 -11.2987 5658.1 324s [5,] -27.01 0.2401 0.0307 -43.3 324s [6,] 1.64 -0.0877 0.0732 -11.8 324s [7,] 2.47 -0.1324 0.1104 -16.4 324s supply_price supply_farmPrice supply_trend 324s [1,] -27.0066 1.6369 2.4699 324s [2,] 0.2401 -0.0877 -0.1324 324s [3,] 0.0307 0.0732 0.1104 324s [4,] -43.3336 -11.7989 -16.3581 324s [5,] 0.3974 0.0325 0.0428 324s [6,] 0.0325 0.0774 0.1019 324s [7,] 0.0428 0.1019 0.2125 324s > 324s > bread( fit3sls[[ 2 ]]$e1e ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s [1,] 2133.15 -22.8963 1.6763 2082.83 324s [2,] -22.90 0.3165 -0.0898 -11.67 324s [3,] 1.68 -0.0898 0.0749 -9.32 324s [4,] 2082.83 -11.6667 -9.3172 4526.47 324s [5,] -22.27 0.1980 0.0253 -34.67 324s [6,] 1.35 -0.0723 0.0603 -9.44 324s [7,] 2.04 -0.1091 0.0910 -13.09 324s supply_price supply_farmPrice supply_trend 324s [1,] -22.2702 1.3498 2.0367 324s [2,] 0.1980 -0.0723 -0.1091 324s [3,] 0.0253 0.0603 0.0910 324s [4,] -34.6668 -9.4391 -13.0865 324s [5,] 0.3179 0.0260 0.0342 324s [6,] 0.0260 0.0619 0.0815 324s [7,] 0.0342 0.0815 0.1700 324s > 324s > bread( fit3sls[[ 3 ]]$e1c ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s [1,] 2509.59 -26.9369 1.9721 2610.8 324s [2,] -26.94 0.3724 -0.1057 -14.6 324s [3,] 1.97 -0.1057 0.0881 -11.7 324s [4,] 2610.83 -14.6243 -11.6791 5650.4 324s [5,] -27.92 0.2482 0.0317 -43.3 324s [6,] 1.69 -0.0907 0.0756 -11.7 324s [7,] 2.55 -0.1368 0.1141 -16.7 324s supply_price supply_farmPrice supply_trend 324s [1,] -27.9159 1.6920 2.5531 324s [2,] 0.2482 -0.0907 -0.1368 324s [3,] 0.0317 0.0756 0.1141 324s [4,] -43.3005 -11.7199 -16.6696 324s [5,] 0.3972 0.0321 0.0441 324s [6,] 0.0321 0.0766 0.1051 324s [7,] 0.0441 0.1051 0.1999 324s > 324s > bread( fit3sls[[ 4 ]]$e1wc ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s [1,] 2509.59 -26.9369 1.9721 2610.8 324s [2,] -26.94 0.3724 -0.1057 -14.6 324s [3,] 1.97 -0.1057 0.0881 -11.7 324s [4,] 2610.83 -14.6243 -11.6791 5650.4 324s [5,] -27.92 0.2482 0.0317 -43.3 324s [6,] 1.69 -0.0907 0.0756 -11.7 324s [7,] 2.55 -0.1368 0.1141 -16.7 324s supply_price supply_farmPrice supply_trend 324s [1,] -27.9159 1.6920 2.5531 324s [2,] 0.2482 -0.0907 -0.1368 324s [3,] 0.0317 0.0756 0.1141 324s [4,] -43.3005 -11.7199 -16.6696 324s [5,] 0.3972 0.0321 0.0441 324s [6,] 0.0321 0.0766 0.1051 324s [7,] 0.0441 0.1051 0.1999 324s > 324s > bread( fit3slsd[[ 5 ]]$e1w ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s [1,] 4967.14 -60.707 11.4076 1773.52 324s [2,] -60.71 0.839 -0.2382 -6.24 324s [3,] 11.41 -0.238 0.1273 -11.71 324s [4,] 1773.52 -6.236 -11.7103 5325.96 324s [5,] -21.83 0.185 0.0346 -37.94 324s [6,] 6.07 -0.141 0.0826 -13.55 324s [7,] -16.09 0.136 0.0255 -20.05 324s supply_price supply_farmPrice supply_trend 324s [1,] -21.8336 6.0740 -16.0922 324s [2,] 0.1845 -0.1413 0.1360 324s [3,] 0.0346 0.0826 0.0255 324s [4,] -37.9350 -13.5483 -20.0519 324s [5,] 0.3216 0.0453 0.1323 324s [6,] 0.0453 0.0885 0.0440 324s [7,] 0.1323 0.0440 0.2443 324s > 324s > bread( fit3slsd[[ 4 ]]$e1w ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s [1,] 4967.14 -60.707 11.4076 1773.52 324s [2,] -60.71 0.839 -0.2382 -6.24 324s [3,] 11.41 -0.238 0.1273 -11.71 324s [4,] 1773.52 -6.236 -11.7103 5325.96 324s [5,] -21.83 0.185 0.0346 -37.94 324s [6,] 6.07 -0.141 0.0826 -13.55 324s [7,] -16.09 0.136 0.0255 -20.05 324s supply_price supply_farmPrice supply_trend 324s [1,] -21.8336 6.0740 -16.0922 324s [2,] 0.1845 -0.1413 0.1360 324s [3,] 0.0346 0.0826 0.0255 324s [4,] -37.9350 -13.5483 -20.0519 324s [5,] 0.3216 0.0453 0.1323 324s [6,] 0.0453 0.0885 0.0440 324s [7,] 0.1323 0.0440 0.2443 324s > 324s > bread( fit3slsd[[ 3 ]]$e1w ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s [1,] 4967.14 -60.707 11.4076 1773.52 324s [2,] -60.71 0.839 -0.2382 -6.24 324s [3,] 11.41 -0.238 0.1273 -11.71 324s [4,] 1773.52 -6.236 -11.7103 5325.96 324s [5,] -21.83 0.185 0.0346 -37.94 324s [6,] 6.07 -0.141 0.0826 -13.55 324s [7,] -16.09 0.136 0.0255 -20.05 324s supply_price supply_farmPrice supply_trend 324s [1,] -21.8336 6.0740 -16.0922 324s [2,] 0.1845 -0.1413 0.1360 324s [3,] 0.0346 0.0826 0.0255 324s [4,] -37.9350 -13.5483 -20.0519 324s [5,] 0.3216 0.0453 0.1323 324s [6,] 0.0453 0.0885 0.0440 324s [7,] 0.1323 0.0440 0.2443 324s > 324s > bread( fit3slsd[[ 2 ]]$e1w ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s [1,] 4967.14 -60.707 11.4076 1773.52 324s [2,] -60.71 0.839 -0.2382 -6.24 324s [3,] 11.41 -0.238 0.1273 -11.71 324s [4,] 1773.52 -6.236 -11.7103 5325.96 324s [5,] -21.83 0.185 0.0346 -37.94 324s [6,] 6.07 -0.141 0.0826 -13.55 324s [7,] -16.09 0.136 0.0255 -20.05 324s supply_price supply_farmPrice supply_trend 324s [1,] -21.8336 6.0740 -16.0922 324s [2,] 0.1845 -0.1413 0.1360 324s [3,] 0.0346 0.0826 0.0255 324s [4,] -37.9350 -13.5483 -20.0519 324s [5,] 0.3216 0.0453 0.1323 324s [6,] 0.0453 0.0885 0.0440 324s [7,] 0.1323 0.0440 0.2443 324s > 324s > bread( fit3slsd[[ 1 ]]$e1w ) 324s demand_(Intercept) demand_price demand_income supply_(Intercept) 324s [1,] 4967.14 -60.707 11.4076 1773.52 324s [2,] -60.71 0.839 -0.2382 -6.24 324s [3,] 11.41 -0.238 0.1273 -11.71 324s [4,] 1773.52 -6.236 -11.7103 5325.96 324s [5,] -21.83 0.185 0.0346 -37.94 324s [6,] 6.07 -0.141 0.0826 -13.55 324s [7,] -16.09 0.136 0.0255 -20.05 324s supply_price supply_farmPrice supply_trend 324s [1,] -21.8336 6.0740 -16.0922 324s [2,] 0.1845 -0.1413 0.1360 324s [3,] 0.0346 0.0826 0.0255 324s [4,] -37.9350 -13.5483 -20.0519 324s [5,] 0.3216 0.0453 0.1323 324s [6,] 0.0453 0.0885 0.0440 324s [7,] 0.1323 0.0440 0.2443 324s > 324s BEGIN TEST test_hausman.R 324s 324s R version 4.3.2 (2023-10-31) -- "Eye Holes" 324s Copyright (C) 2023 The R Foundation for Statistical Computing 324s Platform: x86_64-pc-linux-gnu (64-bit) 324s 324s R is free software and comes with ABSOLUTELY NO WARRANTY. 324s You are welcome to redistribute it under certain conditions. 324s Type 'license()' or 'licence()' for distribution details. 324s 324s R is a collaborative project with many contributors. 324s Type 'contributors()' for more information and 324s 'citation()' on how to cite R or R packages in publications. 324s 324s Type 'demo()' for some demos, 'help()' for on-line help, or 324s 'help.start()' for an HTML browser interface to help. 324s Type 'q()' to quit R. 324s 324s > library( "systemfit" ) 324s Loading required package: Matrix 325s Loading required package: car 325s Loading required package: carData 325s Loading required package: lmtest 325s Loading required package: zoo 325s 325s Attaching package: ‘zoo’ 325s 325s The following objects are masked from ‘package:base’: 325s 325s as.Date, as.Date.numeric 325s 325s 325s Please cite the 'systemfit' package as: 325s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 325s 325s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 325s https://r-forge.r-project.org/projects/systemfit/ 325s > options( digits = 5 ) 325s > 325s > data( "Kmenta" ) 325s > useMatrix <- FALSE 325s > 325s > eqDemand <- consump ~ price + income 325s > eqSupply <- consump ~ price + farmPrice + trend 325s > inst <- ~ income + farmPrice + trend 325s > eqSystem <- list( demand = eqDemand, supply = eqSupply ) 325s > restrm <- matrix(0,1,7) # restriction matrix "R" 325s > restrm[1,3] <- 1 325s > restrm[1,7] <- -1 325s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 325s > restr2m[1,3] <- 1 325s > restr2m[1,7] <- -1 325s > restr2m[2,2] <- -1 325s > restr2m[2,5] <- 1 325s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 325s > tc <- matrix(0,7,6) 325s > tc[1,1] <- 1 325s > tc[2,2] <- 1 325s > tc[3,3] <- 1 325s > tc[4,4] <- 1 325s > tc[5,5] <- 1 325s > tc[6,6] <- 1 325s > tc[7,3] <- 1 325s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 325s > restr3m[1,2] <- -1 325s > restr3m[1,5] <- 1 325s > restr3q <- c( 0.5 ) # restriction vector "q" 2 325s > 325s > 325s > ## ******************* unrestricted estimation ***************** 325s > ## ******************** default estimation ********************* 325s > fit2sls1 <- systemfit( eqSystem, "2SLS", data = Kmenta, inst = inst, 325s + useMatrix = useMatrix ) 325s > fit3sls1 <- systemfit( eqSystem, "3SLS", data = Kmenta, inst = inst, 325s + useMatrix = useMatrix ) 325s > print( hausman.systemfit( fit2sls1, fit3sls1 ) ) 325s 325s Hausman specification test for consistency of the 3SLS estimation 325s 325s data: Kmenta 325s Hausman = 2.54, df = 7, p-value = 0.92 325s 325s > 325s > ## ************** 2SLS estimation with singleEqSigma = FALSE ***************** 325s > fit2sls1s <- systemfit( eqSystem, "2SLS", data = Kmenta, inst = inst, 325s + singleEqSigma = FALSE, useMatrix = useMatrix ) 325s > print( hausman.systemfit( fit2sls1s, fit3sls1 ) ) 325s 325s Hausman specification test for consistency of the 3SLS estimation 325s 325s data: Kmenta 325s Hausman = 3.28, df = 7, p-value = 0.86 325s 325s > 325s > ## ******************* estimations with methodResidCov = 0 ***************** 325s > fit2sls1r <- systemfit( eqSystem, "2SLS", data = Kmenta, inst = inst, 325s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 325s > fit3sls1r <- systemfit( eqSystem, "3SLS", data = Kmenta, inst = inst, 325s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 325s > print( hausman.systemfit( fit2sls1r, fit3sls1r ) ) 325s 325s Hausman specification test for consistency of the 3SLS estimation 325s 325s data: Kmenta 325s Hausman = 2.98, df = 7, p-value = 0.89 325s 325s > 325s > 325s > ## ********************* estimation with restriction ******************** 325s > ## *********************** default estimation *********************** 325s > fit2sls2 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restrm, 325s + inst = inst, useMatrix = useMatrix ) 325s > fit3sls2 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restrm, 325s + inst = inst, useMatrix = useMatrix ) 325s > # print( hausman.systemfit( fit2sls2, fit3sls2 ) ) 325s > 325s > ## ************* 2SLS estimation with singleEqSigma = TRUE ***************** 325s > fit2sls2s <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restrm, 325s + inst = inst, singleEqSigma = TRUE, useMatrix = useMatrix ) 325s > # print( hausman.systemfit( fit2sls2s, fit3sls2 ) ) 325s > 325s > ## ********************* estimations with methodResidCov = 0 ************** 325s > fit2sls2r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restrm, 325s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 325s > fit3sls2r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restrm, 325s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 325s > # print( hausman.systemfit( fit2sls2r, fit3sls2r ) ) 325s > 325s > 325s > ## ****************** estimation with restriction via restrict.regMat ****************** 325s > ## ********************** default estimation ******************** 325s > fit2sls3 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.regMat = tc, 325s + inst = inst, useMatrix = useMatrix ) 325s > fit3sls3 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.regMat = tc, 325s + inst = inst, useMatrix = useMatrix ) 325s > print( hausman.systemfit( fit2sls3, fit3sls3 ) ) 325s 325s Hausman specification test for consistency of the 3SLS estimation 325s 325s data: Kmenta 325s Hausman = -0.281, df = 6, p-value = 1 325s 325s > 325s > ## ******************* estimations with methodResidCov = 0 ******* 325s > fit2sls3r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.regMat = tc, 325s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 325s > fit3sls3r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.regMat = tc, 325s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 325s > print( hausman.systemfit( fit2sls3r, fit3sls3r ) ) 325s 325s Hausman specification test for consistency of the 3SLS estimation 325s 325s data: Kmenta 325s Hausman = -0.0132, df = 6, p-value = 1 325s 325s > 325s > 325s > ## ***************** estimations with 2 restrictions ******************* 325s > ## *********************** default estimations ************** 325s > fit2sls4 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr2m, 325s + restrict.rhs = restr2q, inst = inst, useMatrix = useMatrix ) 326s > fit3sls4 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr2m, 326s + restrict.rhs = restr2q, inst = inst, useMatrix = useMatrix ) 326s > # print( hausman.systemfit( fit2sls4, fit3sls4 ) ) 326s > 326s > ## ***************** estimations with methodResidCov = 0 ************** 326s > fit2sls4r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr2m, 326s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 326s + useMatrix = useMatrix ) 326s > fit3sls4r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr2m, 326s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 326s + useMatrix = useMatrix ) 326s > # print( hausman.systemfit( fit2sls4r, fit3sls4r ) ) 326s > 326s > 326s > ## *********** estimations with 2 restrictions via R and restrict.regMat *************** 326s > ## ***************** default estimations ******************* 326s > fit2sls5 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr3m, 326s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 326s + useMatrix = useMatrix ) 326s > fit3sls5 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr3m, 326s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 326s + useMatrix = useMatrix ) 326s > # print( hausman.systemfit( fit2sls5, fit3sls5 ) ) 326s > 326s > ## ************* estimations with methodResidCov = 0 ********* 326s > fit2sls5r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr3m, 326s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 326s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 326s > fit3sls5r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr3m, 326s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 326s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 326s > # print( hausman.systemfit( fit2sls5r, fit3sls5r ) ) 326s > 326s BEGIN TEST test_ols.R 326s 326s R version 4.3.2 (2023-10-31) -- "Eye Holes" 326s Copyright (C) 2023 The R Foundation for Statistical Computing 326s Platform: x86_64-pc-linux-gnu (64-bit) 326s 326s R is free software and comes with ABSOLUTELY NO WARRANTY. 326s You are welcome to redistribute it under certain conditions. 326s Type 'license()' or 'licence()' for distribution details. 326s 326s R is a collaborative project with many contributors. 326s Type 'contributors()' for more information and 326s 'citation()' on how to cite R or R packages in publications. 326s 326s Type 'demo()' for some demos, 'help()' for on-line help, or 326s 'help.start()' for an HTML browser interface to help. 326s Type 'q()' to quit R. 326s 326s > library( systemfit ) 326s Loading required package: Matrix 327s Loading required package: car 327s Loading required package: carData 327s Loading required package: lmtest 327s Loading required package: zoo 327s 327s Attaching package: ‘zoo’ 327s 327s The following objects are masked from ‘package:base’: 327s 327s as.Date, as.Date.numeric 327s 327s 327s Please cite the 'systemfit' package as: 327s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 327s 327s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 327s https://r-forge.r-project.org/projects/systemfit/ 327s > options( digits = 3 ) 327s > 327s > data( "Kmenta" ) 327s > useMatrix <- FALSE 327s > 327s > demand <- consump ~ price + income 327s > supply <- consump ~ price + farmPrice + trend 327s > system <- list( demand = demand, supply = supply ) 327s > restrm <- matrix(0,1,7) # restriction matrix "R" 327s > restrm[1,3] <- 1 327s > restrm[1,7] <- -1 327s > restrict <- "demand_income - supply_trend = 0" 327s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 327s > restr2m[1,3] <- 1 327s > restr2m[1,7] <- -1 327s > restr2m[2,2] <- -1 327s > restr2m[2,5] <- 1 327s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 327s > restrict2 <- c( "demand_income - supply_trend = 0", 327s + "- demand_price + supply_price = 0.5" ) 327s > tc <- matrix(0,7,6) 327s > tc[1,1] <- 1 327s > tc[2,2] <- 1 327s > tc[3,3] <- 1 327s > tc[4,4] <- 1 327s > tc[5,5] <- 1 327s > tc[6,6] <- 1 327s > tc[7,3] <- 1 327s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 327s > restr3m[1,2] <- -1 327s > restr3m[1,5] <- 1 327s > restr3q <- c( 0.5 ) # restriction vector "q" 2 327s > restrict3 <- "- C2 + C5 = 0.5" 327s > 327s > # It is not possible to estimate OLS with systemfit 327s > # exactly as EViews does, because EViews uses 327s > # methodResidCov == "geomean" for the coefficient covariance matrix and 327s > # methodResidCov == "noDfCor" for the residual covariance matrix, while 327s > # systemfit uses always the same formulas for both calculations. 327s > 327s > ## ******* single-equation OLS estimations ********************* 327s > lmDemand <- lm( demand, data = Kmenta ) 327s > lmSupply <- lm( supply, data = Kmenta ) 327s > 327s > ## *************** OLS estimation ************************ 327s > ## ********** OLS estimation (default) ******************** 327s > fitols1 <- systemfit( system, "OLS", data = Kmenta, useMatrix = useMatrix ) 327s > print( summary( fitols1 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 33 156 4.43 0.709 0.558 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 63.3 3.73 1.93 0.764 0.736 327s supply 20 16 92.6 5.78 2.40 0.655 0.590 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.73 4.14 327s supply 4.14 5.78 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.891 327s supply 0.891 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 327s price -0.3163 0.0907 -3.49 0.0028 ** 327s income 0.3346 0.0454 7.37 1.1e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.93 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 327s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 327s price 0.1604 0.0949 1.69 0.11039 327s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 327s trend 0.2483 0.0975 2.55 0.02157 * 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.405 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 327s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 327s 327s > nobs( fitols1 ) 327s [1] 40 327s > all.equal( coef( fitols1 ), c( coef( lmDemand ), coef( lmSupply ) ), 327s + check.attributes = FALSE ) 327s [1] TRUE 327s > all.equal( coef( summary( fitols1 ) ), 327s + rbind( coef( summary( lmDemand ) ), coef( summary( lmSupply ) ) ), 327s + check.attributes = FALSE ) 327s [1] TRUE 327s > all.equal( vcov( fitols1 ), 327s + as.matrix( bdiag( vcov( lmDemand ), vcov( lmSupply ) ) ), 327s + check.attributes = FALSE ) 327s [1] TRUE 327s > 327s > ## ********** OLS estimation (no singleEqSigma=F) ****************** 327s > fitols1s <- systemfit( system, "OLS", data = Kmenta, 327s + singleEqSigma = FALSE, useMatrix = useMatrix ) 327s > print( summary( fitols1s ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 33 156 4.43 0.709 0.558 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 63.3 3.73 1.93 0.764 0.736 327s supply 20 16 92.6 5.78 2.40 0.655 0.590 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.73 4.14 327s supply 4.14 5.78 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.891 327s supply 0.891 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.8954 8.4671 11.80 1.3e-09 *** 327s price -0.3163 0.1021 -3.10 0.0065 ** 327s income 0.3346 0.0511 6.54 5.0e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.93 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 327s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 58.2754 10.3587 5.63 3.8e-05 *** 327s price 0.1604 0.0857 1.87 0.080 . 327s farmPrice 0.2481 0.0417 5.94 2.1e-05 *** 327s trend 0.2483 0.0881 2.82 0.012 * 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.405 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 327s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 327s 327s > all.equal( coef( fitols1s ), c( coef( lmDemand ), coef( lmSupply ) ), 327s + check.attributes = FALSE ) 327s [1] TRUE 327s > 327s > ## **************** OLS (useDfSys=T) *********************** 327s > print( summary( fitols1, useDfSys = TRUE ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 33 156 4.43 0.709 0.558 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 63.3 3.73 1.93 0.764 0.736 327s supply 20 16 92.6 5.78 2.40 0.655 0.590 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.73 4.14 327s supply 4.14 5.78 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.891 327s supply 0.891 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.8954 7.5194 13.29 8.4e-15 *** 327s price -0.3163 0.0907 -3.49 0.0014 ** 327s income 0.3346 0.0454 7.37 1.8e-08 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.93 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 327s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 58.2754 11.4629 5.08 1.4e-05 *** 327s price 0.1604 0.0949 1.69 0.100 327s farmPrice 0.2481 0.0462 5.37 6.1e-06 *** 327s trend 0.2483 0.0975 2.55 0.016 * 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.405 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 327s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 327s 327s > 327s > ## **************** OLS (methodResidCov="noDfCor") *********************** 327s > fitols1r <- systemfit( system, "OLS", data = Kmenta, 327s + methodResidCov = "noDfCor", x = TRUE, 327s + useMatrix = useMatrix ) 327s > print( summary( fitols1r ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 33 156 3.02 0.709 0.537 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 63.3 3.73 1.93 0.764 0.736 327s supply 20 16 92.6 5.78 2.40 0.655 0.590 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.17 3.41 327s supply 3.41 4.63 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.891 327s supply 0.891 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.8954 6.9325 14.41 5.8e-11 *** 327s price -0.3163 0.0836 -3.78 0.0015 ** 327s income 0.3346 0.0419 7.99 3.7e-07 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.93 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 327s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 58.2754 10.2527 5.68 3.4e-05 *** 327s price 0.1604 0.0849 1.89 0.077 . 327s farmPrice 0.2481 0.0413 6.01 1.8e-05 *** 327s trend 0.2483 0.0872 2.85 0.012 * 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.405 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 327s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 327s 327s > all.equal( coef( fitols1r ), c( coef( lmDemand ), coef( lmSupply ) ), 327s + check.attributes = FALSE ) 327s [1] TRUE 327s > 327s > ## ******** OLS (methodResidCov="noDfCor", singleEqSigma=F) *********** 327s > fitols1rs <- systemfit( system, "OLS", data = Kmenta, 327s + methodResidCov = "noDfCor", singleEqSigma = FALSE, 327s + useMatrix = useMatrix ) 327s > print( summary( fitols1rs ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 33 156 3.02 0.709 0.537 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 63.3 3.73 1.93 0.764 0.736 327s supply 20 16 92.6 5.78 2.40 0.655 0.590 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.17 3.41 327s supply 3.41 4.63 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.891 327s supply 0.891 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.8954 7.6907 12.99 3.0e-10 *** 327s price -0.3163 0.0927 -3.41 0.0033 ** 327s income 0.3346 0.0465 7.20 1.5e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.93 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 327s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 58.2754 9.4088 6.19 1.3e-05 *** 327s price 0.1604 0.0779 2.06 0.0561 . 327s farmPrice 0.2481 0.0379 6.55 6.7e-06 *** 327s trend 0.2483 0.0800 3.10 0.0068 ** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.405 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 327s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 327s 327s > all.equal( coef( fitols1rs ), c( coef( lmDemand ), coef( lmSupply ) ), 327s + check.attributes = FALSE ) 327s [1] TRUE 327s > 327s > ## **************** OLS (methodResidCov="Theil" ) *********************** 327s > fitols1r <- systemfit( system, "OLS", data = Kmenta, 327s + methodResidCov = "Theil", x = TRUE, 327s + useMatrix = useMatrix ) 327s > print( summary( fitols1r ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 33 156 3.26 0.709 0.503 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 63.3 3.73 1.93 0.764 0.736 327s supply 20 16 92.6 5.78 2.40 0.655 0.590 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.73 4.28 327s supply 4.28 5.78 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.891 327s supply 0.891 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 327s price -0.3163 0.0907 -3.49 0.0028 ** 327s income 0.3346 0.0454 7.37 1.1e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.93 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 327s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 327s price 0.1604 0.0949 1.69 0.11039 327s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 327s trend 0.2483 0.0975 2.55 0.02157 * 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.405 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 327s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 327s 327s > all.equal( coef( fitols1r ), c( coef( lmDemand ), coef( lmSupply ) ), 327s + check.attributes = FALSE ) 327s [1] TRUE 327s > 327s > ## **************** OLS (methodResidCov="max") *********************** 327s > fitols1r <- systemfit( system, "OLS", data = Kmenta, 327s + methodResidCov = "max", x = TRUE, 327s + useMatrix = useMatrix ) 327s > print( summary( fitols1r ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 33 156 3.37 0.709 0.509 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 63.3 3.73 1.93 0.764 0.736 327s supply 20 16 92.6 5.78 2.40 0.655 0.590 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.73 4.26 327s supply 4.26 5.78 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.891 327s supply 0.891 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 327s price -0.3163 0.0907 -3.49 0.0028 ** 327s income 0.3346 0.0454 7.37 1.1e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.93 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 327s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 327s price 0.1604 0.0949 1.69 0.11039 327s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 327s trend 0.2483 0.0975 2.55 0.02157 * 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.405 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 327s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 327s 327s > 327s > ## ******** OLS (methodResidCov="max", singleEqSigma=F) *********** 327s > fitols1rs <- systemfit( system, "OLS", data = Kmenta, 327s + methodResidCov = "max", singleEqSigma = FALSE, 327s + useMatrix = useMatrix ) 327s > print( summary( fitols1rs ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 33 156 3.37 0.709 0.509 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 63.3 3.73 1.93 0.764 0.736 327s supply 20 16 92.6 5.78 2.40 0.655 0.590 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.73 4.26 327s supply 4.26 5.78 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.891 327s supply 0.891 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.8954 8.4671 11.80 1.3e-09 *** 327s price -0.3163 0.1021 -3.10 0.0065 ** 327s income 0.3346 0.0511 6.54 5.0e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.93 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 327s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 58.2754 10.3587 5.63 3.8e-05 *** 327s price 0.1604 0.0857 1.87 0.080 . 327s farmPrice 0.2481 0.0417 5.94 2.1e-05 *** 327s trend 0.2483 0.0881 2.82 0.012 * 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.405 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 327s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 327s 327s > 327s > 327s > ## ********* OLS with cross-equation restriction ************ 327s > ## ****** OLS with cross-equation restriction (default) ********* 327s > fitols2 <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.matrix = restrm, useMatrix = useMatrix ) 327s > print( summary( fitols2 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 2.5 0.703 0.608 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.78 4.47 327s supply 4.47 5.94 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 8.4225 11.82 1.4e-13 *** 327s price -0.2917 0.0975 -2.99 0.0051 ** 327s income 0.3129 0.0441 7.10 3.3e-08 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 10.0721 5.60 2.9e-06 *** 327s price 0.1639 0.0853 1.92 0.063 . 327s farmPrice 0.2571 0.0402 6.39 2.7e-07 *** 327s trend 0.3129 0.0441 7.10 3.3e-08 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > # the same with symbolically specified restrictions 327s > fitols2Sym <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.matrix = restrict, useMatrix = useMatrix ) 327s > all.equal( fitols2, fitols2Sym ) 327s [1] "Component “call”: target, current do not match when deparsed" 327s > 327s > ## ****** OLS with cross-equation restriction (singleEqSigma=T) ******* 327s > fitols2s <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.matrix = restrm, singleEqSigma = TRUE, 327s + useMatrix = useMatrix ) 327s > print( summary( fitols2s ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 2.5 0.703 0.608 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.78 4.47 327s supply 4.47 5.94 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 7.5640 13.16 6.7e-15 *** 327s price -0.2917 0.0887 -3.29 0.0023 ** 327s income 0.3129 0.0415 7.54 9.4e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 11.3165 4.98 1.8e-05 *** 327s price 0.1639 0.0960 1.71 0.097 . 327s farmPrice 0.2571 0.0451 5.69 2.1e-06 *** 327s trend 0.3129 0.0415 7.54 9.4e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > ## ****** OLS with cross-equation restriction (useDfSys=F) ******* 327s > print( summary( fitols2, useDfSys = FALSE ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 2.5 0.703 0.608 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.78 4.47 327s supply 4.47 5.94 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 8.4225 11.82 1.3e-09 *** 327s price -0.2917 0.0975 -2.99 0.0082 ** 327s income 0.3129 0.0441 7.10 1.8e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 10.0721 5.60 4.0e-05 *** 327s price 0.1639 0.0853 1.92 0.073 . 327s farmPrice 0.2571 0.0402 6.39 8.9e-06 *** 327s trend 0.3129 0.0441 7.10 2.5e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > ## ****** OLS with cross-equation restriction (methodResidCov="noDfCor") ******* 327s > fitols2r <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.matrix = restrm, methodResidCov = "noDfCor", 327s + useMatrix = useMatrix ) 327s > print( summary( fitols2r ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 1.7 0.703 0.577 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.21 3.68 327s supply 3.68 4.75 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 327s price -0.2917 0.0899 -3.25 0.0026 ** 327s income 0.3129 0.0406 7.70 5.9e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 327s price 0.1639 0.0786 2.08 0.045 * 327s farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 327s trend 0.3129 0.0406 7.70 5.9e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > ## ** OLS with cross-equation restriction (methodResidCov="noDfCor",singleEqSigma=T) *** 327s > fitols2rs <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.matrix = restrm, methodResidCov = "noDfCor", 327s + x = TRUE, useMatrix = useMatrix ) 327s > print( summary( fitols2rs ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 1.7 0.703 0.577 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.21 3.68 327s supply 3.68 4.75 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 327s price -0.2917 0.0899 -3.25 0.0026 ** 327s income 0.3129 0.0406 7.70 5.9e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 327s price 0.1639 0.0786 2.08 0.045 * 327s farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 327s trend 0.3129 0.0406 7.70 5.9e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > ## *** OLS with cross-equation restriction via restrict.regMat *** 327s > ## *** OLS with cross-equation restriction via restrict.regMat (default) *** 327s > fitols3 <- systemfit( system, "OLS", data = Kmenta, restrict.regMat = tc, 327s + x = TRUE, useMatrix = useMatrix ) 327s > print( summary( fitols3 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 2.5 0.703 0.608 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.78 4.47 327s supply 4.47 5.94 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 8.4225 11.82 1.4e-13 *** 327s price -0.2917 0.0975 -2.99 0.0051 ** 327s income 0.3129 0.0441 7.10 3.3e-08 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 10.0721 5.60 2.9e-06 *** 327s price 0.1639 0.0853 1.92 0.063 . 327s farmPrice 0.2571 0.0402 6.39 2.7e-07 *** 327s trend 0.3129 0.0441 7.10 3.3e-08 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > ## *** OLS with cross-equation restriction via restrict.regMat (singleEqSigma=T) *** 327s > fitols3s <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.regMat = tc, singleEqSigma = TRUE, useMatrix = useMatrix ) 327s > print( summary( fitols3s ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 2.5 0.703 0.608 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.78 4.47 327s supply 4.47 5.94 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 7.5640 13.16 6.7e-15 *** 327s price -0.2917 0.0887 -3.29 0.0023 ** 327s income 0.3129 0.0415 7.54 9.4e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 11.3165 4.98 1.8e-05 *** 327s price 0.1639 0.0960 1.71 0.097 . 327s farmPrice 0.2571 0.0451 5.69 2.1e-06 *** 327s trend 0.3129 0.0415 7.54 9.4e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > ## *** OLS with cross-equation restriction via restrict.regMat (useDfSys=F) *** 327s > print( summary( fitols3, useDfSys = FALSE ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 2.5 0.703 0.608 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.78 4.47 327s supply 4.47 5.94 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 8.4225 11.82 1.3e-09 *** 327s price -0.2917 0.0975 -2.99 0.0082 ** 327s income 0.3129 0.0441 7.10 1.8e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 10.0721 5.60 4.0e-05 *** 327s price 0.1639 0.0853 1.92 0.073 . 327s farmPrice 0.2571 0.0402 6.39 8.9e-06 *** 327s trend 0.3129 0.0441 7.10 2.5e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > ## *** OLS with cross-equation restriction via restrict.regMat (methodResidCov="noDfCor") *** 327s > fitols3r <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.regMat = tc, methodResidCov = "noDfCor", 327s + useMatrix = useMatrix ) 327s > print( summary( fitols3r ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 1.7 0.703 0.577 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.21 3.68 327s supply 3.68 4.75 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 327s price -0.2917 0.0899 -3.25 0.0026 ** 327s income 0.3129 0.0406 7.70 5.9e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 327s price 0.1639 0.0786 2.08 0.045 * 327s farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 327s trend 0.3129 0.0406 7.70 5.9e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > ## OLS with cross-equation restriction via restrict.regMat (methodResidCov="noDfCor",singleEqSigma=T) 327s > fitols3rs <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.regMat = tc, methodResidCov = "noDfCor", singleEqSigma = TRUE, 327s + useMatrix = useMatrix ) 327s > print( summary( fitols3rs ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 1.7 0.703 0.577 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.21 3.68 327s supply 3.68 4.75 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 6.9734 14.28 6.7e-16 *** 327s price -0.2917 0.0816 -3.57 0.0011 ** 327s income 0.3129 0.0381 8.22 1.4e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 10.1248 5.57 3.1e-06 *** 327s price 0.1639 0.0859 1.91 0.065 . 327s farmPrice 0.2571 0.0404 6.36 2.9e-07 *** 327s trend 0.3129 0.0381 8.22 1.4e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > ## ********* OLS with 2 cross-equation restrictions *********** 327s > ## ********* OLS with 2 cross-equation restrictions (default) *********** 327s > fitols4 <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 327s + restrict.rhs = restr2q, useMatrix = useMatrix ) 327s > print( summary( fitols4 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 2.69 0.702 0.605 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.76 4.46 327s supply 4.46 5.99 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.938 327s supply 0.938 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.4817 6.1599 16.47 < 2e-16 *** 327s price -0.3168 0.0629 -5.04 1.4e-05 *** 327s income 0.3189 0.0399 8.00 2.0e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.94 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.1494 7.5515 7.17 2.3e-08 *** 327s price 0.1832 0.0629 2.91 0.0062 ** 327s farmPrice 0.2595 0.0391 6.64 1.1e-07 *** 327s trend 0.3189 0.0399 8.00 2.0e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.447 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 327s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 327s 327s > # the same with symbolically specified restrictions 327s > fitols4Sym <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.matrix = restrict2, useMatrix = useMatrix ) 327s > all.equal( fitols4, fitols4Sym ) 327s [1] "Component “call”: target, current do not match when deparsed" 327s > 327s > ## ****** OLS with 2 cross-equation restrictions (singleEqSigma=T) ******* 327s > fitols4s <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 327s + restrict.rhs = restr2q, singleEqSigma = TRUE, x = TRUE, 327s + useMatrix = useMatrix ) 327s > print( summary( fitols4s ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 2.69 0.702 0.605 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.76 4.46 327s supply 4.46 5.99 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.938 327s supply 0.938 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.4817 6.0474 16.78 < 2e-16 *** 327s price -0.3168 0.0648 -4.89 2.3e-05 *** 327s income 0.3189 0.0385 8.29 9.1e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.94 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.1494 7.9687 6.80 7.0e-08 *** 327s price 0.1832 0.0648 2.83 0.0077 ** 327s farmPrice 0.2595 0.0446 5.82 1.3e-06 *** 327s trend 0.3189 0.0385 8.29 9.1e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.447 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 327s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 327s 327s > 327s > ## ****** OLS with 2 cross-equation restrictions (useDfSys=F) ******* 327s > print( summary( fitols4, useDfSys = FALSE ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 2.69 0.702 0.605 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.76 4.46 327s supply 4.46 5.99 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.938 327s supply 0.938 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.4817 6.1599 16.47 6.9e-12 *** 327s price -0.3168 0.0629 -5.04 1e-04 *** 327s income 0.3189 0.0399 8.00 3.6e-07 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.94 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.1494 7.5515 7.17 2.2e-06 *** 327s price 0.1832 0.0629 2.91 0.01 * 327s farmPrice 0.2595 0.0391 6.64 5.6e-06 *** 327s trend 0.3189 0.0399 8.00 5.5e-07 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.447 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 327s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 327s 327s > 327s > ## ****** OLS with 2 cross-equation restrictions (methodResidCov="noDfCor") ******* 327s > fitols4r <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 327s + restrict.rhs = restr2q, methodResidCov = "noDfCor", 327s + useMatrix = useMatrix ) 327s > print( summary( fitols4r ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 1.83 0.702 0.575 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.20 3.67 327s supply 3.67 4.79 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.938 327s supply 0.938 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.4817 5.7621 17.61 < 2e-16 *** 327s price -0.3168 0.0589 -5.38 5.0e-06 *** 327s income 0.3189 0.0373 8.55 4.3e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.94 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.1494 7.0638 7.67 5.4e-09 *** 327s price 0.1832 0.0589 3.11 0.0037 ** 327s farmPrice 0.2595 0.0365 7.10 2.8e-08 *** 327s trend 0.3189 0.0373 8.55 4.3e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.447 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 327s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 327s 327s > 327s > ## OLS with 2 cross-equation restrictions (methodResidCov="noDfCor", singleEqSigma=T) * 327s > fitols4rs <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 327s + restrict.rhs = restr2q, methodResidCov = "noDfCor", 327s + singleEqSigma = TRUE, useMatrix = useMatrix ) 327s > print( summary( fitols4rs ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 1.83 0.702 0.575 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.20 3.67 327s supply 3.67 4.79 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.938 327s supply 0.938 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.4817 5.5234 18.37 < 2e-16 *** 327s price -0.3168 0.0589 -5.38 5.0e-06 *** 327s income 0.3189 0.0352 9.05 1.1e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.94 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.1494 7.2089 7.51 8.5e-09 *** 327s price 0.1832 0.0589 3.11 0.0037 ** 327s farmPrice 0.2595 0.0399 6.51 1.7e-07 *** 327s trend 0.3189 0.0352 9.05 1.1e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.447 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 327s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 327s 327s > 327s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat **** 327s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat (default) **** 327s > fitols5 <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr3m, 327s + restrict.rhs = restr3q, restrict.regMat = tc, methodResidCov = "noDfCor", 327s + useMatrix = useMatrix ) 327s > print( summary( fitols5 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 1.83 0.702 0.575 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.20 3.67 327s supply 3.67 4.79 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.938 327s supply 0.938 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.4817 5.7621 17.61 < 2e-16 *** 327s price -0.3168 0.0589 -5.38 5.0e-06 *** 327s income 0.3189 0.0373 8.55 4.3e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.94 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.1494 7.0638 7.67 5.4e-09 *** 327s price 0.1832 0.0589 3.11 0.0037 ** 327s farmPrice 0.2595 0.0365 7.10 2.8e-08 *** 327s trend 0.3189 0.0373 8.55 4.3e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.447 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 327s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 327s 327s > # the same with symbolically specified restrictions 327s > fitols5Sym <- systemfit( system, "OLS", data = Kmenta, 327s + restrict.matrix = restrict3, restrict.regMat = tc, 327s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 327s > all.equal( fitols5, fitols5Sym ) 327s [1] "Component “call”: target, current do not match when deparsed" 327s > 327s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat (singleEqSigma=T) **** 327s > fitols5s <- systemfit( system, "OLS", data = Kmenta,restrict.matrix = restr3m, 327s + restrict.rhs = restr3q, restrict.regMat = tc, singleEqSigma = T, 327s + x = TRUE, useMatrix = useMatrix ) 327s > print( summary( fitols5s ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 2.69 0.702 0.605 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.76 4.46 327s supply 4.46 5.99 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.938 327s supply 0.938 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.4817 6.0474 16.78 < 2e-16 *** 327s price -0.3168 0.0648 -4.89 2.3e-05 *** 327s income 0.3189 0.0385 8.29 9.1e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.94 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.1494 7.9687 6.80 7.0e-08 *** 327s price 0.1832 0.0648 2.83 0.0077 ** 327s farmPrice 0.2595 0.0446 5.82 1.3e-06 *** 327s trend 0.3189 0.0385 8.29 9.1e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.447 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 327s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 327s 327s > 327s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat (useDfSys=F) **** 327s > fitols5o <- systemfit( system, "OLS", data = Kmenta,restrict.matrix = restr3m, 327s + restrict.rhs = restr3q, restrict.regMat = tc, useMatrix = useMatrix ) 327s > print( summary( fitols5o, useDfSys = FALSE ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 2.69 0.702 0.605 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.76 4.46 327s supply 4.46 5.99 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.938 327s supply 0.938 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.4817 6.1599 16.47 6.9e-12 *** 327s price -0.3168 0.0629 -5.04 1e-04 *** 327s income 0.3189 0.0399 8.00 3.6e-07 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.94 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.1494 7.5515 7.17 2.2e-06 *** 327s price 0.1832 0.0629 2.91 0.01 * 327s farmPrice 0.2595 0.0391 6.64 5.6e-06 *** 327s trend 0.3189 0.0399 8.00 5.5e-07 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.447 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 327s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 327s 327s > 327s > ## OLS with 2 cross-equation restr. via R and restrict.regMat (methodResidCov="noDfCor",singleEqSigma=T) 327s > fitols5rs <- systemfit( system, "OLS", data = Kmenta,restrict.matrix = restr3m, 327s + restrict.rhs = restr3q, restrict.regMat = tc, methodResidCov = "noDfCor", 327s + singleEqSigma = TRUE, useMatrix = useMatrix ) 327s > print( summary( fitols5rs ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 1.83 0.702 0.575 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.20 3.67 327s supply 3.67 4.79 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.938 327s supply 0.938 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.4817 5.5234 18.37 < 2e-16 *** 327s price -0.3168 0.0589 -5.38 5.0e-06 *** 327s income 0.3189 0.0352 9.05 1.1e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.94 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.1494 7.2089 7.51 8.5e-09 *** 327s price 0.1832 0.0589 3.11 0.0037 ** 327s farmPrice 0.2595 0.0399 6.51 1.7e-07 *** 327s trend 0.3189 0.0352 9.05 1.1e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.447 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 327s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 327s 327s > 327s > 327s > ## *********** estimations with a single regressor ************ 327s > fitolsS1 <- systemfit( 327s + list( consump ~ price - 1, consump ~ price + trend ), "OLS", 327s + data = Kmenta, useMatrix = useMatrix ) 327s > print( summary( fitolsS1 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 36 1121 484 -1.09 -1.05 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s eq1 20 19 861 45.3 6.73 -2.213 -2.213 327s eq2 20 17 259 15.3 3.91 0.032 -0.082 327s 327s The covariance matrix of the residuals 327s eq1 eq2 327s eq1 45.3 14.4 327s eq2 14.4 15.3 327s 327s The correlations of the residuals 327s eq1 eq2 327s eq1 1.000 0.549 327s eq2 0.549 1.000 327s 327s 327s OLS estimates for 'eq1' (equation 1) 327s Model Formula: consump ~ price - 1 327s 327s Estimate Std. Error t value Pr(>|t|) 327s price 1.006 0.015 66.9 <2e-16 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 6.733 on 19 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 19 327s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 327s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 327s 327s 327s OLS estimates for 'eq2' (equation 2) 327s Model Formula: consump ~ price + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 93.6767 15.2367 6.15 1.1e-05 *** 327s price 0.0622 0.1513 0.41 0.69 327s trend 0.0953 0.1515 0.63 0.54 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 3.907 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 259.497 MSE: 15.265 Root MSE: 3.907 327s Multiple R-Squared: 0.032 Adjusted R-Squared: -0.082 327s 327s > fitolsS2 <- systemfit( 327s + list( consump ~ price - 1, consump ~ trend - 1 ), "OLS", 327s + data = Kmenta, useMatrix = useMatrix ) 327s > print( summary( fitolsS2 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 38 47370 110957 -87.3 -5.28 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s eq1 20 19 861 45.3 6.73 -2.21 -2.21 327s eq2 20 19 46509 2447.8 49.48 -172.47 -172.47 327s 327s The covariance matrix of the residuals 327s eq1 eq2 327s eq1 45.34 -5.15 327s eq2 -5.15 2447.84 327s 327s The correlations of the residuals 327s eq1 eq2 327s eq1 1.0000 -0.0439 327s eq2 -0.0439 1.0000 327s 327s 327s OLS estimates for 'eq1' (equation 1) 327s Model Formula: consump ~ price - 1 327s 327s Estimate Std. Error t value Pr(>|t|) 327s price 1.006 0.015 66.9 <2e-16 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 6.733 on 19 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 19 327s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 327s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 327s 327s 327s OLS estimates for 'eq2' (equation 2) 327s Model Formula: consump ~ trend - 1 327s 327s Estimate Std. Error t value Pr(>|t|) 327s trend 7.405 0.924 8.02 1.6e-07 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 49.476 on 19 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 19 327s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 327s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 327s 327s > fitolsS3 <- systemfit( 327s + list( consump ~ trend - 1, price ~ trend - 1 ), "OLS", 327s + data = Kmenta, useMatrix = useMatrix ) 327s > print( summary( fitolsS3 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 38 93537 108970 -99 -0.977 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s eq1 20 19 46509 2448 49.5 -172.5 -172.5 327s eq2 20 19 47028 2475 49.8 -69.5 -69.5 327s 327s The covariance matrix of the residuals 327s eq1 eq2 327s eq1 2448 2439 327s eq2 2439 2475 327s 327s The correlations of the residuals 327s eq1 eq2 327s eq1 1.000 0.988 327s eq2 0.988 1.000 327s 327s 327s OLS estimates for 'eq1' (equation 1) 327s Model Formula: consump ~ trend - 1 327s 327s Estimate Std. Error t value Pr(>|t|) 327s trend 7.405 0.924 8.02 1.6e-07 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 49.476 on 19 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 19 327s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 327s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 327s 327s 327s OLS estimates for 'eq2' (equation 2) 327s Model Formula: price ~ trend - 1 327s 327s Estimate Std. Error t value Pr(>|t|) 327s trend 7.318 0.929 7.88 2.1e-07 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 49.751 on 19 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 19 327s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 327s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 327s 327s > fitolsS4 <- systemfit( 327s + list( consump ~ trend - 1, price ~ trend - 1 ), "OLS", 327s + data = Kmenta, restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), 327s + useMatrix = useMatrix ) 327s > print( summary( fitolsS4 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 39 93548 111736 -99 -1.03 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s eq1 20 19 46514 2448 49.5 -172.5 -172.5 327s eq2 20 19 47033 2475 49.8 -69.5 -69.5 327s 327s The covariance matrix of the residuals 327s eq1 eq2 327s eq1 2448 2439 327s eq2 2439 2475 327s 327s The correlations of the residuals 327s eq1 eq2 327s eq1 1.000 0.988 327s eq2 0.988 1.000 327s 327s 327s OLS estimates for 'eq1' (equation 1) 327s Model Formula: consump ~ trend - 1 327s 327s Estimate Std. Error t value Pr(>|t|) 327s trend 7.362 0.646 11.4 5.7e-14 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 49.478 on 19 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 19 327s SSR: 46514.283 MSE: 2448.12 Root MSE: 49.478 327s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 327s 327s 327s OLS estimates for 'eq2' (equation 2) 327s Model Formula: price ~ trend - 1 327s 327s Estimate Std. Error t value Pr(>|t|) 327s trend 7.362 0.646 11.4 5.7e-14 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 49.754 on 19 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 19 327s SSR: 47033.469 MSE: 2475.446 Root MSE: 49.754 327s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 327s 327s > fitolsS5 <- systemfit( 327s + list( consump ~ 1, farmPrice ~ 1 ), "OLS", 327s + data = Kmenta, useMatrix = useMatrix ) 327s > print( summary( fitolsS5 ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 38 3337 1224 0 0 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s eq1 20 19 268 14.1 3.76 0 0 327s eq2 20 19 3069 161.5 12.71 0 0 327s 327s The covariance matrix of the residuals 327s eq1 eq2 327s eq1 14.1 32.5 327s eq2 32.5 161.5 327s 327s The correlations of the residuals 327s eq1 eq2 327s eq1 1.000 0.681 327s eq2 0.681 1.000 327s 327s 327s OLS estimates for 'eq1' (equation 1) 327s Model Formula: consump ~ 1 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 100.90 0.84 120 <2e-16 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 3.756 on 19 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 19 327s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 327s Multiple R-Squared: 0 Adjusted R-Squared: 0 327s 327s 327s OLS estimates for 'eq2' (equation 2) 327s Model Formula: farmPrice ~ 1 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 96.62 2.84 34 <2e-16 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 12.709 on 19 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 19 327s SSR: 3068.757 MSE: 161.514 Root MSE: 12.709 327s Multiple R-Squared: 0 Adjusted R-Squared: 0 327s 327s > 327s > 327s > ## **************** shorter summaries ********************** 327s > print( summary( fitols1, useDfSys = TRUE, equations = FALSE ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 33 156 4.43 0.709 0.558 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 63.3 3.73 1.93 0.764 0.736 327s supply 20 16 92.6 5.78 2.40 0.655 0.590 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.73 4.14 327s supply 4.14 5.78 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.891 327s supply 0.891 1.000 327s 327s 327s Coefficients: 327s Estimate Std. Error t value Pr(>|t|) 327s demand_(Intercept) 99.8954 7.5194 13.29 8.4e-15 *** 327s demand_price -0.3163 0.0907 -3.49 0.0014 ** 327s demand_income 0.3346 0.0454 7.37 1.8e-08 *** 327s supply_(Intercept) 58.2754 11.4629 5.08 1.4e-05 *** 327s supply_price 0.1604 0.0949 1.69 0.1004 327s supply_farmPrice 0.2481 0.0462 5.37 6.1e-06 *** 327s supply_trend 0.2483 0.0975 2.55 0.0157 * 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s > 327s > print( summary( fitols2r ), residCov = FALSE, equations = FALSE ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 1.7 0.703 0.577 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s 327s Coefficients: 327s Estimate Std. Error t value Pr(>|t|) 327s demand_(Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 327s demand_price -0.2917 0.0899 -3.25 0.0026 ** 327s demand_income 0.3129 0.0406 7.70 5.9e-09 *** 327s supply_(Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 327s supply_price 0.1639 0.0786 2.08 0.0447 * 327s supply_farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 327s supply_trend 0.3129 0.0406 7.70 5.9e-09 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s > 327s > print( summary( fitols3s, useDfSys = FALSE ), residCov = TRUE ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 34 159 2.5 0.703 0.608 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.2 3.78 1.94 0.761 0.732 327s supply 20 16 95.1 5.94 2.44 0.645 0.579 327s 327s The covariance matrix of the residuals 327s demand supply 327s demand 3.78 4.47 327s supply 4.47 5.94 327s 327s The correlations of the residuals 327s demand supply 327s demand 1.000 0.943 327s supply 0.943 1.000 327s 327s 327s OLS estimates for 'demand' (equation 1) 327s Model Formula: consump ~ price + income 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.5563 7.5640 13.16 2.4e-10 *** 327s price -0.2917 0.0887 -3.29 0.0043 ** 327s income 0.3129 0.0415 7.54 8.1e-07 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 1.943 on 17 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 17 327s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 327s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 327s 327s 327s OLS estimates for 'supply' (equation 2) 327s Model Formula: consump ~ price + farmPrice + trend 327s 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.3795 11.3165 4.98 0.00014 *** 327s price 0.1639 0.0960 1.71 0.10724 327s farmPrice 0.2571 0.0451 5.69 3.3e-05 *** 327s trend 0.3129 0.0415 7.54 1.2e-06 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s 327s Residual standard error: 2.438 on 16 degrees of freedom 327s Number of observations: 20 Degrees of Freedom: 16 327s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 327s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 327s 327s > 327s > print( summary( fitols4rs, residCov = FALSE, equations = FALSE ) ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 1.83 0.702 0.575 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s 327s Coefficients: 327s Estimate Std. Error t value Pr(>|t|) 327s demand_(Intercept) 101.4817 5.5234 18.37 < 2e-16 *** 327s demand_price -0.3168 0.0589 -5.38 5.0e-06 *** 327s demand_income 0.3189 0.0352 9.05 1.1e-10 *** 327s supply_(Intercept) 54.1494 7.2089 7.51 8.5e-09 *** 327s supply_price 0.1832 0.0589 3.11 0.0037 ** 327s supply_farmPrice 0.2595 0.0399 6.51 1.7e-07 *** 327s supply_trend 0.3189 0.0352 9.05 1.1e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s > 327s > print( summary( fitols5, equations = FALSE ), residCov = FALSE ) 327s 327s systemfit results 327s method: OLS 327s 327s N DF SSR detRCov OLS-R2 McElroy-R2 327s system 40 35 160 1.83 0.702 0.575 327s 327s N DF SSR MSE RMSE R2 Adj R2 327s demand 20 17 64.0 3.77 1.94 0.761 0.733 327s supply 20 16 95.8 5.99 2.45 0.643 0.576 327s 327s 327s Coefficients: 327s Estimate Std. Error t value Pr(>|t|) 327s demand_(Intercept) 101.4817 5.7621 17.61 < 2e-16 *** 327s demand_price -0.3168 0.0589 -5.38 5.0e-06 *** 327s demand_income 0.3189 0.0373 8.55 4.3e-10 *** 327s supply_(Intercept) 54.1494 7.0638 7.67 5.4e-09 *** 327s supply_price 0.1832 0.0589 3.11 0.0037 ** 327s supply_farmPrice 0.2595 0.0365 7.10 2.8e-08 *** 327s supply_trend 0.3189 0.0373 8.55 4.3e-10 *** 327s --- 327s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 327s > 327s > 327s > ## ****************** residuals ************************** 327s > print( residuals( fitols1 ) ) 327s demand supply 327s 1 1.074 -0.444 327s 2 -0.390 -0.896 327s 3 2.625 1.965 327s 4 1.802 1.134 327s 5 1.946 1.514 327s 6 1.175 0.680 327s 7 1.530 1.569 327s 8 -2.933 -4.407 327s 9 -1.365 -2.599 327s 10 2.031 2.469 327s 11 -0.149 -0.598 327s 12 -1.954 -1.697 327s 13 -1.121 -1.064 327s 14 -0.220 0.970 327s 15 1.487 3.159 327s 16 -3.701 -3.866 327s 17 -1.273 -0.265 327s 18 -2.002 -2.449 327s 19 1.738 3.110 327s 20 -0.299 1.714 327s > print( residuals( fitols1$eq[[ 2 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 11 327s -0.444 -0.896 1.965 1.134 1.514 0.680 1.569 -4.407 -2.599 2.469 -0.598 327s 12 13 14 15 16 17 18 19 20 327s -1.697 -1.064 0.970 3.159 -3.866 -0.265 -2.449 3.110 1.714 327s > 327s > print( residuals( fitols2r ) ) 327s demand supply 327s 1 0.8465 0.156 327s 2 -0.4933 -0.384 327s 3 2.5225 2.415 327s 4 1.7066 1.525 327s 5 2.0445 1.750 327s 6 1.2529 0.870 327s 7 1.6277 1.711 327s 8 -2.8261 -4.380 327s 9 -1.2979 -2.597 327s 10 2.0592 2.497 327s 11 -0.4663 -0.466 327s 12 -2.3732 -1.540 327s 13 -1.4734 -1.006 327s 14 -0.3398 0.885 327s 15 1.7283 2.835 327s 16 -3.4975 -4.290 327s 17 -0.9651 -0.760 327s 18 -1.9512 -2.911 327s 19 1.8829 2.606 327s 20 0.0129 1.085 327s > print( residuals( fitols2r$eq[[ 1 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 327s 0.8465 -0.4933 2.5225 1.7066 2.0445 1.2529 1.6277 -2.8261 -1.2979 2.0592 327s 11 12 13 14 15 16 17 18 19 20 327s -0.4663 -2.3732 -1.4734 -0.3398 1.7283 -3.4975 -0.9651 -1.9512 1.8829 0.0129 327s > 327s > print( residuals( fitols3s ) ) 327s demand supply 327s 1 0.8465 0.156 327s 2 -0.4933 -0.384 327s 3 2.5225 2.415 327s 4 1.7066 1.525 327s 5 2.0445 1.750 327s 6 1.2529 0.870 327s 7 1.6277 1.711 327s 8 -2.8261 -4.380 327s 9 -1.2979 -2.597 327s 10 2.0592 2.497 327s 11 -0.4663 -0.466 327s 12 -2.3732 -1.540 327s 13 -1.4734 -1.006 327s 14 -0.3398 0.885 327s 15 1.7283 2.835 327s 16 -3.4975 -4.290 327s 17 -0.9651 -0.760 327s 18 -1.9512 -2.911 327s 19 1.8829 2.606 327s 20 0.0129 1.085 327s > print( residuals( fitols3s$eq[[ 2 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 11 327s 0.156 -0.384 2.415 1.525 1.750 0.870 1.711 -4.380 -2.597 2.497 -0.466 327s 12 13 14 15 16 17 18 19 20 327s -1.540 -1.006 0.885 2.835 -4.290 -0.760 -2.911 2.606 1.085 327s > 327s > print( residuals( fitols4rs ) ) 327s demand supply 327s 1 0.915 0.204 327s 2 -0.387 -0.421 327s 3 2.613 2.388 327s 4 1.815 1.474 327s 5 1.980 1.787 327s 6 1.221 0.879 327s 7 1.620 1.690 327s 8 -2.769 -4.489 327s 9 -1.382 -2.549 327s 10 1.890 2.660 327s 11 -0.506 -0.297 327s 12 -2.280 -1.456 327s 13 -1.323 -1.013 327s 14 -0.330 0.925 327s 15 1.572 2.889 327s 16 -3.582 -4.313 327s 17 -1.298 -0.573 327s 18 -1.892 -3.023 327s 19 1.948 2.462 327s 20 0.174 0.777 327s > print( residuals( fitols4rs$eq[[ 1 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 11 327s 0.915 -0.387 2.613 1.815 1.980 1.221 1.620 -2.769 -1.382 1.890 -0.506 327s 12 13 14 15 16 17 18 19 20 327s -2.280 -1.323 -0.330 1.572 -3.582 -1.298 -1.892 1.948 0.174 327s > 327s > print( residuals( fitols5 ) ) 327s demand supply 327s 1 0.915 0.204 327s 2 -0.387 -0.421 327s 3 2.613 2.388 327s 4 1.815 1.474 327s 5 1.980 1.787 327s 6 1.221 0.879 327s 7 1.620 1.690 327s 8 -2.769 -4.489 327s 9 -1.382 -2.549 327s 10 1.890 2.660 327s 11 -0.506 -0.297 327s 12 -2.280 -1.456 327s 13 -1.323 -1.013 327s 14 -0.330 0.925 327s 15 1.572 2.889 327s 16 -3.582 -4.313 327s 17 -1.298 -0.573 327s 18 -1.892 -3.023 327s 19 1.948 2.462 327s 20 0.174 0.777 327s > print( residuals( fitols5$eq[[ 2 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 11 327s 0.204 -0.421 2.388 1.474 1.787 0.879 1.690 -4.489 -2.549 2.660 -0.297 327s 12 13 14 15 16 17 18 19 20 327s -1.456 -1.013 0.925 2.889 -4.313 -0.573 -3.023 2.462 0.777 327s > 327s > 327s > ## *************** coefficients ********************* 327s > print( round( coef( fitols1rs ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s 99.895 -0.316 0.335 58.275 327s supply_price supply_farmPrice supply_trend 327s 0.160 0.248 0.248 327s > print( round( coef( fitols1rs$eq[[ 2 ]] ), digits = 6 ) ) 327s (Intercept) price farmPrice trend 327s 58.275 0.160 0.248 0.248 327s > 327s > print( round( coef( fitols2s ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s 99.556 -0.292 0.313 56.380 327s supply_price supply_farmPrice supply_trend 327s 0.164 0.257 0.313 327s > print( round( coef( fitols2s$eq[[ 1 ]] ), digits = 6 ) ) 327s (Intercept) price income 327s 99.556 -0.292 0.313 327s > 327s > print( round( coef( fitols3 ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s 99.556 -0.292 0.313 56.380 327s supply_price supply_farmPrice supply_trend 327s 0.164 0.257 0.313 327s > print( round( coef( fitols3, modified.regMat = TRUE ), digits = 6 ) ) 327s C1 C2 C3 C4 C5 C6 327s 99.556 -0.292 0.313 56.380 0.164 0.257 327s > print( round( coef( fitols3$eq[[ 2 ]] ), digits = 6 ) ) 327s (Intercept) price farmPrice trend 327s 56.380 0.164 0.257 0.313 327s > 327s > print( round( coef( fitols4r ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s 101.482 -0.317 0.319 54.149 327s supply_price supply_farmPrice supply_trend 327s 0.183 0.260 0.319 327s > print( round( coef( fitols4r$eq[[ 1 ]] ), digits = 6 ) ) 327s (Intercept) price income 327s 101.482 -0.317 0.319 327s > 327s > print( round( coef( fitols5 ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s 101.482 -0.317 0.319 54.149 327s supply_price supply_farmPrice supply_trend 327s 0.183 0.260 0.319 327s > print( round( coef( fitols5, modified.regMat = TRUE ), digits = 6 ) ) 327s C1 C2 C3 C4 C5 C6 327s 101.482 -0.317 0.319 54.149 0.183 0.260 327s > print( round( coef( fitols5$eq[[ 2 ]] ), digits = 6 ) ) 327s (Intercept) price farmPrice trend 327s 54.149 0.183 0.260 0.319 327s > 327s > 327s > ## *************** coefficients with stats ********************* 327s > print( round( coef( summary( fitols1rs, useDfSys = FALSE ) ), digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s demand_(Intercept) 99.895 8.4671 11.80 0.000000 327s demand_price -0.316 0.1021 -3.10 0.006536 327s demand_income 0.335 0.0511 6.54 0.000005 327s supply_(Intercept) 58.275 10.3587 5.63 0.000038 327s supply_price 0.160 0.0857 1.87 0.079851 327s supply_farmPrice 0.248 0.0417 5.94 0.000021 327s supply_trend 0.248 0.0881 2.82 0.012382 327s > print( round( coef( summary( fitols1rs$eq[[ 2 ]], useDfSys = FALSE ) ), 327s + digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 58.275 10.3587 5.63 0.000038 327s price 0.160 0.0857 1.87 0.079851 327s farmPrice 0.248 0.0417 5.94 0.000021 327s trend 0.248 0.0881 2.82 0.012382 327s > 327s > print( round( coef( summary( fitols2s ) ), digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s demand_(Intercept) 99.556 7.5640 13.16 0.000000 327s demand_price -0.292 0.0887 -3.29 0.002340 327s demand_income 0.313 0.0415 7.54 0.000000 327s supply_(Intercept) 56.380 11.3165 4.98 0.000018 327s supply_price 0.164 0.0960 1.71 0.097028 327s supply_farmPrice 0.257 0.0451 5.69 0.000002 327s supply_trend 0.313 0.0415 7.54 0.000000 327s > print( round( coef( summary( fitols2s$eq[[ 1 ]] ) ), digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 99.556 7.5640 13.16 0.00000 327s price -0.292 0.0887 -3.29 0.00234 327s income 0.313 0.0415 7.54 0.00000 327s > 327s > print( round( coef( summary( fitols3, useDfSys = FALSE ) ), digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s demand_(Intercept) 99.556 8.4225 11.82 0.000000 327s demand_price -0.292 0.0975 -2.99 0.008189 327s demand_income 0.313 0.0441 7.10 0.000002 327s supply_(Intercept) 56.380 10.0721 5.60 0.000040 327s supply_price 0.164 0.0853 1.92 0.072611 327s supply_farmPrice 0.257 0.0402 6.39 0.000009 327s supply_trend 0.313 0.0441 7.10 0.000003 327s > print( round( coef( summary( fitols3, useDfSys = FALSE ), modified.regMat = TRUE ), 327s + digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s C1 99.556 8.4225 11.82 NA 327s C2 -0.292 0.0975 -2.99 NA 327s C3 0.313 0.0441 7.10 NA 327s C4 56.380 10.0721 5.60 NA 327s C5 0.164 0.0853 1.92 NA 327s C6 0.257 0.0402 6.39 NA 327s > print( round( coef( summary( fitols3$eq[[ 2 ]], useDfSys = FALSE ) ), 327s + digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 56.380 10.0721 5.60 0.000040 327s price 0.164 0.0853 1.92 0.072611 327s farmPrice 0.257 0.0402 6.39 0.000009 327s trend 0.313 0.0441 7.10 0.000003 327s > 327s > print( round( coef( summary( fitols4r, useDfSys = FALSE ) ), digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s demand_(Intercept) 101.482 5.7621 17.61 0.0e+00 327s demand_price -0.317 0.0589 -5.38 5.0e-05 327s demand_income 0.319 0.0373 8.55 0.0e+00 327s supply_(Intercept) 54.149 7.0638 7.67 1.0e-06 327s supply_price 0.183 0.0589 3.11 6.7e-03 327s supply_farmPrice 0.260 0.0365 7.10 3.0e-06 327s supply_trend 0.319 0.0373 8.55 0.0e+00 327s > print( round( coef( summary( fitols4r$eq[[ 1 ]], useDfSys = FALSE ) ), 327s + digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 101.482 5.7621 17.61 0e+00 327s price -0.317 0.0589 -5.38 5e-05 327s income 0.319 0.0373 8.55 0e+00 327s > 327s > print( round( coef( summary( fitols5 ) ), digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s demand_(Intercept) 101.482 5.7621 17.61 0.000000 327s demand_price -0.317 0.0589 -5.38 0.000005 327s demand_income 0.319 0.0373 8.55 0.000000 327s supply_(Intercept) 54.149 7.0638 7.67 0.000000 327s supply_price 0.183 0.0589 3.11 0.003680 327s supply_farmPrice 0.260 0.0365 7.10 0.000000 327s supply_trend 0.319 0.0373 8.55 0.000000 327s > print( round( coef( summary( fitols5 ), modified.regMat = TRUE ), digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s C1 101.482 5.7621 17.61 0.000000 327s C2 -0.317 0.0589 -5.38 0.000005 327s C3 0.319 0.0373 8.55 0.000000 327s C4 54.149 7.0638 7.67 0.000000 327s C5 0.183 0.0589 3.11 0.003680 327s C6 0.260 0.0365 7.10 0.000000 327s > print( round( coef( summary( fitols5$eq[[ 2 ]] ) ), digits = 6 ) ) 327s Estimate Std. Error t value Pr(>|t|) 327s (Intercept) 54.149 7.0638 7.67 0.00000 327s price 0.183 0.0589 3.11 0.00368 327s farmPrice 0.260 0.0365 7.10 0.00000 327s trend 0.319 0.0373 8.55 0.00000 327s > 327s > 327s > ## *********** variance covariance matrix of the coefficients ******* 327s > print( round( vcov( fitols1rs ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income 327s demand_(Intercept) 71.6926 -0.75420 0.04078 327s demand_price -0.7542 0.01043 -0.00296 327s demand_income 0.0408 -0.00296 0.00262 327s supply_(Intercept) 0.0000 0.00000 0.00000 327s supply_price 0.0000 0.00000 0.00000 327s supply_farmPrice 0.0000 0.00000 0.00000 327s supply_trend 0.0000 0.00000 0.00000 327s supply_(Intercept) supply_price supply_farmPrice 327s demand_(Intercept) 0.000 0.000000 0.000000 327s demand_price 0.000 0.000000 0.000000 327s demand_income 0.000 0.000000 0.000000 327s supply_(Intercept) 107.303 -0.806417 -0.248549 327s supply_price -0.806 0.007352 0.000689 327s supply_farmPrice -0.249 0.000689 0.001742 327s supply_trend -0.228 0.000426 0.001074 327s supply_trend 327s demand_(Intercept) 0.000000 327s demand_price 0.000000 327s demand_income 0.000000 327s supply_(Intercept) -0.227988 327s supply_price 0.000426 327s supply_farmPrice 0.001074 327s supply_trend 0.007766 327s > print( round( vcov( fitols1rs$eq[[ 2 ]] ), digits = 6 ) ) 327s (Intercept) price farmPrice trend 327s (Intercept) 107.303 -0.806417 -0.248549 -0.227988 327s price -0.806 0.007352 0.000689 0.000426 327s farmPrice -0.249 0.000689 0.001742 0.001074 327s trend -0.228 0.000426 0.001074 0.007766 327s > 327s > print( round( vcov( fitols2s ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income 327s demand_(Intercept) 57.21413 -0.596328 0.026850 327s demand_price -0.59633 0.007862 -0.001948 327s demand_income 0.02685 -0.001948 0.001722 327s supply_(Intercept) -0.78825 0.057190 -0.050565 327s supply_price 0.00147 -0.000107 0.000095 327s supply_farmPrice 0.00371 -0.000269 0.000238 327s supply_trend 0.02685 -0.001948 0.001722 327s supply_(Intercept) supply_price supply_farmPrice 327s demand_(Intercept) -0.7883 0.001474 0.003714 327s demand_price 0.0572 -0.000107 -0.000269 327s demand_income -0.0506 0.000095 0.000238 327s supply_(Intercept) 128.0635 -1.001596 -0.280017 327s supply_price -1.0016 0.009225 0.000806 327s supply_farmPrice -0.2800 0.000806 0.002038 327s supply_trend -0.0506 0.000095 0.000238 327s supply_trend 327s demand_(Intercept) 0.026850 327s demand_price -0.001948 327s demand_income 0.001722 327s supply_(Intercept) -0.050565 327s supply_price 0.000095 327s supply_farmPrice 0.000238 327s supply_trend 0.001722 327s > print( round( vcov( fitols2s$eq[[ 1 ]] ), digits = 6 ) ) 327s (Intercept) price income 327s (Intercept) 57.2141 -0.59633 0.02685 327s price -0.5963 0.00786 -0.00195 327s income 0.0268 -0.00195 0.00172 327s > 327s > print( round( vcov( fitols3 ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income 327s demand_(Intercept) 70.93892 -0.736413 0.030252 327s demand_price -0.73641 0.009503 -0.002195 327s demand_income 0.03025 -0.002195 0.001941 327s supply_(Intercept) -0.88813 0.064436 -0.056972 327s supply_price 0.00166 -0.000120 0.000107 327s supply_farmPrice 0.00419 -0.000304 0.000268 327s supply_trend 0.03025 -0.002195 0.001941 327s supply_(Intercept) supply_price supply_farmPrice 327s demand_(Intercept) -0.8881 0.001661 0.004185 327s demand_price 0.0644 -0.000120 -0.000304 327s demand_income -0.0570 0.000107 0.000268 327s supply_(Intercept) 101.4478 -0.790443 -0.223090 327s supply_price -0.7904 0.007274 0.000640 327s supply_farmPrice -0.2231 0.000640 0.001617 327s supply_trend -0.0570 0.000107 0.000268 327s supply_trend 327s demand_(Intercept) 0.030252 327s demand_price -0.002195 327s demand_income 0.001941 327s supply_(Intercept) -0.056972 327s supply_price 0.000107 327s supply_farmPrice 0.000268 327s supply_trend 0.001941 327s > print( round( vcov( fitols3, modified.regMat = TRUE ), digits = 6 ) ) 327s C1 C2 C3 C4 C5 C6 327s C1 70.93892 -0.736413 0.030252 -0.8881 0.001661 0.004185 327s C2 -0.73641 0.009503 -0.002195 0.0644 -0.000120 -0.000304 327s C3 0.03025 -0.002195 0.001941 -0.0570 0.000107 0.000268 327s C4 -0.88813 0.064436 -0.056972 101.4478 -0.790443 -0.223090 327s C5 0.00166 -0.000120 0.000107 -0.7904 0.007274 0.000640 327s C6 0.00419 -0.000304 0.000268 -0.2231 0.000640 0.001617 327s > print( round( vcov( fitols3$eq[[ 2 ]] ), digits = 6 ) ) 327s (Intercept) price farmPrice trend 327s (Intercept) 101.448 -0.790443 -0.223090 -0.056972 327s price -0.790 0.007274 0.000640 0.000107 327s farmPrice -0.223 0.000640 0.001617 0.000268 327s trend -0.057 0.000107 0.000268 0.001941 327s > 327s > print( round( vcov( fitols4r ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income 327s demand_(Intercept) 33.2016 -0.272100 -0.059329 327s demand_price -0.2721 0.003464 -0.000762 327s demand_income -0.0593 -0.000762 0.001390 327s supply_(Intercept) 30.8652 -0.357363 0.050012 327s supply_price -0.2721 0.003464 -0.000762 327s supply_farmPrice -0.0313 0.000196 0.000120 327s supply_trend -0.0593 -0.000762 0.001390 327s supply_(Intercept) supply_price supply_farmPrice 327s demand_(Intercept) 30.865 -0.272100 -0.031328 327s demand_price -0.357 0.003464 0.000196 327s demand_income 0.050 -0.000762 0.000120 327s supply_(Intercept) 49.897 -0.357363 -0.149852 327s supply_price -0.357 0.003464 0.000196 327s supply_farmPrice -0.150 0.000196 0.001335 327s supply_trend 0.050 -0.000762 0.000120 327s supply_trend 327s demand_(Intercept) -0.059329 327s demand_price -0.000762 327s demand_income 0.001390 327s supply_(Intercept) 0.050012 327s supply_price -0.000762 327s supply_farmPrice 0.000120 327s supply_trend 0.001390 327s > print( round( vcov( fitols4r$eq[[ 1 ]] ), digits = 6 ) ) 327s (Intercept) price income 327s (Intercept) 33.2016 -0.272100 -0.059329 327s price -0.2721 0.003464 -0.000762 327s income -0.0593 -0.000762 0.001390 327s > 327s > print( round( vcov( fitols5 ), digits = 6 ) ) 327s demand_(Intercept) demand_price demand_income 327s demand_(Intercept) 33.2016 -0.272100 -0.059329 327s demand_price -0.2721 0.003464 -0.000762 327s demand_income -0.0593 -0.000762 0.001390 327s supply_(Intercept) 30.8652 -0.357363 0.050012 327s supply_price -0.2721 0.003464 -0.000762 327s supply_farmPrice -0.0313 0.000196 0.000120 327s supply_trend -0.0593 -0.000762 0.001390 327s supply_(Intercept) supply_price supply_farmPrice 327s demand_(Intercept) 30.865 -0.272100 -0.031328 327s demand_price -0.357 0.003464 0.000196 327s demand_income 0.050 -0.000762 0.000120 327s supply_(Intercept) 49.897 -0.357363 -0.149852 327s supply_price -0.357 0.003464 0.000196 327s supply_farmPrice -0.150 0.000196 0.001335 327s supply_trend 0.050 -0.000762 0.000120 327s supply_trend 327s demand_(Intercept) -0.059329 327s demand_price -0.000762 327s demand_income 0.001390 327s supply_(Intercept) 0.050012 327s supply_price -0.000762 327s supply_farmPrice 0.000120 327s supply_trend 0.001390 327s > print( round( vcov( fitols5, modified.regMat = TRUE ), digits = 6 ) ) 327s C1 C2 C3 C4 C5 C6 327s C1 33.2016 -0.272100 -0.059329 30.865 -0.272100 -0.031328 327s C2 -0.2721 0.003464 -0.000762 -0.357 0.003464 0.000196 327s C3 -0.0593 -0.000762 0.001390 0.050 -0.000762 0.000120 327s C4 30.8652 -0.357363 0.050012 49.897 -0.357363 -0.149852 327s C5 -0.2721 0.003464 -0.000762 -0.357 0.003464 0.000196 327s C6 -0.0313 0.000196 0.000120 -0.150 0.000196 0.001335 327s > print( round( vcov( fitols5$eq[[ 2 ]] ), digits = 6 ) ) 327s (Intercept) price farmPrice trend 327s (Intercept) 49.897 -0.357363 -0.149852 0.050012 327s price -0.357 0.003464 0.000196 -0.000762 327s farmPrice -0.150 0.000196 0.001335 0.000120 327s trend 0.050 -0.000762 0.000120 0.001390 327s > 327s > 327s > ## *********** confidence intervals of coefficients ************* 327s > print( confint( fitols1, useDfSys = TRUE ) ) 327s 2.5 % 97.5 % 327s demand_(Intercept) 84.597 115.194 327s demand_price -0.501 -0.132 327s demand_income 0.242 0.427 327s supply_(Intercept) 34.954 81.597 327s supply_price -0.033 0.353 327s supply_farmPrice 0.154 0.342 327s supply_trend 0.050 0.447 327s > print( confint( fitols1$eq[[ 2 ]], level = 0.9, useDfSys = TRUE ) ) 327s 5 % 95 % 327s (Intercept) 38.876 77.675 327s price 0.000 0.321 327s farmPrice 0.170 0.326 327s trend 0.083 0.413 327s > 327s > print( confint( fitols2r, level = 0.9 ) ) 327s 5 % 95 % 327s demand_(Intercept) 83.776 115.337 327s demand_price -0.474 -0.109 327s demand_income 0.230 0.395 327s supply_(Intercept) 37.508 75.251 327s supply_price 0.004 0.324 327s supply_farmPrice 0.182 0.332 327s supply_trend 0.230 0.395 327s > print( confint( fitols2r$eq[[ 1 ]], level = 0.99 ) ) 327s 0.5 % 99.5 % 327s (Intercept) 78.370 120.743 327s price -0.537 -0.046 327s income 0.202 0.424 327s > 327s > print( confint( fitols3s, level = 0.99 ) ) 327s 0.5 % 99.5 % 327s demand_(Intercept) 84.184 114.928 327s demand_price -0.472 -0.112 327s demand_income 0.229 0.397 327s supply_(Intercept) 33.382 79.377 327s supply_price -0.031 0.359 327s supply_farmPrice 0.165 0.349 327s supply_trend 0.229 0.397 327s > print( confint( fitols3s$eq[[ 2 ]], level = 0.5 ) ) 327s 25 % 75 % 327s (Intercept) 48.664 64.095 327s price 0.098 0.229 327s farmPrice 0.226 0.288 327s trend 0.285 0.341 327s > 327s > print( confint( fitols4rs, level = 0.5 ) ) 327s 25 % 75 % 327s demand_(Intercept) 90.269 112.695 327s demand_price -0.436 -0.197 327s demand_income 0.247 0.390 327s supply_(Intercept) 39.515 68.784 327s supply_price 0.064 0.303 327s supply_farmPrice 0.179 0.340 327s supply_trend 0.247 0.390 327s > print( confint( fitols4rs$eq[[ 1 ]], level = 0.25 ) ) 327s 37.5 % 62.5 % 327s (Intercept) 99.708 103.256 327s price -0.336 -0.298 327s income 0.308 0.330 327s > 327s > print( confint( fitols5, level = 0.25 ) ) 327s 37.5 % 62.5 % 327s demand_(Intercept) 89.784 113.179 327s demand_price -0.436 -0.197 327s demand_income 0.243 0.395 327s supply_(Intercept) 39.809 68.490 327s supply_price 0.064 0.303 327s supply_farmPrice 0.185 0.334 327s supply_trend 0.243 0.395 327s > print( confint( fitols5$eq[[ 2 ]], level = 0.999 ) ) 327s 0.1 % 100 % 327s (Intercept) 28.782 79.517 327s price -0.028 0.395 327s farmPrice 0.128 0.391 327s trend 0.185 0.453 327s > 327s > print( confint( fitols3, level = 0.999, useDfSys = FALSE ) ) 327s 0.1 % 100 % 327s demand_(Intercept) 81.786 117.326 327s demand_price -0.497 -0.086 327s demand_income 0.220 0.406 327s supply_(Intercept) 35.028 77.731 327s supply_price -0.017 0.345 327s supply_farmPrice 0.172 0.342 327s supply_trend 0.219 0.406 327s > print( confint( fitols3$eq[[ 1 ]], useDfSys = FALSE ) ) 327s 2.5 % 97.5 % 327s (Intercept) 81.786 117.326 327s price -0.497 -0.086 327s income 0.220 0.406 327s > 327s > 327s > ## *********** fitted values ************* 327s > print( fitted( fitols1 ) ) 327s demand supply 327s 1 97.4 98.9 327s 2 99.6 100.1 327s 3 99.5 100.2 327s 4 99.7 100.4 327s 5 102.3 102.7 327s 6 102.1 102.6 327s 7 102.5 102.4 327s 8 102.8 104.3 327s 9 101.7 102.9 327s 10 100.8 100.4 327s 11 95.6 96.0 327s 12 94.4 94.1 327s 13 95.7 95.6 327s 14 99.0 97.8 327s 15 104.3 102.6 327s 16 103.9 104.1 327s 17 104.8 103.8 327s 18 101.9 102.4 327s 19 103.5 102.1 327s 20 106.5 104.5 327s > print( fitted( fitols1$eq[[ 2 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 11 12 13 327s 98.9 100.1 100.2 100.4 102.7 102.6 102.4 104.3 102.9 100.4 96.0 94.1 95.6 327s 14 15 16 17 18 19 20 327s 97.8 102.6 104.1 103.8 102.4 102.1 104.5 327s > 327s > print( fitted( fitols2r ) ) 327s demand supply 327s 1 97.6 98.3 327s 2 99.7 99.6 327s 3 99.6 99.7 327s 4 99.8 100.0 327s 5 102.2 102.5 327s 6 102.0 102.4 327s 7 102.4 102.3 327s 8 102.7 104.3 327s 9 101.6 102.9 327s 10 100.8 100.3 327s 11 95.9 95.9 327s 12 94.8 94.0 327s 13 96.0 95.5 327s 14 99.1 97.9 327s 15 104.1 103.0 327s 16 103.7 104.5 327s 17 104.5 104.3 327s 18 101.9 102.8 327s 19 103.3 102.6 327s 20 106.2 105.1 327s > print( fitted( fitols2r$eq[[ 1 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 11 12 13 327s 97.6 99.7 99.6 99.8 102.2 102.0 102.4 102.7 101.6 100.8 95.9 94.8 96.0 327s 14 15 16 17 18 19 20 327s 99.1 104.1 103.7 104.5 101.9 103.3 106.2 327s > 327s > print( fitted( fitols3s ) ) 327s demand supply 327s 1 97.6 98.3 327s 2 99.7 99.6 327s 3 99.6 99.7 327s 4 99.8 100.0 327s 5 102.2 102.5 327s 6 102.0 102.4 327s 7 102.4 102.3 327s 8 102.7 104.3 327s 9 101.6 102.9 327s 10 100.8 100.3 327s 11 95.9 95.9 327s 12 94.8 94.0 327s 13 96.0 95.5 327s 14 99.1 97.9 327s 15 104.1 103.0 327s 16 103.7 104.5 327s 17 104.5 104.3 327s 18 101.9 102.8 327s 19 103.3 102.6 327s 20 106.2 105.1 327s > print( fitted( fitols3s$eq[[ 2 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 11 12 13 327s 98.3 99.6 99.7 100.0 102.5 102.4 102.3 104.3 102.9 100.3 95.9 94.0 95.5 327s 14 15 16 17 18 19 20 327s 97.9 103.0 104.5 104.3 102.8 102.6 105.1 327s > 327s > print( fitted( fitols4rs ) ) 327s demand supply 327s 1 97.6 98.3 327s 2 99.6 99.6 327s 3 99.5 99.8 327s 4 99.7 100.0 327s 5 102.3 102.5 327s 6 102.0 102.4 327s 7 102.4 102.3 327s 8 102.7 104.4 327s 9 101.7 102.9 327s 10 100.9 100.2 327s 11 95.9 95.7 327s 12 94.7 93.9 327s 13 95.9 95.5 327s 14 99.1 97.8 327s 15 104.2 102.9 327s 16 103.8 104.5 327s 17 104.8 104.1 327s 18 101.8 103.0 327s 19 103.3 102.8 327s 20 106.1 105.5 327s > print( fitted( fitols4rs$eq[[ 1 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 11 12 13 327s 97.6 99.6 99.5 99.7 102.3 102.0 102.4 102.7 101.7 100.9 95.9 94.7 95.9 327s 14 15 16 17 18 19 20 327s 99.1 104.2 103.8 104.8 101.8 103.3 106.1 327s > 327s > print( fitted( fitols5 ) ) 327s demand supply 327s 1 97.6 98.3 327s 2 99.6 99.6 327s 3 99.5 99.8 327s 4 99.7 100.0 327s 5 102.3 102.5 327s 6 102.0 102.4 327s 7 102.4 102.3 327s 8 102.7 104.4 327s 9 101.7 102.9 327s 10 100.9 100.2 327s 11 95.9 95.7 327s 12 94.7 93.9 327s 13 95.9 95.5 327s 14 99.1 97.8 327s 15 104.2 102.9 327s 16 103.8 104.5 327s 17 104.8 104.1 327s 18 101.8 103.0 327s 19 103.3 102.8 327s 20 106.1 105.5 327s > print( fitted( fitols5$eq[[ 2 ]] ) ) 327s 1 2 3 4 5 6 7 8 9 10 11 12 13 327s 98.3 99.6 99.8 100.0 102.5 102.4 102.3 104.4 102.9 100.2 95.7 93.9 95.5 327s 14 15 16 17 18 19 20 327s 97.8 102.9 104.5 104.1 103.0 102.8 105.5 327s > 327s > 327s > ## *********** predicted values ************* 327s > predictData <- Kmenta 327s > predictData$consump <- NULL 327s > predictData$price <- Kmenta$price * 0.9 327s > predictData$income <- Kmenta$income * 1.1 327s > 327s > print( predict( fitols1, se.fit = TRUE, interval = "prediction", 327s + useDfSys = TRUE ) ) 327s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 327s 1 97.4 0.643 93.3 101.5 98.9 1.056 327s 2 99.6 0.577 95.5 103.7 100.1 1.037 327s 3 99.5 0.545 95.5 103.6 100.2 0.939 327s 4 99.7 0.582 95.6 103.8 100.4 0.912 327s 5 102.3 0.502 98.2 106.4 102.7 0.895 327s 6 102.1 0.463 98.0 106.1 102.6 0.791 327s 7 102.5 0.484 98.4 106.5 102.4 0.719 327s 8 102.8 0.601 98.7 106.9 104.3 0.963 327s 9 101.7 0.527 97.6 105.8 102.9 0.788 327s 10 100.8 0.788 96.5 105.0 100.4 0.981 327s 11 95.6 0.946 91.2 100.0 96.0 1.185 327s 12 94.4 0.980 90.0 98.8 94.1 1.394 327s 13 95.7 0.880 91.3 100.0 95.6 1.244 327s 14 99.0 0.508 94.9 103.0 97.8 0.896 327s 15 104.3 0.758 100.1 108.5 102.6 0.874 327s 16 103.9 0.616 99.8 108.0 104.1 0.916 327s 17 104.8 1.273 100.1 109.5 103.8 1.605 327s 18 101.9 0.536 97.9 106.0 102.4 0.962 327s 19 103.5 0.680 99.3 107.6 102.1 1.098 327s 20 106.5 1.274 101.8 111.2 104.5 1.664 327s supply.lwr supply.upr 327s 1 93.6 104.3 327s 2 94.8 105.4 327s 3 94.9 105.5 327s 4 95.1 105.6 327s 5 97.5 107.9 327s 6 97.4 107.7 327s 7 97.3 107.5 327s 8 99.0 109.6 327s 9 97.8 108.1 327s 10 95.1 105.6 327s 11 90.6 101.5 327s 12 88.5 99.8 327s 13 90.1 101.1 327s 14 92.6 103.0 327s 15 97.4 107.8 327s 16 98.9 109.3 327s 17 97.9 109.7 327s 18 97.1 107.6 327s 19 96.7 107.5 327s 20 98.6 110.5 327s > print( predict( fitols1$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 327s + useDfSys = TRUE ) ) 327s fit se.fit lwr upr 327s 1 98.9 1.056 93.6 104.3 327s 2 100.1 1.037 94.8 105.4 327s 3 100.2 0.939 94.9 105.5 327s 4 100.4 0.912 95.1 105.6 327s 5 102.7 0.895 97.5 107.9 327s 6 102.6 0.791 97.4 107.7 327s 7 102.4 0.719 97.3 107.5 327s 8 104.3 0.963 99.0 109.6 327s 9 102.9 0.788 97.8 108.1 327s 10 100.4 0.981 95.1 105.6 327s 11 96.0 1.185 90.6 101.5 327s 12 94.1 1.394 88.5 99.8 327s 13 95.6 1.244 90.1 101.1 327s 14 97.8 0.896 92.6 103.0 327s 15 102.6 0.874 97.4 107.8 327s 16 104.1 0.916 98.9 109.3 327s 17 103.8 1.605 97.9 109.7 327s 18 102.4 0.962 97.1 107.6 327s 19 102.1 1.098 96.7 107.5 327s 20 104.5 1.664 98.6 110.5 327s > 327s > print( predict( fitols2r, se.pred = TRUE, interval = "confidence", 327s + level = 0.999, newdata = predictData ) ) 327s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 327s 1 103 2.17 99.9 107 96.7 2.62 327s 2 106 2.16 102.4 109 97.9 2.55 327s 3 106 2.17 102.2 109 98.1 2.55 327s 4 106 2.16 102.5 109 98.3 2.54 327s 5 108 2.43 102.9 113 100.9 2.67 327s 6 108 2.38 103.1 113 100.7 2.63 327s 7 109 2.37 103.7 113 100.6 2.59 327s 8 109 2.33 104.5 114 102.6 2.55 327s 9 107 2.44 102.2 113 101.4 2.69 327s 10 106 2.57 100.2 112 98.8 2.84 327s 11 101 2.36 96.1 106 94.4 2.89 327s 12 100 2.17 96.6 104 92.3 2.88 327s 13 102 2.08 99.0 104 93.9 2.75 327s 14 105 2.25 100.7 109 96.3 2.72 327s 15 110 2.63 103.7 116 101.4 2.72 327s 16 110 2.52 104.1 116 102.9 2.65 327s 17 110 2.96 102.0 118 102.9 3.03 327s 18 108 2.28 103.9 112 101.1 2.55 327s 19 110 2.36 105.1 115 100.9 2.55 327s 20 114 2.57 107.4 120 103.3 2.51 327s supply.lwr supply.upr 327s 1 93.2 100.2 327s 2 95.2 100.5 327s 3 95.3 100.8 327s 4 95.8 100.8 327s 5 97.0 104.8 327s 6 97.2 104.3 327s 7 97.5 103.7 327s 8 99.9 105.2 327s 9 97.3 105.5 327s 10 93.6 104.1 327s 11 88.8 100.0 327s 12 86.8 97.9 327s 13 89.3 98.5 327s 14 91.9 100.6 327s 15 97.0 105.8 327s 16 99.2 106.6 327s 17 96.4 109.4 327s 18 98.4 103.9 327s 19 98.2 103.5 327s 20 101.1 105.5 327s > print( predict( fitols2r$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 327s + level = 0.999, newdata = predictData ) ) 327s fit se.pred lwr upr 327s 1 103 2.17 99.9 107 327s 2 106 2.16 102.4 109 327s 3 106 2.17 102.2 109 327s 4 106 2.16 102.5 109 327s 5 108 2.43 102.9 113 327s 6 108 2.38 103.1 113 327s 7 109 2.37 103.7 113 327s 8 109 2.33 104.5 114 327s 9 107 2.44 102.2 113 327s 10 106 2.57 100.2 112 327s 11 101 2.36 96.1 106 327s 12 100 2.17 96.6 104 327s 13 102 2.08 99.0 104 327s 14 105 2.25 100.7 109 327s 15 110 2.63 103.7 116 327s 16 110 2.52 104.1 116 327s 17 110 2.96 102.0 118 327s 18 108 2.28 103.9 112 327s 19 110 2.36 105.1 115 327s 20 114 2.57 107.4 120 327s > 327s > print( predict( fitols3s, se.fit = TRUE, se.pred = TRUE, 327s + interval = "prediction", level = 0.5, newdata = predictData ) ) 327s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 327s 1 103 0.940 2.16 101.8 105 96.7 327s 2 106 0.944 2.16 104.3 107 97.9 327s 3 106 0.969 2.17 104.2 107 98.1 327s 4 106 0.949 2.16 104.4 107 98.3 327s 5 108 1.452 2.43 106.5 110 100.9 327s 6 108 1.372 2.38 106.4 110 100.7 327s 7 109 1.356 2.37 106.9 110 100.6 327s 8 109 1.296 2.34 107.6 111 102.6 327s 9 107 1.464 2.43 105.8 109 101.4 327s 10 106 1.652 2.55 104.5 108 98.8 327s 11 101 1.305 2.34 99.4 103 94.4 327s 12 100 0.941 2.16 98.6 102 92.3 327s 13 102 0.725 2.07 100.2 103 93.9 327s 14 105 1.124 2.24 103.3 106 96.3 327s 15 110 1.774 2.63 108.3 112 101.4 327s 16 110 1.606 2.52 108.2 112 102.9 327s 17 110 2.216 2.95 108.0 112 102.9 327s 18 108 1.208 2.29 106.6 110 101.1 327s 19 110 1.356 2.37 108.3 112 100.9 327s 20 114 1.718 2.59 111.7 115 103.3 327s supply.se.fit supply.se.pred supply.lwr supply.upr 327s 1 1.149 2.69 94.8 98.5 327s 2 0.873 2.59 96.1 99.6 327s 3 0.907 2.60 96.3 99.8 327s 4 0.831 2.58 96.5 100.0 327s 5 1.324 2.77 99.0 102.8 327s 6 1.188 2.71 98.9 102.6 327s 7 1.049 2.65 98.8 102.4 327s 8 0.911 2.60 100.8 104.3 327s 9 1.396 2.81 99.5 103.3 327s 10 1.782 3.02 96.8 100.9 327s 11 1.906 3.09 92.3 96.5 327s 12 1.875 3.08 90.2 94.4 327s 13 1.560 2.89 91.9 95.8 327s 14 1.475 2.85 94.3 98.2 327s 15 1.477 2.85 99.5 103.3 327s 16 1.245 2.74 101.0 104.8 327s 17 2.195 3.28 100.6 105.1 327s 18 0.909 2.60 99.4 102.9 327s 19 0.875 2.59 99.1 102.6 327s 20 0.704 2.54 101.6 105.0 327s > print( predict( fitols3s$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 327s + interval = "prediction", level = 0.5, newdata = predictData ) ) 327s fit se.fit se.pred lwr upr 327s 1 96.7 1.149 2.69 94.8 98.5 327s 2 97.9 0.873 2.59 96.1 99.6 327s 3 98.1 0.907 2.60 96.3 99.8 327s 4 98.3 0.831 2.58 96.5 100.0 327s 5 100.9 1.324 2.77 99.0 102.8 327s 6 100.7 1.188 2.71 98.9 102.6 327s 7 100.6 1.049 2.65 98.8 102.4 327s 8 102.6 0.911 2.60 100.8 104.3 327s 9 101.4 1.396 2.81 99.5 103.3 327s 10 98.8 1.782 3.02 96.8 100.9 327s 11 94.4 1.906 3.09 92.3 96.5 327s 12 92.3 1.875 3.08 90.2 94.4 327s 13 93.9 1.560 2.89 91.9 95.8 327s 14 96.3 1.475 2.85 94.3 98.2 327s 15 101.4 1.477 2.85 99.5 103.3 327s 16 102.9 1.245 2.74 101.0 104.8 327s 17 102.9 2.195 3.28 100.6 105.1 327s 18 101.1 0.909 2.60 99.4 102.9 327s 19 100.9 0.875 2.59 99.1 102.6 327s 20 103.3 0.704 2.54 101.6 105.0 327s > 327s > print( predict( fitols4rs, se.fit = TRUE, se.pred = TRUE, 327s + interval = "confidence", level = 0.99 ) ) 327s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 327s 1 97.6 0.541 2.01 96.1 99.0 98.3 327s 2 99.6 0.471 2.00 98.3 100.9 99.6 327s 3 99.5 0.454 1.99 98.3 100.8 99.8 327s 4 99.7 0.475 2.00 98.4 101.0 100.0 327s 5 102.3 0.434 1.99 101.1 103.4 102.5 327s 6 102.0 0.418 1.98 100.9 103.2 102.4 327s 7 102.4 0.440 1.99 101.2 103.6 102.3 327s 8 102.7 0.537 2.01 101.2 104.1 104.4 327s 9 101.7 0.447 1.99 100.5 102.9 102.9 327s 10 100.9 0.628 2.04 99.2 102.6 100.2 327s 11 95.9 0.833 2.11 93.7 98.2 95.7 327s 12 94.7 0.807 2.10 92.5 96.9 93.9 327s 13 95.9 0.677 2.06 94.0 97.7 95.5 327s 14 99.1 0.459 1.99 97.8 100.3 97.8 327s 15 104.2 0.572 2.02 102.7 105.8 102.9 327s 16 103.8 0.509 2.01 102.4 105.2 104.5 327s 17 104.8 0.877 2.13 102.4 107.2 104.1 327s 18 101.8 0.478 2.00 100.5 103.1 103.0 327s 19 103.3 0.604 2.03 101.6 104.9 102.8 327s 20 106.1 1.102 2.23 103.1 109.1 105.5 327s supply.se.fit supply.se.pred supply.lwr supply.upr 327s 1 0.598 2.52 96.7 99.9 327s 2 0.679 2.54 97.8 101.5 327s 3 0.634 2.53 98.0 101.5 327s 4 0.643 2.53 98.3 101.8 327s 5 0.753 2.56 100.4 104.5 327s 6 0.680 2.54 100.5 104.2 327s 7 0.625 2.53 100.6 104.0 327s 8 0.799 2.57 102.2 106.6 327s 9 0.700 2.55 101.0 104.8 327s 10 0.716 2.55 98.2 102.1 327s 11 0.916 2.61 93.2 98.2 327s 12 1.226 2.74 90.5 97.2 327s 13 1.130 2.70 92.5 98.6 327s 14 0.796 2.57 95.7 100.0 327s 15 0.656 2.53 101.1 104.7 327s 16 0.644 2.53 102.8 106.3 327s 17 1.150 2.70 101.0 107.2 327s 18 0.575 2.51 101.4 104.5 327s 19 0.649 2.53 101.0 104.5 327s 20 0.875 2.60 103.1 107.8 327s > print( predict( fitols4rs$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 327s + interval = "confidence", level = 0.99 ) ) 327s fit se.fit se.pred lwr upr 327s 1 97.6 0.541 2.01 96.1 99.0 327s 2 99.6 0.471 2.00 98.3 100.9 327s 3 99.5 0.454 1.99 98.3 100.8 327s 4 99.7 0.475 2.00 98.4 101.0 327s 5 102.3 0.434 1.99 101.1 103.4 327s 6 102.0 0.418 1.98 100.9 103.2 327s 7 102.4 0.440 1.99 101.2 103.6 327s 8 102.7 0.537 2.01 101.2 104.1 327s 9 101.7 0.447 1.99 100.5 102.9 327s 10 100.9 0.628 2.04 99.2 102.6 327s 11 95.9 0.833 2.11 93.7 98.2 327s 12 94.7 0.807 2.10 92.5 96.9 327s 13 95.9 0.677 2.06 94.0 97.7 327s 14 99.1 0.459 1.99 97.8 100.3 327s 15 104.2 0.572 2.02 102.7 105.8 327s 16 103.8 0.509 2.01 102.4 105.2 327s 17 104.8 0.877 2.13 102.4 107.2 327s 18 101.8 0.478 2.00 100.5 103.1 327s 19 103.3 0.604 2.03 101.6 104.9 327s 20 106.1 1.102 2.23 103.1 109.1 327s > 327s > print( predict( fitols5, se.fit = TRUE, interval = "prediction", 327s + level = 0.9, newdata = predictData ) ) 327s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 327s 1 104 0.714 100.0 107 96.4 0.712 327s 2 106 0.748 102.5 110 97.7 0.591 327s 3 106 0.753 102.4 109 97.9 0.602 327s 4 106 0.756 102.6 110 98.1 0.565 327s 5 109 1.055 104.8 112 100.7 0.900 327s 6 108 1.013 104.7 112 100.5 0.811 327s 7 109 1.029 105.2 113 100.5 0.722 327s 8 109 1.055 105.7 113 102.5 0.703 327s 9 108 1.042 104.1 112 101.1 0.952 327s 10 107 1.148 102.8 110 98.5 1.136 327s 11 101 1.026 97.6 105 94.0 1.245 327s 12 100 0.800 96.7 104 92.1 1.347 327s 13 102 0.606 98.4 105 93.7 1.170 327s 14 105 0.820 101.5 109 96.0 1.034 327s 15 111 1.272 106.6 114 101.2 1.031 327s 16 110 1.191 106.4 114 102.7 0.925 327s 17 111 1.513 106.5 115 102.5 1.529 327s 18 108 0.963 104.8 112 101.0 0.720 327s 19 110 1.129 106.4 114 100.8 0.717 327s 20 114 1.601 109.5 118 103.4 0.562 327s supply.lwr supply.upr 327s 1 92.1 100.7 327s 2 93.4 102.0 327s 3 93.6 102.1 327s 4 93.9 102.4 327s 5 96.3 105.1 327s 6 96.2 104.9 327s 7 96.1 104.8 327s 8 98.2 106.8 327s 9 96.7 105.6 327s 10 93.9 103.0 327s 11 89.4 98.7 327s 12 87.4 96.8 327s 13 89.1 98.2 327s 14 91.5 100.5 327s 15 96.7 105.7 327s 16 98.3 107.2 327s 17 97.6 107.4 327s 18 96.7 105.4 327s 19 96.5 105.1 327s 20 99.1 107.6 327s > print( predict( fitols5$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 327s + level = 0.9, newdata = predictData ) ) 327s fit se.fit lwr upr 327s 1 96.4 0.712 92.1 100.7 327s 2 97.7 0.591 93.4 102.0 327s 3 97.9 0.602 93.6 102.1 327s 4 98.1 0.565 93.9 102.4 327s 5 100.7 0.900 96.3 105.1 327s 6 100.5 0.811 96.2 104.9 327s 7 100.5 0.722 96.1 104.8 327s 8 102.5 0.703 98.2 106.8 327s 9 101.1 0.952 96.7 105.6 327s 10 98.5 1.136 93.9 103.0 327s 11 94.0 1.245 89.4 98.7 327s 12 92.1 1.347 87.4 96.8 327s 13 93.7 1.170 89.1 98.2 327s 14 96.0 1.034 91.5 100.5 327s 15 101.2 1.031 96.7 105.7 327s 16 102.7 0.925 98.3 107.2 327s 17 102.5 1.529 97.6 107.4 327s 18 101.0 0.720 96.7 105.4 327s 19 100.8 0.717 96.5 105.1 327s 20 103.4 0.562 99.1 107.6 327s > 327s > # predict just one observation 327s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 327s + trend = 25 ) 327s > 327s > print( predict( fitols1, newdata = smallData ) ) 327s demand.pred supply.pred 327s 1 109 115 327s > print( predict( fitols1$eq[[ 1 ]], newdata = smallData ) ) 327s fit 327s 1 109 327s > 327s > print( predict( fitols2r, se.fit = TRUE, level = 0.9, 327s + newdata = smallData ) ) 327s demand.pred demand.se.fit supply.pred supply.se.fit 327s 1 109 2.48 116 2.8 327s > print( predict( fitols2r$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 327s + newdata = smallData ) ) 327s fit se.pred 327s 1 109 3.15 327s > 327s > print( predict( fitols3s, interval = "prediction", level = 0.975, 327s + newdata = smallData ) ) 327s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 327s 1 109 101 116 116 107 126 327s > print( predict( fitols3s$eq[[ 1 ]], interval = "confidence", level = 0.8, 327s + newdata = smallData ) ) 327s fit lwr upr 327s 1 109 105 112 327s > 327s > print( predict( fitols4rs, se.fit = TRUE, interval = "confidence", 327s + level = 0.999, newdata = smallData ) ) 327s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 327s 1 108 2.02 101 115 117 2.02 327s supply.lwr supply.upr 327s 1 110 124 327s > print( predict( fitols4rs$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 327s + level = 0.75, newdata = smallData ) ) 327s fit se.pred lwr upr 327s 1 117 3.18 113 121 327s > 327s > print( predict( fitols5, se.fit = TRUE, interval = "prediction", 327s + newdata = smallData ) ) 327s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 327s 1 108 2.18 102 114 117 2.01 327s supply.lwr supply.upr 327s 1 111 124 327s > print( predict( fitols5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 327s + newdata = smallData ) ) 327s fit se.pred lwr upr 327s 1 108 2.92 104 113 327s > 327s > print( predict( fitols5rs, se.fit = TRUE, se.pred = TRUE, 327s + interval = "prediction", level = 0.5, newdata = smallData ) ) 327s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 327s 1 108 2.02 2.8 106 110 117 327s supply.se.fit supply.se.pred supply.lwr supply.upr 327s 1 2.02 3.18 115 119 327s > print( predict( fitols5rs$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 327s + interval = "confidence", level = 0.25, newdata = smallData ) ) 327s fit se.fit se.pred lwr upr 327s 1 108 2.02 2.8 107 109 327s > 327s > 327s > ## ************ correlation of predicted values *************** 327s > print( correlation.systemfit( fitols1, 1, 2 ) ) 327s [,1] 327s [1,] 0 327s [2,] 0 327s [3,] 0 327s [4,] 0 327s [5,] 0 327s [6,] 0 327s [7,] 0 327s [8,] 0 327s [9,] 0 327s [10,] 0 327s [11,] 0 327s [12,] 0 327s [13,] 0 327s [14,] 0 327s [15,] 0 327s [16,] 0 327s [17,] 0 327s [18,] 0 327s [19,] 0 327s [20,] 0 327s > 327s > print( correlation.systemfit( fitols2r, 2, 1 ) ) 327s [,1] 327s [1,] 0.443122 327s [2,] 0.160426 327s [3,] 0.161091 327s [4,] 0.118312 327s [5,] -0.077411 327s [6,] -0.059235 327s [7,] -0.057777 327s [8,] -0.006908 327s [9,] -0.000372 327s [10,] -0.001410 327s [11,] 0.055233 327s [12,] 0.074936 327s [13,] 0.028274 327s [14,] -0.032082 327s [15,] 0.196029 327s [16,] 0.279921 327s [17,] 0.115570 327s [18,] 0.080620 327s [19,] 0.171681 327s [20,] 0.150544 327s > 327s > print( correlation.systemfit( fitols3s, 1, 2 ) ) 327s [,1] 327s [1,] 0.405901 327s [2,] 0.145364 327s [3,] 0.145375 327s [4,] 0.105835 327s [5,] -0.067958 327s [6,] -0.052026 327s [7,] -0.050543 327s [8,] -0.006031 327s [9,] -0.000326 327s [10,] -0.001237 327s [11,] 0.047534 327s [12,] 0.063493 327s [13,] 0.024060 327s [14,] -0.027910 327s [15,] 0.171580 327s [16,] 0.248212 327s [17,] 0.101409 327s [18,] 0.073084 327s [19,] 0.153950 327s [20,] 0.132944 327s > 327s > print( correlation.systemfit( fitols4rs, 2, 1 ) ) 327s [,1] 327s [1,] 0.38162 327s [2,] 0.29173 327s [3,] 0.25421 327s [4,] 0.28598 327s [5,] -0.02775 327s [6,] -0.04974 327s [7,] -0.05850 327s [8,] 0.09388 327s [9,] 0.09469 327s [10,] 0.43814 327s [11,] 0.10559 327s [12,] 0.00876 327s [13,] 0.04090 327s [14,] -0.03984 327s [15,] 0.40767 327s [16,] 0.24571 327s [17,] 0.64160 327s [18,] 0.24037 327s [19,] 0.34075 327s [20,] 0.54270 327s > 327s > print( correlation.systemfit( fitols5, 1, 2 ) ) 327s [,1] 327s [1,] 0.4051 327s [2,] 0.2729 327s [3,] 0.2415 327s [4,] 0.2693 327s [5,] -0.0301 327s [6,] -0.0527 327s [7,] -0.0624 327s [8,] 0.0971 327s [9,] 0.0945 327s [10,] 0.4365 327s [11,] 0.1258 327s [12,] 0.0210 327s [13,] 0.0436 327s [14,] -0.0405 327s [15,] 0.4102 327s [16,] 0.2610 327s [17,] 0.6400 327s [18,] 0.2661 327s [19,] 0.3796 327s [20,] 0.5742 327s > 327s > 327s > ## ************ Log-Likelihood values *************** 327s > print( logLik( fitols1 ) ) 327s 'log Lik.' -67.8 (df=8) 327s > print( logLik( fitols1, residCovDiag = TRUE ) ) 327s 'log Lik.' -83.6 (df=8) 327s > all.equal( logLik( fitols1, residCovDiag = TRUE ), 327s + logLik( lmDemand ) + logLik( lmSupply ), 327s + check.attributes = FALSE ) 327s [1] TRUE 327s > 327s > print( logLik( fitols2r ) ) 327s 'log Lik.' -62 (df=7) 327s > print( logLik( fitols2r, residCovDiag = TRUE ) ) 327s 'log Lik.' -84 (df=7) 327s > 327s > print( logLik( fitols3s ) ) 327s 'log Lik.' -62 (df=7) 327s > print( logLik( fitols3s, residCovDiag = TRUE ) ) 327s 'log Lik.' -84 (df=7) 327s > 327s > print( logLik( fitols4rs ) ) 327s 'log Lik.' -62.8 (df=6) 327s > print( logLik( fitols4rs, residCovDiag = TRUE ) ) 327s 'log Lik.' -84.1 (df=6) 327s > 327s > print( logLik( fitols5 ) ) 327s 'log Lik.' -62.8 (df=6) 327s > print( logLik( fitols5, residCovDiag = TRUE ) ) 327s 'log Lik.' -84.1 (df=6) 327s > 327s > 327s > ## ************** F tests **************** 327s > # testing first restriction 327s > print( linearHypothesis( fitols1, restrm ) ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.14 0.71 327s > linearHypothesis( fitols1, restrict ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.14 0.71 327s > 327s > print( linearHypothesis( fitols1s, restrm ) ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1s 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.15 0.7 327s > linearHypothesis( fitols1s, restrict ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1s 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.15 0.7 327s > 327s > print( linearHypothesis( fitols1, restrm ) ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.14 0.71 327s > linearHypothesis( fitols1, restrict ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.14 0.71 327s > 327s > print( linearHypothesis( fitols1r, restrm ) ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1r 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.14 0.71 327s > linearHypothesis( fitols1r, restrict ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1r 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.14 0.71 327s > 327s > # testing second restriction 327s > restrOnly2m <- matrix(0,1,7) 327s > restrOnly2q <- 0.5 327s > restrOnly2m[1,2] <- -1 327s > restrOnly2m[1,5] <- 1 327s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 327s > # first restriction not imposed 327s > print( linearHypothesis( fitols1, restrOnly2m, restrOnly2q ) ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.01 0.94 327s > linearHypothesis( fitols1, restrictOnly2 ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df F Pr(>F) 327s 1 34 327s 2 33 1 0.01 0.94 327s > 327s > # first restriction imposed 327s > print( linearHypothesis( fitols2, restrOnly2m, restrOnly2q ) ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols2 327s 327s Res.Df Df F Pr(>F) 327s 1 35 327s 2 34 1 0.02 0.88 327s > linearHypothesis( fitols2, restrictOnly2 ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols2 327s 327s Res.Df Df F Pr(>F) 327s 1 35 327s 2 34 1 0.02 0.88 327s > 327s > print( linearHypothesis( fitols3, restrOnly2m, restrOnly2q ) ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols3 327s 327s Res.Df Df F Pr(>F) 327s 1 35 327s 2 34 1 0.02 0.88 327s > linearHypothesis( fitols3, restrictOnly2 ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols3 327s 327s Res.Df Df F Pr(>F) 327s 1 35 327s 2 34 1 0.02 0.88 327s > 327s > # testing both of the restrictions 327s > print( linearHypothesis( fitols1, restr2m, restr2q ) ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df F Pr(>F) 327s 1 35 327s 2 33 2 0.08 0.93 327s > linearHypothesis( fitols1, restrict2 ) 327s Linear hypothesis test (Theil's F test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df F Pr(>F) 327s 1 35 327s 2 33 2 0.08 0.93 327s > 327s > 327s > ## ************** Wald tests **************** 327s > # testing first restriction 327s > print( linearHypothesis( fitols1, restrm, test = "Chisq" ) ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.64 0.42 327s > linearHypothesis( fitols1, restrict, test = "Chisq" ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.64 0.42 327s > 327s > print( linearHypothesis( fitols1s, restrm, test = "Chisq" ) ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1s 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.72 0.4 327s > linearHypothesis( fitols1s, restrict, test = "Chisq" ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1s 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.72 0.4 327s > 327s > print( linearHypothesis( fitols1, restrm, test = "Chisq" ) ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.64 0.42 327s > linearHypothesis( fitols1, restrict, test = "Chisq" ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.64 0.42 327s > 327s > print( linearHypothesis( fitols1r, restrm, test = "Chisq" ) ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1r 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.64 0.42 327s > linearHypothesis( fitols1r, restrict, test = "Chisq" ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s 327s Model 1: restricted model 327s Model 2: fitols1r 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.64 0.42 327s > 327s > # testing second restriction 327s > # first restriction not imposed 327s > print( linearHypothesis( fitols1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.03 0.86 327s > linearHypothesis( fitols1, restrictOnly2, test = "Chisq" ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 34 327s 2 33 1 0.03 0.86 327s > # first restriction imposed 327s > print( linearHypothesis( fitols2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols2 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 35 327s 2 34 1 0.12 0.73 327s > linearHypothesis( fitols2, restrictOnly2, test = "Chisq" ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols2 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 35 327s 2 34 1 0.12 0.73 327s > 327s > print( linearHypothesis( fitols3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols3 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 35 327s 2 34 1 0.12 0.73 327s > linearHypothesis( fitols3, restrictOnly2, test = "Chisq" ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols3 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 35 327s 2 34 1 0.12 0.73 327s > 327s > # testing both of the restrictions 327s > print( linearHypothesis( fitols1, restr2m, restr2q, test = "Chisq" ) ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 35 327s 2 33 2 0.72 0.7 327s > linearHypothesis( fitols1, restrict2, test = "Chisq" ) 327s Linear hypothesis test (Chi^2 statistic of a Wald test) 327s 327s Hypothesis: 327s demand_income - supply_trend = 0 327s - demand_price + supply_price = 0.5 327s 327s Model 1: restricted model 327s Model 2: fitols1 327s 327s Res.Df Df Chisq Pr(>Chisq) 327s 1 35 327s 2 33 2 0.72 0.7 327s > 327s > 327s > ## ****************** model frame ************************** 327s > print( mf <- model.frame( fitols1 ) ) 327s consump price income farmPrice trend 327s 1 98.5 100.3 87.4 98.0 1 327s 2 99.2 104.3 97.6 99.1 2 327s 3 102.2 103.4 96.7 99.1 3 327s 4 101.5 104.5 98.2 98.1 4 327s 5 104.2 98.0 99.8 110.8 5 327s 6 103.2 99.5 100.5 108.2 6 327s 7 104.0 101.1 103.2 105.6 7 327s 8 99.9 104.8 107.8 109.8 8 327s 9 100.3 96.4 96.6 108.7 9 327s 10 102.8 91.2 88.9 100.6 10 327s 11 95.4 93.1 75.1 81.0 11 327s 12 92.4 98.8 76.9 68.6 12 327s 13 94.5 102.9 84.6 70.9 13 327s 14 98.8 98.8 90.6 81.4 14 327s 15 105.8 95.1 103.1 102.3 15 327s 16 100.2 98.5 105.1 105.0 16 327s 17 103.5 86.5 96.4 110.5 17 327s 18 99.9 104.0 104.4 92.5 18 327s 19 105.2 105.8 110.7 89.3 19 327s 20 106.2 113.5 127.1 93.0 20 327s > print( mf1 <- model.frame( fitols1$eq[[ 1 ]] ) ) 327s consump price income 327s 1 98.5 100.3 87.4 327s 2 99.2 104.3 97.6 327s 3 102.2 103.4 96.7 327s 4 101.5 104.5 98.2 327s 5 104.2 98.0 99.8 327s 6 103.2 99.5 100.5 327s 7 104.0 101.1 103.2 327s 8 99.9 104.8 107.8 327s 9 100.3 96.4 96.6 327s 10 102.8 91.2 88.9 327s 11 95.4 93.1 75.1 327s 12 92.4 98.8 76.9 327s 13 94.5 102.9 84.6 327s 14 98.8 98.8 90.6 327s 15 105.8 95.1 103.1 327s 16 100.2 98.5 105.1 327s 17 103.5 86.5 96.4 327s 18 99.9 104.0 104.4 327s 19 105.2 105.8 110.7 327s 20 106.2 113.5 127.1 327s > print( attributes( mf1 )$terms ) 327s consump ~ price + income 327s attr(,"variables") 327s list(consump, price, income) 327s attr(,"factors") 327s price income 327s consump 0 0 327s price 1 0 327s income 0 1 327s attr(,"term.labels") 327s [1] "price" "income" 327s attr(,"order") 327s [1] 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, income) 327s attr(,"dataClasses") 327s consump price income 327s "numeric" "numeric" "numeric" 327s > print( mf2 <- model.frame( fitols1$eq[[ 2 ]] ) ) 327s consump price farmPrice trend 327s 1 98.5 100.3 98.0 1 327s 2 99.2 104.3 99.1 2 327s 3 102.2 103.4 99.1 3 327s 4 101.5 104.5 98.1 4 327s 5 104.2 98.0 110.8 5 327s 6 103.2 99.5 108.2 6 327s 7 104.0 101.1 105.6 7 327s 8 99.9 104.8 109.8 8 327s 9 100.3 96.4 108.7 9 327s 10 102.8 91.2 100.6 10 327s 11 95.4 93.1 81.0 11 327s 12 92.4 98.8 68.6 12 327s 13 94.5 102.9 70.9 13 327s 14 98.8 98.8 81.4 14 327s 15 105.8 95.1 102.3 15 327s 16 100.2 98.5 105.0 16 327s 17 103.5 86.5 110.5 17 327s 18 99.9 104.0 92.5 18 327s 19 105.2 105.8 89.3 19 327s 20 106.2 113.5 93.0 20 327s > print( attributes( mf2 )$terms ) 327s consump ~ price + farmPrice + trend 327s attr(,"variables") 327s list(consump, price, farmPrice, trend) 327s attr(,"factors") 327s price farmPrice trend 327s consump 0 0 0 327s price 1 0 0 327s farmPrice 0 1 0 327s trend 0 0 1 327s attr(,"term.labels") 327s [1] "price" "farmPrice" "trend" 327s attr(,"order") 327s [1] 1 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, farmPrice, trend) 327s attr(,"dataClasses") 327s consump price farmPrice trend 327s "numeric" "numeric" "numeric" "numeric" 327s > 327s > print( all.equal( mf, model.frame( fitols2r ) ) ) 327s [1] TRUE 327s > print( all.equal( mf1, model.frame( fitols2r$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > 327s > print( all.equal( mf, model.frame( fitols3s ) ) ) 327s [1] TRUE 327s > print( all.equal( mf2, model.frame( fitols3s$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > 327s > print( all.equal( mf, model.frame( fitols4rs ) ) ) 327s [1] TRUE 327s > print( all.equal( mf1, model.frame( fitols4rs$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > 327s > print( all.equal( mf, model.frame( fitols5 ) ) ) 327s [1] TRUE 327s > print( all.equal( mf2, model.frame( fitols5$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > 327s > 327s > ## **************** model matrix ************************ 327s > # with x (returnModelMatrix) = TRUE 327s > print( !is.null( fitols1r$eq[[ 1 ]]$x ) ) 327s [1] TRUE 327s > print( mm <- model.matrix( fitols1r ) ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s demand_1 1 100.3 87.4 0 327s demand_2 1 104.3 97.6 0 327s demand_3 1 103.4 96.7 0 327s demand_4 1 104.5 98.2 0 327s demand_5 1 98.0 99.8 0 327s demand_6 1 99.5 100.5 0 327s demand_7 1 101.1 103.2 0 327s demand_8 1 104.8 107.8 0 327s demand_9 1 96.4 96.6 0 327s demand_10 1 91.2 88.9 0 327s demand_11 1 93.1 75.1 0 327s demand_12 1 98.8 76.9 0 327s demand_13 1 102.9 84.6 0 327s demand_14 1 98.8 90.6 0 327s demand_15 1 95.1 103.1 0 327s demand_16 1 98.5 105.1 0 327s demand_17 1 86.5 96.4 0 327s demand_18 1 104.0 104.4 0 327s demand_19 1 105.8 110.7 0 327s demand_20 1 113.5 127.1 0 327s supply_1 0 0.0 0.0 1 327s supply_2 0 0.0 0.0 1 327s supply_3 0 0.0 0.0 1 327s supply_4 0 0.0 0.0 1 327s supply_5 0 0.0 0.0 1 327s supply_6 0 0.0 0.0 1 327s supply_7 0 0.0 0.0 1 327s supply_8 0 0.0 0.0 1 327s supply_9 0 0.0 0.0 1 327s supply_10 0 0.0 0.0 1 327s supply_11 0 0.0 0.0 1 327s supply_12 0 0.0 0.0 1 327s supply_13 0 0.0 0.0 1 327s supply_14 0 0.0 0.0 1 327s supply_15 0 0.0 0.0 1 327s supply_16 0 0.0 0.0 1 327s supply_17 0 0.0 0.0 1 327s supply_18 0 0.0 0.0 1 327s supply_19 0 0.0 0.0 1 327s supply_20 0 0.0 0.0 1 327s supply_price supply_farmPrice supply_trend 327s demand_1 0.0 0.0 0 327s demand_2 0.0 0.0 0 327s demand_3 0.0 0.0 0 327s demand_4 0.0 0.0 0 327s demand_5 0.0 0.0 0 327s demand_6 0.0 0.0 0 327s demand_7 0.0 0.0 0 327s demand_8 0.0 0.0 0 327s demand_9 0.0 0.0 0 327s demand_10 0.0 0.0 0 327s demand_11 0.0 0.0 0 327s demand_12 0.0 0.0 0 327s demand_13 0.0 0.0 0 327s demand_14 0.0 0.0 0 327s demand_15 0.0 0.0 0 327s demand_16 0.0 0.0 0 327s demand_17 0.0 0.0 0 327s demand_18 0.0 0.0 0 327s demand_19 0.0 0.0 0 327s demand_20 0.0 0.0 0 327s supply_1 100.3 98.0 1 327s supply_2 104.3 99.1 2 327s supply_3 103.4 99.1 3 327s supply_4 104.5 98.1 4 327s supply_5 98.0 110.8 5 327s supply_6 99.5 108.2 6 327s supply_7 101.1 105.6 7 327s supply_8 104.8 109.8 8 327s supply_9 96.4 108.7 9 327s supply_10 91.2 100.6 10 327s supply_11 93.1 81.0 11 327s supply_12 98.8 68.6 12 327s supply_13 102.9 70.9 13 327s supply_14 98.8 81.4 14 327s supply_15 95.1 102.3 15 327s supply_16 98.5 105.0 16 327s supply_17 86.5 110.5 17 327s supply_18 104.0 92.5 18 327s supply_19 105.8 89.3 19 327s supply_20 113.5 93.0 20 327s > print( mm1 <- model.matrix( fitols1r$eq[[ 1 ]] ) ) 327s (Intercept) price income 327s 1 1 100.3 87.4 327s 2 1 104.3 97.6 327s 3 1 103.4 96.7 327s 4 1 104.5 98.2 327s 5 1 98.0 99.8 327s 6 1 99.5 100.5 327s 7 1 101.1 103.2 327s 8 1 104.8 107.8 327s 9 1 96.4 96.6 327s 10 1 91.2 88.9 327s 11 1 93.1 75.1 327s 12 1 98.8 76.9 327s 13 1 102.9 84.6 327s 14 1 98.8 90.6 327s 15 1 95.1 103.1 327s 16 1 98.5 105.1 327s 17 1 86.5 96.4 327s 18 1 104.0 104.4 327s 19 1 105.8 110.7 327s 20 1 113.5 127.1 327s attr(,"assign") 327s [1] 0 1 2 327s > print( mm2 <- model.matrix( fitols1r$eq[[ 2 ]] ) ) 327s (Intercept) price farmPrice trend 327s 1 1 100.3 98.0 1 327s 2 1 104.3 99.1 2 327s 3 1 103.4 99.1 3 327s 4 1 104.5 98.1 4 327s 5 1 98.0 110.8 5 327s 6 1 99.5 108.2 6 327s 7 1 101.1 105.6 7 327s 8 1 104.8 109.8 8 327s 9 1 96.4 108.7 9 327s 10 1 91.2 100.6 10 327s 11 1 93.1 81.0 11 327s 12 1 98.8 68.6 12 327s 13 1 102.9 70.9 13 327s 14 1 98.8 81.4 14 327s 15 1 95.1 102.3 15 327s 16 1 98.5 105.0 16 327s 17 1 86.5 110.5 17 327s 18 1 104.0 92.5 18 327s 19 1 105.8 89.3 19 327s 20 1 113.5 93.0 20 327s attr(,"assign") 327s [1] 0 1 2 3 327s > 327s > # with x (returnModelMatrix) = FALSE 327s > print( all.equal( mm, model.matrix( fitols1rs ) ) ) 327s [1] TRUE 327s > print( all.equal( mm1, model.matrix( fitols1rs$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > print( all.equal( mm2, model.matrix( fitols1rs$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > print( !is.null( fitols1rs$eq[[ 1 ]]$x ) ) 327s [1] FALSE 327s > 327s > # with x (returnModelMatrix) = TRUE 327s > print( !is.null( fitols2rs$eq[[ 1 ]]$x ) ) 327s [1] TRUE 327s > print( all.equal( mm, model.matrix( fitols2rs ) ) ) 327s [1] TRUE 327s > print( all.equal( mm1, model.matrix( fitols2rs$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > print( all.equal( mm2, model.matrix( fitols2rs$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > 327s > # with x (returnModelMatrix) = FALSE 327s > print( all.equal( mm, model.matrix( fitols2 ) ) ) 327s [1] TRUE 327s > print( all.equal( mm1, model.matrix( fitols2$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > print( all.equal( mm2, model.matrix( fitols2$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > print( !is.null( fitols2$eq[[ 1 ]]$x ) ) 327s [1] FALSE 327s > 327s > # with x (returnModelMatrix) = TRUE 327s > print( !is.null( fitols3$eq[[ 1 ]]$x ) ) 327s [1] TRUE 327s > print( all.equal( mm, model.matrix( fitols3 ) ) ) 327s [1] TRUE 327s > print( all.equal( mm1, model.matrix( fitols3$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > print( all.equal( mm2, model.matrix( fitols3$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > 327s > # with x (returnModelMatrix) = FALSE 327s > print( all.equal( mm, model.matrix( fitols3r ) ) ) 327s [1] TRUE 327s > print( all.equal( mm1, model.matrix( fitols3r$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > print( all.equal( mm2, model.matrix( fitols3r$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > print( !is.null( fitols3r$eq[[ 1 ]]$x ) ) 327s [1] FALSE 327s > 327s > # with x (returnModelMatrix) = TRUE 327s > print( !is.null( fitols4s$eq[[ 1 ]]$x ) ) 327s [1] TRUE 327s > print( all.equal( mm, model.matrix( fitols4s ) ) ) 327s [1] TRUE 327s > print( all.equal( mm1, model.matrix( fitols4s$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > print( all.equal( mm2, model.matrix( fitols4s$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > 327s > # with x (returnModelMatrix) = FALSE 327s > print( all.equal( mm, model.matrix( fitols4Sym ) ) ) 327s [1] TRUE 327s > print( all.equal( mm1, model.matrix( fitols4Sym$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > print( all.equal( mm2, model.matrix( fitols4Sym$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > print( !is.null( fitols4Sym$eq[[ 1 ]]$x ) ) 327s [1] FALSE 327s > 327s > # with x (returnModelMatrix) = TRUE 327s > print( !is.null( fitols5s$eq[[ 1 ]]$x ) ) 327s [1] TRUE 327s > print( all.equal( mm, model.matrix( fitols5s ) ) ) 327s [1] TRUE 327s > print( all.equal( mm1, model.matrix( fitols5s$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > print( all.equal( mm2, model.matrix( fitols5s$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > 327s > # with x (returnModelMatrix) = FALSE 327s > print( all.equal( mm, model.matrix( fitols5 ) ) ) 327s [1] TRUE 327s > print( all.equal( mm1, model.matrix( fitols5$eq[[ 1 ]] ) ) ) 327s [1] TRUE 327s > print( all.equal( mm2, model.matrix( fitols5$eq[[ 2 ]] ) ) ) 327s [1] TRUE 327s > print( !is.null( fitols5$eq[[ 1 ]]$x ) ) 327s [1]Error in model.matrix.systemfit.equation(object$eq[[i]], which = which) : 327s argument 'which' can only be set to "xHat" or "z" if instruments were used 327s FALSE 327s > 327s > try( model.matrix( fitols1, which = "z" ) ) 327s > 327s > 327s > ## **************** formulas ************************ 327s > formula( fitols1 ) 327s $demand 327s consump ~ price + income 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s 327s > formula( fitols1$eq[[ 2 ]] ) 327s consump ~ price + farmPrice + trend 327s > 327s > formula( fitols2r ) 327s $demand 327s consump ~ price + income 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s 327s > formula( fitols2r$eq[[ 1 ]] ) 327s consump ~ price + income 327s > 327s > formula( fitols3s ) 327s $demand 327s consump ~ price + income 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s 327s > formula( fitols3s$eq[[ 2 ]] ) 327s consump ~ price + farmPrice + trend 327s > 327s > formula( fitols4rs ) 327s $demand 327s consump ~ price + income 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s 327s > formula( fitols4rs$eq[[ 1 ]] ) 327s consump ~ price + income 327s > 327s > formula( fitols5 ) 327s $demand 327s consump ~ price + income 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s 327s > formula( fitols5$eq[[ 2 ]] ) 327s consump ~ price + farmPrice + trend 327s > 327s > 327s > ## **************** model terms ******************* 327s > terms( fitols1 ) 327s $demand 327s consump ~ price + income 327s attr(,"variables") 327s list(consump, price, income) 327s attr(,"factors") 327s price income 327s consump 0 0 327s price 1 0 327s income 0 1 327s attr(,"term.labels") 327s [1] "price" "income" 327s attr(,"order") 327s [1] 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, income) 327s attr(,"dataClasses") 327s consump price income 327s "numeric" "numeric" "numeric" 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s attr(,"variables") 327s list(consump, price, farmPrice, trend) 327s attr(,"factors") 327s price farmPrice trend 327s consump 0 0 0 327s price 1 0 0 327s farmPrice 0 1 0 327s trend 0 0 1 327s attr(,"term.labels") 327s [1] "price" "farmPrice" "trend" 327s attr(,"order") 327s [1] 1 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, farmPrice, trend) 327s attr(,"dataClasses") 327s consump price farmPrice trend 327s "numeric" "numeric" "numeric" "numeric" 327s 327s > terms( fitols1$eq[[ 2 ]] ) 327s consump ~ price + farmPrice + trend 327s attr(,"variables") 327s list(consump, price, farmPrice, trend) 327s attr(,"factors") 327s price farmPrice trend 327s consump 0 0 0 327s price 1 0 0 327s farmPrice 0 1 0 327s trend 0 0 1 327s attr(,"term.labels") 327s [1] "price" "farmPrice" "trend" 327s attr(,"order") 327s [1] 1 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, farmPrice, trend) 327s attr(,"dataClasses") 327s consump price farmPrice trend 327s "numeric" "numeric" "numeric" "numeric" 327s > 327s > terms( fitols2r ) 327s $demand 327s consump ~ price + income 327s attr(,"variables") 327s list(consump, price, income) 327s attr(,"factors") 327s price income 327s consump 0 0 327s price 1 0 327s income 0 1 327s attr(,"term.labels") 327s [1] "price" "income" 327s attr(,"order") 327s [1] 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, income) 327s attr(,"dataClasses") 327s consump price income 327s "numeric" "numeric" "numeric" 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s attr(,"variables") 327s list(consump, price, farmPrice, trend) 327s attr(,"factors") 327s price farmPrice trend 327s consump 0 0 0 327s price 1 0 0 327s farmPrice 0 1 0 327s trend 0 0 1 327s attr(,"term.labels") 327s [1] "price" "farmPrice" "trend" 327s attr(,"order") 327s [1] 1 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, farmPrice, trend) 327s attr(,"dataClasses") 327s consump price farmPrice trend 327s "numeric" "numeric" "numeric" "numeric" 327s 327s > terms( fitols2r$eq[[ 1 ]] ) 327s consump ~ price + income 327s attr(,"variables") 327s list(consump, price, income) 327s attr(,"factors") 327s price income 327s consump 0 0 327s price 1 0 327s income 0 1 327s attr(,"term.labels") 327s [1] "price" "income" 327s attr(,"order") 327s [1] 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, income) 327s attr(,"dataClasses") 327s consump price income 327s "numeric" "numeric" "numeric" 327s > 327s > terms( fitols3s ) 327s $demand 327s consump ~ price + income 327s attr(,"variables") 327s list(consump, price, income) 327s attr(,"factors") 327s price income 327s consump 0 0 327s price 1 0 327s income 0 1 327s attr(,"term.labels") 327s [1] "price" "income" 327s attr(,"order") 327s [1] 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, income) 327s attr(,"dataClasses") 327s consump price income 327s "numeric" "numeric" "numeric" 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s attr(,"variables") 327s list(consump, price, farmPrice, trend) 327s attr(,"factors") 327s price farmPrice trend 327s consump 0 0 0 327s price 1 0 0 327s farmPrice 0 1 0 327s trend 0 0 1 327s attr(,"term.labels") 327s [1] "price" "farmPrice" "trend" 327s attr(,"order") 327s [1] 1 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, farmPrice, trend) 327s attr(,"dataClasses") 327s consump price farmPrice trend 327s "numeric" "numeric" "numeric" "numeric" 327s 327s > terms( fitols3s$eq[[ 2 ]] ) 327s consump ~ price + farmPrice + trend 327s attr(,"variables") 327s list(consump, price, farmPrice, trend) 327s attr(,"factors") 327s price farmPrice trend 327s consump 0 0 0 327s price 1 0 0 327s farmPrice 0 1 0 327s trend 0 0 1 327s attr(,"term.labels") 327s [1] "price" "farmPrice" "trend" 327s attr(,"order") 327s [1] 1 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, farmPrice, trend) 327s attr(,"dataClasses") 327s consump price farmPrice trend 327s "numeric" "numeric" "numeric" "numeric" 327s > 327s > terms( fitols4rs ) 327s $demand 327s consump ~ price + income 327s attr(,"variables") 327s list(consump, price, income) 327s attr(,"factors") 327s price income 327s consump 0 0 327s price 1 0 327s income 0 1 327s attr(,"term.labels") 327s [1] "price" "income" 327s attr(,"order") 327s [1] 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, income) 327s attr(,"dataClasses") 327s consump price income 327s "numeric" "numeric" "numeric" 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s attr(,"variables") 327s list(consump, price, farmPrice, trend) 327s attr(,"factors") 327s price farmPrice trend 327s consump 0 0 0 327s price 1 0 0 327s farmPrice 0 1 0 327s trend 0 0 1 327s attr(,"term.labels") 327s [1] "price" "farmPrice" "trend" 327s attr(,"order") 327s [1] 1 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, farmPrice, trend) 327s attr(,"dataClasses") 327s consump price farmPrice trend 327s "numeric" "numeric" "numeric" "numeric" 327s 327s > terms( fitols4rs$eq[[ 1 ]] ) 327s consump ~ price + income 327s attr(,"variables") 327s list(consump, price, income) 327s attr(,"factors") 327s price income 327s consump 0 0 327s price 1 0 327s income 0 1 327s attr(,"term.labels") 327s [1] "price" "income" 327s attr(,"order") 327s [1] 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, income) 327s attr(,"dataClasses") 327s consump price income 327s "numeric" "numeric" "numeric" 327s > 327s > terms( fitols5 ) 327s $demand 327s consump ~ price + income 327s attr(,"variables") 327s list(consump, price, income) 327s attr(,"factors") 327s price income 327s consump 0 0 327s price 1 0 327s income 0 1 327s attr(,"term.labels") 327s [1] "price" "income" 327s attr(,"order") 327s [1] 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, income) 327s attr(,"dataClasses") 327s consump price income 327s "numeric" "numeric" "numeric" 327s 327s $supply 327s consump ~ price + farmPrice + trend 327s attr(,"variables") 327s list(consump, price, farmPrice, trend) 327s attr(,"factors") 327s price farmPrice trend 327s consump 0 0 0 327s price 1 0 0 327s farmPrice 0 1 0 327s trend 0 0 1 327s attr(,"term.labels") 327s [1] "price" "farmPrice" "trend" 327s attr(,"order") 327s [1] 1 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, farmPrice, trend) 327s attr(,"dataClasses") 327s consump price farmPrice trend 327s "numeric" "numeric" "numeric" "numeric" 327s 327s > terms( fitols5$eq[[ 2 ]] ) 327s consump ~ price + farmPrice + trend 327s attr(,"variables") 327s list(consump, price, farmPrice, trend) 327s attr(,"factors") 327s price farmPrice trend 327s consump 0 0 0 327s price 1 0 0 327s farmPrice 0 1 0 327s trend 0 0 1 327s attr(,"term.labels") 327s [1] "price" "farmPrice" "trend" 327s attr(,"order") 327s [1] 1 1 1 327s attr(,"intercept") 327s [1] 1 327s attr(,"response") 327s [1] 1 327s attr(,".Environment") 327s 327s attr(,"predvars") 327s list(consump, price, farmPrice, trend) 327s attr(,"dataClasses") 327s consump price farmPrice trend 327s "numeric" "numeric" "numeric" "numeric" 327s > 327s > 327s > ## **************** estfun ************************ 327s > library( "sandwich" ) 327s > 327s > estfun( fitols1 ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s demand_1 1.074 107.8 93.9 0.000 327s demand_2 -0.390 -40.7 -38.1 0.000 327s demand_3 2.625 271.5 253.8 0.000 327s demand_4 1.802 188.4 177.0 0.000 327s demand_5 1.946 190.7 194.2 0.000 327s demand_6 1.175 116.8 118.0 0.000 327s demand_7 1.530 154.7 157.9 0.000 327s demand_8 -2.933 -307.2 -316.1 0.000 327s demand_9 -1.365 -131.7 -131.9 0.000 327s demand_10 2.031 185.3 180.5 0.000 327s demand_11 -0.149 -13.9 -11.2 0.000 327s demand_12 -1.954 -193.1 -150.3 0.000 327s demand_13 -1.121 -115.4 -94.8 0.000 327s demand_14 -0.220 -21.7 -19.9 0.000 327s demand_15 1.487 141.4 153.3 0.000 327s demand_16 -3.701 -364.3 -388.9 0.000 327s demand_17 -1.273 -110.1 -122.7 0.000 327s demand_18 -2.002 -208.3 -209.0 0.000 327s demand_19 1.738 183.8 192.4 0.000 327s demand_20 -0.299 -33.9 -38.0 0.000 327s supply_1 0.000 0.0 0.0 -0.444 327s supply_2 0.000 0.0 0.0 -0.896 327s supply_3 0.000 0.0 0.0 1.965 327s supply_4 0.000 0.0 0.0 1.134 327s supply_5 0.000 0.0 0.0 1.514 327s supply_6 0.000 0.0 0.0 0.680 327s supply_7 0.000 0.0 0.0 1.569 327s supply_8 0.000 0.0 0.0 -4.407 327s supply_9 0.000 0.0 0.0 -2.599 327s supply_10 0.000 0.0 0.0 2.469 327s supply_11 0.000 0.0 0.0 -0.598 327s supply_12 0.000 0.0 0.0 -1.697 327s supply_13 0.000 0.0 0.0 -1.064 327s supply_14 0.000 0.0 0.0 0.970 327s supply_15 0.000 0.0 0.0 3.159 327s supply_16 0.000 0.0 0.0 -3.866 327s supply_17 0.000 0.0 0.0 -0.265 327s supply_18 0.000 0.0 0.0 -2.449 327s supply_19 0.000 0.0 0.0 3.110 327s supply_20 0.000 0.0 0.0 1.714 327s supply_price supply_farmPrice supply_trend 327s demand_1 0.0 0.0 0.000 327s demand_2 0.0 0.0 0.000 327s demand_3 0.0 0.0 0.000 327s demand_4 0.0 0.0 0.000 327s demand_5 0.0 0.0 0.000 327s demand_6 0.0 0.0 0.000 327s demand_7 0.0 0.0 0.000 327s demand_8 0.0 0.0 0.000 327s demand_9 0.0 0.0 0.000 327s demand_10 0.0 0.0 0.000 327s demand_11 0.0 0.0 0.000 327s demand_12 0.0 0.0 0.000 327s demand_13 0.0 0.0 0.000 327s demand_14 0.0 0.0 0.000 327s demand_15 0.0 0.0 0.000 327s demand_16 0.0 0.0 0.000 327s demand_17 0.0 0.0 0.000 327s demand_18 0.0 0.0 0.000 327s demand_19 0.0 0.0 0.000 327s demand_20 0.0 0.0 0.000 327s supply_1 -44.6 -43.5 -0.444 327s supply_2 -93.4 -88.7 -1.791 327s supply_3 203.3 194.7 5.895 327s supply_4 118.5 111.3 4.537 327s supply_5 148.4 167.7 7.569 327s supply_6 67.7 73.6 4.082 327s supply_7 158.6 165.7 10.983 327s supply_8 -461.7 -483.9 -35.259 327s supply_9 -250.7 -282.5 -23.391 327s supply_10 225.3 248.4 24.694 327s supply_11 -55.7 -48.5 -6.581 327s supply_12 -167.7 -116.4 -20.369 327s supply_13 -109.5 -75.4 -13.832 327s supply_14 95.8 79.0 13.582 327s supply_15 300.5 323.2 47.386 327s supply_16 -380.6 -405.9 -61.848 327s supply_17 -22.9 -29.2 -4.500 327s supply_18 -254.7 -226.5 -44.080 327s supply_19 328.9 277.7 59.084 327s supply_20 194.5 159.4 34.282 327s > round( colSums( estfun( fitols1 ) ), digits = 7 ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s 0 0 0 0 327s supply_price supply_farmPrice supply_trend 327s 0 0 0 327s > 327s > estfun( fitols1s ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s demand_1 1.074 107.8 93.9 0.000 327s demand_2 -0.390 -40.7 -38.1 0.000 327s demand_3 2.625 271.5 253.8 0.000 327s demand_4 1.802 188.4 177.0 0.000 327s demand_5 1.946 190.7 194.2 0.000 327s demand_6 1.175 116.8 118.0 0.000 327s demand_7 1.530 154.7 157.9 0.000 327s demand_8 -2.933 -307.2 -316.1 0.000 327s demand_9 -1.365 -131.7 -131.9 0.000 327s demand_10 2.031 185.3 180.5 0.000 327s demand_11 -0.149 -13.9 -11.2 0.000 327s demand_12 -1.954 -193.1 -150.3 0.000 327s demand_13 -1.121 -115.4 -94.8 0.000 327s demand_14 -0.220 -21.7 -19.9 0.000 327s demand_15 1.487 141.4 153.3 0.000 327s demand_16 -3.701 -364.3 -388.9 0.000 327s demand_17 -1.273 -110.1 -122.7 0.000 327s demand_18 -2.002 -208.3 -209.0 0.000 327s demand_19 1.738 183.8 192.4 0.000 327s demand_20 -0.299 -33.9 -38.0 0.000 327s supply_1 0.000 0.0 0.0 -0.444 327s supply_2 0.000 0.0 0.0 -0.896 327s supply_3 0.000 0.0 0.0 1.965 327s supply_4 0.000 0.0 0.0 1.134 327s supply_5 0.000 0.0 0.0 1.514 327s supply_6 0.000 0.0 0.0 0.680 327s supply_7 0.000 0.0 0.0 1.569 327s supply_8 0.000 0.0 0.0 -4.407 327s supply_9 0.000 0.0 0.0 -2.599 327s supply_10 0.000 0.0 0.0 2.469 327s supply_11 0.000 0.0 0.0 -0.598 327s supply_12 0.000 0.0 0.0 -1.697 327s supply_13 0.000 0.0 0.0 -1.064 327s supply_14 0.000 0.0 0.0 0.970 327s supply_15 0.000 0.0 0.0 3.159 327s supply_16 0.000 0.0 0.0 -3.866 327s supply_17 0.000 0.0 0.0 -0.265 327s supply_18 0.000 0.0 0.0 -2.449 327s supply_19 0.000 0.0 0.0 3.110 327s supply_20 0.000 0.0 0.0 1.714 327s supply_price supply_farmPrice supply_trend 327s demand_1 0.0 0.0 0.000 327s demand_2 0.0 0.0 0.000 327s demand_3 0.0 0.0 0.000 327s demand_4 0.0 0.0 0.000 327s demand_5 0.0 0.0 0.000 327s demand_6 0.0 0.0 0.000 327s demand_7 0.0 0.0 0.000 327s demand_8 0.0 0.0 0.000 327s demand_9 0.0 0.0 0.000 327s demand_10 0.0 0.0 0.000 327s demand_11 0.0 0.0 0.000 327s demand_12 0.0 0.0 0.000 327s demand_13 0.0 0.0 0.000 327s demand_14 0.0 0.0 0.000 327s demand_15 0.0 0.0 0.000 327s demand_16 0.0 0.0 0.000 327s demand_17 0.0 0.0 0.000 327s demand_18 0.0 0.0 0.000 327s demand_19 0.0 0.0 0.000 327s demand_20 0.0 0.0 0.000 327s supply_1 -44.6 -43.5 -0.444 327s supply_2 -93.4 -88.7 -1.791 327s supply_3 203.3 194.7 5.895 327s supply_4 118.5 111.3 4.537 327s supply_5 148.4 167.7 7.569 327s supply_6 67.7 73.6 4.082 327s supply_7 158.6 165.7 10.983 327s supply_8 -461.7 -483.9 -35.259 327s supply_9 -250.7 -282.5 -23.391 327s supply_10 225.3 248.4 24.694 327s supply_11 -55.7 -48.5 -6.581 327s supply_12 -167.7 -116.4 -20.369 327s supply_13 -109.5 -75.4 -13.832 327s supply_14 95.8 79.0 13.582 327s supply_15 300.5 323.2 47.386 327s supply_16 -380.6 -405.9 -61.848 327s supply_17 -22.9 -29.2 -4.500 327s supply_18 -254.7 -226.5 -44.080 327s supply_19 328.9 277.7 59.084 327s supply_20 194.5 159.4 34.282 327s > round( colSums( estfun( fitols1s ) ), digits = 7 ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s 0 0 0 0 327s supply_price supply_farmPrice supply_trend 327s 0 0 0 327s > 327s > estfun( fitols1r ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s demand_1 1.074 107.8 93.9 0.000 327s demand_2 -0.390 -40.7 -38.1 0.000 327s demand_3 2.625 271.5 253.8 0.000 327s demand_4 1.802 188.4 177.0 0.000 327s demand_5 1.946 190.7 194.2 0.000 327s demand_6 1.175 116.8 118.0 0.000 327s demand_7 1.530 154.7 157.9 0.000 327s demand_8 -2.933 -307.2 -316.1 0.000 327s demand_9 -1.365 -131.7 -131.9 0.000 327s demand_10 2.031 185.3 180.5 0.000 327s demand_11 -0.149 -13.9 -11.2 0.000 327s demand_12 -1.954 -193.1 -150.3 0.000 327s demand_13 -1.121 -115.4 -94.8 0.000 327s demand_14 -0.220 -21.7 -19.9 0.000 327s demand_15 1.487 141.4 153.3 0.000 327s demand_16 -3.701 -364.3 -388.9 0.000 327s demand_17 -1.273 -110.1 -122.7 0.000 327s demand_18 -2.002 -208.3 -209.0 0.000 327s demand_19 1.738 183.8 192.4 0.000 327s demand_20 -0.299 -33.9 -38.0 0.000 327s supply_1 0.000 0.0 0.0 -0.444 327s supply_2 0.000 0.0 0.0 -0.896 327s supply_3 0.000 0.0 0.0 1.965 327s supply_4 0.000 0.0 0.0 1.134 327s supply_5 0.000 0.0 0.0 1.514 327s supply_6 0.000 0.0 0.0 0.680 327s supply_7 0.000 0.0 0.0 1.569 327s supply_8 0.000 0.0 0.0 -4.407 327s supply_9 0.000 0.0 0.0 -2.599 327s supply_10 0.000 0.0 0.0 2.469 327s supply_11 0.000 0.0 0.0 -0.598 327s supply_12 0.000 0.0 0.0 -1.697 327s supply_13 0.000 0.0 0.0 -1.064 327s supply_14 0.000 0.0 0.0 0.970 327s supply_15 0.000 0.0 0.0 3.159 327s supply_16 0.000 0.0 0.0 -3.866 327s supply_17 0.000 0.0 0.0 -0.265 327s supply_18 0.000 0.0 0.0 -2.449 327s supply_19 0.000 0.0 0.0 3.110 327s supply_20 0.000 0.0 0.0 1.714 327s supply_price supply_farmPrice supply_trend 327s demand_1 0.0 0.0 0.000 327s demand_2 0.0 0.0 0.000 327s demand_3 0.0 0.0 0.000 327s demand_4 0.0 0.0 0.000 327s demand_5 0.0 0.0 0.000 327s demand_6 0.0 0.0 0.000 327s demand_7 0.0 0.0 0.000 327s demand_8 0.0 0.0 0.000 327s demand_9 0.0 0.0 0.000 327s demand_10 0.0 0.0 0.000 327s demand_11 0.0 0.0 0.000 327s demand_12 0.0 0.0 0.000 327s demand_13 0.0 0.0 0.000 327s demand_14 0.0 0.0 0.000 327s demand_15 0.0 0.0 0.000 327s demand_16 0.0 0.0 0.000 327s demand_17 0.0 0.0 0.000 327s demand_18 0.0 0.0 0.000 327s demand_19 0.0 0.0 0.000 327s demand_20 0.0 0.0 0.000 327s supply_1 -44.6 -43.5 -0.444 327s supply_2 -93.4 -88.7 -1.791 327s supply_3 203.3 194.7 5.895 327s supply_4 118.5 111.3 4.537 327s supply_5 148.4 167.7 7.569 327s supply_6 67.7 73.6 4.082 327s supply_7 158.6 165.7 10.983 327s supply_8 -461.7 -483.9 -35.259 327s supply_9 -250.7 -282.5 -23.391 327s supply_10 225.3 248.4 24.694 327s supply_11 -55.7 -48.5 -6.581 327s supply_12 -167.7 -116.4 -20.369 327s supply_13 -109.5 -75.4 -13.832 327s supply_14 95.8 79.0 13.582 327s supply_15 300.5 323.2 47.386 327s supply_16 -380.6 -405.9 -61.848 327s supply_17 -22.9 -29.2 -4.500 327s supply_18 -254.7 -226.5 -44.080 327s supply_19 328.9 277.7 59.084 327s supply_20 194.5 159.4 34.282 327s > round( colSums( estfun( fitols1r ) ), digits = 7 ) 327s demand_(Intercept) demand_price demand_income supply_(Intercept) 327s 0 0 0 0 327s supply_price supply_farmPrice supply_trend 327s 0 0 0 327s > 327s > try( estfun( fitols2 ) ) 327s > 327s > try( estfun( fitols2Sym ) ) 327s Error in estfun.systemfit(fitols2) : 327s returning the estimation function for models with restrictions has not yet been implemented. 327s Error in estfun.systemfit(fitols2Sym) : 327s returning the estimation function for models with restrictions has not yet been implemented. 327s > 327s > try( estfun( fitols3s ) ) 327s Error in estfun.systemfit(fitols3s) : 327s returning the estimation function for models with restrictions has not yet been implemented. 327s > 327s > try( estfun( fitols4r ) ) 327s Error in estfun.systemfit(fitols4r) : 327s returning the estimation function for models with restrictions has not yet been implemented. 327s > 327s > try( estfun( fitols4Sym ) ) 327s Error in estfun.systemfit(fitols4Sym) : 327s returning the estimation function for models with restrictions has not yet been implemented. 327s > 327s > try( estfun( fitols5 ) ) 327s Error in estfun.systemfit(fitols5) : 327s returning the estimation function for models with restrictions has not yet been implemented. 327s > 327s > try( estfun( fitols5Sym ) ) 327s Error in estfun.systemfit(fitols5Sym) : 327s returning the estimation function for models with restrictions has not yet been implemented. 327s > 327s > 327s > ## **************** bread ************************ 327s > bread( fitols1 ) 327s demand_(Intercept) demand_price demand_income 327s demand_(Intercept) 607.086 -6.3865 0.3453 327s demand_price -6.386 0.0883 -0.0251 327s demand_income 0.345 -0.0251 0.0222 327s supply_(Intercept) 0.000 0.0000 0.0000 327s supply_price 0.000 0.0000 0.0000 327s supply_farmPrice 0.000 0.0000 0.0000 327s supply_trend 0.000 0.0000 0.0000 327s supply_(Intercept) supply_price supply_farmPrice 327s demand_(Intercept) 0.00 0.00000 0.00000 327s demand_price 0.00 0.00000 0.00000 327s demand_income 0.00 0.00000 0.00000 327s supply_(Intercept) 908.63 -6.82866 -2.10469 327s supply_price -6.83 0.06226 0.00584 327s supply_farmPrice -2.10 0.00584 0.01475 327s supply_trend -1.93 0.00361 0.00910 327s supply_trend 327s demand_(Intercept) 0.00000 327s demand_price 0.00000 327s demand_income 0.00000 327s supply_(Intercept) -1.93058 327s supply_price 0.00361 327s supply_farmPrice 0.00910 327s supply_trend 0.06576 327s > 327s > bread( fitols1s ) 327s demand_(Intercept) demand_price demand_income 327s demand_(Intercept) 607.086 -6.3865 0.3453 327s demand_price -6.386 0.0883 -0.0251 327s demand_income 0.345 -0.0251 0.0222 327s supply_(Intercept) 0.000 0.0000 0.0000 327s supply_price 0.000 0.0000 0.0000 327s supply_farmPrice 0.000 0.0000 0.0000 327s supply_trend 0.000 0.0000 0.0000 327s supply_(Intercept) supply_price supply_farmPrice 327s demand_(Intercept) 0.00 0.00000 0.00000 327s demand_price 0.00 0.00000 0.00000 327s demand_income 0.00 0.00000 0.00000 327s supply_(Intercept) 908.63 -6.82866 -2.10469 327s supply_price -6.83 0.06226 0.00584 327s supply_farmPrice -2.10 0.00584 0.01475 327s supply_trend -1.93 0.00361 0.00910 327s supply_trend 327s demand_(Intercept) 0.00000 327s demand_price 0.00000 327s demand_income 0.00000 327s supply_(Intercept) -1.93058 327s supply_price 0.00361 327s supply_farmPrice 0.00910 327s supply_trend 0.06576 327s > 327s > bread( fitols1r ) 327s demand_(Intercept) demand_price demand_income 327s demand_(Intercept) 607.086 -6.3865 0.3453 327s demand_price -6.386 0.0883 -0.0251 327s demand_income 0.345 -0.0251 0.0222 327s supply_(Intercept) 0.000 0.0000 0.0000 327s supply_price 0.000 0.0000 0.0000 327s supply_farmPrice 0.000 0.0000 0.0000 327s supply_trend 0.000 0.0000 0.0000 327s supply_(Intercept) supply_price supply_farmPrice 327s demand_(Intercept) 0.00 0.00000 0.00000 327s demand_price 0.00 0.00000 0.00000 327s demand_income 0.00 0.00000 0.00000 327s supply_(Intercept) 908.63 -6.82866 -2.10469 327s supply_price -6.83 0.06226 0.00584 327s supply_farmPrice -2.10 0.00584 0.01475 327s supply_trend -1.93 0.00361 0.00910 327s supply_trend 327s demand_(Intercept) 0.00000 327s demand_price 0.00000 327s demand_income 0.00000 327s supply_(Intercept) -1.93058 327s supply_price 0.00361 327s supply_farmPrice 0.00910 327s supply_trend 0.06576 327s > 327s > try( bread( fitols2 ) ) 327s > 327s Error in bread.systemfit(fitols2) : 327s returning the 'bread' for models with restrictions has not yet been implemented. 327s BEGIN TEST test_panel.R 328s 328s R version 4.3.2 (2023-10-31) -- "Eye Holes" 328s Copyright (C) 2023 The R Foundation for Statistical Computing 328s Platform: x86_64-pc-linux-gnu (64-bit) 328s 328s R is free software and comes with ABSOLUTELY NO WARRANTY. 328s You are welcome to redistribute it under certain conditions. 328s Type 'license()' or 'licence()' for distribution details. 328s 328s R is a collaborative project with many contributors. 328s Type 'contributors()' for more information and 328s 'citation()' on how to cite R or R packages in publications. 328s 328s Type 'demo()' for some demos, 'help()' for on-line help, or 328s 'help.start()' for an HTML browser interface to help. 328s Type 'q()' to quit R. 328s 328s > library( systemfit ) 328s Loading required package: Matrix 329s Loading required package: car 329s Loading required package: carData 329s Loading required package: lmtest 329s Loading required package: zoo 329s 329s Attaching package: ‘zoo’ 329s 329s The following objects are masked from ‘package:base’: 329s 329s as.Date, as.Date.numeric 329s 329s 329s Please cite the 'systemfit' package as: 329s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 329s 329s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 329s https://r-forge.r-project.org/projects/systemfit/ 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + library( plm ) 329s + options( digits = 3 ) 329s + useMatrix <- FALSE 329s + } 329s > 329s > ## Repeating the OLS and SUR estimations in Theil (1971, pp. 295, 300) 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + data( "GrunfeldGreene" ) 329s + GrunfeldTheil <- subset( GrunfeldGreene, 329s + firm %in% c( "General Electric", "Westinghouse" ) ) 329s + GrunfeldTheil <- pdata.frame( GrunfeldTheil, c( "firm", "year" ) ) 329s + formulaGrunfeld <- invest ~ value + capital 329s + } 329s > 329s > # OLS 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + theilOls <- systemfit( formulaGrunfeld, "OLS", 329s + data = GrunfeldTheil, useMatrix = useMatrix ) 329s + print( theilOls ) 329s + print( summary( theilOls ) ) 329s + print( summary( theilOls, useDfSys = TRUE, residCov = FALSE, 329s + equations = FALSE ) ) 329s + print( summary( theilOls, equations = FALSE ) ) 329s + print( coef( theilOls ) ) 329s + print( coef( summary(theilOls ) ) ) 329s + print( vcov( theilOls ) ) 329s + print( residuals( theilOls ) ) 329s + print( confint( theilOls ) ) 329s + print( fitted(theilOls ) ) 329s + print( logLik( theilOls ) ) 329s + print( logLik( theilOls, residCovDiag = TRUE ) ) 329s + print( nobs( theilOls ) ) 329s + print( model.frame( theilOls ) ) 329s + print( model.matrix( theilOls ) ) 329s + print( formula( theilOls ) ) 329s + print( formula( theilOls$eq[[ 1 ]] ) ) 329s + print( terms( theilOls ) ) 329s + print( terms( theilOls$eq[[ 1 ]] ) ) 329s + } 329s 329s systemfit results 329s method: OLS 329s 329s Coefficients: 329s General.Electric_(Intercept) General.Electric_value 329s -9.9563 0.0266 329s General.Electric_capital Westinghouse_(Intercept) 329s 0.1517 -0.5094 329s Westinghouse_value Westinghouse_capital 329s 0.0529 0.0924 329s 329s systemfit results 329s method: OLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 40 34 14990 38001 0.711 0.618 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s General.Electric 20 17 13217 777 27.9 0.705 0.671 329s Westinghouse 20 17 1773 104 10.2 0.744 0.714 329s 329s The covariance matrix of the residuals 329s General.Electric Westinghouse 329s General.Electric 777 208 329s Westinghouse 208 104 329s 329s The correlations of the residuals 329s General.Electric Westinghouse 329s General.Electric 1.000 0.729 329s Westinghouse 0.729 1.000 329s 329s 329s OLS estimates for 'General.Electric' (equation 1) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -9.9563 31.3742 -0.32 0.75 329s value 0.0266 0.0156 1.71 0.11 329s capital 0.1517 0.0257 5.90 1.7e-05 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 27.883 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 329s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 329s 329s 329s OLS estimates for 'Westinghouse' (equation 2) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -0.5094 8.0153 -0.06 0.9501 329s value 0.0529 0.0157 3.37 0.0037 ** 329s capital 0.0924 0.0561 1.65 0.1179 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 10.213 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 329s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 329s 329s 329s systemfit results 329s method: OLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 40 34 14990 38001 0.711 0.618 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s General.Electric 20 17 13217 777 27.9 0.705 0.671 329s Westinghouse 20 17 1773 104 10.2 0.744 0.714 329s 329s 329s Coefficients: 329s Estimate Std. Error t value Pr(>|t|) 329s General.Electric_(Intercept) -9.9563 31.3742 -0.32 0.7529 329s General.Electric_value 0.0266 0.0156 1.71 0.0972 . 329s General.Electric_capital 0.1517 0.0257 5.90 1.2e-06 *** 329s Westinghouse_(Intercept) -0.5094 8.0153 -0.06 0.9497 329s Westinghouse_value 0.0529 0.0157 3.37 0.0019 ** 329s Westinghouse_capital 0.0924 0.0561 1.65 0.1087 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s systemfit results 329s method: OLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 40 34 14990 38001 0.711 0.618 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s General.Electric 20 17 13217 777 27.9 0.705 0.671 329s Westinghouse 20 17 1773 104 10.2 0.744 0.714 329s 329s The covariance matrix of the residuals 329s General.Electric Westinghouse 329s General.Electric 777 208 329s Westinghouse 208 104 329s 329s The correlations of the residuals 329s General.Electric Westinghouse 329s General.Electric 1.000 0.729 329s Westinghouse 0.729 1.000 329s 329s 329s Coefficients: 329s Estimate Std. Error t value Pr(>|t|) 329s General.Electric_(Intercept) -9.9563 31.3742 -0.32 0.7548 329s General.Electric_value 0.0266 0.0156 1.71 0.1063 329s General.Electric_capital 0.1517 0.0257 5.90 1.7e-05 *** 329s Westinghouse_(Intercept) -0.5094 8.0153 -0.06 0.9501 329s Westinghouse_value 0.0529 0.0157 3.37 0.0037 ** 329s Westinghouse_capital 0.0924 0.0561 1.65 0.1179 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s General.Electric_(Intercept) General.Electric_value 329s -9.9563 0.0266 329s General.Electric_capital Westinghouse_(Intercept) 329s 0.1517 -0.5094 329s Westinghouse_value Westinghouse_capital 329s 0.0529 0.0924 329s Estimate Std. Error t value Pr(>|t|) 329s General.Electric_(Intercept) -9.9563 31.3742 -0.3173 7.55e-01 329s General.Electric_value 0.0266 0.0156 1.7057 1.06e-01 329s General.Electric_capital 0.1517 0.0257 5.9015 1.74e-05 329s Westinghouse_(Intercept) -0.5094 8.0153 -0.0636 9.50e-01 329s Westinghouse_value 0.0529 0.0157 3.3677 3.65e-03 329s Westinghouse_capital 0.0924 0.0561 1.6472 1.18e-01 329s General.Electric_(Intercept) 329s General.Electric_(Intercept) 984.344 329s General.Electric_value -0.451 329s General.Electric_capital -0.173 329s Westinghouse_(Intercept) 0.000 329s Westinghouse_value 0.000 329s Westinghouse_capital 0.000 329s General.Electric_value General.Electric_capital 329s General.Electric_(Intercept) -4.51e-01 -1.73e-01 329s General.Electric_value 2.42e-04 -4.73e-05 329s General.Electric_capital -4.73e-05 6.61e-04 329s Westinghouse_(Intercept) 0.00e+00 0.00e+00 329s Westinghouse_value 0.00e+00 0.00e+00 329s Westinghouse_capital 0.00e+00 0.00e+00 329s Westinghouse_(Intercept) Westinghouse_value 329s General.Electric_(Intercept) 0.000 0.000000 329s General.Electric_value 0.000 0.000000 329s General.Electric_capital 0.000 0.000000 329s Westinghouse_(Intercept) 64.245 -0.109545 329s Westinghouse_value -0.110 0.000247 329s Westinghouse_capital 0.169 -0.000653 329s Westinghouse_capital 329s General.Electric_(Intercept) 0.000000 329s General.Electric_value 0.000000 329s General.Electric_capital 0.000000 329s Westinghouse_(Intercept) 0.168911 329s Westinghouse_value -0.000653 329s Westinghouse_capital 0.003147 329s General.Electric Westinghouse 329s X1935 -2.860 3.144 329s X1936 -14.402 -0.958 329s X1937 -5.175 -3.684 329s X1938 -23.295 -7.915 329s X1939 -28.031 -10.322 329s X1940 -0.562 -6.613 329s X1941 40.750 17.265 329s X1942 16.036 8.547 329s X1943 -23.719 -2.916 329s X1944 -26.780 -3.257 329s X1945 1.768 -7.753 329s X1946 58.737 5.796 329s X1947 43.936 15.050 329s X1948 31.227 2.969 329s X1949 -23.552 -11.433 329s X1950 -37.511 -13.481 329s X1951 -4.983 4.619 329s X1952 1.893 13.138 329s X1953 5.087 11.308 329s X1954 -8.563 -13.505 329s 2.5 % 97.5 % 329s General.Electric_(Intercept) -76.150 56.238 329s General.Electric_value -0.006 0.059 329s General.Electric_capital 0.097 0.206 329s Westinghouse_(Intercept) -17.420 16.401 329s Westinghouse_value 0.020 0.086 329s Westinghouse_capital -0.026 0.211 329s General.Electric Westinghouse 329s X1935 36.0 9.79 329s X1936 59.4 26.86 329s X1937 82.4 38.73 329s X1938 67.9 30.81 329s X1939 76.1 29.16 329s X1940 75.0 35.18 329s X1941 72.3 31.25 329s X1942 75.9 34.79 329s X1943 85.0 39.94 329s X1944 83.6 41.07 329s X1945 91.8 47.02 329s X1946 101.2 47.66 329s X1947 103.3 40.51 329s X1948 115.1 46.59 329s X1949 121.9 43.47 329s X1950 131.0 45.72 329s X1951 140.2 49.76 329s X1952 155.4 58.64 329s X1953 174.4 78.77 329s X1954 198.2 82.11 329s 'log Lik.' -159 (df=7) 329s 'log Lik.' -167 (df=7) 329s [1] 40 329s General.Electric_invest General.Electric_value General.Electric_capital 329s X1935 33.1 1171 97.8 329s X1936 45.0 2016 104.4 329s X1937 77.2 2803 118.0 329s X1938 44.6 2040 156.2 329s X1939 48.1 2256 172.6 329s X1940 74.4 2132 186.6 329s X1941 113.0 1834 220.9 329s X1942 91.9 1588 287.8 329s X1943 61.3 1749 319.9 329s X1944 56.8 1687 321.3 329s X1945 93.6 2008 319.6 329s X1946 159.9 2208 346.0 329s X1947 147.2 1657 456.4 329s X1948 146.3 1604 543.4 329s X1949 98.3 1432 618.3 329s X1950 93.5 1610 647.4 329s X1951 135.2 1819 671.3 329s X1952 157.3 2080 726.1 329s X1953 179.5 2372 800.3 329s X1954 189.6 2760 888.9 329s Westinghouse_invest Westinghouse_value Westinghouse_capital 329s X1935 12.9 192 1.8 329s X1936 25.9 516 0.8 329s X1937 35.0 729 7.4 329s X1938 22.9 560 18.1 329s X1939 18.8 520 23.5 329s X1940 28.6 628 26.5 329s X1941 48.5 537 36.2 329s X1942 43.3 561 60.8 329s X1943 37.0 617 84.4 329s X1944 37.8 627 91.2 329s X1945 39.3 737 92.4 329s X1946 53.5 760 86.0 329s X1947 55.6 581 111.1 329s X1948 49.6 662 130.6 329s X1949 32.0 584 141.8 329s X1950 32.2 635 136.7 329s X1951 54.4 724 129.7 329s X1952 71.8 864 145.5 329s X1953 90.1 1194 174.8 329s X1954 68.6 1189 213.5 329s General.Electric_(Intercept) General.Electric_value 329s General.Electric_X1935 1 1171 329s General.Electric_X1936 1 2016 329s General.Electric_X1937 1 2803 329s General.Electric_X1938 1 2040 329s General.Electric_X1939 1 2256 329s General.Electric_X1940 1 2132 329s General.Electric_X1941 1 1834 329s General.Electric_X1942 1 1588 329s General.Electric_X1943 1 1749 329s General.Electric_X1944 1 1687 329s General.Electric_X1945 1 2008 329s General.Electric_X1946 1 2208 329s General.Electric_X1947 1 1657 329s General.Electric_X1948 1 1604 329s General.Electric_X1949 1 1432 329s General.Electric_X1950 1 1610 329s General.Electric_X1951 1 1819 329s General.Electric_X1952 1 2080 329s General.Electric_X1953 1 2372 329s General.Electric_X1954 1 2760 329s Westinghouse_X1935 0 0 329s Westinghouse_X1936 0 0 329s Westinghouse_X1937 0 0 329s Westinghouse_X1938 0 0 329s Westinghouse_X1939 0 0 329s Westinghouse_X1940 0 0 329s Westinghouse_X1941 0 0 329s Westinghouse_X1942 0 0 329s Westinghouse_X1943 0 0 329s Westinghouse_X1944 0 0 329s Westinghouse_X1945 0 0 329s Westinghouse_X1946 0 0 329s Westinghouse_X1947 0 0 329s Westinghouse_X1948 0 0 329s Westinghouse_X1949 0 0 329s Westinghouse_X1950 0 0 329s Westinghouse_X1951 0 0 329s Westinghouse_X1952 0 0 329s Westinghouse_X1953 0 0 329s Westinghouse_X1954 0 0 329s General.Electric_capital Westinghouse_(Intercept) 329s General.Electric_X1935 97.8 0 329s General.Electric_X1936 104.4 0 329s General.Electric_X1937 118.0 0 329s General.Electric_X1938 156.2 0 329s General.Electric_X1939 172.6 0 329s General.Electric_X1940 186.6 0 329s General.Electric_X1941 220.9 0 329s General.Electric_X1942 287.8 0 329s General.Electric_X1943 319.9 0 329s General.Electric_X1944 321.3 0 329s General.Electric_X1945 319.6 0 329s General.Electric_X1946 346.0 0 329s General.Electric_X1947 456.4 0 329s General.Electric_X1948 543.4 0 329s General.Electric_X1949 618.3 0 329s General.Electric_X1950 647.4 0 329s General.Electric_X1951 671.3 0 329s General.Electric_X1952 726.1 0 329s General.Electric_X1953 800.3 0 329s General.Electric_X1954 888.9 0 329s Westinghouse_X1935 0.0 1 329s Westinghouse_X1936 0.0 1 329s Westinghouse_X1937 0.0 1 329s Westinghouse_X1938 0.0 1 329s Westinghouse_X1939 0.0 1 329s Westinghouse_X1940 0.0 1 329s Westinghouse_X1941 0.0 1 329s Westinghouse_X1942 0.0 1 329s Westinghouse_X1943 0.0 1 329s Westinghouse_X1944 0.0 1 329s Westinghouse_X1945 0.0 1 329s Westinghouse_X1946 0.0 1 329s Westinghouse_X1947 0.0 1 329s Westinghouse_X1948 0.0 1 329s Westinghouse_X1949 0.0 1 329s Westinghouse_X1950 0.0 1 329s Westinghouse_X1951 0.0 1 329s Westinghouse_X1952 0.0 1 329s Westinghouse_X1953 0.0 1 329s Westinghouse_X1954 0.0 1 329s Westinghouse_value Westinghouse_capital 329s General.Electric_X1935 0 0.0 329s General.Electric_X1936 0 0.0 329s General.Electric_X1937 0 0.0 329s General.Electric_X1938 0 0.0 329s General.Electric_X1939 0 0.0 329s General.Electric_X1940 0 0.0 329s General.Electric_X1941 0 0.0 329s General.Electric_X1942 0 0.0 329s General.Electric_X1943 0 0.0 329s General.Electric_X1944 0 0.0 329s General.Electric_X1945 0 0.0 329s General.Electric_X1946 0 0.0 329s General.Electric_X1947 0 0.0 329s General.Electric_X1948 0 0.0 329s General.Electric_X1949 0 0.0 329s General.Electric_X1950 0 0.0 329s General.Electric_X1951 0 0.0 329s General.Electric_X1952 0 0.0 329s General.Electric_X1953 0 0.0 329s General.Electric_X1954 0 0.0 329s Westinghouse_X1935 192 1.8 329s Westinghouse_X1936 516 0.8 329s Westinghouse_X1937 729 7.4 329s Westinghouse_X1938 560 18.1 329s Westinghouse_X1939 520 23.5 329s Westinghouse_X1940 628 26.5 329s Westinghouse_X1941 537 36.2 329s Westinghouse_X1942 561 60.8 329s Westinghouse_X1943 617 84.4 329s Westinghouse_X1944 627 91.2 329s Westinghouse_X1945 737 92.4 329s Westinghouse_X1946 760 86.0 329s Westinghouse_X1947 581 111.1 329s Westinghouse_X1948 662 130.6 329s Westinghouse_X1949 584 141.8 329s Westinghouse_X1950 635 136.7 329s Westinghouse_X1951 724 129.7 329s Westinghouse_X1952 864 145.5 329s Westinghouse_X1953 1194 174.8 329s Westinghouse_X1954 1189 213.5 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s attr(,"variables") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"factors") 329s General.Electric_value General.Electric_capital 329s General.Electric_invest 0 0 329s General.Electric_value 1 0 329s General.Electric_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Electric_value" "General.Electric_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"dataClasses") 329s General.Electric_invest General.Electric_value General.Electric_capital 329s "numeric" "numeric" "numeric" 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s attr(,"variables") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"factors") 329s Westinghouse_value Westinghouse_capital 329s Westinghouse_invest 0 0 329s Westinghouse_value 1 0 329s Westinghouse_capital 0 1 329s attr(,"term.labels") 329s [1] "Westinghouse_value" "Westinghouse_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"dataClasses") 329s Westinghouse_invest Westinghouse_value Westinghouse_capital 329s "numeric" "numeric" "numeric" 329s 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s attr(,"variables") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"factors") 329s General.Electric_value General.Electric_capital 329s General.Electric_invest 0 0 329s General.Electric_value 1 0 329s General.Electric_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Electric_value" "General.Electric_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"dataClasses") 329s General.Electric_invest General.Electric_value General.Electric_capital 329s "numeric" "numeric" "numeric" 329s > 329s > # SUR 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + theilSur <- systemfit( formulaGrunfeld, "SUR", 329s + data = GrunfeldTheil, methodResidCov = "noDfCor", useMatrix = useMatrix ) 329s + print( theilSur ) 329s + print( summary( theilSur ) ) 329s + print( summary( theilSur, useDfSys = TRUE, equations = FALSE ) ) 329s + print( summary( theilSur, residCov = FALSE, equations = FALSE ) ) 329s + print( coef( theilSur ) ) 329s + print( coef( summary( theilSur ) ) ) 329s + print( vcov( theilSur ) ) 329s + print( residuals( theilSur ) ) 329s + print( confint( theilSur ) ) 329s + print( fitted( theilSur ) ) 329s + print( logLik( theilSur ) ) 329s + print( logLik( theilSur, residCovDiag = TRUE ) ) 329s + print( nobs( theilSur ) ) 329s + print( model.frame( theilSur ) ) 329s + print( model.matrix( theilSur ) ) 329s + print( formula( theilSur ) ) 329s + print( formula( theilSur$eq[[ 2 ]] ) ) 329s + print( terms( theilSur ) ) 329s + print( terms( theilSur$eq[[ 2 ]] ) ) 329s + } 329s 329s systemfit results 329s method: SUR 329s 329s Coefficients: 329s General.Electric_(Intercept) General.Electric_value 329s -27.7193 0.0383 329s General.Electric_capital Westinghouse_(Intercept) 329s 0.1390 -1.2520 329s Westinghouse_value Westinghouse_capital 329s 0.0576 0.0640 329s 329s systemfit results 329s method: SUR 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 40 34 15590 25750 0.699 0.615 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s General.Electric 20 17 13788 811 28.5 0.693 0.656 329s Westinghouse 20 17 1801 106 10.3 0.740 0.710 329s 329s The covariance matrix of the residuals used for estimation 329s General.Electric Westinghouse 329s General.Electric 661 176.4 329s Westinghouse 176 88.7 329s 329s The covariance matrix of the residuals 329s General.Electric Westinghouse 329s General.Electric 689 190.6 329s Westinghouse 191 90.1 329s 329s The correlations of the residuals 329s General.Electric Westinghouse 329s General.Electric 1.000 0.765 329s Westinghouse 0.765 1.000 329s 329s 329s SUR estimates for 'General.Electric' (equation 1) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -27.7193 27.0328 -1.03 0.32 329s value 0.0383 0.0133 2.88 0.01 * 329s capital 0.1390 0.0230 6.04 1.3e-05 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 28.479 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 13788.376 MSE: 811.081 Root MSE: 28.479 329s Multiple R-Squared: 0.693 Adjusted R-Squared: 0.656 329s 329s 329s SUR estimates for 'Westinghouse' (equation 2) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -1.2520 6.9563 -0.18 0.85930 329s value 0.0576 0.0134 4.30 0.00049 *** 329s capital 0.0640 0.0489 1.31 0.20818 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 10.294 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 1801.301 MSE: 105.959 Root MSE: 10.294 329s Multiple R-Squared: 0.74 Adjusted R-Squared: 0.71 329s 329s 329s systemfit results 329s method: SUR 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 40 34 15590 25750 0.699 0.615 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s General.Electric 20 17 13788 811 28.5 0.693 0.656 329s Westinghouse 20 17 1801 106 10.3 0.740 0.710 329s 329s The covariance matrix of the residuals used for estimation 329s General.Electric Westinghouse 329s General.Electric 661 176.4 329s Westinghouse 176 88.7 329s 329s The covariance matrix of the residuals 329s General.Electric Westinghouse 329s General.Electric 689 190.6 329s Westinghouse 191 90.1 329s 329s The correlations of the residuals 329s General.Electric Westinghouse 329s General.Electric 1.000 0.765 329s Westinghouse 0.765 1.000 329s 329s 329s Coefficients: 329s Estimate Std. Error t value Pr(>|t|) 329s General.Electric_(Intercept) -27.7193 27.0328 -1.03 0.31242 329s General.Electric_value 0.0383 0.0133 2.88 0.00679 ** 329s General.Electric_capital 0.1390 0.0230 6.04 7.7e-07 *** 329s Westinghouse_(Intercept) -1.2520 6.9563 -0.18 0.85824 329s Westinghouse_value 0.0576 0.0134 4.30 0.00014 *** 329s Westinghouse_capital 0.0640 0.0489 1.31 0.19954 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s systemfit results 329s method: SUR 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 40 34 15590 25750 0.699 0.615 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s General.Electric 20 17 13788 811 28.5 0.693 0.656 329s Westinghouse 20 17 1801 106 10.3 0.740 0.710 329s 329s 329s Coefficients: 329s Estimate Std. Error t value Pr(>|t|) 329s General.Electric_(Intercept) -27.7193 27.0328 -1.03 0.31955 329s General.Electric_value 0.0383 0.0133 2.88 0.01034 * 329s General.Electric_capital 0.1390 0.0230 6.04 1.3e-05 *** 329s Westinghouse_(Intercept) -1.2520 6.9563 -0.18 0.85930 329s Westinghouse_value 0.0576 0.0134 4.30 0.00049 *** 329s Westinghouse_capital 0.0640 0.0489 1.31 0.20818 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s General.Electric_(Intercept) General.Electric_value 329s -27.7193 0.0383 329s General.Electric_capital Westinghouse_(Intercept) 329s 0.1390 -1.2520 329s Westinghouse_value Westinghouse_capital 329s 0.0576 0.0640 329s Estimate Std. Error t value Pr(>|t|) 329s General.Electric_(Intercept) -27.7193 27.0328 -1.03 3.20e-01 329s General.Electric_value 0.0383 0.0133 2.88 1.03e-02 329s General.Electric_capital 0.1390 0.0230 6.04 1.34e-05 329s Westinghouse_(Intercept) -1.2520 6.9563 -0.18 8.59e-01 329s Westinghouse_value 0.0576 0.0134 4.30 4.88e-04 329s Westinghouse_capital 0.0640 0.0489 1.31 2.08e-01 329s General.Electric_(Intercept) 329s General.Electric_(Intercept) 730.774 329s General.Electric_value -0.329 329s General.Electric_capital -0.146 329s Westinghouse_(Intercept) 126.963 329s Westinghouse_value -0.226 329s Westinghouse_capital 0.393 329s General.Electric_value General.Electric_capital 329s General.Electric_(Intercept) -0.329266 -1.46e-01 329s General.Electric_value 0.000177 -3.40e-05 329s General.Electric_capital -0.000034 5.31e-04 329s Westinghouse_(Intercept) -0.052688 -3.96e-02 329s Westinghouse_value 0.000120 -1.69e-05 329s Westinghouse_capital -0.000325 5.95e-04 329s Westinghouse_(Intercept) Westinghouse_value 329s General.Electric_(Intercept) 126.9626 -2.26e-01 329s General.Electric_value -0.0527 1.20e-04 329s General.Electric_capital -0.0396 -1.69e-05 329s Westinghouse_(Intercept) 48.3908 -8.00e-02 329s Westinghouse_value -0.0800 1.80e-04 329s Westinghouse_capital 0.1136 -4.75e-04 329s Westinghouse_capital 329s General.Electric_(Intercept) 0.392515 329s General.Electric_value -0.000325 329s General.Electric_capital 0.000595 329s Westinghouse_(Intercept) 0.113618 329s Westinghouse_value -0.000475 329s Westinghouse_capital 0.002391 329s General.Electric Westinghouse 329s X1935 2.3756 3.03 329s X1936 -19.0218 -2.64 329s X1937 -18.8820 -6.18 329s X1938 -27.5395 -9.31 329s X1939 -34.6138 -11.37 329s X1940 -5.5099 -8.09 329s X1941 39.7415 16.49 329s X1942 18.7681 8.36 329s X1943 -22.4783 -2.70 329s X1944 -24.7900 -2.89 329s X1945 -0.0321 -7.87 329s X1946 54.9123 5.38 329s X1947 47.9946 16.20 329s X1948 37.0021 4.29 329s X1949 -14.7994 -9.42 329s X1950 -30.4914 -11.86 329s X1951 -0.1173 5.62 329s X1952 4.3913 13.93 329s X1953 5.0921 11.37 329s X1954 -12.0024 -12.32 329s 2.5 % 97.5 % 329s General.Electric_(Intercept) -84.754 29.315 329s General.Electric_value 0.010 0.066 329s General.Electric_capital 0.090 0.188 329s Westinghouse_(Intercept) -15.929 13.425 329s Westinghouse_value 0.029 0.086 329s Westinghouse_capital -0.039 0.167 329s General.Electric Westinghouse 329s X1935 30.7 9.9 329s X1936 64.0 28.5 329s X1937 96.1 41.2 329s X1938 72.1 32.2 329s X1939 82.7 30.2 329s X1940 79.9 36.7 329s X1941 73.3 32.0 329s X1942 73.1 35.0 329s X1943 83.8 39.7 329s X1944 81.6 40.7 329s X1945 93.6 47.1 329s X1946 105.0 48.1 329s X1947 99.2 39.4 329s X1948 109.3 45.3 329s X1949 113.1 41.5 329s X1950 124.0 44.1 329s X1951 135.3 48.8 329s X1952 152.9 57.9 329s X1953 174.4 78.7 329s X1954 201.6 80.9 329s 'log Lik.' -158 (df=9) 329s 'log Lik.' -167 (df=9) 329s [1] 40 329s General.Electric_invest General.Electric_value General.Electric_capital 329s X1935 33.1 1171 97.8 329s X1936 45.0 2016 104.4 329s X1937 77.2 2803 118.0 329s X1938 44.6 2040 156.2 329s X1939 48.1 2256 172.6 329s X1940 74.4 2132 186.6 329s X1941 113.0 1834 220.9 329s X1942 91.9 1588 287.8 329s X1943 61.3 1749 319.9 329s X1944 56.8 1687 321.3 329s X1945 93.6 2008 319.6 329s X1946 159.9 2208 346.0 329s X1947 147.2 1657 456.4 329s X1948 146.3 1604 543.4 329s X1949 98.3 1432 618.3 329s X1950 93.5 1610 647.4 329s X1951 135.2 1819 671.3 329s X1952 157.3 2080 726.1 329s X1953 179.5 2372 800.3 329s X1954 189.6 2760 888.9 329s Westinghouse_invest Westinghouse_value Westinghouse_capital 329s X1935 12.9 192 1.8 329s X1936 25.9 516 0.8 329s X1937 35.0 729 7.4 329s X1938 22.9 560 18.1 329s X1939 18.8 520 23.5 329s X1940 28.6 628 26.5 329s X1941 48.5 537 36.2 329s X1942 43.3 561 60.8 329s X1943 37.0 617 84.4 329s X1944 37.8 627 91.2 329s X1945 39.3 737 92.4 329s X1946 53.5 760 86.0 329s X1947 55.6 581 111.1 329s X1948 49.6 662 130.6 329s X1949 32.0 584 141.8 329s X1950 32.2 635 136.7 329s X1951 54.4 724 129.7 329s X1952 71.8 864 145.5 329s X1953 90.1 1194 174.8 329s X1954 68.6 1189 213.5 329s General.Electric_(Intercept) General.Electric_value 329s General.Electric_X1935 1 1171 329s General.Electric_X1936 1 2016 329s General.Electric_X1937 1 2803 329s General.Electric_X1938 1 2040 329s General.Electric_X1939 1 2256 329s General.Electric_X1940 1 2132 329s General.Electric_X1941 1 1834 329s General.Electric_X1942 1 1588 329s General.Electric_X1943 1 1749 329s General.Electric_X1944 1 1687 329s General.Electric_X1945 1 2008 329s General.Electric_X1946 1 2208 329s General.Electric_X1947 1 1657 329s General.Electric_X1948 1 1604 329s General.Electric_X1949 1 1432 329s General.Electric_X1950 1 1610 329s General.Electric_X1951 1 1819 329s General.Electric_X1952 1 2080 329s General.Electric_X1953 1 2372 329s General.Electric_X1954 1 2760 329s Westinghouse_X1935 0 0 329s Westinghouse_X1936 0 0 329s Westinghouse_X1937 0 0 329s Westinghouse_X1938 0 0 329s Westinghouse_X1939 0 0 329s Westinghouse_X1940 0 0 329s Westinghouse_X1941 0 0 329s Westinghouse_X1942 0 0 329s Westinghouse_X1943 0 0 329s Westinghouse_X1944 0 0 329s Westinghouse_X1945 0 0 329s Westinghouse_X1946 0 0 329s Westinghouse_X1947 0 0 329s Westinghouse_X1948 0 0 329s Westinghouse_X1949 0 0 329s Westinghouse_X1950 0 0 329s Westinghouse_X1951 0 0 329s Westinghouse_X1952 0 0 329s Westinghouse_X1953 0 0 329s Westinghouse_X1954 0 0 329s General.Electric_capital Westinghouse_(Intercept) 329s General.Electric_X1935 97.8 0 329s General.Electric_X1936 104.4 0 329s General.Electric_X1937 118.0 0 329s General.Electric_X1938 156.2 0 329s General.Electric_X1939 172.6 0 329s General.Electric_X1940 186.6 0 329s General.Electric_X1941 220.9 0 329s General.Electric_X1942 287.8 0 329s General.Electric_X1943 319.9 0 329s General.Electric_X1944 321.3 0 329s General.Electric_X1945 319.6 0 329s General.Electric_X1946 346.0 0 329s General.Electric_X1947 456.4 0 329s General.Electric_X1948 543.4 0 329s General.Electric_X1949 618.3 0 329s General.Electric_X1950 647.4 0 329s General.Electric_X1951 671.3 0 329s General.Electric_X1952 726.1 0 329s General.Electric_X1953 800.3 0 329s General.Electric_X1954 888.9 0 329s Westinghouse_X1935 0.0 1 329s Westinghouse_X1936 0.0 1 329s Westinghouse_X1937 0.0 1 329s Westinghouse_X1938 0.0 1 329s Westinghouse_X1939 0.0 1 329s Westinghouse_X1940 0.0 1 329s Westinghouse_X1941 0.0 1 329s Westinghouse_X1942 0.0 1 329s Westinghouse_X1943 0.0 1 329s Westinghouse_X1944 0.0 1 329s Westinghouse_X1945 0.0 1 329s Westinghouse_X1946 0.0 1 329s Westinghouse_X1947 0.0 1 329s Westinghouse_X1948 0.0 1 329s Westinghouse_X1949 0.0 1 329s Westinghouse_X1950 0.0 1 329s Westinghouse_X1951 0.0 1 329s Westinghouse_X1952 0.0 1 329s Westinghouse_X1953 0.0 1 329s Westinghouse_X1954 0.0 1 329s Westinghouse_value Westinghouse_capital 329s General.Electric_X1935 0 0.0 329s General.Electric_X1936 0 0.0 329s General.Electric_X1937 0 0.0 329s General.Electric_X1938 0 0.0 329s General.Electric_X1939 0 0.0 329s General.Electric_X1940 0 0.0 329s General.Electric_X1941 0 0.0 329s General.Electric_X1942 0 0.0 329s General.Electric_X1943 0 0.0 329s General.Electric_X1944 0 0.0 329s General.Electric_X1945 0 0.0 329s General.Electric_X1946 0 0.0 329s General.Electric_X1947 0 0.0 329s General.Electric_X1948 0 0.0 329s General.Electric_X1949 0 0.0 329s General.Electric_X1950 0 0.0 329s General.Electric_X1951 0 0.0 329s General.Electric_X1952 0 0.0 329s General.Electric_X1953 0 0.0 329s General.Electric_X1954 0 0.0 329s Westinghouse_X1935 192 1.8 329s Westinghouse_X1936 516 0.8 329s Westinghouse_X1937 729 7.4 329s Westinghouse_X1938 560 18.1 329s Westinghouse_X1939 520 23.5 329s Westinghouse_X1940 628 26.5 329s Westinghouse_X1941 537 36.2 329s Westinghouse_X1942 561 60.8 329s Westinghouse_X1943 617 84.4 329s Westinghouse_X1944 627 91.2 329s Westinghouse_X1945 737 92.4 329s Westinghouse_X1946 760 86.0 329s Westinghouse_X1947 581 111.1 329s Westinghouse_X1948 662 130.6 329s Westinghouse_X1949 584 141.8 329s Westinghouse_X1950 635 136.7 329s Westinghouse_X1951 724 129.7 329s Westinghouse_X1952 864 145.5 329s Westinghouse_X1953 1194 174.8 329s Westinghouse_X1954 1189 213.5 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s attr(,"variables") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"factors") 329s General.Electric_value General.Electric_capital 329s General.Electric_invest 0 0 329s General.Electric_value 1 0 329s General.Electric_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Electric_value" "General.Electric_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"dataClasses") 329s General.Electric_invest General.Electric_value General.Electric_capital 329s "numeric" "numeric" "numeric" 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s attr(,"variables") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"factors") 329s Westinghouse_value Westinghouse_capital 329s Westinghouse_invest 0 0 329s Westinghouse_value 1 0 329s Westinghouse_capital 0 1 329s attr(,"term.labels") 329s [1] "Westinghouse_value" "Westinghouse_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"dataClasses") 329s Westinghouse_invest Westinghouse_value Westinghouse_capital 329s "numeric" "numeric" "numeric" 329s 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s attr(,"variables") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"factors") 329s Westinghouse_value Westinghouse_capital 329s Westinghouse_invest 0 0 329s Westinghouse_value 1 0 329s Westinghouse_capital 0 1 329s attr(,"term.labels") 329s [1] "Westinghouse_value" "Westinghouse_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"dataClasses") 329s Westinghouse_invest Westinghouse_value Westinghouse_capital 329s "numeric" "numeric" "numeric" 329s > 329s > ## Repeating the OLS and SUR estimations in Greene (2003, pp. 351) 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + GrunfeldGreene <- pdata.frame( GrunfeldGreene, c( "firm", "year" ) ) 329s + formulaGrunfeld <- invest ~ value + capital 329s + } 329s > 329s > # OLS 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + greeneOls <- systemfit( formulaGrunfeld, "OLS", 329s + data = GrunfeldGreene, useMatrix = useMatrix ) 329s + print( greeneOls ) 329s + print( summary( greeneOls ) ) 329s + print( summary( greeneOls, useDfSys = TRUE, equations = FALSE ) ) 329s + print( summary( greeneOls, residCov = FALSE ) ) 329s + print( sapply( greeneOls$eq, function(x){return(summary(x)$ssr/20)} ) ) # sigma^2 329s + print( coef( greeneOls ) ) 329s + print( coef( summary( greeneOls ) ) ) 329s + print( vcov( greeneOls ) ) 329s + print( residuals( greeneOls ) ) 329s + print( confint(greeneOls ) ) 329s + print( fitted( greeneOls ) ) 329s + print( logLik( greeneOls ) ) 329s + print( logLik( greeneOls, residCovDiag = TRUE ) ) 329s + print( nobs( greeneOls ) ) 329s + print( model.frame( greeneOls ) ) 329s + print( model.matrix( greeneOls ) ) 329s + print( formula( greeneOls ) ) 329s + print( formula( greeneOls$eq[[ 2 ]] ) ) 329s + print( terms( greeneOls ) ) 329s + print( terms( greeneOls$eq[[ 2 ]] ) ) 329s + } 329s 329s systemfit results 329s method: OLS 329s 329s Coefficients: 329s Chrysler_(Intercept) Chrysler_value 329s -6.1900 0.0779 329s Chrysler_capital General.Electric_(Intercept) 329s 0.3157 -9.9563 329s General.Electric_value General.Electric_capital 329s 0.0266 0.1517 329s General.Motors_(Intercept) General.Motors_value 329s -149.7825 0.1193 329s General.Motors_capital US.Steel_(Intercept) 329s 0.3714 -30.3685 329s US.Steel_value US.Steel_capital 329s 0.1566 0.4239 329s Westinghouse_(Intercept) Westinghouse_value 329s -0.5094 0.0529 329s Westinghouse_capital 329s 0.0924 329s 329s systemfit results 329s method: OLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 85 339121 2.09e+14 0.848 0.862 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 2997 176 13.3 0.914 0.903 329s General.Electric 20 17 13217 777 27.9 0.705 0.671 329s General.Motors 20 17 143206 8424 91.8 0.921 0.912 329s US.Steel 20 17 177928 10466 102.3 0.440 0.374 329s Westinghouse 20 17 1773 104 10.2 0.744 0.714 329s 329s The covariance matrix of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 176.3 -25.1 -333 492 15.7 329s General.Electric -25.1 777.4 715 1065 207.6 329s General.Motors -332.7 714.7 8424 -2614 148.4 329s US.Steel 491.9 1064.6 -2614 10466 642.6 329s Westinghouse 15.7 207.6 148 643 104.3 329s 329s The correlations of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 1.0000 -0.0679 -0.273 0.362 0.115 329s General.Electric -0.0679 1.0000 0.279 0.373 0.729 329s General.Motors -0.2730 0.2793 1.000 -0.278 0.158 329s US.Steel 0.3621 0.3732 -0.278 1.000 0.615 329s Westinghouse 0.1154 0.7290 0.158 0.615 1.000 329s 329s 329s OLS estimates for 'Chrysler' (equation 1) 329s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -6.1900 13.5065 -0.46 0.6525 329s value 0.0779 0.0200 3.90 0.0011 ** 329s capital 0.3157 0.0288 10.96 4e-09 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 13.279 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 2997.444 MSE: 176.32 Root MSE: 13.279 329s Multiple R-Squared: 0.914 Adjusted R-Squared: 0.903 329s 329s 329s OLS estimates for 'General.Electric' (equation 2) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -9.9563 31.3742 -0.32 0.75 329s value 0.0266 0.0156 1.71 0.11 329s capital 0.1517 0.0257 5.90 1.7e-05 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 27.883 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 329s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 329s 329s 329s OLS estimates for 'General.Motors' (equation 3) 329s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -149.7825 105.8421 -1.42 0.17508 329s value 0.1193 0.0258 4.62 0.00025 *** 329s capital 0.3714 0.0371 10.02 1.5e-08 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 91.782 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 143205.877 MSE: 8423.875 Root MSE: 91.782 329s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.912 329s 329s 329s OLS estimates for 'US.Steel' (equation 4) 329s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -30.3685 157.0477 -0.19 0.849 329s value 0.1566 0.0789 1.98 0.064 . 329s capital 0.4239 0.1552 2.73 0.014 * 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 102.305 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 177928.314 MSE: 10466.371 Root MSE: 102.305 329s Multiple R-Squared: 0.44 Adjusted R-Squared: 0.374 329s 329s 329s OLS estimates for 'Westinghouse' (equation 5) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -0.5094 8.0153 -0.06 0.9501 329s value 0.0529 0.0157 3.37 0.0037 ** 329s capital 0.0924 0.0561 1.65 0.1179 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 10.213 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 329s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 329s 329s 329s systemfit results 329s method: OLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 85 339121 2.09e+14 0.848 0.862 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 2997 176 13.3 0.914 0.903 329s General.Electric 20 17 13217 777 27.9 0.705 0.671 329s General.Motors 20 17 143206 8424 91.8 0.921 0.912 329s US.Steel 20 17 177928 10466 102.3 0.440 0.374 329s Westinghouse 20 17 1773 104 10.2 0.744 0.714 329s 329s The covariance matrix of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 176.3 -25.1 -333 492 15.7 329s General.Electric -25.1 777.4 715 1065 207.6 329s General.Motors -332.7 714.7 8424 -2614 148.4 329s US.Steel 491.9 1064.6 -2614 10466 642.6 329s Westinghouse 15.7 207.6 148 643 104.3 329s 329s The correlations of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 1.0000 -0.0679 -0.273 0.362 0.115 329s General.Electric -0.0679 1.0000 0.279 0.373 0.729 329s General.Motors -0.2730 0.2793 1.000 -0.278 0.158 329s US.Steel 0.3621 0.3732 -0.278 1.000 0.615 329s Westinghouse 0.1154 0.7290 0.158 0.615 1.000 329s 329s 329s Coefficients: 329s Estimate Std. Error t value Pr(>|t|) 329s Chrysler_(Intercept) -6.1900 13.5065 -0.46 0.64791 329s Chrysler_value 0.0779 0.0200 3.90 0.00019 *** 329s Chrysler_capital 0.3157 0.0288 10.96 < 2e-16 *** 329s General.Electric_(Intercept) -9.9563 31.3742 -0.32 0.75176 329s General.Electric_value 0.0266 0.0156 1.71 0.09171 . 329s General.Electric_capital 0.1517 0.0257 5.90 7.2e-08 *** 329s General.Motors_(Intercept) -149.7825 105.8421 -1.42 0.16068 329s General.Motors_value 0.1193 0.0258 4.62 1.4e-05 *** 329s General.Motors_capital 0.3714 0.0371 10.02 4.4e-16 *** 329s US.Steel_(Intercept) -30.3685 157.0477 -0.19 0.84713 329s US.Steel_value 0.1566 0.0789 1.98 0.05039 . 329s US.Steel_capital 0.4239 0.1552 2.73 0.00768 ** 329s Westinghouse_(Intercept) -0.5094 8.0153 -0.06 0.94948 329s Westinghouse_value 0.0529 0.0157 3.37 0.00114 ** 329s Westinghouse_capital 0.0924 0.0561 1.65 0.10321 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s systemfit results 329s method: OLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 85 339121 2.09e+14 0.848 0.862 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 2997 176 13.3 0.914 0.903 329s General.Electric 20 17 13217 777 27.9 0.705 0.671 329s General.Motors 20 17 143206 8424 91.8 0.921 0.912 329s US.Steel 20 17 177928 10466 102.3 0.440 0.374 329s Westinghouse 20 17 1773 104 10.2 0.744 0.714 329s 329s 329s OLS estimates for 'Chrysler' (equation 1) 329s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -6.1900 13.5065 -0.46 0.6525 329s value 0.0779 0.0200 3.90 0.0011 ** 329s capital 0.3157 0.0288 10.96 4e-09 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 13.279 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 2997.444 MSE: 176.32 Root MSE: 13.279 329s Multiple R-Squared: 0.914 Adjusted R-Squared: 0.903 329s 329s 329s OLS estimates for 'General.Electric' (equation 2) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -9.9563 31.3742 -0.32 0.75 329s value 0.0266 0.0156 1.71 0.11 329s capital 0.1517 0.0257 5.90 1.7e-05 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 27.883 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 329s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 329s 329s 329s OLS estimates for 'General.Motors' (equation 3) 329s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -149.7825 105.8421 -1.42 0.17508 329s value 0.1193 0.0258 4.62 0.00025 *** 329s capital 0.3714 0.0371 10.02 1.5e-08 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 91.782 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 143205.877 MSE: 8423.875 Root MSE: 91.782 329s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.912 329s 329s 329s OLS estimates for 'US.Steel' (equation 4) 329s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -30.3685 157.0477 -0.19 0.849 329s value 0.1566 0.0789 1.98 0.064 . 329s capital 0.4239 0.1552 2.73 0.014 * 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 102.305 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 177928.314 MSE: 10466.371 Root MSE: 102.305 329s Multiple R-Squared: 0.44 Adjusted R-Squared: 0.374 329s 329s 329s OLS estimates for 'Westinghouse' (equation 5) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -0.5094 8.0153 -0.06 0.9501 329s value 0.0529 0.0157 3.37 0.0037 ** 329s capital 0.0924 0.0561 1.65 0.1179 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 10.213 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 329s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 329s 329s [1] 149.9 660.8 7160.3 8896.4 88.7 329s Chrysler_(Intercept) Chrysler_value 329s -6.1900 0.0779 329s Chrysler_capital General.Electric_(Intercept) 329s 0.3157 -9.9563 329s General.Electric_value General.Electric_capital 329s 0.0266 0.1517 329s General.Motors_(Intercept) General.Motors_value 329s -149.7825 0.1193 329s General.Motors_capital US.Steel_(Intercept) 329s 0.3714 -30.3685 329s US.Steel_value US.Steel_capital 329s 0.1566 0.4239 329s Westinghouse_(Intercept) Westinghouse_value 329s -0.5094 0.0529 329s Westinghouse_capital 329s 0.0924 329s Estimate Std. Error t value Pr(>|t|) 329s Chrysler_(Intercept) -6.1900 13.5065 -0.4583 6.53e-01 329s Chrysler_value 0.0779 0.0200 3.9026 1.15e-03 329s Chrysler_capital 0.3157 0.0288 10.9574 3.99e-09 329s General.Electric_(Intercept) -9.9563 31.3742 -0.3173 7.55e-01 329s General.Electric_value 0.0266 0.0156 1.7057 1.06e-01 329s General.Electric_capital 0.1517 0.0257 5.9015 1.74e-05 329s General.Motors_(Intercept) -149.7825 105.8421 -1.4151 1.75e-01 329s General.Motors_value 0.1193 0.0258 4.6172 2.46e-04 329s General.Motors_capital 0.3714 0.0371 10.0193 1.51e-08 329s US.Steel_(Intercept) -30.3685 157.0477 -0.1934 8.49e-01 329s US.Steel_value 0.1566 0.0789 1.9848 6.35e-02 329s US.Steel_capital 0.4239 0.1552 2.7308 1.42e-02 329s Westinghouse_(Intercept) -0.5094 8.0153 -0.0636 9.50e-01 329s Westinghouse_value 0.0529 0.0157 3.3677 3.65e-03 329s Westinghouse_capital 0.0924 0.0561 1.6472 1.18e-01 329s Chrysler_(Intercept) Chrysler_value 329s Chrysler_(Intercept) 182.4250 -0.254690 329s Chrysler_value -0.2547 0.000399 329s Chrysler_capital 0.0243 -0.000180 329s General.Electric_(Intercept) 0.0000 0.000000 329s General.Electric_value 0.0000 0.000000 329s General.Electric_capital 0.0000 0.000000 329s General.Motors_(Intercept) 0.0000 0.000000 329s General.Motors_value 0.0000 0.000000 329s General.Motors_capital 0.0000 0.000000 329s US.Steel_(Intercept) 0.0000 0.000000 329s US.Steel_value 0.0000 0.000000 329s US.Steel_capital 0.0000 0.000000 329s Westinghouse_(Intercept) 0.0000 0.000000 329s Westinghouse_value 0.0000 0.000000 329s Westinghouse_capital 0.0000 0.000000 329s Chrysler_capital General.Electric_(Intercept) 329s Chrysler_(Intercept) 0.02429 0.000 329s Chrysler_value -0.00018 0.000 329s Chrysler_capital 0.00083 0.000 329s General.Electric_(Intercept) 0.00000 984.344 329s General.Electric_value 0.00000 -0.451 329s General.Electric_capital 0.00000 -0.173 329s General.Motors_(Intercept) 0.00000 0.000 329s General.Motors_value 0.00000 0.000 329s General.Motors_capital 0.00000 0.000 329s US.Steel_(Intercept) 0.00000 0.000 329s US.Steel_value 0.00000 0.000 329s US.Steel_capital 0.00000 0.000 329s Westinghouse_(Intercept) 0.00000 0.000 329s Westinghouse_value 0.00000 0.000 329s Westinghouse_capital 0.00000 0.000 329s General.Electric_value General.Electric_capital 329s Chrysler_(Intercept) 0.00e+00 0.00e+00 329s Chrysler_value 0.00e+00 0.00e+00 329s Chrysler_capital 0.00e+00 0.00e+00 329s General.Electric_(Intercept) -4.51e-01 -1.73e-01 329s General.Electric_value 2.42e-04 -4.73e-05 329s General.Electric_capital -4.73e-05 6.61e-04 329s General.Motors_(Intercept) 0.00e+00 0.00e+00 329s General.Motors_value 0.00e+00 0.00e+00 329s General.Motors_capital 0.00e+00 0.00e+00 329s US.Steel_(Intercept) 0.00e+00 0.00e+00 329s US.Steel_value 0.00e+00 0.00e+00 329s US.Steel_capital 0.00e+00 0.00e+00 329s Westinghouse_(Intercept) 0.00e+00 0.00e+00 329s Westinghouse_value 0.00e+00 0.00e+00 329s Westinghouse_capital 0.00e+00 0.00e+00 329s General.Motors_(Intercept) General.Motors_value 329s Chrysler_(Intercept) 0.000 0.000000 329s Chrysler_value 0.000 0.000000 329s Chrysler_capital 0.000 0.000000 329s General.Electric_(Intercept) 0.000 0.000000 329s General.Electric_value 0.000 0.000000 329s General.Electric_capital 0.000 0.000000 329s General.Motors_(Intercept) 11202.555 -2.623398 329s General.Motors_value -2.623 0.000667 329s General.Motors_capital 0.907 -0.000415 329s US.Steel_(Intercept) 0.000 0.000000 329s US.Steel_value 0.000 0.000000 329s US.Steel_capital 0.000 0.000000 329s Westinghouse_(Intercept) 0.000 0.000000 329s Westinghouse_value 0.000 0.000000 329s Westinghouse_capital 0.000 0.000000 329s General.Motors_capital US.Steel_(Intercept) 329s Chrysler_(Intercept) 0.000000 0.00 329s Chrysler_value 0.000000 0.00 329s Chrysler_capital 0.000000 0.00 329s General.Electric_(Intercept) 0.000000 0.00 329s General.Electric_value 0.000000 0.00 329s General.Electric_capital 0.000000 0.00 329s General.Motors_(Intercept) 0.906860 0.00 329s General.Motors_value -0.000415 0.00 329s General.Motors_capital 0.001374 0.00 329s US.Steel_(Intercept) 0.000000 24663.98 329s US.Steel_value 0.000000 -11.71 329s US.Steel_capital 0.000000 -3.52 329s Westinghouse_(Intercept) 0.000000 0.00 329s Westinghouse_value 0.000000 0.00 329s Westinghouse_capital 0.000000 0.00 329s US.Steel_value US.Steel_capital 329s Chrysler_(Intercept) 0.00000 0.00000 329s Chrysler_value 0.00000 0.00000 329s Chrysler_capital 0.00000 0.00000 329s General.Electric_(Intercept) 0.00000 0.00000 329s General.Electric_value 0.00000 0.00000 329s General.Electric_capital 0.00000 0.00000 329s General.Motors_(Intercept) 0.00000 0.00000 329s General.Motors_value 0.00000 0.00000 329s General.Motors_capital 0.00000 0.00000 329s US.Steel_(Intercept) -11.70740 -3.52078 329s US.Steel_value 0.00622 -0.00188 329s US.Steel_capital -0.00188 0.02409 329s Westinghouse_(Intercept) 0.00000 0.00000 329s Westinghouse_value 0.00000 0.00000 329s Westinghouse_capital 0.00000 0.00000 329s Westinghouse_(Intercept) Westinghouse_value 329s Chrysler_(Intercept) 0.000 0.000000 329s Chrysler_value 0.000 0.000000 329s Chrysler_capital 0.000 0.000000 329s General.Electric_(Intercept) 0.000 0.000000 329s General.Electric_value 0.000 0.000000 329s General.Electric_capital 0.000 0.000000 329s General.Motors_(Intercept) 0.000 0.000000 329s General.Motors_value 0.000 0.000000 329s General.Motors_capital 0.000 0.000000 329s US.Steel_(Intercept) 0.000 0.000000 329s US.Steel_value 0.000 0.000000 329s US.Steel_capital 0.000 0.000000 329s Westinghouse_(Intercept) 64.245 -0.109545 329s Westinghouse_value -0.110 0.000247 329s Westinghouse_capital 0.169 -0.000653 329s Westinghouse_capital 329s Chrysler_(Intercept) 0.000000 329s Chrysler_value 0.000000 329s Chrysler_capital 0.000000 329s General.Electric_(Intercept) 0.000000 329s General.Electric_value 0.000000 329s General.Electric_capital 0.000000 329s General.Motors_(Intercept) 0.000000 329s General.Motors_value 0.000000 329s General.Motors_capital 0.000000 329s US.Steel_(Intercept) 0.000000 329s US.Steel_value 0.000000 329s US.Steel_capital 0.000000 329s Westinghouse_(Intercept) 0.168911 329s Westinghouse_value -0.000653 329s Westinghouse_capital 0.003147 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s X1935 10.622 -2.860 99.14 4.15 3.144 329s X1936 10.425 -14.402 -34.01 81.32 -0.958 329s X1937 -7.404 -5.175 -140.48 31.18 -3.684 329s X1938 7.302 -23.295 -3.28 -99.75 -7.915 329s X1939 -14.682 -28.031 -109.45 -178.23 -10.322 329s X1940 -2.315 -0.562 -19.91 -160.69 -6.613 329s X1941 0.631 40.750 24.12 19.65 17.265 329s X1942 -1.581 16.036 98.02 9.82 8.547 329s X1943 -13.459 -23.719 67.76 -46.76 -2.916 329s X1944 -7.780 -26.780 100.03 -83.74 -3.257 329s X1945 11.757 1.768 35.12 -91.24 -7.753 329s X1946 -16.133 58.737 103.90 28.34 5.796 329s X1947 -6.823 43.936 15.18 57.32 15.050 329s X1948 6.615 31.227 -51.86 140.23 2.969 329s X1949 -7.379 -23.552 -115.39 25.65 -11.433 329s X1950 1.268 -37.511 -63.51 34.88 -13.481 329s X1951 39.502 -4.983 -119.40 115.10 4.619 329s X1952 2.774 1.893 -77.82 149.19 13.138 329s X1953 -6.215 5.087 49.50 89.00 11.308 329s X1954 -7.124 -8.563 142.33 -125.42 -13.505 329s 2.5 % 97.5 % 329s Chrysler_(Intercept) -34.686 22.306 329s Chrysler_value 0.036 0.120 329s Chrysler_capital 0.255 0.377 329s General.Electric_(Intercept) -76.150 56.238 329s General.Electric_value -0.006 0.059 329s General.Electric_capital 0.097 0.206 329s General.Motors_(Intercept) -373.090 73.525 329s General.Motors_value 0.065 0.174 329s General.Motors_capital 0.293 0.450 329s US.Steel_(Intercept) -361.710 300.973 329s US.Steel_value -0.010 0.323 329s US.Steel_capital 0.096 0.751 329s Westinghouse_(Intercept) -17.420 16.401 329s Westinghouse_value 0.020 0.086 329s Westinghouse_capital -0.026 0.211 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s X1935 29.7 36.0 218 206 9.79 329s X1936 62.3 59.4 426 274 26.86 329s X1937 73.7 82.4 551 439 38.73 329s X1938 44.3 67.9 261 362 30.81 329s X1939 67.1 76.1 440 409 29.16 329s X1940 71.7 75.0 481 422 35.18 329s X1941 67.7 72.3 488 453 31.25 329s X1942 48.4 75.9 350 436 34.79 329s X1943 60.9 85.0 432 408 39.94 329s X1944 67.3 83.6 447 372 41.07 329s X1945 77.0 91.8 526 350 47.02 329s X1946 90.3 101.2 584 392 47.66 329s X1947 69.5 103.3 554 363 40.51 329s X1948 82.7 115.1 581 354 46.59 329s X1949 86.4 121.9 670 379 43.47 329s X1950 99.4 131.0 706 384 45.72 329s X1951 121.1 140.2 875 473 49.76 329s X1952 142.2 155.4 969 496 58.64 329s X1953 181.1 174.4 1255 552 78.77 329s X1954 179.6 198.2 1344 585 82.11 329s 'log Lik.' -464 (df=16) 329s 'log Lik.' -481 (df=16) 329s [1] 100 329s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 329s X1935 40.3 418 10.5 33.1 329s X1936 72.8 838 10.2 45.0 329s X1937 66.3 884 34.7 77.2 329s X1938 51.6 438 51.8 44.6 329s X1939 52.4 680 64.3 48.1 329s X1940 69.4 728 67.1 74.4 329s X1941 68.3 644 75.2 113.0 329s X1942 46.8 411 71.4 91.9 329s X1943 47.4 588 67.1 61.3 329s X1944 59.6 698 60.5 56.8 329s X1945 88.8 846 54.6 93.6 329s X1946 74.1 894 84.8 159.9 329s X1947 62.7 579 96.8 147.2 329s X1948 89.4 695 110.2 146.3 329s X1949 79.0 590 147.4 98.3 329s X1950 100.7 694 163.2 93.5 329s X1951 160.6 809 203.5 135.2 329s X1952 145.0 727 290.6 157.3 329s X1953 174.9 1002 346.1 179.5 329s X1954 172.5 703 414.9 189.6 329s General.Electric_value General.Electric_capital General.Motors_invest 329s X1935 1171 97.8 318 329s X1936 2016 104.4 392 329s X1937 2803 118.0 411 329s X1938 2040 156.2 258 329s X1939 2256 172.6 331 329s X1940 2132 186.6 461 329s X1941 1834 220.9 512 329s X1942 1588 287.8 448 329s X1943 1749 319.9 500 329s X1944 1687 321.3 548 329s X1945 2008 319.6 561 329s X1946 2208 346.0 688 329s X1947 1657 456.4 569 329s X1948 1604 543.4 529 329s X1949 1432 618.3 555 329s X1950 1610 647.4 643 329s X1951 1819 671.3 756 329s X1952 2080 726.1 891 329s X1953 2372 800.3 1304 329s X1954 2760 888.9 1487 329s General.Motors_value General.Motors_capital US.Steel_invest 329s X1935 3078 2.8 210 329s X1936 4662 52.6 355 329s X1937 5387 156.9 470 329s X1938 2792 209.2 262 329s X1939 4313 203.4 230 329s X1940 4644 207.2 262 329s X1941 4551 255.2 473 329s X1942 3244 303.7 446 329s X1943 4054 264.1 362 329s X1944 4379 201.6 288 329s X1945 4841 265.0 259 329s X1946 4901 402.2 420 329s X1947 3526 761.5 420 329s X1948 3255 922.4 494 329s X1949 3700 1020.1 405 329s X1950 3756 1099.0 419 329s X1951 4833 1207.7 588 329s X1952 4925 1430.5 645 329s X1953 6242 1777.3 641 329s X1954 5594 2226.3 459 329s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 329s X1935 1362 53.8 12.9 192 329s X1936 1807 50.5 25.9 516 329s X1937 2676 118.1 35.0 729 329s X1938 1802 260.2 22.9 560 329s X1939 1957 312.7 18.8 520 329s X1940 2203 254.2 28.6 628 329s X1941 2380 261.4 48.5 537 329s X1942 2169 298.7 43.3 561 329s X1943 1985 301.8 37.0 617 329s X1944 1814 279.1 37.8 627 329s X1945 1850 213.8 39.3 737 329s X1946 2068 232.6 53.5 760 329s X1947 1797 264.8 55.6 581 329s X1948 1626 306.9 49.6 662 329s X1949 1667 351.1 32.0 584 329s X1950 1677 357.8 32.2 635 329s X1951 2290 342.1 54.4 724 329s X1952 2159 444.2 71.8 864 329s X1953 2031 623.6 90.1 1194 329s X1954 2116 669.7 68.6 1189 329s Westinghouse_capital 329s X1935 1.8 329s X1936 0.8 329s X1937 7.4 329s X1938 18.1 329s X1939 23.5 329s X1940 26.5 329s X1941 36.2 329s X1942 60.8 329s X1943 84.4 329s X1944 91.2 329s X1945 92.4 329s X1946 86.0 329s X1947 111.1 329s X1948 130.6 329s X1949 141.8 329s X1950 136.7 329s X1951 129.7 329s X1952 145.5 329s X1953 174.8 329s X1954 213.5 329s Chrysler_(Intercept) Chrysler_value Chrysler_capital 329s Chrysler_X1935 1 418 10.5 329s Chrysler_X1936 1 838 10.2 329s Chrysler_X1937 1 884 34.7 329s Chrysler_X1938 1 438 51.8 329s Chrysler_X1939 1 680 64.3 329s Chrysler_X1940 1 728 67.1 329s Chrysler_X1941 1 644 75.2 329s Chrysler_X1942 1 411 71.4 329s Chrysler_X1943 1 588 67.1 329s Chrysler_X1944 1 698 60.5 329s Chrysler_X1945 1 846 54.6 329s Chrysler_X1946 1 894 84.8 329s Chrysler_X1947 1 579 96.8 329s Chrysler_X1948 1 695 110.2 329s Chrysler_X1949 1 590 147.4 329s Chrysler_X1950 1 694 163.2 329s Chrysler_X1951 1 809 203.5 329s Chrysler_X1952 1 727 290.6 329s Chrysler_X1953 1 1002 346.1 329s Chrysler_X1954 1 703 414.9 329s General.Electric_X1935 0 0 0.0 329s General.Electric_X1936 0 0 0.0 329s General.Electric_X1937 0 0 0.0 329s General.Electric_X1938 0 0 0.0 329s General.Electric_X1939 0 0 0.0 329s General.Electric_X1940 0 0 0.0 329s General.Electric_X1941 0 0 0.0 329s General.Electric_X1942 0 0 0.0 329s General.Electric_X1943 0 0 0.0 329s General.Electric_X1944 0 0 0.0 329s General.Electric_X1945 0 0 0.0 329s General.Electric_X1946 0 0 0.0 329s General.Electric_X1947 0 0 0.0 329s General.Electric_X1948 0 0 0.0 329s General.Electric_X1949 0 0 0.0 329s General.Electric_X1950 0 0 0.0 329s General.Electric_X1951 0 0 0.0 329s General.Electric_X1952 0 0 0.0 329s General.Electric_X1953 0 0 0.0 329s General.Electric_X1954 0 0 0.0 329s General.Motors_X1935 0 0 0.0 329s General.Motors_X1936 0 0 0.0 329s General.Motors_X1937 0 0 0.0 329s General.Motors_X1938 0 0 0.0 329s General.Motors_X1939 0 0 0.0 329s General.Motors_X1940 0 0 0.0 329s General.Motors_X1941 0 0 0.0 329s General.Motors_X1942 0 0 0.0 329s General.Motors_X1943 0 0 0.0 329s General.Motors_X1944 0 0 0.0 329s General.Motors_X1945 0 0 0.0 329s General.Motors_X1946 0 0 0.0 329s General.Motors_X1947 0 0 0.0 329s General.Motors_X1948 0 0 0.0 329s General.Motors_X1949 0 0 0.0 329s General.Motors_X1950 0 0 0.0 329s General.Motors_X1951 0 0 0.0 329s General.Motors_X1952 0 0 0.0 329s General.Motors_X1953 0 0 0.0 329s General.Motors_X1954 0 0 0.0 329s US.Steel_X1935 0 0 0.0 329s US.Steel_X1936 0 0 0.0 329s US.Steel_X1937 0 0 0.0 329s US.Steel_X1938 0 0 0.0 329s US.Steel_X1939 0 0 0.0 329s US.Steel_X1940 0 0 0.0 329s US.Steel_X1941 0 0 0.0 329s US.Steel_X1942 0 0 0.0 329s US.Steel_X1943 0 0 0.0 329s US.Steel_X1944 0 0 0.0 329s US.Steel_X1945 0 0 0.0 329s US.Steel_X1946 0 0 0.0 329s US.Steel_X1947 0 0 0.0 329s US.Steel_X1948 0 0 0.0 329s US.Steel_X1949 0 0 0.0 329s US.Steel_X1950 0 0 0.0 329s US.Steel_X1951 0 0 0.0 329s US.Steel_X1952 0 0 0.0 329s US.Steel_X1953 0 0 0.0 329s US.Steel_X1954 0 0 0.0 329s Westinghouse_X1935 0 0 0.0 329s Westinghouse_X1936 0 0 0.0 329s Westinghouse_X1937 0 0 0.0 329s Westinghouse_X1938 0 0 0.0 329s Westinghouse_X1939 0 0 0.0 329s Westinghouse_X1940 0 0 0.0 329s Westinghouse_X1941 0 0 0.0 329s Westinghouse_X1942 0 0 0.0 329s Westinghouse_X1943 0 0 0.0 329s Westinghouse_X1944 0 0 0.0 329s Westinghouse_X1945 0 0 0.0 329s Westinghouse_X1946 0 0 0.0 329s Westinghouse_X1947 0 0 0.0 329s Westinghouse_X1948 0 0 0.0 329s Westinghouse_X1949 0 0 0.0 329s Westinghouse_X1950 0 0 0.0 329s Westinghouse_X1951 0 0 0.0 329s Westinghouse_X1952 0 0 0.0 329s Westinghouse_X1953 0 0 0.0 329s Westinghouse_X1954 0 0 0.0 329s General.Electric_(Intercept) General.Electric_value 329s Chrysler_X1935 0 0 329s Chrysler_X1936 0 0 329s Chrysler_X1937 0 0 329s Chrysler_X1938 0 0 329s Chrysler_X1939 0 0 329s Chrysler_X1940 0 0 329s Chrysler_X1941 0 0 329s Chrysler_X1942 0 0 329s Chrysler_X1943 0 0 329s Chrysler_X1944 0 0 329s Chrysler_X1945 0 0 329s Chrysler_X1946 0 0 329s Chrysler_X1947 0 0 329s Chrysler_X1948 0 0 329s Chrysler_X1949 0 0 329s Chrysler_X1950 0 0 329s Chrysler_X1951 0 0 329s Chrysler_X1952 0 0 329s Chrysler_X1953 0 0 329s Chrysler_X1954 0 0 329s General.Electric_X1935 1 1171 329s General.Electric_X1936 1 2016 329s General.Electric_X1937 1 2803 329s General.Electric_X1938 1 2040 329s General.Electric_X1939 1 2256 329s General.Electric_X1940 1 2132 329s General.Electric_X1941 1 1834 329s General.Electric_X1942 1 1588 329s General.Electric_X1943 1 1749 329s General.Electric_X1944 1 1687 329s General.Electric_X1945 1 2008 329s General.Electric_X1946 1 2208 329s General.Electric_X1947 1 1657 329s General.Electric_X1948 1 1604 329s General.Electric_X1949 1 1432 329s General.Electric_X1950 1 1610 329s General.Electric_X1951 1 1819 329s General.Electric_X1952 1 2080 329s General.Electric_X1953 1 2372 329s General.Electric_X1954 1 2760 329s General.Motors_X1935 0 0 329s General.Motors_X1936 0 0 329s General.Motors_X1937 0 0 329s General.Motors_X1938 0 0 329s General.Motors_X1939 0 0 329s General.Motors_X1940 0 0 329s General.Motors_X1941 0 0 329s General.Motors_X1942 0 0 329s General.Motors_X1943 0 0 329s General.Motors_X1944 0 0 329s General.Motors_X1945 0 0 329s General.Motors_X1946 0 0 329s General.Motors_X1947 0 0 329s General.Motors_X1948 0 0 329s General.Motors_X1949 0 0 329s General.Motors_X1950 0 0 329s General.Motors_X1951 0 0 329s General.Motors_X1952 0 0 329s General.Motors_X1953 0 0 329s General.Motors_X1954 0 0 329s US.Steel_X1935 0 0 329s US.Steel_X1936 0 0 329s US.Steel_X1937 0 0 329s US.Steel_X1938 0 0 329s US.Steel_X1939 0 0 329s US.Steel_X1940 0 0 329s US.Steel_X1941 0 0 329s US.Steel_X1942 0 0 329s US.Steel_X1943 0 0 329s US.Steel_X1944 0 0 329s US.Steel_X1945 0 0 329s US.Steel_X1946 0 0 329s US.Steel_X1947 0 0 329s US.Steel_X1948 0 0 329s US.Steel_X1949 0 0 329s US.Steel_X1950 0 0 329s US.Steel_X1951 0 0 329s US.Steel_X1952 0 0 329s US.Steel_X1953 0 0 329s US.Steel_X1954 0 0 329s Westinghouse_X1935 0 0 329s Westinghouse_X1936 0 0 329s Westinghouse_X1937 0 0 329s Westinghouse_X1938 0 0 329s Westinghouse_X1939 0 0 329s Westinghouse_X1940 0 0 329s Westinghouse_X1941 0 0 329s Westinghouse_X1942 0 0 329s Westinghouse_X1943 0 0 329s Westinghouse_X1944 0 0 329s Westinghouse_X1945 0 0 329s Westinghouse_X1946 0 0 329s Westinghouse_X1947 0 0 329s Westinghouse_X1948 0 0 329s Westinghouse_X1949 0 0 329s Westinghouse_X1950 0 0 329s Westinghouse_X1951 0 0 329s Westinghouse_X1952 0 0 329s Westinghouse_X1953 0 0 329s Westinghouse_X1954 0 0 329s General.Electric_capital General.Motors_(Intercept) 329s Chrysler_X1935 0.0 0 329s Chrysler_X1936 0.0 0 329s Chrysler_X1937 0.0 0 329s Chrysler_X1938 0.0 0 329s Chrysler_X1939 0.0 0 329s Chrysler_X1940 0.0 0 329s Chrysler_X1941 0.0 0 329s Chrysler_X1942 0.0 0 329s Chrysler_X1943 0.0 0 329s Chrysler_X1944 0.0 0 329s Chrysler_X1945 0.0 0 329s Chrysler_X1946 0.0 0 329s Chrysler_X1947 0.0 0 329s Chrysler_X1948 0.0 0 329s Chrysler_X1949 0.0 0 329s Chrysler_X1950 0.0 0 329s Chrysler_X1951 0.0 0 329s Chrysler_X1952 0.0 0 329s Chrysler_X1953 0.0 0 329s Chrysler_X1954 0.0 0 329s General.Electric_X1935 97.8 0 329s General.Electric_X1936 104.4 0 329s General.Electric_X1937 118.0 0 329s General.Electric_X1938 156.2 0 329s General.Electric_X1939 172.6 0 329s General.Electric_X1940 186.6 0 329s General.Electric_X1941 220.9 0 329s General.Electric_X1942 287.8 0 329s General.Electric_X1943 319.9 0 329s General.Electric_X1944 321.3 0 329s General.Electric_X1945 319.6 0 329s General.Electric_X1946 346.0 0 329s General.Electric_X1947 456.4 0 329s General.Electric_X1948 543.4 0 329s General.Electric_X1949 618.3 0 329s General.Electric_X1950 647.4 0 329s General.Electric_X1951 671.3 0 329s General.Electric_X1952 726.1 0 329s General.Electric_X1953 800.3 0 329s General.Electric_X1954 888.9 0 329s General.Motors_X1935 0.0 1 329s General.Motors_X1936 0.0 1 329s General.Motors_X1937 0.0 1 329s General.Motors_X1938 0.0 1 329s General.Motors_X1939 0.0 1 329s General.Motors_X1940 0.0 1 329s General.Motors_X1941 0.0 1 329s General.Motors_X1942 0.0 1 329s General.Motors_X1943 0.0 1 329s General.Motors_X1944 0.0 1 329s General.Motors_X1945 0.0 1 329s General.Motors_X1946 0.0 1 329s General.Motors_X1947 0.0 1 329s General.Motors_X1948 0.0 1 329s General.Motors_X1949 0.0 1 329s General.Motors_X1950 0.0 1 329s General.Motors_X1951 0.0 1 329s General.Motors_X1952 0.0 1 329s General.Motors_X1953 0.0 1 329s General.Motors_X1954 0.0 1 329s US.Steel_X1935 0.0 0 329s US.Steel_X1936 0.0 0 329s US.Steel_X1937 0.0 0 329s US.Steel_X1938 0.0 0 329s US.Steel_X1939 0.0 0 329s US.Steel_X1940 0.0 0 329s US.Steel_X1941 0.0 0 329s US.Steel_X1942 0.0 0 329s US.Steel_X1943 0.0 0 329s US.Steel_X1944 0.0 0 329s US.Steel_X1945 0.0 0 329s US.Steel_X1946 0.0 0 329s US.Steel_X1947 0.0 0 329s US.Steel_X1948 0.0 0 329s US.Steel_X1949 0.0 0 329s US.Steel_X1950 0.0 0 329s US.Steel_X1951 0.0 0 329s US.Steel_X1952 0.0 0 329s US.Steel_X1953 0.0 0 329s US.Steel_X1954 0.0 0 329s Westinghouse_X1935 0.0 0 329s Westinghouse_X1936 0.0 0 329s Westinghouse_X1937 0.0 0 329s Westinghouse_X1938 0.0 0 329s Westinghouse_X1939 0.0 0 329s Westinghouse_X1940 0.0 0 329s Westinghouse_X1941 0.0 0 329s Westinghouse_X1942 0.0 0 329s Westinghouse_X1943 0.0 0 329s Westinghouse_X1944 0.0 0 329s Westinghouse_X1945 0.0 0 329s Westinghouse_X1946 0.0 0 329s Westinghouse_X1947 0.0 0 329s Westinghouse_X1948 0.0 0 329s Westinghouse_X1949 0.0 0 329s Westinghouse_X1950 0.0 0 329s Westinghouse_X1951 0.0 0 329s Westinghouse_X1952 0.0 0 329s Westinghouse_X1953 0.0 0 329s Westinghouse_X1954 0.0 0 329s General.Motors_value General.Motors_capital 329s Chrysler_X1935 0 0.0 329s Chrysler_X1936 0 0.0 329s Chrysler_X1937 0 0.0 329s Chrysler_X1938 0 0.0 329s Chrysler_X1939 0 0.0 329s Chrysler_X1940 0 0.0 329s Chrysler_X1941 0 0.0 329s Chrysler_X1942 0 0.0 329s Chrysler_X1943 0 0.0 329s Chrysler_X1944 0 0.0 329s Chrysler_X1945 0 0.0 329s Chrysler_X1946 0 0.0 329s Chrysler_X1947 0 0.0 329s Chrysler_X1948 0 0.0 329s Chrysler_X1949 0 0.0 329s Chrysler_X1950 0 0.0 329s Chrysler_X1951 0 0.0 329s Chrysler_X1952 0 0.0 329s Chrysler_X1953 0 0.0 329s Chrysler_X1954 0 0.0 329s General.Electric_X1935 0 0.0 329s General.Electric_X1936 0 0.0 329s General.Electric_X1937 0 0.0 329s General.Electric_X1938 0 0.0 329s General.Electric_X1939 0 0.0 329s General.Electric_X1940 0 0.0 329s General.Electric_X1941 0 0.0 329s General.Electric_X1942 0 0.0 329s General.Electric_X1943 0 0.0 329s General.Electric_X1944 0 0.0 329s General.Electric_X1945 0 0.0 329s General.Electric_X1946 0 0.0 329s General.Electric_X1947 0 0.0 329s General.Electric_X1948 0 0.0 329s General.Electric_X1949 0 0.0 329s General.Electric_X1950 0 0.0 329s General.Electric_X1951 0 0.0 329s General.Electric_X1952 0 0.0 329s General.Electric_X1953 0 0.0 329s General.Electric_X1954 0 0.0 329s General.Motors_X1935 3078 2.8 329s General.Motors_X1936 4662 52.6 329s General.Motors_X1937 5387 156.9 329s General.Motors_X1938 2792 209.2 329s General.Motors_X1939 4313 203.4 329s General.Motors_X1940 4644 207.2 329s General.Motors_X1941 4551 255.2 329s General.Motors_X1942 3244 303.7 329s General.Motors_X1943 4054 264.1 329s General.Motors_X1944 4379 201.6 329s General.Motors_X1945 4841 265.0 329s General.Motors_X1946 4901 402.2 329s General.Motors_X1947 3526 761.5 329s General.Motors_X1948 3255 922.4 329s General.Motors_X1949 3700 1020.1 329s General.Motors_X1950 3756 1099.0 329s General.Motors_X1951 4833 1207.7 329s General.Motors_X1952 4925 1430.5 329s General.Motors_X1953 6242 1777.3 329s General.Motors_X1954 5594 2226.3 329s US.Steel_X1935 0 0.0 329s US.Steel_X1936 0 0.0 329s US.Steel_X1937 0 0.0 329s US.Steel_X1938 0 0.0 329s US.Steel_X1939 0 0.0 329s US.Steel_X1940 0 0.0 329s US.Steel_X1941 0 0.0 329s US.Steel_X1942 0 0.0 329s US.Steel_X1943 0 0.0 329s US.Steel_X1944 0 0.0 329s US.Steel_X1945 0 0.0 329s US.Steel_X1946 0 0.0 329s US.Steel_X1947 0 0.0 329s US.Steel_X1948 0 0.0 329s US.Steel_X1949 0 0.0 329s US.Steel_X1950 0 0.0 329s US.Steel_X1951 0 0.0 329s US.Steel_X1952 0 0.0 329s US.Steel_X1953 0 0.0 329s US.Steel_X1954 0 0.0 329s Westinghouse_X1935 0 0.0 329s Westinghouse_X1936 0 0.0 329s Westinghouse_X1937 0 0.0 329s Westinghouse_X1938 0 0.0 329s Westinghouse_X1939 0 0.0 329s Westinghouse_X1940 0 0.0 329s Westinghouse_X1941 0 0.0 329s Westinghouse_X1942 0 0.0 329s Westinghouse_X1943 0 0.0 329s Westinghouse_X1944 0 0.0 329s Westinghouse_X1945 0 0.0 329s Westinghouse_X1946 0 0.0 329s Westinghouse_X1947 0 0.0 329s Westinghouse_X1948 0 0.0 329s Westinghouse_X1949 0 0.0 329s Westinghouse_X1950 0 0.0 329s Westinghouse_X1951 0 0.0 329s Westinghouse_X1952 0 0.0 329s Westinghouse_X1953 0 0.0 329s Westinghouse_X1954 0 0.0 329s US.Steel_(Intercept) US.Steel_value US.Steel_capital 329s Chrysler_X1935 0 0 0.0 329s Chrysler_X1936 0 0 0.0 329s Chrysler_X1937 0 0 0.0 329s Chrysler_X1938 0 0 0.0 329s Chrysler_X1939 0 0 0.0 329s Chrysler_X1940 0 0 0.0 329s Chrysler_X1941 0 0 0.0 329s Chrysler_X1942 0 0 0.0 329s Chrysler_X1943 0 0 0.0 329s Chrysler_X1944 0 0 0.0 329s Chrysler_X1945 0 0 0.0 329s Chrysler_X1946 0 0 0.0 329s Chrysler_X1947 0 0 0.0 329s Chrysler_X1948 0 0 0.0 329s Chrysler_X1949 0 0 0.0 329s Chrysler_X1950 0 0 0.0 329s Chrysler_X1951 0 0 0.0 329s Chrysler_X1952 0 0 0.0 329s Chrysler_X1953 0 0 0.0 329s Chrysler_X1954 0 0 0.0 329s General.Electric_X1935 0 0 0.0 329s General.Electric_X1936 0 0 0.0 329s General.Electric_X1937 0 0 0.0 329s General.Electric_X1938 0 0 0.0 329s General.Electric_X1939 0 0 0.0 329s General.Electric_X1940 0 0 0.0 329s General.Electric_X1941 0 0 0.0 329s General.Electric_X1942 0 0 0.0 329s General.Electric_X1943 0 0 0.0 329s General.Electric_X1944 0 0 0.0 329s General.Electric_X1945 0 0 0.0 329s General.Electric_X1946 0 0 0.0 329s General.Electric_X1947 0 0 0.0 329s General.Electric_X1948 0 0 0.0 329s General.Electric_X1949 0 0 0.0 329s General.Electric_X1950 0 0 0.0 329s General.Electric_X1951 0 0 0.0 329s General.Electric_X1952 0 0 0.0 329s General.Electric_X1953 0 0 0.0 329s General.Electric_X1954 0 0 0.0 329s General.Motors_X1935 0 0 0.0 329s General.Motors_X1936 0 0 0.0 329s General.Motors_X1937 0 0 0.0 329s General.Motors_X1938 0 0 0.0 329s General.Motors_X1939 0 0 0.0 329s General.Motors_X1940 0 0 0.0 329s General.Motors_X1941 0 0 0.0 329s General.Motors_X1942 0 0 0.0 329s General.Motors_X1943 0 0 0.0 329s General.Motors_X1944 0 0 0.0 329s General.Motors_X1945 0 0 0.0 329s General.Motors_X1946 0 0 0.0 329s General.Motors_X1947 0 0 0.0 329s General.Motors_X1948 0 0 0.0 329s General.Motors_X1949 0 0 0.0 329s General.Motors_X1950 0 0 0.0 329s General.Motors_X1951 0 0 0.0 329s General.Motors_X1952 0 0 0.0 329s General.Motors_X1953 0 0 0.0 329s General.Motors_X1954 0 0 0.0 329s US.Steel_X1935 1 1362 53.8 329s US.Steel_X1936 1 1807 50.5 329s US.Steel_X1937 1 2676 118.1 329s US.Steel_X1938 1 1802 260.2 329s US.Steel_X1939 1 1957 312.7 329s US.Steel_X1940 1 2203 254.2 329s US.Steel_X1941 1 2380 261.4 329s US.Steel_X1942 1 2169 298.7 329s US.Steel_X1943 1 1985 301.8 329s US.Steel_X1944 1 1814 279.1 329s US.Steel_X1945 1 1850 213.8 329s US.Steel_X1946 1 2068 232.6 329s US.Steel_X1947 1 1797 264.8 329s US.Steel_X1948 1 1626 306.9 329s US.Steel_X1949 1 1667 351.1 329s US.Steel_X1950 1 1677 357.8 329s US.Steel_X1951 1 2290 342.1 329s US.Steel_X1952 1 2159 444.2 329s US.Steel_X1953 1 2031 623.6 329s US.Steel_X1954 1 2116 669.7 329s Westinghouse_X1935 0 0 0.0 329s Westinghouse_X1936 0 0 0.0 329s Westinghouse_X1937 0 0 0.0 329s Westinghouse_X1938 0 0 0.0 329s Westinghouse_X1939 0 0 0.0 329s Westinghouse_X1940 0 0 0.0 329s Westinghouse_X1941 0 0 0.0 329s Westinghouse_X1942 0 0 0.0 329s Westinghouse_X1943 0 0 0.0 329s Westinghouse_X1944 0 0 0.0 329s Westinghouse_X1945 0 0 0.0 329s Westinghouse_X1946 0 0 0.0 329s Westinghouse_X1947 0 0 0.0 329s Westinghouse_X1948 0 0 0.0 329s Westinghouse_X1949 0 0 0.0 329s Westinghouse_X1950 0 0 0.0 329s Westinghouse_X1951 0 0 0.0 329s Westinghouse_X1952 0 0 0.0 329s Westinghouse_X1953 0 0 0.0 329s Westinghouse_X1954 0 0 0.0 329s Westinghouse_(Intercept) Westinghouse_value 329s Chrysler_X1935 0 0 329s Chrysler_X1936 0 0 329s Chrysler_X1937 0 0 329s Chrysler_X1938 0 0 329s Chrysler_X1939 0 0 329s Chrysler_X1940 0 0 329s Chrysler_X1941 0 0 329s Chrysler_X1942 0 0 329s Chrysler_X1943 0 0 329s Chrysler_X1944 0 0 329s Chrysler_X1945 0 0 329s Chrysler_X1946 0 0 329s Chrysler_X1947 0 0 329s Chrysler_X1948 0 0 329s Chrysler_X1949 0 0 329s Chrysler_X1950 0 0 329s Chrysler_X1951 0 0 329s Chrysler_X1952 0 0 329s Chrysler_X1953 0 0 329s Chrysler_X1954 0 0 329s General.Electric_X1935 0 0 329s General.Electric_X1936 0 0 329s General.Electric_X1937 0 0 329s General.Electric_X1938 0 0 329s General.Electric_X1939 0 0 329s General.Electric_X1940 0 0 329s General.Electric_X1941 0 0 329s General.Electric_X1942 0 0 329s General.Electric_X1943 0 0 329s General.Electric_X1944 0 0 329s General.Electric_X1945 0 0 329s General.Electric_X1946 0 0 329s General.Electric_X1947 0 0 329s General.Electric_X1948 0 0 329s General.Electric_X1949 0 0 329s General.Electric_X1950 0 0 329s General.Electric_X1951 0 0 329s General.Electric_X1952 0 0 329s General.Electric_X1953 0 0 329s General.Electric_X1954 0 0 329s General.Motors_X1935 0 0 329s General.Motors_X1936 0 0 329s General.Motors_X1937 0 0 329s General.Motors_X1938 0 0 329s General.Motors_X1939 0 0 329s General.Motors_X1940 0 0 329s General.Motors_X1941 0 0 329s General.Motors_X1942 0 0 329s General.Motors_X1943 0 0 329s General.Motors_X1944 0 0 329s General.Motors_X1945 0 0 329s General.Motors_X1946 0 0 329s General.Motors_X1947 0 0 329s General.Motors_X1948 0 0 329s General.Motors_X1949 0 0 329s General.Motors_X1950 0 0 329s General.Motors_X1951 0 0 329s General.Motors_X1952 0 0 329s General.Motors_X1953 0 0 329s General.Motors_X1954 0 0 329s US.Steel_X1935 0 0 329s US.Steel_X1936 0 0 329s US.Steel_X1937 0 0 329s US.Steel_X1938 0 0 329s US.Steel_X1939 0 0 329s US.Steel_X1940 0 0 329s US.Steel_X1941 0 0 329s US.Steel_X1942 0 0 329s US.Steel_X1943 0 0 329s US.Steel_X1944 0 0 329s US.Steel_X1945 0 0 329s US.Steel_X1946 0 0 329s US.Steel_X1947 0 0 329s US.Steel_X1948 0 0 329s US.Steel_X1949 0 0 329s US.Steel_X1950 0 0 329s US.Steel_X1951 0 0 329s US.Steel_X1952 0 0 329s US.Steel_X1953 0 0 329s US.Steel_X1954 0 0 329s Westinghouse_X1935 1 192 329s Westinghouse_X1936 1 516 329s Westinghouse_X1937 1 729 329s Westinghouse_X1938 1 560 329s Westinghouse_X1939 1 520 329s Westinghouse_X1940 1 628 329s Westinghouse_X1941 1 537 329s Westinghouse_X1942 1 561 329s Westinghouse_X1943 1 617 329s Westinghouse_X1944 1 627 329s Westinghouse_X1945 1 737 329s Westinghouse_X1946 1 760 329s Westinghouse_X1947 1 581 329s Westinghouse_X1948 1 662 329s Westinghouse_X1949 1 584 329s Westinghouse_X1950 1 635 329s Westinghouse_X1951 1 724 329s Westinghouse_X1952 1 864 329s Westinghouse_X1953 1 1194 329s Westinghouse_X1954 1 1189 329s Westinghouse_capital 329s Chrysler_X1935 0.0 329s Chrysler_X1936 0.0 329s Chrysler_X1937 0.0 329s Chrysler_X1938 0.0 329s Chrysler_X1939 0.0 329s Chrysler_X1940 0.0 329s Chrysler_X1941 0.0 329s Chrysler_X1942 0.0 329s Chrysler_X1943 0.0 329s Chrysler_X1944 0.0 329s Chrysler_X1945 0.0 329s Chrysler_X1946 0.0 329s Chrysler_X1947 0.0 329s Chrysler_X1948 0.0 329s Chrysler_X1949 0.0 329s Chrysler_X1950 0.0 329s Chrysler_X1951 0.0 329s Chrysler_X1952 0.0 329s Chrysler_X1953 0.0 329s Chrysler_X1954 0.0 329s General.Electric_X1935 0.0 329s General.Electric_X1936 0.0 329s General.Electric_X1937 0.0 329s General.Electric_X1938 0.0 329s General.Electric_X1939 0.0 329s General.Electric_X1940 0.0 329s General.Electric_X1941 0.0 329s General.Electric_X1942 0.0 329s General.Electric_X1943 0.0 329s General.Electric_X1944 0.0 329s General.Electric_X1945 0.0 329s General.Electric_X1946 0.0 329s General.Electric_X1947 0.0 329s General.Electric_X1948 0.0 329s General.Electric_X1949 0.0 329s General.Electric_X1950 0.0 329s General.Electric_X1951 0.0 329s General.Electric_X1952 0.0 329s General.Electric_X1953 0.0 329s General.Electric_X1954 0.0 329s General.Motors_X1935 0.0 329s General.Motors_X1936 0.0 329s General.Motors_X1937 0.0 329s General.Motors_X1938 0.0 329s General.Motors_X1939 0.0 329s General.Motors_X1940 0.0 329s General.Motors_X1941 0.0 329s General.Motors_X1942 0.0 329s General.Motors_X1943 0.0 329s General.Motors_X1944 0.0 329s General.Motors_X1945 0.0 329s General.Motors_X1946 0.0 329s General.Motors_X1947 0.0 329s General.Motors_X1948 0.0 329s General.Motors_X1949 0.0 329s General.Motors_X1950 0.0 329s General.Motors_X1951 0.0 329s General.Motors_X1952 0.0 329s General.Motors_X1953 0.0 329s General.Motors_X1954 0.0 329s US.Steel_X1935 0.0 329s US.Steel_X1936 0.0 329s US.Steel_X1937 0.0 329s US.Steel_X1938 0.0 329s US.Steel_X1939 0.0 329s US.Steel_X1940 0.0 329s US.Steel_X1941 0.0 329s US.Steel_X1942 0.0 329s US.Steel_X1943 0.0 329s US.Steel_X1944 0.0 329s US.Steel_X1945 0.0 329s US.Steel_X1946 0.0 329s US.Steel_X1947 0.0 329s US.Steel_X1948 0.0 329s US.Steel_X1949 0.0 329s US.Steel_X1950 0.0 329s US.Steel_X1951 0.0 329s US.Steel_X1952 0.0 329s US.Steel_X1953 0.0 329s US.Steel_X1954 0.0 329s Westinghouse_X1935 1.8 329s Westinghouse_X1936 0.8 329s Westinghouse_X1937 7.4 329s Westinghouse_X1938 18.1 329s Westinghouse_X1939 23.5 329s Westinghouse_X1940 26.5 329s Westinghouse_X1941 36.2 329s Westinghouse_X1942 60.8 329s Westinghouse_X1943 84.4 329s Westinghouse_X1944 91.2 329s Westinghouse_X1945 92.4 329s Westinghouse_X1946 86.0 329s Westinghouse_X1947 111.1 329s Westinghouse_X1948 130.6 329s Westinghouse_X1949 141.8 329s Westinghouse_X1950 136.7 329s Westinghouse_X1951 129.7 329s Westinghouse_X1952 145.5 329s Westinghouse_X1953 174.8 329s Westinghouse_X1954 213.5 329s $Chrysler 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s $General.Motors 329s General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s $US.Steel 329s US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s $Chrysler 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s attr(,"variables") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"factors") 329s Chrysler_value Chrysler_capital 329s Chrysler_invest 0 0 329s Chrysler_value 1 0 329s Chrysler_capital 0 1 329s attr(,"term.labels") 329s [1] "Chrysler_value" "Chrysler_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"dataClasses") 329s Chrysler_invest Chrysler_value Chrysler_capital 329s "numeric" "numeric" "numeric" 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s attr(,"variables") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"factors") 329s General.Electric_value General.Electric_capital 329s General.Electric_invest 0 0 329s General.Electric_value 1 0 329s General.Electric_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Electric_value" "General.Electric_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"dataClasses") 329s General.Electric_invest General.Electric_value General.Electric_capital 329s "numeric" "numeric" "numeric" 329s 329s $General.Motors 329s General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s attr(,"variables") 329s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 329s attr(,"factors") 329s General.Motors_value General.Motors_capital 329s General.Motors_invest 0 0 329s General.Motors_value 1 0 329s General.Motors_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Motors_value" "General.Motors_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 329s attr(,"dataClasses") 329s General.Motors_invest General.Motors_value General.Motors_capital 329s "numeric" "numeric" "numeric" 329s 329s $US.Steel 329s US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s attr(,"variables") 329s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 329s attr(,"factors") 329s US.Steel_value US.Steel_capital 329s US.Steel_invest 0 0 329s US.Steel_value 1 0 329s US.Steel_capital 0 1 329s attr(,"term.labels") 329s [1] "US.Steel_value" "US.Steel_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 329s attr(,"dataClasses") 329s US.Steel_invest US.Steel_value US.Steel_capital 329s "numeric" "numeric" "numeric" 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s attr(,"variables") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"factors") 329s Westinghouse_value Westinghouse_capital 329s Westinghouse_invest 0 0 329s Westinghouse_value 1 0 329s Westinghouse_capital 0 1 329s attr(,"term.labels") 329s [1] "Westinghouse_value" "Westinghouse_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"dataClasses") 329s Westinghouse_invest Westinghouse_value Westinghouse_capital 329s "numeric" "numeric" "numeric" 329s 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s attr(,"variables") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"factors") 329s General.Electric_value General.Electric_capital 329s General.Electric_invest 0 0 329s General.Electric_value 1 0 329s General.Electric_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Electric_value" "General.Electric_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"dataClasses") 329s General.Electric_invest General.Electric_value General.Electric_capital 329s "numeric" "numeric" "numeric" 329s > 329s > # OLS Pooled 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + greeneOlsPooled <- systemfit( formulaGrunfeld, "OLS", 329s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix ) 329s + print( greeneOlsPooled ) 329s + print( summary( greeneOlsPooled ) ) 329s + print( summary( greeneOlsPooled, useDfSys = FALSE, residCov = FALSE ) ) 329s + print( summary( greeneOlsPooled, residCov = FALSE, equations = FALSE ) ) 329s + print( sum( sapply( greeneOlsPooled$eq, function(x){return(summary(x)$ssr)}) )/97 ) # sigma^2 329s + print( coef( greeneOlsPooled ) ) 329s + print( coef( greeneOlsPooled, modified.regMat = TRUE ) ) 329s + print( coef( summary( greeneOlsPooled ) ) ) 329s + print( coef( summary( greeneOlsPooled ), modified.regMat = TRUE ) ) 329s + print( vcov( greeneOlsPooled ) ) 329s + print( vcov( greeneOlsPooled, modified.regMat = TRUE ) ) 329s + print( residuals( greeneOlsPooled ) ) 329s + print( confint( greeneOlsPooled ) ) 329s + print( fitted( greeneOlsPooled ) ) 329s + print( logLik( greeneOlsPooled ) ) 329s + print( logLik( greeneOlsPooled, residCovDiag = TRUE ) ) 329s + print( nobs( greeneOlsPooled ) ) 329s + print( model.frame( greeneOlsPooled ) ) 329s + print( model.matrix( greeneOlsPooled ) ) 329s + print( formula( greeneOlsPooled ) ) 329s + print( formula( greeneOlsPooled$eq[[ 1 ]] ) ) 329s + print( terms( greeneOlsPooled ) ) 329s + print( terms( greeneOlsPooled$eq[[ 1 ]] ) ) 329s + } 329s 329s systemfit results 329s method: OLS 329s 329s Coefficients: 329s Chrysler_(Intercept) Chrysler_value 329s -48.030 0.105 329s Chrysler_capital General.Electric_(Intercept) 329s 0.305 -48.030 329s General.Electric_value General.Electric_capital 329s 0.105 0.305 329s General.Motors_(Intercept) General.Motors_value 329s -48.030 0.105 329s General.Motors_capital US.Steel_(Intercept) 329s 0.305 -48.030 329s US.Steel_value US.Steel_capital 329s 0.105 0.305 329s Westinghouse_(Intercept) Westinghouse_value 329s -48.030 0.105 329s Westinghouse_capital 329s 0.305 329s 329s systemfit results 329s method: OLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 97 1570884 4.2e+17 0.294 0.812 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 15117 889 29.8 0.564 0.513 329s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 329s General.Motors 20 17 188218 11072 105.2 0.897 0.884 329s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 329s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 329s 329s The covariance matrix of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 889.2 -4898 -198 4748 -94.6 329s General.Electric -4898.1 40339 -2254 -32821 2658.0 329s General.Motors -197.7 -2254 11072 304 -1328.6 329s US.Steel 4748.1 -32821 304 39359 -1377.3 329s Westinghouse -94.6 2658 -1329 -1377 745.2 329s 329s The correlations of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 1.000 0.144 -0.1852 0.2218 0.186 329s General.Electric 0.144 1.000 -0.2592 -0.1216 0.881 329s General.Motors -0.185 -0.259 1.0000 -0.0155 -0.469 329s US.Steel 0.222 -0.122 -0.0155 1.0000 -0.119 329s Westinghouse 0.186 0.881 -0.4689 -0.1186 1.000 329s 329s 329s OLS estimates for 'Chrysler' (equation 1) 329s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.028 * 329s value 0.1051 0.0114 9.24 6.0e-15 *** 329s capital 0.3054 0.0435 7.02 3.1e-10 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 29.82 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 15117.016 MSE: 889.236 Root MSE: 29.82 329s Multiple R-Squared: 0.564 Adjusted R-Squared: 0.513 329s 329s 329s OLS estimates for 'General.Electric' (equation 2) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.028 * 329s value 0.1051 0.0114 9.24 6.0e-15 *** 329s capital 0.3054 0.0435 7.02 3.1e-10 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 200.847 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 685769.815 MSE: 40339.401 Root MSE: 200.847 329s Multiple R-Squared: -14.291 Adjusted R-Squared: -16.09 329s 329s 329s OLS estimates for 'General.Motors' (equation 3) 329s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.028 * 329s value 0.1051 0.0114 9.24 6.0e-15 *** 329s capital 0.3054 0.0435 7.02 3.1e-10 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 105.222 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 188218.158 MSE: 11071.656 Root MSE: 105.222 329s Multiple R-Squared: 0.897 Adjusted R-Squared: 0.884 329s 329s 329s OLS estimates for 'US.Steel' (equation 4) 329s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.028 * 329s value 0.1051 0.0114 9.24 6.0e-15 *** 329s capital 0.3054 0.0435 7.02 3.1e-10 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 198.392 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 669110.225 MSE: 39359.425 Root MSE: 198.392 329s Multiple R-Squared: -1.105 Adjusted R-Squared: -1.352 329s 329s 329s OLS estimates for 'Westinghouse' (equation 5) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.028 * 329s value 0.1051 0.0114 9.24 6.0e-15 *** 329s capital 0.3054 0.0435 7.02 3.1e-10 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 27.298 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 12668.473 MSE: 745.204 Root MSE: 27.298 329s Multiple R-Squared: -0.826 Adjusted R-Squared: -1.041 329s 329s 329s systemfit results 329s method: OLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 97 1570884 4.2e+17 0.294 0.812 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 15117 889 29.8 0.564 0.513 329s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 329s General.Motors 20 17 188218 11072 105.2 0.897 0.884 329s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 329s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 329s 329s 329s OLS estimates for 'Chrysler' (equation 1) 329s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.039 * 329s value 0.1051 0.0114 9.24 4.9e-08 *** 329s capital 0.3054 0.0435 7.02 2.1e-06 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 29.82 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 15117.016 MSE: 889.236 Root MSE: 29.82 329s Multiple R-Squared: 0.564 Adjusted R-Squared: 0.513 329s 329s 329s OLS estimates for 'General.Electric' (equation 2) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.039 * 329s value 0.1051 0.0114 9.24 4.9e-08 *** 329s capital 0.3054 0.0435 7.02 2.1e-06 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 200.847 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 685769.815 MSE: 40339.401 Root MSE: 200.847 329s Multiple R-Squared: -14.291 Adjusted R-Squared: -16.09 329s 329s 329s OLS estimates for 'General.Motors' (equation 3) 329s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.039 * 329s value 0.1051 0.0114 9.24 4.9e-08 *** 329s capital 0.3054 0.0435 7.02 2.1e-06 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 105.222 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 188218.158 MSE: 11071.656 Root MSE: 105.222 329s Multiple R-Squared: 0.897 Adjusted R-Squared: 0.884 329s 329s 329s OLS estimates for 'US.Steel' (equation 4) 329s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.039 * 329s value 0.1051 0.0114 9.24 4.9e-08 *** 329s capital 0.3054 0.0435 7.02 2.1e-06 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 198.392 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 669110.225 MSE: 39359.425 Root MSE: 198.392 329s Multiple R-Squared: -1.105 Adjusted R-Squared: -1.352 329s 329s 329s OLS estimates for 'Westinghouse' (equation 5) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -48.0297 21.4802 -2.24 0.039 * 329s value 0.1051 0.0114 9.24 4.9e-08 *** 329s capital 0.3054 0.0435 7.02 2.1e-06 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 27.298 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 12668.473 MSE: 745.204 Root MSE: 27.298 329s Multiple R-Squared: -0.826 Adjusted R-Squared: -1.041 329s 329s 329s systemfit results 329s method: OLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 97 1570884 4.2e+17 0.294 0.812 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 15117 889 29.8 0.564 0.513 329s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 329s General.Motors 20 17 188218 11072 105.2 0.897 0.884 329s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 329s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 329s 329s 329s Coefficients: 329s Estimate Std. Error t value Pr(>|t|) 329s Chrysler_(Intercept) -48.0297 21.4802 -2.24 0.028 * 329s Chrysler_value 0.1051 0.0114 9.24 6.0e-15 *** 329s Chrysler_capital 0.3054 0.0435 7.02 3.1e-10 *** 329s General.Electric_(Intercept) -48.0297 21.4802 -2.24 0.028 * 329s General.Electric_value 0.1051 0.0114 9.24 6.0e-15 *** 329s General.Electric_capital 0.3054 0.0435 7.02 3.1e-10 *** 329s General.Motors_(Intercept) -48.0297 21.4802 -2.24 0.028 * 329s General.Motors_value 0.1051 0.0114 9.24 6.0e-15 *** 329s General.Motors_capital 0.3054 0.0435 7.02 3.1e-10 *** 329s US.Steel_(Intercept) -48.0297 21.4802 -2.24 0.028 * 329s US.Steel_value 0.1051 0.0114 9.24 6.0e-15 *** 329s US.Steel_capital 0.3054 0.0435 7.02 3.1e-10 *** 329s Westinghouse_(Intercept) -48.0297 21.4802 -2.24 0.028 * 329s Westinghouse_value 0.1051 0.0114 9.24 6.0e-15 *** 329s Westinghouse_capital 0.3054 0.0435 7.02 3.1e-10 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s [1] 16195 329s Chrysler_(Intercept) Chrysler_value 329s -48.030 0.105 329s Chrysler_capital General.Electric_(Intercept) 329s 0.305 -48.030 329s General.Electric_value General.Electric_capital 329s 0.105 0.305 329s General.Motors_(Intercept) General.Motors_value 329s -48.030 0.105 329s General.Motors_capital US.Steel_(Intercept) 329s 0.305 -48.030 329s US.Steel_value US.Steel_capital 329s 0.105 0.305 329s Westinghouse_(Intercept) Westinghouse_value 329s -48.030 0.105 329s Westinghouse_capital 329s 0.305 329s C1 C2 C3 329s -48.030 0.105 0.305 329s Estimate Std. Error t value Pr(>|t|) 329s Chrysler_(Intercept) -48.030 21.4802 -2.24 2.76e-02 329s Chrysler_value 0.105 0.0114 9.24 6.00e-15 329s Chrysler_capital 0.305 0.0435 7.02 3.06e-10 329s General.Electric_(Intercept) -48.030 21.4802 -2.24 2.76e-02 329s General.Electric_value 0.105 0.0114 9.24 6.00e-15 329s General.Electric_capital 0.305 0.0435 7.02 3.06e-10 329s General.Motors_(Intercept) -48.030 21.4802 -2.24 2.76e-02 329s General.Motors_value 0.105 0.0114 9.24 6.00e-15 329s General.Motors_capital 0.305 0.0435 7.02 3.06e-10 329s US.Steel_(Intercept) -48.030 21.4802 -2.24 2.76e-02 329s US.Steel_value 0.105 0.0114 9.24 6.00e-15 329s US.Steel_capital 0.305 0.0435 7.02 3.06e-10 329s Westinghouse_(Intercept) -48.030 21.4802 -2.24 2.76e-02 329s Westinghouse_value 0.105 0.0114 9.24 6.00e-15 329s Westinghouse_capital 0.305 0.0435 7.02 3.06e-10 329s Estimate Std. Error t value Pr(>|t|) 329s C1 -48.030 21.4802 -2.24 2.76e-02 329s C2 0.105 0.0114 9.24 6.00e-15 329s C3 0.305 0.0435 7.02 3.06e-10 329s Chrysler_(Intercept) Chrysler_value 329s Chrysler_(Intercept) 461.39750 -0.154668 329s Chrysler_value -0.15467 0.000129 329s Chrysler_capital -0.00689 -0.000303 329s General.Electric_(Intercept) 461.39750 -0.154668 329s General.Electric_value -0.15467 0.000129 329s General.Electric_capital -0.00689 -0.000303 329s General.Motors_(Intercept) 461.39750 -0.154668 329s General.Motors_value -0.15467 0.000129 329s General.Motors_capital -0.00689 -0.000303 329s US.Steel_(Intercept) 461.39750 -0.154668 329s US.Steel_value -0.15467 0.000129 329s US.Steel_capital -0.00689 -0.000303 329s Westinghouse_(Intercept) 461.39750 -0.154668 329s Westinghouse_value -0.15467 0.000129 329s Westinghouse_capital -0.00689 -0.000303 329s Chrysler_capital General.Electric_(Intercept) 329s Chrysler_(Intercept) -0.006891 461.39750 329s Chrysler_value -0.000303 -0.15467 329s Chrysler_capital 0.001893 -0.00689 329s General.Electric_(Intercept) -0.006891 461.39750 329s General.Electric_value -0.000303 -0.15467 329s General.Electric_capital 0.001893 -0.00689 329s General.Motors_(Intercept) -0.006891 461.39750 329s General.Motors_value -0.000303 -0.15467 329s General.Motors_capital 0.001893 -0.00689 329s US.Steel_(Intercept) -0.006891 461.39750 329s US.Steel_value -0.000303 -0.15467 329s US.Steel_capital 0.001893 -0.00689 329s Westinghouse_(Intercept) -0.006891 461.39750 329s Westinghouse_value -0.000303 -0.15467 329s Westinghouse_capital 0.001893 -0.00689 329s General.Electric_value General.Electric_capital 329s Chrysler_(Intercept) -0.154668 -0.006891 329s Chrysler_value 0.000129 -0.000303 329s Chrysler_capital -0.000303 0.001893 329s General.Electric_(Intercept) -0.154668 -0.006891 329s General.Electric_value 0.000129 -0.000303 329s General.Electric_capital -0.000303 0.001893 329s General.Motors_(Intercept) -0.154668 -0.006891 329s General.Motors_value 0.000129 -0.000303 329s General.Motors_capital -0.000303 0.001893 329s US.Steel_(Intercept) -0.154668 -0.006891 329s US.Steel_value 0.000129 -0.000303 329s US.Steel_capital -0.000303 0.001893 329s Westinghouse_(Intercept) -0.154668 -0.006891 329s Westinghouse_value 0.000129 -0.000303 329s Westinghouse_capital -0.000303 0.001893 329s General.Motors_(Intercept) General.Motors_value 329s Chrysler_(Intercept) 461.39750 -0.154668 329s Chrysler_value -0.15467 0.000129 329s Chrysler_capital -0.00689 -0.000303 329s General.Electric_(Intercept) 461.39750 -0.154668 329s General.Electric_value -0.15467 0.000129 329s General.Electric_capital -0.00689 -0.000303 329s General.Motors_(Intercept) 461.39750 -0.154668 329s General.Motors_value -0.15467 0.000129 329s General.Motors_capital -0.00689 -0.000303 329s US.Steel_(Intercept) 461.39750 -0.154668 329s US.Steel_value -0.15467 0.000129 329s US.Steel_capital -0.00689 -0.000303 329s Westinghouse_(Intercept) 461.39750 -0.154668 329s Westinghouse_value -0.15467 0.000129 329s Westinghouse_capital -0.00689 -0.000303 329s General.Motors_capital US.Steel_(Intercept) 329s Chrysler_(Intercept) -0.006891 461.39750 329s Chrysler_value -0.000303 -0.15467 329s Chrysler_capital 0.001893 -0.00689 329s General.Electric_(Intercept) -0.006891 461.39750 329s General.Electric_value -0.000303 -0.15467 329s General.Electric_capital 0.001893 -0.00689 329s General.Motors_(Intercept) -0.006891 461.39750 329s General.Motors_value -0.000303 -0.15467 329s General.Motors_capital 0.001893 -0.00689 329s US.Steel_(Intercept) -0.006891 461.39750 329s US.Steel_value -0.000303 -0.15467 329s US.Steel_capital 0.001893 -0.00689 329s Westinghouse_(Intercept) -0.006891 461.39750 329s Westinghouse_value -0.000303 -0.15467 329s Westinghouse_capital 0.001893 -0.00689 329s US.Steel_value US.Steel_capital 329s Chrysler_(Intercept) -0.154668 -0.006891 329s Chrysler_value 0.000129 -0.000303 329s Chrysler_capital -0.000303 0.001893 329s General.Electric_(Intercept) -0.154668 -0.006891 329s General.Electric_value 0.000129 -0.000303 329s General.Electric_capital -0.000303 0.001893 329s General.Motors_(Intercept) -0.154668 -0.006891 329s General.Motors_value 0.000129 -0.000303 329s General.Motors_capital -0.000303 0.001893 329s US.Steel_(Intercept) -0.154668 -0.006891 329s US.Steel_value 0.000129 -0.000303 329s US.Steel_capital -0.000303 0.001893 329s Westinghouse_(Intercept) -0.154668 -0.006891 329s Westinghouse_value 0.000129 -0.000303 329s Westinghouse_capital -0.000303 0.001893 329s Westinghouse_(Intercept) Westinghouse_value 329s Chrysler_(Intercept) 461.39750 -0.154668 329s Chrysler_value -0.15467 0.000129 329s Chrysler_capital -0.00689 -0.000303 329s General.Electric_(Intercept) 461.39750 -0.154668 329s General.Electric_value -0.15467 0.000129 329s General.Electric_capital -0.00689 -0.000303 329s General.Motors_(Intercept) 461.39750 -0.154668 329s General.Motors_value -0.15467 0.000129 329s General.Motors_capital -0.00689 -0.000303 329s US.Steel_(Intercept) 461.39750 -0.154668 329s US.Steel_value -0.15467 0.000129 329s US.Steel_capital -0.00689 -0.000303 329s Westinghouse_(Intercept) 461.39750 -0.154668 329s Westinghouse_value -0.15467 0.000129 329s Westinghouse_capital -0.00689 -0.000303 329s Westinghouse_capital 329s Chrysler_(Intercept) -0.006891 329s Chrysler_value -0.000303 329s Chrysler_capital 0.001893 329s General.Electric_(Intercept) -0.006891 329s General.Electric_value -0.000303 329s General.Electric_capital 0.001893 329s General.Motors_(Intercept) -0.006891 329s General.Motors_value -0.000303 329s General.Motors_capital 0.001893 329s US.Steel_(Intercept) -0.006891 329s US.Steel_value -0.000303 329s US.Steel_capital 0.001893 329s Westinghouse_(Intercept) -0.006891 329s Westinghouse_value -0.000303 329s Westinghouse_capital 0.001893 329s C1 C2 C3 329s C1 461.39750 -0.154668 -0.006891 329s C2 -0.15467 0.000129 -0.000303 329s C3 -0.00689 -0.000303 0.001893 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s X1935 41.24 -71.7 41.27 98.333 40.29 329s X1936 29.63 -150.7 -66.11 198.009 19.46 329s X1937 10.81 -205.4 -155.39 200.626 4.21 329s X1938 37.79 -169.4 -51.57 41.520 6.50 329s X1939 9.38 -193.7 -136.54 -22.742 5.06 329s X1940 20.47 -158.6 -42.05 0.513 2.46 329s X1941 25.78 -99.2 3.84 190.851 29.04 329s X1942 29.85 -114.8 62.38 174.529 13.83 329s X1943 13.11 -172.2 41.00 108.865 -5.58 329s X1944 15.73 -170.6 73.77 60.388 -7.87 329s X1945 31.19 -166.9 19.60 47.014 -18.39 329s X1946 2.33 -129.8 98.30 180.017 -4.69 329s X1947 20.31 -118.2 13.81 198.862 8.57 329s X1948 30.75 -140.2 -46.46 277.965 -11.89 329s X1949 19.97 -192.9 -97.21 170.739 -24.58 329s X1950 25.98 -225.4 -39.33 181.300 -28.22 329s X1951 61.49 -213.0 -72.74 291.171 -13.26 329s X1952 27.89 -234.9 -15.13 330.665 -15.43 329s X1953 12.03 -266.1 153.79 285.144 -40.69 329s X1954 19.93 -323.8 267.09 80.518 -73.50 329s 2.5 % 97.5 % 329s Chrysler_(Intercept) -90.662 -5.398 329s Chrysler_value 0.083 0.128 329s Chrysler_capital 0.219 0.392 329s General.Electric_(Intercept) -90.662 -5.398 329s General.Electric_value 0.083 0.128 329s General.Electric_capital 0.219 0.392 329s General.Motors_(Intercept) -90.662 -5.398 329s General.Motors_value 0.083 0.128 329s General.Motors_capital 0.219 0.392 329s US.Steel_(Intercept) -90.662 -5.398 329s US.Steel_value 0.083 0.128 329s US.Steel_capital 0.219 0.392 329s Westinghouse_(Intercept) -90.662 -5.398 329s Westinghouse_value 0.083 0.128 329s Westinghouse_capital 0.219 0.392 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s X1935 -0.95 105 276 112 -27.36 329s X1936 43.13 196 458 157 6.44 329s X1937 55.45 283 566 269 30.84 329s X1938 13.81 214 309 221 16.39 329s X1939 43.03 242 467 253 13.78 329s X1940 48.94 233 503 261 26.11 329s X1941 42.57 212 508 282 19.47 329s X1942 16.95 207 386 271 29.51 329s X1943 34.29 233 459 253 42.60 329s X1944 43.84 227 474 228 45.68 329s X1945 57.59 261 542 212 57.66 329s X1946 71.79 290 590 240 58.15 329s X1947 42.37 265 555 222 46.99 329s X1948 58.61 287 576 217 61.45 329s X1949 59.01 291 652 234 56.62 329s X1950 74.68 319 682 238 60.46 329s X1951 99.13 348 829 297 67.64 329s X1952 117.11 392 906 315 87.21 329s X1953 162.90 446 1151 356 130.77 329s X1954 152.56 513 1220 379 142.10 329s 'log Lik.' -540 (df=4) 329s 'log Lik.' -573 (df=4) 329s [1] 100 329s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 329s X1935 40.3 418 10.5 33.1 329s X1936 72.8 838 10.2 45.0 329s X1937 66.3 884 34.7 77.2 329s X1938 51.6 438 51.8 44.6 329s X1939 52.4 680 64.3 48.1 329s X1940 69.4 728 67.1 74.4 329s X1941 68.3 644 75.2 113.0 329s X1942 46.8 411 71.4 91.9 329s X1943 47.4 588 67.1 61.3 329s X1944 59.6 698 60.5 56.8 329s X1945 88.8 846 54.6 93.6 329s X1946 74.1 894 84.8 159.9 329s X1947 62.7 579 96.8 147.2 329s X1948 89.4 695 110.2 146.3 329s X1949 79.0 590 147.4 98.3 329s X1950 100.7 694 163.2 93.5 329s X1951 160.6 809 203.5 135.2 329s X1952 145.0 727 290.6 157.3 329s X1953 174.9 1002 346.1 179.5 329s X1954 172.5 703 414.9 189.6 329s General.Electric_value General.Electric_capital General.Motors_invest 329s X1935 1171 97.8 318 329s X1936 2016 104.4 392 329s X1937 2803 118.0 411 329s X1938 2040 156.2 258 329s X1939 2256 172.6 331 329s X1940 2132 186.6 461 329s X1941 1834 220.9 512 329s X1942 1588 287.8 448 329s X1943 1749 319.9 500 329s X1944 1687 321.3 548 329s X1945 2008 319.6 561 329s X1946 2208 346.0 688 329s X1947 1657 456.4 569 329s X1948 1604 543.4 529 329s X1949 1432 618.3 555 329s X1950 1610 647.4 643 329s X1951 1819 671.3 756 329s X1952 2080 726.1 891 329s X1953 2372 800.3 1304 329s X1954 2760 888.9 1487 329s General.Motors_value General.Motors_capital US.Steel_invest 329s X1935 3078 2.8 210 329s X1936 4662 52.6 355 329s X1937 5387 156.9 470 329s X1938 2792 209.2 262 329s X1939 4313 203.4 230 329s X1940 4644 207.2 262 329s X1941 4551 255.2 473 329s X1942 3244 303.7 446 329s X1943 4054 264.1 362 329s X1944 4379 201.6 288 329s X1945 4841 265.0 259 329s X1946 4901 402.2 420 329s X1947 3526 761.5 420 329s X1948 3255 922.4 494 329s X1949 3700 1020.1 405 329s X1950 3756 1099.0 419 329s X1951 4833 1207.7 588 329s X1952 4925 1430.5 645 329s X1953 6242 1777.3 641 329s X1954 5594 2226.3 459 329s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 329s X1935 1362 53.8 12.9 192 329s X1936 1807 50.5 25.9 516 329s X1937 2676 118.1 35.0 729 329s X1938 1802 260.2 22.9 560 329s X1939 1957 312.7 18.8 520 329s X1940 2203 254.2 28.6 628 329s X1941 2380 261.4 48.5 537 329s X1942 2169 298.7 43.3 561 329s X1943 1985 301.8 37.0 617 329s X1944 1814 279.1 37.8 627 329s X1945 1850 213.8 39.3 737 329s X1946 2068 232.6 53.5 760 329s X1947 1797 264.8 55.6 581 329s X1948 1626 306.9 49.6 662 329s X1949 1667 351.1 32.0 584 329s X1950 1677 357.8 32.2 635 329s X1951 2290 342.1 54.4 724 329s X1952 2159 444.2 71.8 864 329s X1953 2031 623.6 90.1 1194 329s X1954 2116 669.7 68.6 1189 329s Westinghouse_capital 329s X1935 1.8 329s X1936 0.8 329s X1937 7.4 329s X1938 18.1 329s X1939 23.5 329s X1940 26.5 329s X1941 36.2 329s X1942 60.8 329s X1943 84.4 329s X1944 91.2 329s X1945 92.4 329s X1946 86.0 329s X1947 111.1 329s X1948 130.6 329s X1949 141.8 329s X1950 136.7 329s X1951 129.7 329s X1952 145.5 329s X1953 174.8 329s X1954 213.5 329s Chrysler_(Intercept) Chrysler_value Chrysler_capital 329s Chrysler_X1935 1 418 10.5 329s Chrysler_X1936 1 838 10.2 329s Chrysler_X1937 1 884 34.7 329s Chrysler_X1938 1 438 51.8 329s Chrysler_X1939 1 680 64.3 329s Chrysler_X1940 1 728 67.1 329s Chrysler_X1941 1 644 75.2 329s Chrysler_X1942 1 411 71.4 329s Chrysler_X1943 1 588 67.1 329s Chrysler_X1944 1 698 60.5 329s Chrysler_X1945 1 846 54.6 329s Chrysler_X1946 1 894 84.8 329s Chrysler_X1947 1 579 96.8 329s Chrysler_X1948 1 695 110.2 329s Chrysler_X1949 1 590 147.4 329s Chrysler_X1950 1 694 163.2 329s Chrysler_X1951 1 809 203.5 329s Chrysler_X1952 1 727 290.6 329s Chrysler_X1953 1 1002 346.1 329s Chrysler_X1954 1 703 414.9 329s General.Electric_X1935 0 0 0.0 329s General.Electric_X1936 0 0 0.0 329s General.Electric_X1937 0 0 0.0 329s General.Electric_X1938 0 0 0.0 329s General.Electric_X1939 0 0 0.0 329s General.Electric_X1940 0 0 0.0 329s General.Electric_X1941 0 0 0.0 329s General.Electric_X1942 0 0 0.0 329s General.Electric_X1943 0 0 0.0 329s General.Electric_X1944 0 0 0.0 329s General.Electric_X1945 0 0 0.0 329s General.Electric_X1946 0 0 0.0 329s General.Electric_X1947 0 0 0.0 329s General.Electric_X1948 0 0 0.0 329s General.Electric_X1949 0 0 0.0 329s General.Electric_X1950 0 0 0.0 329s General.Electric_X1951 0 0 0.0 329s General.Electric_X1952 0 0 0.0 329s General.Electric_X1953 0 0 0.0 329s General.Electric_X1954 0 0 0.0 329s General.Motors_X1935 0 0 0.0 329s General.Motors_X1936 0 0 0.0 329s General.Motors_X1937 0 0 0.0 329s General.Motors_X1938 0 0 0.0 329s General.Motors_X1939 0 0 0.0 329s General.Motors_X1940 0 0 0.0 329s General.Motors_X1941 0 0 0.0 329s General.Motors_X1942 0 0 0.0 329s General.Motors_X1943 0 0 0.0 329s General.Motors_X1944 0 0 0.0 329s General.Motors_X1945 0 0 0.0 329s General.Motors_X1946 0 0 0.0 329s General.Motors_X1947 0 0 0.0 329s General.Motors_X1948 0 0 0.0 329s General.Motors_X1949 0 0 0.0 329s General.Motors_X1950 0 0 0.0 329s General.Motors_X1951 0 0 0.0 329s General.Motors_X1952 0 0 0.0 329s General.Motors_X1953 0 0 0.0 329s General.Motors_X1954 0 0 0.0 329s US.Steel_X1935 0 0 0.0 329s US.Steel_X1936 0 0 0.0 329s US.Steel_X1937 0 0 0.0 329s US.Steel_X1938 0 0 0.0 329s US.Steel_X1939 0 0 0.0 329s US.Steel_X1940 0 0 0.0 329s US.Steel_X1941 0 0 0.0 329s US.Steel_X1942 0 0 0.0 329s US.Steel_X1943 0 0 0.0 329s US.Steel_X1944 0 0 0.0 329s US.Steel_X1945 0 0 0.0 329s US.Steel_X1946 0 0 0.0 329s US.Steel_X1947 0 0 0.0 329s US.Steel_X1948 0 0 0.0 329s US.Steel_X1949 0 0 0.0 329s US.Steel_X1950 0 0 0.0 329s US.Steel_X1951 0 0 0.0 329s US.Steel_X1952 0 0 0.0 329s US.Steel_X1953 0 0 0.0 329s US.Steel_X1954 0 0 0.0 329s Westinghouse_X1935 0 0 0.0 329s Westinghouse_X1936 0 0 0.0 329s Westinghouse_X1937 0 0 0.0 329s Westinghouse_X1938 0 0 0.0 329s Westinghouse_X1939 0 0 0.0 329s Westinghouse_X1940 0 0 0.0 329s Westinghouse_X1941 0 0 0.0 329s Westinghouse_X1942 0 0 0.0 329s Westinghouse_X1943 0 0 0.0 329s Westinghouse_X1944 0 0 0.0 329s Westinghouse_X1945 0 0 0.0 329s Westinghouse_X1946 0 0 0.0 329s Westinghouse_X1947 0 0 0.0 329s Westinghouse_X1948 0 0 0.0 329s Westinghouse_X1949 0 0 0.0 329s Westinghouse_X1950 0 0 0.0 329s Westinghouse_X1951 0 0 0.0 329s Westinghouse_X1952 0 0 0.0 329s Westinghouse_X1953 0 0 0.0 329s Westinghouse_X1954 0 0 0.0 329s General.Electric_(Intercept) General.Electric_value 329s Chrysler_X1935 0 0 329s Chrysler_X1936 0 0 329s Chrysler_X1937 0 0 329s Chrysler_X1938 0 0 329s Chrysler_X1939 0 0 329s Chrysler_X1940 0 0 329s Chrysler_X1941 0 0 329s Chrysler_X1942 0 0 329s Chrysler_X1943 0 0 329s Chrysler_X1944 0 0 329s Chrysler_X1945 0 0 329s Chrysler_X1946 0 0 329s Chrysler_X1947 0 0 329s Chrysler_X1948 0 0 329s Chrysler_X1949 0 0 329s Chrysler_X1950 0 0 329s Chrysler_X1951 0 0 329s Chrysler_X1952 0 0 329s Chrysler_X1953 0 0 329s Chrysler_X1954 0 0 329s General.Electric_X1935 1 1171 329s General.Electric_X1936 1 2016 329s General.Electric_X1937 1 2803 329s General.Electric_X1938 1 2040 329s General.Electric_X1939 1 2256 329s General.Electric_X1940 1 2132 329s General.Electric_X1941 1 1834 329s General.Electric_X1942 1 1588 329s General.Electric_X1943 1 1749 329s General.Electric_X1944 1 1687 329s General.Electric_X1945 1 2008 329s General.Electric_X1946 1 2208 329s General.Electric_X1947 1 1657 329s General.Electric_X1948 1 1604 329s General.Electric_X1949 1 1432 329s General.Electric_X1950 1 1610 329s General.Electric_X1951 1 1819 329s General.Electric_X1952 1 2080 329s General.Electric_X1953 1 2372 329s General.Electric_X1954 1 2760 329s General.Motors_X1935 0 0 329s General.Motors_X1936 0 0 329s General.Motors_X1937 0 0 329s General.Motors_X1938 0 0 329s General.Motors_X1939 0 0 329s General.Motors_X1940 0 0 329s General.Motors_X1941 0 0 329s General.Motors_X1942 0 0 329s General.Motors_X1943 0 0 329s General.Motors_X1944 0 0 329s General.Motors_X1945 0 0 329s General.Motors_X1946 0 0 329s General.Motors_X1947 0 0 329s General.Motors_X1948 0 0 329s General.Motors_X1949 0 0 329s General.Motors_X1950 0 0 329s General.Motors_X1951 0 0 329s General.Motors_X1952 0 0 329s General.Motors_X1953 0 0 329s General.Motors_X1954 0 0 329s US.Steel_X1935 0 0 329s US.Steel_X1936 0 0 329s US.Steel_X1937 0 0 329s US.Steel_X1938 0 0 329s US.Steel_X1939 0 0 329s US.Steel_X1940 0 0 329s US.Steel_X1941 0 0 329s US.Steel_X1942 0 0 329s US.Steel_X1943 0 0 329s US.Steel_X1944 0 0 329s US.Steel_X1945 0 0 329s US.Steel_X1946 0 0 329s US.Steel_X1947 0 0 329s US.Steel_X1948 0 0 329s US.Steel_X1949 0 0 329s US.Steel_X1950 0 0 329s US.Steel_X1951 0 0 329s US.Steel_X1952 0 0 329s US.Steel_X1953 0 0 329s US.Steel_X1954 0 0 329s Westinghouse_X1935 0 0 329s Westinghouse_X1936 0 0 329s Westinghouse_X1937 0 0 329s Westinghouse_X1938 0 0 329s Westinghouse_X1939 0 0 329s Westinghouse_X1940 0 0 329s Westinghouse_X1941 0 0 329s Westinghouse_X1942 0 0 329s Westinghouse_X1943 0 0 329s Westinghouse_X1944 0 0 329s Westinghouse_X1945 0 0 329s Westinghouse_X1946 0 0 329s Westinghouse_X1947 0 0 329s Westinghouse_X1948 0 0 329s Westinghouse_X1949 0 0 329s Westinghouse_X1950 0 0 329s Westinghouse_X1951 0 0 329s Westinghouse_X1952 0 0 329s Westinghouse_X1953 0 0 329s Westinghouse_X1954 0 0 329s General.Electric_capital General.Motors_(Intercept) 329s Chrysler_X1935 0.0 0 329s Chrysler_X1936 0.0 0 329s Chrysler_X1937 0.0 0 329s Chrysler_X1938 0.0 0 329s Chrysler_X1939 0.0 0 329s Chrysler_X1940 0.0 0 329s Chrysler_X1941 0.0 0 329s Chrysler_X1942 0.0 0 329s Chrysler_X1943 0.0 0 329s Chrysler_X1944 0.0 0 329s Chrysler_X1945 0.0 0 329s Chrysler_X1946 0.0 0 329s Chrysler_X1947 0.0 0 329s Chrysler_X1948 0.0 0 329s Chrysler_X1949 0.0 0 329s Chrysler_X1950 0.0 0 329s Chrysler_X1951 0.0 0 329s Chrysler_X1952 0.0 0 329s Chrysler_X1953 0.0 0 329s Chrysler_X1954 0.0 0 329s General.Electric_X1935 97.8 0 329s General.Electric_X1936 104.4 0 329s General.Electric_X1937 118.0 0 329s General.Electric_X1938 156.2 0 329s General.Electric_X1939 172.6 0 329s General.Electric_X1940 186.6 0 329s General.Electric_X1941 220.9 0 329s General.Electric_X1942 287.8 0 329s General.Electric_X1943 319.9 0 329s General.Electric_X1944 321.3 0 329s General.Electric_X1945 319.6 0 329s General.Electric_X1946 346.0 0 329s General.Electric_X1947 456.4 0 329s General.Electric_X1948 543.4 0 329s General.Electric_X1949 618.3 0 329s General.Electric_X1950 647.4 0 329s General.Electric_X1951 671.3 0 329s General.Electric_X1952 726.1 0 329s General.Electric_X1953 800.3 0 329s General.Electric_X1954 888.9 0 329s General.Motors_X1935 0.0 1 329s General.Motors_X1936 0.0 1 329s General.Motors_X1937 0.0 1 329s General.Motors_X1938 0.0 1 329s General.Motors_X1939 0.0 1 329s General.Motors_X1940 0.0 1 329s General.Motors_X1941 0.0 1 329s General.Motors_X1942 0.0 1 329s General.Motors_X1943 0.0 1 329s General.Motors_X1944 0.0 1 329s General.Motors_X1945 0.0 1 329s General.Motors_X1946 0.0 1 329s General.Motors_X1947 0.0 1 329s General.Motors_X1948 0.0 1 329s General.Motors_X1949 0.0 1 329s General.Motors_X1950 0.0 1 329s General.Motors_X1951 0.0 1 329s General.Motors_X1952 0.0 1 329s General.Motors_X1953 0.0 1 329s General.Motors_X1954 0.0 1 329s US.Steel_X1935 0.0 0 329s US.Steel_X1936 0.0 0 329s US.Steel_X1937 0.0 0 329s US.Steel_X1938 0.0 0 329s US.Steel_X1939 0.0 0 329s US.Steel_X1940 0.0 0 329s US.Steel_X1941 0.0 0 329s US.Steel_X1942 0.0 0 329s US.Steel_X1943 0.0 0 329s US.Steel_X1944 0.0 0 329s US.Steel_X1945 0.0 0 329s US.Steel_X1946 0.0 0 329s US.Steel_X1947 0.0 0 329s US.Steel_X1948 0.0 0 329s US.Steel_X1949 0.0 0 329s US.Steel_X1950 0.0 0 329s US.Steel_X1951 0.0 0 329s US.Steel_X1952 0.0 0 329s US.Steel_X1953 0.0 0 329s US.Steel_X1954 0.0 0 329s Westinghouse_X1935 0.0 0 329s Westinghouse_X1936 0.0 0 329s Westinghouse_X1937 0.0 0 329s Westinghouse_X1938 0.0 0 329s Westinghouse_X1939 0.0 0 329s Westinghouse_X1940 0.0 0 329s Westinghouse_X1941 0.0 0 329s Westinghouse_X1942 0.0 0 329s Westinghouse_X1943 0.0 0 329s Westinghouse_X1944 0.0 0 329s Westinghouse_X1945 0.0 0 329s Westinghouse_X1946 0.0 0 329s Westinghouse_X1947 0.0 0 329s Westinghouse_X1948 0.0 0 329s Westinghouse_X1949 0.0 0 329s Westinghouse_X1950 0.0 0 329s Westinghouse_X1951 0.0 0 329s Westinghouse_X1952 0.0 0 329s Westinghouse_X1953 0.0 0 329s Westinghouse_X1954 0.0 0 329s General.Motors_value General.Motors_capital 329s Chrysler_X1935 0 0.0 329s Chrysler_X1936 0 0.0 329s Chrysler_X1937 0 0.0 329s Chrysler_X1938 0 0.0 329s Chrysler_X1939 0 0.0 329s Chrysler_X1940 0 0.0 329s Chrysler_X1941 0 0.0 329s Chrysler_X1942 0 0.0 329s Chrysler_X1943 0 0.0 329s Chrysler_X1944 0 0.0 329s Chrysler_X1945 0 0.0 329s Chrysler_X1946 0 0.0 329s Chrysler_X1947 0 0.0 329s Chrysler_X1948 0 0.0 329s Chrysler_X1949 0 0.0 329s Chrysler_X1950 0 0.0 329s Chrysler_X1951 0 0.0 329s Chrysler_X1952 0 0.0 329s Chrysler_X1953 0 0.0 329s Chrysler_X1954 0 0.0 329s General.Electric_X1935 0 0.0 329s General.Electric_X1936 0 0.0 329s General.Electric_X1937 0 0.0 329s General.Electric_X1938 0 0.0 329s General.Electric_X1939 0 0.0 329s General.Electric_X1940 0 0.0 329s General.Electric_X1941 0 0.0 329s General.Electric_X1942 0 0.0 329s General.Electric_X1943 0 0.0 329s General.Electric_X1944 0 0.0 329s General.Electric_X1945 0 0.0 329s General.Electric_X1946 0 0.0 329s General.Electric_X1947 0 0.0 329s General.Electric_X1948 0 0.0 329s General.Electric_X1949 0 0.0 329s General.Electric_X1950 0 0.0 329s General.Electric_X1951 0 0.0 329s General.Electric_X1952 0 0.0 329s General.Electric_X1953 0 0.0 329s General.Electric_X1954 0 0.0 329s General.Motors_X1935 3078 2.8 329s General.Motors_X1936 4662 52.6 329s General.Motors_X1937 5387 156.9 329s General.Motors_X1938 2792 209.2 329s General.Motors_X1939 4313 203.4 329s General.Motors_X1940 4644 207.2 329s General.Motors_X1941 4551 255.2 329s General.Motors_X1942 3244 303.7 329s General.Motors_X1943 4054 264.1 329s General.Motors_X1944 4379 201.6 329s General.Motors_X1945 4841 265.0 329s General.Motors_X1946 4901 402.2 329s General.Motors_X1947 3526 761.5 329s General.Motors_X1948 3255 922.4 329s General.Motors_X1949 3700 1020.1 329s General.Motors_X1950 3756 1099.0 329s General.Motors_X1951 4833 1207.7 329s General.Motors_X1952 4925 1430.5 329s General.Motors_X1953 6242 1777.3 329s General.Motors_X1954 5594 2226.3 329s US.Steel_X1935 0 0.0 329s US.Steel_X1936 0 0.0 329s US.Steel_X1937 0 0.0 329s US.Steel_X1938 0 0.0 329s US.Steel_X1939 0 0.0 329s US.Steel_X1940 0 0.0 329s US.Steel_X1941 0 0.0 329s US.Steel_X1942 0 0.0 329s US.Steel_X1943 0 0.0 329s US.Steel_X1944 0 0.0 329s US.Steel_X1945 0 0.0 329s US.Steel_X1946 0 0.0 329s US.Steel_X1947 0 0.0 329s US.Steel_X1948 0 0.0 329s US.Steel_X1949 0 0.0 329s US.Steel_X1950 0 0.0 329s US.Steel_X1951 0 0.0 329s US.Steel_X1952 0 0.0 329s US.Steel_X1953 0 0.0 329s US.Steel_X1954 0 0.0 329s Westinghouse_X1935 0 0.0 329s Westinghouse_X1936 0 0.0 329s Westinghouse_X1937 0 0.0 329s Westinghouse_X1938 0 0.0 329s Westinghouse_X1939 0 0.0 329s Westinghouse_X1940 0 0.0 329s Westinghouse_X1941 0 0.0 329s Westinghouse_X1942 0 0.0 329s Westinghouse_X1943 0 0.0 329s Westinghouse_X1944 0 0.0 329s Westinghouse_X1945 0 0.0 329s Westinghouse_X1946 0 0.0 329s Westinghouse_X1947 0 0.0 329s Westinghouse_X1948 0 0.0 329s Westinghouse_X1949 0 0.0 329s Westinghouse_X1950 0 0.0 329s Westinghouse_X1951 0 0.0 329s Westinghouse_X1952 0 0.0 329s Westinghouse_X1953 0 0.0 329s Westinghouse_X1954 0 0.0 329s US.Steel_(Intercept) US.Steel_value US.Steel_capital 329s Chrysler_X1935 0 0 0.0 329s Chrysler_X1936 0 0 0.0 329s Chrysler_X1937 0 0 0.0 329s Chrysler_X1938 0 0 0.0 329s Chrysler_X1939 0 0 0.0 329s Chrysler_X1940 0 0 0.0 329s Chrysler_X1941 0 0 0.0 329s Chrysler_X1942 0 0 0.0 329s Chrysler_X1943 0 0 0.0 329s Chrysler_X1944 0 0 0.0 329s Chrysler_X1945 0 0 0.0 329s Chrysler_X1946 0 0 0.0 329s Chrysler_X1947 0 0 0.0 329s Chrysler_X1948 0 0 0.0 329s Chrysler_X1949 0 0 0.0 329s Chrysler_X1950 0 0 0.0 329s Chrysler_X1951 0 0 0.0 329s Chrysler_X1952 0 0 0.0 329s Chrysler_X1953 0 0 0.0 329s Chrysler_X1954 0 0 0.0 329s General.Electric_X1935 0 0 0.0 329s General.Electric_X1936 0 0 0.0 329s General.Electric_X1937 0 0 0.0 329s General.Electric_X1938 0 0 0.0 329s General.Electric_X1939 0 0 0.0 329s General.Electric_X1940 0 0 0.0 329s General.Electric_X1941 0 0 0.0 329s General.Electric_X1942 0 0 0.0 329s General.Electric_X1943 0 0 0.0 329s General.Electric_X1944 0 0 0.0 329s General.Electric_X1945 0 0 0.0 329s General.Electric_X1946 0 0 0.0 329s General.Electric_X1947 0 0 0.0 329s General.Electric_X1948 0 0 0.0 329s General.Electric_X1949 0 0 0.0 329s General.Electric_X1950 0 0 0.0 329s General.Electric_X1951 0 0 0.0 329s General.Electric_X1952 0 0 0.0 329s General.Electric_X1953 0 0 0.0 329s General.Electric_X1954 0 0 0.0 329s General.Motors_X1935 0 0 0.0 329s General.Motors_X1936 0 0 0.0 329s General.Motors_X1937 0 0 0.0 329s General.Motors_X1938 0 0 0.0 329s General.Motors_X1939 0 0 0.0 329s General.Motors_X1940 0 0 0.0 329s General.Motors_X1941 0 0 0.0 329s General.Motors_X1942 0 0 0.0 329s General.Motors_X1943 0 0 0.0 329s General.Motors_X1944 0 0 0.0 329s General.Motors_X1945 0 0 0.0 329s General.Motors_X1946 0 0 0.0 329s General.Motors_X1947 0 0 0.0 329s General.Motors_X1948 0 0 0.0 329s General.Motors_X1949 0 0 0.0 329s General.Motors_X1950 0 0 0.0 329s General.Motors_X1951 0 0 0.0 329s General.Motors_X1952 0 0 0.0 329s General.Motors_X1953 0 0 0.0 329s General.Motors_X1954 0 0 0.0 329s US.Steel_X1935 1 1362 53.8 329s US.Steel_X1936 1 1807 50.5 329s US.Steel_X1937 1 2676 118.1 329s US.Steel_X1938 1 1802 260.2 329s US.Steel_X1939 1 1957 312.7 329s US.Steel_X1940 1 2203 254.2 329s US.Steel_X1941 1 2380 261.4 329s US.Steel_X1942 1 2169 298.7 329s US.Steel_X1943 1 1985 301.8 329s US.Steel_X1944 1 1814 279.1 329s US.Steel_X1945 1 1850 213.8 329s US.Steel_X1946 1 2068 232.6 329s US.Steel_X1947 1 1797 264.8 329s US.Steel_X1948 1 1626 306.9 329s US.Steel_X1949 1 1667 351.1 329s US.Steel_X1950 1 1677 357.8 329s US.Steel_X1951 1 2290 342.1 329s US.Steel_X1952 1 2159 444.2 329s US.Steel_X1953 1 2031 623.6 329s US.Steel_X1954 1 2116 669.7 329s Westinghouse_X1935 0 0 0.0 329s Westinghouse_X1936 0 0 0.0 329s Westinghouse_X1937 0 0 0.0 329s Westinghouse_X1938 0 0 0.0 329s Westinghouse_X1939 0 0 0.0 329s Westinghouse_X1940 0 0 0.0 329s Westinghouse_X1941 0 0 0.0 329s Westinghouse_X1942 0 0 0.0 329s Westinghouse_X1943 0 0 0.0 329s Westinghouse_X1944 0 0 0.0 329s Westinghouse_X1945 0 0 0.0 329s Westinghouse_X1946 0 0 0.0 329s Westinghouse_X1947 0 0 0.0 329s Westinghouse_X1948 0 0 0.0 329s Westinghouse_X1949 0 0 0.0 329s Westinghouse_X1950 0 0 0.0 329s Westinghouse_X1951 0 0 0.0 329s Westinghouse_X1952 0 0 0.0 329s Westinghouse_X1953 0 0 0.0 329s Westinghouse_X1954 0 0 0.0 329s Westinghouse_(Intercept) Westinghouse_value 329s Chrysler_X1935 0 0 329s Chrysler_X1936 0 0 329s Chrysler_X1937 0 0 329s Chrysler_X1938 0 0 329s Chrysler_X1939 0 0 329s Chrysler_X1940 0 0 329s Chrysler_X1941 0 0 329s Chrysler_X1942 0 0 329s Chrysler_X1943 0 0 329s Chrysler_X1944 0 0 329s Chrysler_X1945 0 0 329s Chrysler_X1946 0 0 329s Chrysler_X1947 0 0 329s Chrysler_X1948 0 0 329s Chrysler_X1949 0 0 329s Chrysler_X1950 0 0 329s Chrysler_X1951 0 0 329s Chrysler_X1952 0 0 329s Chrysler_X1953 0 0 329s Chrysler_X1954 0 0 329s General.Electric_X1935 0 0 329s General.Electric_X1936 0 0 329s General.Electric_X1937 0 0 329s General.Electric_X1938 0 0 329s General.Electric_X1939 0 0 329s General.Electric_X1940 0 0 329s General.Electric_X1941 0 0 329s General.Electric_X1942 0 0 329s General.Electric_X1943 0 0 329s General.Electric_X1944 0 0 329s General.Electric_X1945 0 0 329s General.Electric_X1946 0 0 329s General.Electric_X1947 0 0 329s General.Electric_X1948 0 0 329s General.Electric_X1949 0 0 329s General.Electric_X1950 0 0 329s General.Electric_X1951 0 0 329s General.Electric_X1952 0 0 329s General.Electric_X1953 0 0 329s General.Electric_X1954 0 0 329s General.Motors_X1935 0 0 329s General.Motors_X1936 0 0 329s General.Motors_X1937 0 0 329s General.Motors_X1938 0 0 329s General.Motors_X1939 0 0 329s General.Motors_X1940 0 0 329s General.Motors_X1941 0 0 329s General.Motors_X1942 0 0 329s General.Motors_X1943 0 0 329s General.Motors_X1944 0 0 329s General.Motors_X1945 0 0 329s General.Motors_X1946 0 0 329s General.Motors_X1947 0 0 329s General.Motors_X1948 0 0 329s General.Motors_X1949 0 0 329s General.Motors_X1950 0 0 329s General.Motors_X1951 0 0 329s General.Motors_X1952 0 0 329s General.Motors_X1953 0 0 329s General.Motors_X1954 0 0 329s US.Steel_X1935 0 0 329s US.Steel_X1936 0 0 329s US.Steel_X1937 0 0 329s US.Steel_X1938 0 0 329s US.Steel_X1939 0 0 329s US.Steel_X1940 0 0 329s US.Steel_X1941 0 0 329s US.Steel_X1942 0 0 329s US.Steel_X1943 0 0 329s US.Steel_X1944 0 0 329s US.Steel_X1945 0 0 329s US.Steel_X1946 0 0 329s US.Steel_X1947 0 0 329s US.Steel_X1948 0 0 329s US.Steel_X1949 0 0 329s US.Steel_X1950 0 0 329s US.Steel_X1951 0 0 329s US.Steel_X1952 0 0 329s US.Steel_X1953 0 0 329s US.Steel_X1954 0 0 329s Westinghouse_X1935 1 192 329s Westinghouse_X1936 1 516 329s Westinghouse_X1937 1 729 329s Westinghouse_X1938 1 560 329s Westinghouse_X1939 1 520 329s Westinghouse_X1940 1 628 329s Westinghouse_X1941 1 537 329s Westinghouse_X1942 1 561 329s Westinghouse_X1943 1 617 329s Westinghouse_X1944 1 627 329s Westinghouse_X1945 1 737 329s Westinghouse_X1946 1 760 329s Westinghouse_X1947 1 581 329s Westinghouse_X1948 1 662 329s Westinghouse_X1949 1 584 329s Westinghouse_X1950 1 635 329s Westinghouse_X1951 1 724 329s Westinghouse_X1952 1 864 329s Westinghouse_X1953 1 1194 329s Westinghouse_X1954 1 1189 329s Westinghouse_capital 329s Chrysler_X1935 0.0 329s Chrysler_X1936 0.0 329s Chrysler_X1937 0.0 329s Chrysler_X1938 0.0 329s Chrysler_X1939 0.0 329s Chrysler_X1940 0.0 329s Chrysler_X1941 0.0 329s Chrysler_X1942 0.0 329s Chrysler_X1943 0.0 329s Chrysler_X1944 0.0 329s Chrysler_X1945 0.0 329s Chrysler_X1946 0.0 329s Chrysler_X1947 0.0 329s Chrysler_X1948 0.0 329s Chrysler_X1949 0.0 329s Chrysler_X1950 0.0 329s Chrysler_X1951 0.0 329s Chrysler_X1952 0.0 329s Chrysler_X1953 0.0 329s Chrysler_X1954 0.0 329s General.Electric_X1935 0.0 329s General.Electric_X1936 0.0 329s General.Electric_X1937 0.0 329s General.Electric_X1938 0.0 329s General.Electric_X1939 0.0 329s General.Electric_X1940 0.0 329s General.Electric_X1941 0.0 329s General.Electric_X1942 0.0 329s General.Electric_X1943 0.0 329s General.Electric_X1944 0.0 329s General.Electric_X1945 0.0 329s General.Electric_X1946 0.0 329s General.Electric_X1947 0.0 329s General.Electric_X1948 0.0 329s General.Electric_X1949 0.0 329s General.Electric_X1950 0.0 329s General.Electric_X1951 0.0 329s General.Electric_X1952 0.0 329s General.Electric_X1953 0.0 329s General.Electric_X1954 0.0 329s General.Motors_X1935 0.0 329s General.Motors_X1936 0.0 329s General.Motors_X1937 0.0 329s General.Motors_X1938 0.0 329s General.Motors_X1939 0.0 329s General.Motors_X1940 0.0 329s General.Motors_X1941 0.0 329s General.Motors_X1942 0.0 329s General.Motors_X1943 0.0 329s General.Motors_X1944 0.0 329s General.Motors_X1945 0.0 329s General.Motors_X1946 0.0 329s General.Motors_X1947 0.0 329s General.Motors_X1948 0.0 329s General.Motors_X1949 0.0 329s General.Motors_X1950 0.0 329s General.Motors_X1951 0.0 329s General.Motors_X1952 0.0 329s General.Motors_X1953 0.0 329s General.Motors_X1954 0.0 329s US.Steel_X1935 0.0 329s US.Steel_X1936 0.0 329s US.Steel_X1937 0.0 329s US.Steel_X1938 0.0 329s US.Steel_X1939 0.0 329s US.Steel_X1940 0.0 329s US.Steel_X1941 0.0 329s US.Steel_X1942 0.0 329s US.Steel_X1943 0.0 329s US.Steel_X1944 0.0 329s US.Steel_X1945 0.0 329s US.Steel_X1946 0.0 329s US.Steel_X1947 0.0 329s US.Steel_X1948 0.0 329s US.Steel_X1949 0.0 329s US.Steel_X1950 0.0 329s US.Steel_X1951 0.0 329s US.Steel_X1952 0.0 329s US.Steel_X1953 0.0 329s US.Steel_X1954 0.0 329s Westinghouse_X1935 1.8 329s Westinghouse_X1936 0.8 329s Westinghouse_X1937 7.4 329s Westinghouse_X1938 18.1 329s Westinghouse_X1939 23.5 329s Westinghouse_X1940 26.5 329s Westinghouse_X1941 36.2 329s Westinghouse_X1942 60.8 329s Westinghouse_X1943 84.4 329s Westinghouse_X1944 91.2 329s Westinghouse_X1945 92.4 329s Westinghouse_X1946 86.0 329s Westinghouse_X1947 111.1 329s Westinghouse_X1948 130.6 329s Westinghouse_X1949 141.8 329s Westinghouse_X1950 136.7 329s Westinghouse_X1951 129.7 329s Westinghouse_X1952 145.5 329s Westinghouse_X1953 174.8 329s Westinghouse_X1954 213.5 329s $Chrysler 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s $General.Motors 329s General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s $US.Steel 329s US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s $Chrysler 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s attr(,"variables") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"factors") 329s Chrysler_value Chrysler_capital 329s Chrysler_invest 0 0 329s Chrysler_value 1 0 329s Chrysler_capital 0 1 329s attr(,"term.labels") 329s [1] "Chrysler_value" "Chrysler_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"dataClasses") 329s Chrysler_invest Chrysler_value Chrysler_capital 329s "numeric" "numeric" "numeric" 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s attr(,"variables") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"factors") 329s General.Electric_value General.Electric_capital 329s General.Electric_invest 0 0 329s General.Electric_value 1 0 329s General.Electric_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Electric_value" "General.Electric_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"dataClasses") 329s General.Electric_invest General.Electric_value General.Electric_capital 329s "numeric" "numeric" "numeric" 329s 329s $General.Motors 329s General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s attr(,"variables") 329s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 329s attr(,"factors") 329s General.Motors_value General.Motors_capital 329s General.Motors_invest 0 0 329s General.Motors_value 1 0 329s General.Motors_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Motors_value" "General.Motors_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 329s attr(,"dataClasses") 329s General.Motors_invest General.Motors_value General.Motors_capital 329s "numeric" "numeric" "numeric" 329s 329s $US.Steel 329s US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s attr(,"variables") 329s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 329s attr(,"factors") 329s US.Steel_value US.Steel_capital 329s US.Steel_invest 0 0 329s US.Steel_value 1 0 329s US.Steel_capital 0 1 329s attr(,"term.labels") 329s [1] "US.Steel_value" "US.Steel_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 329s attr(,"dataClasses") 329s US.Steel_invest US.Steel_value US.Steel_capital 329s "numeric" "numeric" "numeric" 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s attr(,"variables") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"factors") 329s Westinghouse_value Westinghouse_capital 329s Westinghouse_invest 0 0 329s Westinghouse_value 1 0 329s Westinghouse_capital 0 1 329s attr(,"term.labels") 329s [1] "Westinghouse_value" "Westinghouse_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"dataClasses") 329s Westinghouse_invest Westinghouse_value Westinghouse_capital 329s "numeric" "numeric" "numeric" 329s 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s attr(,"variables") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"factors") 329s Chrysler_value Chrysler_capital 329s Chrysler_invest 0 0 329s Chrysler_value 1 0 329s Chrysler_capital 0 1 329s attr(,"term.labels") 329s [1] "Chrysler_value" "Chrysler_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"dataClasses") 329s Chrysler_invest Chrysler_value Chrysler_capital 329s "numeric" "numeric" "numeric" 329s > 329s > # SUR 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + greeneSur <- systemfit( formulaGrunfeld, "SUR", 329s + data = GrunfeldGreene, methodResidCov = "noDfCor", useMatrix = useMatrix ) 329s + print( greeneSur ) 329s + print( summary( greeneSur ) ) 329s + print( summary( greeneSur, useDfSys = TRUE, residCov = FALSE ) ) 329s + print( summary( greeneSur, equations = FALSE ) ) 329s + print( coef( greeneSur ) ) 329s + print( coef( summary( greeneSur ) ) ) 329s + print( vcov( greeneSur ) ) 329s + print( residuals( greeneSur ) ) 329s + print( confint( greeneSur ) ) 329s + print( fitted( greeneSur ) ) 329s + print( logLik( greeneSur ) ) 329s + print( logLik( greeneSur, residCovDiag = TRUE ) ) 329s + print( nobs( greeneSur ) ) 329s + print( model.frame( greeneSur ) ) 329s + print( model.matrix( greeneSur ) ) 329s + print( formula( greeneSur ) ) 329s + print( formula( greeneSur$eq[[ 1 ]] ) ) 329s + print( terms( greeneSur ) ) 329s + print( terms( greeneSur$eq[[ 1 ]] ) ) 329s + } 329s 329s systemfit results 329s method: SUR 329s 329s Coefficients: 329s Chrysler_(Intercept) Chrysler_value 329s 0.5043 0.0695 329s Chrysler_capital General.Electric_(Intercept) 329s 0.3085 -22.4389 329s General.Electric_value General.Electric_capital 329s 0.0373 0.1308 329s General.Motors_(Intercept) General.Motors_value 329s -162.3641 0.1205 329s General.Motors_capital US.Steel_(Intercept) 329s 0.3827 85.4233 329s US.Steel_value US.Steel_capital 329s 0.1015 0.4000 329s Westinghouse_(Intercept) Westinghouse_value 329s 1.0889 0.0570 329s Westinghouse_capital 329s 0.0415 329s 329s systemfit results 329s method: SUR 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 85 347048 6.18e+13 0.844 0.869 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 3057 180 13.4 0.912 0.901 329s General.Electric 20 17 14009 824 28.7 0.688 0.651 329s General.Motors 20 17 144321 8489 92.1 0.921 0.911 329s US.Steel 20 17 183763 10810 104.0 0.422 0.354 329s Westinghouse 20 17 1898 112 10.6 0.726 0.694 329s 329s The covariance matrix of the residuals used for estimation 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 149.9 -21.4 -283 418 13.3 329s General.Electric -21.4 660.8 608 905 176.4 329s General.Motors -282.8 607.5 7160 -2222 126.2 329s US.Steel 418.1 905.0 -2222 8896 546.2 329s Westinghouse 13.3 176.4 126 546 88.7 329s 329s The covariance matrix of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 152.85 2.05 -314 455 16.7 329s General.Electric 2.05 700.46 605 1224 200.3 329s General.Motors -313.70 605.34 7216 -2687 129.9 329s US.Steel 455.09 1224.41 -2687 9188 652.7 329s Westinghouse 16.66 200.32 130 653 94.9 329s 329s The correlations of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 1.00000 0.00626 -0.299 0.384 0.138 329s General.Electric 0.00626 1.00000 0.269 0.483 0.777 329s General.Motors -0.29870 0.26925 1.000 -0.330 0.157 329s US.Steel 0.38402 0.48264 -0.330 1.000 0.699 329s Westinghouse 0.13832 0.77690 0.157 0.699 1.000 329s 329s 329s SUR estimates for 'Chrysler' (equation 1) 329s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) 0.5043 11.5128 0.04 0.96557 329s value 0.0695 0.0169 4.12 0.00072 *** 329s capital 0.3085 0.0259 11.93 1.1e-09 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 13.41 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 3056.985 MSE: 179.823 Root MSE: 13.41 329s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.901 329s 329s 329s SUR estimates for 'General.Electric' (equation 2) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -22.4389 25.5186 -0.88 0.3915 329s value 0.0373 0.0123 3.04 0.0074 ** 329s capital 0.1308 0.0220 5.93 1.6e-05 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 28.707 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 14009.115 MSE: 824.066 Root MSE: 28.707 329s Multiple R-Squared: 0.688 Adjusted R-Squared: 0.651 329s 329s 329s SUR estimates for 'General.Motors' (equation 3) 329s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -162.3641 89.4592 -1.81 0.087 . 329s value 0.1205 0.0216 5.57 3.4e-05 *** 329s capital 0.3827 0.0328 11.68 1.5e-09 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 92.138 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 144320.876 MSE: 8489.463 Root MSE: 92.138 329s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.911 329s 329s 329s SUR estimates for 'US.Steel' (equation 4) 329s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) 85.4233 111.8774 0.76 0.4556 329s value 0.1015 0.0548 1.85 0.0814 . 329s capital 0.4000 0.1278 3.13 0.0061 ** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 103.969 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 183763.011 MSE: 10809.589 Root MSE: 103.969 329s Multiple R-Squared: 0.422 Adjusted R-Squared: 0.354 329s 329s 329s SUR estimates for 'Westinghouse' (equation 5) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) 1.0889 6.2588 0.17 0.86394 329s value 0.0570 0.0114 5.02 0.00011 *** 329s capital 0.0415 0.0412 1.01 0.32787 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 10.567 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 1898.249 MSE: 111.662 Root MSE: 10.567 329s Multiple R-Squared: 0.726 Adjusted R-Squared: 0.694 329s 329s 329s systemfit results 329s method: SUR 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 85 347048 6.18e+13 0.844 0.869 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 3057 180 13.4 0.912 0.901 329s General.Electric 20 17 14009 824 28.7 0.688 0.651 329s General.Motors 20 17 144321 8489 92.1 0.921 0.911 329s US.Steel 20 17 183763 10810 104.0 0.422 0.354 329s Westinghouse 20 17 1898 112 10.6 0.726 0.694 329s 329s 329s SUR estimates for 'Chrysler' (equation 1) 329s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) 0.5043 11.5128 0.04 0.97 329s value 0.0695 0.0169 4.12 8.9e-05 *** 329s capital 0.3085 0.0259 11.93 < 2e-16 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 13.41 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 3056.985 MSE: 179.823 Root MSE: 13.41 329s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.901 329s 329s 329s SUR estimates for 'General.Electric' (equation 2) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -22.4389 25.5186 -0.88 0.3817 329s value 0.0373 0.0123 3.04 0.0031 ** 329s capital 0.1308 0.0220 5.93 6.3e-08 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 28.707 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 14009.115 MSE: 824.066 Root MSE: 28.707 329s Multiple R-Squared: 0.688 Adjusted R-Squared: 0.651 329s 329s 329s SUR estimates for 'General.Motors' (equation 3) 329s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -162.3641 89.4592 -1.81 0.073 . 329s value 0.1205 0.0216 5.57 2.9e-07 *** 329s capital 0.3827 0.0328 11.68 < 2e-16 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 92.138 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 144320.876 MSE: 8489.463 Root MSE: 92.138 329s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.911 329s 329s 329s SUR estimates for 'US.Steel' (equation 4) 329s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) 85.4233 111.8774 0.76 0.4473 329s value 0.1015 0.0548 1.85 0.0674 . 329s capital 0.4000 0.1278 3.13 0.0024 ** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 103.969 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 183763.011 MSE: 10809.589 Root MSE: 103.969 329s Multiple R-Squared: 0.422 Adjusted R-Squared: 0.354 329s 329s 329s SUR estimates for 'Westinghouse' (equation 5) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) 1.0889 6.2588 0.17 0.86 329s value 0.0570 0.0114 5.02 2.8e-06 *** 329s capital 0.0415 0.0412 1.01 0.32 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 10.567 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 1898.249 MSE: 111.662 Root MSE: 10.567 329s Multiple R-Squared: 0.726 Adjusted R-Squared: 0.694 329s 329s 329s systemfit results 329s method: SUR 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 85 347048 6.18e+13 0.844 0.869 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 3057 180 13.4 0.912 0.901 329s General.Electric 20 17 14009 824 28.7 0.688 0.651 329s General.Motors 20 17 144321 8489 92.1 0.921 0.911 329s US.Steel 20 17 183763 10810 104.0 0.422 0.354 329s Westinghouse 20 17 1898 112 10.6 0.726 0.694 329s 329s The covariance matrix of the residuals used for estimation 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 149.9 -21.4 -283 418 13.3 329s General.Electric -21.4 660.8 608 905 176.4 329s General.Motors -282.8 607.5 7160 -2222 126.2 329s US.Steel 418.1 905.0 -2222 8896 546.2 329s Westinghouse 13.3 176.4 126 546 88.7 329s 329s The covariance matrix of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 152.85 2.05 -314 455 16.7 329s General.Electric 2.05 700.46 605 1224 200.3 329s General.Motors -313.70 605.34 7216 -2687 129.9 329s US.Steel 455.09 1224.41 -2687 9188 652.7 329s Westinghouse 16.66 200.32 130 653 94.9 329s 329s The correlations of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 1.00000 0.00626 -0.299 0.384 0.138 329s General.Electric 0.00626 1.00000 0.269 0.483 0.777 329s General.Motors -0.29870 0.26925 1.000 -0.330 0.157 329s US.Steel 0.38402 0.48264 -0.330 1.000 0.699 329s Westinghouse 0.13832 0.77690 0.157 0.699 1.000 329s 329s 329s Coefficients: 329s Estimate Std. Error t value Pr(>|t|) 329s Chrysler_(Intercept) 0.5043 11.5128 0.04 0.96557 329s Chrysler_value 0.0695 0.0169 4.12 0.00072 *** 329s Chrysler_capital 0.3085 0.0259 11.93 1.1e-09 *** 329s General.Electric_(Intercept) -22.4389 25.5186 -0.88 0.39149 329s General.Electric_value 0.0373 0.0123 3.04 0.00738 ** 329s General.Electric_capital 0.1308 0.0220 5.93 1.6e-05 *** 329s General.Motors_(Intercept) -162.3641 89.4592 -1.81 0.08722 . 329s General.Motors_value 0.1205 0.0216 5.57 3.4e-05 *** 329s General.Motors_capital 0.3827 0.0328 11.68 1.5e-09 *** 329s US.Steel_(Intercept) 85.4233 111.8774 0.76 0.45561 329s US.Steel_value 0.1015 0.0548 1.85 0.08142 . 329s US.Steel_capital 0.4000 0.1278 3.13 0.00610 ** 329s Westinghouse_(Intercept) 1.0889 6.2588 0.17 0.86394 329s Westinghouse_value 0.0570 0.0114 5.02 0.00011 *** 329s Westinghouse_capital 0.0415 0.0412 1.01 0.32787 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s Chrysler_(Intercept) Chrysler_value 329s 0.5043 0.0695 329s Chrysler_capital General.Electric_(Intercept) 329s 0.3085 -22.4389 329s General.Electric_value General.Electric_capital 329s 0.0373 0.1308 329s General.Motors_(Intercept) General.Motors_value 329s -162.3641 0.1205 329s General.Motors_capital US.Steel_(Intercept) 329s 0.3827 85.4233 329s US.Steel_value US.Steel_capital 329s 0.1015 0.4000 329s Westinghouse_(Intercept) Westinghouse_value 329s 1.0889 0.0570 329s Westinghouse_capital 329s 0.0415 329s Estimate Std. Error t value Pr(>|t|) 329s Chrysler_(Intercept) 0.5043 11.5128 0.0438 9.66e-01 329s Chrysler_value 0.0695 0.0169 4.1157 7.22e-04 329s Chrysler_capital 0.3085 0.0259 11.9297 1.10e-09 329s General.Electric_(Intercept) -22.4389 25.5186 -0.8793 3.91e-01 329s General.Electric_value 0.0373 0.0123 3.0409 7.38e-03 329s General.Electric_capital 0.1308 0.0220 5.9313 1.64e-05 329s General.Motors_(Intercept) -162.3641 89.4592 -1.8150 8.72e-02 329s General.Motors_value 0.1205 0.0216 5.5709 3.38e-05 329s General.Motors_capital 0.3827 0.0328 11.6805 1.52e-09 329s US.Steel_(Intercept) 85.4233 111.8774 0.7635 4.56e-01 329s US.Steel_value 0.1015 0.0548 1.8523 8.14e-02 329s US.Steel_capital 0.4000 0.1278 3.1300 6.10e-03 329s Westinghouse_(Intercept) 1.0889 6.2588 0.1740 8.64e-01 329s Westinghouse_value 0.0570 0.0114 5.0174 1.06e-04 329s Westinghouse_capital 0.0415 0.0412 1.0074 3.28e-01 329s Chrysler_(Intercept) Chrysler_value 329s Chrysler_(Intercept) 1.33e+02 -1.82e-01 329s Chrysler_value -1.82e-01 2.86e-04 329s Chrysler_capital 9.57e-03 -1.31e-04 329s General.Electric_(Intercept) -2.94e+01 3.74e-02 329s General.Electric_value 1.28e-02 -1.86e-05 329s General.Electric_capital 8.80e-03 -2.96e-06 329s General.Motors_(Intercept) -1.56e+02 1.91e-01 329s General.Motors_value 3.28e-02 -4.91e-05 329s General.Motors_capital -8.18e-04 3.42e-05 329s US.Steel_(Intercept) 1.80e+02 -1.87e-01 329s US.Steel_value -7.46e-02 1.13e-04 329s US.Steel_capital -4.03e-02 -1.22e-04 329s Westinghouse_(Intercept) -3.04e-01 3.03e-03 329s Westinghouse_value 1.14e-03 -3.70e-06 329s Westinghouse_capital 2.42e-03 -6.41e-06 329s Chrysler_capital General.Electric_(Intercept) 329s Chrysler_(Intercept) 9.57e-03 -29.3642 329s Chrysler_value -1.31e-04 0.0374 329s Chrysler_capital 6.69e-04 0.0198 329s General.Electric_(Intercept) 1.98e-02 651.1982 329s General.Electric_value 1.28e-06 -0.2851 329s General.Electric_capital -5.56e-05 -0.1615 329s General.Motors_(Intercept) 7.79e-02 571.3402 329s General.Motors_value 1.03e-05 -0.1196 329s General.Motors_capital -1.89e-04 -0.0352 329s US.Steel_(Intercept) -2.45e-01 644.2920 329s US.Steel_value -3.26e-05 -0.2201 329s US.Steel_capital 1.03e-03 -0.5505 329s Westinghouse_(Intercept) -9.35e-03 102.8679 329s Westinghouse_value 1.18e-05 -0.1700 329s Westinghouse_capital 1.67e-05 0.2338 329s General.Electric_value General.Electric_capital 329s Chrysler_(Intercept) 1.28e-02 8.80e-03 329s Chrysler_value -1.86e-05 -2.96e-06 329s Chrysler_capital 1.28e-06 -5.56e-05 329s General.Electric_(Intercept) -2.85e-01 -1.61e-01 329s General.Electric_value 1.50e-04 -1.70e-05 329s General.Electric_capital -1.70e-05 4.86e-04 329s General.Motors_(Intercept) -2.61e-01 -8.74e-02 329s General.Motors_value 6.35e-05 -9.49e-06 329s General.Motors_capital -2.27e-05 1.98e-04 329s US.Steel_(Intercept) -3.04e-01 -2.30e-02 329s US.Steel_value 1.35e-04 -1.07e-04 329s US.Steel_capital 1.23e-04 7.77e-04 329s Westinghouse_(Intercept) -4.02e-02 -4.02e-02 329s Westinghouse_value 8.74e-05 1.04e-06 329s Westinghouse_capital -2.16e-04 4.61e-04 329s General.Motors_(Intercept) General.Motors_value 329s Chrysler_(Intercept) -1.56e+02 3.28e-02 329s Chrysler_value 1.91e-01 -4.91e-05 329s Chrysler_capital 7.79e-02 1.03e-05 329s General.Electric_(Intercept) 5.71e+02 -1.20e-01 329s General.Electric_value -2.61e-01 6.35e-05 329s General.Electric_capital -8.74e-02 -9.49e-06 329s General.Motors_(Intercept) 8.00e+03 -1.84e+00 329s General.Motors_value -1.84e+00 4.68e-04 329s General.Motors_capital 5.32e-01 -2.83e-04 329s US.Steel_(Intercept) -1.75e+03 3.73e-01 329s US.Steel_value 8.02e-01 -2.06e-04 329s US.Steel_capital 2.01e-01 1.09e-04 329s Westinghouse_(Intercept) 1.10e+02 -2.33e-02 329s Westinghouse_value -2.06e-01 5.10e-05 329s Westinghouse_capital 3.98e-01 -1.28e-04 329s General.Motors_capital US.Steel_(Intercept) 329s Chrysler_(Intercept) -8.18e-04 1.80e+02 329s Chrysler_value 3.42e-05 -1.87e-01 329s Chrysler_capital -1.89e-04 -2.45e-01 329s General.Electric_(Intercept) -3.52e-02 6.44e+02 329s General.Electric_value -2.27e-05 -3.04e-01 329s General.Electric_capital 1.98e-04 -2.30e-02 329s General.Motors_(Intercept) 5.32e-01 -1.75e+03 329s General.Motors_value -2.83e-04 3.73e-01 329s General.Motors_capital 1.07e-03 3.74e-02 329s US.Steel_(Intercept) 3.74e-02 1.25e+04 329s US.Steel_value 1.39e-04 -5.65e+00 329s US.Steel_capital -1.04e-03 -3.12e+00 329s Westinghouse_(Intercept) -4.87e-03 2.74e+02 329s Westinghouse_value -2.38e-05 -5.09e-01 329s Westinghouse_capital 2.43e-04 1.10e+00 329s US.Steel_value US.Steel_capital 329s Chrysler_(Intercept) -7.46e-02 -0.040281 329s Chrysler_value 1.13e-04 -0.000122 329s Chrysler_capital -3.26e-05 0.001031 329s General.Electric_(Intercept) -2.20e-01 -0.550482 329s General.Electric_value 1.35e-04 0.000123 329s General.Electric_capital -1.07e-04 0.000777 329s General.Motors_(Intercept) 8.02e-01 0.200945 329s General.Motors_value -2.06e-04 0.000109 329s General.Motors_capital 1.39e-04 -0.001036 329s US.Steel_(Intercept) -5.65e+00 -3.119830 329s US.Steel_value 3.00e-03 -0.000901 329s US.Steel_capital -9.01e-04 0.016331 329s Westinghouse_(Intercept) -8.35e-02 -0.275101 329s Westinghouse_value 2.23e-04 0.000229 329s Westinghouse_capital -7.74e-04 0.001422 329s Westinghouse_(Intercept) Westinghouse_value 329s Chrysler_(Intercept) -0.30387 1.14e-03 329s Chrysler_value 0.00303 -3.70e-06 329s Chrysler_capital -0.00935 1.18e-05 329s General.Electric_(Intercept) 102.86790 -1.70e-01 329s General.Electric_value -0.04016 8.74e-05 329s General.Electric_capital -0.04021 1.04e-06 329s General.Motors_(Intercept) 110.26166 -2.06e-01 329s General.Motors_value -0.02326 5.10e-05 329s General.Motors_capital -0.00487 -2.38e-05 329s US.Steel_(Intercept) 274.40848 -5.09e-01 329s US.Steel_value -0.08348 2.23e-04 329s US.Steel_capital -0.27510 2.29e-04 329s Westinghouse_(Intercept) 39.17263 -5.99e-02 329s Westinghouse_value -0.05992 1.29e-04 329s Westinghouse_capital 0.06376 -3.12e-04 329s Westinghouse_capital 329s Chrysler_(Intercept) 2.42e-03 329s Chrysler_value -6.41e-06 329s Chrysler_capital 1.67e-05 329s General.Electric_(Intercept) 2.34e-01 329s General.Electric_value -2.16e-04 329s General.Electric_capital 4.61e-04 329s General.Motors_(Intercept) 3.98e-01 329s General.Motors_value -1.28e-04 329s General.Motors_capital 2.43e-04 329s US.Steel_(Intercept) 1.10e+00 329s US.Steel_value -7.74e-04 329s US.Steel_capital 1.42e-03 329s Westinghouse_(Intercept) 6.38e-02 329s Westinghouse_value -3.12e-04 329s Westinghouse_capital 1.70e-03 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s X1935 7.511 -0.905 107.95 -35.3 0.849 329s X1936 10.843 -21.387 -27.67 66.3 -4.639 329s X1937 -6.422 -20.333 -136.20 65.7 -7.906 329s X1938 4.659 -29.453 3.55 -110.1 -10.898 329s X1939 -15.204 -36.171 -104.40 -178.7 -12.863 329s X1940 -2.413 -7.078 -15.30 -149.0 -9.449 329s X1941 -0.116 38.153 28.30 41.3 15.299 329s X1942 -4.311 17.481 103.23 20.6 7.734 329s X1943 -14.728 -23.336 72.44 -46.0 -2.758 329s X1944 -8.172 -25.700 105.03 -92.9 -2.792 329s X1945 12.566 -0.629 38.84 -100.0 -7.681 329s X1946 -14.709 54.737 106.00 32.0 5.446 329s X1947 -7.958 48.169 14.88 46.8 16.715 329s X1948 6.548 37.841 -53.65 121.3 5.293 329s X1949 -8.057 -13.518 -118.82 10.1 -8.216 329s X1950 1.571 -28.788 -67.90 20.0 -10.735 329s X1951 41.064 1.996 -126.32 133.6 6.645 329s X1952 4.273 7.222 -87.37 163.0 15.390 329s X1953 -2.011 8.833 34.43 100.0 13.695 329s X1954 -4.934 -7.135 122.97 -108.7 -9.129 329s 2.5 % 97.5 % 329s Chrysler_(Intercept) -23.786 24.794 329s Chrysler_value 0.034 0.105 329s Chrysler_capital 0.254 0.363 329s General.Electric_(Intercept) -76.278 31.401 329s General.Electric_value 0.011 0.063 329s General.Electric_capital 0.084 0.177 329s General.Motors_(Intercept) -351.107 26.378 329s General.Motors_value 0.075 0.166 329s General.Motors_capital 0.314 0.452 329s US.Steel_(Intercept) -150.617 321.464 329s US.Steel_value -0.014 0.217 329s US.Steel_capital 0.130 0.670 329s Westinghouse_(Intercept) -12.116 14.294 329s Westinghouse_value 0.033 0.081 329s Westinghouse_capital -0.045 0.128 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s X1935 32.8 34.0 210 245 12.1 329s X1936 61.9 66.4 419 289 30.5 329s X1937 72.7 97.5 547 404 43.0 329s X1938 46.9 74.1 254 372 33.8 329s X1939 67.6 84.3 435 409 31.7 329s X1940 71.8 81.5 476 411 38.0 329s X1941 68.5 74.8 484 432 33.2 329s X1942 51.1 74.4 345 425 35.6 329s X1943 62.1 84.6 427 408 39.8 329s X1944 67.7 82.5 442 381 40.6 329s X1945 76.2 94.2 522 359 47.0 329s X1946 88.8 105.2 582 388 48.0 329s X1947 70.6 99.0 554 374 38.8 329s X1948 82.8 108.5 583 373 44.3 329s X1949 87.0 111.8 674 395 40.3 329s X1950 99.1 122.3 711 399 43.0 329s X1951 119.6 133.2 882 455 47.7 329s X1952 140.7 150.1 979 482 56.4 329s X1953 176.9 170.7 1270 541 76.4 329s X1954 177.4 196.7 1364 568 77.7 329s 'log Lik.' -459 (df=30) 329s 'log Lik.' -483 (df=30) 329s [1] 100 329s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 329s X1935 40.3 418 10.5 33.1 329s X1936 72.8 838 10.2 45.0 329s X1937 66.3 884 34.7 77.2 329s X1938 51.6 438 51.8 44.6 329s X1939 52.4 680 64.3 48.1 329s X1940 69.4 728 67.1 74.4 329s X1941 68.3 644 75.2 113.0 329s X1942 46.8 411 71.4 91.9 329s X1943 47.4 588 67.1 61.3 329s X1944 59.6 698 60.5 56.8 329s X1945 88.8 846 54.6 93.6 329s X1946 74.1 894 84.8 159.9 329s X1947 62.7 579 96.8 147.2 329s X1948 89.4 695 110.2 146.3 329s X1949 79.0 590 147.4 98.3 329s X1950 100.7 694 163.2 93.5 329s X1951 160.6 809 203.5 135.2 329s X1952 145.0 727 290.6 157.3 329s X1953 174.9 1002 346.1 179.5 329s X1954 172.5 703 414.9 189.6 329s General.Electric_value General.Electric_capital General.Motors_invest 329s X1935 1171 97.8 318 329s X1936 2016 104.4 392 329s X1937 2803 118.0 411 329s X1938 2040 156.2 258 329s X1939 2256 172.6 331 329s X1940 2132 186.6 461 329s X1941 1834 220.9 512 329s X1942 1588 287.8 448 329s X1943 1749 319.9 500 329s X1944 1687 321.3 548 329s X1945 2008 319.6 561 329s X1946 2208 346.0 688 329s X1947 1657 456.4 569 329s X1948 1604 543.4 529 329s X1949 1432 618.3 555 329s X1950 1610 647.4 643 329s X1951 1819 671.3 756 329s X1952 2080 726.1 891 329s X1953 2372 800.3 1304 329s X1954 2760 888.9 1487 329s General.Motors_value General.Motors_capital US.Steel_invest 329s X1935 3078 2.8 210 329s X1936 4662 52.6 355 329s X1937 5387 156.9 470 329s X1938 2792 209.2 262 329s X1939 4313 203.4 230 329s X1940 4644 207.2 262 329s X1941 4551 255.2 473 329s X1942 3244 303.7 446 329s X1943 4054 264.1 362 329s X1944 4379 201.6 288 329s X1945 4841 265.0 259 329s X1946 4901 402.2 420 329s X1947 3526 761.5 420 329s X1948 3255 922.4 494 329s X1949 3700 1020.1 405 329s X1950 3756 1099.0 419 329s X1951 4833 1207.7 588 329s X1952 4925 1430.5 645 329s X1953 6242 1777.3 641 329s X1954 5594 2226.3 459 329s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 329s X1935 1362 53.8 12.9 192 329s X1936 1807 50.5 25.9 516 329s X1937 2676 118.1 35.0 729 329s X1938 1802 260.2 22.9 560 329s X1939 1957 312.7 18.8 520 329s X1940 2203 254.2 28.6 628 329s X1941 2380 261.4 48.5 537 329s X1942 2169 298.7 43.3 561 329s X1943 1985 301.8 37.0 617 329s X1944 1814 279.1 37.8 627 329s X1945 1850 213.8 39.3 737 329s X1946 2068 232.6 53.5 760 329s X1947 1797 264.8 55.6 581 329s X1948 1626 306.9 49.6 662 329s X1949 1667 351.1 32.0 584 329s X1950 1677 357.8 32.2 635 329s X1951 2290 342.1 54.4 724 329s X1952 2159 444.2 71.8 864 329s X1953 2031 623.6 90.1 1194 329s X1954 2116 669.7 68.6 1189 329s Westinghouse_capital 329s X1935 1.8 329s X1936 0.8 329s X1937 7.4 329s X1938 18.1 329s X1939 23.5 329s X1940 26.5 329s X1941 36.2 329s X1942 60.8 329s X1943 84.4 329s X1944 91.2 329s X1945 92.4 329s X1946 86.0 329s X1947 111.1 329s X1948 130.6 329s X1949 141.8 329s X1950 136.7 329s X1951 129.7 329s X1952 145.5 329s X1953 174.8 329s X1954 213.5 329s Chrysler_(Intercept) Chrysler_value Chrysler_capital 329s Chrysler_X1935 1 418 10.5 329s Chrysler_X1936 1 838 10.2 329s Chrysler_X1937 1 884 34.7 329s Chrysler_X1938 1 438 51.8 329s Chrysler_X1939 1 680 64.3 329s Chrysler_X1940 1 728 67.1 329s Chrysler_X1941 1 644 75.2 329s Chrysler_X1942 1 411 71.4 329s Chrysler_X1943 1 588 67.1 329s Chrysler_X1944 1 698 60.5 329s Chrysler_X1945 1 846 54.6 329s Chrysler_X1946 1 894 84.8 329s Chrysler_X1947 1 579 96.8 329s Chrysler_X1948 1 695 110.2 329s Chrysler_X1949 1 590 147.4 329s Chrysler_X1950 1 694 163.2 329s Chrysler_X1951 1 809 203.5 329s Chrysler_X1952 1 727 290.6 329s Chrysler_X1953 1 1002 346.1 329s Chrysler_X1954 1 703 414.9 329s General.Electric_X1935 0 0 0.0 329s General.Electric_X1936 0 0 0.0 329s General.Electric_X1937 0 0 0.0 329s General.Electric_X1938 0 0 0.0 329s General.Electric_X1939 0 0 0.0 329s General.Electric_X1940 0 0 0.0 329s General.Electric_X1941 0 0 0.0 329s General.Electric_X1942 0 0 0.0 329s General.Electric_X1943 0 0 0.0 329s General.Electric_X1944 0 0 0.0 329s General.Electric_X1945 0 0 0.0 329s General.Electric_X1946 0 0 0.0 329s General.Electric_X1947 0 0 0.0 329s General.Electric_X1948 0 0 0.0 329s General.Electric_X1949 0 0 0.0 329s General.Electric_X1950 0 0 0.0 329s General.Electric_X1951 0 0 0.0 329s General.Electric_X1952 0 0 0.0 329s General.Electric_X1953 0 0 0.0 329s General.Electric_X1954 0 0 0.0 329s General.Motors_X1935 0 0 0.0 329s General.Motors_X1936 0 0 0.0 329s General.Motors_X1937 0 0 0.0 329s General.Motors_X1938 0 0 0.0 329s General.Motors_X1939 0 0 0.0 329s General.Motors_X1940 0 0 0.0 329s General.Motors_X1941 0 0 0.0 329s General.Motors_X1942 0 0 0.0 329s General.Motors_X1943 0 0 0.0 329s General.Motors_X1944 0 0 0.0 329s General.Motors_X1945 0 0 0.0 329s General.Motors_X1946 0 0 0.0 329s General.Motors_X1947 0 0 0.0 329s General.Motors_X1948 0 0 0.0 329s General.Motors_X1949 0 0 0.0 329s General.Motors_X1950 0 0 0.0 329s General.Motors_X1951 0 0 0.0 329s General.Motors_X1952 0 0 0.0 329s General.Motors_X1953 0 0 0.0 329s General.Motors_X1954 0 0 0.0 329s US.Steel_X1935 0 0 0.0 329s US.Steel_X1936 0 0 0.0 329s US.Steel_X1937 0 0 0.0 329s US.Steel_X1938 0 0 0.0 329s US.Steel_X1939 0 0 0.0 329s US.Steel_X1940 0 0 0.0 329s US.Steel_X1941 0 0 0.0 329s US.Steel_X1942 0 0 0.0 329s US.Steel_X1943 0 0 0.0 329s US.Steel_X1944 0 0 0.0 329s US.Steel_X1945 0 0 0.0 329s US.Steel_X1946 0 0 0.0 329s US.Steel_X1947 0 0 0.0 329s US.Steel_X1948 0 0 0.0 329s US.Steel_X1949 0 0 0.0 329s US.Steel_X1950 0 0 0.0 329s US.Steel_X1951 0 0 0.0 329s US.Steel_X1952 0 0 0.0 329s US.Steel_X1953 0 0 0.0 329s US.Steel_X1954 0 0 0.0 329s Westinghouse_X1935 0 0 0.0 329s Westinghouse_X1936 0 0 0.0 329s Westinghouse_X1937 0 0 0.0 329s Westinghouse_X1938 0 0 0.0 329s Westinghouse_X1939 0 0 0.0 329s Westinghouse_X1940 0 0 0.0 329s Westinghouse_X1941 0 0 0.0 329s Westinghouse_X1942 0 0 0.0 329s Westinghouse_X1943 0 0 0.0 329s Westinghouse_X1944 0 0 0.0 329s Westinghouse_X1945 0 0 0.0 329s Westinghouse_X1946 0 0 0.0 329s Westinghouse_X1947 0 0 0.0 329s Westinghouse_X1948 0 0 0.0 329s Westinghouse_X1949 0 0 0.0 329s Westinghouse_X1950 0 0 0.0 329s Westinghouse_X1951 0 0 0.0 329s Westinghouse_X1952 0 0 0.0 329s Westinghouse_X1953 0 0 0.0 329s Westinghouse_X1954 0 0 0.0 329s General.Electric_(Intercept) General.Electric_value 329s Chrysler_X1935 0 0 329s Chrysler_X1936 0 0 329s Chrysler_X1937 0 0 329s Chrysler_X1938 0 0 329s Chrysler_X1939 0 0 329s Chrysler_X1940 0 0 329s Chrysler_X1941 0 0 329s Chrysler_X1942 0 0 329s Chrysler_X1943 0 0 329s Chrysler_X1944 0 0 329s Chrysler_X1945 0 0 329s Chrysler_X1946 0 0 329s Chrysler_X1947 0 0 329s Chrysler_X1948 0 0 329s Chrysler_X1949 0 0 329s Chrysler_X1950 0 0 329s Chrysler_X1951 0 0 329s Chrysler_X1952 0 0 329s Chrysler_X1953 0 0 329s Chrysler_X1954 0 0 329s General.Electric_X1935 1 1171 329s General.Electric_X1936 1 2016 329s General.Electric_X1937 1 2803 329s General.Electric_X1938 1 2040 329s General.Electric_X1939 1 2256 329s General.Electric_X1940 1 2132 329s General.Electric_X1941 1 1834 329s General.Electric_X1942 1 1588 329s General.Electric_X1943 1 1749 329s General.Electric_X1944 1 1687 329s General.Electric_X1945 1 2008 329s General.Electric_X1946 1 2208 329s General.Electric_X1947 1 1657 329s General.Electric_X1948 1 1604 329s General.Electric_X1949 1 1432 329s General.Electric_X1950 1 1610 329s General.Electric_X1951 1 1819 329s General.Electric_X1952 1 2080 329s General.Electric_X1953 1 2372 329s General.Electric_X1954 1 2760 329s General.Motors_X1935 0 0 329s General.Motors_X1936 0 0 329s General.Motors_X1937 0 0 329s General.Motors_X1938 0 0 329s General.Motors_X1939 0 0 329s General.Motors_X1940 0 0 329s General.Motors_X1941 0 0 329s General.Motors_X1942 0 0 329s General.Motors_X1943 0 0 329s General.Motors_X1944 0 0 329s General.Motors_X1945 0 0 329s General.Motors_X1946 0 0 329s General.Motors_X1947 0 0 329s General.Motors_X1948 0 0 329s General.Motors_X1949 0 0 329s General.Motors_X1950 0 0 329s General.Motors_X1951 0 0 329s General.Motors_X1952 0 0 329s General.Motors_X1953 0 0 329s General.Motors_X1954 0 0 329s US.Steel_X1935 0 0 329s US.Steel_X1936 0 0 329s US.Steel_X1937 0 0 329s US.Steel_X1938 0 0 329s US.Steel_X1939 0 0 329s US.Steel_X1940 0 0 329s US.Steel_X1941 0 0 329s US.Steel_X1942 0 0 329s US.Steel_X1943 0 0 329s US.Steel_X1944 0 0 329s US.Steel_X1945 0 0 329s US.Steel_X1946 0 0 329s US.Steel_X1947 0 0 329s US.Steel_X1948 0 0 329s US.Steel_X1949 0 0 329s US.Steel_X1950 0 0 329s US.Steel_X1951 0 0 329s US.Steel_X1952 0 0 329s US.Steel_X1953 0 0 329s US.Steel_X1954 0 0 329s Westinghouse_X1935 0 0 329s Westinghouse_X1936 0 0 329s Westinghouse_X1937 0 0 329s Westinghouse_X1938 0 0 329s Westinghouse_X1939 0 0 329s Westinghouse_X1940 0 0 329s Westinghouse_X1941 0 0 329s Westinghouse_X1942 0 0 329s Westinghouse_X1943 0 0 329s Westinghouse_X1944 0 0 329s Westinghouse_X1945 0 0 329s Westinghouse_X1946 0 0 329s Westinghouse_X1947 0 0 329s Westinghouse_X1948 0 0 329s Westinghouse_X1949 0 0 329s Westinghouse_X1950 0 0 329s Westinghouse_X1951 0 0 329s Westinghouse_X1952 0 0 329s Westinghouse_X1953 0 0 329s Westinghouse_X1954 0 0 329s General.Electric_capital General.Motors_(Intercept) 329s Chrysler_X1935 0.0 0 329s Chrysler_X1936 0.0 0 329s Chrysler_X1937 0.0 0 329s Chrysler_X1938 0.0 0 329s Chrysler_X1939 0.0 0 329s Chrysler_X1940 0.0 0 329s Chrysler_X1941 0.0 0 329s Chrysler_X1942 0.0 0 329s Chrysler_X1943 0.0 0 329s Chrysler_X1944 0.0 0 329s Chrysler_X1945 0.0 0 329s Chrysler_X1946 0.0 0 329s Chrysler_X1947 0.0 0 329s Chrysler_X1948 0.0 0 329s Chrysler_X1949 0.0 0 329s Chrysler_X1950 0.0 0 329s Chrysler_X1951 0.0 0 329s Chrysler_X1952 0.0 0 329s Chrysler_X1953 0.0 0 329s Chrysler_X1954 0.0 0 329s General.Electric_X1935 97.8 0 329s General.Electric_X1936 104.4 0 329s General.Electric_X1937 118.0 0 329s General.Electric_X1938 156.2 0 329s General.Electric_X1939 172.6 0 329s General.Electric_X1940 186.6 0 329s General.Electric_X1941 220.9 0 329s General.Electric_X1942 287.8 0 329s General.Electric_X1943 319.9 0 329s General.Electric_X1944 321.3 0 329s General.Electric_X1945 319.6 0 329s General.Electric_X1946 346.0 0 329s General.Electric_X1947 456.4 0 329s General.Electric_X1948 543.4 0 329s General.Electric_X1949 618.3 0 329s General.Electric_X1950 647.4 0 329s General.Electric_X1951 671.3 0 329s General.Electric_X1952 726.1 0 329s General.Electric_X1953 800.3 0 329s General.Electric_X1954 888.9 0 329s General.Motors_X1935 0.0 1 329s General.Motors_X1936 0.0 1 329s General.Motors_X1937 0.0 1 329s General.Motors_X1938 0.0 1 329s General.Motors_X1939 0.0 1 329s General.Motors_X1940 0.0 1 329s General.Motors_X1941 0.0 1 329s General.Motors_X1942 0.0 1 329s General.Motors_X1943 0.0 1 329s General.Motors_X1944 0.0 1 329s General.Motors_X1945 0.0 1 329s General.Motors_X1946 0.0 1 329s General.Motors_X1947 0.0 1 329s General.Motors_X1948 0.0 1 329s General.Motors_X1949 0.0 1 329s General.Motors_X1950 0.0 1 329s General.Motors_X1951 0.0 1 329s General.Motors_X1952 0.0 1 329s General.Motors_X1953 0.0 1 329s General.Motors_X1954 0.0 1 329s US.Steel_X1935 0.0 0 329s US.Steel_X1936 0.0 0 329s US.Steel_X1937 0.0 0 329s US.Steel_X1938 0.0 0 329s US.Steel_X1939 0.0 0 329s US.Steel_X1940 0.0 0 329s US.Steel_X1941 0.0 0 329s US.Steel_X1942 0.0 0 329s US.Steel_X1943 0.0 0 329s US.Steel_X1944 0.0 0 329s US.Steel_X1945 0.0 0 329s US.Steel_X1946 0.0 0 329s US.Steel_X1947 0.0 0 329s US.Steel_X1948 0.0 0 329s US.Steel_X1949 0.0 0 329s US.Steel_X1950 0.0 0 329s US.Steel_X1951 0.0 0 329s US.Steel_X1952 0.0 0 329s US.Steel_X1953 0.0 0 329s US.Steel_X1954 0.0 0 329s Westinghouse_X1935 0.0 0 329s Westinghouse_X1936 0.0 0 329s Westinghouse_X1937 0.0 0 329s Westinghouse_X1938 0.0 0 329s Westinghouse_X1939 0.0 0 329s Westinghouse_X1940 0.0 0 329s Westinghouse_X1941 0.0 0 329s Westinghouse_X1942 0.0 0 329s Westinghouse_X1943 0.0 0 329s Westinghouse_X1944 0.0 0 329s Westinghouse_X1945 0.0 0 329s Westinghouse_X1946 0.0 0 329s Westinghouse_X1947 0.0 0 329s Westinghouse_X1948 0.0 0 329s Westinghouse_X1949 0.0 0 329s Westinghouse_X1950 0.0 0 329s Westinghouse_X1951 0.0 0 329s Westinghouse_X1952 0.0 0 329s Westinghouse_X1953 0.0 0 329s Westinghouse_X1954 0.0 0 329s General.Motors_value General.Motors_capital 329s Chrysler_X1935 0 0.0 329s Chrysler_X1936 0 0.0 329s Chrysler_X1937 0 0.0 329s Chrysler_X1938 0 0.0 329s Chrysler_X1939 0 0.0 329s Chrysler_X1940 0 0.0 329s Chrysler_X1941 0 0.0 329s Chrysler_X1942 0 0.0 329s Chrysler_X1943 0 0.0 329s Chrysler_X1944 0 0.0 329s Chrysler_X1945 0 0.0 329s Chrysler_X1946 0 0.0 329s Chrysler_X1947 0 0.0 329s Chrysler_X1948 0 0.0 329s Chrysler_X1949 0 0.0 329s Chrysler_X1950 0 0.0 329s Chrysler_X1951 0 0.0 329s Chrysler_X1952 0 0.0 329s Chrysler_X1953 0 0.0 329s Chrysler_X1954 0 0.0 329s General.Electric_X1935 0 0.0 329s General.Electric_X1936 0 0.0 329s General.Electric_X1937 0 0.0 329s General.Electric_X1938 0 0.0 329s General.Electric_X1939 0 0.0 329s General.Electric_X1940 0 0.0 329s General.Electric_X1941 0 0.0 329s General.Electric_X1942 0 0.0 329s General.Electric_X1943 0 0.0 329s General.Electric_X1944 0 0.0 329s General.Electric_X1945 0 0.0 329s General.Electric_X1946 0 0.0 329s General.Electric_X1947 0 0.0 329s General.Electric_X1948 0 0.0 329s General.Electric_X1949 0 0.0 329s General.Electric_X1950 0 0.0 329s General.Electric_X1951 0 0.0 329s General.Electric_X1952 0 0.0 329s General.Electric_X1953 0 0.0 329s General.Electric_X1954 0 0.0 329s General.Motors_X1935 3078 2.8 329s General.Motors_X1936 4662 52.6 329s General.Motors_X1937 5387 156.9 329s General.Motors_X1938 2792 209.2 329s General.Motors_X1939 4313 203.4 329s General.Motors_X1940 4644 207.2 329s General.Motors_X1941 4551 255.2 329s General.Motors_X1942 3244 303.7 329s General.Motors_X1943 4054 264.1 329s General.Motors_X1944 4379 201.6 329s General.Motors_X1945 4841 265.0 329s General.Motors_X1946 4901 402.2 329s General.Motors_X1947 3526 761.5 329s General.Motors_X1948 3255 922.4 329s General.Motors_X1949 3700 1020.1 329s General.Motors_X1950 3756 1099.0 329s General.Motors_X1951 4833 1207.7 329s General.Motors_X1952 4925 1430.5 329s General.Motors_X1953 6242 1777.3 329s General.Motors_X1954 5594 2226.3 329s US.Steel_X1935 0 0.0 329s US.Steel_X1936 0 0.0 329s US.Steel_X1937 0 0.0 329s US.Steel_X1938 0 0.0 329s US.Steel_X1939 0 0.0 329s US.Steel_X1940 0 0.0 329s US.Steel_X1941 0 0.0 329s US.Steel_X1942 0 0.0 329s US.Steel_X1943 0 0.0 329s US.Steel_X1944 0 0.0 329s US.Steel_X1945 0 0.0 329s US.Steel_X1946 0 0.0 329s US.Steel_X1947 0 0.0 329s US.Steel_X1948 0 0.0 329s US.Steel_X1949 0 0.0 329s US.Steel_X1950 0 0.0 329s US.Steel_X1951 0 0.0 329s US.Steel_X1952 0 0.0 329s US.Steel_X1953 0 0.0 329s US.Steel_X1954 0 0.0 329s Westinghouse_X1935 0 0.0 329s Westinghouse_X1936 0 0.0 329s Westinghouse_X1937 0 0.0 329s Westinghouse_X1938 0 0.0 329s Westinghouse_X1939 0 0.0 329s Westinghouse_X1940 0 0.0 329s Westinghouse_X1941 0 0.0 329s Westinghouse_X1942 0 0.0 329s Westinghouse_X1943 0 0.0 329s Westinghouse_X1944 0 0.0 329s Westinghouse_X1945 0 0.0 329s Westinghouse_X1946 0 0.0 329s Westinghouse_X1947 0 0.0 329s Westinghouse_X1948 0 0.0 329s Westinghouse_X1949 0 0.0 329s Westinghouse_X1950 0 0.0 329s Westinghouse_X1951 0 0.0 329s Westinghouse_X1952 0 0.0 329s Westinghouse_X1953 0 0.0 329s Westinghouse_X1954 0 0.0 329s US.Steel_(Intercept) US.Steel_value US.Steel_capital 329s Chrysler_X1935 0 0 0.0 329s Chrysler_X1936 0 0 0.0 329s Chrysler_X1937 0 0 0.0 329s Chrysler_X1938 0 0 0.0 329s Chrysler_X1939 0 0 0.0 329s Chrysler_X1940 0 0 0.0 329s Chrysler_X1941 0 0 0.0 329s Chrysler_X1942 0 0 0.0 329s Chrysler_X1943 0 0 0.0 329s Chrysler_X1944 0 0 0.0 329s Chrysler_X1945 0 0 0.0 329s Chrysler_X1946 0 0 0.0 329s Chrysler_X1947 0 0 0.0 329s Chrysler_X1948 0 0 0.0 329s Chrysler_X1949 0 0 0.0 329s Chrysler_X1950 0 0 0.0 329s Chrysler_X1951 0 0 0.0 329s Chrysler_X1952 0 0 0.0 329s Chrysler_X1953 0 0 0.0 329s Chrysler_X1954 0 0 0.0 329s General.Electric_X1935 0 0 0.0 329s General.Electric_X1936 0 0 0.0 329s General.Electric_X1937 0 0 0.0 329s General.Electric_X1938 0 0 0.0 329s General.Electric_X1939 0 0 0.0 329s General.Electric_X1940 0 0 0.0 329s General.Electric_X1941 0 0 0.0 329s General.Electric_X1942 0 0 0.0 329s General.Electric_X1943 0 0 0.0 329s General.Electric_X1944 0 0 0.0 329s General.Electric_X1945 0 0 0.0 329s General.Electric_X1946 0 0 0.0 329s General.Electric_X1947 0 0 0.0 329s General.Electric_X1948 0 0 0.0 329s General.Electric_X1949 0 0 0.0 329s General.Electric_X1950 0 0 0.0 329s General.Electric_X1951 0 0 0.0 329s General.Electric_X1952 0 0 0.0 329s General.Electric_X1953 0 0 0.0 329s General.Electric_X1954 0 0 0.0 329s General.Motors_X1935 0 0 0.0 329s General.Motors_X1936 0 0 0.0 329s General.Motors_X1937 0 0 0.0 329s General.Motors_X1938 0 0 0.0 329s General.Motors_X1939 0 0 0.0 329s General.Motors_X1940 0 0 0.0 329s General.Motors_X1941 0 0 0.0 329s General.Motors_X1942 0 0 0.0 329s General.Motors_X1943 0 0 0.0 329s General.Motors_X1944 0 0 0.0 329s General.Motors_X1945 0 0 0.0 329s General.Motors_X1946 0 0 0.0 329s General.Motors_X1947 0 0 0.0 329s General.Motors_X1948 0 0 0.0 329s General.Motors_X1949 0 0 0.0 329s General.Motors_X1950 0 0 0.0 329s General.Motors_X1951 0 0 0.0 329s General.Motors_X1952 0 0 0.0 329s General.Motors_X1953 0 0 0.0 329s General.Motors_X1954 0 0 0.0 329s US.Steel_X1935 1 1362 53.8 329s US.Steel_X1936 1 1807 50.5 329s US.Steel_X1937 1 2676 118.1 329s US.Steel_X1938 1 1802 260.2 329s US.Steel_X1939 1 1957 312.7 329s US.Steel_X1940 1 2203 254.2 329s US.Steel_X1941 1 2380 261.4 329s US.Steel_X1942 1 2169 298.7 329s US.Steel_X1943 1 1985 301.8 329s US.Steel_X1944 1 1814 279.1 329s US.Steel_X1945 1 1850 213.8 329s US.Steel_X1946 1 2068 232.6 329s US.Steel_X1947 1 1797 264.8 329s US.Steel_X1948 1 1626 306.9 329s US.Steel_X1949 1 1667 351.1 329s US.Steel_X1950 1 1677 357.8 329s US.Steel_X1951 1 2290 342.1 329s US.Steel_X1952 1 2159 444.2 329s US.Steel_X1953 1 2031 623.6 329s US.Steel_X1954 1 2116 669.7 329s Westinghouse_X1935 0 0 0.0 329s Westinghouse_X1936 0 0 0.0 329s Westinghouse_X1937 0 0 0.0 329s Westinghouse_X1938 0 0 0.0 329s Westinghouse_X1939 0 0 0.0 329s Westinghouse_X1940 0 0 0.0 329s Westinghouse_X1941 0 0 0.0 329s Westinghouse_X1942 0 0 0.0 329s Westinghouse_X1943 0 0 0.0 329s Westinghouse_X1944 0 0 0.0 329s Westinghouse_X1945 0 0 0.0 329s Westinghouse_X1946 0 0 0.0 329s Westinghouse_X1947 0 0 0.0 329s Westinghouse_X1948 0 0 0.0 329s Westinghouse_X1949 0 0 0.0 329s Westinghouse_X1950 0 0 0.0 329s Westinghouse_X1951 0 0 0.0 329s Westinghouse_X1952 0 0 0.0 329s Westinghouse_X1953 0 0 0.0 329s Westinghouse_X1954 0 0 0.0 329s Westinghouse_(Intercept) Westinghouse_value 329s Chrysler_X1935 0 0 329s Chrysler_X1936 0 0 329s Chrysler_X1937 0 0 329s Chrysler_X1938 0 0 329s Chrysler_X1939 0 0 329s Chrysler_X1940 0 0 329s Chrysler_X1941 0 0 329s Chrysler_X1942 0 0 329s Chrysler_X1943 0 0 329s Chrysler_X1944 0 0 329s Chrysler_X1945 0 0 329s Chrysler_X1946 0 0 329s Chrysler_X1947 0 0 329s Chrysler_X1948 0 0 329s Chrysler_X1949 0 0 329s Chrysler_X1950 0 0 329s Chrysler_X1951 0 0 329s Chrysler_X1952 0 0 329s Chrysler_X1953 0 0 329s Chrysler_X1954 0 0 329s General.Electric_X1935 0 0 329s General.Electric_X1936 0 0 329s General.Electric_X1937 0 0 329s General.Electric_X1938 0 0 329s General.Electric_X1939 0 0 329s General.Electric_X1940 0 0 329s General.Electric_X1941 0 0 329s General.Electric_X1942 0 0 329s General.Electric_X1943 0 0 329s General.Electric_X1944 0 0 329s General.Electric_X1945 0 0 329s General.Electric_X1946 0 0 329s General.Electric_X1947 0 0 329s General.Electric_X1948 0 0 329s General.Electric_X1949 0 0 329s General.Electric_X1950 0 0 329s General.Electric_X1951 0 0 329s General.Electric_X1952 0 0 329s General.Electric_X1953 0 0 329s General.Electric_X1954 0 0 329s General.Motors_X1935 0 0 329s General.Motors_X1936 0 0 329s General.Motors_X1937 0 0 329s General.Motors_X1938 0 0 329s General.Motors_X1939 0 0 329s General.Motors_X1940 0 0 329s General.Motors_X1941 0 0 329s General.Motors_X1942 0 0 329s General.Motors_X1943 0 0 329s General.Motors_X1944 0 0 329s General.Motors_X1945 0 0 329s General.Motors_X1946 0 0 329s General.Motors_X1947 0 0 329s General.Motors_X1948 0 0 329s General.Motors_X1949 0 0 329s General.Motors_X1950 0 0 329s General.Motors_X1951 0 0 329s General.Motors_X1952 0 0 329s General.Motors_X1953 0 0 329s General.Motors_X1954 0 0 329s US.Steel_X1935 0 0 329s US.Steel_X1936 0 0 329s US.Steel_X1937 0 0 329s US.Steel_X1938 0 0 329s US.Steel_X1939 0 0 329s US.Steel_X1940 0 0 329s US.Steel_X1941 0 0 329s US.Steel_X1942 0 0 329s US.Steel_X1943 0 0 329s US.Steel_X1944 0 0 329s US.Steel_X1945 0 0 329s US.Steel_X1946 0 0 329s US.Steel_X1947 0 0 329s US.Steel_X1948 0 0 329s US.Steel_X1949 0 0 329s US.Steel_X1950 0 0 329s US.Steel_X1951 0 0 329s US.Steel_X1952 0 0 329s US.Steel_X1953 0 0 329s US.Steel_X1954 0 0 329s Westinghouse_X1935 1 192 329s Westinghouse_X1936 1 516 329s Westinghouse_X1937 1 729 329s Westinghouse_X1938 1 560 329s Westinghouse_X1939 1 520 329s Westinghouse_X1940 1 628 329s Westinghouse_X1941 1 537 329s Westinghouse_X1942 1 561 329s Westinghouse_X1943 1 617 329s Westinghouse_X1944 1 627 329s Westinghouse_X1945 1 737 329s Westinghouse_X1946 1 760 329s Westinghouse_X1947 1 581 329s Westinghouse_X1948 1 662 329s Westinghouse_X1949 1 584 329s Westinghouse_X1950 1 635 329s Westinghouse_X1951 1 724 329s Westinghouse_X1952 1 864 329s Westinghouse_X1953 1 1194 329s Westinghouse_X1954 1 1189 329s Westinghouse_capital 329s Chrysler_X1935 0.0 329s Chrysler_X1936 0.0 329s Chrysler_X1937 0.0 329s Chrysler_X1938 0.0 329s Chrysler_X1939 0.0 329s Chrysler_X1940 0.0 329s Chrysler_X1941 0.0 329s Chrysler_X1942 0.0 329s Chrysler_X1943 0.0 329s Chrysler_X1944 0.0 329s Chrysler_X1945 0.0 329s Chrysler_X1946 0.0 329s Chrysler_X1947 0.0 329s Chrysler_X1948 0.0 329s Chrysler_X1949 0.0 329s Chrysler_X1950 0.0 329s Chrysler_X1951 0.0 329s Chrysler_X1952 0.0 329s Chrysler_X1953 0.0 329s Chrysler_X1954 0.0 329s General.Electric_X1935 0.0 329s General.Electric_X1936 0.0 329s General.Electric_X1937 0.0 329s General.Electric_X1938 0.0 329s General.Electric_X1939 0.0 329s General.Electric_X1940 0.0 329s General.Electric_X1941 0.0 329s General.Electric_X1942 0.0 329s General.Electric_X1943 0.0 329s General.Electric_X1944 0.0 329s General.Electric_X1945 0.0 329s General.Electric_X1946 0.0 329s General.Electric_X1947 0.0 329s General.Electric_X1948 0.0 329s General.Electric_X1949 0.0 329s General.Electric_X1950 0.0 329s General.Electric_X1951 0.0 329s General.Electric_X1952 0.0 329s General.Electric_X1953 0.0 329s General.Electric_X1954 0.0 329s General.Motors_X1935 0.0 329s General.Motors_X1936 0.0 329s General.Motors_X1937 0.0 329s General.Motors_X1938 0.0 329s General.Motors_X1939 0.0 329s General.Motors_X1940 0.0 329s General.Motors_X1941 0.0 329s General.Motors_X1942 0.0 329s General.Motors_X1943 0.0 329s General.Motors_X1944 0.0 329s General.Motors_X1945 0.0 329s General.Motors_X1946 0.0 329s General.Motors_X1947 0.0 329s General.Motors_X1948 0.0 329s General.Motors_X1949 0.0 329s General.Motors_X1950 0.0 329s General.Motors_X1951 0.0 329s General.Motors_X1952 0.0 329s General.Motors_X1953 0.0 329s General.Motors_X1954 0.0 329s US.Steel_X1935 0.0 329s US.Steel_X1936 0.0 329s US.Steel_X1937 0.0 329s US.Steel_X1938 0.0 329s US.Steel_X1939 0.0 329s US.Steel_X1940 0.0 329s US.Steel_X1941 0.0 329s US.Steel_X1942 0.0 329s US.Steel_X1943 0.0 329s US.Steel_X1944 0.0 329s US.Steel_X1945 0.0 329s US.Steel_X1946 0.0 329s US.Steel_X1947 0.0 329s US.Steel_X1948 0.0 329s US.Steel_X1949 0.0 329s US.Steel_X1950 0.0 329s US.Steel_X1951 0.0 329s US.Steel_X1952 0.0 329s US.Steel_X1953 0.0 329s US.Steel_X1954 0.0 329s Westinghouse_X1935 1.8 329s Westinghouse_X1936 0.8 329s Westinghouse_X1937 7.4 329s Westinghouse_X1938 18.1 329s Westinghouse_X1939 23.5 329s Westinghouse_X1940 26.5 329s Westinghouse_X1941 36.2 329s Westinghouse_X1942 60.8 329s Westinghouse_X1943 84.4 329s Westinghouse_X1944 91.2 329s Westinghouse_X1945 92.4 329s Westinghouse_X1946 86.0 329s Westinghouse_X1947 111.1 329s Westinghouse_X1948 130.6 329s Westinghouse_X1949 141.8 329s Westinghouse_X1950 136.7 329s Westinghouse_X1951 129.7 329s Westinghouse_X1952 145.5 329s Westinghouse_X1953 174.8 329s Westinghouse_X1954 213.5 329s $Chrysler 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s $General.Motors 329s General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s $US.Steel 329s US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s $Chrysler 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s attr(,"variables") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"factors") 329s Chrysler_value Chrysler_capital 329s Chrysler_invest 0 0 329s Chrysler_value 1 0 329s Chrysler_capital 0 1 329s attr(,"term.labels") 329s [1] "Chrysler_value" "Chrysler_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"dataClasses") 329s Chrysler_invest Chrysler_value Chrysler_capital 329s "numeric" "numeric" "numeric" 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s attr(,"variables") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"factors") 329s General.Electric_value General.Electric_capital 329s General.Electric_invest 0 0 329s General.Electric_value 1 0 329s General.Electric_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Electric_value" "General.Electric_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"dataClasses") 329s General.Electric_invest General.Electric_value General.Electric_capital 329s "numeric" "numeric" "numeric" 329s 329s $General.Motors 329s General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s attr(,"variables") 329s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 329s attr(,"factors") 329s General.Motors_value General.Motors_capital 329s General.Motors_invest 0 0 329s General.Motors_value 1 0 329s General.Motors_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Motors_value" "General.Motors_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 329s attr(,"dataClasses") 329s General.Motors_invest General.Motors_value General.Motors_capital 329s "numeric" "numeric" "numeric" 329s 329s $US.Steel 329s US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s attr(,"variables") 329s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 329s attr(,"factors") 329s US.Steel_value US.Steel_capital 329s US.Steel_invest 0 0 329s US.Steel_value 1 0 329s US.Steel_capital 0 1 329s attr(,"term.labels") 329s [1] "US.Steel_value" "US.Steel_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 329s attr(,"dataClasses") 329s US.Steel_invest US.Steel_value US.Steel_capital 329s "numeric" "numeric" "numeric" 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s attr(,"variables") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"factors") 329s Westinghouse_value Westinghouse_capital 329s Westinghouse_invest 0 0 329s Westinghouse_value 1 0 329s Westinghouse_capital 0 1 329s attr(,"term.labels") 329s [1] "Westinghouse_value" "Westinghouse_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"dataClasses") 329s Westinghouse_invest Westinghouse_value Westinghouse_capital 329s "numeric" "numeric" "numeric" 329s 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s attr(,"variables") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"factors") 329s Chrysler_value Chrysler_capital 329s Chrysler_invest 0 0 329s Chrysler_value 1 0 329s Chrysler_capital 0 1 329s attr(,"term.labels") 329s [1] "Chrysler_value" "Chrysler_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"dataClasses") 329s Chrysler_invest Chrysler_value Chrysler_capital 329s "numeric" "numeric" "numeric" 329s > 329s > # SUR Pooled 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + greeneSurPooled <- systemfit( formulaGrunfeld, "SUR", 329s + data = GrunfeldGreene, pooled = TRUE, methodResidCov = "noDfCor", 329s + residCovWeighted = TRUE, useMatrix = useMatrix ) 329s + print( greeneSurPooled ) 329s + print( summary( greeneSurPooled ) ) 329s + print( summary( greeneSurPooled, useDfSys = FALSE, equations = FALSE ) ) 329s + print( summary( greeneSurPooled, residCov = FALSE, equations = FALSE ) ) 329s + print( coef( greeneSurPooled ) ) 329s + print( coef( greeneSurPooled, modified.regMat = TRUE ) ) 329s + print( coef( summary( greeneSurPooled ) ) ) 329s + print( coef( summary( greeneSurPooled ), modified.regMat = TRUE ) ) 329s + print( vcov( greeneSurPooled ) ) 329s + print( vcov( greeneSurPooled, modified.regMat = TRUE ) ) 329s + print( residuals( greeneSurPooled ) ) 329s + print( confint( greeneSurPooled ) ) 329s + print( fitted( greeneSurPooled ) ) 329s + print( logLik( greeneSurPooled ) ) 329s + print( logLik( greeneSurPooled, residCovDiag = TRUE ) ) 329s + print( nobs( greeneSurPooled ) ) 329s + print( model.frame( greeneSurPooled ) ) 329s + print( model.matrix( greeneSurPooled ) ) 329s + print( formula( greeneSurPooled ) ) 329s + print( formula( greeneSurPooled$eq[[ 1 ]] ) ) 329s + print( terms( greeneSurPooled ) ) 329s + print( terms( greeneSurPooled$eq[[ 1 ]] ) ) 329s + } 329s 329s systemfit results 329s method: SUR 329s 329s Coefficients: 329s Chrysler_(Intercept) Chrysler_value 329s -28.2467 0.0891 329s Chrysler_capital General.Electric_(Intercept) 329s 0.3340 -28.2467 329s General.Electric_value General.Electric_capital 329s 0.0891 0.3340 329s General.Motors_(Intercept) General.Motors_value 329s -28.2467 0.0891 329s General.Motors_capital US.Steel_(Intercept) 329s 0.3340 -28.2467 329s US.Steel_value US.Steel_capital 329s 0.0891 0.3340 329s Westinghouse_(Intercept) Westinghouse_value 329s -28.2467 0.0891 329s Westinghouse_capital 329s 0.3340 329s 329s systemfit results 329s method: SUR 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 97 1604301 9.95e+16 0.279 0.844 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 6112 360 19.0 0.824 0.803 329s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 329s General.Motors 20 17 201010 11824 108.7 0.890 0.877 329s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 329s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 329s 329s The covariance matrix of the residuals used for estimation 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 409 -2594 -197 2594 -102 329s General.Electric -2594 36563 -3480 -28623 3797 329s General.Motors -197 -3480 8612 996 -971 329s US.Steel 2594 -28623 996 32903 -2272 329s Westinghouse -102 3797 -971 -2272 778 329s 329s The covariance matrix of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 305.61 -1967 -4.81 2159 -124 329s General.Electric -1966.65 34557 -7160.67 -28722 4274 329s General.Motors -4.81 -7161 10050.52 4440 -1401 329s US.Steel 2158.60 -28722 4439.99 34469 -2894 329s Westinghouse -123.92 4274 -1400.75 -2894 833 329s 329s The correlations of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 1.000 0.220 -0.3447 0.2008 0.2907 329s General.Electric 0.220 1.000 -0.2233 -0.1587 0.8973 329s General.Motors -0.345 -0.223 1.0000 -0.0924 -0.3760 329s US.Steel 0.201 -0.159 -0.0924 1.0000 -0.0757 329s Westinghouse 0.291 0.897 -0.3760 -0.0757 1.0000 329s 329s 329s SUR estimates for 'Chrysler' (equation 1) 329s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s value 0.08910 0.00507 17.57 < 2e-16 *** 329s capital 0.33402 0.01671 19.99 < 2e-16 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 18.962 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 6112.2 MSE: 359.541 Root MSE: 18.962 329s Multiple R-Squared: 0.824 Adjusted R-Squared: 0.803 329s 329s 329s SUR estimates for 'General.Electric' (equation 2) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s value 0.08910 0.00507 17.57 < 2e-16 *** 329s capital 0.33402 0.01671 19.99 < 2e-16 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 201.63 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 691132.056 MSE: 40654.827 Root MSE: 201.63 329s Multiple R-Squared: -14.41 Adjusted R-Squared: -16.223 329s 329s 329s SUR estimates for 'General.Motors' (equation 3) 329s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s value 0.08910 0.00507 17.57 < 2e-16 *** 329s capital 0.33402 0.01671 19.99 < 2e-16 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 108.739 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 201010.497 MSE: 11824.147 Root MSE: 108.739 329s Multiple R-Squared: 0.89 Adjusted R-Squared: 0.877 329s 329s 329s SUR estimates for 'US.Steel' (equation 4) 329s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s value 0.08910 0.00507 17.57 < 2e-16 *** 329s capital 0.33402 0.01671 19.99 < 2e-16 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 201.375 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 689379.52 MSE: 40551.736 Root MSE: 201.375 329s Multiple R-Squared: -1.168 Adjusted R-Squared: -1.424 329s 329s 329s SUR estimates for 'Westinghouse' (equation 5) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s value 0.08910 0.00507 17.57 < 2e-16 *** 329s capital 0.33402 0.01671 19.99 < 2e-16 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 31.312 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 16667.149 MSE: 980.421 Root MSE: 31.312 329s Multiple R-Squared: -1.402 Adjusted R-Squared: -1.685 329s 329s 329s systemfit results 329s method: SUR 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 97 1604301 9.95e+16 0.279 0.844 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 6112 360 19.0 0.824 0.803 329s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 329s General.Motors 20 17 201010 11824 108.7 0.890 0.877 329s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 329s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 329s 329s The covariance matrix of the residuals used for estimation 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 409 -2594 -197 2594 -102 329s General.Electric -2594 36563 -3480 -28623 3797 329s General.Motors -197 -3480 8612 996 -971 329s US.Steel 2594 -28623 996 32903 -2272 329s Westinghouse -102 3797 -971 -2272 778 329s 329s The covariance matrix of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 305.61 -1967 -4.81 2159 -124 329s General.Electric -1966.65 34557 -7160.67 -28722 4274 329s General.Motors -4.81 -7161 10050.52 4440 -1401 329s US.Steel 2158.60 -28722 4439.99 34469 -2894 329s Westinghouse -123.92 4274 -1400.75 -2894 833 329s 329s The correlations of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 1.000 0.220 -0.3447 0.2008 0.2907 329s General.Electric 0.220 1.000 -0.2233 -0.1587 0.8973 329s General.Motors -0.345 -0.223 1.0000 -0.0924 -0.3760 329s US.Steel 0.201 -0.159 -0.0924 1.0000 -0.0757 329s Westinghouse 0.291 0.897 -0.3760 -0.0757 1.0000 329s 329s 329s Coefficients: 329s Estimate Std. Error t value Pr(>|t|) 329s Chrysler_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 329s Chrysler_value 0.08910 0.00507 17.57 2.5e-12 *** 329s Chrysler_capital 0.33402 0.01671 19.99 3.0e-13 *** 329s General.Electric_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 329s General.Electric_value 0.08910 0.00507 17.57 2.5e-12 *** 329s General.Electric_capital 0.33402 0.01671 19.99 3.0e-13 *** 329s General.Motors_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 329s General.Motors_value 0.08910 0.00507 17.57 2.5e-12 *** 329s General.Motors_capital 0.33402 0.01671 19.99 3.0e-13 *** 329s US.Steel_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 329s US.Steel_value 0.08910 0.00507 17.57 2.5e-12 *** 329s US.Steel_capital 0.33402 0.01671 19.99 3.0e-13 *** 329s Westinghouse_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 329s Westinghouse_value 0.08910 0.00507 17.57 2.5e-12 *** 329s Westinghouse_capital 0.33402 0.01671 19.99 3.0e-13 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s systemfit results 329s method: SUR 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 97 1604301 9.95e+16 0.279 0.844 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 6112 360 19.0 0.824 0.803 329s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 329s General.Motors 20 17 201010 11824 108.7 0.890 0.877 329s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 329s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 329s 329s 329s Coefficients: 329s Estimate Std. Error t value Pr(>|t|) 329s Chrysler_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s Chrysler_value 0.08910 0.00507 17.57 < 2e-16 *** 329s Chrysler_capital 0.33402 0.01671 19.99 < 2e-16 *** 329s General.Electric_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s General.Electric_value 0.08910 0.00507 17.57 < 2e-16 *** 329s General.Electric_capital 0.33402 0.01671 19.99 < 2e-16 *** 329s General.Motors_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s General.Motors_value 0.08910 0.00507 17.57 < 2e-16 *** 329s General.Motors_capital 0.33402 0.01671 19.99 < 2e-16 *** 329s US.Steel_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s US.Steel_value 0.08910 0.00507 17.57 < 2e-16 *** 329s US.Steel_capital 0.33402 0.01671 19.99 < 2e-16 *** 329s Westinghouse_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 329s Westinghouse_value 0.08910 0.00507 17.57 < 2e-16 *** 329s Westinghouse_capital 0.33402 0.01671 19.99 < 2e-16 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s Chrysler_(Intercept) Chrysler_value 329s -28.2467 0.0891 329s Chrysler_capital General.Electric_(Intercept) 329s 0.3340 -28.2467 329s General.Electric_value General.Electric_capital 329s 0.0891 0.3340 329s General.Motors_(Intercept) General.Motors_value 329s -28.2467 0.0891 329s General.Motors_capital US.Steel_(Intercept) 329s 0.3340 -28.2467 329s US.Steel_value US.Steel_capital 329s 0.0891 0.3340 329s Westinghouse_(Intercept) Westinghouse_value 329s -28.2467 0.0891 329s Westinghouse_capital 329s 0.3340 329s C1 C2 C3 329s -28.2467 0.0891 0.3340 329s Estimate Std. Error t value Pr(>|t|) 329s Chrysler_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 329s Chrysler_value 0.0891 0.00507 17.57 0.00e+00 329s Chrysler_capital 0.3340 0.01671 19.99 0.00e+00 329s General.Electric_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 329s General.Electric_value 0.0891 0.00507 17.57 0.00e+00 329s General.Electric_capital 0.3340 0.01671 19.99 0.00e+00 329s General.Motors_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 329s General.Motors_value 0.0891 0.00507 17.57 0.00e+00 329s General.Motors_capital 0.3340 0.01671 19.99 0.00e+00 329s US.Steel_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 329s US.Steel_value 0.0891 0.00507 17.57 0.00e+00 329s US.Steel_capital 0.3340 0.01671 19.99 0.00e+00 329s Westinghouse_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 329s Westinghouse_value 0.0891 0.00507 17.57 0.00e+00 329s Westinghouse_capital 0.3340 0.01671 19.99 0.00e+00 329s Estimate Std. Error t value Pr(>|t|) 329s C1 -28.2467 4.88824 -5.78 9.12e-08 329s C2 0.0891 0.00507 17.57 0.00e+00 329s C3 0.3340 0.01671 19.99 0.00e+00 329s Chrysler_(Intercept) Chrysler_value 329s Chrysler_(Intercept) 23.89487 -1.73e-02 329s Chrysler_value -0.01729 2.57e-05 329s Chrysler_capital 0.00114 -4.74e-05 329s General.Electric_(Intercept) 23.89487 -1.73e-02 329s General.Electric_value -0.01729 2.57e-05 329s General.Electric_capital 0.00114 -4.74e-05 329s General.Motors_(Intercept) 23.89487 -1.73e-02 329s General.Motors_value -0.01729 2.57e-05 329s General.Motors_capital 0.00114 -4.74e-05 329s US.Steel_(Intercept) 23.89487 -1.73e-02 329s US.Steel_value -0.01729 2.57e-05 329s US.Steel_capital 0.00114 -4.74e-05 329s Westinghouse_(Intercept) 23.89487 -1.73e-02 329s Westinghouse_value -0.01729 2.57e-05 329s Westinghouse_capital 0.00114 -4.74e-05 329s Chrysler_capital General.Electric_(Intercept) 329s Chrysler_(Intercept) 1.14e-03 23.89487 329s Chrysler_value -4.74e-05 -0.01729 329s Chrysler_capital 2.79e-04 0.00114 329s General.Electric_(Intercept) 1.14e-03 23.89487 329s General.Electric_value -4.74e-05 -0.01729 329s General.Electric_capital 2.79e-04 0.00114 329s General.Motors_(Intercept) 1.14e-03 23.89487 329s General.Motors_value -4.74e-05 -0.01729 329s General.Motors_capital 2.79e-04 0.00114 329s US.Steel_(Intercept) 1.14e-03 23.89487 329s US.Steel_value -4.74e-05 -0.01729 329s US.Steel_capital 2.79e-04 0.00114 329s Westinghouse_(Intercept) 1.14e-03 23.89487 329s Westinghouse_value -4.74e-05 -0.01729 329s Westinghouse_capital 2.79e-04 0.00114 329s General.Electric_value General.Electric_capital 329s Chrysler_(Intercept) -1.73e-02 1.14e-03 329s Chrysler_value 2.57e-05 -4.74e-05 329s Chrysler_capital -4.74e-05 2.79e-04 329s General.Electric_(Intercept) -1.73e-02 1.14e-03 329s General.Electric_value 2.57e-05 -4.74e-05 329s General.Electric_capital -4.74e-05 2.79e-04 329s General.Motors_(Intercept) -1.73e-02 1.14e-03 329s General.Motors_value 2.57e-05 -4.74e-05 329s General.Motors_capital -4.74e-05 2.79e-04 329s US.Steel_(Intercept) -1.73e-02 1.14e-03 329s US.Steel_value 2.57e-05 -4.74e-05 329s US.Steel_capital -4.74e-05 2.79e-04 329s Westinghouse_(Intercept) -1.73e-02 1.14e-03 329s Westinghouse_value 2.57e-05 -4.74e-05 329s Westinghouse_capital -4.74e-05 2.79e-04 329s General.Motors_(Intercept) General.Motors_value 329s Chrysler_(Intercept) 23.89487 -1.73e-02 329s Chrysler_value -0.01729 2.57e-05 329s Chrysler_capital 0.00114 -4.74e-05 329s General.Electric_(Intercept) 23.89487 -1.73e-02 329s General.Electric_value -0.01729 2.57e-05 329s General.Electric_capital 0.00114 -4.74e-05 329s General.Motors_(Intercept) 23.89487 -1.73e-02 329s General.Motors_value -0.01729 2.57e-05 329s General.Motors_capital 0.00114 -4.74e-05 329s US.Steel_(Intercept) 23.89487 -1.73e-02 329s US.Steel_value -0.01729 2.57e-05 329s US.Steel_capital 0.00114 -4.74e-05 329s Westinghouse_(Intercept) 23.89487 -1.73e-02 329s Westinghouse_value -0.01729 2.57e-05 329s Westinghouse_capital 0.00114 -4.74e-05 329s General.Motors_capital US.Steel_(Intercept) 329s Chrysler_(Intercept) 1.14e-03 23.89487 329s Chrysler_value -4.74e-05 -0.01729 329s Chrysler_capital 2.79e-04 0.00114 329s General.Electric_(Intercept) 1.14e-03 23.89487 329s General.Electric_value -4.74e-05 -0.01729 329s General.Electric_capital 2.79e-04 0.00114 329s General.Motors_(Intercept) 1.14e-03 23.89487 329s General.Motors_value -4.74e-05 -0.01729 329s General.Motors_capital 2.79e-04 0.00114 329s US.Steel_(Intercept) 1.14e-03 23.89487 329s US.Steel_value -4.74e-05 -0.01729 329s US.Steel_capital 2.79e-04 0.00114 329s Westinghouse_(Intercept) 1.14e-03 23.89487 329s Westinghouse_value -4.74e-05 -0.01729 329s Westinghouse_capital 2.79e-04 0.00114 329s US.Steel_value US.Steel_capital 329s Chrysler_(Intercept) -1.73e-02 1.14e-03 329s Chrysler_value 2.57e-05 -4.74e-05 329s Chrysler_capital -4.74e-05 2.79e-04 329s General.Electric_(Intercept) -1.73e-02 1.14e-03 329s General.Electric_value 2.57e-05 -4.74e-05 329s General.Electric_capital -4.74e-05 2.79e-04 329s General.Motors_(Intercept) -1.73e-02 1.14e-03 329s General.Motors_value 2.57e-05 -4.74e-05 329s General.Motors_capital -4.74e-05 2.79e-04 329s US.Steel_(Intercept) -1.73e-02 1.14e-03 329s US.Steel_value 2.57e-05 -4.74e-05 329s US.Steel_capital -4.74e-05 2.79e-04 329s Westinghouse_(Intercept) -1.73e-02 1.14e-03 329s Westinghouse_value 2.57e-05 -4.74e-05 329s Westinghouse_capital -4.74e-05 2.79e-04 329s Westinghouse_(Intercept) Westinghouse_value 329s Chrysler_(Intercept) 23.89487 -1.73e-02 329s Chrysler_value -0.01729 2.57e-05 329s Chrysler_capital 0.00114 -4.74e-05 329s General.Electric_(Intercept) 23.89487 -1.73e-02 329s General.Electric_value -0.01729 2.57e-05 329s General.Electric_capital 0.00114 -4.74e-05 329s General.Motors_(Intercept) 23.89487 -1.73e-02 329s General.Motors_value -0.01729 2.57e-05 329s General.Motors_capital 0.00114 -4.74e-05 329s US.Steel_(Intercept) 23.89487 -1.73e-02 329s US.Steel_value -0.01729 2.57e-05 329s US.Steel_capital 0.00114 -4.74e-05 329s Westinghouse_(Intercept) 23.89487 -1.73e-02 329s Westinghouse_value -0.01729 2.57e-05 329s Westinghouse_capital 0.00114 -4.74e-05 329s Westinghouse_capital 329s Chrysler_(Intercept) 1.14e-03 329s Chrysler_value -4.74e-05 329s Chrysler_capital 2.79e-04 329s General.Electric_(Intercept) 1.14e-03 329s General.Electric_value -4.74e-05 329s General.Electric_capital 2.79e-04 329s General.Motors_(Intercept) 1.14e-03 329s General.Motors_value -4.74e-05 329s General.Motors_capital 2.79e-04 329s US.Steel_(Intercept) 1.14e-03 329s US.Steel_value -4.74e-05 329s US.Steel_capital 2.79e-04 329s Westinghouse_(Intercept) 1.14e-03 329s Westinghouse_value -4.74e-05 329s Westinghouse_capital 2.79e-04 329s C1 C2 C3 329s C1 23.89487 -1.73e-02 1.14e-03 329s C2 -0.01729 2.57e-05 -4.74e-05 329s C3 0.00114 -4.74e-05 2.79e-04 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s X1935 27.830 -75.6 70.61 98.79 23.51 329s X1936 22.951 -141.2 -12.88 205.66 7.90 329s X1937 4.160 -183.7 -93.56 220.24 -4.13 329s X1938 23.527 -161.1 -32.72 43.09 -4.84 329s X1939 -1.382 -182.3 -93.20 -20.20 -7.09 329s X1940 10.397 -149.7 6.46 8.66 -8.03 329s X1941 14.133 -96.0 49.49 201.63 16.81 329s X1942 14.586 -117.5 85.75 180.85 1.28 329s X1943 0.807 -173.2 78.44 112.17 -17.92 329s X1944 5.381 -172.6 118.21 61.60 -20.25 329s X1945 23.374 -163.8 69.60 50.68 -29.03 329s X1946 -5.596 -124.2 145.33 186.62 -14.78 329s X1947 7.005 -124.6 28.58 200.21 -5.11 329s X1948 18.909 -149.9 -40.65 275.38 -24.83 329s X1949 5.397 -207.5 -87.07 167.54 -39.09 329s X1950 12.604 -238.0 -30.56 178.08 -41.77 329s X1951 48.812 -222.9 -49.87 298.18 -25.19 329s X1952 11.406 -242.3 2.83 332.67 -25.56 329s X1953 -1.660 -270.9 182.86 279.96 -46.40 329s X1954 -0.502 -325.0 272.93 75.36 -80.40 329s 2.5 % 97.5 % 329s Chrysler_(Intercept) -37.948 -18.545 329s Chrysler_value 0.079 0.099 329s Chrysler_capital 0.301 0.367 329s General.Electric_(Intercept) -37.948 -18.545 329s General.Electric_value 0.079 0.099 329s General.Electric_capital 0.301 0.367 329s General.Motors_(Intercept) -37.948 -18.545 329s General.Motors_value 0.079 0.099 329s General.Motors_capital 0.301 0.367 329s US.Steel_(Intercept) -37.948 -18.545 329s US.Steel_value 0.079 0.099 329s US.Steel_capital 0.301 0.367 329s Westinghouse_(Intercept) -37.948 -18.545 329s Westinghouse_value 0.079 0.099 329s Westinghouse_capital 0.301 0.367 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s X1935 12.5 109 247 111 -10.6 329s X1936 49.8 186 405 150 18.0 329s X1937 62.1 261 504 250 39.2 329s X1938 28.1 206 290 219 27.7 329s X1939 53.8 230 424 251 25.9 329s X1940 59.0 224 455 253 36.6 329s X1941 54.2 209 463 271 31.7 329s X1942 32.2 209 362 265 42.1 329s X1943 46.6 234 421 249 54.9 329s X1944 54.2 229 429 227 58.1 329s X1945 65.4 257 492 208 68.3 329s X1946 79.7 284 543 234 68.2 329s X1947 55.7 272 540 220 60.7 329s X1948 70.5 296 570 219 74.4 329s X1949 73.6 306 642 238 71.1 329s X1950 88.1 331 673 241 74.0 329s X1951 111.8 358 806 290 79.6 329s X1952 133.6 400 888 313 97.3 329s X1953 176.6 450 1122 361 136.5 329s X1954 173.0 515 1214 384 149.0 329s 'log Lik.' -533 (df=18) 329s 'log Lik.' -568 (df=18) 329s [1] 100 329s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 329s X1935 40.3 418 10.5 33.1 329s X1936 72.8 838 10.2 45.0 329s X1937 66.3 884 34.7 77.2 329s X1938 51.6 438 51.8 44.6 329s X1939 52.4 680 64.3 48.1 329s X1940 69.4 728 67.1 74.4 329s X1941 68.3 644 75.2 113.0 329s X1942 46.8 411 71.4 91.9 329s X1943 47.4 588 67.1 61.3 329s X1944 59.6 698 60.5 56.8 329s X1945 88.8 846 54.6 93.6 329s X1946 74.1 894 84.8 159.9 329s X1947 62.7 579 96.8 147.2 329s X1948 89.4 695 110.2 146.3 329s X1949 79.0 590 147.4 98.3 329s X1950 100.7 694 163.2 93.5 329s X1951 160.6 809 203.5 135.2 329s X1952 145.0 727 290.6 157.3 329s X1953 174.9 1002 346.1 179.5 329s X1954 172.5 703 414.9 189.6 329s General.Electric_value General.Electric_capital General.Motors_invest 329s X1935 1171 97.8 318 329s X1936 2016 104.4 392 329s X1937 2803 118.0 411 329s X1938 2040 156.2 258 329s X1939 2256 172.6 331 329s X1940 2132 186.6 461 329s X1941 1834 220.9 512 329s X1942 1588 287.8 448 329s X1943 1749 319.9 500 329s X1944 1687 321.3 548 329s X1945 2008 319.6 561 329s X1946 2208 346.0 688 329s X1947 1657 456.4 569 329s X1948 1604 543.4 529 329s X1949 1432 618.3 555 329s X1950 1610 647.4 643 329s X1951 1819 671.3 756 329s X1952 2080 726.1 891 329s X1953 2372 800.3 1304 329s X1954 2760 888.9 1487 329s General.Motors_value General.Motors_capital US.Steel_invest 329s X1935 3078 2.8 210 329s X1936 4662 52.6 355 329s X1937 5387 156.9 470 329s X1938 2792 209.2 262 329s X1939 4313 203.4 230 329s X1940 4644 207.2 262 329s X1941 4551 255.2 473 329s X1942 3244 303.7 446 329s X1943 4054 264.1 362 329s X1944 4379 201.6 288 329s X1945 4841 265.0 259 329s X1946 4901 402.2 420 329s X1947 3526 761.5 420 329s X1948 3255 922.4 494 329s X1949 3700 1020.1 405 329s X1950 3756 1099.0 419 329s X1951 4833 1207.7 588 329s X1952 4925 1430.5 645 329s X1953 6242 1777.3 641 329s X1954 5594 2226.3 459 329s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 329s X1935 1362 53.8 12.9 192 329s X1936 1807 50.5 25.9 516 329s X1937 2676 118.1 35.0 729 329s X1938 1802 260.2 22.9 560 329s X1939 1957 312.7 18.8 520 329s X1940 2203 254.2 28.6 628 329s X1941 2380 261.4 48.5 537 329s X1942 2169 298.7 43.3 561 329s X1943 1985 301.8 37.0 617 329s X1944 1814 279.1 37.8 627 329s X1945 1850 213.8 39.3 737 329s X1946 2068 232.6 53.5 760 329s X1947 1797 264.8 55.6 581 329s X1948 1626 306.9 49.6 662 329s X1949 1667 351.1 32.0 584 329s X1950 1677 357.8 32.2 635 329s X1951 2290 342.1 54.4 724 329s X1952 2159 444.2 71.8 864 329s X1953 2031 623.6 90.1 1194 329s X1954 2116 669.7 68.6 1189 329s Westinghouse_capital 329s X1935 1.8 329s X1936 0.8 329s X1937 7.4 329s X1938 18.1 329s X1939 23.5 329s X1940 26.5 329s X1941 36.2 329s X1942 60.8 329s X1943 84.4 329s X1944 91.2 329s X1945 92.4 329s X1946 86.0 329s X1947 111.1 329s X1948 130.6 329s X1949 141.8 329s X1950 136.7 329s X1951 129.7 329s X1952 145.5 329s X1953 174.8 329s X1954 213.5 329s Chrysler_(Intercept) Chrysler_value Chrysler_capital 329s Chrysler_X1935 1 418 10.5 329s Chrysler_X1936 1 838 10.2 329s Chrysler_X1937 1 884 34.7 329s Chrysler_X1938 1 438 51.8 329s Chrysler_X1939 1 680 64.3 329s Chrysler_X1940 1 728 67.1 329s Chrysler_X1941 1 644 75.2 329s Chrysler_X1942 1 411 71.4 329s Chrysler_X1943 1 588 67.1 329s Chrysler_X1944 1 698 60.5 329s Chrysler_X1945 1 846 54.6 329s Chrysler_X1946 1 894 84.8 329s Chrysler_X1947 1 579 96.8 329s Chrysler_X1948 1 695 110.2 329s Chrysler_X1949 1 590 147.4 329s Chrysler_X1950 1 694 163.2 329s Chrysler_X1951 1 809 203.5 329s Chrysler_X1952 1 727 290.6 329s Chrysler_X1953 1 1002 346.1 329s Chrysler_X1954 1 703 414.9 329s General.Electric_X1935 0 0 0.0 329s General.Electric_X1936 0 0 0.0 329s General.Electric_X1937 0 0 0.0 329s General.Electric_X1938 0 0 0.0 329s General.Electric_X1939 0 0 0.0 329s General.Electric_X1940 0 0 0.0 329s General.Electric_X1941 0 0 0.0 329s General.Electric_X1942 0 0 0.0 329s General.Electric_X1943 0 0 0.0 329s General.Electric_X1944 0 0 0.0 329s General.Electric_X1945 0 0 0.0 329s General.Electric_X1946 0 0 0.0 329s General.Electric_X1947 0 0 0.0 329s General.Electric_X1948 0 0 0.0 329s General.Electric_X1949 0 0 0.0 329s General.Electric_X1950 0 0 0.0 329s General.Electric_X1951 0 0 0.0 329s General.Electric_X1952 0 0 0.0 329s General.Electric_X1953 0 0 0.0 329s General.Electric_X1954 0 0 0.0 329s General.Motors_X1935 0 0 0.0 329s General.Motors_X1936 0 0 0.0 329s General.Motors_X1937 0 0 0.0 329s General.Motors_X1938 0 0 0.0 329s General.Motors_X1939 0 0 0.0 329s General.Motors_X1940 0 0 0.0 329s General.Motors_X1941 0 0 0.0 329s General.Motors_X1942 0 0 0.0 329s General.Motors_X1943 0 0 0.0 329s General.Motors_X1944 0 0 0.0 329s General.Motors_X1945 0 0 0.0 329s General.Motors_X1946 0 0 0.0 329s General.Motors_X1947 0 0 0.0 329s General.Motors_X1948 0 0 0.0 329s General.Motors_X1949 0 0 0.0 329s General.Motors_X1950 0 0 0.0 329s General.Motors_X1951 0 0 0.0 329s General.Motors_X1952 0 0 0.0 329s General.Motors_X1953 0 0 0.0 329s General.Motors_X1954 0 0 0.0 329s US.Steel_X1935 0 0 0.0 329s US.Steel_X1936 0 0 0.0 329s US.Steel_X1937 0 0 0.0 329s US.Steel_X1938 0 0 0.0 329s US.Steel_X1939 0 0 0.0 329s US.Steel_X1940 0 0 0.0 329s US.Steel_X1941 0 0 0.0 329s US.Steel_X1942 0 0 0.0 329s US.Steel_X1943 0 0 0.0 329s US.Steel_X1944 0 0 0.0 329s US.Steel_X1945 0 0 0.0 329s US.Steel_X1946 0 0 0.0 329s US.Steel_X1947 0 0 0.0 329s US.Steel_X1948 0 0 0.0 329s US.Steel_X1949 0 0 0.0 329s US.Steel_X1950 0 0 0.0 329s US.Steel_X1951 0 0 0.0 329s US.Steel_X1952 0 0 0.0 329s US.Steel_X1953 0 0 0.0 329s US.Steel_X1954 0 0 0.0 329s Westinghouse_X1935 0 0 0.0 329s Westinghouse_X1936 0 0 0.0 329s Westinghouse_X1937 0 0 0.0 329s Westinghouse_X1938 0 0 0.0 329s Westinghouse_X1939 0 0 0.0 329s Westinghouse_X1940 0 0 0.0 329s Westinghouse_X1941 0 0 0.0 329s Westinghouse_X1942 0 0 0.0 329s Westinghouse_X1943 0 0 0.0 329s Westinghouse_X1944 0 0 0.0 329s Westinghouse_X1945 0 0 0.0 329s Westinghouse_X1946 0 0 0.0 329s Westinghouse_X1947 0 0 0.0 329s Westinghouse_X1948 0 0 0.0 329s Westinghouse_X1949 0 0 0.0 329s Westinghouse_X1950 0 0 0.0 329s Westinghouse_X1951 0 0 0.0 329s Westinghouse_X1952 0 0 0.0 329s Westinghouse_X1953 0 0 0.0 329s Westinghouse_X1954 0 0 0.0 329s General.Electric_(Intercept) General.Electric_value 329s Chrysler_X1935 0 0 329s Chrysler_X1936 0 0 329s Chrysler_X1937 0 0 329s Chrysler_X1938 0 0 329s Chrysler_X1939 0 0 329s Chrysler_X1940 0 0 329s Chrysler_X1941 0 0 329s Chrysler_X1942 0 0 329s Chrysler_X1943 0 0 329s Chrysler_X1944 0 0 329s Chrysler_X1945 0 0 329s Chrysler_X1946 0 0 329s Chrysler_X1947 0 0 329s Chrysler_X1948 0 0 329s Chrysler_X1949 0 0 329s Chrysler_X1950 0 0 329s Chrysler_X1951 0 0 329s Chrysler_X1952 0 0 329s Chrysler_X1953 0 0 329s Chrysler_X1954 0 0 329s General.Electric_X1935 1 1171 329s General.Electric_X1936 1 2016 329s General.Electric_X1937 1 2803 329s General.Electric_X1938 1 2040 329s General.Electric_X1939 1 2256 329s General.Electric_X1940 1 2132 329s General.Electric_X1941 1 1834 329s General.Electric_X1942 1 1588 329s General.Electric_X1943 1 1749 329s General.Electric_X1944 1 1687 329s General.Electric_X1945 1 2008 329s General.Electric_X1946 1 2208 329s General.Electric_X1947 1 1657 329s General.Electric_X1948 1 1604 329s General.Electric_X1949 1 1432 329s General.Electric_X1950 1 1610 329s General.Electric_X1951 1 1819 329s General.Electric_X1952 1 2080 329s General.Electric_X1953 1 2372 329s General.Electric_X1954 1 2760 329s General.Motors_X1935 0 0 329s General.Motors_X1936 0 0 329s General.Motors_X1937 0 0 329s General.Motors_X1938 0 0 329s General.Motors_X1939 0 0 329s General.Motors_X1940 0 0 329s General.Motors_X1941 0 0 329s General.Motors_X1942 0 0 329s General.Motors_X1943 0 0 329s General.Motors_X1944 0 0 329s General.Motors_X1945 0 0 329s General.Motors_X1946 0 0 329s General.Motors_X1947 0 0 329s General.Motors_X1948 0 0 329s General.Motors_X1949 0 0 329s General.Motors_X1950 0 0 329s General.Motors_X1951 0 0 329s General.Motors_X1952 0 0 329s General.Motors_X1953 0 0 329s General.Motors_X1954 0 0 329s US.Steel_X1935 0 0 329s US.Steel_X1936 0 0 329s US.Steel_X1937 0 0 329s US.Steel_X1938 0 0 329s US.Steel_X1939 0 0 329s US.Steel_X1940 0 0 329s US.Steel_X1941 0 0 329s US.Steel_X1942 0 0 329s US.Steel_X1943 0 0 329s US.Steel_X1944 0 0 329s US.Steel_X1945 0 0 329s US.Steel_X1946 0 0 329s US.Steel_X1947 0 0 329s US.Steel_X1948 0 0 329s US.Steel_X1949 0 0 329s US.Steel_X1950 0 0 329s US.Steel_X1951 0 0 329s US.Steel_X1952 0 0 329s US.Steel_X1953 0 0 329s US.Steel_X1954 0 0 329s Westinghouse_X1935 0 0 329s Westinghouse_X1936 0 0 329s Westinghouse_X1937 0 0 329s Westinghouse_X1938 0 0 329s Westinghouse_X1939 0 0 329s Westinghouse_X1940 0 0 329s Westinghouse_X1941 0 0 329s Westinghouse_X1942 0 0 329s Westinghouse_X1943 0 0 329s Westinghouse_X1944 0 0 329s Westinghouse_X1945 0 0 329s Westinghouse_X1946 0 0 329s Westinghouse_X1947 0 0 329s Westinghouse_X1948 0 0 329s Westinghouse_X1949 0 0 329s Westinghouse_X1950 0 0 329s Westinghouse_X1951 0 0 329s Westinghouse_X1952 0 0 329s Westinghouse_X1953 0 0 329s Westinghouse_X1954 0 0 329s General.Electric_capital General.Motors_(Intercept) 329s Chrysler_X1935 0.0 0 329s Chrysler_X1936 0.0 0 329s Chrysler_X1937 0.0 0 329s Chrysler_X1938 0.0 0 329s Chrysler_X1939 0.0 0 329s Chrysler_X1940 0.0 0 329s Chrysler_X1941 0.0 0 329s Chrysler_X1942 0.0 0 329s Chrysler_X1943 0.0 0 329s Chrysler_X1944 0.0 0 329s Chrysler_X1945 0.0 0 329s Chrysler_X1946 0.0 0 329s Chrysler_X1947 0.0 0 329s Chrysler_X1948 0.0 0 329s Chrysler_X1949 0.0 0 329s Chrysler_X1950 0.0 0 329s Chrysler_X1951 0.0 0 329s Chrysler_X1952 0.0 0 329s Chrysler_X1953 0.0 0 329s Chrysler_X1954 0.0 0 329s General.Electric_X1935 97.8 0 329s General.Electric_X1936 104.4 0 329s General.Electric_X1937 118.0 0 329s General.Electric_X1938 156.2 0 329s General.Electric_X1939 172.6 0 329s General.Electric_X1940 186.6 0 329s General.Electric_X1941 220.9 0 329s General.Electric_X1942 287.8 0 329s General.Electric_X1943 319.9 0 329s General.Electric_X1944 321.3 0 329s General.Electric_X1945 319.6 0 329s General.Electric_X1946 346.0 0 329s General.Electric_X1947 456.4 0 329s General.Electric_X1948 543.4 0 329s General.Electric_X1949 618.3 0 329s General.Electric_X1950 647.4 0 329s General.Electric_X1951 671.3 0 329s General.Electric_X1952 726.1 0 329s General.Electric_X1953 800.3 0 329s General.Electric_X1954 888.9 0 329s General.Motors_X1935 0.0 1 329s General.Motors_X1936 0.0 1 329s General.Motors_X1937 0.0 1 329s General.Motors_X1938 0.0 1 329s General.Motors_X1939 0.0 1 329s General.Motors_X1940 0.0 1 329s General.Motors_X1941 0.0 1 329s General.Motors_X1942 0.0 1 329s General.Motors_X1943 0.0 1 329s General.Motors_X1944 0.0 1 329s General.Motors_X1945 0.0 1 329s General.Motors_X1946 0.0 1 329s General.Motors_X1947 0.0 1 329s General.Motors_X1948 0.0 1 329s General.Motors_X1949 0.0 1 329s General.Motors_X1950 0.0 1 329s General.Motors_X1951 0.0 1 329s General.Motors_X1952 0.0 1 329s General.Motors_X1953 0.0 1 329s General.Motors_X1954 0.0 1 329s US.Steel_X1935 0.0 0 329s US.Steel_X1936 0.0 0 329s US.Steel_X1937 0.0 0 329s US.Steel_X1938 0.0 0 329s US.Steel_X1939 0.0 0 329s US.Steel_X1940 0.0 0 329s US.Steel_X1941 0.0 0 329s US.Steel_X1942 0.0 0 329s US.Steel_X1943 0.0 0 329s US.Steel_X1944 0.0 0 329s US.Steel_X1945 0.0 0 329s US.Steel_X1946 0.0 0 329s US.Steel_X1947 0.0 0 329s US.Steel_X1948 0.0 0 329s US.Steel_X1949 0.0 0 329s US.Steel_X1950 0.0 0 329s US.Steel_X1951 0.0 0 329s US.Steel_X1952 0.0 0 329s US.Steel_X1953 0.0 0 329s US.Steel_X1954 0.0 0 329s Westinghouse_X1935 0.0 0 329s Westinghouse_X1936 0.0 0 329s Westinghouse_X1937 0.0 0 329s Westinghouse_X1938 0.0 0 329s Westinghouse_X1939 0.0 0 329s Westinghouse_X1940 0.0 0 329s Westinghouse_X1941 0.0 0 329s Westinghouse_X1942 0.0 0 329s Westinghouse_X1943 0.0 0 329s Westinghouse_X1944 0.0 0 329s Westinghouse_X1945 0.0 0 329s Westinghouse_X1946 0.0 0 329s Westinghouse_X1947 0.0 0 329s Westinghouse_X1948 0.0 0 329s Westinghouse_X1949 0.0 0 329s Westinghouse_X1950 0.0 0 329s Westinghouse_X1951 0.0 0 329s Westinghouse_X1952 0.0 0 329s Westinghouse_X1953 0.0 0 329s Westinghouse_X1954 0.0 0 329s General.Motors_value General.Motors_capital 329s Chrysler_X1935 0 0.0 329s Chrysler_X1936 0 0.0 329s Chrysler_X1937 0 0.0 329s Chrysler_X1938 0 0.0 329s Chrysler_X1939 0 0.0 329s Chrysler_X1940 0 0.0 329s Chrysler_X1941 0 0.0 329s Chrysler_X1942 0 0.0 329s Chrysler_X1943 0 0.0 329s Chrysler_X1944 0 0.0 329s Chrysler_X1945 0 0.0 329s Chrysler_X1946 0 0.0 329s Chrysler_X1947 0 0.0 329s Chrysler_X1948 0 0.0 329s Chrysler_X1949 0 0.0 329s Chrysler_X1950 0 0.0 329s Chrysler_X1951 0 0.0 329s Chrysler_X1952 0 0.0 329s Chrysler_X1953 0 0.0 329s Chrysler_X1954 0 0.0 329s General.Electric_X1935 0 0.0 329s General.Electric_X1936 0 0.0 329s General.Electric_X1937 0 0.0 329s General.Electric_X1938 0 0.0 329s General.Electric_X1939 0 0.0 329s General.Electric_X1940 0 0.0 329s General.Electric_X1941 0 0.0 329s General.Electric_X1942 0 0.0 329s General.Electric_X1943 0 0.0 329s General.Electric_X1944 0 0.0 329s General.Electric_X1945 0 0.0 329s General.Electric_X1946 0 0.0 329s General.Electric_X1947 0 0.0 329s General.Electric_X1948 0 0.0 329s General.Electric_X1949 0 0.0 329s General.Electric_X1950 0 0.0 329s General.Electric_X1951 0 0.0 329s General.Electric_X1952 0 0.0 329s General.Electric_X1953 0 0.0 329s General.Electric_X1954 0 0.0 329s General.Motors_X1935 3078 2.8 329s General.Motors_X1936 4662 52.6 329s General.Motors_X1937 5387 156.9 329s General.Motors_X1938 2792 209.2 329s General.Motors_X1939 4313 203.4 329s General.Motors_X1940 4644 207.2 329s General.Motors_X1941 4551 255.2 329s General.Motors_X1942 3244 303.7 329s General.Motors_X1943 4054 264.1 329s General.Motors_X1944 4379 201.6 329s General.Motors_X1945 4841 265.0 329s General.Motors_X1946 4901 402.2 329s General.Motors_X1947 3526 761.5 329s General.Motors_X1948 3255 922.4 329s General.Motors_X1949 3700 1020.1 329s General.Motors_X1950 3756 1099.0 329s General.Motors_X1951 4833 1207.7 329s General.Motors_X1952 4925 1430.5 329s General.Motors_X1953 6242 1777.3 329s General.Motors_X1954 5594 2226.3 329s US.Steel_X1935 0 0.0 329s US.Steel_X1936 0 0.0 329s US.Steel_X1937 0 0.0 329s US.Steel_X1938 0 0.0 329s US.Steel_X1939 0 0.0 329s US.Steel_X1940 0 0.0 329s US.Steel_X1941 0 0.0 329s US.Steel_X1942 0 0.0 329s US.Steel_X1943 0 0.0 329s US.Steel_X1944 0 0.0 329s US.Steel_X1945 0 0.0 329s US.Steel_X1946 0 0.0 329s US.Steel_X1947 0 0.0 329s US.Steel_X1948 0 0.0 329s US.Steel_X1949 0 0.0 329s US.Steel_X1950 0 0.0 329s US.Steel_X1951 0 0.0 329s US.Steel_X1952 0 0.0 329s US.Steel_X1953 0 0.0 329s US.Steel_X1954 0 0.0 329s Westinghouse_X1935 0 0.0 329s Westinghouse_X1936 0 0.0 329s Westinghouse_X1937 0 0.0 329s Westinghouse_X1938 0 0.0 329s Westinghouse_X1939 0 0.0 329s Westinghouse_X1940 0 0.0 329s Westinghouse_X1941 0 0.0 329s Westinghouse_X1942 0 0.0 329s Westinghouse_X1943 0 0.0 329s Westinghouse_X1944 0 0.0 329s Westinghouse_X1945 0 0.0 329s Westinghouse_X1946 0 0.0 329s Westinghouse_X1947 0 0.0 329s Westinghouse_X1948 0 0.0 329s Westinghouse_X1949 0 0.0 329s Westinghouse_X1950 0 0.0 329s Westinghouse_X1951 0 0.0 329s Westinghouse_X1952 0 0.0 329s Westinghouse_X1953 0 0.0 329s Westinghouse_X1954 0 0.0 329s US.Steel_(Intercept) US.Steel_value US.Steel_capital 329s Chrysler_X1935 0 0 0.0 329s Chrysler_X1936 0 0 0.0 329s Chrysler_X1937 0 0 0.0 329s Chrysler_X1938 0 0 0.0 329s Chrysler_X1939 0 0 0.0 329s Chrysler_X1940 0 0 0.0 329s Chrysler_X1941 0 0 0.0 329s Chrysler_X1942 0 0 0.0 329s Chrysler_X1943 0 0 0.0 329s Chrysler_X1944 0 0 0.0 329s Chrysler_X1945 0 0 0.0 329s Chrysler_X1946 0 0 0.0 329s Chrysler_X1947 0 0 0.0 329s Chrysler_X1948 0 0 0.0 329s Chrysler_X1949 0 0 0.0 329s Chrysler_X1950 0 0 0.0 329s Chrysler_X1951 0 0 0.0 329s Chrysler_X1952 0 0 0.0 329s Chrysler_X1953 0 0 0.0 329s Chrysler_X1954 0 0 0.0 329s General.Electric_X1935 0 0 0.0 329s General.Electric_X1936 0 0 0.0 329s General.Electric_X1937 0 0 0.0 329s General.Electric_X1938 0 0 0.0 329s General.Electric_X1939 0 0 0.0 329s General.Electric_X1940 0 0 0.0 329s General.Electric_X1941 0 0 0.0 329s General.Electric_X1942 0 0 0.0 329s General.Electric_X1943 0 0 0.0 329s General.Electric_X1944 0 0 0.0 329s General.Electric_X1945 0 0 0.0 329s General.Electric_X1946 0 0 0.0 329s General.Electric_X1947 0 0 0.0 329s General.Electric_X1948 0 0 0.0 329s General.Electric_X1949 0 0 0.0 329s General.Electric_X1950 0 0 0.0 329s General.Electric_X1951 0 0 0.0 329s General.Electric_X1952 0 0 0.0 329s General.Electric_X1953 0 0 0.0 329s General.Electric_X1954 0 0 0.0 329s General.Motors_X1935 0 0 0.0 329s General.Motors_X1936 0 0 0.0 329s General.Motors_X1937 0 0 0.0 329s General.Motors_X1938 0 0 0.0 329s General.Motors_X1939 0 0 0.0 329s General.Motors_X1940 0 0 0.0 329s General.Motors_X1941 0 0 0.0 329s General.Motors_X1942 0 0 0.0 329s General.Motors_X1943 0 0 0.0 329s General.Motors_X1944 0 0 0.0 329s General.Motors_X1945 0 0 0.0 329s General.Motors_X1946 0 0 0.0 329s General.Motors_X1947 0 0 0.0 329s General.Motors_X1948 0 0 0.0 329s General.Motors_X1949 0 0 0.0 329s General.Motors_X1950 0 0 0.0 329s General.Motors_X1951 0 0 0.0 329s General.Motors_X1952 0 0 0.0 329s General.Motors_X1953 0 0 0.0 329s General.Motors_X1954 0 0 0.0 329s US.Steel_X1935 1 1362 53.8 329s US.Steel_X1936 1 1807 50.5 329s US.Steel_X1937 1 2676 118.1 329s US.Steel_X1938 1 1802 260.2 329s US.Steel_X1939 1 1957 312.7 329s US.Steel_X1940 1 2203 254.2 329s US.Steel_X1941 1 2380 261.4 329s US.Steel_X1942 1 2169 298.7 329s US.Steel_X1943 1 1985 301.8 329s US.Steel_X1944 1 1814 279.1 329s US.Steel_X1945 1 1850 213.8 329s US.Steel_X1946 1 2068 232.6 329s US.Steel_X1947 1 1797 264.8 329s US.Steel_X1948 1 1626 306.9 329s US.Steel_X1949 1 1667 351.1 329s US.Steel_X1950 1 1677 357.8 329s US.Steel_X1951 1 2290 342.1 329s US.Steel_X1952 1 2159 444.2 329s US.Steel_X1953 1 2031 623.6 329s US.Steel_X1954 1 2116 669.7 329s Westinghouse_X1935 0 0 0.0 329s Westinghouse_X1936 0 0 0.0 329s Westinghouse_X1937 0 0 0.0 329s Westinghouse_X1938 0 0 0.0 329s Westinghouse_X1939 0 0 0.0 329s Westinghouse_X1940 0 0 0.0 329s Westinghouse_X1941 0 0 0.0 329s Westinghouse_X1942 0 0 0.0 329s Westinghouse_X1943 0 0 0.0 329s Westinghouse_X1944 0 0 0.0 329s Westinghouse_X1945 0 0 0.0 329s Westinghouse_X1946 0 0 0.0 329s Westinghouse_X1947 0 0 0.0 329s Westinghouse_X1948 0 0 0.0 329s Westinghouse_X1949 0 0 0.0 329s Westinghouse_X1950 0 0 0.0 329s Westinghouse_X1951 0 0 0.0 329s Westinghouse_X1952 0 0 0.0 329s Westinghouse_X1953 0 0 0.0 329s Westinghouse_X1954 0 0 0.0 329s Westinghouse_(Intercept) Westinghouse_value 329s Chrysler_X1935 0 0 329s Chrysler_X1936 0 0 329s Chrysler_X1937 0 0 329s Chrysler_X1938 0 0 329s Chrysler_X1939 0 0 329s Chrysler_X1940 0 0 329s Chrysler_X1941 0 0 329s Chrysler_X1942 0 0 329s Chrysler_X1943 0 0 329s Chrysler_X1944 0 0 329s Chrysler_X1945 0 0 329s Chrysler_X1946 0 0 329s Chrysler_X1947 0 0 329s Chrysler_X1948 0 0 329s Chrysler_X1949 0 0 329s Chrysler_X1950 0 0 329s Chrysler_X1951 0 0 329s Chrysler_X1952 0 0 329s Chrysler_X1953 0 0 329s Chrysler_X1954 0 0 329s General.Electric_X1935 0 0 329s General.Electric_X1936 0 0 329s General.Electric_X1937 0 0 329s General.Electric_X1938 0 0 329s General.Electric_X1939 0 0 329s General.Electric_X1940 0 0 329s General.Electric_X1941 0 0 329s General.Electric_X1942 0 0 329s General.Electric_X1943 0 0 329s General.Electric_X1944 0 0 329s General.Electric_X1945 0 0 329s General.Electric_X1946 0 0 329s General.Electric_X1947 0 0 329s General.Electric_X1948 0 0 329s General.Electric_X1949 0 0 329s General.Electric_X1950 0 0 329s General.Electric_X1951 0 0 329s General.Electric_X1952 0 0 329s General.Electric_X1953 0 0 329s General.Electric_X1954 0 0 329s General.Motors_X1935 0 0 329s General.Motors_X1936 0 0 329s General.Motors_X1937 0 0 329s General.Motors_X1938 0 0 329s General.Motors_X1939 0 0 329s General.Motors_X1940 0 0 329s General.Motors_X1941 0 0 329s General.Motors_X1942 0 0 329s General.Motors_X1943 0 0 329s General.Motors_X1944 0 0 329s General.Motors_X1945 0 0 329s General.Motors_X1946 0 0 329s General.Motors_X1947 0 0 329s General.Motors_X1948 0 0 329s General.Motors_X1949 0 0 329s General.Motors_X1950 0 0 329s General.Motors_X1951 0 0 329s General.Motors_X1952 0 0 329s General.Motors_X1953 0 0 329s General.Motors_X1954 0 0 329s US.Steel_X1935 0 0 329s US.Steel_X1936 0 0 329s US.Steel_X1937 0 0 329s US.Steel_X1938 0 0 329s US.Steel_X1939 0 0 329s US.Steel_X1940 0 0 329s US.Steel_X1941 0 0 329s US.Steel_X1942 0 0 329s US.Steel_X1943 0 0 329s US.Steel_X1944 0 0 329s US.Steel_X1945 0 0 329s US.Steel_X1946 0 0 329s US.Steel_X1947 0 0 329s US.Steel_X1948 0 0 329s US.Steel_X1949 0 0 329s US.Steel_X1950 0 0 329s US.Steel_X1951 0 0 329s US.Steel_X1952 0 0 329s US.Steel_X1953 0 0 329s US.Steel_X1954 0 0 329s Westinghouse_X1935 1 192 329s Westinghouse_X1936 1 516 329s Westinghouse_X1937 1 729 329s Westinghouse_X1938 1 560 329s Westinghouse_X1939 1 520 329s Westinghouse_X1940 1 628 329s Westinghouse_X1941 1 537 329s Westinghouse_X1942 1 561 329s Westinghouse_X1943 1 617 329s Westinghouse_X1944 1 627 329s Westinghouse_X1945 1 737 329s Westinghouse_X1946 1 760 329s Westinghouse_X1947 1 581 329s Westinghouse_X1948 1 662 329s Westinghouse_X1949 1 584 329s Westinghouse_X1950 1 635 329s Westinghouse_X1951 1 724 329s Westinghouse_X1952 1 864 329s Westinghouse_X1953 1 1194 329s Westinghouse_X1954 1 1189 329s Westinghouse_capital 329s Chrysler_X1935 0.0 329s Chrysler_X1936 0.0 329s Chrysler_X1937 0.0 329s Chrysler_X1938 0.0 329s Chrysler_X1939 0.0 329s Chrysler_X1940 0.0 329s Chrysler_X1941 0.0 329s Chrysler_X1942 0.0 329s Chrysler_X1943 0.0 329s Chrysler_X1944 0.0 329s Chrysler_X1945 0.0 329s Chrysler_X1946 0.0 329s Chrysler_X1947 0.0 329s Chrysler_X1948 0.0 329s Chrysler_X1949 0.0 329s Chrysler_X1950 0.0 329s Chrysler_X1951 0.0 329s Chrysler_X1952 0.0 329s Chrysler_X1953 0.0 329s Chrysler_X1954 0.0 329s General.Electric_X1935 0.0 329s General.Electric_X1936 0.0 329s General.Electric_X1937 0.0 329s General.Electric_X1938 0.0 329s General.Electric_X1939 0.0 329s General.Electric_X1940 0.0 329s General.Electric_X1941 0.0 329s General.Electric_X1942 0.0 329s General.Electric_X1943 0.0 329s General.Electric_X1944 0.0 329s General.Electric_X1945 0.0 329s General.Electric_X1946 0.0 329s General.Electric_X1947 0.0 329s General.Electric_X1948 0.0 329s General.Electric_X1949 0.0 329s General.Electric_X1950 0.0 329s General.Electric_X1951 0.0 329s General.Electric_X1952 0.0 329s General.Electric_X1953 0.0 329s General.Electric_X1954 0.0 329s General.Motors_X1935 0.0 329s General.Motors_X1936 0.0 329s General.Motors_X1937 0.0 329s General.Motors_X1938 0.0 329s General.Motors_X1939 0.0 329s General.Motors_X1940 0.0 329s General.Motors_X1941 0.0 329s General.Motors_X1942 0.0 329s General.Motors_X1943 0.0 329s General.Motors_X1944 0.0 329s General.Motors_X1945 0.0 329s General.Motors_X1946 0.0 329s General.Motors_X1947 0.0 329s General.Motors_X1948 0.0 329s General.Motors_X1949 0.0 329s General.Motors_X1950 0.0 329s General.Motors_X1951 0.0 329s General.Motors_X1952 0.0 329s General.Motors_X1953 0.0 329s General.Motors_X1954 0.0 329s US.Steel_X1935 0.0 329s US.Steel_X1936 0.0 329s US.Steel_X1937 0.0 329s US.Steel_X1938 0.0 329s US.Steel_X1939 0.0 329s US.Steel_X1940 0.0 329s US.Steel_X1941 0.0 329s US.Steel_X1942 0.0 329s US.Steel_X1943 0.0 329s US.Steel_X1944 0.0 329s US.Steel_X1945 0.0 329s US.Steel_X1946 0.0 329s US.Steel_X1947 0.0 329s US.Steel_X1948 0.0 329s US.Steel_X1949 0.0 329s US.Steel_X1950 0.0 329s US.Steel_X1951 0.0 329s US.Steel_X1952 0.0 329s US.Steel_X1953 0.0 329s US.Steel_X1954 0.0 329s Westinghouse_X1935 1.8 329s Westinghouse_X1936 0.8 329s Westinghouse_X1937 7.4 329s Westinghouse_X1938 18.1 329s Westinghouse_X1939 23.5 329s Westinghouse_X1940 26.5 329s Westinghouse_X1941 36.2 329s Westinghouse_X1942 60.8 329s Westinghouse_X1943 84.4 329s Westinghouse_X1944 91.2 329s Westinghouse_X1945 92.4 329s Westinghouse_X1946 86.0 329s Westinghouse_X1947 111.1 329s Westinghouse_X1948 130.6 329s Westinghouse_X1949 141.8 329s Westinghouse_X1950 136.7 329s Westinghouse_X1951 129.7 329s Westinghouse_X1952 145.5 329s Westinghouse_X1953 174.8 329s Westinghouse_X1954 213.5 329s $Chrysler 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s 329s $General.Motors 329s General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s 329s $US.Steel 329s US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s $Chrysler 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s attr(,"variables") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"factors") 329s Chrysler_value Chrysler_capital 329s Chrysler_invest 0 0 329s Chrysler_value 1 0 329s Chrysler_capital 0 1 329s attr(,"term.labels") 329s [1] "Chrysler_value" "Chrysler_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"dataClasses") 329s Chrysler_invest Chrysler_value Chrysler_capital 329s "numeric" "numeric" "numeric" 329s 329s $General.Electric 329s General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s attr(,"variables") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"factors") 329s General.Electric_value General.Electric_capital 329s General.Electric_invest 0 0 329s General.Electric_value 1 0 329s General.Electric_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Electric_value" "General.Electric_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 329s attr(,"dataClasses") 329s General.Electric_invest General.Electric_value General.Electric_capital 329s "numeric" "numeric" "numeric" 329s 329s $General.Motors 329s General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s attr(,"variables") 329s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 329s attr(,"factors") 329s General.Motors_value General.Motors_capital 329s General.Motors_invest 0 0 329s General.Motors_value 1 0 329s General.Motors_capital 0 1 329s attr(,"term.labels") 329s [1] "General.Motors_value" "General.Motors_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 329s attr(,"dataClasses") 329s General.Motors_invest General.Motors_value General.Motors_capital 329s "numeric" "numeric" "numeric" 329s 329s $US.Steel 329s US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s attr(,"variables") 329s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 329s attr(,"factors") 329s US.Steel_value US.Steel_capital 329s US.Steel_invest 0 0 329s US.Steel_value 1 0 329s US.Steel_capital 0 1 329s attr(,"term.labels") 329s [1] "US.Steel_value" "US.Steel_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 329s attr(,"dataClasses") 329s US.Steel_invest US.Steel_value US.Steel_capital 329s "numeric" "numeric" "numeric" 329s 329s $Westinghouse 329s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s attr(,"variables") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"factors") 329s Westinghouse_value Westinghouse_capital 329s Westinghouse_invest 0 0 329s Westinghouse_value 1 0 329s Westinghouse_capital 0 1 329s attr(,"term.labels") 329s [1] "Westinghouse_value" "Westinghouse_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 329s attr(,"dataClasses") 329s Westinghouse_invest Westinghouse_value Westinghouse_capital 329s "numeric" "numeric" "numeric" 329s 329s Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s attr(,"variables") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"factors") 329s Chrysler_value Chrysler_capital 329s Chrysler_invest 0 0 329s Chrysler_value 1 0 329s Chrysler_capital 0 1 329s attr(,"term.labels") 329s [1] "Chrysler_value" "Chrysler_capital" 329s attr(,"order") 329s [1] 1 1 329s attr(,"intercept") 329s [1] 1 329s attr(,"response") 329s [1] 1 329s attr(,".Environment") 329s 329s attr(,"predvars") 329s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 329s attr(,"dataClasses") 329s Chrysler_invest Chrysler_value Chrysler_capital 329s "numeric" "numeric" "numeric" 329s > 329s > 329s > ######### IV estimation ####################### 329s > ### 2SLS ### 329s > # instruments = explanatory variables -> 2SLS estimates = OLS estimates 329s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 329s + greene2sls <- systemfit( formulaGrunfeld, inst = ~ value + capital, "2SLS", 329s + data = GrunfeldGreene, useMatrix = useMatrix ) 329s + print( greene2sls ) 329s + print( summary( greene2sls ) ) 329s + print( all.equal( coef( summary( greene2sls ) ), coef( summary( greeneOls ) ) ) ) 329s + print( all.equal( greene2sls[ -c(1,2,6) ], greeneOls[ -c(1,2,6) ] ) ) 329s + for( i in 1:length( greene2sls$eq ) ) { 329s + print( all.equal( greene2sls$eq[[i]][ -c(3,15:17) ], 329s + greeneOls$eq[[i]][-3] ) ) 329s + } 329s + } 329s 329s systemfit results 329s method: 2SLS 329s 329s Coefficients: 329s Chrysler_(Intercept) Chrysler_value 329s -6.1900 0.0779 329s Chrysler_capital General.Electric_(Intercept) 329s 0.3157 -9.9563 329s General.Electric_value General.Electric_capital 329s 0.0266 0.1517 329s General.Motors_(Intercept) General.Motors_value 329s -149.7825 0.1193 329s General.Motors_capital US.Steel_(Intercept) 329s 0.3714 -30.3685 329s US.Steel_value US.Steel_capital 329s 0.1566 0.4239 329s Westinghouse_(Intercept) Westinghouse_value 329s -0.5094 0.0529 329s Westinghouse_capital 329s 0.0924 329s 329s systemfit results 329s method: 2SLS 329s 329s N DF SSR detRCov OLS-R2 McElroy-R2 329s system 100 85 339121 2.09e+14 0.848 0.862 329s 329s N DF SSR MSE RMSE R2 Adj R2 329s Chrysler 20 17 2997 176 13.3 0.914 0.903 329s General.Electric 20 17 13217 777 27.9 0.705 0.671 329s General.Motors 20 17 143206 8424 91.8 0.921 0.912 329s US.Steel 20 17 177928 10466 102.3 0.440 0.374 329s Westinghouse 20 17 1773 104 10.2 0.744 0.714 329s 329s The covariance matrix of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 176.3 -25.1 -333 492 15.7 329s General.Electric -25.1 777.4 715 1065 207.6 329s General.Motors -332.7 714.7 8424 -2614 148.4 329s US.Steel 491.9 1064.6 -2614 10466 642.6 329s Westinghouse 15.7 207.6 148 643 104.3 329s 329s The correlations of the residuals 329s Chrysler General.Electric General.Motors US.Steel Westinghouse 329s Chrysler 1.0000 -0.0679 -0.273 0.362 0.115 329s General.Electric -0.0679 1.0000 0.279 0.373 0.729 329s General.Motors -0.2730 0.2793 1.000 -0.278 0.158 329s US.Steel 0.3621 0.3732 -0.278 1.000 0.615 329s Westinghouse 0.1154 0.7290 0.158 0.615 1.000 329s 329s 329s 2SLS estimates for 'Chrysler' (equation 1) 329s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 329s 329s Instruments: ~Chrysler_value + Chrysler_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -6.1900 13.5065 -0.46 0.6525 329s value 0.0779 0.0200 3.90 0.0011 ** 329s capital 0.3157 0.0288 10.96 4e-09 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 13.279 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 2997.444 MSE: 176.32 Root MSE: 13.279 329s Multiple R-Squared: 0.914 Adjusted R-Squared: 0.903 329s 329s 329s 2SLS estimates for 'General.Electric' (equation 2) 329s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 329s 329s Instruments: ~General.Electric_value + General.Electric_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -9.9563 31.3742 -0.32 0.75 329s value 0.0266 0.0156 1.71 0.11 329s capital 0.1517 0.0257 5.90 1.7e-05 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 27.883 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 329s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 329s 329s 329s 2SLS estimates for 'General.Motors' (equation 3) 329s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 329s 329s Instruments: ~General.Motors_value + General.Motors_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -149.7825 105.8421 -1.42 0.17508 329s value 0.1193 0.0258 4.62 0.00025 *** 329s capital 0.3714 0.0371 10.02 1.5e-08 *** 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 91.782 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 143205.877 MSE: 8423.875 Root MSE: 91.782 329s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.912 329s 329s 329s 2SLS estimates for 'US.Steel' (equation 4) 329s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 329s 329s Instruments: ~US.Steel_value + US.Steel_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -30.3685 157.0477 -0.19 0.849 329s value 0.1566 0.0789 1.98 0.064 . 329s capital 0.4239 0.1552 2.73 0.014 * 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 102.305 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 177928.314 MSE: 10466.371 Root MSE: 102.305 329s Multiple R-Squared: 0.44 Adjusted R-Squared: 0.374 329s 329s 329s 2SLS estimates for 'Westinghouse' (equation 5) 329s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 329s 329s Instruments: ~Westinghouse_value + Westinghouse_capital 329s 329s 329s Estimate Std. Error t value Pr(>|t|) 329s (Intercept) -0.5094 8.0153 -0.06 0.9501 329s value 0.0529 0.0157 3.37 0.0037 ** 329s capital 0.0924 0.0561 1.65 0.1179 329s --- 329s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 329s 329s Residual standard error: 10.213 on 17 degrees of freedom 329s Number of observations: 20 Degrees of Freedom: 17 329s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 329s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 329s 329s [1] TRUE 329s [1] TRUE 329s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s > # 'real' IV/2SLS estimation 330s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 330s + greene2slsR <- systemfit( invest ~ capital, inst = ~ value, "2SLS", 330s + data = GrunfeldGreene, useMatrix = useMatrix ) 330s + print( greene2slsR ) 330s + print( summary( greene2slsR ) ) 330s + } 330s 330s systemfit results 330s method: 2SLS 330s 330s Coefficients: 330s Chrysler_(Intercept) Chrysler_capital 330s 4.314 0.675 330s General.Electric_(Intercept) General.Electric_capital 330s -106.788 0.522 330s General.Motors_(Intercept) General.Motors_capital 330s 110.940 0.767 330s US.Steel_(Intercept) US.Steel_capital 330s -323.878 2.432 330s Westinghouse_(Intercept) Westinghouse_capital 330s 13.163 0.347 330s 330s systemfit results 330s method: 2SLS 330s 330s N DF SSR detRCov OLS-R2 McElroy-R2 330s system 100 90 3239824 2.75e+17 -0.456 0.476 330s 330s N DF SSR MSE RMSE R2 Adj R2 330s Chrysler 20 18 30374 1687 41.1 0.124 0.076 330s General.Electric 20 18 174998 9722 98.6 -2.902 -3.119 330s General.Motors 20 18 1100181 61121 247.2 0.396 0.362 330s US.Steel 20 18 1930347 107242 327.5 -5.072 -5.409 330s Westinghouse 20 18 3924 218 14.8 0.434 0.403 330s 330s The covariance matrix of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1687 3089 6820 11741 179 330s General.Electric 3089 9722 20780 23319 886 330s General.Motors 6820 20780 61121 44203 1908 330s US.Steel 11741 23319 44203 107242 1977 330s Westinghouse 179 886 1908 1977 218 330s 330s The correlations of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1.000 0.763 0.672 0.873 0.295 330s General.Electric 0.763 1.000 0.852 0.722 0.608 330s General.Motors 0.672 0.852 1.000 0.546 0.523 330s US.Steel 0.873 0.722 0.546 1.000 0.409 330s Westinghouse 0.295 0.608 0.523 0.409 1.000 330s 330s 330s 2SLS estimates for 'Chrysler' (equation 1) 330s Model Formula: Chrysler_invest ~ Chrysler_capital 330s 330s Instruments: ~Chrysler_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 4.314 34.033 0.13 0.901 330s capital 0.675 0.270 2.50 0.022 * 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 41.078 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 30373.531 MSE: 1687.418 Root MSE: 41.078 330s Multiple R-Squared: 0.124 Adjusted R-Squared: 0.076 330s 330s 330s 2SLS estimates for 'General.Electric' (equation 2) 330s Model Formula: General.Electric_invest ~ General.Electric_capital 330s 330s Instruments: ~General.Electric_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -106.788 306.251 -0.35 0.73 330s capital 0.522 0.763 0.68 0.50 330s 330s Residual standard error: 98.601 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 174998.166 MSE: 9722.12 Root MSE: 98.601 330s Multiple R-Squared: -2.902 Adjusted R-Squared: -3.119 330s 330s 330s 2SLS estimates for 'General.Motors' (equation 3) 330s Model Formula: General.Motors_invest ~ General.Motors_capital 330s 330s Instruments: ~General.Motors_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 110.940 145.626 0.76 0.4560 330s capital 0.767 0.208 3.69 0.0017 ** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 247.227 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 1100180.666 MSE: 61121.148 Root MSE: 247.227 330s Multiple R-Squared: 0.396 Adjusted R-Squared: 0.362 330s 330s 330s 2SLS estimates for 'US.Steel' (equation 4) 330s Model Formula: US.Steel_invest ~ US.Steel_capital 330s 330s Instruments: ~US.Steel_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -323.88 962.57 -0.34 0.74 330s capital 2.43 3.20 0.76 0.46 330s 330s Residual standard error: 327.478 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 1930347.395 MSE: 107241.522 Root MSE: 327.478 330s Multiple R-Squared: -5.072 Adjusted R-Squared: -5.409 330s 330s 330s 2SLS estimates for 'Westinghouse' (equation 5) 330s Model Formula: Westinghouse_invest ~ Westinghouse_capital 330s 330s Instruments: ~Westinghouse_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 13.1626 7.0965 1.85 0.08008 . 330s capital 0.3471 0.0734 4.73 0.00017 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 14.765 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 3923.899 MSE: 217.994 Root MSE: 14.765 330s Multiple R-Squared: 0.434 Adjusted R-Squared: 0.403 330s 330s > 330s > ### 2SLS, pooled ### 330s > # instruments = explanatory variables -> 2SLS estimates = OLS estimates 330s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 330s + greene2slsPooled <- systemfit( formulaGrunfeld, inst = ~ value + capital, "2SLS", 330s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix ) 330s + print( greene2slsPooled ) 330s + print( summary( greene2slsPooled ) ) 330s + print( all.equal( coef( summary( greene2slsPooled ) ), 330s + coef( summary( greeneOlsPooled ) ) ) ) 330s + print( all.equal( greene2slsPooled[ -c(1,2,6) ], greeneOlsPooled[ -c(1,2,6) ] ) ) 330s + for( i in 1:length( greene2slsPooled$eq ) ) { 330s + print( all.equal( greene2slsPooled$eq[[i]][ -c(3,15:17) ], 330s + greeneOlsPooled$eq[[i]][-3] ) ) 330s + } 330s + } 330s 330s systemfit results 330s method: 2SLS 330s 330s Coefficients: 330s Chrysler_(Intercept) Chrysler_value 330s -48.030 0.105 330s Chrysler_capital General.Electric_(Intercept) 330s 0.305 -48.030 330s General.Electric_value General.Electric_capital 330s 0.105 0.305 330s General.Motors_(Intercept) General.Motors_value 330s -48.030 0.105 330s General.Motors_capital US.Steel_(Intercept) 330s 0.305 -48.030 330s US.Steel_value US.Steel_capital 330s 0.105 0.305 330s Westinghouse_(Intercept) Westinghouse_value 330s -48.030 0.105 330s Westinghouse_capital 330s 0.305 330s 330s systemfit results 330s method: 2SLS 330s 330s N DF SSR detRCov OLS-R2 McElroy-R2 330s system 100 97 1570884 4.2e+17 0.294 0.812 330s 330s N DF SSR MSE RMSE R2 Adj R2 330s Chrysler 20 17 15117 889 29.8 0.564 0.513 330s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 330s General.Motors 20 17 188218 11072 105.2 0.897 0.884 330s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 330s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 330s 330s The covariance matrix of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 889.2 -4898 -198 4748 -94.6 330s General.Electric -4898.1 40339 -2254 -32821 2658.0 330s General.Motors -197.7 -2254 11072 304 -1328.6 330s US.Steel 4748.1 -32821 304 39359 -1377.3 330s Westinghouse -94.6 2658 -1329 -1377 745.2 330s 330s The correlations of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1.000 0.144 -0.1852 0.2218 0.186 330s General.Electric 0.144 1.000 -0.2592 -0.1216 0.881 330s General.Motors -0.185 -0.259 1.0000 -0.0155 -0.469 330s US.Steel 0.222 -0.122 -0.0155 1.0000 -0.119 330s Westinghouse 0.186 0.881 -0.4689 -0.1186 1.000 330s 330s 330s 2SLS estimates for 'Chrysler' (equation 1) 330s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 330s 330s Instruments: ~Chrysler_value + Chrysler_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -48.0297 21.4802 -2.24 0.028 * 330s value 0.1051 0.0114 9.24 6.0e-15 *** 330s capital 0.3054 0.0435 7.02 3.1e-10 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 29.82 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 15117.016 MSE: 889.236 Root MSE: 29.82 330s Multiple R-Squared: 0.564 Adjusted R-Squared: 0.513 330s 330s 330s 2SLS estimates for 'General.Electric' (equation 2) 330s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 330s 330s Instruments: ~General.Electric_value + General.Electric_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -48.0297 21.4802 -2.24 0.028 * 330s value 0.1051 0.0114 9.24 6.0e-15 *** 330s capital 0.3054 0.0435 7.02 3.1e-10 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 200.847 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 685769.815 MSE: 40339.401 Root MSE: 200.847 330s Multiple R-Squared: -14.291 Adjusted R-Squared: -16.09 330s 330s 330s 2SLS estimates for 'General.Motors' (equation 3) 330s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 330s 330s Instruments: ~General.Motors_value + General.Motors_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -48.0297 21.4802 -2.24 0.028 * 330s value 0.1051 0.0114 9.24 6.0e-15 *** 330s capital 0.3054 0.0435 7.02 3.1e-10 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 105.222 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 188218.158 MSE: 11071.656 Root MSE: 105.222 330s Multiple R-Squared: 0.897 Adjusted R-Squared: 0.884 330s 330s 330s 2SLS estimates for 'US.Steel' (equation 4) 330s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 330s 330s Instruments: ~US.Steel_value + US.Steel_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -48.0297 21.4802 -2.24 0.028 * 330s value 0.1051 0.0114 9.24 6.0e-15 *** 330s capital 0.3054 0.0435 7.02 3.1e-10 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 198.392 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 669110.225 MSE: 39359.425 Root MSE: 198.392 330s Multiple R-Squared: -1.105 Adjusted R-Squared: -1.352 330s 330s 330s 2SLS estimates for 'Westinghouse' (equation 5) 330s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 330s 330s Instruments: ~Westinghouse_value + Westinghouse_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -48.0297 21.4802 -2.24 0.028 * 330s value 0.1051 0.0114 9.24 6.0e-15 *** 330s capital 0.3054 0.0435 7.02 3.1e-10 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 27.298 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 12668.473 MSE: 745.204 Root MSE: 27.298 330s Multiple R-Squared: -0.826 Adjusted R-Squared: -1.041 330s 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s > # 'real' IV/2SLS estimation 330s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 330s + greene2slsRPooled <- systemfit( invest ~ capital, inst = ~ value, "2SLS", 330s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix ) 330s + print( greene2slsRPooled ) 330s + print( summary( greene2slsRPooled ) ) 330s + } 330s 330s systemfit results 330s method: 2SLS 330s 330s Coefficients: 330s Chrysler_(Intercept) Chrysler_capital 330s -15.105 0.849 330s General.Electric_(Intercept) General.Electric_capital 330s -15.105 0.849 330s General.Motors_(Intercept) General.Motors_capital 330s -15.105 0.849 330s US.Steel_(Intercept) US.Steel_capital 330s -15.105 0.849 330s Westinghouse_(Intercept) Westinghouse_capital 330s -15.105 0.849 330s 330s systemfit results 330s method: 2SLS 330s 330s N DF SSR detRCov OLS-R2 McElroy-R2 330s system 100 98 4164182 2.53e+19 -0.871 -0.832 330s 330s N DF SSR MSE RMSE R2 Adj R2 330s Chrysler 20 18 64130 3563 59.7 -0.849 -0.952 330s General.Electric 20 18 1575287 87516 295.8 -34.125 -36.076 330s General.Motors 20 18 1655592 91977 303.3 0.091 0.040 330s US.Steel 20 18 833908 46328 215.2 -1.623 -1.769 330s Westinghouse 20 18 35264 1959 44.3 -4.082 -4.365 330s 330s The covariance matrix of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 3563 9506 13222 2659 1862 330s General.Electric 9506 87516 29381 -35898 10615 330s General.Motors 13222 29381 91977 17584 8562 330s US.Steel 2659 -35898 17584 46328 -762 330s Westinghouse 1862 10615 8562 -762 1959 330s 330s The correlations of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1.000 0.843 0.763 0.397 0.742 330s General.Electric 0.843 1.000 0.893 0.226 0.933 330s General.Motors 0.763 0.893 1.000 0.114 0.801 330s US.Steel 0.397 0.226 0.114 1.000 0.375 330s Westinghouse 0.742 0.933 0.801 0.375 1.000 330s 330s 330s 2SLS estimates for 'Chrysler' (equation 1) 330s Model Formula: Chrysler_invest ~ Chrysler_capital 330s 330s Instruments: ~Chrysler_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -15.1045 33.8915 -0.45 0.66 330s capital 0.8489 0.0865 9.82 4.4e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 59.689 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 64130.003 MSE: 3562.778 Root MSE: 59.689 330s Multiple R-Squared: -0.849 Adjusted R-Squared: -0.952 330s 330s 330s 2SLS estimates for 'General.Electric' (equation 2) 330s Model Formula: General.Electric_invest ~ General.Electric_capital 330s 330s Instruments: ~General.Electric_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -15.1045 33.8915 -0.45 0.66 330s capital 0.8489 0.0865 9.82 4.4e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 295.831 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 1575287.29 MSE: 87515.961 Root MSE: 295.831 330s Multiple R-Squared: -34.125 Adjusted R-Squared: -36.076 330s 330s 330s 2SLS estimates for 'General.Motors' (equation 3) 330s Model Formula: General.Motors_invest ~ General.Motors_capital 330s 330s Instruments: ~General.Motors_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -15.1045 33.8915 -0.45 0.66 330s capital 0.8489 0.0865 9.82 4.4e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 303.278 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 1655591.854 MSE: 91977.325 Root MSE: 303.278 330s Multiple R-Squared: 0.091 Adjusted R-Squared: 0.04 330s 330s 330s 2SLS estimates for 'US.Steel' (equation 4) 330s Model Formula: US.Steel_invest ~ US.Steel_capital 330s 330s Instruments: ~US.Steel_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -15.1045 33.8915 -0.45 0.66 330s capital 0.8489 0.0865 9.82 4.4e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 215.24 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 833908.389 MSE: 46328.244 Root MSE: 215.24 330s Multiple R-Squared: -1.623 Adjusted R-Squared: -1.769 330s 330s 330s 2SLS estimates for 'Westinghouse' (equation 5) 330s Model Formula: Westinghouse_invest ~ Westinghouse_capital 330s 330s Instruments: ~Westinghouse_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -15.1045 33.8915 -0.45 0.66 330s capital 0.8489 0.0865 9.82 4.4e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 44.262 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 35264.462 MSE: 1959.137 Root MSE: 44.262 330s Multiple R-Squared: -4.082 Adjusted R-Squared: -4.365 330s 330s > 330s > ### 3SLS ### 330s > # instruments = explanatory variables -> 3SLS estimates = SUR estimates 330s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 330s + greene3sls <- systemfit( formulaGrunfeld, inst = ~ value + capital, "3SLS", 330s + data = GrunfeldGreene, useMatrix = useMatrix, methodResidCov = "noDfCor" ) 330s + print( greene3sls ) 330s + print( summary( greene3sls ) ) 330s + print( all.equal( coef( summary( greene3sls ) ), coef( summary( greeneSur ) ) ) ) 330s + print( all.equal( greene3sls[ -c(1,2,7) ], greeneSur[ -c(1,2,7) ] ) ) 330s + for( i in 1:length( greene3sls$eq ) ) { 330s + print( all.equal( greene3sls$eq[[i]][ -c(3,15:17) ], 330s + greeneSur$eq[[i]][-3] ) ) 330s + } 330s + } 330s 330s systemfit results 330s method: 3SLS 330s 330s Coefficients: 330s Chrysler_(Intercept) Chrysler_value 330s 0.5043 0.0695 330s Chrysler_capital General.Electric_(Intercept) 330s 0.3085 -22.4389 330s General.Electric_value General.Electric_capital 330s 0.0373 0.1308 330s General.Motors_(Intercept) General.Motors_value 330s -162.3641 0.1205 330s General.Motors_capital US.Steel_(Intercept) 330s 0.3827 85.4233 330s US.Steel_value US.Steel_capital 330s 0.1015 0.4000 330s Westinghouse_(Intercept) Westinghouse_value 330s 1.0889 0.0570 330s Westinghouse_capital 330s 0.0415 330s 330s systemfit results 330s method: 3SLS 330s 330s N DF SSR detRCov OLS-R2 McElroy-R2 330s system 100 85 347048 6.18e+13 0.844 0.869 330s 330s N DF SSR MSE RMSE R2 Adj R2 330s Chrysler 20 17 3057 180 13.4 0.912 0.901 330s General.Electric 20 17 14009 824 28.7 0.688 0.651 330s General.Motors 20 17 144321 8489 92.1 0.921 0.911 330s US.Steel 20 17 183763 10810 104.0 0.422 0.354 330s Westinghouse 20 17 1898 112 10.6 0.726 0.694 330s 330s The covariance matrix of the residuals used for estimation 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 149.9 -21.4 -283 418 13.3 330s General.Electric -21.4 660.8 608 905 176.4 330s General.Motors -282.8 607.5 7160 -2222 126.2 330s US.Steel 418.1 905.0 -2222 8896 546.2 330s Westinghouse 13.3 176.4 126 546 88.7 330s 330s The covariance matrix of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 152.85 2.05 -314 455 16.7 330s General.Electric 2.05 700.46 605 1224 200.3 330s General.Motors -313.70 605.34 7216 -2687 129.9 330s US.Steel 455.09 1224.41 -2687 9188 652.7 330s Westinghouse 16.66 200.32 130 653 94.9 330s 330s The correlations of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1.00000 0.00626 -0.299 0.384 0.138 330s General.Electric 0.00626 1.00000 0.269 0.483 0.777 330s General.Motors -0.29870 0.26925 1.000 -0.330 0.157 330s US.Steel 0.38402 0.48264 -0.330 1.000 0.699 330s Westinghouse 0.13832 0.77690 0.157 0.699 1.000 330s 330s 330s 3SLS estimates for 'Chrysler' (equation 1) 330s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 330s 330s Instruments: ~Chrysler_value + Chrysler_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 0.5043 11.5128 0.04 0.96557 330s value 0.0695 0.0169 4.12 0.00072 *** 330s capital 0.3085 0.0259 11.93 1.1e-09 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 13.41 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 3056.985 MSE: 179.823 Root MSE: 13.41 330s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.901 330s 330s 330s 3SLS estimates for 'General.Electric' (equation 2) 330s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 330s 330s Instruments: ~General.Electric_value + General.Electric_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -22.4389 25.5186 -0.88 0.3915 330s value 0.0373 0.0123 3.04 0.0074 ** 330s capital 0.1308 0.0220 5.93 1.6e-05 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 28.707 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 14009.115 MSE: 824.066 Root MSE: 28.707 330s Multiple R-Squared: 0.688 Adjusted R-Squared: 0.651 330s 330s 330s 3SLS estimates for 'General.Motors' (equation 3) 330s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 330s 330s Instruments: ~General.Motors_value + General.Motors_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -162.3641 89.4592 -1.81 0.087 . 330s value 0.1205 0.0216 5.57 3.4e-05 *** 330s capital 0.3827 0.0328 11.68 1.5e-09 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 92.138 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 144320.876 MSE: 8489.463 Root MSE: 92.138 330s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.911 330s 330s 330s 3SLS estimates for 'US.Steel' (equation 4) 330s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 330s 330s Instruments: ~US.Steel_value + US.Steel_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 85.4233 111.8774 0.76 0.4556 330s value 0.1015 0.0548 1.85 0.0814 . 330s capital 0.4000 0.1278 3.13 0.0061 ** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 103.969 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 183763.011 MSE: 10809.589 Root MSE: 103.969 330s Multiple R-Squared: 0.422 Adjusted R-Squared: 0.354 330s 330s 330s 3SLS estimates for 'Westinghouse' (equation 5) 330s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 330s 330s Instruments: ~Westinghouse_value + Westinghouse_capital 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 1.0889 6.2588 0.17 0.86394 330s value 0.0570 0.0114 5.02 0.00011 *** 330s capital 0.0415 0.0412 1.01 0.32787 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 10.567 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 1898.249 MSE: 111.662 Root MSE: 10.567 330s Multiple R-Squared: 0.726 Adjusted R-Squared: 0.694 330s 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s > # 'real' IV/3SLS estimation 330s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 330s + greene3slsR <- systemfit( invest ~ capital, inst = ~ value, "3SLS", 330s + data = GrunfeldGreene, useMatrix = useMatrix ) 330s + print( greene3slsR ) 330s + print( summary( greene3slsR ) ) 330s + } 330s 330s systemfit results 330s method: 3SLS 330s 330s Coefficients: 330s Chrysler_(Intercept) Chrysler_capital 330s 23.499 0.517 330s General.Electric_(Intercept) General.Electric_capital 330s -108.596 0.527 330s General.Motors_(Intercept) General.Motors_capital 330s 199.856 0.629 330s US.Steel_(Intercept) US.Steel_capital 330s 181.691 0.746 330s Westinghouse_(Intercept) Westinghouse_capital 330s 11.668 0.365 330s 330s systemfit results 330s method: 3SLS 330s 330s N DF SSR detRCov OLS-R2 McElroy-R2 330s system 100 90 1026043 4.46e+16 0.539 0.539 330s 330s N DF SSR MSE RMSE R2 Adj R2 330s Chrysler 20 18 12139 674 26.0 0.650 0.631 330s General.Electric 20 18 178965 9942 99.7 -2.990 -3.212 330s General.Motors 20 18 577860 32103 179.2 0.683 0.665 330s US.Steel 20 18 252838 14047 118.5 0.205 0.160 330s Westinghouse 20 18 4241 236 15.3 0.389 0.355 330s 330s The covariance matrix of the residuals used for estimation 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1687 3089 6820 11741 179 330s General.Electric 3089 9722 20780 23319 886 330s General.Motors 6820 20780 61121 44203 1908 330s US.Steel 11741 23319 44203 107242 1977 330s Westinghouse 179 886 1908 1977 218 330s 330s The covariance matrix of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 674 1587 1944 1371 137 330s General.Electric 1587 9942 13003 2009 996 330s General.Motors 1944 13003 32103 -908 1571 330s US.Steel 1371 2009 -908 14047 888 330s Westinghouse 137 996 1571 888 236 330s 330s The correlations of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1.000 0.613 0.4178 0.4454 0.343 330s General.Electric 0.613 1.000 0.7278 0.1700 0.651 330s General.Motors 0.418 0.728 1.0000 -0.0428 0.571 330s US.Steel 0.445 0.170 -0.0428 1.0000 0.488 330s Westinghouse 0.343 0.651 0.5713 0.4880 1.000 330s 330s 330s 3SLS estimates for 'Chrysler' (equation 1) 330s Model Formula: Chrysler_invest ~ Chrysler_capital 330s 330s Instruments: ~Chrysler_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 23.499 17.165 1.37 0.18784 330s capital 0.517 0.120 4.32 0.00041 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 25.969 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 12138.974 MSE: 674.387 Root MSE: 25.969 330s Multiple R-Squared: 0.65 Adjusted R-Squared: 0.631 330s 330s 330s 3SLS estimates for 'General.Electric' (equation 2) 330s Model Formula: General.Electric_invest ~ General.Electric_capital 330s 330s Instruments: ~General.Electric_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -108.596 152.939 -0.71 0.49 330s capital 0.527 0.378 1.39 0.18 330s 330s Residual standard error: 99.712 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 178964.956 MSE: 9942.498 Root MSE: 99.712 330s Multiple R-Squared: -2.99 Adjusted R-Squared: -3.212 330s 330s 330s 3SLS estimates for 'General.Motors' (equation 3) 330s Model Formula: General.Motors_invest ~ General.Motors_capital 330s 330s Instruments: ~General.Motors_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 199.856 98.953 2.02 0.059 . 330s capital 0.629 0.127 4.97 9.8e-05 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 179.174 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 577859.714 MSE: 32103.317 Root MSE: 179.174 330s Multiple R-Squared: 0.683 Adjusted R-Squared: 0.665 330s 330s 330s 3SLS estimates for 'US.Steel' (equation 4) 330s Model Formula: US.Steel_invest ~ US.Steel_capital 330s 330s Instruments: ~US.Steel_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 181.691 448.797 0.40 0.69 330s capital 0.746 1.477 0.51 0.62 330s 330s Residual standard error: 118.518 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 252838.286 MSE: 14046.571 Root MSE: 118.518 330s Multiple R-Squared: 0.205 Adjusted R-Squared: 0.16 330s 330s 330s 3SLS estimates for 'Westinghouse' (equation 5) 330s Model Formula: Westinghouse_invest ~ Westinghouse_capital 330s 330s Instruments: ~Westinghouse_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 11.6685 5.9043 1.98 0.064 . 330s capital 0.3646 0.0572 6.38 5.2e-06 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 15.349 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 4240.92 MSE: 235.607 Root MSE: 15.349 330s Multiple R-Squared: 0.389 Adjusted R-Squared: 0.355 330s 330s > 330s > ### 3SLS, Pooled ### 330s > # instruments = explanatory variables -> 3SLS estimates = SUR estimates 330s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 330s + greene3slsPooled <- systemfit( formulaGrunfeld, inst = ~ capital + value, "3SLS", 330s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix, 330s + residCovWeighted = TRUE, methodResidCov = "noDfCor" ) 330s + print( greene3slsPooled ) 330s + print( summary( greene3slsPooled ) ) 330s + print( all.equal( coef( summary( greene3slsPooled ) ), 330s + coef( summary( greeneSurPooled ) ) ) ) 330s + print( all.equal( greene3slsPooled[ -c(1,2,7) ], greeneSurPooled[ -c(1,2,7) ] ) ) 330s + for( i in 1:length( greene3slsPooled$eq ) ) { 330s + print( all.equal( greene3slsPooled$eq[[i]][ -c(3,15:17) ], 330s + greeneSurPooled$eq[[i]][-3] ) ) 330s + } 330s + } 330s 330s systemfit results 330s method: 3SLS 330s 330s Coefficients: 330s Chrysler_(Intercept) Chrysler_value 330s -28.2467 0.0891 330s Chrysler_capital General.Electric_(Intercept) 330s 0.3340 -28.2467 330s General.Electric_value General.Electric_capital 330s 0.0891 0.3340 330s General.Motors_(Intercept) General.Motors_value 330s -28.2467 0.0891 330s General.Motors_capital US.Steel_(Intercept) 330s 0.3340 -28.2467 330s US.Steel_value US.Steel_capital 330s 0.0891 0.3340 330s Westinghouse_(Intercept) Westinghouse_value 330s -28.2467 0.0891 330s Westinghouse_capital 330s 0.3340 330s 330s systemfit results 330s method: 3SLS 330s 330s N DF SSR detRCov OLS-R2 McElroy-R2 330s system 100 97 1604301 9.95e+16 0.279 0.844 330s 330s N DF SSR MSE RMSE R2 Adj R2 330s Chrysler 20 17 6112 360 19.0 0.824 0.803 330s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 330s General.Motors 20 17 201010 11824 108.7 0.890 0.877 330s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 330s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 330s 330s The covariance matrix of the residuals used for estimation 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 409 -2594 -197 2594 -102 330s General.Electric -2594 36563 -3480 -28623 3797 330s General.Motors -197 -3480 8612 996 -971 330s US.Steel 2594 -28623 996 32903 -2272 330s Westinghouse -102 3797 -971 -2272 778 330s 330s The covariance matrix of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 305.61 -1967 -4.81 2159 -124 330s General.Electric -1966.65 34557 -7160.67 -28722 4274 330s General.Motors -4.81 -7161 10050.52 4440 -1401 330s US.Steel 2158.60 -28722 4439.99 34469 -2894 330s Westinghouse -123.92 4274 -1400.75 -2894 833 330s 330s The correlations of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1.000 0.220 -0.3447 0.2008 0.2907 330s General.Electric 0.220 1.000 -0.2233 -0.1587 0.8973 330s General.Motors -0.345 -0.223 1.0000 -0.0924 -0.3760 330s US.Steel 0.201 -0.159 -0.0924 1.0000 -0.0757 330s Westinghouse 0.291 0.897 -0.3760 -0.0757 1.0000 330s 330s 330s 3SLS estimates for 'Chrysler' (equation 1) 330s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 330s 330s Instruments: ~Chrysler_capital + Chrysler_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 330s value 0.08910 0.00507 17.57 < 2e-16 *** 330s capital 0.33402 0.01671 19.99 < 2e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 18.962 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 6112.2 MSE: 359.541 Root MSE: 18.962 330s Multiple R-Squared: 0.824 Adjusted R-Squared: 0.803 330s 330s 330s 3SLS estimates for 'General.Electric' (equation 2) 330s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 330s 330s Instruments: ~General.Electric_capital + General.Electric_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 330s value 0.08910 0.00507 17.57 < 2e-16 *** 330s capital 0.33402 0.01671 19.99 < 2e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 201.63 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 691132.056 MSE: 40654.827 Root MSE: 201.63 330s Multiple R-Squared: -14.41 Adjusted R-Squared: -16.223 330s 330s 330s 3SLS estimates for 'General.Motors' (equation 3) 330s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 330s 330s Instruments: ~General.Motors_capital + General.Motors_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 330s value 0.08910 0.00507 17.57 < 2e-16 *** 330s capital 0.33402 0.01671 19.99 < 2e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 108.739 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 201010.497 MSE: 11824.147 Root MSE: 108.739 330s Multiple R-Squared: 0.89 Adjusted R-Squared: 0.877 330s 330s 330s 3SLS estimates for 'US.Steel' (equation 4) 330s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 330s 330s Instruments: ~US.Steel_capital + US.Steel_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 330s value 0.08910 0.00507 17.57 < 2e-16 *** 330s capital 0.33402 0.01671 19.99 < 2e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 201.375 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 689379.52 MSE: 40551.736 Root MSE: 201.375 330s Multiple R-Squared: -1.168 Adjusted R-Squared: -1.424 330s 330s 330s 3SLS estimates for 'Westinghouse' (equation 5) 330s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 330s 330s Instruments: ~Westinghouse_capital + Westinghouse_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 330s value 0.08910 0.00507 17.57 < 2e-16 *** 330s capital 0.33402 0.01671 19.99 < 2e-16 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 31.312 on 17 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 17 330s SSR: 16667.149 MSE: 980.421 Root MSE: 31.312 330s Multiple R-Squared: -1.402 Adjusted R-Squared: -1.685 330s 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s [1] TRUE 330s > # 'real' IV/3SLS estimation 330s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 330s + greene3slsRPooled <- systemfit( invest ~ capital, inst = ~ value, "3SLS", 330s + data = GrunfeldGreene, useMatrix = useMatrix ) 330s + print( greene3slsRPooled ) 330s + print( summary( greene3slsRPooled ) ) 330s + } 330s 330s systemfit results 330s method: 3SLS 330s 330s Coefficients: 330s Chrysler_(Intercept) Chrysler_capital 330s 23.499 0.517 330s General.Electric_(Intercept) General.Electric_capital 330s -108.596 0.527 330s General.Motors_(Intercept) General.Motors_capital 330s 199.856 0.629 330s US.Steel_(Intercept) US.Steel_capital 330s 181.691 0.746 330s Westinghouse_(Intercept) Westinghouse_capital 330s 11.668 0.365 330s 330s systemfit results 330s method: 3SLS 330s 330s N DF SSR detRCov OLS-R2 McElroy-R2 330s system 100 90 1026043 4.46e+16 0.539 0.539 330s 330s N DF SSR MSE RMSE R2 Adj R2 330s Chrysler 20 18 12139 674 26.0 0.650 0.631 330s General.Electric 20 18 178965 9942 99.7 -2.990 -3.212 330s General.Motors 20 18 577860 32103 179.2 0.683 0.665 330s US.Steel 20 18 252838 14047 118.5 0.205 0.160 330s Westinghouse 20 18 4241 236 15.3 0.389 0.355 330s 330s The covariance matrix of the residuals used for estimation 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1687 3089 6820 11741 179 330s General.Electric 3089 9722 20780 23319 886 330s General.Motors 6820 20780 61121 44203 1908 330s US.Steel 11741 23319 44203 107242 1977 330s Westinghouse 179 886 1908 1977 218 330s 330s The covariance matrix of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 674 1587 1944 1371 137 330s General.Electric 1587 9942 13003 2009 996 330s General.Motors 1944 13003 32103 -908 1571 330s US.Steel 1371 2009 -908 14047 888 330s Westinghouse 137 996 1571 888 236 330s 330s The correlations of the residuals 330s Chrysler General.Electric General.Motors US.Steel Westinghouse 330s Chrysler 1.000 0.613 0.4178 0.4454 0.343 330s General.Electric 0.613 1.000 0.7278 0.1700 0.651 330s General.Motors 0.418 0.728 1.0000 -0.0428 0.571 330s US.Steel 0.445 0.170 -0.0428 1.0000 0.488 330s Westinghouse 0.343 0.651 0.5713 0.4880 1.000 330s 330s 330s 3SLS estimates for 'Chrysler' (equation 1) 330s Model Formula: Chrysler_invest ~ Chrysler_capital 330s 330s Instruments: ~Chrysler_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 23.499 17.165 1.37 0.18784 330s capital 0.517 0.120 4.32 0.00041 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 25.969 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 12138.974 MSE: 674.387 Root MSE: 25.969 330s Multiple R-Squared: 0.65 Adjusted R-Squared: 0.631 330s 330s 330s 3SLS estimates for 'General.Electric' (equation 2) 330s Model Formula: General.Electric_invest ~ General.Electric_capital 330s 330s Instruments: ~General.Electric_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) -108.596 152.939 -0.71 0.49 330s capital 0.527 0.378 1.39 0.18 330s 330s Residual standard error: 99.712 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 178964.956 MSE: 9942.498 Root MSE: 99.712 330s Multiple R-Squared: -2.99 Adjusted R-Squared: -3.212 330s 330s 330s 3SLS estimates for 'General.Motors' (equation 3) 330s Model Formula: General.Motors_invest ~ General.Motors_capital 330s 330s Instruments: ~General.Motors_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 199.856 98.953 2.02 0.059 . 330s capital 0.629 0.127 4.97 9.8e-05 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 179.174 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 577859.714 MSE: 32103.317 Root MSE: 179.174 330s Multiple R-Squared: 0.683 Adjusted R-Squared: 0.665 330s 330s 330s 3SLS estimates for 'US.Steel' (equation 4) 330s Model Formula: US.Steel_invest ~ US.Steel_capital 330s 330s Instruments: ~US.Steel_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 181.691 448.797 0.40 0.69 330s capital 0.746 1.477 0.51 0.62 330s 330s Residual standard error: 118.518 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 252838.286 MSE: 14046.571 Root MSE: 118.518 330s Multiple R-Squared: 0.205 Adjusted R-Squared: 0.16 330s 330s 330s 3SLS estimates for 'Westinghouse' (equation 5) 330s Model Formula: Westinghouse_invest ~ Westinghouse_capital 330s 330s Instruments: ~Westinghouse_value 330s 330s 330s Estimate Std. Error t value Pr(>|t|) 330s (Intercept) 11.6685 5.9043 1.98 0.064 . 330s capital 0.3646 0.0572 6.38 5.2e-06 *** 330s --- 330s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 330s 330s Residual standard error: 15.349 on 18 degrees of freedom 330s Number of observations: 20 Degrees of Freedom: 18 330s SSR: 4240.92 MSE: 235.607 Root MSE: 15.349 330s Multiple R-Squared: 0.389 Adjusted R-Squared: 0.355 330s 330s > 330s > 330s > ## **************** estfun ************************ 330s > library( "sandwich" ) 330s > 330s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 330s + print( estfun( theilOls ) ) 330s + print( round( colSums( estfun( theilOls ) ), digits = 7 ) ) 330s + 330s + print( estfun( theilSur ) ) 330s + print( round( colSums( estfun( theilSur ) ), digits = 7 ) ) 330s + 330s + print( estfun( greeneOls ) ) 330s + print( round( colSums( estfun( greeneOls ) ), digits = 7 ) ) 330s + 330s + print( try( estfun( greeneOlsPooled ) ) ) 330s + 330s + print( estfun( greeneSur ) ) 330s + print( round( colSums( estfun( greeneSur ) ), digits = 7 ) ) 330s + 330s + print( try( estfun( greeneSurPooled ) ) ) 330s + } 330s General.Electric_(Intercept) General.Electric_value 330s General.Electric_X1935 -2.860 -3348 330s General.Electric_X1936 -14.402 -29032 330s General.Electric_X1937 -5.175 -14506 330s General.Electric_X1938 -23.295 -47514 330s General.Electric_X1939 -28.031 -63243 330s General.Electric_X1940 -0.562 -1199 330s General.Electric_X1941 40.750 74739 330s General.Electric_X1942 16.036 25464 330s General.Electric_X1943 -23.719 -41494 330s General.Electric_X1944 -26.780 -45183 330s General.Electric_X1945 1.768 3550 330s General.Electric_X1946 58.737 129709 330s General.Electric_X1947 43.936 72789 330s General.Electric_X1948 31.227 50101 330s General.Electric_X1949 -23.552 -33722 330s General.Electric_X1950 -37.511 -60411 330s General.Electric_X1951 -4.983 -9066 330s General.Electric_X1952 1.893 3937 330s General.Electric_X1953 5.087 12064 330s General.Electric_X1954 -8.563 -23633 330s Westinghouse_X1935 0.000 0 330s Westinghouse_X1936 0.000 0 330s Westinghouse_X1937 0.000 0 330s Westinghouse_X1938 0.000 0 330s Westinghouse_X1939 0.000 0 330s Westinghouse_X1940 0.000 0 330s Westinghouse_X1941 0.000 0 330s Westinghouse_X1942 0.000 0 330s Westinghouse_X1943 0.000 0 330s Westinghouse_X1944 0.000 0 330s Westinghouse_X1945 0.000 0 330s Westinghouse_X1946 0.000 0 330s Westinghouse_X1947 0.000 0 330s Westinghouse_X1948 0.000 0 330s Westinghouse_X1949 0.000 0 330s Westinghouse_X1950 0.000 0 330s Westinghouse_X1951 0.000 0 330s Westinghouse_X1952 0.000 0 330s Westinghouse_X1953 0.000 0 330s Westinghouse_X1954 0.000 0 330s General.Electric_capital Westinghouse_(Intercept) 330s General.Electric_X1935 -280 0.000 330s General.Electric_X1936 -1504 0.000 330s General.Electric_X1937 -611 0.000 330s General.Electric_X1938 -3639 0.000 330s General.Electric_X1939 -4838 0.000 330s General.Electric_X1940 -105 0.000 330s General.Electric_X1941 9002 0.000 330s General.Electric_X1942 4615 0.000 330s General.Electric_X1943 -7588 0.000 330s General.Electric_X1944 -8604 0.000 330s General.Electric_X1945 565 0.000 330s General.Electric_X1946 20323 0.000 330s General.Electric_X1947 20052 0.000 330s General.Electric_X1948 16969 0.000 330s General.Electric_X1949 -14562 0.000 330s General.Electric_X1950 -24285 0.000 330s General.Electric_X1951 -3345 0.000 330s General.Electric_X1952 1374 0.000 330s General.Electric_X1953 4071 0.000 330s General.Electric_X1954 -7612 0.000 330s Westinghouse_X1935 0 3.144 330s Westinghouse_X1936 0 -0.958 330s Westinghouse_X1937 0 -3.684 330s Westinghouse_X1938 0 -7.915 330s Westinghouse_X1939 0 -10.322 330s Westinghouse_X1940 0 -6.613 330s Westinghouse_X1941 0 17.265 330s Westinghouse_X1942 0 8.547 330s Westinghouse_X1943 0 -2.916 330s Westinghouse_X1944 0 -3.257 330s Westinghouse_X1945 0 -7.753 330s Westinghouse_X1946 0 5.796 330s Westinghouse_X1947 0 15.050 330s Westinghouse_X1948 0 2.969 330s Westinghouse_X1949 0 -11.433 330s Westinghouse_X1950 0 -13.481 330s Westinghouse_X1951 0 4.619 330s Westinghouse_X1952 0 13.138 330s Westinghouse_X1953 0 11.308 330s Westinghouse_X1954 0 -13.505 330s Westinghouse_value Westinghouse_capital 330s General.Electric_X1935 0 0.000 330s General.Electric_X1936 0 0.000 330s General.Electric_X1937 0 0.000 330s General.Electric_X1938 0 0.000 330s General.Electric_X1939 0 0.000 330s General.Electric_X1940 0 0.000 330s General.Electric_X1941 0 0.000 330s General.Electric_X1942 0 0.000 330s General.Electric_X1943 0 0.000 330s General.Electric_X1944 0 0.000 330s General.Electric_X1945 0 0.000 330s General.Electric_X1946 0 0.000 330s General.Electric_X1947 0 0.000 330s General.Electric_X1948 0 0.000 330s General.Electric_X1949 0 0.000 330s General.Electric_X1950 0 0.000 330s General.Electric_X1951 0 0.000 330s General.Electric_X1952 0 0.000 330s General.Electric_X1953 0 0.000 330s General.Electric_X1954 0 0.000 330s Westinghouse_X1935 602 5.659 330s Westinghouse_X1936 -494 -0.766 330s Westinghouse_X1937 -2686 -27.263 330s Westinghouse_X1938 -4436 -143.262 330s Westinghouse_X1939 -5366 -242.563 330s Westinghouse_X1940 -4156 -175.254 330s Westinghouse_X1941 9273 624.987 330s Westinghouse_X1942 4797 519.651 330s Westinghouse_X1943 -1800 -246.108 330s Westinghouse_X1944 -2041 -297.023 330s Westinghouse_X1945 -5715 -716.333 330s Westinghouse_X1946 4408 498.495 330s Westinghouse_X1947 8750 1672.098 330s Westinghouse_X1948 1967 387.794 330s Westinghouse_X1949 -6675 -1621.262 330s Westinghouse_X1950 -8563 -1842.843 330s Westinghouse_X1951 3344 599.149 330s Westinghouse_X1952 11353 1911.642 330s Westinghouse_X1953 13496 1976.568 330s Westinghouse_X1954 -16056 -2883.365 330s General.Electric_(Intercept) General.Electric_value 330s 0 0 330s General.Electric_capital Westinghouse_(Intercept) 330s 0 0 330s Westinghouse_value Westinghouse_capital 330s 0 0 330s General.Electric_(Intercept) General.Electric_value 330s General.Electric_X1935 0.007671 8.980 330s General.Electric_X1936 -0.061426 -123.822 330s General.Electric_X1937 -0.060974 -170.929 330s General.Electric_X1938 -0.088931 -181.393 330s General.Electric_X1939 -0.111776 -252.189 330s General.Electric_X1940 -0.017793 -37.937 330s General.Electric_X1941 0.128334 235.378 330s General.Electric_X1942 0.060606 96.243 330s General.Electric_X1943 -0.072587 -126.985 330s General.Electric_X1944 -0.080053 -135.065 330s General.Electric_X1945 -0.000104 -0.208 330s General.Electric_X1946 0.177325 391.586 330s General.Electric_X1947 0.154986 256.765 330s General.Electric_X1948 0.119488 191.707 330s General.Electric_X1949 -0.047791 -68.427 330s General.Electric_X1950 -0.098464 -158.576 330s General.Electric_X1951 -0.000379 -0.689 330s General.Electric_X1952 0.014181 29.492 330s General.Electric_X1953 0.016444 38.998 330s General.Electric_X1954 -0.038758 -106.969 330s Westinghouse_X1935 -0.019477 -22.800 330s Westinghouse_X1936 0.016942 34.151 330s Westinghouse_X1937 0.039739 111.402 330s Westinghouse_X1938 0.059843 122.062 330s Westinghouse_X1939 0.073091 164.909 330s Westinghouse_X1940 0.052015 110.907 330s Westinghouse_X1941 -0.105994 -194.404 330s Westinghouse_X1942 -0.053728 -85.321 330s Westinghouse_X1943 0.017332 30.320 330s Westinghouse_X1944 0.018569 31.330 330s Westinghouse_X1945 0.050605 101.599 330s Westinghouse_X1946 -0.034591 -76.387 330s Westinghouse_X1947 -0.104099 -172.460 330s Westinghouse_X1948 -0.027559 -44.215 330s Westinghouse_X1949 0.060567 86.720 330s Westinghouse_X1950 0.076221 122.754 330s Westinghouse_X1951 -0.036128 -65.731 330s Westinghouse_X1952 -0.089492 -186.117 330s Westinghouse_X1953 -0.073054 -173.256 330s Westinghouse_X1954 0.079198 218.578 330s General.Electric_capital Westinghouse_(Intercept) 330s General.Electric_X1935 0.7503 -0.015267 330s General.Electric_X1936 -6.4128 0.122246 330s General.Electric_X1937 -7.1950 0.121347 330s General.Electric_X1938 -13.8911 0.176986 330s General.Electric_X1939 -19.2925 0.222450 330s General.Electric_X1940 -3.3201 0.035410 330s General.Electric_X1941 28.3490 -0.255403 330s General.Electric_X1942 17.4425 -0.120615 330s General.Electric_X1943 -23.2207 0.144459 330s General.Electric_X1944 -25.7209 0.159316 330s General.Electric_X1945 -0.0331 0.000206 330s General.Electric_X1946 61.3543 -0.352901 330s General.Electric_X1947 70.7355 -0.308443 330s General.Electric_X1948 64.9300 -0.237798 330s General.Electric_X1949 -29.5489 0.095110 330s General.Electric_X1950 -63.7453 0.195956 330s General.Electric_X1951 -0.2543 0.000754 330s General.Electric_X1952 10.2966 -0.028221 330s General.Electric_X1953 13.1598 -0.032725 330s General.Electric_X1954 -34.4523 0.077135 330s Westinghouse_X1935 -1.9049 0.072945 330s Westinghouse_X1936 1.7687 -0.063449 330s Westinghouse_X1937 4.6893 -0.148830 330s Westinghouse_X1938 9.3475 -0.224122 330s Westinghouse_X1939 12.6156 -0.273739 330s Westinghouse_X1940 9.7061 -0.194806 330s Westinghouse_X1941 -23.4141 0.396965 330s Westinghouse_X1942 -15.4630 0.201221 330s Westinghouse_X1943 5.5444 -0.064910 330s Westinghouse_X1944 5.9663 -0.069544 330s Westinghouse_X1945 16.1733 -0.189523 330s Westinghouse_X1946 -11.9684 0.129548 330s Westinghouse_X1947 -47.5107 0.389866 330s Westinghouse_X1948 -14.9755 0.103212 330s Westinghouse_X1949 37.4485 -0.226832 330s Westinghouse_X1950 49.3457 -0.285461 330s Westinghouse_X1951 -24.2526 0.135304 330s Westinghouse_X1952 -64.9804 0.335163 330s Westinghouse_X1953 -58.4654 0.273600 330s Westinghouse_X1954 70.3989 -0.296608 330s Westinghouse_value Westinghouse_capital 330s General.Electric_X1935 -2.924 -0.0275 330s General.Electric_X1936 63.079 0.0978 330s General.Electric_X1937 88.462 0.8980 330s General.Electric_X1938 99.183 3.2034 330s General.Electric_X1939 115.652 5.2276 330s General.Electric_X1940 22.255 0.9384 330s General.Electric_X1941 -137.177 -9.2456 330s General.Electric_X1942 -67.689 -7.3334 330s General.Electric_X1943 89.160 12.1924 330s General.Electric_X1944 99.843 14.5296 330s General.Electric_X1945 0.152 0.0190 330s General.Electric_X1946 -268.381 -30.3494 330s General.Electric_X1947 -179.329 -34.2680 330s General.Electric_X1948 -157.494 -31.0565 330s General.Electric_X1949 55.525 13.4866 330s General.Electric_X1950 124.471 26.7872 330s General.Electric_X1951 0.546 0.0978 330s General.Electric_X1952 -24.386 -4.1062 330s General.Electric_X1953 -39.057 -5.7203 330s General.Electric_X1954 91.705 16.4682 330s Westinghouse_X1935 13.969 0.1313 330s Westinghouse_X1936 -32.740 -0.0508 330s Westinghouse_X1937 -108.497 -1.1013 330s Westinghouse_X1938 -125.598 -4.0566 330s Westinghouse_X1939 -142.317 -6.4329 330s Westinghouse_X1940 -122.436 -5.1624 330s Westinghouse_X1941 213.210 14.3701 330s Westinghouse_X1942 112.925 12.2342 330s Westinghouse_X1943 -40.063 -5.4784 330s Westinghouse_X1944 -43.583 -6.3424 330s Westinghouse_X1945 -139.717 -17.5120 330s Westinghouse_X1946 98.521 11.1411 330s Westinghouse_X1947 226.668 43.3141 330s Westinghouse_X1948 68.357 13.4795 330s Westinghouse_X1949 -132.425 -32.1648 330s Westinghouse_X1950 -181.325 -39.0225 330s Westinghouse_X1951 97.933 17.5490 330s Westinghouse_X1952 289.614 48.7662 330s Westinghouse_X1953 326.541 47.8252 330s Westinghouse_X1954 -352.637 -63.3258 330s General.Electric_(Intercept) General.Electric_value 330s 0 0 330s General.Electric_capital Westinghouse_(Intercept) 330s 0 0 330s Westinghouse_value Westinghouse_capital 330s 0 0 330s Chrysler_(Intercept) Chrysler_value Chrysler_capital 330s Chrysler_X1935 10.622 4435 111.5 330s Chrysler_X1936 10.425 8734 106.3 330s Chrysler_X1937 -7.404 -6544 -256.9 330s Chrysler_X1938 7.302 3198 378.3 330s Chrysler_X1939 -14.682 -9979 -944.0 330s Chrysler_X1940 -2.315 -1685 -155.3 330s Chrysler_X1941 0.631 406 47.4 330s Chrysler_X1942 -1.581 -650 -112.9 330s Chrysler_X1943 -13.459 -7919 -903.1 330s Chrysler_X1944 -7.780 -5433 -470.7 330s Chrysler_X1945 11.757 9951 641.9 330s Chrysler_X1946 -16.133 -14419 -1368.1 330s Chrysler_X1947 -6.823 -3951 -660.5 330s Chrysler_X1948 6.615 4595 729.0 330s Chrysler_X1949 -7.379 -4356 -1087.7 330s Chrysler_X1950 1.268 879 206.9 330s Chrysler_X1951 39.502 31957 8038.6 330s Chrysler_X1952 2.774 2017 806.2 330s Chrysler_X1953 -6.215 -6224 -2151.0 330s Chrysler_X1954 -7.124 -5010 -2955.9 330s General.Electric_X1935 0.000 0 0.0 330s General.Electric_X1936 0.000 0 0.0 330s General.Electric_X1937 0.000 0 0.0 330s General.Electric_X1938 0.000 0 0.0 330s General.Electric_X1939 0.000 0 0.0 330s General.Electric_X1940 0.000 0 0.0 330s General.Electric_X1941 0.000 0 0.0 330s General.Electric_X1942 0.000 0 0.0 330s General.Electric_X1943 0.000 0 0.0 330s General.Electric_X1944 0.000 0 0.0 330s General.Electric_X1945 0.000 0 0.0 330s General.Electric_X1946 0.000 0 0.0 330s General.Electric_X1947 0.000 0 0.0 330s General.Electric_X1948 0.000 0 0.0 330s General.Electric_X1949 0.000 0 0.0 330s General.Electric_X1950 0.000 0 0.0 330s General.Electric_X1951 0.000 0 0.0 330s General.Electric_X1952 0.000 0 0.0 330s General.Electric_X1953 0.000 0 0.0 330s General.Electric_X1954 0.000 0 0.0 330s General.Motors_X1935 0.000 0 0.0 330s General.Motors_X1936 0.000 0 0.0 330s General.Motors_X1937 0.000 0 0.0 330s General.Motors_X1938 0.000 0 0.0 330s General.Motors_X1939 0.000 0 0.0 330s General.Motors_X1940 0.000 0 0.0 330s General.Motors_X1941 0.000 0 0.0 330s General.Motors_X1942 0.000 0 0.0 330s General.Motors_X1943 0.000 0 0.0 330s General.Motors_X1944 0.000 0 0.0 330s General.Motors_X1945 0.000 0 0.0 330s General.Motors_X1946 0.000 0 0.0 330s General.Motors_X1947 0.000 0 0.0 330s General.Motors_X1948 0.000 0 0.0 330s General.Motors_X1949 0.000 0 0.0 330s General.Motors_X1950 0.000 0 0.0 330s General.Motors_X1951 0.000 0 0.0 330s General.Motors_X1952 0.000 0 0.0 330s General.Motors_X1953 0.000 0 0.0 330s General.Motors_X1954 0.000 0 0.0 330s US.Steel_X1935 0.000 0 0.0 330s US.Steel_X1936 0.000 0 0.0 330s US.Steel_X1937 0.000 0 0.0 330s US.Steel_X1938 0.000 0 0.0 330s US.Steel_X1939 0.000 0 0.0 330s US.Steel_X1940 0.000 0 0.0 330s US.Steel_X1941 0.000 0 0.0 330s US.Steel_X1942 0.000 0 0.0 330s US.Steel_X1943 0.000 0 0.0 330s US.Steel_X1944 0.000 0 0.0 330s US.Steel_X1945 0.000 0 0.0 330s US.Steel_X1946 0.000 0 0.0 330s US.Steel_X1947 0.000 0 0.0 330s US.Steel_X1948 0.000 0 0.0 330s US.Steel_X1949 0.000 0 0.0 330s US.Steel_X1950 0.000 0 0.0 330s US.Steel_X1951 0.000 0 0.0 330s US.Steel_X1952 0.000 0 0.0 330s US.Steel_X1953 0.000 0 0.0 330s US.Steel_X1954 0.000 0 0.0 330s Westinghouse_X1935 0.000 0 0.0 330s Westinghouse_X1936 0.000 0 0.0 330s Westinghouse_X1937 0.000 0 0.0 330s Westinghouse_X1938 0.000 0 0.0 330s Westinghouse_X1939 0.000 0 0.0 330s Westinghouse_X1940 0.000 0 0.0 330s Westinghouse_X1941 0.000 0 0.0 330s Westinghouse_X1942 0.000 0 0.0 330s Westinghouse_X1943 0.000 0 0.0 330s Westinghouse_X1944 0.000 0 0.0 330s Westinghouse_X1945 0.000 0 0.0 330s Westinghouse_X1946 0.000 0 0.0 330s Westinghouse_X1947 0.000 0 0.0 330s Westinghouse_X1948 0.000 0 0.0 330s Westinghouse_X1949 0.000 0 0.0 330s Westinghouse_X1950 0.000 0 0.0 330s Westinghouse_X1951 0.000 0 0.0 330s Westinghouse_X1952 0.000 0 0.0 330s Westinghouse_X1953 0.000 0 0.0 330s Westinghouse_X1954 0.000 0 0.0 330s General.Electric_(Intercept) General.Electric_value 330s Chrysler_X1935 0.000 0 330s Chrysler_X1936 0.000 0 330s Chrysler_X1937 0.000 0 330s Chrysler_X1938 0.000 0 330s Chrysler_X1939 0.000 0 330s Chrysler_X1940 0.000 0 330s Chrysler_X1941 0.000 0 330s Chrysler_X1942 0.000 0 330s Chrysler_X1943 0.000 0 330s Chrysler_X1944 0.000 0 330s Chrysler_X1945 0.000 0 330s Chrysler_X1946 0.000 0 330s Chrysler_X1947 0.000 0 330s Chrysler_X1948 0.000 0 330s Chrysler_X1949 0.000 0 330s Chrysler_X1950 0.000 0 330s Chrysler_X1951 0.000 0 330s Chrysler_X1952 0.000 0 330s Chrysler_X1953 0.000 0 330s Chrysler_X1954 0.000 0 330s General.Electric_X1935 -2.860 -3348 330s General.Electric_X1936 -14.402 -29032 330s General.Electric_X1937 -5.175 -14506 330s General.Electric_X1938 -23.295 -47514 330s General.Electric_X1939 -28.031 -63243 330s General.Electric_X1940 -0.562 -1199 330s General.Electric_X1941 40.750 74739 330s General.Electric_X1942 16.036 25464 330s General.Electric_X1943 -23.719 -41494 330s General.Electric_X1944 -26.780 -45183 330s General.Electric_X1945 1.768 3550 330s General.Electric_X1946 58.737 129709 330s General.Electric_X1947 43.936 72789 330s General.Electric_X1948 31.227 50101 330s General.Electric_X1949 -23.552 -33722 330s General.Electric_X1950 -37.511 -60411 330s General.Electric_X1951 -4.983 -9066 330s General.Electric_X1952 1.893 3937 330s General.Electric_X1953 5.087 12064 330s General.Electric_X1954 -8.563 -23633 330s General.Motors_X1935 0.000 0 330s General.Motors_X1936 0.000 0 330s General.Motors_X1937 0.000 0 330s General.Motors_X1938 0.000 0 330s General.Motors_X1939 0.000 0 330s General.Motors_X1940 0.000 0 330s General.Motors_X1941 0.000 0 330s General.Motors_X1942 0.000 0 330s General.Motors_X1943 0.000 0 330s General.Motors_X1944 0.000 0 330s General.Motors_X1945 0.000 0 330s General.Motors_X1946 0.000 0 330s General.Motors_X1947 0.000 0 330s General.Motors_X1948 0.000 0 330s General.Motors_X1949 0.000 0 330s General.Motors_X1950 0.000 0 330s General.Motors_X1951 0.000 0 330s General.Motors_X1952 0.000 0 330s General.Motors_X1953 0.000 0 330s General.Motors_X1954 0.000 0 330s US.Steel_X1935 0.000 0 330s US.Steel_X1936 0.000 0 330s US.Steel_X1937 0.000 0 330s US.Steel_X1938 0.000 0 330s US.Steel_X1939 0.000 0 330s US.Steel_X1940 0.000 0 330s US.Steel_X1941 0.000 0 330s US.Steel_X1942 0.000 0 330s US.Steel_X1943 0.000 0 330s US.Steel_X1944 0.000 0 330s US.Steel_X1945 0.000 0 330s US.Steel_X1946 0.000 0 330s US.Steel_X1947 0.000 0 330s US.Steel_X1948 0.000 0 330s US.Steel_X1949 0.000 0 330s US.Steel_X1950 0.000 0 330s US.Steel_X1951 0.000 0 330s US.Steel_X1952 0.000 0 330s US.Steel_X1953 0.000 0 330s US.Steel_X1954 0.000 0 330s Westinghouse_X1935 0.000 0 330s Westinghouse_X1936 0.000 0 330s Westinghouse_X1937 0.000 0 330s Westinghouse_X1938 0.000 0 330s Westinghouse_X1939 0.000 0 330s Westinghouse_X1940 0.000 0 330s Westinghouse_X1941 0.000 0 330s Westinghouse_X1942 0.000 0 330s Westinghouse_X1943 0.000 0 330s Westinghouse_X1944 0.000 0 330s Westinghouse_X1945 0.000 0 330s Westinghouse_X1946 0.000 0 330s Westinghouse_X1947 0.000 0 330s Westinghouse_X1948 0.000 0 330s Westinghouse_X1949 0.000 0 330s Westinghouse_X1950 0.000 0 330s Westinghouse_X1951 0.000 0 330s Westinghouse_X1952 0.000 0 330s Westinghouse_X1953 0.000 0 330s Westinghouse_X1954 0.000 0 330s General.Electric_capital General.Motors_(Intercept) 330s Chrysler_X1935 0 0.00 330s Chrysler_X1936 0 0.00 330s Chrysler_X1937 0 0.00 330s Chrysler_X1938 0 0.00 330s Chrysler_X1939 0 0.00 330s Chrysler_X1940 0 0.00 330s Chrysler_X1941 0 0.00 330s Chrysler_X1942 0 0.00 330s Chrysler_X1943 0 0.00 330s Chrysler_X1944 0 0.00 330s Chrysler_X1945 0 0.00 330s Chrysler_X1946 0 0.00 330s Chrysler_X1947 0 0.00 330s Chrysler_X1948 0 0.00 330s Chrysler_X1949 0 0.00 330s Chrysler_X1950 0 0.00 330s Chrysler_X1951 0 0.00 330s Chrysler_X1952 0 0.00 330s Chrysler_X1953 0 0.00 330s Chrysler_X1954 0 0.00 330s General.Electric_X1935 -280 0.00 330s General.Electric_X1936 -1504 0.00 330s General.Electric_X1937 -611 0.00 330s General.Electric_X1938 -3639 0.00 330s General.Electric_X1939 -4838 0.00 330s General.Electric_X1940 -105 0.00 330s General.Electric_X1941 9002 0.00 330s General.Electric_X1942 4615 0.00 330s General.Electric_X1943 -7588 0.00 330s General.Electric_X1944 -8604 0.00 330s General.Electric_X1945 565 0.00 330s General.Electric_X1946 20323 0.00 330s General.Electric_X1947 20052 0.00 330s General.Electric_X1948 16969 0.00 330s General.Electric_X1949 -14562 0.00 330s General.Electric_X1950 -24285 0.00 330s General.Electric_X1951 -3345 0.00 330s General.Electric_X1952 1374 0.00 330s General.Electric_X1953 4071 0.00 330s General.Electric_X1954 -7612 0.00 330s General.Motors_X1935 0 99.14 330s General.Motors_X1936 0 -34.01 330s General.Motors_X1937 0 -140.48 330s General.Motors_X1938 0 -3.28 330s General.Motors_X1939 0 -109.45 330s General.Motors_X1940 0 -19.91 330s General.Motors_X1941 0 24.12 330s General.Motors_X1942 0 98.02 330s General.Motors_X1943 0 67.76 330s General.Motors_X1944 0 100.03 330s General.Motors_X1945 0 35.12 330s General.Motors_X1946 0 103.90 330s General.Motors_X1947 0 15.18 330s General.Motors_X1948 0 -51.86 330s General.Motors_X1949 0 -115.39 330s General.Motors_X1950 0 -63.51 330s General.Motors_X1951 0 -119.40 330s General.Motors_X1952 0 -77.82 330s General.Motors_X1953 0 49.50 330s General.Motors_X1954 0 142.33 330s US.Steel_X1935 0 0.00 330s US.Steel_X1936 0 0.00 330s US.Steel_X1937 0 0.00 330s US.Steel_X1938 0 0.00 330s US.Steel_X1939 0 0.00 330s US.Steel_X1940 0 0.00 330s US.Steel_X1941 0 0.00 330s US.Steel_X1942 0 0.00 330s US.Steel_X1943 0 0.00 330s US.Steel_X1944 0 0.00 330s US.Steel_X1945 0 0.00 330s US.Steel_X1946 0 0.00 330s US.Steel_X1947 0 0.00 330s US.Steel_X1948 0 0.00 330s US.Steel_X1949 0 0.00 330s US.Steel_X1950 0 0.00 330s US.Steel_X1951 0 0.00 330s US.Steel_X1952 0 0.00 330s US.Steel_X1953 0 0.00 330s US.Steel_X1954 0 0.00 330s Westinghouse_X1935 0 0.00 330s Westinghouse_X1936 0 0.00 330s Westinghouse_X1937 0 0.00 330s Westinghouse_X1938 0 0.00 330s Westinghouse_X1939 0 0.00 330s Westinghouse_X1940 0 0.00 330s Westinghouse_X1941 0 0.00 330s Westinghouse_X1942 0 0.00 330s Westinghouse_X1943 0 0.00 330s Westinghouse_X1944 0 0.00 330s Westinghouse_X1945 0 0.00 330s Westinghouse_X1946 0 0.00 330s Westinghouse_X1947 0 0.00 330s Westinghouse_X1948 0 0.00 330s Westinghouse_X1949 0 0.00 330s Westinghouse_X1950 0 0.00 330s Westinghouse_X1951 0 0.00 330s Westinghouse_X1952 0 0.00 330s Westinghouse_X1953 0 0.00 330s Westinghouse_X1954 0 0.00 330s General.Motors_value General.Motors_capital 330s Chrysler_X1935 0 0 330s Chrysler_X1936 0 0 330s Chrysler_X1937 0 0 330s Chrysler_X1938 0 0 330s Chrysler_X1939 0 0 330s Chrysler_X1940 0 0 330s Chrysler_X1941 0 0 330s Chrysler_X1942 0 0 330s Chrysler_X1943 0 0 330s Chrysler_X1944 0 0 330s Chrysler_X1945 0 0 330s Chrysler_X1946 0 0 330s Chrysler_X1947 0 0 330s Chrysler_X1948 0 0 330s Chrysler_X1949 0 0 330s Chrysler_X1950 0 0 330s Chrysler_X1951 0 0 330s Chrysler_X1952 0 0 330s Chrysler_X1953 0 0 330s Chrysler_X1954 0 0 330s General.Electric_X1935 0 0 330s General.Electric_X1936 0 0 330s General.Electric_X1937 0 0 330s General.Electric_X1938 0 0 330s General.Electric_X1939 0 0 330s General.Electric_X1940 0 0 330s General.Electric_X1941 0 0 330s General.Electric_X1942 0 0 330s General.Electric_X1943 0 0 330s General.Electric_X1944 0 0 330s General.Electric_X1945 0 0 330s General.Electric_X1946 0 0 330s General.Electric_X1947 0 0 330s General.Electric_X1948 0 0 330s General.Electric_X1949 0 0 330s General.Electric_X1950 0 0 330s General.Electric_X1951 0 0 330s General.Electric_X1952 0 0 330s General.Electric_X1953 0 0 330s General.Electric_X1954 0 0 330s General.Motors_X1935 305191 278 330s General.Motors_X1936 -158530 -1789 330s General.Motors_X1937 -756753 -22041 330s General.Motors_X1938 -9158 -686 330s General.Motors_X1939 -472086 -22262 330s General.Motors_X1940 -92456 -4125 330s General.Motors_X1941 109770 6155 330s General.Motors_X1942 317973 29767 330s General.Motors_X1943 274659 17894 330s General.Motors_X1944 438073 20167 330s General.Motors_X1945 170027 9308 330s General.Motors_X1946 509223 41790 330s General.Motors_X1947 53544 11562 330s General.Motors_X1948 -168794 -47837 330s General.Motors_X1949 -426971 -117711 330s General.Motors_X1950 -238505 -69794 330s General.Motors_X1951 -577039 -144194 330s General.Motors_X1952 -383234 -111315 330s General.Motors_X1953 308954 87974 330s General.Motors_X1954 796113 316860 330s US.Steel_X1935 0 0 330s US.Steel_X1936 0 0 330s US.Steel_X1937 0 0 330s US.Steel_X1938 0 0 330s US.Steel_X1939 0 0 330s US.Steel_X1940 0 0 330s US.Steel_X1941 0 0 330s US.Steel_X1942 0 0 330s US.Steel_X1943 0 0 330s US.Steel_X1944 0 0 330s US.Steel_X1945 0 0 330s US.Steel_X1946 0 0 330s US.Steel_X1947 0 0 330s US.Steel_X1948 0 0 330s US.Steel_X1949 0 0 330s US.Steel_X1950 0 0 330s US.Steel_X1951 0 0 330s US.Steel_X1952 0 0 330s US.Steel_X1953 0 0 330s US.Steel_X1954 0 0 330s Westinghouse_X1935 0 0 330s Westinghouse_X1936 0 0 330s Westinghouse_X1937 0 0 330s Westinghouse_X1938 0 0 330s Westinghouse_X1939 0 0 330s Westinghouse_X1940 0 0 330s Westinghouse_X1941 0 0 330s Westinghouse_X1942 0 0 330s Westinghouse_X1943 0 0 330s Westinghouse_X1944 0 0 330s Westinghouse_X1945 0 0 330s Westinghouse_X1946 0 0 330s Westinghouse_X1947 0 0 330s Westinghouse_X1948 0 0 330s Westinghouse_X1949 0 0 330s Westinghouse_X1950 0 0 330s Westinghouse_X1951 0 0 330s Westinghouse_X1952 0 0 330s Westinghouse_X1953 0 0 330s Westinghouse_X1954 0 0 330s US.Steel_(Intercept) US.Steel_value US.Steel_capital 330s Chrysler_X1935 0.00 0 0 330s Chrysler_X1936 0.00 0 0 330s Chrysler_X1937 0.00 0 0 330s Chrysler_X1938 0.00 0 0 330s Chrysler_X1939 0.00 0 0 330s Chrysler_X1940 0.00 0 0 330s Chrysler_X1941 0.00 0 0 330s Chrysler_X1942 0.00 0 0 330s Chrysler_X1943 0.00 0 0 330s Chrysler_X1944 0.00 0 0 330s Chrysler_X1945 0.00 0 0 330s Chrysler_X1946 0.00 0 0 330s Chrysler_X1947 0.00 0 0 330s Chrysler_X1948 0.00 0 0 330s Chrysler_X1949 0.00 0 0 330s Chrysler_X1950 0.00 0 0 330s Chrysler_X1951 0.00 0 0 330s Chrysler_X1952 0.00 0 0 330s Chrysler_X1953 0.00 0 0 330s Chrysler_X1954 0.00 0 0 330s General.Electric_X1935 0.00 0 0 330s General.Electric_X1936 0.00 0 0 330s General.Electric_X1937 0.00 0 0 330s General.Electric_X1938 0.00 0 0 330s General.Electric_X1939 0.00 0 0 330s General.Electric_X1940 0.00 0 0 330s General.Electric_X1941 0.00 0 0 330s General.Electric_X1942 0.00 0 0 330s General.Electric_X1943 0.00 0 0 330s General.Electric_X1944 0.00 0 0 330s General.Electric_X1945 0.00 0 0 330s General.Electric_X1946 0.00 0 0 330s General.Electric_X1947 0.00 0 0 330s General.Electric_X1948 0.00 0 0 330s General.Electric_X1949 0.00 0 0 330s General.Electric_X1950 0.00 0 0 330s General.Electric_X1951 0.00 0 0 330s General.Electric_X1952 0.00 0 0 330s General.Electric_X1953 0.00 0 0 330s General.Electric_X1954 0.00 0 0 330s General.Motors_X1935 0.00 0 0 330s General.Motors_X1936 0.00 0 0 330s General.Motors_X1937 0.00 0 0 330s General.Motors_X1938 0.00 0 0 330s General.Motors_X1939 0.00 0 0 330s General.Motors_X1940 0.00 0 0 330s General.Motors_X1941 0.00 0 0 330s General.Motors_X1942 0.00 0 0 330s General.Motors_X1943 0.00 0 0 330s General.Motors_X1944 0.00 0 0 330s General.Motors_X1945 0.00 0 0 330s General.Motors_X1946 0.00 0 0 330s General.Motors_X1947 0.00 0 0 330s General.Motors_X1948 0.00 0 0 330s General.Motors_X1949 0.00 0 0 330s General.Motors_X1950 0.00 0 0 330s General.Motors_X1951 0.00 0 0 330s General.Motors_X1952 0.00 0 0 330s General.Motors_X1953 0.00 0 0 330s General.Motors_X1954 0.00 0 0 330s US.Steel_X1935 4.15 5657 223 330s US.Steel_X1936 81.32 146961 4107 330s US.Steel_X1937 31.18 83446 3682 330s US.Steel_X1938 -99.75 -179733 -25954 330s US.Steel_X1939 -178.23 -348850 -55733 330s US.Steel_X1940 -160.69 -353980 -40847 330s US.Steel_X1941 19.65 46784 5137 330s US.Steel_X1942 9.82 21296 2933 330s US.Steel_X1943 -46.76 -92829 -14113 330s US.Steel_X1944 -83.74 -151889 -23371 330s US.Steel_X1945 -91.24 -168815 -19507 330s US.Steel_X1946 28.34 58590 6591 330s US.Steel_X1947 57.32 102983 15178 330s US.Steel_X1948 140.23 227988 43037 330s US.Steel_X1949 25.65 42751 9004 330s US.Steel_X1950 34.88 58503 12479 330s US.Steel_X1951 115.10 263510 39374 330s US.Steel_X1952 149.19 322157 66269 330s US.Steel_X1953 89.00 180793 55503 330s US.Steel_X1954 -125.42 -265326 -83994 330s Westinghouse_X1935 0.00 0 0 330s Westinghouse_X1936 0.00 0 0 330s Westinghouse_X1937 0.00 0 0 330s Westinghouse_X1938 0.00 0 0 330s Westinghouse_X1939 0.00 0 0 330s Westinghouse_X1940 0.00 0 0 330s Westinghouse_X1941 0.00 0 0 330s Westinghouse_X1942 0.00 0 0 330s Westinghouse_X1943 0.00 0 0 330s Westinghouse_X1944 0.00 0 0 330s Westinghouse_X1945 0.00 0 0 330s Westinghouse_X1946 0.00 0 0 330s Westinghouse_X1947 0.00 0 0 330s Westinghouse_X1948 0.00 0 0 330s Westinghouse_X1949 0.00 0 0 330s Westinghouse_X1950 0.00 0 0 330s Westinghouse_X1951 0.00 0 0 330s Westinghouse_X1952 0.00 0 0 330s Westinghouse_X1953 0.00 0 0 330s Westinghouse_X1954 0.00 0 0 330s Westinghouse_(Intercept) Westinghouse_value 330s Chrysler_X1935 0.000 0 330s Chrysler_X1936 0.000 0 330s Chrysler_X1937 0.000 0 330s Chrysler_X1938 0.000 0 330s Chrysler_X1939 0.000 0 330s Chrysler_X1940 0.000 0 330s Chrysler_X1941 0.000 0 330s Chrysler_X1942 0.000 0 330s Chrysler_X1943 0.000 0 330s Chrysler_X1944 0.000 0 330s Chrysler_X1945 0.000 0 330s Chrysler_X1946 0.000 0 330s Chrysler_X1947 0.000 0 330s Chrysler_X1948 0.000 0 330s Chrysler_X1949 0.000 0 330s Chrysler_X1950 0.000 0 330s Chrysler_X1951 0.000 0 330s Chrysler_X1952 0.000 0 330s Chrysler_X1953 0.000 0 330s Chrysler_X1954 0.000 0 330s General.Electric_X1935 0.000 0 330s General.Electric_X1936 0.000 0 330s General.Electric_X1937 0.000 0 330s General.Electric_X1938 0.000 0 330s General.Electric_X1939 0.000 0 330s General.Electric_X1940 0.000 0 330s General.Electric_X1941 0.000 0 330s General.Electric_X1942 0.000 0 330s General.Electric_X1943 0.000 0 330s General.Electric_X1944 0.000 0 330s General.Electric_X1945 0.000 0 330s General.Electric_X1946 0.000 0 330s General.Electric_X1947 0.000 0 330s General.Electric_X1948 0.000 0 330s General.Electric_X1949 0.000 0 330s General.Electric_X1950 0.000 0 330s General.Electric_X1951 0.000 0 330s General.Electric_X1952 0.000 0 330s General.Electric_X1953 0.000 0 330s General.Electric_X1954 0.000 0 330s General.Motors_X1935 0.000 0 330s General.Motors_X1936 0.000 0 330s General.Motors_X1937 0.000 0 330s General.Motors_X1938 0.000 0 330s General.Motors_X1939 0.000 0 330s General.Motors_X1940 0.000 0 330s General.Motors_X1941 0.000 0 330s General.Motors_X1942 0.000 0 330s General.Motors_X1943 0.000 0 330s General.Motors_X1944 0.000 0 330s General.Motors_X1945 0.000 0 330s General.Motors_X1946 0.000 0 330s General.Motors_X1947 0.000 0 330s General.Motors_X1948 0.000 0 330s General.Motors_X1949 0.000 0 330s General.Motors_X1950 0.000 0 330s General.Motors_X1951 0.000 0 330s General.Motors_X1952 0.000 0 330s General.Motors_X1953 0.000 0 330s General.Motors_X1954 0.000 0 330s US.Steel_X1935 0.000 0 330s US.Steel_X1936 0.000 0 330s US.Steel_X1937 0.000 0 330s US.Steel_X1938 0.000 0 330s US.Steel_X1939 0.000 0 330s US.Steel_X1940 0.000 0 330s US.Steel_X1941 0.000 0 330s US.Steel_X1942 0.000 0 330s US.Steel_X1943 0.000 0 330s US.Steel_X1944 0.000 0 330s US.Steel_X1945 0.000 0 330s US.Steel_X1946 0.000 0 330s US.Steel_X1947 0.000 0 330s US.Steel_X1948 0.000 0 330s US.Steel_X1949 0.000 0 330s US.Steel_X1950 0.000 0 330s US.Steel_X1951 0.000 0 330s US.Steel_X1952 0.000 0 330s US.Steel_X1953 0.000 0 330s US.Steel_X1954 0.000 0 330s Westinghouse_X1935 3.144 602 330s Westinghouse_X1936 -0.958 -494 330s Westinghouse_X1937 -3.684 -2686 330s Westinghouse_X1938 -7.915 -4436 330s Westinghouse_X1939 -10.322 -5366 330s Westinghouse_X1940 -6.613 -4156 330s Westinghouse_X1941 17.265 9273 330s Westinghouse_X1942 8.547 4797 330s Westinghouse_X1943 -2.916 -1800 330s Westinghouse_X1944 -3.257 -2041 330s Westinghouse_X1945 -7.753 -5715 330s Westinghouse_X1946 5.796 4408 330s Westinghouse_X1947 15.050 8750 330s Westinghouse_X1948 2.969 1967 330s Westinghouse_X1949 -11.433 -6675 330s Westinghouse_X1950 -13.481 -8563 330s Westinghouse_X1951 4.619 3344 330s Westinghouse_X1952 13.138 11353 330s Westinghouse_X1953 11.308 13496 330s Westinghouse_X1954 -13.505 -16056 330s Westinghouse_capital 330s Chrysler_X1935 0.000 330s Chrysler_X1936 0.000 330s Chrysler_X1937 0.000 330s Chrysler_X1938 0.000 330s Chrysler_X1939 0.000 330s Chrysler_X1940 0.000 330s Chrysler_X1941 0.000 330s Chrysler_X1942 0.000 330s Chrysler_X1943 0.000 330s Chrysler_X1944 0.000 330s Chrysler_X1945 0.000 330s Chrysler_X1946 0.000 330s Chrysler_X1947 0.000 330s Chrysler_X1948 0.000 330s Chrysler_X1949 0.000 330s Chrysler_X1950 0.000 330s Chrysler_X1951 0.000 330s Chrysler_X1952 0.000 330s Chrysler_X1953 0.000 330s Chrysler_X1954 0.000 330s General.Electric_X1935 0.000 330s General.Electric_X1936 0.000 330s General.Electric_X1937 0.000 330s General.Electric_X1938 0.000 330s General.Electric_X1939 0.000 330s General.Electric_X1940 0.000 330s General.Electric_X1941 0.000 330s General.Electric_X1942 0.000 330s General.Electric_X1943 0.000 330s General.Electric_X1944 0.000 330s General.Electric_X1945 0.000 330s General.Electric_X1946 0.000 330s General.Electric_X1947 0.000 330s General.Electric_X1948 0.000 330s General.Electric_X1949 0.000 330s General.Electric_X1950 0.000 330s General.Electric_X1951 0.000 330s General.Electric_X1952 0.000 330s General.Electric_X1953 0.000 330s General.Electric_X1954 0.000 330s General.Motors_X1935 0.000 330s General.Motors_X1936 0.000 330s General.Motors_X1937 0.000 330s General.Motors_X1938 0.000 330s General.Motors_X1939 0.000 330s General.Motors_X1940 0.000 330s General.Motors_X1941 0.000 330s General.Motors_X1942 0.000 330s General.Motors_X1943 0.000 330s General.Motors_X1944 0.000 330s General.Motors_X1945 0.000 330s General.Motors_X1946 0.000 330s General.Motors_X1947 0.000 330s General.Motors_X1948 0.000 330s General.Motors_X1949 0.000 330s General.Motors_X1950 0.000 330s General.Motors_X1951 0.000 330s General.Motors_X1952 0.000 330s General.Motors_X1953 0.000 330s General.Motors_X1954 0.000 330s US.Steel_X1935 0.000 330s US.Steel_X1936 0.000 330s US.Steel_X1937 0.000 330s US.Steel_X1938 0.000 330s US.Steel_X1939 0.000 330s US.Steel_X1940 0.000 330s US.Steel_X1941 0.000 330s US.Steel_X1942 0.000 330s US.Steel_X1943 0.000 330s US.Steel_X1944 0.000 330s US.Steel_X1945 0.000 330s US.Steel_X1946 0.000 330s US.Steel_X1947 0.000 330s US.Steel_X1948 0.000 330s US.Steel_X1949 0.000 330s US.Steel_X1950 0.000 330s US.Steel_X1951 0.000 330s US.Steel_X1952 0.000 330s US.Steel_X1953 0.000 330s US.Steel_X1954 0.000 330s Westinghouse_X1935 5.659 330s Westinghouse_X1936 -0.766 330s Westinghouse_X1937 -27.263 330s Westinghouse_X1938 -143.262 330s Westinghouse_X1939 -242.563 330s Westinghouse_X1940 -175.254 330s Westinghouse_X1941 624.987 330s Westinghouse_X1942 519.651 330s Westinghouse_X1943 -246.108 330s Westinghouse_X1944 -297.023 330s Westinghouse_X1945 -716.333 330s Westinghouse_X1946 498.495 330s Westinghouse_X1947 1672.098 330s Westinghouse_X1948 387.794 330s Westinghouse_X1949 -1621.262 330s Westinghouse_X1950 -1842.843 330s Westinghouse_X1951 Error in estfun.systemfit(greeneOlsPooled) : 330s returning the estimation function for models with restrictions has not yet been implemented. 330s 599.149 330s Westinghouse_X1952 1911.642 330s Westinghouse_X1953 1976.568 330s Westinghouse_X1954 -2883.365 330s Chrysler_(Intercept) Chrysler_value 330s 0 0 330s Chrysler_capital General.Electric_(Intercept) 330s 0 0 330s General.Electric_value General.Electric_capital 330s 0 0 330s General.Motors_(Intercept) General.Motors_value 330s 0 0 330s General.Motors_capital US.Steel_(Intercept) 330s 0 0 330s US.Steel_value US.Steel_capital 330s 0 0 330s Westinghouse_(Intercept) Westinghouse_value 330s 0 0 330s Westinghouse_capital 330s 0 330s [1] "Error in estfun.systemfit(greeneOlsPooled) : \n returning the estimation function for models with restrictions has not yet been implemented.\n" 330s attr(,"class") 330s [1] "try-error" 330s attr(,"condition") 330s 330s Chrysler_(Intercept) Chrysler_value Chrysler_capital 330s Chrysler_X1935 0.061827 25.813 0.64918 330s Chrysler_X1936 0.089260 74.782 0.91045 330s Chrysler_X1937 -0.052866 -46.729 -1.83447 330s Chrysler_X1938 0.038353 16.795 1.98668 330s Chrysler_X1939 -0.125156 -85.069 -8.04755 330s Chrysler_X1940 -0.019863 -14.456 -1.33281 330s Chrysler_X1941 -0.000958 -0.617 -0.07206 330s Chrysler_X1942 -0.035485 -14.581 -2.53362 330s Chrysler_X1943 -0.121241 -71.338 -8.13529 330s Chrysler_X1944 -0.067270 -46.981 -4.06984 330s Chrysler_X1945 0.103440 87.551 5.64781 330s Chrysler_X1946 -0.121081 -108.222 -10.26763 330s Chrysler_X1947 -0.065512 -37.931 -6.34155 330s Chrysler_X1948 0.053900 37.439 5.93977 330s Chrysler_X1949 -0.066320 -39.149 -9.77563 330s Chrysler_X1950 0.012935 8.971 2.11101 330s Chrysler_X1951 0.338038 273.472 68.79064 330s Chrysler_X1952 0.035175 25.572 10.22178 330s Chrysler_X1953 -0.016558 -16.583 -5.73086 330s Chrysler_X1954 -0.040615 -28.561 -16.85128 330s General.Electric_X1935 -0.000794 -0.332 -0.00834 330s General.Electric_X1936 -0.018766 -15.722 -0.19142 330s General.Electric_X1937 -0.017841 -15.770 -0.61909 330s General.Electric_X1938 -0.025844 -11.317 -1.33872 330s General.Electric_X1939 -0.031739 -21.573 -2.04083 330s General.Electric_X1940 -0.006211 -4.520 -0.41674 330s General.Electric_X1941 0.033478 21.546 2.51754 330s General.Electric_X1942 0.015339 6.303 1.09520 330s General.Electric_X1943 -0.020477 -12.049 -1.37400 330s General.Electric_X1944 -0.022551 -15.749 -1.36432 330s General.Electric_X1945 -0.000552 -0.467 -0.03015 330s General.Electric_X1946 0.048030 42.930 4.07298 330s General.Electric_X1947 0.042267 24.472 4.09142 330s General.Electric_X1948 0.033204 23.064 3.65913 330s General.Electric_X1949 -0.011862 -7.002 -1.74842 330s General.Electric_X1950 -0.025261 -17.518 -4.12252 330s General.Electric_X1951 0.001752 1.417 0.35646 330s General.Electric_X1952 0.006337 4.607 1.84166 330s General.Electric_X1953 0.007751 7.762 2.68249 330s General.Electric_X1954 -0.006261 -4.402 -2.59748 330s General.Motors_X1935 0.015266 6.374 0.16030 330s General.Motors_X1936 -0.003913 -3.278 -0.03991 330s General.Motors_X1937 -0.019260 -17.024 -0.66833 330s General.Motors_X1938 0.000502 0.220 0.02603 330s General.Motors_X1939 -0.014763 -10.035 -0.94928 330s General.Motors_X1940 -0.002163 -1.575 -0.14517 330s General.Motors_X1941 0.004002 2.576 0.30095 330s General.Motors_X1942 0.014599 5.999 1.04234 330s General.Motors_X1943 0.010244 6.027 0.68736 330s General.Motors_X1944 0.014852 10.373 0.89857 330s General.Motors_X1945 0.005493 4.649 0.29991 330s General.Motors_X1946 0.014990 13.398 1.27114 330s General.Motors_X1947 0.002105 1.219 0.20375 330s General.Motors_X1948 -0.007587 -5.270 -0.83607 330s General.Motors_X1949 -0.016803 -9.919 -2.47682 330s General.Motors_X1950 -0.009602 -6.659 -1.56700 330s General.Motors_X1951 -0.017864 -14.452 -3.63526 330s General.Motors_X1952 -0.012355 -8.982 -3.59050 330s General.Motors_X1953 0.004869 4.876 1.68503 330s General.Motors_X1954 0.017389 12.228 7.21481 330s US.Steel_X1935 0.013928 5.815 0.14625 330s US.Steel_X1936 -0.026161 -21.918 -0.26684 330s US.Steel_X1937 -0.025907 -22.899 -0.89897 330s US.Steel_X1938 0.043429 19.017 2.24961 330s US.Steel_X1939 0.070526 47.937 4.53484 330s US.Steel_X1940 0.058816 42.806 3.94653 330s US.Steel_X1941 -0.016278 -10.476 -1.22408 330s US.Steel_X1942 -0.008142 -3.346 -0.58136 330s US.Steel_X1943 0.018146 10.677 1.21761 330s US.Steel_X1944 0.036672 25.612 2.21866 330s US.Steel_X1945 0.039460 33.399 2.15450 330s US.Steel_X1946 -0.012632 -11.291 -1.07122 330s US.Steel_X1947 -0.018481 -10.700 -1.78894 330s US.Steel_X1948 -0.047880 -33.258 -5.27643 330s US.Steel_X1949 -0.003976 -2.347 -0.58605 330s US.Steel_X1950 -0.007908 -5.484 -1.29060 330s US.Steel_X1951 -0.052722 -42.652 -10.72894 330s US.Steel_X1952 -0.064309 -46.753 -18.68822 330s US.Steel_X1953 -0.039465 -39.524 -13.65875 330s US.Steel_X1954 0.042884 30.156 17.79265 330s Westinghouse_X1935 -0.000639 -0.267 -0.00671 330s Westinghouse_X1936 0.003489 2.923 0.03559 330s Westinghouse_X1937 0.005946 5.256 0.20632 330s Westinghouse_X1938 0.008196 3.589 0.42458 330s Westinghouse_X1939 0.009675 6.576 0.62207 330s Westinghouse_X1940 0.007107 5.172 0.47686 330s Westinghouse_X1941 -0.011506 -7.406 -0.86528 330s Westinghouse_X1942 -0.005817 -2.390 -0.41532 330s Westinghouse_X1943 0.002074 1.221 0.13919 330s Westinghouse_X1944 0.002100 1.466 0.12704 330s Westinghouse_X1945 0.005777 4.890 0.31543 330s Westinghouse_X1946 -0.004096 -3.661 -0.34734 330s Westinghouse_X1947 -0.012571 -7.279 -1.21688 330s Westinghouse_X1948 -0.003981 -2.765 -0.43871 330s Westinghouse_X1949 0.006180 3.648 0.91087 330s Westinghouse_X1950 0.008074 5.599 1.31765 330s Westinghouse_X1951 -0.004997 -4.043 -1.01696 330s Westinghouse_X1952 -0.011575 -8.415 -3.36372 330s Westinghouse_X1953 -0.010300 -10.316 -3.56494 330s Westinghouse_X1954 0.006866 4.828 2.84858 330s General.Electric_(Intercept) General.Electric_value 330s Chrysler_X1935 0.006590 7.715 330s Chrysler_X1936 0.009515 19.180 330s Chrysler_X1937 -0.005635 -15.797 330s Chrysler_X1938 0.004088 8.339 330s Chrysler_X1939 -0.013341 -30.100 330s Chrysler_X1940 -0.002117 -4.514 330s Chrysler_X1941 -0.000102 -0.187 330s Chrysler_X1942 -0.003782 -6.007 330s Chrysler_X1943 -0.012924 -22.609 330s Chrysler_X1944 -0.007171 -12.098 330s Chrysler_X1945 0.011026 22.137 330s Chrysler_X1946 -0.012907 -28.501 330s Chrysler_X1947 -0.006983 -11.569 330s Chrysler_X1948 0.005745 9.218 330s Chrysler_X1949 -0.007069 -10.122 330s Chrysler_X1950 0.001379 2.221 330s Chrysler_X1951 0.036033 65.558 330s Chrysler_X1952 0.003749 7.798 330s Chrysler_X1953 -0.001765 -4.186 330s Chrysler_X1954 -0.004329 -11.949 330s General.Electric_X1935 -0.003192 -3.736 330s General.Electric_X1936 -0.075425 -152.042 330s General.Electric_X1937 -0.071707 -201.016 330s General.Electric_X1938 -0.103871 -211.866 330s General.Electric_X1939 -0.127565 -287.812 330s General.Electric_X1940 -0.024962 -53.224 330s General.Electric_X1941 0.134553 246.784 330s General.Electric_X1942 0.061649 97.899 330s General.Electric_X1943 -0.082300 -143.975 330s General.Electric_X1944 -0.090635 -152.920 330s General.Electric_X1945 -0.002219 -4.456 330s General.Electric_X1946 0.193042 426.295 330s General.Electric_X1947 0.169877 281.435 330s General.Electric_X1948 0.133454 214.114 330s General.Electric_X1949 -0.047674 -68.260 330s General.Electric_X1950 -0.101526 -163.508 330s General.Electric_X1951 0.007040 12.809 330s General.Electric_X1952 0.025471 52.972 330s General.Electric_X1953 0.031151 73.878 330s General.Electric_X1954 -0.025162 -69.445 330s General.Motors_X1935 -0.016212 -18.978 330s General.Motors_X1936 0.004155 8.376 330s General.Motors_X1937 0.020453 57.337 330s General.Motors_X1938 -0.000534 -1.088 330s General.Motors_X1939 0.015678 35.372 330s General.Motors_X1940 0.002297 4.899 330s General.Motors_X1941 -0.004250 -7.795 330s General.Motors_X1942 -0.015503 -24.619 330s General.Motors_X1943 -0.010878 -19.031 330s General.Motors_X1944 -0.015772 -26.611 330s General.Motors_X1945 -0.005833 -11.711 330s General.Motors_X1946 -0.015918 -35.152 330s General.Motors_X1947 -0.002235 -3.703 330s General.Motors_X1948 0.008057 12.926 330s General.Motors_X1949 0.017844 25.549 330s General.Motors_X1950 0.010196 16.421 330s General.Motors_X1951 0.018970 34.514 330s General.Motors_X1952 0.013121 27.287 330s General.Motors_X1953 -0.005170 -12.262 330s General.Motors_X1954 -0.018466 -50.965 330s US.Steel_X1935 0.000660 0.772 330s US.Steel_X1936 -0.001239 -2.497 330s US.Steel_X1937 -0.001227 -3.439 330s US.Steel_X1938 0.002057 4.195 330s US.Steel_X1939 0.003340 7.535 330s US.Steel_X1940 0.002785 5.939 330s US.Steel_X1941 -0.000771 -1.414 330s US.Steel_X1942 -0.000386 -0.612 330s US.Steel_X1943 0.000859 1.503 330s US.Steel_X1944 0.001737 2.930 330s US.Steel_X1945 0.001869 3.752 330s US.Steel_X1946 -0.000598 -1.321 330s US.Steel_X1947 -0.000875 -1.450 330s US.Steel_X1948 -0.002267 -3.638 330s US.Steel_X1949 -0.000188 -0.270 330s US.Steel_X1950 -0.000374 -0.603 330s US.Steel_X1951 -0.002497 -4.542 330s US.Steel_X1952 -0.003045 -6.333 330s US.Steel_X1953 -0.001869 -4.432 330s US.Steel_X1954 0.002031 5.605 330s Westinghouse_X1935 -0.005793 -6.781 330s Westinghouse_X1936 0.031644 63.787 330s Westinghouse_X1937 0.053929 151.178 330s Westinghouse_X1938 0.074341 151.634 330s Westinghouse_X1939 0.087747 197.975 330s Westinghouse_X1940 0.064457 137.434 330s Westinghouse_X1941 -0.104362 -191.410 330s Westinghouse_X1942 -0.052757 -83.779 330s Westinghouse_X1943 0.018814 32.913 330s Westinghouse_X1944 0.019045 32.133 330s Westinghouse_X1945 0.052397 105.198 330s Westinghouse_X1946 -0.037151 -82.040 330s Westinghouse_X1947 -0.114019 -188.895 330s Westinghouse_X1948 -0.036108 -57.931 330s Westinghouse_X1949 0.056048 80.250 330s Westinghouse_X1950 0.073229 117.935 330s Westinghouse_X1951 -0.045325 -82.465 330s Westinghouse_X1952 -0.104985 -218.337 330s Westinghouse_X1953 -0.093423 -221.562 330s Westinghouse_X1954 0.062271 171.863 330s General.Electric_capital General.Motors_(Intercept) 330s Chrysler_X1935 0.6445 1.06e-03 330s Chrysler_X1936 0.9933 1.53e-03 330s Chrysler_X1937 -0.6650 -9.08e-04 330s Chrysler_X1938 0.6386 6.59e-04 330s Chrysler_X1939 -2.3026 -2.15e-03 330s Chrysler_X1940 -0.3951 -3.41e-04 330s Chrysler_X1941 -0.0226 -1.65e-05 330s Chrysler_X1942 -1.0886 -6.10e-04 330s Chrysler_X1943 -4.1343 -2.08e-03 330s Chrysler_X1944 -2.3039 -1.16e-03 330s Chrysler_X1945 3.5239 1.78e-03 330s Chrysler_X1946 -4.4657 -2.08e-03 330s Chrysler_X1947 -3.1871 -1.13e-03 330s Chrysler_X1948 3.1221 9.26e-04 330s Chrysler_X1949 -4.3710 -1.14e-03 330s Chrysler_X1950 0.8926 2.22e-04 330s Chrysler_X1951 24.1889 5.81e-03 330s Chrysler_X1952 2.7225 6.04e-04 330s Chrysler_X1953 -1.4126 -2.84e-04 330s Chrysler_X1954 -3.8484 -6.98e-04 330s General.Electric_X1935 -0.3121 1.36e-04 330s General.Electric_X1936 -7.8744 3.21e-03 330s General.Electric_X1937 -8.4614 3.05e-03 330s General.Electric_X1938 -16.2246 4.42e-03 330s General.Electric_X1939 -22.0177 5.43e-03 330s General.Electric_X1940 -4.6579 1.06e-03 330s General.Electric_X1941 29.7228 -5.73e-03 330s General.Electric_X1942 17.7427 -2.63e-03 330s General.Electric_X1943 -26.3277 3.50e-03 330s General.Electric_X1944 -29.1212 3.86e-03 330s General.Electric_X1945 -0.7094 9.45e-05 330s General.Electric_X1946 66.7926 -8.22e-03 330s General.Electric_X1947 77.5319 -7.23e-03 330s General.Electric_X1948 72.5190 -5.68e-03 330s General.Electric_X1949 -29.4770 2.03e-03 330s General.Electric_X1950 -65.7280 4.32e-03 330s General.Electric_X1951 4.7261 -3.00e-04 330s General.Electric_X1952 18.4946 -1.08e-03 330s General.Electric_X1953 24.9302 -1.33e-03 330s General.Electric_X1954 -22.3665 1.07e-03 330s General.Motors_X1935 -1.5855 2.13e-02 330s General.Motors_X1936 0.4338 -5.46e-03 330s General.Motors_X1937 2.4135 -2.69e-02 330s General.Motors_X1938 -0.0833 7.00e-04 330s General.Motors_X1939 2.7060 -2.06e-02 330s General.Motors_X1940 0.4287 -3.02e-03 330s General.Motors_X1941 -0.9388 5.58e-03 330s General.Motors_X1942 -4.4617 2.04e-02 330s General.Motors_X1943 -3.4800 1.43e-02 330s General.Motors_X1944 -5.0677 2.07e-02 330s General.Motors_X1945 -1.8642 7.66e-03 330s General.Motors_X1946 -5.5077 2.09e-02 330s General.Motors_X1947 -1.0202 2.93e-03 330s General.Motors_X1948 4.3781 -1.06e-02 330s General.Motors_X1949 11.0331 -2.34e-02 330s General.Motors_X1950 6.6012 -1.34e-02 330s General.Motors_X1951 12.7347 -2.49e-02 330s General.Motors_X1952 9.5270 -1.72e-02 330s General.Motors_X1953 -4.1377 6.79e-03 330s General.Motors_X1954 -16.4148 2.42e-02 330s US.Steel_X1935 0.0645 -3.30e-03 330s US.Steel_X1936 -0.1293 6.19e-03 330s US.Steel_X1937 -0.1448 6.13e-03 330s US.Steel_X1938 0.3212 -1.03e-02 330s US.Steel_X1939 0.5764 -1.67e-02 330s US.Steel_X1940 0.5197 -1.39e-02 330s US.Steel_X1941 -0.1703 3.85e-03 330s US.Steel_X1942 -0.1110 1.93e-03 330s US.Steel_X1943 0.2749 -4.29e-03 330s US.Steel_X1944 0.5580 -8.68e-03 330s US.Steel_X1945 0.5972 -9.34e-03 330s US.Steel_X1946 -0.2070 2.99e-03 330s US.Steel_X1947 -0.3994 4.37e-03 330s US.Steel_X1948 -1.2321 1.13e-02 330s US.Steel_X1949 -0.1164 9.41e-04 330s US.Steel_X1950 -0.2424 1.87e-03 330s US.Steel_X1951 -1.6760 1.25e-02 330s US.Steel_X1952 -2.2112 1.52e-02 330s US.Steel_X1953 -1.4956 9.34e-03 330s US.Steel_X1954 1.8051 -1.01e-02 330s Westinghouse_X1935 -0.5665 -4.91e-04 330s Westinghouse_X1936 3.3036 2.68e-03 330s Westinghouse_X1937 6.3636 4.57e-03 330s Westinghouse_X1938 11.6121 6.30e-03 330s Westinghouse_X1939 15.1452 7.44e-03 330s Westinghouse_X1940 12.0276 5.46e-03 330s Westinghouse_X1941 -23.0535 -8.84e-03 330s Westinghouse_X1942 -15.1836 -4.47e-03 330s Westinghouse_X1943 6.0186 1.59e-03 330s Westinghouse_X1944 6.1191 1.61e-03 330s Westinghouse_X1945 16.7462 4.44e-03 330s Westinghouse_X1946 -12.8541 -3.15e-03 330s Westinghouse_X1947 -52.0382 -9.66e-03 330s Westinghouse_X1948 -19.6209 -3.06e-03 330s Westinghouse_X1949 34.6547 4.75e-03 330s Westinghouse_X1950 47.4084 6.21e-03 330s Westinghouse_X1951 -30.4270 -3.84e-03 330s Westinghouse_X1952 -76.2296 -8.90e-03 330s Westinghouse_X1953 -74.7663 -7.92e-03 330s Westinghouse_X1954 55.3529 5.28e-03 330s General.Motors_value General.Motors_capital 330s Chrysler_X1935 3.2697 2.97e-03 330s Chrysler_X1936 7.1482 8.07e-02 330s Chrysler_X1937 -4.8925 -1.42e-01 330s Chrysler_X1938 1.8397 1.38e-01 330s Chrysler_X1939 -9.2736 -4.37e-01 330s Chrysler_X1940 -1.5846 -7.07e-02 330s Chrysler_X1941 -0.0749 -4.20e-03 330s Chrysler_X1942 -1.9776 -1.85e-01 330s Chrysler_X1943 -8.4430 -5.50e-01 330s Chrysler_X1944 -5.0608 -2.33e-01 330s Chrysler_X1945 8.6022 4.71e-01 330s Chrysler_X1946 -10.1940 -8.37e-01 330s Chrysler_X1947 -3.9688 -8.57e-01 330s Chrysler_X1948 3.0137 8.54e-01 330s Chrysler_X1949 -4.2157 -1.16e+00 330s Chrysler_X1950 0.8345 2.44e-01 330s Chrysler_X1951 28.0658 7.01e+00 330s Chrysler_X1952 2.9759 8.64e-01 330s Chrysler_X1953 -1.7755 -5.06e-01 330s Chrysler_X1954 -3.9028 -1.55e+00 330s General.Electric_X1935 0.4184 3.81e-04 330s General.Electric_X1936 14.9723 1.69e-01 330s General.Electric_X1937 16.4491 4.79e-01 330s General.Electric_X1938 12.3500 9.25e-01 330s General.Electric_X1939 23.4292 1.10e+00 330s General.Electric_X1940 4.9361 2.20e-01 330s General.Electric_X1941 -26.0763 -1.46e+00 330s General.Electric_X1942 -8.5163 -7.97e-01 330s General.Electric_X1943 14.2062 9.26e-01 330s General.Electric_X1944 16.9016 7.78e-01 330s General.Electric_X1945 0.4575 2.50e-02 330s General.Electric_X1946 -40.2860 -3.31e+00 330s General.Electric_X1947 -25.5097 -5.51e+00 330s General.Electric_X1948 -18.4956 -5.24e+00 330s General.Electric_X1949 7.5116 2.07e+00 330s General.Electric_X1950 16.2362 4.75e+00 330s General.Electric_X1951 -1.4489 -3.62e-01 330s General.Electric_X1952 -5.3416 -1.55e+00 330s General.Electric_X1953 -8.2795 -2.36e+00 330s General.Electric_X1954 5.9933 2.39e+00 330s General.Motors_X1935 65.5183 5.96e-02 330s General.Motors_X1936 -25.4300 -2.87e-01 330s General.Motors_X1937 -144.6452 -4.21e+00 330s General.Motors_X1938 1.9558 1.47e-01 330s General.Motors_X1939 -88.7707 -4.19e+00 330s General.Motors_X1940 -14.0060 -6.25e-01 330s General.Motors_X1941 25.3914 1.42e+00 330s General.Motors_X1942 66.0227 6.18e+00 330s General.Motors_X1943 57.8898 3.77e+00 330s General.Motors_X1944 90.6754 4.17e+00 330s General.Motors_X1945 37.0686 2.03e+00 330s General.Motors_X1946 102.4144 8.40e+00 330s General.Motors_X1947 10.3479 2.23e+00 330s General.Motors_X1948 -34.4239 -9.76e+00 330s General.Motors_X1949 -86.6782 -2.39e+01 330s General.Motors_X1950 -50.2708 -1.47e+01 330s General.Motors_X1951 -120.3581 -3.01e+01 330s General.Motors_X1952 -84.8289 -2.46e+01 330s General.Motors_X1953 42.3640 1.21e+01 330s General.Motors_X1954 135.6002 5.40e+01 330s US.Steel_X1935 -10.1444 -9.23e-03 330s US.Steel_X1936 28.8526 3.26e-01 330s US.Steel_X1937 33.0183 9.62e-01 330s US.Steel_X1938 -28.6886 -2.15e+00 330s US.Steel_X1939 -71.9676 -3.39e+00 330s US.Steel_X1940 -64.6193 -2.88e+00 330s US.Steel_X1941 17.5269 9.83e-01 330s US.Steel_X1942 6.2492 5.85e-01 330s US.Steel_X1943 -17.4030 -1.13e+00 330s US.Steel_X1944 -37.9949 -1.75e+00 330s US.Steel_X1945 -45.1924 -2.47e+00 330s US.Steel_X1946 14.6469 1.20e+00 330s US.Steel_X1947 15.4188 3.33e+00 330s US.Steel_X1948 36.8685 1.04e+01 330s US.Steel_X1949 3.4806 9.60e-01 330s US.Steel_X1950 7.0265 2.06e+00 330s US.Steel_X1951 60.2830 1.51e+01 330s US.Steel_X1952 74.9299 2.18e+01 330s US.Steel_X1953 58.2771 1.66e+01 330s US.Steel_X1954 -56.7511 -2.26e+01 330s Westinghouse_X1935 -1.5111 -1.37e-03 330s Westinghouse_X1936 12.4999 1.41e-01 330s Westinghouse_X1937 24.6178 7.17e-01 330s Westinghouse_X1938 17.5894 1.32e+00 330s Westinghouse_X1939 32.0707 1.51e+00 330s Westinghouse_X1940 25.3645 1.13e+00 330s Westinghouse_X1941 -40.2479 -2.26e+00 330s Westinghouse_X1942 -14.5028 -1.36e+00 330s Westinghouse_X1943 6.4627 4.21e-01 330s Westinghouse_X1944 7.0674 3.25e-01 330s Westinghouse_X1945 21.4937 1.18e+00 330s Westinghouse_X1946 -15.4283 -1.27e+00 330s Westinghouse_X1947 -34.0718 -7.36e+00 330s Westinghouse_X1948 -9.9583 -2.82e+00 330s Westinghouse_X1949 17.5737 4.84e+00 330s Westinghouse_X1950 23.3044 6.82e+00 330s Westinghouse_X1951 -18.5624 -4.64e+00 330s Westinghouse_X1952 -43.8127 -1.27e+01 330s Westinghouse_X1953 -49.4119 -1.41e+01 330s Westinghouse_X1954 29.5158 1.17e+01 330s US.Steel_(Intercept) US.Steel_value US.Steel_capital 330s Chrysler_X1935 -2.96e-03 -4.0379 -0.15945 330s Chrysler_X1936 -4.28e-03 -7.7323 -0.21608 330s Chrysler_X1937 2.53e-03 6.7824 0.29930 330s Chrysler_X1938 -1.84e-03 -3.3128 -0.47838 330s Chrysler_X1939 6.00e-03 11.7430 1.87608 330s Chrysler_X1940 9.52e-04 2.0975 0.24204 330s Chrysler_X1941 4.59e-05 0.1094 0.01201 330s Chrysler_X1942 1.70e-03 3.6889 0.50810 330s Chrysler_X1943 5.81e-03 11.5373 1.75404 330s Chrysler_X1944 3.22e-03 5.8493 0.90002 330s Chrysler_X1945 -4.96e-03 -9.1744 -1.06014 330s Chrysler_X1946 5.80e-03 12.0014 1.35006 330s Chrysler_X1947 3.14e-03 5.6424 0.83159 330s Chrysler_X1948 -2.58e-03 -4.2007 -0.79297 330s Chrysler_X1949 3.18e-03 5.2997 1.11622 330s Chrysler_X1950 -6.20e-04 -1.0401 -0.22186 330s Chrysler_X1951 -1.62e-02 -37.1002 -5.54355 330s Chrysler_X1952 -1.69e-03 -3.6411 -0.74900 330s Chrysler_X1953 7.94e-04 1.6124 0.49499 330s Chrysler_X1954 1.95e-03 4.1188 1.30389 330s General.Electric_X1935 1.69e-05 0.0230 0.00091 330s General.Electric_X1936 4.00e-04 0.7222 0.02018 330s General.Electric_X1937 3.80e-04 1.0168 0.04487 330s General.Electric_X1938 5.50e-04 0.9917 0.14321 330s General.Electric_X1939 6.76e-04 1.3230 0.21136 330s General.Electric_X1940 1.32e-04 0.2914 0.03362 330s General.Electric_X1941 -7.13e-04 -1.6972 -0.18636 330s General.Electric_X1942 -3.27e-04 -0.7084 -0.09757 330s General.Electric_X1943 4.36e-04 0.8656 0.13161 330s General.Electric_X1944 4.80e-04 0.8711 0.13403 330s General.Electric_X1945 1.18e-05 0.0218 0.00251 330s General.Electric_X1946 -1.02e-03 -2.1149 -0.23791 330s General.Electric_X1947 -9.00e-04 -1.6172 -0.23835 330s General.Electric_X1948 -7.07e-04 -1.1496 -0.21701 330s General.Electric_X1949 2.53e-04 0.4211 0.08869 330s General.Electric_X1950 5.38e-04 0.9023 0.19248 330s General.Electric_X1951 -3.73e-05 -0.0854 -0.01276 330s General.Electric_X1952 -1.35e-04 -0.2914 -0.05995 330s General.Electric_X1953 -1.65e-04 -0.3353 -0.10293 330s General.Electric_X1954 1.33e-04 0.2820 0.08929 330s General.Motors_X1935 1.01e-02 13.7309 0.54222 330s General.Motors_X1936 -2.58e-03 -4.6683 -0.13046 330s General.Motors_X1937 -1.27e-02 -34.0295 -1.50166 330s General.Motors_X1938 3.32e-04 0.5977 0.08631 330s General.Motors_X1939 -9.75e-03 -19.0765 -3.04769 330s General.Motors_X1940 -1.43e-03 -3.1463 -0.36306 330s General.Motors_X1941 2.64e-03 6.2893 0.69062 330s General.Motors_X1942 9.64e-03 20.9002 2.87877 330s General.Motors_X1943 6.76e-03 13.4247 2.04099 330s General.Motors_X1944 9.81e-03 17.7857 2.73663 330s General.Motors_X1945 3.63e-03 6.7092 0.77528 330s General.Motors_X1946 9.90e-03 20.4619 2.30180 330s General.Motors_X1947 1.39e-03 2.4966 0.36796 330s General.Motors_X1948 -5.01e-03 -8.1431 -1.53716 330s General.Motors_X1949 -1.11e-02 -18.4924 -3.89482 330s General.Motors_X1950 -6.34e-03 -10.6327 -2.26803 330s General.Motors_X1951 -1.18e-02 -27.0005 -4.03445 330s General.Motors_X1952 -8.16e-03 -17.6138 -3.62324 330s General.Motors_X1953 3.21e-03 6.5289 2.00435 330s General.Motors_X1954 1.15e-02 24.2859 7.68815 330s US.Steel_X1935 -8.99e-03 -12.2508 -0.48377 330s US.Steel_X1936 1.69e-02 30.5206 0.85291 330s US.Steel_X1937 1.67e-02 44.7615 1.97524 330s US.Steel_X1938 -2.80e-02 -50.5201 -7.29526 330s US.Steel_X1939 -4.55e-02 -89.1179 -14.23756 330s US.Steel_X1940 -3.80e-02 -83.6458 -9.65217 330s US.Steel_X1941 1.05e-02 25.0160 2.74698 330s US.Steel_X1942 5.26e-03 11.3993 1.57013 330s US.Steel_X1943 -1.17e-02 -23.2554 -3.53559 330s US.Steel_X1944 -2.37e-02 -42.9442 -6.60771 330s US.Steel_X1945 -2.55e-02 -47.1333 -5.44650 330s US.Steel_X1946 8.16e-03 16.8627 1.89692 330s US.Steel_X1947 1.19e-02 21.4365 3.15933 330s US.Steel_X1948 3.09e-02 50.2553 9.48663 330s US.Steel_X1949 2.57e-03 4.2789 0.90121 330s US.Steel_X1950 5.11e-03 8.5638 1.82670 330s US.Steel_X1951 3.40e-02 77.9272 11.64398 330s US.Steel_X1952 4.15e-02 89.6523 18.44196 330s US.Steel_X1953 2.55e-02 51.7535 15.88809 330s US.Steel_X1954 -2.77e-02 -58.5688 -18.54102 330s Westinghouse_X1935 -1.36e-03 -1.8578 -0.07336 330s Westinghouse_X1936 7.45e-03 13.4613 0.37618 330s Westinghouse_X1937 1.27e-02 33.9762 1.49930 330s Westinghouse_X1938 1.75e-02 31.5341 4.55362 330s Westinghouse_X1939 2.07e-02 40.4306 6.45923 330s Westinghouse_X1940 1.52e-02 33.4258 3.85712 330s Westinghouse_X1941 -2.46e-02 -58.4830 -6.42196 330s Westinghouse_X1942 -1.24e-02 -26.9329 -3.70970 330s Westinghouse_X1943 4.43e-03 8.7920 1.33667 330s Westinghouse_X1944 4.48e-03 8.1323 1.25129 330s Westinghouse_X1945 1.23e-02 22.8217 2.63717 330s Westinghouse_X1946 -8.75e-03 -18.0831 -2.03421 330s Westinghouse_X1947 -2.68e-02 -48.2250 -7.10746 330s Westinghouse_X1948 -8.50e-03 -13.8193 -2.60865 330s Westinghouse_X1949 1.32e-02 21.9947 4.63248 330s Westinghouse_X1950 1.72e-02 28.9161 6.16798 330s Westinghouse_X1951 -1.07e-02 -24.4289 -3.65019 330s Westinghouse_X1952 -2.47e-02 -53.3679 -10.97807 330s Westinghouse_X1953 -2.20e-02 -44.6732 -13.71448 330s Westinghouse_X1954 1.47e-02 31.0114 9.81721 330s Westinghouse_(Intercept) Westinghouse_value 330s Chrysler_X1935 -5.65e-03 -1.082 330s Chrysler_X1936 -8.16e-03 -4.208 330s Chrysler_X1937 4.83e-03 3.521 330s Chrysler_X1938 -3.50e-03 -1.964 330s Chrysler_X1939 1.14e-02 5.945 330s Chrysler_X1940 1.81e-03 1.141 330s Chrysler_X1941 8.76e-05 0.047 330s Chrysler_X1942 3.24e-03 1.819 330s Chrysler_X1943 1.11e-02 6.837 330s Chrysler_X1944 6.15e-03 3.852 330s Chrysler_X1945 -9.45e-03 -6.967 330s Chrysler_X1946 1.11e-02 8.413 330s Chrysler_X1947 5.99e-03 3.480 330s Chrysler_X1948 -4.92e-03 -3.262 330s Chrysler_X1949 6.06e-03 3.537 330s Chrysler_X1950 -1.18e-03 -0.751 330s Chrysler_X1951 -3.09e-02 -22.354 330s Chrysler_X1952 -3.21e-03 -2.777 330s Chrysler_X1953 1.51e-03 1.806 330s Chrysler_X1954 3.71e-03 4.412 330s General.Electric_X1935 6.17e-03 1.182 330s General.Electric_X1936 1.46e-01 75.280 330s General.Electric_X1937 1.39e-01 101.111 330s General.Electric_X1938 2.01e-01 112.591 330s General.Electric_X1939 2.47e-01 128.281 330s General.Electric_X1940 4.83e-02 30.346 330s General.Electric_X1941 -2.60e-01 -139.785 330s General.Electric_X1942 -1.19e-01 -66.920 330s General.Electric_X1943 1.59e-01 98.251 330s General.Electric_X1944 1.75e-01 109.867 330s General.Electric_X1945 4.29e-03 3.165 330s General.Electric_X1946 -3.73e-01 -283.963 330s General.Electric_X1947 -3.29e-01 -191.038 330s General.Electric_X1948 -2.58e-01 -170.961 330s General.Electric_X1949 9.22e-02 53.834 330s General.Electric_X1950 1.96e-01 124.738 330s General.Electric_X1951 -1.36e-02 -9.856 330s General.Electric_X1952 -4.93e-02 -42.572 330s General.Electric_X1953 -6.03e-02 -71.913 330s General.Electric_X1954 4.87e-02 57.863 330s General.Motors_X1935 -6.24e-02 -11.950 330s General.Motors_X1936 1.60e-02 8.253 330s General.Motors_X1937 7.87e-02 57.392 330s General.Motors_X1938 -2.05e-03 -1.151 330s General.Motors_X1939 6.03e-02 31.373 330s General.Motors_X1940 8.84e-03 5.558 330s General.Motors_X1941 -1.64e-02 -8.786 330s General.Motors_X1942 -5.97e-02 -33.488 330s General.Motors_X1943 -4.19e-02 -25.843 330s General.Motors_X1944 -6.07e-02 -38.047 330s General.Motors_X1945 -2.25e-02 -16.552 330s General.Motors_X1946 -6.13e-02 -46.597 330s General.Motors_X1947 -8.60e-03 -5.002 330s General.Motors_X1948 3.10e-02 20.539 330s General.Motors_X1949 6.87e-02 40.098 330s General.Motors_X1950 3.92e-02 24.930 330s General.Motors_X1951 7.30e-02 52.851 330s General.Motors_X1952 5.05e-02 43.640 330s General.Motors_X1953 -1.99e-02 -23.751 330s General.Motors_X1954 -7.11e-02 -84.506 330s US.Steel_X1935 5.67e-02 10.854 330s US.Steel_X1936 -1.06e-01 -54.933 330s US.Steel_X1937 -1.05e-01 -76.855 330s US.Steel_X1938 1.77e-01 99.039 330s US.Steel_X1939 2.87e-01 149.211 330s US.Steel_X1940 2.39e-01 150.428 330s US.Steel_X1941 -6.62e-02 -35.578 330s US.Steel_X1942 -3.31e-02 -18.595 330s US.Steel_X1943 7.38e-02 45.577 330s US.Steel_X1944 1.49e-01 93.525 330s US.Steel_X1945 1.61e-01 118.378 330s US.Steel_X1946 -5.14e-02 -39.094 330s US.Steel_X1947 -7.52e-02 -43.725 330s US.Steel_X1948 -1.95e-01 -129.046 330s US.Steel_X1949 -1.62e-02 -9.446 330s US.Steel_X1950 -3.22e-02 -20.441 330s US.Steel_X1951 -2.15e-01 -155.289 330s US.Steel_X1952 -2.62e-01 -226.135 330s US.Steel_X1953 -1.61e-01 -191.674 330s US.Steel_X1954 1.75e-01 207.479 330s Westinghouse_X1935 3.03e-02 5.802 330s Westinghouse_X1936 -1.66e-01 -85.410 330s Westinghouse_X1937 -2.82e-01 -205.647 330s Westinghouse_X1938 -3.89e-01 -217.923 330s Westinghouse_X1939 -4.59e-01 -238.632 330s Westinghouse_X1940 -3.37e-01 -211.909 330s Westinghouse_X1941 5.46e-01 293.206 330s Westinghouse_X1942 2.76e-01 154.873 330s Westinghouse_X1943 -9.84e-02 -60.742 330s Westinghouse_X1944 -9.96e-02 -62.433 330s Westinghouse_X1945 -2.74e-01 -202.055 330s Westinghouse_X1946 1.94e-01 147.788 330s Westinghouse_X1947 5.96e-01 346.758 330s Westinghouse_X1948 1.89e-01 125.092 330s Westinghouse_X1949 -2.93e-01 -171.160 330s Westinghouse_X1950 -3.83e-01 -243.315 330s Westinghouse_X1951 2.37e-01 171.608 330s Westinghouse_X1952 5.49e-01 474.533 330s Westinghouse_X1953 4.89e-01 583.245 330s Westinghouse_X1954 -3.26e-01 -387.265 330s Westinghouse_capital 330s Chrysler_X1935 -0.01017 330s Chrysler_X1936 -0.00652 330s Chrysler_X1937 0.03574 330s Chrysler_X1938 -0.06342 330s Chrysler_X1939 0.26872 330s Chrysler_X1940 0.04809 330s Chrysler_X1941 0.00317 330s Chrysler_X1942 0.19712 330s Chrysler_X1943 0.93491 330s Chrysler_X1944 0.56053 330s Chrysler_X1945 -0.87325 330s Chrysler_X1946 0.95137 330s Chrysler_X1947 0.66499 330s Chrysler_X1948 -0.64315 330s Chrysler_X1949 0.85922 330s Chrysler_X1950 -0.16155 330s Chrysler_X1951 -4.00575 330s Chrysler_X1952 -0.46760 330s Chrysler_X1953 0.26445 330s Chrysler_X1954 0.79226 330s General.Electric_X1935 0.01111 330s General.Electric_X1936 0.11671 330s General.Electric_X1937 1.02637 330s General.Electric_X1938 3.63650 330s General.Electric_X1939 5.79842 330s General.Electric_X1940 1.27948 330s General.Electric_X1941 -9.42136 330s General.Electric_X1942 -7.25009 330s General.Electric_X1943 13.43544 330s General.Electric_X1944 15.98834 330s General.Electric_X1945 0.39668 330s General.Electric_X1946 -32.11157 330s General.Electric_X1947 -36.50562 330s General.Electric_X1948 -33.71211 330s General.Electric_X1949 13.07588 330s General.Electric_X1950 26.84462 330s General.Electric_X1951 -1.76618 330s General.Electric_X1952 -7.16842 330s General.Electric_X1953 -10.53235 330s General.Electric_X1954 10.39092 330s General.Motors_X1935 -0.11232 330s General.Motors_X1936 0.01280 330s General.Motors_X1937 0.58258 330s General.Motors_X1938 -0.03717 330s General.Motors_X1939 1.41811 330s General.Motors_X1940 0.23434 330s General.Motors_X1941 -0.59216 330s General.Motors_X1942 -3.62807 330s General.Motors_X1943 -3.53399 330s General.Motors_X1944 -5.53672 330s General.Motors_X1945 -2.07456 330s General.Motors_X1946 -5.26934 330s General.Motors_X1947 -0.95586 330s General.Motors_X1948 4.05009 330s General.Motors_X1949 9.73943 330s General.Motors_X1950 5.36510 330s General.Motors_X1951 9.47046 330s General.Motors_X1952 7.34822 330s General.Motors_X1953 -3.47863 330s General.Motors_X1954 -15.17538 330s US.Steel_X1935 0.10202 330s US.Steel_X1936 -0.08517 330s US.Steel_X1937 -0.78015 330s US.Steel_X1938 3.19880 330s US.Steel_X1939 6.74450 330s US.Steel_X1940 6.34264 330s US.Steel_X1941 -2.39791 330s US.Steel_X1942 -2.01455 330s US.Steel_X1943 6.23245 330s US.Steel_X1944 13.61008 330s US.Steel_X1945 14.83734 330s US.Steel_X1946 -4.42093 330s US.Steel_X1947 -8.35538 330s US.Steel_X1948 -25.44676 330s US.Steel_X1949 -2.29427 330s US.Steel_X1950 -4.39917 330s US.Steel_X1951 -27.82678 330s US.Steel_X1952 -38.07729 330s US.Steel_X1953 -28.07253 330s US.Steel_X1954 37.25854 330s Westinghouse_X1935 0.05454 330s Westinghouse_X1936 -0.13242 330s Westinghouse_X1937 -2.08750 330s Westinghouse_X1938 -7.03855 330s Westinghouse_X1939 -10.78640 330s Westinghouse_X1940 -8.93489 330s Westinghouse_X1941 19.76178 330s Westinghouse_X1942 16.77886 330s Westinghouse_X1943 -8.30621 330s Westinghouse_X1944 -9.08553 330s Westinghouse_X1945 -25.32546 330s Westinghouse_X1946 16.71244 330s Westinghouse_X1947 66.26222 330s Westinghouse_X1948 24.66709 330s Westinghouse_X1949 -41.57334 330s Westinghouse_X1950 -52.36326 330s Westinghouse_X1951 30.75091 330s Westinghouse_X1952 79.90351 330s Westinghouse_X1953 85.42211 330s Westinghouse_X1954 -69.54427 330s Error in estfun.systemfit(greeneSurPooled) : 330s returning the estimation function for models with restrictions has not yet been Chrysler_(Intercept) Chrysler_value 330s 0 0 330s Chrysler_capital General.Electric_(Intercept) 330s 0 0 330s General.Electric_value General.Electric_capital 330s 0 0 330s General.Motors_(Intercept) General.Motors_value 330s 0 0 330s General.Motors_capital US.Steel_(Intercept) 330s 0 0 330s US.Steel_value US.Steel_capital 330s 0 0 330s Westinghouse_(Intercept) Westinghouse_value 330s 0 0 330s Westinghouse_capital 330s 0 330s [1] "Error in estfun.systemfit(greeneSurPooled) : \n returning the estimation function for models with restrictions has not yet been implemented.\n" 330s attr(,"class") 330s [1] "try-error" 330s attr(,"condition") 330s 330s > 330s > ## **************** bread ************************ 330s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 330s + print( bread( theilOls ) ) 330s + 330s + print( bread( theilSur ) ) 330s + 330s + print( bread( greeneOls ) ) 330s + 330s + print( try( bread( greeneOlsPooled ) ) ) 330s + 330s + print( bread( greeneSur ) ) 330s + 330s + print( try( bread( greeneSurPooled ) ) ) 330s + } 330s implemented. 330s General.Electric_(Intercept) 330s General.Electric_(Intercept) 50.64496 330s General.Electric_value -0.02323 330s General.Electric_capital -0.00888 330s Westinghouse_(Intercept) 0.00000 330s Westinghouse_value 0.00000 330s Westinghouse_capital 0.00000 330s General.Electric_value General.Electric_capital 330s General.Electric_(Intercept) -2.32e-02 -8.88e-03 330s General.Electric_value 1.25e-05 -2.43e-06 330s General.Electric_capital -2.43e-06 3.40e-05 330s Westinghouse_(Intercept) 0.00e+00 0.00e+00 330s Westinghouse_value 0.00e+00 0.00e+00 330s Westinghouse_capital 0.00e+00 0.00e+00 330s Westinghouse_(Intercept) Westinghouse_value 330s General.Electric_(Intercept) 0.0000 0.00e+00 330s General.Electric_value 0.0000 0.00e+00 330s General.Electric_capital 0.0000 0.00e+00 330s Westinghouse_(Intercept) 24.6366 -4.20e-02 330s Westinghouse_value -0.0420 9.46e-05 330s Westinghouse_capital 0.0648 -2.51e-04 330s Westinghouse_capital 330s General.Electric_(Intercept) 0.000000 330s General.Electric_value 0.000000 330s General.Electric_capital 0.000000 330s Westinghouse_(Intercept) 0.064774 330s Westinghouse_value -0.000251 330s Westinghouse_capital 0.001207 330s General.Electric_(Intercept) General.Electric_value 330s [1,] 29230.95 -13.17064 330s [2,] -13.17 0.00707 330s [3,] -5.85 -0.00136 330s [4,] 5078.50 -2.10754 330s [5,] -9.05 0.00480 330s [6,] 15.70 -0.01299 330s General.Electric_capital Westinghouse_(Intercept) Westinghouse_value 330s [1,] -5.849668 5078.50 -9.047719 330s [2,] -0.001362 -2.11 0.004800 330s [3,] 0.021226 -1.58 -0.000675 330s [4,] -1.584851 1935.63 -3.200900 330s [5,] -0.000675 -3.20 0.007194 330s [6,] 0.023793 4.54 -0.018984 330s Westinghouse_capital 330s [1,] 15.7006 330s [2,] -0.0130 330s [3,] 0.0238 330s [4,] 4.5447 330s [5,] -0.0190 330s [6,] 0.0957 330s Chrysler_(Intercept) Chrysler_value 330s Chrysler_(Intercept) 103.4623 -0.144448 330s Chrysler_value -0.1444 0.000226 330s Chrysler_capital 0.0138 -0.000102 330s General.Electric_(Intercept) 0.0000 0.000000 330s General.Electric_value 0.0000 0.000000 330s General.Electric_capital 0.0000 0.000000 330s General.Motors_(Intercept) 0.0000 0.000000 330s General.Motors_value 0.0000 0.000000 330s General.Motors_capital 0.0000 0.000000 330s US.Steel_(Intercept) 0.0000 0.000000 330s US.Steel_value 0.0000 0.000000 330s US.Steel_capital 0.0000 0.000000 330s Westinghouse_(Intercept) 0.0000 0.000000 330s Westinghouse_value 0.0000 0.000000 330s Westinghouse_capital 0.0000 0.000000 330s Chrysler_capital General.Electric_(Intercept) 330s Chrysler_(Intercept) 0.013776 0.0000 330s Chrysler_value -0.000102 0.0000 330s Chrysler_capital 0.000471 0.0000 330s General.Electric_(Intercept) 0.000000 126.6124 330s General.Electric_value 0.000000 -0.0581 330s General.Electric_capital 0.000000 -0.0222 330s General.Motors_(Intercept) 0.000000 0.0000 330s General.Motors_value 0.000000 0.0000 330s General.Motors_capital 0.000000 0.0000 330s US.Steel_(Intercept) 0.000000Error in bread.systemfit(greeneOlsPooled) : 330s returning the 'bread' for models with restrictions has not yet been implemented. 330s Error in bread.systemfit(greeneSurPooled) : 330s returning the 'bread' for models with restrictions has not yet been implemented. 330s 0.0000 330s US.Steel_value 0.000000 0.0000 330s US.Steel_capital 0.000000 0.0000 330s Westinghouse_(Intercept) 0.000000 0.0000 330s Westinghouse_value 0.000000 0.0000 330s Westinghouse_capital 0.000000 0.0000 330s General.Electric_value General.Electric_capital 330s Chrysler_(Intercept) 0.00e+00 0.00e+00 330s Chrysler_value 0.00e+00 0.00e+00 330s Chrysler_capital 0.00e+00 0.00e+00 330s General.Electric_(Intercept) -5.81e-02 -2.22e-02 330s General.Electric_value 3.12e-05 -6.09e-06 330s General.Electric_capital -6.09e-06 8.50e-05 330s General.Motors_(Intercept) 0.00e+00 0.00e+00 330s General.Motors_value 0.00e+00 0.00e+00 330s General.Motors_capital 0.00e+00 0.00e+00 330s US.Steel_(Intercept) 0.00e+00 0.00e+00 330s US.Steel_value 0.00e+00 0.00e+00 330s US.Steel_capital 0.00e+00 0.00e+00 330s Westinghouse_(Intercept) 0.00e+00 0.00e+00 330s Westinghouse_value 0.00e+00 0.00e+00 330s Westinghouse_capital 0.00e+00 0.00e+00 330s General.Motors_(Intercept) General.Motors_value 330s Chrysler_(Intercept) 0.0000 0.00e+00 330s Chrysler_value 0.0000 0.00e+00 330s Chrysler_capital 0.0000 0.00e+00 330s General.Electric_(Intercept) 0.0000 0.00e+00 330s General.Electric_value 0.0000 0.00e+00 330s General.Electric_capital 0.0000 0.00e+00 330s General.Motors_(Intercept) 132.9858 -3.11e-02 330s General.Motors_value -0.0311 7.92e-06 330s General.Motors_capital 0.0108 -4.93e-06 330s US.Steel_(Intercept) 0.0000 0.00e+00 330s US.Steel_value 0.0000 0.00e+00 330s US.Steel_capital 0.0000 0.00e+00 330s Westinghouse_(Intercept) 0.0000 0.00e+00 330s Westinghouse_value 0.0000 0.00e+00 330s Westinghouse_capital 0.0000 0.00e+00 330s General.Motors_capital US.Steel_(Intercept) 330s Chrysler_(Intercept) 0.00e+00 0.0000 330s Chrysler_value 0.00e+00 0.0000 330s Chrysler_capital 0.00e+00 0.0000 330s General.Electric_(Intercept) 0.00e+00 0.0000 330s General.Electric_value 0.00e+00 0.0000 330s General.Electric_capital 0.00e+00 0.0000 330s General.Motors_(Intercept) 1.08e-02 0.0000 330s General.Motors_value -4.93e-06 0.0000 330s General.Motors_capital 1.63e-05 0.0000 330s US.Steel_(Intercept) 0.00e+00 235.6498 330s US.Steel_value 0.00e+00 -0.1119 330s US.Steel_capital 0.00e+00 -0.0336 330s Westinghouse_(Intercept) 0.00e+00 0.0000 330s Westinghouse_value 0.00e+00 0.0000 330s Westinghouse_capital 0.00e+00 0.0000 330s US.Steel_value US.Steel_capital 330s Chrysler_(Intercept) 0.00e+00 0.00e+00 330s Chrysler_value 0.00e+00 0.00e+00 330s Chrysler_capital 0.00e+00 0.00e+00 330s General.Electric_(Intercept) 0.00e+00 0.00e+00 330s General.Electric_value 0.00e+00 0.00e+00 330s General.Electric_capital 0.00e+00 0.00e+00 330s General.Motors_(Intercept) 0.00e+00 0.00e+00 330s General.Motors_value 0.00e+00 0.00e+00 330s General.Motors_capital 0.00e+00 0.00e+00 330s US.Steel_(Intercept) -1.12e-01 -3.36e-02 330s US.Steel_value 5.95e-05 -1.79e-05 330s US.Steel_capital -1.79e-05 2.30e-04 330s Westinghouse_(Intercept) 0.00e+00 0.00e+00 330s Westinghouse_value 0.00e+00 0.00e+00 330s Westinghouse_capital 0.00e+00 0.00e+00 330s Westinghouse_(Intercept) Westinghouse_value 330s Chrysler_(Intercept) 0.000 0.000000 330s Chrysler_value 0.000 0.000000 330s Chrysler_capital 0.000 0.000000 330s General.Electric_(Intercept) 0.000 0.000000 330s General.Electric_value 0.000 0.000000 330s General.Electric_capital 0.000 0.000000 330s General.Motors_(Intercept) 0.000 0.000000 330s General.Motors_value 0.000 0.000000 330s General.Motors_capital 0.000 0.000000 330s US.Steel_(Intercept) 0.000 0.000000 330s US.Steel_value 0.000 0.000000 330s US.Steel_capital 0.000 0.000000 330s Westinghouse_(Intercept) 61.592 -0.105021 330s Westinghouse_value -0.105 0.000237 330s Westinghouse_capital 0.162 -0.000626 330s Westinghouse_capital 330s Chrysler_(Intercept) 0.000000 330s Chrysler_value 0.000000 330s Chrysler_capital 0.000000 330s General.Electric_(Intercept) 0.000000 330s General.Electric_value 0.000000 330s General.Electric_capital 0.000000 330s General.Motors_(Intercept) 0.000000 330s General.Motors_value 0.000000 330s General.Motors_capital 0.000000 330s US.Steel_(Intercept) 0.000000 330s US.Steel_value 0.000000 330s US.Steel_capital 0.000000 330s Westinghouse_(Intercept) 0.161935 330s Westinghouse_value -0.000626 330s Westinghouse_capital 0.003017 330s [1] "Error in bread.systemfit(greeneOlsPooled) : \n returning the 'bread' for models with restrictions has not yet been implemented.\n" 330s attr(,"class") 330s [1] "try-error" 330s attr(,"condition") 330s 330s Chrysler_(Intercept) Chrysler_value Chrysler_capital 330s [1,] 1.33e+04 -1.82e+01 9.57e-01 330s [2,] -1.82e+01 2.86e-02 -1.31e-02 330s [3,] 9.57e-01 -1.31e-02 6.69e-02 330s [4,] -2.94e+03 3.74e+00 1.98e+00 330s [5,] 1.28e+00 -1.86e-03 1.28e-04 330s [6,] 8.80e-01 -2.96e-04 -5.56e-03 330s [7,] -1.56e+04 1.91e+01 7.79e+00 330s [8,] 3.28e+00 -4.91e-03 1.03e-03 330s [9,] -8.18e-02 3.42e-03 -1.89e-02 330s [10,] 1.80e+04 -1.87e+01 -2.45e+01 330s [11,] -7.46e+00 1.13e-02 -3.26e-03 330s [12,] -4.03e+00 -1.22e-02 1.03e-01 330s [13,] -3.04e+01 3.03e-01 -9.35e-01 330s [14,] 1.14e-01 -3.70e-04 1.18e-03 330s [15,] 2.42e-01 -6.41e-04 1.67e-03 330s General.Electric_(Intercept) General.Electric_value 330s [1,] -2936.42 1.28e+00 330s [2,] 3.74 -1.86e-03 330s [3,] 1.98 1.28e-04 330s [4,] 65119.82 -2.85e+01 330s [5,] -28.51 1.50e-02 330s [6,] -16.15 -1.70e-03 330s [7,] 57134.02 -2.61e+01 330s [8,] -11.96 6.35e-03 330s [9,] -3.52 -2.27e-03 330s [10,] 64429.20 -3.04e+01 330s [11,] -22.01 1.35e-02 330s [12,] -55.05 1.23e-02 330s [13,] 10286.79 -4.02e+00 330s [14,] -17.00 8.74e-03 330s [15,] 23.38 -2.16e-02 330s General.Electric_capital General.Motors_(Intercept) General.Motors_value 330s [1,] 8.80e-01 -1.56e+04 3.28e+00 330s [2,] -2.96e-04 1.91e+01 -4.91e-03 330s [3,] -5.56e-03 7.79e+00 1.03e-03 330s [4,] -1.61e+01 5.71e+04 -1.20e+01 330s [5,] -1.70e-03 -2.61e+01 6.35e-03 330s [6,] 4.86e-02 -8.74e+00 -9.49e-04 330s [7,] -8.74e+00 8.00e+05 -1.84e+02 330s [8,] -9.49e-04 -1.84e+02 4.68e-02 330s [9,] 1.98e-02 5.32e+01 -2.83e-02 330s [10,] -2.30e+00 -1.75e+05 3.73e+01 330s [11,] -1.07e-02 8.02e+01 -2.06e-02 330s [12,] 7.77e-02 2.01e+01 1.09e-02 330s [13,] -4.02e+00 1.10e+04 -2.33e+00 330s [14,] 1.04e-04 -2.06e+01 5.10e-03 330s [15,] 4.61e-02 3.98e+01 -1.28e-02 330s General.Motors_capital US.Steel_(Intercept) US.Steel_value 330s [1,] -0.08183 1.80e+04 -7.46e+00 330s [2,] 0.00342 -1.87e+01 1.13e-02 330s [3,] -0.01889 -2.45e+01 -3.26e-03 330s [4,] -3.51957 6.44e+04 -2.20e+01 330s [5,] -0.00227 -3.04e+01 1.35e-02 330s [6,] 0.01982 -2.30e+00 -1.07e-02 330s [7,] 53.22544 -1.75e+05 8.02e+01 330s [8,] -0.02835 3.73e+01 -2.06e-02 330s [9,] 0.10737 3.74e+00 1.39e-02 330s [10,] 3.74276 1.25e+06 -5.65e+02 330s [11,] 0.01386 -5.65e+02 3.00e-01 330s [12,] -0.10360 -3.12e+02 -9.01e-02 330s [13,] -0.48733 2.74e+04 -8.35e+00 330s [14,] -0.00238 -5.09e+01 2.23e-02 330s [15,] 0.02432 1.10e+02 -7.74e-02 330s US.Steel_capital Westinghouse_(Intercept) Westinghouse_value 330s [1,] -4.0281 -30.387 1.14e-01 330s [2,] -0.0122 0.303 -3.70e-04 330s [3,] 0.1031 -0.935 1.18e-03 330s [4,] -55.0482 10286.790 -1.70e+01 330s [5,] 0.0123 -4.016 8.74e-03 330s [6,] 0.0777 -4.021 1.04e-04 330s [7,] 20.0945 11026.166 -2.06e+01 330s [8,] 0.0109 -2.326 5.10e-03 330s [9,] -0.1036 -0.487 -2.38e-03 330s [10,] -311.9830 27440.848 -5.09e+01 330s [11,] -0.0901 -8.348 2.23e-02 330s [12,] 1.6331 -27.510 2.29e-02 330s [13,] -27.5101 3917.263 -5.99e+00 330s [14,] 0.0229 -5.992 1.29e-02 330s [15,] 0.1422 6.376 -3.12e-02 330s Westinghouse_capital 330s [1,] 2.42e-01 330s [2,] -6.41e-04 330s [3,] 1.67e-03 330s [4,] 2.34e+01 330s [5,] -2.16e-02 330s [6,] 4.61e-02 330s [7,] 3.98e+01 330s [8,] -1.28e-02 330s [9,] 2.43e-02 330s [10,] 1.10e+02 330s [11,] -7.74e-02 330s [12,] 1.42e-01 330s [13,] 6.38e+00 330s [14,] -3.12e-02 330s [15,] 1.70e-01 330s [1] "Error in bread.systemfit(greeneSurPooled) : \n returning the 'bread' for models with restrictions has not yet been implemented.\n" 330s attr(,"class") 330s [1] "try-error" 330s attr(,"condition") 330s 330s > 330s BEGIN TEST test_sur.R 330s 330s R version 4.3.2 (2023-10-31) -- "Eye Holes" 330s Copyright (C) 2023 The R Foundation for Statistical Computing 330s Platform: x86_64-pc-linux-gnu (64-bit) 330s 330s R is free software and comes with ABSOLUTELY NO WARRANTY. 330s You are welcome to redistribute it under certain conditions. 330s Type 'license()' or 'licence()' for distribution details. 330s 330s R is a collaborative project with many contributors. 330s Type 'contributors()' for more information and 330s 'citation()' on how to cite R or R packages in publications. 330s 330s Type 'demo()' for some demos, 'help()' for on-line help, or 330s 'help.start()' for an HTML browser interface to help. 330s Type 'q()' to quit R. 330s 330s > library( systemfit ) 330s Loading required package: Matrix 331s Loading required package: car 331s Loading required package: carData 331s Loading required package: lmtest 331s Loading required package: zoo 331s 331s Attaching package: ‘zoo’ 331s 331s The following objects are masked from ‘package:base’: 331s 331s as.Date, as.Date.numeric 331s 331s 331s Please cite the 'systemfit' package as: 331s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 331s 331s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 331s https://r-forge.r-project.org/projects/systemfit/ 331s > options( digits = 3 ) 331s > 331s > data( "Kmenta" ) 331s > useMatrix <- FALSE 331s > 331s > demand <- consump ~ price + income 331s > supply <- consump ~ price + farmPrice + trend 331s > system <- list( demand = demand, supply = supply ) 331s > restrm <- matrix(0,1,7) # restriction matrix "R" 331s > restrm[1,3] <- 1 331s > restrm[1,7] <- -1 331s > restrict <- "demand_income - supply_trend = 0" 331s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 331s > restr2m[1,3] <- 1 331s > restr2m[1,7] <- -1 331s > restr2m[2,2] <- -1 331s > restr2m[2,5] <- 1 331s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 331s > restrict2 <- c( "demand_income - supply_trend = 0", 331s + "- demand_price + supply_price = 0.5" ) 331s > restrict2i <- c( "demand_income - supply_trend = 0", 331s + "- demand_price + supply_income = 0.5" ) 331s > tc <- matrix(0,7,6) 331s > tc[1,1] <- 1 331s > tc[2,2] <- 1 331s > tc[3,3] <- 1 331s > tc[4,4] <- 1 331s > tc[5,5] <- 1 331s > tc[6,6] <- 1 331s > tc[7,3] <- 1 331s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 331s > restr3m[1,2] <- -1 331s > restr3m[1,5] <- 1 331s > restr3q <- c( 0.5 ) # restriction vector "q" 2 331s > restrict3 <- "- C2 + C5 = 0.5" 331s > 331s > # the standard equations do not converge and lead to a singular weighting matrix 331s > # both in R and in EViews, since both equations have the same endogenous variable 331s > supply2 <- price ~ income + farmPrice + trend 331s > system2 <- list( demand = demand, supply = supply2 ) 331s > 331s > 331s > ## *************** SUR estimation ************************ 331s > fitsur1 <- systemfit( system, "SUR", data = Kmenta, useMatrix = useMatrix ) 331s > print( summary( fitsur1 ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 170 0.879 0.683 0.789 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 65.7 3.86 1.97 0.755 0.726 331s supply 20 16 104.1 6.50 2.55 0.612 0.539 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.73 4.14 331s supply 4.14 5.78 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.86 4.92 331s supply 4.92 6.50 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.982 331s supply 0.982 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 99.3329 7.5145 13.22 2.3e-10 *** 331s price -0.2755 0.0885 -3.11 0.0063 ** 331s income 0.2986 0.0419 7.12 1.7e-06 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.966 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 65.683 MSE: 3.864 Root MSE: 1.966 331s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 61.9662 11.0808 5.59 4.0e-05 *** 331s price 0.1469 0.0944 1.56 0.13941 331s farmPrice 0.2140 0.0399 5.37 6.3e-05 *** 331s trend 0.3393 0.0679 5.00 0.00013 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.55 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 104.058 MSE: 6.504 Root MSE: 2.55 331s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 331s 331s > nobs( fitsur1 ) 331s [1] 40 331s > 331s > ## ********************* SUR (EViews-like) ***************** 331s > fitsur1e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 331s + useMatrix = useMatrix ) 331s > print( summary( fitsur1e, useDfSys = TRUE ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 170 0.598 0.683 0.748 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.2 3.89 1.97 0.753 0.724 331s supply 20 16 103.5 6.47 2.54 0.614 0.541 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.17 3.41 331s supply 3.41 4.63 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.31 4.07 331s supply 4.07 5.18 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.982 331s supply 0.982 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 99.2757 6.9280 14.33 8.9e-16 *** 331s price -0.2713 0.0816 -3.33 0.0022 ** 331s income 0.2949 0.0387 7.63 8.9e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.973 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.186 MSE: 3.893 Root MSE: 1.973 331s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 62.2942 9.9110 6.29 4.2e-07 *** 331s price 0.1461 0.0845 1.73 0.093 . 331s farmPrice 0.2121 0.0357 5.95 1.1e-06 *** 331s trend 0.3322 0.0607 5.47 4.6e-06 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.544 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 103.55 MSE: 6.472 Root MSE: 2.544 331s Multiple R-Squared: 0.614 Adjusted R-Squared: 0.541 331s 331s > nobs( fitsur1e ) 331s [1] 40 331s > 331s > ## ********************* SUR (methodResidCov="Theil") ***************** 331s > fitsur1r2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 331s + useMatrix = useMatrix ) 331s > print( summary( fitsur1r2 ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 172 -0.896 0.679 1.01 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.8 3.93 1.98 0.751 0.722 331s supply 20 16 105.3 6.58 2.57 0.607 0.534 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.73 4.28 331s supply 4.28 5.78 331s 331s warning: this covariance matrix is NOT positive semidefinit! 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.93 5.17 331s supply 5.17 6.58 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.984 331s supply 0.984 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 99.2120 7.5127 13.21 2.3e-10 *** 331s price -0.2667 0.0877 -3.04 0.0074 ** 331s income 0.2908 0.0406 7.16 1.6e-06 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.982 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.802 MSE: 3.93 Root MSE: 1.982 331s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 63.0768 10.9735 5.75 3.0e-05 *** 331s price 0.1439 0.0943 1.52 0.15 331s farmPrice 0.2064 0.0384 5.37 6.2e-05 *** 331s trend 0.3325 0.0640 5.19 8.9e-05 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.566 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 105.322 MSE: 6.583 Root MSE: 2.566 331s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.534 331s 331s > 331s > ## *************** SUR (methodResidCov="Theil", useDfSys = TRUE ) *************** 331s > fitsur1e2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 331s + x = TRUE, useMatrix = useMatrix ) 331s > print( summary( fitsur1e2, useDfSys = TRUE ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 172 -0.896 0.679 1.01 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.8 3.93 1.98 0.751 0.722 331s supply 20 16 105.3 6.58 2.57 0.607 0.534 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.73 4.28 331s supply 4.28 5.78 331s 331s warning: this covariance matrix is NOT positive semidefinit! 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.93 5.17 331s supply 5.17 6.58 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.984 331s supply 0.984 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 99.2120 7.5127 13.21 1.0e-14 *** 331s price -0.2667 0.0877 -3.04 0.0046 ** 331s income 0.2908 0.0406 7.16 3.3e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.982 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.802 MSE: 3.93 Root MSE: 1.982 331s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 63.0768 10.9735 5.75 2.0e-06 *** 331s price 0.1439 0.0943 1.52 0.14 331s farmPrice 0.2064 0.0384 5.37 6.1e-06 *** 331s trend 0.3325 0.0640 5.19 1.0e-05 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.566 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 105.322 MSE: 6.583 Root MSE: 2.566 331s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.534 331s 331s > 331s > ## ********************* SUR (methodResidCov="max") ***************** 331s > fitsur1r3 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "max", 331s + useMatrix = useMatrix ) 331s > print( summary( fitsur1r3 ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 172 -0.735 0.68 0.957 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.7 3.92 1.98 0.751 0.722 331s supply 20 16 105.2 6.57 2.56 0.608 0.534 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.73 4.26 331s supply 4.26 5.78 331s 331s warning: this covariance matrix is NOT positive semidefinit! 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.92 5.15 331s supply 5.15 6.57 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.984 331s supply 0.984 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 99.2250 7.5129 13.21 2.3e-10 *** 331s price -0.2677 0.0878 -3.05 0.0073 ** 331s income 0.2916 0.0408 7.15 1.6e-06 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.98 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.671 MSE: 3.922 Root MSE: 1.98 331s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 62.9575 10.9850 5.73 3.1e-05 *** 331s price 0.1442 0.0944 1.53 0.15 331s farmPrice 0.2072 0.0386 5.37 6.2e-05 *** 331s trend 0.3333 0.0644 5.18 9.2e-05 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.564 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 105.187 MSE: 6.574 Root MSE: 2.564 331s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 331s 331s > 331s > ## *************** WSUR estimation ************************ 331s > fitsur1w <- systemfit( system, "SUR", data = Kmenta, residCovWeighted = TRUE, 331s + useMatrix = useMatrix ) 331s > summary( fitsur1w ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 170 0.879 0.683 0.789 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 65.7 3.86 1.97 0.755 0.726 331s supply 20 16 104.1 6.50 2.55 0.612 0.539 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.73 4.14 331s supply 4.14 5.78 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.86 4.92 331s supply 4.92 6.50 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.982 331s supply 0.982 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 99.3329 7.5145 13.22 2.3e-10 *** 331s price -0.2755 0.0885 -3.11 0.0063 ** 331s income 0.2986 0.0419 7.12 1.7e-06 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.966 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 65.683 MSE: 3.864 Root MSE: 1.966 331s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 61.9662 11.0808 5.59 4.0e-05 *** 331s price 0.1469 0.0944 1.56 0.13941 331s farmPrice 0.2140 0.0399 5.37 6.3e-05 *** 331s trend 0.3393 0.0679 5.00 0.00013 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.55 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 104.058 MSE: 6.504 Root MSE: 2.55 331s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 331s 331s > nobs( fitsur1w ) 331s [1] 40 331s > 331s > ## *************** WSUR (methodResidCov="Theil", useDfSys = TRUE ) *************** 331s > fitsur1we2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 331s + residCovWeighted = TRUE, useMatrix = useMatrix ) 331s > summary( fitsur1we2, useDfSys = TRUE ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 172 -0.896 0.679 1.01 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.8 3.93 1.98 0.751 0.722 331s supply 20 16 105.3 6.58 2.57 0.607 0.534 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.73 4.28 331s supply 4.28 5.78 331s 331s warning: this covariance matrix is NOT positive semidefinit! 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.93 5.17 331s supply 5.17 6.58 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.984 331s supply 0.984 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 99.2120 7.5127 13.21 1.0e-14 *** 331s price -0.2667 0.0877 -3.04 0.0046 ** 331s income 0.2908 0.0406 7.16 3.3e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.982 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.802 MSE: 3.93 Root MSE: 1.982 331s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 63.0768 10.9735 5.75 2.0e-06 *** 331s price 0.1439 0.0943 1.52 0.14 331s farmPrice 0.2064 0.0384 5.37 6.1e-06 *** 331s trend 0.3325 0.0640 5.19 1.0e-05 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.566 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 105.322 MSE: 6.583 Root MSE: 2.566 331s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.534 331s 331s > 331s > 331s > ## *************** SUR with cross-equation restriction ************** 331s > fitsur2 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restrm, 331s + useMatrix = useMatrix ) 331s > print( summary( fitsur2 ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 34 179 0.933 0.665 0.753 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 71.6 4.21 2.05 0.733 0.702 331s supply 20 16 107.8 6.74 2.60 0.598 0.523 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.78 4.47 331s supply 4.47 5.94 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 4.21 5.24 331s supply 5.24 6.74 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.983 331s supply 0.983 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 98.8408 7.5581 13.08 8.0e-15 *** 331s price -0.2398 0.0860 -2.79 0.0086 ** 331s income 0.2670 0.0368 7.25 2.2e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.052 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 71.597 MSE: 4.212 Root MSE: 2.052 331s Multiple R-Squared: 0.733 Adjusted R-Squared: 0.702 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 67.4283 10.6647 6.32 3.3e-07 *** 331s price 0.1332 0.0953 1.40 0.17 331s farmPrice 0.1795 0.0337 5.33 6.3e-06 *** 331s trend 0.2670 0.0368 7.25 2.2e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.596 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 107.806 MSE: 6.738 Root MSE: 2.596 331s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 331s 331s > nobs( fitsur2 ) 331s [1] 40 331s > # the same with symbolically specified restrictions 331s > fitsur2Sym <- systemfit( system, "SUR", data = Kmenta, 331s + restrict.matrix = restrict, useMatrix = useMatrix ) 331s > all.equal( fitsur2, fitsur2Sym ) 331s [1] "Component “call”: target, current do not match when deparsed" 331s > nobs( fitsur2Sym ) 331s [1] 40 331s > 331s > ## *************** SUR with cross-equation restriction (EViews-like) ** 331s > fitsur2e <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restrm, 331s + methodResidCov = "noDfCor", x = TRUE, 331s + useMatrix = useMatrix ) 331s > print( summary( fitsur2e ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 34 180 0.62 0.663 0.707 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 72.6 4.27 2.07 0.729 0.697 331s supply 20 16 107.9 6.75 2.60 0.597 0.522 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.21 3.68 331s supply 3.68 4.75 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.63 4.35 331s supply 4.35 5.40 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.984 331s supply 0.984 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 98.7799 6.9687 14.17 8.9e-16 *** 331s price -0.2354 0.0795 -2.96 0.0056 ** 331s income 0.2631 0.0344 7.66 6.7e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.066 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 72.577 MSE: 4.269 Root MSE: 2.066 331s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 67.6039 9.5712 7.06 3.7e-08 *** 331s price 0.1328 0.0853 1.56 0.13 331s farmPrice 0.1785 0.0305 5.85 1.3e-06 *** 331s trend 0.2631 0.0344 7.66 6.7e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.597 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 107.917 MSE: 6.745 Root MSE: 2.597 331s Multiple R-Squared: 0.597 Adjusted R-Squared: 0.522 331s 331s > 331s > ## *************** WSUR with cross-equation restriction (EViews-like) ** 331s > fitsur2we <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restrm, 331s + methodResidCov = "noDfCor", residCovWeighted = TRUE, 331s + x = TRUE, useMatrix = useMatrix ) 331s > summary( fitsur2we ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 34 182 0.609 0.661 0.711 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 73 4.29 2.07 0.728 0.696 331s supply 20 16 109 6.79 2.61 0.595 0.519 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.19 3.69 331s supply 3.69 4.78 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.65 4.38 331s supply 4.38 5.43 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.985 331s supply 0.985 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 98.7542 6.9468 14.22 6.7e-16 *** 331s price -0.2335 0.0790 -2.96 0.0056 ** 331s income 0.2614 0.0338 7.74 5.3e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.072 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 73.009 MSE: 4.295 Root MSE: 2.072 331s Multiple R-Squared: 0.728 Adjusted R-Squared: 0.696 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 67.8882 9.5640 7.10 3.4e-08 *** 331s price 0.1320 0.0855 1.55 0.13 331s farmPrice 0.1765 0.0301 5.86 1.3e-06 *** 331s trend 0.2614 0.0338 7.74 5.3e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.606 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 108.634 MSE: 6.79 Root MSE: 2.606 331s Multiple R-Squared: 0.595 Adjusted R-Squared: 0.519 331s 331s > 331s > 331s > ## *************** SUR with restriction via restrict.regMat ******************* 331s > fitsur3 <- systemfit( system, "SUR", data = Kmenta, restrict.regMat = tc, 331s + useMatrix = useMatrix ) 331s > print( summary( fitsur3 ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 34 179 0.933 0.665 0.753 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 71.6 4.21 2.05 0.733 0.702 331s supply 20 16 107.8 6.74 2.60 0.598 0.523 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.78 4.47 331s supply 4.47 5.94 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 4.21 5.24 331s supply 5.24 6.74 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.983 331s supply 0.983 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 98.8408 7.5581 13.08 8.0e-15 *** 331s price -0.2398 0.0860 -2.79 0.0086 ** 331s income 0.2670 0.0368 7.25 2.2e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.052 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 71.597 MSE: 4.212 Root MSE: 2.052 331s Multiple R-Squared: 0.733 Adjusted R-Squared: 0.702 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 67.4283 10.6647 6.32 3.3e-07 *** 331s price 0.1332 0.0953 1.40 0.17 331s farmPrice 0.1795 0.0337 5.33 6.3e-06 *** 331s trend 0.2670 0.0368 7.25 2.2e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.596 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 107.806 MSE: 6.738 Root MSE: 2.596 331s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 331s 331s > nobs( fitsur3 ) 331s [1] 40 331s > 331s > ## *************** SUR with restriction via restrict.regMat (EViews-like) ************** 331s > fitsur3e <- systemfit( system, "SUR", data = Kmenta, restrict.regMat = tc, 331s + methodResidCov = "noDfCor", x = TRUE, 331s + useMatrix = useMatrix ) 331s > print( summary( fitsur3e ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 34 180 0.62 0.663 0.707 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 72.6 4.27 2.07 0.729 0.697 331s supply 20 16 107.9 6.75 2.60 0.597 0.522 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.21 3.68 331s supply 3.68 4.75 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.63 4.35 331s supply 4.35 5.40 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.984 331s supply 0.984 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 98.7799 6.9687 14.17 8.9e-16 *** 331s price -0.2354 0.0795 -2.96 0.0056 ** 331s income 0.2631 0.0344 7.66 6.7e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.066 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 72.577 MSE: 4.269 Root MSE: 2.066 331s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 67.6039 9.5712 7.06 3.7e-08 *** 331s price 0.1328 0.0853 1.56 0.13 331s farmPrice 0.1785 0.0305 5.85 1.3e-06 *** 331s trend 0.2631 0.0344 7.66 6.7e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.597 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 107.917 MSE: 6.745 Root MSE: 2.597 331s Multiple R-Squared: 0.597 Adjusted R-Squared: 0.522 331s 331s > 331s > ## *************** WSUR with restriction via restrict.regMat ******************* 331s > fitsur3w <- systemfit( system, "SUR", data = Kmenta, restrict.regMat = tc, 331s + residCovWeighted = TRUE, x = TRUE, useMatrix = useMatrix ) 331s > summary( fitsur3w ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 34 181 0.919 0.663 0.757 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 72 4.24 2.06 0.731 0.700 331s supply 20 16 109 6.79 2.60 0.595 0.519 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.75 4.48 331s supply 4.48 5.98 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 4.24 5.28 331s supply 5.28 6.79 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.984 331s supply 0.984 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 98.8139 7.5317 13.12 7.3e-15 *** 331s price -0.2378 0.0854 -2.79 0.0087 ** 331s income 0.2653 0.0361 7.34 1.7e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.058 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 72.023 MSE: 4.237 Root MSE: 2.058 331s Multiple R-Squared: 0.731 Adjusted R-Squared: 0.7 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 67.7366 10.6556 6.36 3.0e-07 *** 331s price 0.1324 0.0955 1.39 0.17 331s farmPrice 0.1774 0.0332 5.35 6.1e-06 *** 331s trend 0.2653 0.0361 7.34 1.7e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.605 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 108.579 MSE: 6.786 Root MSE: 2.605 331s Multiple R-Squared: 0.595 Adjusted R-Squared: 0.519 331s 331s > 331s > 331s > ## *************** SUR with 2 restrictions *************************** 331s > fitsur4 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr2m, 331s + restrict.rhs = restr2q, useMatrix = useMatrix ) 331s > print( summary( fitsur4 ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 35 165 1.76 0.691 0.69 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 64 3.76 1.94 0.761 0.733 331s supply 20 16 101 6.34 2.52 0.622 0.551 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.76 4.46 331s supply 4.46 5.99 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.76 4.70 331s supply 4.70 6.34 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.962 331s supply 0.962 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 96.8275 7.4665 12.97 6.2e-15 *** 331s price -0.2798 0.0840 -3.33 0.002 ** 331s income 0.3286 0.0206 15.93 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.94 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 63.987 MSE: 3.764 Root MSE: 1.94 331s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 52.9386 7.6655 6.91 5.1e-08 *** 331s price 0.2202 0.0840 2.62 0.013 * 331s farmPrice 0.2327 0.0212 10.97 7.2e-13 *** 331s trend 0.3286 0.0206 15.93 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.518 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 101.473 MSE: 6.342 Root MSE: 2.518 331s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 331s 331s > nobs( fitsur4 ) 331s [1] 40 331s > # the same with symbolically specified restrictions 331s > fitsur4Sym <- systemfit( system, "SUR", data = Kmenta, 331s + restrict.matrix = restrict2, useMatrix = useMatrix ) 331s > all.equal( fitsur4, fitsur4Sym ) 331s [1] "Component “call”: target, current do not match when deparsed" 331s > 331s > ## *************** SUR with 2 restrictions (EViews-like) ************** 331s > fitsur4e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 331s + restrict.matrix = restr2m, restrict.rhs = restr2q, useMatrix = useMatrix ) 331s > print( summary( fitsur4e ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 35 165 1.2 0.693 0.653 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 63.8 3.75 1.94 0.762 0.734 331s supply 20 16 100.8 6.30 2.51 0.624 0.553 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.20 3.67 331s supply 3.67 4.79 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.19 3.86 331s supply 3.86 5.04 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.962 331s supply 0.962 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 97.2678 6.9200 14.06 4.4e-16 *** 331s price -0.2851 0.0767 -3.72 7e-04 *** 331s income 0.3296 0.0184 17.86 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.937 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 63.811 MSE: 3.754 Root MSE: 1.937 331s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 53.3040 7.1045 7.5 8.7e-09 *** 331s price 0.2149 0.0767 2.8 0.0082 ** 331s farmPrice 0.2343 0.0187 12.6 1.6e-14 *** 331s trend 0.3296 0.0184 17.9 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.51 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 100.835 MSE: 6.302 Root MSE: 2.51 331s Multiple R-Squared: 0.624 Adjusted R-Squared: 0.553 331s 331s > 331s > ## *************** SUR with 2 restrictions (methodResidCov = "Theil") ************** 331s > fitsur4r2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 331s + restrict.matrix = restr2m, restrict.rhs = restr2q, useMatrix = useMatrix ) 331s > print( summary( fitsur4r2 ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 35 175 0.034 0.673 0.708 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 67 3.94 1.99 0.750 0.721 331s supply 20 16 108 6.76 2.60 0.596 0.521 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.76 4.61 331s supply 4.61 5.99 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.94 5.16 331s supply 5.16 6.76 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.967 331s supply 0.967 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 92.5266 7.2896 12.69 1.2e-14 *** 331s price -0.2304 0.0827 -2.79 0.0086 ** 331s income 0.3221 0.0166 19.37 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.986 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 67.048 MSE: 3.944 Root MSE: 1.986 331s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 48.7011 7.4034 6.58 1.3e-07 *** 331s price 0.2696 0.0827 3.26 0.0025 ** 331s farmPrice 0.2261 0.0166 13.62 1.6e-15 *** 331s trend 0.3221 0.0166 19.37 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.601 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 108.217 MSE: 6.764 Root MSE: 2.601 331s Multiple R-Squared: 0.596 Adjusted R-Squared: 0.521 331s 331s > 331s > ## *************** SUR with 2 restrictions (methodResidCov = "max") ************** 331s > fitsur4r3 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "max", 331s + restrict.matrix = restr2m, restrict.rhs = restr2q, 331s + x = TRUE, useMatrix = useMatrix ) 331s > print( summary( fitsur4r3 ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 35 173 0.217 0.677 0.702 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.4 3.91 1.98 0.752 0.723 331s supply 20 16 106.9 6.68 2.58 0.601 0.526 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.76 4.59 331s supply 4.59 5.99 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.91 5.09 331s supply 5.09 6.68 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.966 331s supply 0.966 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 93.1978 7.3168 12.74 1.1e-14 *** 331s price -0.2381 0.0829 -2.87 0.0069 ** 331s income 0.3231 0.0170 18.96 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.976 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.405 MSE: 3.906 Root MSE: 1.976 331s Multiple R-Squared: 0.752 Adjusted R-Squared: 0.723 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 49.3676 7.4381 6.64 1.1e-07 *** 331s price 0.2619 0.0829 3.16 0.0033 ** 331s farmPrice 0.2271 0.0171 13.29 3.1e-15 *** 331s trend 0.3231 0.0170 18.96 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.585 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 106.924 MSE: 6.683 Root MSE: 2.585 331s Multiple R-Squared: 0.601 Adjusted R-Squared: 0.526 331s 331s > 331s > ## *************** WSUR with 2 restrictions (EViews-like) ************** 331s > fitsur4we <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 331s + restrict.matrix = restr2m, restrict.rhs = restr2q, residCovWeighted = TRUE, 331s + useMatrix = useMatrix ) 331s > summary( fitsur4we ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 35 165 1.2 0.692 0.654 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 63.9 3.76 1.94 0.762 0.733 331s supply 20 16 101.2 6.33 2.52 0.623 0.552 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.18 3.69 331s supply 3.69 4.81 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.20 3.87 331s supply 3.87 5.06 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.962 331s supply 0.962 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 96.9414 6.8894 14.07 4.4e-16 *** 331s price -0.2814 0.0766 -3.67 8e-04 *** 331s income 0.3291 0.0181 18.18 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.939 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 63.936 MSE: 3.761 Root MSE: 1.939 331s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.733 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 52.9963 7.0652 7.50 8.7e-09 *** 331s price 0.2186 0.0766 2.85 0.0072 ** 331s farmPrice 0.2337 0.0183 12.76 1.0e-14 *** 331s trend 0.3291 0.0181 18.18 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.515 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 101.201 MSE: 6.325 Root MSE: 2.515 331s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 331s 331s > 331s > 331s > ## *************** SUR with 2 restrictions via R and restrict.regMat **************** 331s > fitsur5 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr3m, 331s + restrict.rhs = restr3q, restrict.regMat = tc, 331s + x = TRUE, useMatrix = useMatrix ) 331s > print( summary( fitsur5 ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 35 165 1.76 0.691 0.69 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 64 3.76 1.94 0.761 0.733 331s supply 20 16 101 6.34 2.52 0.622 0.551 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.76 4.46 331s supply 4.46 5.99 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.76 4.70 331s supply 4.70 6.34 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.962 331s supply 0.962 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 96.8275 7.4665 12.97 6.2e-15 *** 331s price -0.2798 0.0840 -3.33 0.002 ** 331s income 0.3286 0.0206 15.93 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.94 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 63.987 MSE: 3.764 Root MSE: 1.94 331s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 52.9386 7.6655 6.91 5.1e-08 *** 331s price 0.2202 0.0840 2.62 0.013 * 331s farmPrice 0.2327 0.0212 10.97 7.2e-13 *** 331s trend 0.3286 0.0206 15.93 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.518 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 101.473 MSE: 6.342 Root MSE: 2.518 331s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 331s 331s > nobs( fitsur5 ) 331s [1] 40 331s > # the same with symbolically specified restrictions 331s > fitsur5Sym <- systemfit( system, "SUR", data = Kmenta, 331s + restrict.matrix = restrict3, restrict.regMat = tc, 331s + x = TRUE, useMatrix = useMatrix ) 331s > all.equal( fitsur5, fitsur5Sym ) 331s [1] "Component “call”: target, current do not match when deparsed" 331s > 331s > ## *************** SUR with 2 restrictions via R and restrict.regMat (EViews-like) ************** 331s > fitsur5e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 331s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 331s + useMatrix = useMatrix ) 331s > print( summary( fitsur5e ) ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 35 165 1.2 0.693 0.653 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 63.8 3.75 1.94 0.762 0.734 331s supply 20 16 100.8 6.30 2.51 0.624 0.553 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.20 3.67 331s supply 3.67 4.79 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.19 3.86 331s supply 3.86 5.04 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.962 331s supply 0.962 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 97.2678 6.9200 14.06 4.4e-16 *** 331s price -0.2851 0.0767 -3.72 7e-04 *** 331s income 0.3296 0.0184 17.86 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.937 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 63.811 MSE: 3.754 Root MSE: 1.937 331s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 53.3040 7.1045 7.5 8.7e-09 *** 331s price 0.2149 0.0767 2.8 0.0082 ** 331s farmPrice 0.2343 0.0187 12.6 1.6e-14 *** 331s trend 0.3296 0.0184 17.9 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.51 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 100.835 MSE: 6.302 Root MSE: 2.51 331s Multiple R-Squared: 0.624 Adjusted R-Squared: 0.553 331s 331s > 331s > ## ************ WSUR with 2 restrictions via R and restrict.regMat ************ 331s > fitsur5w <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr3m, 331s + restrict.rhs = restr3q, restrict.regMat = tc, residCovWeighted = TRUE, 331s + useMatrix = useMatrix ) 331s > summary( fitsur5w ) 331s 331s systemfit results 331s method: SUR 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 35 166 1.75 0.69 0.691 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 64.2 3.77 1.94 0.761 0.733 331s supply 20 16 102.0 6.37 2.52 0.620 0.548 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.74 4.47 331s supply 4.47 6.02 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.77 4.72 331s supply 4.72 6.37 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.963 331s supply 0.963 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 96.4421 7.4234 12.99 6e-15 *** 331s price -0.2753 0.0838 -3.29 0.0023 ** 331s income 0.3280 0.0202 16.21 <2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.943 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 64.16 MSE: 3.774 Root MSE: 1.943 331s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: consump ~ price + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 52.5761 7.6099 6.91 5.0e-08 *** 331s price 0.2247 0.0838 2.68 0.011 * 331s farmPrice 0.2318 0.0208 11.14 4.7e-13 *** 331s trend 0.3280 0.0202 16.21 < 2e-16 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 2.524 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 101.967 MSE: 6.373 Root MSE: 2.524 331s Multiple R-Squared: 0.62 Adjusted R-Squared: 0.548 331s 331s > 331s > 331s > ## ************** iterated SUR **************************** 331s > fitsuri1 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 331s + useMatrix = useMatrix ) 331s > print( summary( fitsuri1 ) ) 331s 331s systemfit results 331s method: iterated SUR 331s 331s convergence achieved after 6 iterations 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 108 4.42 0.885 0.958 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.3 3.90 1.98 0.753 0.724 331s supply 20 16 41.4 2.59 1.61 0.938 0.926 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.90 -2.38 331s supply -2.38 2.59 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.90 -2.38 331s supply -2.38 2.59 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 -0.749 331s supply -0.749 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 94.0537 7.4051 12.70 4.2e-10 *** 331s price -0.2355 0.0882 -2.67 0.016 * 331s income 0.3117 0.0457 6.81 3.0e-06 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.975 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.286 MSE: 3.899 Root MSE: 1.975 331s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: price ~ income + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 89.2982 3.3822 26.4 1.3e-14 *** 331s income 0.6655 0.0423 15.7 3.7e-11 *** 331s farmPrice -0.4742 0.0372 -12.7 8.7e-10 *** 331s trend -0.7966 0.0656 -12.2 1.7e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.609 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 41.411 MSE: 2.588 Root MSE: 1.609 331s Multiple R-Squared: 0.938 Adjusted R-Squared: 0.926 331s 331s > nobs( fitsuri1 ) 331s [1] 40 331s > 331s > ## ************** iterated SUR (EViews-like) ***************** 331s > fitsuri1e <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "noDfCor", 331s + maxit = 100, useMatrix = useMatrix ) 331s > print( summary( fitsuri1e, useDfSys = TRUE ) ) 331s 331s systemfit results 331s method: iterated SUR 331s 331s convergence achieved after 7 iterations 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 108 3.01 0.885 0.959 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.7 3.93 1.98 0.751 0.722 331s supply 20 16 41.2 2.57 1.60 0.938 0.927 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.34 -1.97 331s supply -1.97 2.06 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.34 -1.97 331s supply -1.97 2.06 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.00 -0.75 331s supply -0.75 1.00 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 93.6193 6.8499 13.67 4.0e-15 *** 331s price -0.2295 0.0816 -2.81 0.0082 ** 331s income 0.3100 0.0423 7.33 2.1e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.981 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.742 MSE: 3.926 Root MSE: 1.981 331s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: price ~ income + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 89.2690 3.0165 29.6 < 2e-16 *** 331s income 0.6641 0.0377 17.6 < 2e-16 *** 331s farmPrice -0.4730 0.0332 -14.2 1.3e-15 *** 331s trend -0.7919 0.0585 -13.6 4.9e-15 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.604 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 41.176 MSE: 2.573 Root MSE: 1.604 331s Multiple R-Squared: 0.938 Adjusted R-Squared: 0.927 331s 331s > 331s > ## ************** iterated SUR (methodResidCov = "Theil") **************************** 331s > fitsuri1r2 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 331s + methodResidCov = "Theil", useMatrix = useMatrix ) 331s > print( summary( fitsuri1r2 ) ) 331s 331s systemfit results 331s method: iterated SUR 331s 331s convergence achieved after 7 iterations 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 109 4 0.884 0.961 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.9 3.94 1.98 0.750 0.721 331s supply 20 16 41.8 2.61 1.62 0.937 0.926 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.94 -2.51 331s supply -2.51 2.61 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.94 -2.51 331s supply -2.51 2.61 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 -0.754 331s supply -0.754 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 93.4405 7.3821 12.66 4.4e-10 *** 331s price -0.2271 0.0877 -2.59 0.019 * 331s income 0.3093 0.0458 6.75 3.4e-06 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.984 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.939 MSE: 3.938 Root MSE: 1.984 331s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: price ~ income + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 89.1602 3.3868 26.3 1.3e-14 *** 331s income 0.6635 0.0423 15.7 3.9e-11 *** 331s farmPrice -0.4710 0.0369 -12.8 8.5e-10 *** 331s trend -0.7952 0.0643 -12.4 1.3e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.616 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 41.764 MSE: 2.61 Root MSE: 1.616 331s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 331s 331s > 331s > ## ************** iterated SUR (methodResidCov="Theil", useDfSys=TRUE) ***************** 331s > fitsuri1e2 <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "Theil", 331s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 331s > print( summary( fitsuri1e2, useDfSys = TRUE ) ) 331s 331s systemfit results 331s method: iterated SUR 331s 331s convergence achieved after 7 iterations 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 109 4 0.884 0.961 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.9 3.94 1.98 0.750 0.721 331s supply 20 16 41.8 2.61 1.62 0.937 0.926 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.94 -2.51 331s supply -2.51 2.61 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.94 -2.51 331s supply -2.51 2.61 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 -0.754 331s supply -0.754 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 93.4405 7.3821 12.66 3.3e-14 *** 331s price -0.2271 0.0877 -2.59 0.014 * 331s income 0.3093 0.0458 6.75 1.1e-07 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.984 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.939 MSE: 3.938 Root MSE: 1.984 331s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: price ~ income + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 89.1602 3.3868 26.3 < 2e-16 *** 331s income 0.6635 0.0423 15.7 < 2e-16 *** 331s farmPrice -0.4710 0.0369 -12.8 2.7e-14 *** 331s trend -0.7952 0.0643 -12.4 6.0e-14 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.616 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 41.764 MSE: 2.61 Root MSE: 1.616 331s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 331s 331s > 331s > ## ************** iterated SUR (methodResidCov = "max") **************************** 331s > fitsuri1r3 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 331s + methodResidCov = "max", useMatrix = useMatrix ) 331s > print( summary( fitsuri1r3 ) ) 331s 331s systemfit results 331s method: iterated SUR 331s 331s convergence achieved after 7 iterations 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 109 4.06 0.884 0.96 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.8 3.93 1.98 0.751 0.721 331s supply 20 16 41.7 2.61 1.61 0.937 0.926 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.93 -2.49 331s supply -2.49 2.61 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.93 -2.49 331s supply -2.49 2.61 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 -0.754 331s supply -0.754 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 93.5427 7.3858 12.67 4.4e-10 *** 331s price -0.2285 0.0877 -2.60 0.019 * 331s income 0.3097 0.0458 6.76 3.3e-06 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.983 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.826 MSE: 3.931 Root MSE: 1.983 331s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: price ~ income + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 89.1830 3.3861 26.3 1.3e-14 *** 331s income 0.6639 0.0423 15.7 3.8e-11 *** 331s farmPrice -0.4715 0.0370 -12.8 8.5e-10 *** 331s trend -0.7955 0.0645 -12.3 1.4e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.615 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 41.708 MSE: 2.607 Root MSE: 1.615 331s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 331s 331s > 331s > ## ************** iterated WSUR (methodResidCov = "max") **************************** 331s > fitsuri1wr3 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 331s + methodResidCov = "max", residCovWeighted = TRUE, useMatrix = useMatrix ) 331s > summary( fitsuri1wr3 ) 331s 331s systemfit results 331s method: iterated SUR 331s 331s convergence achieved after 7 iterations 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 33 109 4.06 0.884 0.96 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 66.8 3.93 1.98 0.751 0.721 331s supply 20 16 41.7 2.61 1.61 0.937 0.926 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.93 -2.49 331s supply -2.49 2.61 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.93 -2.49 331s supply -2.49 2.61 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 -0.754 331s supply -0.754 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 93.5427 7.3858 12.67 4.4e-10 *** 331s price -0.2285 0.0877 -2.60 0.019 * 331s income 0.3097 0.0458 6.76 3.3e-06 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.983 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 66.826 MSE: 3.931 Root MSE: 1.983 331s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: price ~ income + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 89.1830 3.3861 26.3 1.3e-14 *** 331s income 0.6639 0.0423 15.7 3.8e-11 *** 331s farmPrice -0.4715 0.0370 -12.8 8.5e-10 *** 331s trend -0.7955 0.0645 -12.3 1.4e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.615 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 41.708 MSE: 2.607 Root MSE: 1.615 331s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 331s 331s > 331s > 331s > ## *********** iterated SUR with restriction ******************* 331s > fitsuri2 <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restrm, 331s + maxit = 100, useMatrix = useMatrix ) 331s > print( summary( fitsuri2 ) ) 331s 331s systemfit results 331s method: iterated SUR 331s 331s convergence achieved after 21 iterations 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 34 587 110 0.372 0.669 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 67 3.94 1.99 0.75 0.721 331s supply 20 16 520 32.52 5.70 0.22 0.074 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.94 4.24 331s supply 4.24 32.52 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.94 4.24 331s supply 4.24 32.52 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.375 331s supply 0.375 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 107.3678 7.4986 14.32 4.4e-16 *** 331s price -0.3945 0.0912 -4.33 0.00013 *** 331s income 0.3382 0.0466 7.25 2.1e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.986 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 67.024 MSE: 3.943 Root MSE: 1.986 331s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: price ~ income + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 331s income 0.3125 0.1233 2.53 0.016 * 331s farmPrice -0.1972 0.1157 -1.70 0.097 . 331s trend 0.3382 0.0466 7.25 2.1e-08 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 5.703 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 520.329 MSE: 32.521 Root MSE: 5.703 331s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 331s 331s > 331s > ## *********** iterated SUR with restriction (EViews-like) *************** 331s > fitsuri2e <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restrm, 331s + methodResidCov = "noDfCor", maxit = 100, x = TRUE, 331s + useMatrix = useMatrix ) 331s > print( summary( fitsuri2e ) ) 331s 331s systemfit results 331s method: iterated SUR 331s 331s convergence achieved after 22 iterations 331s 331s N DF SSR detRCov OLS-R2 McElroy-R2 331s system 40 34 588 74.9 0.372 0.664 331s 331s N DF SSR MSE RMSE R2 Adj R2 331s demand 20 17 67.5 3.97 1.99 0.748 0.719 331s supply 20 16 520.2 32.51 5.70 0.220 0.074 331s 331s The covariance matrix of the residuals used for estimation 331s demand supply 331s demand 3.37 3.58 331s supply 3.58 26.01 331s 331s The covariance matrix of the residuals 331s demand supply 331s demand 3.37 3.58 331s supply 3.58 26.01 331s 331s The correlations of the residuals 331s demand supply 331s demand 1.000 0.382 331s supply 0.382 1.000 331s 331s 331s SUR estimates for 'demand' (equation 1) 331s Model Formula: consump ~ price + income 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 107.8051 6.9270 15.56 < 2e-16 *** 331s price -0.3986 0.0843 -4.73 3.8e-05 *** 331s income 0.3379 0.0431 7.84 4.0e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 1.992 on 17 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 17 331s SSR: 67.47 MSE: 3.969 Root MSE: 1.992 331s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 331s 331s 331s SUR estimates for 'supply' (equation 2) 331s Model Formula: price ~ income + farmPrice + trend 331s 331s Estimate Std. Error t value Pr(>|t|) 331s (Intercept) 85.1071 10.8287 7.86 3.8e-09 *** 331s income 0.3106 0.1101 2.82 0.0079 ** 331s farmPrice -0.1960 0.1034 -1.89 0.0667 . 331s trend 0.3379 0.0431 7.84 4.0e-09 *** 331s --- 331s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 331s 331s Residual standard error: 5.702 on 16 degrees of freedom 331s Number of observations: 20 Degrees of Freedom: 16 331s SSR: 520.205 MSE: 32.513 Root MSE: 5.702 331s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 331s 331s > 331s > ## *********** iterated WSUR with restriction ******************* 331s > fitsuri2w <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restrm, 331s + maxit = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 332s > summary( fitsuri2w ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 18 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 34 587 110 0.372 0.669 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67 3.94 1.99 0.75 0.721 332s supply 20 16 520 32.52 5.70 0.22 0.074 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.94 4.24 332s supply 4.24 32.52 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.94 4.24 332s supply 4.24 32.52 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.375 332s supply 0.375 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 107.3672 7.4986 14.32 4.4e-16 *** 332s price -0.3945 0.0912 -4.33 0.00013 *** 332s income 0.3382 0.0466 7.25 2.1e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.986 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 67.023 MSE: 3.943 Root MSE: 1.986 332s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 332s income 0.3125 0.1233 2.53 0.016 * 332s farmPrice -0.1972 0.1157 -1.70 0.097 . 332s trend 0.3382 0.0466 7.25 2.1e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.703 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 520.327 MSE: 32.52 Root MSE: 5.703 332s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 332s 332s > 332s > 332s > ## *********** iterated SUR with restriction via restrict.regMat ******************** 332s > fitsuri3 <- systemfit( system2, "SUR", data = Kmenta, restrict.regMat = tc, 332s + maxit = 100, useMatrix = useMatrix ) 332s > print( summary( fitsuri3 ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 21 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 34 587 110 0.372 0.669 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67 3.94 1.99 0.75 0.721 332s supply 20 16 520 32.52 5.70 0.22 0.074 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.94 4.24 332s supply 4.24 32.52 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.94 4.24 332s supply 4.24 32.52 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.375 332s supply 0.375 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 107.3678 7.4986 14.32 4.4e-16 *** 332s price -0.3945 0.0912 -4.33 0.00013 *** 332s income 0.3382 0.0466 7.25 2.1e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.986 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 67.024 MSE: 3.943 Root MSE: 1.986 332s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 332s income 0.3125 0.1233 2.53 0.016 * 332s farmPrice -0.1972 0.1157 -1.70 0.097 . 332s trend 0.3382 0.0466 7.25 2.1e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.703 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 520.329 MSE: 32.521 Root MSE: 5.703 332s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 332s 332s > 332s > ## *********** iterated SUR with restriction via restrict.regMat (EViews-like) *************** 332s > fitsuri3e <- systemfit( system2, "SUR", data = Kmenta, restrict.regMat = tc, 332s + methodResidCov = "noDfCor", maxit = 100, x = TRUE, 332s + useMatrix = useMatrix ) 332s > print( summary( fitsuri3e ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 22 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 34 588 74.9 0.372 0.664 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67.5 3.97 1.99 0.748 0.719 332s supply 20 16 520.2 32.51 5.70 0.220 0.074 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.37 3.58 332s supply 3.58 26.01 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.37 3.58 332s supply 3.58 26.01 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.382 332s supply 0.382 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 107.8051 6.9270 15.56 < 2e-16 *** 332s price -0.3986 0.0843 -4.73 3.8e-05 *** 332s income 0.3379 0.0431 7.84 4.0e-09 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.992 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 67.47 MSE: 3.969 Root MSE: 1.992 332s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 85.1071 10.8287 7.86 3.8e-09 *** 332s income 0.3106 0.1101 2.82 0.0079 ** 332s farmPrice -0.1960 0.1034 -1.89 0.0667 . 332s trend 0.3379 0.0431 7.84 4.0e-09 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.702 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 520.205 MSE: 32.513 Root MSE: 5.702 332s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 332s 332s > 332s > ## *********** iterated WSUR with restriction via restrict.regMat (EViews-like) *************** 332s > fitsuri3we <- systemfit( system2, "SUR", data = Kmenta, restrict.regMat = tc, 332s + methodResidCov = "noDfCor", maxit = 100, residCovWeighted = TRUE, 332s + useMatrix = useMatrix ) 332s > summary( fitsuri3we ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 20 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 34 588 74.9 0.372 0.664 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67.5 3.97 1.99 0.748 0.719 332s supply 20 16 520.2 32.51 5.70 0.220 0.074 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.37 3.58 332s supply 3.58 26.01 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.37 3.58 332s supply 3.58 26.01 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.382 332s supply 0.382 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 107.8055 6.9270 15.56 < 2e-16 *** 332s price -0.3986 0.0843 -4.73 3.8e-05 *** 332s income 0.3379 0.0431 7.84 4.0e-09 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.992 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 67.471 MSE: 3.969 Root MSE: 1.992 332s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 85.1071 10.8288 7.86 3.8e-09 *** 332s income 0.3106 0.1101 2.82 0.008 ** 332s farmPrice -0.1960 0.1034 -1.89 0.067 . 332s trend 0.3379 0.0431 7.84 4.0e-09 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.702 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 520.206 MSE: 32.513 Root MSE: 5.702 332s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 332s 332s > 332s > 332s > ## *************** iterated SUR with 2 restrictions *************************** 332s > fitsurio4 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr2m, 332s + restrict.rhs = restr2q, maxit = 100, useMatrix = useMatrix ) 332s > print( summary( fitsurio4 ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 10 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 176 1.74 0.671 0.705 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67.2 3.95 1.99 0.749 0.720 332s supply 20 16 109.2 6.83 2.61 0.593 0.516 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.95 5.02 332s supply 5.02 6.83 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.95 5.02 332s supply 5.02 6.83 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.967 332s supply 0.967 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 332s price -0.2276 0.0850 -2.68 0.011 * 332s income 0.3203 0.0185 17.32 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.988 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 67.206 MSE: 3.953 Root MSE: 1.988 332s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.72 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: consump ~ price + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 48.7295 7.4587 6.53 1.5e-07 *** 332s price 0.2724 0.0850 3.20 0.0029 ** 332s farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 332s trend 0.3203 0.0185 17.32 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.613 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 109.234 MSE: 6.827 Root MSE: 2.613 332s Multiple R-Squared: 0.593 Adjusted R-Squared: 0.516 332s 332s > fitsuri4 <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restr2m, 332s + restrict.rhs = restr2q, maxit = 100, useMatrix = useMatrix ) 332s > print( summary( fitsuri4 ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 19 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 575 121 0.385 0.637 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 65.5 3.85 1.96 0.756 0.727 332s supply 20 16 509.3 31.83 5.64 0.237 0.094 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.85 1.23 332s supply 1.23 31.83 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.85 1.23 332s supply 1.23 31.83 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.111 332s supply 0.111 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 98.0356 6.7437 14.54 2.2e-16 *** 332s price -0.2646 0.0777 -3.40 0.0017 ** 332s income 0.3007 0.0436 6.89 5.3e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.963 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 65.532 MSE: 3.855 Root MSE: 1.963 332s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 90.0046 10.4367 8.62 3.5e-10 *** 332s income 0.2354 0.0777 3.03 0.0046 ** 332s farmPrice -0.1667 0.1108 -1.50 0.1416 332s trend 0.3007 0.0436 6.89 5.3e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.642 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 509.345 MSE: 31.834 Root MSE: 5.642 332s Multiple R-Squared: 0.237 Adjusted R-Squared: 0.094 332s 332s > 332s > ## *************** iterated SUR with 2 restrictions (EViews-like) ************** 332s > fitsurio4e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 332s + restrict.matrix = restr2m, restrict.rhs = restr2q, maxit = 100, 332s + useMatrix = useMatrix ) 332s > print( summary( fitsurio4e ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 9 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 173 1.18 0.677 0.665 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 66.3 3.90 1.97 0.753 0.724 332s supply 20 16 106.7 6.67 2.58 0.602 0.527 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.31 4.06 332s supply 4.06 5.34 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.31 4.06 332s supply 4.06 5.34 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.966 332s supply 0.966 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 93.3596 6.8576 13.61 1.6e-15 *** 332s price -0.2398 0.0779 -3.08 0.0041 ** 332s income 0.3232 0.0163 19.81 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.974 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 66.265 MSE: 3.898 Root MSE: 1.974 332s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: consump ~ price + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 49.5456 6.9727 7.11 2.8e-08 *** 332s price 0.2602 0.0779 3.34 0.002 ** 332s farmPrice 0.2270 0.0164 13.81 8.9e-16 *** 332s trend 0.3232 0.0163 19.81 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.583 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 106.722 MSE: 6.67 Root MSE: 2.583 332s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.527 332s 332s > fitsuri4e <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "noDfCor", 332s + restrict.matrix = restr2m, restrict.rhs = restr2q, maxit = 100, 332s + useMatrix = useMatrix ) 332s > print( summary( fitsuri4e ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 20 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 570 82.4 0.391 0.629 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 66 3.88 1.97 0.754 0.725 332s supply 20 16 504 31.50 5.61 0.245 0.103 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.300 0.876 332s supply 0.876 25.203 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.300 0.876 332s supply 0.876 25.203 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.0000 0.0961 332s supply 0.0961 1.0000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 97.6297 6.1560 15.86 < 2e-16 *** 332s price -0.2576 0.0709 -3.63 0.00089 *** 332s income 0.2976 0.0403 7.38 1.2e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.97 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 65.995 MSE: 3.882 Root MSE: 1.97 332s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 89.5437 9.3372 9.59 2.5e-11 *** 332s income 0.2424 0.0709 3.42 0.0016 ** 332s farmPrice -0.1687 0.0988 -1.71 0.0967 . 332s trend 0.2976 0.0403 7.38 1.2e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.613 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 504.066 MSE: 31.504 Root MSE: 5.613 332s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.103 332s 332s > 332s > ## *************** iterated WSUR with 2 restrictions *************************** 332s > fitsurio4w <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr2m, 332s + restrict.rhs = restr2q, maxit = 100, residCovWeighted = TRUE, 332s + useMatrix = useMatrix ) 332s > summary( fitsurio4w ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 10 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 176 1.74 0.671 0.705 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67.2 3.95 1.99 0.749 0.720 332s supply 20 16 109.2 6.83 2.61 0.593 0.516 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.95 5.02 332s supply 5.02 6.83 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.95 5.02 332s supply 5.02 6.83 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.967 332s supply 0.967 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 332s price -0.2276 0.0850 -2.68 0.011 * 332s income 0.3203 0.0185 17.32 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.988 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 67.206 MSE: 3.953 Root MSE: 1.988 332s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.72 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: consump ~ price + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 48.7294 7.4587 6.53 1.5e-07 *** 332s price 0.2724 0.0850 3.20 0.0029 ** 332s farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 332s trend 0.3203 0.0185 17.32 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.613 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 109.234 MSE: 6.827 Root MSE: 2.613 332s Multiple R-Squared: 0.593 Adjusted R-Squared: 0.516 332s 332s > fitsuri4w <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restr2m, 332s + restrict.rhs = restr2q, maxit = 100, residCovWeighted = TRUE, 332s + useMatrix = useMatrix ) 332s > summary( fitsuri4w ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 18 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 575 121 0.385 0.637 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 65.5 3.85 1.96 0.756 0.727 332s supply 20 16 509.3 31.83 5.64 0.237 0.094 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.85 1.23 332s supply 1.23 31.83 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.85 1.23 332s supply 1.23 31.83 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.111 332s supply 0.111 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 98.0361 6.7437 14.54 2.2e-16 *** 332s price -0.2646 0.0777 -3.40 0.0017 ** 332s income 0.3007 0.0436 6.89 5.3e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.963 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 65.531 MSE: 3.855 Root MSE: 1.963 332s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 90.0052 10.4368 8.62 3.5e-10 *** 332s income 0.2354 0.0777 3.03 0.0046 ** 332s farmPrice -0.1667 0.1108 -1.50 0.1416 332s trend 0.3007 0.0436 6.89 5.3e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.642 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 509.349 MSE: 31.834 Root MSE: 5.642 332s Multiple R-Squared: 0.237 Adjusted R-Squared: 0.094 332s 332s > 332s > 332s > ## *************** iterated SUR with 2 restrictions via R and restrict.regMat **************** 332s > fitsurio5 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr3m, 332s + restrict.rhs = restr3q, restrict.regMat = tc, maxit = 100, 332s + useMatrix = useMatrix ) 332s > print( summary( fitsurio5 ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 10 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 176 1.74 0.671 0.705 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67.2 3.95 1.99 0.749 0.720 332s supply 20 16 109.2 6.83 2.61 0.593 0.516 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.95 5.02 332s supply 5.02 6.83 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.95 5.02 332s supply 5.02 6.83 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.967 332s supply 0.967 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 332s price -0.2276 0.0850 -2.68 0.011 * 332s income 0.3203 0.0185 17.32 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.988 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 67.206 MSE: 3.953 Root MSE: 1.988 332s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.72 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: consump ~ price + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 48.7295 7.4587 6.53 1.5e-07 *** 332s price 0.2724 0.0850 3.20 0.0029 ** 332s farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 332s trend 0.3203 0.0185 17.32 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.613 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 109.234 MSE: 6.827 Root MSE: 2.613 332s Multiple R-Squared: 0.593 Adjusted R-Squared: 0.516 332s 332s > fitsuri5 <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restr3m, 332s + restrict.rhs = restr3q, restrict.regMat = tc, maxit = 100, 332s + useMatrix = useMatrix ) 332s > print( summary( fitsuri5 ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 19 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 575 121 0.385 0.637 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 65.5 3.85 1.96 0.756 0.727 332s supply 20 16 509.3 31.83 5.64 0.237 0.094 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.85 1.23 332s supply 1.23 31.83 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.85 1.23 332s supply 1.23 31.83 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.111 332s supply 0.111 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 98.0356 6.7437 14.54 2.2e-16 *** 332s price -0.2646 0.0777 -3.40 0.0017 ** 332s income 0.3007 0.0436 6.89 5.3e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.963 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 65.532 MSE: 3.855 Root MSE: 1.963 332s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 90.0046 10.4367 8.62 3.5e-10 *** 332s income 0.2354 0.0777 3.03 0.0046 ** 332s farmPrice -0.1667 0.1108 -1.50 0.1416 332s trend 0.3007 0.0436 6.89 5.3e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.642 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 509.345 MSE: 31.834 Root MSE: 5.642 332s Multiple R-Squared: 0.237 Adjusted R-Squared: 0.094 332s 332s > 332s > ## ********* iterated SUR with 2 restrictions via R and restrict.regMat (EViews-like) ********** 332s > fitsurio5e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 332s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 332s + maxit = 100, useMatrix = useMatrix ) 332s > print( summary( fitsurio5e ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 9 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 173 1.18 0.677 0.665 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 66.3 3.90 1.97 0.753 0.724 332s supply 20 16 106.7 6.67 2.58 0.602 0.527 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.31 4.06 332s supply 4.06 5.34 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.31 4.06 332s supply 4.06 5.34 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.966 332s supply 0.966 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 93.3596 6.8576 13.61 1.6e-15 *** 332s price -0.2398 0.0779 -3.08 0.0041 ** 332s income 0.3232 0.0163 19.81 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.974 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 66.265 MSE: 3.898 Root MSE: 1.974 332s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: consump ~ price + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 49.5456 6.9727 7.11 2.8e-08 *** 332s price 0.2602 0.0779 3.34 0.002 ** 332s farmPrice 0.2270 0.0164 13.81 8.9e-16 *** 332s trend 0.3232 0.0163 19.81 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.583 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 106.722 MSE: 6.67 Root MSE: 2.583 332s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.527 332s 332s > fitsuri5e <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "noDfCor", 332s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 332s + maxit = 100, useMatrix = useMatrix ) 332s > print( summary( fitsuri5e ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 20 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 570 82.4 0.391 0.629 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 66 3.88 1.97 0.754 0.725 332s supply 20 16 504 31.50 5.61 0.245 0.103 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.300 0.876 332s supply 0.876 25.203 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.300 0.876 332s supply 0.876 25.203 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.0000 0.0961 332s supply 0.0961 1.0000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 97.6297 6.1560 15.86 < 2e-16 *** 332s price -0.2576 0.0709 -3.63 0.00089 *** 332s income 0.2976 0.0403 7.38 1.2e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.97 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 65.995 MSE: 3.882 Root MSE: 1.97 332s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 89.5437 9.3372 9.59 2.5e-11 *** 332s income 0.2424 0.0709 3.42 0.0016 ** 332s farmPrice -0.1687 0.0988 -1.71 0.0967 . 332s trend 0.2976 0.0403 7.38 1.2e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.613 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 504.066 MSE: 31.504 Root MSE: 5.613 332s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.103 332s 332s > nobs( fitsuri5e ) 332s [1] 40 332s > 332s > ## ********* iterated SUR with 2 restrictions via R and restrict.regMat (methodResidCov="Theil") ********** 332s > fitsurio5r2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 332s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 332s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 332s > print( summary( fitsurio5r2 ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s warning: convergence not achieved after 100 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 253 -1.67 0.527 0.927 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 95.8 5.63 2.37 0.643 0.601 332s supply 20 16 157.7 9.86 3.14 0.412 0.301 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 4.26 5.29 332s supply 5.29 6.69 332s 332s warning: this covariance matrix is NOT positive semidefinit! 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 5.63 7.56 332s supply 7.56 9.86 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.982 332s supply 0.982 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 78.0342 7.1638 10.89 8.6e-13 *** 332s price -0.0647 0.0815 -0.79 0.43 332s income 0.3007 0.0131 23.01 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.373 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 95.76 MSE: 5.633 Root MSE: 2.373 332s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.601 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: consump ~ price + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 34.1958 7.2257 4.73 3.6e-05 *** 332s price 0.4353 0.0815 5.34 5.7e-06 *** 332s farmPrice 0.2070 0.0124 16.68 < 2e-16 *** 332s trend 0.3007 0.0131 23.01 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 3.14 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 157.737 MSE: 9.859 Root MSE: 3.14 332s Multiple R-Squared: 0.412 Adjusted R-Squared: 0.301 332s 332s > fitsuri5r2 <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "Theil", 332s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 332s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 332s > print( summary( fitsuri5r2 ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 21 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 576 121 0.384 0.637 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 65.4 3.85 1.96 0.756 0.727 332s supply 20 16 510.8 31.92 5.65 0.235 0.091 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.85 1.34 332s supply 1.34 31.92 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.85 1.34 332s supply 1.34 31.92 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.117 332s supply 0.117 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 98.2200 6.7593 14.53 2.2e-16 *** 332s price -0.2669 0.0778 -3.43 0.0016 ** 332s income 0.3011 0.0435 6.92 4.9e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.962 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 65.447 MSE: 3.85 Root MSE: 1.962 332s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 90.2167 10.4342 8.65 3.3e-10 *** 332s income 0.2331 0.0778 3.00 0.005 ** 332s farmPrice -0.1666 0.1111 -1.50 0.143 332s trend 0.3011 0.0435 6.92 4.9e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.65 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 510.75 MSE: 31.922 Root MSE: 5.65 332s Multiple R-Squared: 0.235 Adjusted R-Squared: 0.091 332s 332s > 332s > ## ********* iterated SUR with 2 restrictions via R and restrict.regMat (methodResidCov="max") ********** 332s > # fitsuri5e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "max", 332s > # restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 332s > # maxit = 100, useMatrix = useMatrix ) 332s > # print( summary( fitsuri5e ) ) 332s > # print( round( vcov( fitsuri5e ), digits = 6 ) ) 332s > # disabled, because the estimation does not converge 332s > 332s > ## ********* iterated WSUR with 2 restrictions via R and restrict.regMat (methodResidCov="Theil") ********** 332s > fitsurio5wr2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 332s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 332s + maxit = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 332s > summary( fitsurio5wr2 ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s warning: convergence not achieved after 100 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 253 -1.67 0.527 0.927 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 95.8 5.63 2.37 0.643 0.601 332s supply 20 16 157.7 9.86 3.14 0.412 0.301 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 4.26 5.29 332s supply 5.29 6.69 332s 332s warning: this covariance matrix is NOT positive semidefinit! 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 5.63 7.56 332s supply 7.56 9.86 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.982 332s supply 0.982 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 78.0342 7.1638 10.89 8.6e-13 *** 332s price -0.0647 0.0815 -0.79 0.43 332s income 0.3007 0.0131 23.01 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.373 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 95.76 MSE: 5.633 Root MSE: 2.373 332s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.601 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: consump ~ price + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 34.1958 7.2257 4.73 3.6e-05 *** 332s price 0.4353 0.0815 5.34 5.7e-06 *** 332s farmPrice 0.2070 0.0124 16.68 < 2e-16 *** 332s trend 0.3007 0.0131 23.01 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 3.14 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 157.737 MSE: 9.859 Root MSE: 3.14 332s Multiple R-Squared: 0.412 Adjusted R-Squared: 0.301 332s 332s > fitsuri5wr2 <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "Theil", 332s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 332s + maxit = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 332s > summary( fitsuri5wr2 ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 19 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 576 121 0.384 0.637 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 65.4 3.85 1.96 0.756 0.727 332s supply 20 16 510.8 31.92 5.65 0.235 0.091 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.85 1.34 332s supply 1.34 31.92 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.85 1.34 332s supply 1.34 31.92 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.117 332s supply 0.117 1.000 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 98.2200 6.7593 14.53 2.2e-16 *** 332s price -0.2669 0.0778 -3.43 0.0016 ** 332s income 0.3011 0.0435 6.92 4.9e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.962 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 65.447 MSE: 3.85 Root MSE: 1.962 332s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 90.2168 10.4342 8.65 3.3e-10 *** 332s income 0.2331 0.0778 3.00 0.005 ** 332s farmPrice -0.1666 0.1111 -1.50 0.143 332s trend 0.3011 0.0435 6.92 4.9e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.65 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 510.75 MSE: 31.922 Root MSE: 5.65 332s Multiple R-Squared: 0.235 Adjusted R-Squared: 0.091 332s 332s > 332s > 332s > ## *********** estimations with a single regressor ************ 332s > fitsurS1 <- systemfit( 332s + list( price ~ consump - 1, farmPrice ~ consump + trend ), "SUR", 332s + data = Kmenta, useMatrix = useMatrix ) 332s > print( summary( fitsurS1 ) ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 36 2060 2543 0.449 0.465 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s eq1 20 19 848 44.6 6.68 -0.271 -0.271 332s eq2 20 17 1211 71.3 8.44 0.605 0.559 332s 332s The covariance matrix of the residuals used for estimation 332s eq1 eq2 332s eq1 44.6 -20.5 332s eq2 -20.5 68.9 332s 332s The covariance matrix of the residuals 332s eq1 eq2 332s eq1 44.6 -25.3 332s eq2 -25.3 71.3 332s 332s The correlations of the residuals 332s eq1 eq2 332s eq1 1.000 -0.448 332s eq2 -0.448 1.000 332s 332s 332s SUR estimates for 'eq1' (equation 1) 332s Model Formula: price ~ consump - 1 332s 332s Estimate Std. Error t value Pr(>|t|) 332s consump 0.9902 0.0148 66.9 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 6.682 on 19 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 19 332s SSR: 848.208 MSE: 44.643 Root MSE: 6.682 332s Multiple R-Squared: -0.271 Adjusted R-Squared: -0.271 332s 332s 332s SUR estimates for 'eq2' (equation 2) 332s Model Formula: farmPrice ~ consump + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) -108.487 47.754 -2.27 0.03638 * 332s consump 2.123 0.477 4.45 0.00035 *** 332s trend -0.862 0.303 -2.85 0.01111 * 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 8.441 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 1211.393 MSE: 71.258 Root MSE: 8.441 332s Multiple R-Squared: 0.605 Adjusted R-Squared: 0.559 332s 332s > nobs( fitsurS1 ) 332s [1] 40 332s > fitsurS2 <- systemfit( 332s + list( consump ~ price - 1, consump ~ trend - 1 ), "SUR", 332s + data = Kmenta, useMatrix = useMatrix ) 332s > print( summary( fitsurS2 ) ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 38 47370 110949 -87.3 -5.28 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s eq1 20 19 861 45.3 6.73 -2.21 -2.21 332s eq2 20 19 46509 2447.8 49.48 -172.47 -172.47 332s 332s The covariance matrix of the residuals used for estimation 332s eq1 eq2 332s eq1 45.34 -5.15 332s eq2 -5.15 2447.84 332s 332s The covariance matrix of the residuals 332s eq1 eq2 332s eq1 45.34 -6.37 332s eq2 -6.37 2447.84 332s 332s The correlations of the residuals 332s eq1 eq2 332s eq1 1.0000 -0.0439 332s eq2 -0.0439 1.0000 332s 332s 332s SUR estimates for 'eq1' (equation 1) 332s Model Formula: consump ~ price - 1 332s 332s Estimate Std. Error t value Pr(>|t|) 332s price 1.006 0.015 67 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 6.734 on 19 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 19 332s SSR: 861.496 MSE: 45.342 Root MSE: 6.734 332s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 332s 332s 332s SUR estimates for 'eq2' (equation 2) 332s Model Formula: consump ~ trend - 1 332s 332s Estimate Std. Error t value Pr(>|t|) 332s trend 7.410 0.924 8.02 1.6e-07 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 49.476 on 19 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 19 332s SSR: 46508.986 MSE: 2447.841 Root MSE: 49.476 332s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 332s 332s > nobs( fitsurS2 ) 332s [1] 40 332s > fitsurS3 <- systemfit( 332s + list( consump ~ trend - 1, price ~ trend - 1 ), "SUR", 332s + data = Kmenta, useMatrix = useMatrix ) 332s > nobs( fitsurS3 ) 332s [1] 40 332s > print( summary( fitsurS3 ) ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 38 93537 108970 -99 -0.977 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s eq1 20 19 46509 2448 49.5 -172.5 -172.5 332s eq2 20 19 47028 2475 49.8 -69.5 -69.5 332s 332s The covariance matrix of the residuals used for estimation 332s eq1 eq2 332s eq1 2448 2439 332s eq2 2439 2475 332s 332s The covariance matrix of the residuals 332s eq1 eq2 332s eq1 2448 2439 332s eq2 2439 2475 332s 332s The correlations of the residuals 332s eq1 eq2 332s eq1 1.000 0.988 332s eq2 0.988 1.000 332s 332s 332s SUR estimates for 'eq1' (equation 1) 332s Model Formula: consump ~ trend - 1 332s 332s Estimate Std. Error t value Pr(>|t|) 332s trend 7.405 0.924 8.02 1.6e-07 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 49.476 on 19 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 19 332s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 332s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 332s 332s 332s SUR estimates for 'eq2' (equation 2) 332s Model Formula: price ~ trend - 1 332s 332s Estimate Std. Error t value Pr(>|t|) 332s trend 7.318 0.929 7.88 2.1e-07 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 49.751 on 19 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 19 332s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 332s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 332s 332s > fitsurS4 <- systemfit( 332s + list( consump ~ trend - 1, price ~ trend - 1 ), "SUR", 332s + data = Kmenta, restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), 332s + useMatrix = useMatrix ) 332s > print( summary( fitsurS4 ) ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 39 93552 111731 -99 -1.03 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s eq1 20 19 46510 2448 49.5 -172.5 -172.5 332s eq2 20 19 47042 2476 49.8 -69.5 -69.5 332s 332s The covariance matrix of the residuals used for estimation 332s eq1 eq2 332s eq1 2448 2439 332s eq2 2439 2475 332s 332s The covariance matrix of the residuals 332s eq1 eq2 332s eq1 2448 2439 332s eq2 2439 2476 332s 332s The correlations of the residuals 332s eq1 eq2 332s eq1 1.000 0.988 332s eq2 0.988 1.000 332s 332s 332s SUR estimates for 'eq1' (equation 1) 332s Model Formula: consump ~ trend - 1 332s 332s Estimate Std. Error t value Pr(>|t|) 332s trend 7.388 0.923 8 9.4e-10 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 49.476 on 19 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 19 332s SSR: 46509.787 MSE: 2447.884 Root MSE: 49.476 332s Multiple R-Squared: -172.47 Adjusted R-Squared: -172.47 332s 332s 332s SUR estimates for 'eq2' (equation 2) 332s Model Formula: price ~ trend - 1 332s 332s Estimate Std. Error t value Pr(>|t|) 332s trend 7.388 0.923 8 9.4e-10 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 49.758 on 19 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 19 332s SSR: 47041.803 MSE: 2475.884 Root MSE: 49.758 332s Multiple R-Squared: -69.501 Adjusted R-Squared: -69.501 332s 332s > nobs( fitsurS4 ) 332s [1] 40 332s > fitsurS5 <- systemfit( 332s + list( consump ~ 1, price ~ 1 ), "SUR", 332s + data = Kmenta, useMatrix = useMatrix ) 332s > print( summary( fitsurS5 ) ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 38 935 491 0 0 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s eq1 20 19 268 14.1 3.76 0 0 332s eq2 20 19 667 35.1 5.93 0 0 332s 332s The covariance matrix of the residuals used for estimation 332s eq1 eq2 332s eq1 14.11 2.18 332s eq2 2.18 35.12 332s 332s The covariance matrix of the residuals 332s eq1 eq2 332s eq1 14.11 2.18 332s eq2 2.18 35.12 332s 332s The correlations of the residuals 332s eq1 eq2 332s eq1 1.0000 0.0981 332s eq2 0.0981 1.0000 332s 332s 332s SUR estimates for 'eq1' (equation 1) 332s Model Formula: consump ~ 1 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 100.90 0.84 120 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 3.756 on 19 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 19 332s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 332s Multiple R-Squared: 0 Adjusted R-Squared: 0 332s 332s 332s SUR estimates for 'eq2' (equation 2) 332s Model Formula: price ~ 1 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 100.02 1.33 75.5 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.926 on 19 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 19 332s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 332s Multiple R-Squared: 0 Adjusted R-Squared: 0 332s 332s > nobs( fitsurS5 ) 332s [1] 40 332s > 332s > 332s > ## **************** shorter summaries ********************** 332s > print( summary( fitsur1e2, useDfSys = TRUE, equations = FALSE ) ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 33 172 -0.896 0.679 1.01 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 66.8 3.93 1.98 0.751 0.722 332s supply 20 16 105.3 6.58 2.57 0.607 0.534 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.73 4.28 332s supply 4.28 5.78 332s 332s warning: this covariance matrix is NOT positive semidefinit! 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.93 5.17 332s supply 5.17 6.58 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.984 332s supply 0.984 1.000 332s 332s 332s Coefficients: 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 99.2120 7.5127 13.21 1.0e-14 *** 332s demand_price -0.2667 0.0877 -3.04 0.0046 ** 332s demand_income 0.2908 0.0406 7.16 3.3e-08 *** 332s supply_(Intercept) 63.0768 10.9735 5.75 2.0e-06 *** 332s supply_price 0.1439 0.0943 1.52 0.1368 332s supply_farmPrice 0.2064 0.0384 5.37 6.1e-06 *** 332s supply_trend 0.3325 0.0640 5.19 1.0e-05 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > 332s > print( summary( fitsur2e, useDfSys = FALSE, residCov = FALSE ) ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 34 180 0.62 0.663 0.707 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 72.6 4.27 2.07 0.729 0.697 332s supply 20 16 107.9 6.75 2.60 0.597 0.522 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 98.7799 6.9687 14.17 7.6e-11 *** 332s price -0.2354 0.0795 -2.96 0.0088 ** 332s income 0.2631 0.0344 7.66 6.6e-07 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.066 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 72.577 MSE: 4.269 Root MSE: 2.066 332s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: consump ~ price + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 67.6039 9.5712 7.06 2.7e-06 *** 332s price 0.1328 0.0853 1.56 0.14 332s farmPrice 0.1785 0.0305 5.85 2.5e-05 *** 332s trend 0.2631 0.0344 7.66 9.7e-07 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.597 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 107.917 MSE: 6.745 Root MSE: 2.597 332s Multiple R-Squared: 0.597 Adjusted R-Squared: 0.522 332s 332s > 332s > print( summary( fitsur3 ), equations = FALSE ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 34 179 0.933 0.665 0.753 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 71.6 4.21 2.05 0.733 0.702 332s supply 20 16 107.8 6.74 2.60 0.598 0.523 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.78 4.47 332s supply 4.47 5.94 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 4.21 5.24 332s supply 5.24 6.74 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.983 332s supply 0.983 1.000 332s 332s 332s Coefficients: 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 98.8408 7.5581 13.08 8.0e-15 *** 332s demand_price -0.2398 0.0860 -2.79 0.0086 ** 332s demand_income 0.2670 0.0368 7.25 2.2e-08 *** 332s supply_(Intercept) 67.4283 10.6647 6.32 3.3e-07 *** 332s supply_price 0.1332 0.0953 1.40 0.1713 332s supply_farmPrice 0.1795 0.0337 5.33 6.3e-06 *** 332s supply_trend 0.2670 0.0368 7.25 2.2e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > 332s > print( summary( fitsur4r3 ), residCov = FALSE, equations = FALSE ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 173 0.217 0.677 0.702 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 66.4 3.91 1.98 0.752 0.723 332s supply 20 16 106.9 6.68 2.58 0.601 0.526 332s 332s 332s Coefficients: 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 93.1978 7.3168 12.74 1.1e-14 *** 332s demand_price -0.2381 0.0829 -2.87 0.0069 ** 332s demand_income 0.3231 0.0170 18.96 < 2e-16 *** 332s supply_(Intercept) 49.3676 7.4381 6.64 1.1e-07 *** 332s supply_price 0.2619 0.0829 3.16 0.0033 ** 332s supply_farmPrice 0.2271 0.0171 13.29 3.1e-15 *** 332s supply_trend 0.3231 0.0170 18.96 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > 332s > print( summary( fitsur5, residCov = FALSE ), equations = FALSE ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 165 1.76 0.691 0.69 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 64 3.76 1.94 0.761 0.733 332s supply 20 16 101 6.34 2.52 0.622 0.551 332s 332s 332s Coefficients: 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 96.8275 7.4665 12.97 6.2e-15 *** 332s demand_price -0.2798 0.0840 -3.33 0.002 ** 332s demand_income 0.3286 0.0206 15.93 < 2e-16 *** 332s supply_(Intercept) 52.9386 7.6655 6.91 5.1e-08 *** 332s supply_price 0.2202 0.0840 2.62 0.013 * 332s supply_farmPrice 0.2327 0.0212 10.97 7.2e-13 *** 332s supply_trend 0.3286 0.0206 15.93 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > 332s > print( summary( fitsur5w, equations = FALSE, residCov = FALSE ), 332s + equations = TRUE ) 332s 332s systemfit results 332s method: SUR 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 166 1.75 0.69 0.691 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 64.2 3.77 1.94 0.761 0.733 332s supply 20 16 102.0 6.37 2.52 0.620 0.548 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 96.4421 7.4234 12.99 6e-15 *** 332s price -0.2753 0.0838 -3.29 0.0023 ** 332s income 0.3280 0.0202 16.21 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.943 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 64.16 MSE: 3.774 Root MSE: 1.943 332s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: consump ~ price + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 52.5761 7.6099 6.91 5.0e-08 *** 332s price 0.2247 0.0838 2.68 0.011 * 332s farmPrice 0.2318 0.0208 11.14 4.7e-13 *** 332s trend 0.3280 0.0202 16.21 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 2.524 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 101.967 MSE: 6.373 Root MSE: 2.524 332s Multiple R-Squared: 0.62 Adjusted R-Squared: 0.548 332s 332s > 332s > print( summary( fitsuri1r3, useDfSys = FALSE ), residCov = FALSE ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 7 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 33 109 4.06 0.884 0.96 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 66.8 3.93 1.98 0.751 0.721 332s supply 20 16 41.7 2.61 1.61 0.937 0.926 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 93.5427 7.3858 12.67 4.4e-10 *** 332s price -0.2285 0.0877 -2.60 0.019 * 332s income 0.3097 0.0458 6.76 3.3e-06 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.983 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 66.826 MSE: 3.931 Root MSE: 1.983 332s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 89.1830 3.3861 26.3 1.3e-14 *** 332s income 0.6639 0.0423 15.7 3.8e-11 *** 332s farmPrice -0.4715 0.0370 -12.8 8.5e-10 *** 332s trend -0.7955 0.0645 -12.3 1.4e-09 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.615 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 41.708 MSE: 2.607 Root MSE: 1.615 332s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 332s 332s > 332s > print( summary( fitsuri2 ), residCov = FALSE ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 21 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 34 587 110 0.372 0.669 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67 3.94 1.99 0.75 0.721 332s supply 20 16 520 32.52 5.70 0.22 0.074 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 107.3678 7.4986 14.32 4.4e-16 *** 332s price -0.3945 0.0912 -4.33 0.00013 *** 332s income 0.3382 0.0466 7.25 2.1e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.986 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 67.024 MSE: 3.943 Root MSE: 1.986 332s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 332s income 0.3125 0.1233 2.53 0.016 * 332s farmPrice -0.1972 0.1157 -1.70 0.097 . 332s trend 0.3382 0.0466 7.25 2.1e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.703 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 520.329 MSE: 32.521 Root MSE: 5.703 332s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 332s 332s > 332s > print( summary( fitsuri3e, residCov = FALSE, equations = FALSE ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 22 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 34 588 74.9 0.372 0.664 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67.5 3.97 1.99 0.748 0.719 332s supply 20 16 520.2 32.51 5.70 0.220 0.074 332s 332s 332s Coefficients: 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 107.8051 6.9270 15.56 < 2e-16 *** 332s demand_price -0.3986 0.0843 -4.73 3.8e-05 *** 332s demand_income 0.3379 0.0431 7.84 4.0e-09 *** 332s supply_(Intercept) 85.1071 10.8287 7.86 3.8e-09 *** 332s supply_income 0.3106 0.1101 2.82 0.0079 ** 332s supply_farmPrice -0.1960 0.1034 -1.89 0.0667 . 332s supply_trend 0.3379 0.0431 7.84 4.0e-09 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > 332s > print( summary( fitsurio4, residCov = FALSE ), equations = FALSE ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 10 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 176 1.74 0.671 0.705 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 67.2 3.95 1.99 0.749 0.720 332s supply 20 16 109.2 6.83 2.61 0.593 0.516 332s 332s 332s Coefficients: 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 332s demand_price -0.2276 0.0850 -2.68 0.0112 * 332s demand_income 0.3203 0.0185 17.32 < 2e-16 *** 332s supply_(Intercept) 48.7295 7.4587 6.53 1.5e-07 *** 332s supply_price 0.2724 0.0850 3.20 0.0029 ** 332s supply_farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 332s supply_trend 0.3203 0.0185 17.32 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( summary( fitsuri4, equations = FALSE ), residCov = FALSE ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 19 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 575 121 0.385 0.637 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 65.5 3.85 1.96 0.756 0.727 332s supply 20 16 509.3 31.83 5.64 0.237 0.094 332s 332s 332s Coefficients: 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 98.0356 6.7437 14.54 2.2e-16 *** 332s demand_price -0.2646 0.0777 -3.40 0.0017 ** 332s demand_income 0.3007 0.0436 6.89 5.3e-08 *** 332s supply_(Intercept) 90.0046 10.4367 8.62 3.5e-10 *** 332s supply_income 0.2354 0.0777 3.03 0.0046 ** 332s supply_farmPrice -0.1667 0.1108 -1.50 0.1416 332s supply_trend 0.3007 0.0436 6.89 5.3e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > 332s > print( summary( fitsuri4w, useDfSys = FALSE, equations = FALSE ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 18 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 575 121 0.385 0.637 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 65.5 3.85 1.96 0.756 0.727 332s supply 20 16 509.3 31.83 5.64 0.237 0.094 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 3.85 1.23 332s supply 1.23 31.83 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 3.85 1.23 332s supply 1.23 31.83 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.111 332s supply 0.111 1.000 332s 332s 332s Coefficients: 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 98.0361 6.7437 14.54 5.1e-11 *** 332s demand_price -0.2646 0.0777 -3.40 0.0034 ** 332s demand_income 0.3007 0.0436 6.89 2.6e-06 *** 332s supply_(Intercept) 90.0052 10.4368 8.62 2.1e-07 *** 332s supply_income 0.2354 0.0777 3.03 0.0080 ** 332s supply_farmPrice -0.1667 0.1108 -1.50 0.1521 332s supply_trend 0.3007 0.0436 6.89 3.6e-06 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > 332s > print( summary( fitsurio5r2, equations = FALSE ) ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s warning: convergence not achieved after 100 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 253 -1.67 0.527 0.927 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 95.8 5.63 2.37 0.643 0.601 332s supply 20 16 157.7 9.86 3.14 0.412 0.301 332s 332s The covariance matrix of the residuals used for estimation 332s demand supply 332s demand 4.26 5.29 332s supply 5.29 6.69 332s 332s warning: this covariance matrix is NOT positive semidefinit! 332s 332s The covariance matrix of the residuals 332s demand supply 332s demand 5.63 7.56 332s supply 7.56 9.86 332s 332s The correlations of the residuals 332s demand supply 332s demand 1.000 0.982 332s supply 0.982 1.000 332s 332s 332s Coefficients: 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 78.0342 7.1638 10.89 8.6e-13 *** 332s demand_price -0.0647 0.0815 -0.79 0.43 332s demand_income 0.3007 0.0131 23.01 < 2e-16 *** 332s supply_(Intercept) 34.1958 7.2257 4.73 3.6e-05 *** 332s supply_price 0.4353 0.0815 5.34 5.7e-06 *** 332s supply_farmPrice 0.2070 0.0124 16.68 < 2e-16 *** 332s supply_trend 0.3007 0.0131 23.01 < 2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( summary( fitsuri5r2 ), residCov = FALSE ) 332s 332s systemfit results 332s method: iterated SUR 332s 332s convergence achieved after 21 iterations 332s 332s N DF SSR detRCov OLS-R2 McElroy-R2 332s system 40 35 576 121 0.384 0.637 332s 332s N DF SSR MSE RMSE R2 Adj R2 332s demand 20 17 65.4 3.85 1.96 0.756 0.727 332s supply 20 16 510.8 31.92 5.65 0.235 0.091 332s 332s 332s SUR estimates for 'demand' (equation 1) 332s Model Formula: consump ~ price + income 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 98.2200 6.7593 14.53 2.2e-16 *** 332s price -0.2669 0.0778 -3.43 0.0016 ** 332s income 0.3011 0.0435 6.92 4.9e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 1.962 on 17 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 17 332s SSR: 65.447 MSE: 3.85 Root MSE: 1.962 332s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 332s 332s 332s SUR estimates for 'supply' (equation 2) 332s Model Formula: price ~ income + farmPrice + trend 332s 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 90.2167 10.4342 8.65 3.3e-10 *** 332s income 0.2331 0.0778 3.00 0.005 ** 332s farmPrice -0.1666 0.1111 -1.50 0.143 332s trend 0.3011 0.0435 6.92 4.9e-08 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s 332s Residual standard error: 5.65 on 16 degrees of freedom 332s Number of observations: 20 Degrees of Freedom: 16 332s SSR: 510.75 MSE: 31.922 Root MSE: 5.65 332s Multiple R-Squared: 0.235 Adjusted R-Squared: 0.091 332s 332s > 332s > 332s > ## ****************** residuals ************************** 332s > print( residuals( fitsur1e2 ) ) 332s demand supply 332s 1 0.615 0.41825 332s 2 -0.598 -0.00625 332s 3 2.419 2.75649 332s 4 1.609 1.81727 332s 5 2.145 2.53566 332s 6 1.332 1.53338 332s 7 1.727 2.25581 332s 8 -2.718 -3.56834 332s 9 -1.229 -2.02733 332s 10 2.088 2.53245 332s 11 -0.789 -1.40733 332s 12 -2.799 -3.01416 332s 13 -1.831 -2.30119 332s 14 -0.461 0.01871 332s 15 1.974 2.93624 332s 16 -3.291 -4.00484 332s 17 -0.652 -0.45580 332s 18 -1.899 -3.18683 332s 19 2.030 2.18284 332s 20 0.329 0.98497 332s > print( residuals( fitsur1e2$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 332s 0.41825 -0.00625 2.75649 1.81727 2.53566 1.53338 2.25581 -3.56834 332s 9 10 11 12 13 14 15 16 332s -2.02733 2.53245 -1.40733 -3.01416 -2.30119 0.01871 2.93624 -4.00484 332s 17 18 19 20 332s -0.45580 -3.18683 2.18284 0.98497 332s > 332s > print( residuals( fitsur1w ) ) 332s demand supply 332s 1 0.696 0.4713 332s 2 -0.561 0.0197 332s 3 2.455 2.7782 332s 4 1.643 1.8366 332s 5 2.110 2.4709 332s 6 1.304 1.4773 332s 7 1.692 2.2079 332s 8 -2.756 -3.6663 332s 9 -1.253 -2.0985 332s 10 2.078 2.5321 332s 11 -0.675 -1.2705 332s 12 -2.649 -2.8068 332s 13 -1.706 -2.1305 332s 14 -0.419 0.1150 332s 15 1.887 2.8772 332s 16 -3.364 -4.1013 332s 17 -0.762 -0.5650 332s 18 -1.918 -3.2183 332s 19 1.978 2.1637 332s 20 0.218 0.9075 332s > print( residuals( fitsur1w$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 332s 0.4713 0.0197 2.7782 1.8366 2.4709 1.4773 2.2079 -3.6663 -2.0985 2.5321 332s 11 12 13 14 15 16 17 18 19 20 332s -1.2705 -2.8068 -2.1305 0.1150 2.8772 -4.1013 -0.5650 -3.2183 2.1637 0.9075 332s > 332s > print( residuals( fitsur2e ) ) 332s demand supply 332s 1 0.325 -0.200 332s 2 -0.729 -0.481 332s 3 2.288 2.342 332s 4 1.487 1.457 332s 5 2.271 2.527 332s 6 1.432 1.537 332s 7 1.851 2.275 332s 8 -2.582 -3.322 332s 9 -1.143 -1.834 332s 10 2.124 2.512 332s 11 -1.193 -1.885 332s 12 -3.332 -3.705 332s 13 -2.280 -2.813 332s 14 -0.614 -0.177 332s 15 2.281 3.353 332s 16 -3.032 -3.407 332s 17 -0.260 0.233 332s 18 -1.834 -2.737 332s 19 2.215 2.632 332s 20 0.726 1.692 332s > print( residuals( fitsur2e$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 332s 0.325 -0.729 2.288 1.487 2.271 1.432 1.851 -2.582 -1.143 2.124 -1.193 332s 12 13 14 15 16 17 18 19 20 332s -3.332 -2.280 -0.614 2.281 -3.032 -0.260 -1.834 2.215 0.726 332s > 332s > print( residuals( fitsur3 ) ) 332s demand supply 332s 1 0.366 -0.164 332s 2 -0.711 -0.452 332s 3 2.307 2.368 332s 4 1.504 1.479 332s 5 2.253 2.535 332s 6 1.418 1.544 332s 7 1.833 2.279 332s 8 -2.601 -3.327 332s 9 -1.155 -1.839 332s 10 2.119 2.513 332s 11 -1.136 -1.869 332s 12 -3.257 -3.682 332s 13 -2.217 -2.798 332s 14 -0.593 -0.175 332s 15 2.238 3.332 332s 16 -3.069 -3.436 332s 17 -0.315 0.199 332s 18 -1.844 -2.764 332s 19 2.189 2.604 332s 20 0.671 1.654 332s > print( residuals( fitsur3$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 332s -0.164 -0.452 2.368 1.479 2.535 1.544 2.279 -3.327 -1.839 2.513 -1.869 332s 12 13 14 15 16 17 18 19 20 332s -3.682 -2.798 -0.175 3.332 -3.436 0.199 -2.764 2.604 1.654 332s > 332s > print( residuals( fitsur4r3 ) ) 332s demand supply 332s 1 0.934 0.265 332s 2 -0.721 -0.638 332s 3 2.348 2.232 332s 4 1.459 1.196 332s 5 2.129 2.428 332s 6 1.253 1.318 332s 7 1.514 1.913 332s 8 -3.185 -4.425 332s 9 -1.097 -1.870 332s 10 2.619 3.483 332s 11 0.135 -0.260 332s 12 -2.097 -2.275 332s 13 -1.496 -2.085 332s 14 -0.201 0.516 332s 15 1.934 3.439 332s 16 -3.491 -3.942 332s 17 -0.229 0.913 332s 18 -2.236 -3.503 332s 19 1.440 1.736 332s 20 -1.012 -0.441 332s > print( residuals( fitsur4r3$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 332s 0.934 -0.721 2.348 1.459 2.129 1.253 1.514 -3.185 -1.097 2.619 0.135 332s 12 13 14 15 16 17 18 19 20 332s -2.097 -1.496 -0.201 1.934 -3.491 -0.229 -2.236 1.440 -1.012 332s > 332s > print( residuals( fitsur5 ) ) 332s demand supply 332s 1 1.0025 0.3219 332s 2 -0.5449 -0.4286 332s 3 2.4949 2.4014 332s 4 1.6426 1.4106 332s 5 2.0329 2.2956 332s 6 1.2129 1.2545 332s 7 1.5260 1.9262 332s 8 -3.0444 -4.2868 332s 9 -1.2406 -2.0779 332s 10 2.3001 3.0973 332s 11 -0.0303 -0.4650 332s 12 -2.0337 -2.1783 332s 13 -1.3041 -1.8356 332s 14 -0.2155 0.5292 332s 15 1.6991 3.1787 332s 16 -3.5980 -4.0840 332s 17 -0.7860 0.2371 332s 18 -2.1070 -3.3544 332s 19 1.6070 1.9694 332s 20 -0.6134 0.0885 332s > print( residuals( fitsur5$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 332s 0.3219 -0.4286 2.4014 1.4106 2.2956 1.2545 1.9262 -4.2868 -2.0779 3.0973 332s 11 12 13 14 15 16 17 18 19 20 332s -0.4650 -2.1783 -1.8356 0.5292 3.1787 -4.0840 0.2371 -3.3544 1.9694 0.0885 332s > 332s > print( residuals( fitsuri1r3 ) ) 332s demand supply 332s 1 0.7952 0.123 332s 2 -0.7614 -1.393 332s 3 2.3039 -0.829 332s 4 1.4250 -0.430 332s 5 2.1792 -1.213 332s 6 1.2979 -0.653 332s 7 1.5795 -1.266 332s 8 -3.0935 2.153 332s 9 -1.0750 1.548 332s 10 2.5876 -1.582 332s 11 -0.0991 0.990 332s 12 -2.3616 0.460 332s 13 -1.6970 1.335 332s 14 -0.2819 -1.054 332s 15 2.0557 -2.339 332s 16 -3.3745 1.734 332s 17 -0.1140 -1.054 332s 18 -2.1822 3.461 332s 19 1.5612 0.318 332s 20 -0.7450 -0.308 332s > print( residuals( fitsuri1r3$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 332s 0.7952 -0.7614 2.3039 1.4250 2.1792 1.2979 1.5795 -3.0935 -1.0750 2.5876 332s 11 12 13 14 15 16 17 18 19 20 332s -0.0991 -2.3616 -1.6970 -0.2819 2.0557 -3.3745 -0.1140 -2.1822 1.5612 -0.7450 332s > 332s > print( residuals( fitsuri2 ) ) 332s demand supply 332s 1 1.1341 6.955 332s 2 -0.0587 7.587 332s 3 2.8946 6.701 332s 4 2.1508 6.768 332s 5 1.7798 1.930 332s 6 1.1200 2.315 332s 7 1.5920 2.230 332s 8 -2.5983 4.980 332s 9 -1.6414 -0.392 332s 10 1.3742 -5.140 332s 11 -0.6115 -3.174 332s 12 -1.9764 -0.804 332s 13 -0.8493 1.012 332s 14 -0.2942 -3.282 332s 15 1.0840 -7.042 332s 16 -3.8500 -4.140 332s 17 -2.3259 -12.628 332s 18 -1.7141 -1.498 332s 19 2.1409 -2.683 332s 20 0.6494 0.305 332s > print( residuals( fitsuri2$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 332s 6.955 7.587 6.701 6.768 1.930 2.315 2.230 4.980 -0.392 -5.140 332s 11 12 13 14 15 16 17 18 19 20 332s -3.174 -0.804 1.012 -3.282 -7.042 -4.140 -12.628 -1.498 -2.683 0.305 332s > 332s > print( residuals( fitsuri3e ) ) 332s demand supply 332s 1 1.1327 6.932 332s 2 -0.0412 7.582 332s 3 2.9085 6.695 332s 4 2.1695 6.766 332s 5 1.7721 1.915 332s 6 1.1185 2.305 332s 7 1.5978 2.229 332s 8 -2.5761 4.982 332s 9 -1.6564 -0.410 332s 10 1.3358 -5.161 332s 11 -0.6458 -3.196 332s 12 -1.9868 -0.807 332s 13 -0.8408 1.021 332s 14 -0.3012 -3.275 332s 15 1.0652 -7.037 332s 16 -3.8545 -4.135 332s 17 -2.3819 -12.646 332s 18 -1.6959 -1.478 332s 19 2.1679 -2.647 332s 20 0.7125 0.366 332s > print( residuals( fitsuri3e$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 332s 1.1327 -0.0412 2.9085 2.1695 1.7721 1.1185 1.5978 -2.5761 -1.6564 1.3358 332s 11 12 13 14 15 16 17 18 19 20 332s -0.6458 -1.9868 -0.8408 -0.3012 1.0652 -3.8545 -2.3819 -1.6959 2.1679 0.7125 332s > 332s > print( residuals( fitsurio4 ) ) 332s demand supply 332s 1 0.9019 0.240 332s 2 -0.7658 -0.697 332s 3 2.3097 2.184 332s 4 1.4141 1.136 332s 5 2.1571 2.490 332s 6 1.2670 1.356 332s 7 1.5188 1.928 332s 8 -3.2060 -4.430 332s 9 -1.0620 -1.789 332s 10 2.6864 3.589 332s 11 0.1438 -0.248 332s 12 -2.1427 -2.369 332s 13 -1.5629 -2.210 332s 14 -0.2076 0.479 332s 15 2.0012 3.526 332s 16 -3.4530 -3.876 332s 17 -0.0902 1.129 332s 18 -2.2581 -3.539 332s 19 1.4172 1.671 332s 20 -1.0688 -0.569 332s > print( residuals( fitsurio4$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 332s 0.240 -0.697 2.184 1.136 2.490 1.356 1.928 -4.430 -1.789 3.589 -0.248 332s 12 13 14 15 16 17 18 19 20 332s -2.369 -2.210 0.479 3.526 -3.876 1.129 -3.539 1.671 -0.569 332s > print( residuals( fitsuri4 ) ) 332s demand supply 332s 1 0.7146 5.775 332s 2 -0.6076 7.198 332s 3 2.4197 6.280 332s 4 1.5931 6.531 332s 5 2.1268 1.465 332s 6 1.3043 2.021 332s 7 1.6685 2.261 332s 8 -2.8295 5.275 332s 9 -1.2125 -0.890 332s 10 2.1921 -5.945 332s 11 -0.5521 -4.407 332s 12 -2.5920 -1.482 332s 13 -1.7095 0.895 332s 14 -0.3902 -3.220 332s 15 1.9290 -6.617 332s 16 -3.3627 -3.607 332s 17 -0.6125 -12.896 332s 18 -1.9758 -0.562 332s 19 1.8877 -1.126 332s 20 0.0085 3.051 332s > print( residuals( fitsuri4$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 332s 5.775 7.198 6.280 6.531 1.465 2.021 2.261 5.275 -0.890 -5.945 332s 11 12 13 14 15 16 17 18 19 20 332s -4.407 -1.482 0.895 -3.220 -6.617 -3.607 -12.896 -0.562 -1.126 3.051 332s > 332s > print( residuals( fitsuri4w ) ) 332s demand supply 332s 1 0.71463 5.775 332s 2 -0.60754 7.198 332s 3 2.41972 6.280 332s 4 1.59308 6.531 332s 5 2.12679 1.465 332s 6 1.30430 2.021 332s 7 1.66846 2.262 332s 8 -2.82945 5.275 332s 9 -1.21248 -0.890 332s 10 2.19209 -5.946 332s 11 -0.55215 -4.407 332s 12 -2.59194 -1.482 332s 13 -1.70948 0.895 332s 14 -0.39018 -3.220 332s 15 1.92897 -6.617 332s 16 -3.36276 -3.607 332s 17 -0.61256 -12.896 332s 18 -1.97579 -0.562 332s 19 1.88776 -1.126 332s 20 0.00854 3.051 332s > print( residuals( fitsuri4w$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 332s 5.775 7.198 6.280 6.531 1.465 2.021 2.262 5.275 -0.890 -5.946 332s 11 12 13 14 15 16 17 18 19 20 332s -4.407 -1.482 0.895 -3.220 -6.617 -3.607 -12.896 -0.562 -1.126 3.051 332s > 332s > print( residuals( fitsurio5r2 ) ) 332s demand supply 332s 1 0.655 0.0269 332s 2 -1.456 -1.5152 332s 3 1.737 1.5210 332s 4 0.696 0.3020 332s 5 2.530 2.9397 332s 6 1.417 1.5469 332s 7 1.459 1.8336 332s 8 -3.779 -5.0391 332s 9 -0.498 -1.0416 332s 10 3.950 5.0761 332s 11 0.836 0.6398 332s 12 -2.347 -2.5930 332s 13 -2.286 -3.0468 332s 14 -0.137 0.5081 332s 15 2.908 4.5036 332s 16 -3.050 -3.3786 332s 17 2.091 3.6824 332s 18 -2.775 -4.1107 332s 19 0.737 0.7819 332s 20 -2.686 -2.6370 332s > print( residuals( fitsurio5r2$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 332s 0.655 -1.456 1.737 0.696 2.530 1.417 1.459 -3.779 -0.498 3.950 0.836 332s 12 13 14 15 16 17 18 19 20 332s -2.347 -2.286 -0.137 2.908 -3.050 2.091 -2.775 0.737 -2.686 332s > print( residuals( fitsuri5r2 ) ) 332s demand supply 332s 1 0.7199 5.756 332s 2 -0.5979 7.202 332s 3 2.4279 6.281 332s 4 1.6030 6.535 332s 5 2.1212 1.472 332s 6 1.3017 2.029 332s 7 1.6683 2.275 332s 8 -2.8233 5.299 332s 9 -1.2202 -0.892 332s 10 2.1760 -5.965 332s 11 -0.5578 -4.458 332s 12 -2.5854 -1.528 332s 13 -1.6970 0.866 332s 14 -0.3899 -3.237 332s 15 1.9153 -6.607 332s 16 -3.3698 -3.593 332s 17 -0.6429 -12.902 332s 18 -1.9698 -0.549 332s 19 1.8949 -1.099 332s 20 0.0259 3.114 332s > print( residuals( fitsuri5r2$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 332s 0.7199 -0.5979 2.4279 1.6030 2.1212 1.3017 1.6683 -2.8233 -1.2202 2.1760 332s 11 12 13 14 15 16 17 18 19 20 332s -0.5578 -2.5854 -1.6970 -0.3899 1.9153 -3.3698 -0.6429 -1.9698 1.8949 0.0259 332s > 332s > 332s > ## *************** coefficients ********************* 332s > print( round( coef( fitsur1r3 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income supply_(Intercept) 332s 99.225 -0.268 0.292 62.958 332s supply_price supply_farmPrice supply_trend 332s 0.144 0.207 0.333 332s > print( round( coef( fitsur1r3$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) price farmPrice trend 332s 62.958 0.144 0.207 0.333 332s > 332s > print( round( coef( fitsuri2 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income supply_(Intercept) 332s 107.368 -0.394 0.338 85.045 332s supply_income supply_farmPrice supply_trend 332s 0.312 -0.197 0.338 332s > print( round( coef( fitsuri2$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s 107.368 -0.394 0.338 332s > 332s > print( round( coef( fitsur2we ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income supply_(Intercept) 332s 98.754 -0.234 0.261 67.888 332s supply_price supply_farmPrice supply_trend 332s 0.132 0.177 0.261 332s > print( round( coef( fitsur2we$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s 98.754 -0.234 0.261 332s > 332s > print( round( coef( fitsur3 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income supply_(Intercept) 332s 98.841 -0.240 0.267 67.428 332s supply_price supply_farmPrice supply_trend 332s 0.133 0.179 0.267 332s > print( round( coef( fitsur3, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s 98.841 -0.240 0.267 67.428 0.133 0.179 332s > print( round( coef( fitsur3$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) price farmPrice trend 332s 67.428 0.133 0.179 0.267 332s > 332s > print( round( coef( fitsur4r2 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income supply_(Intercept) 332s 92.527 -0.230 0.322 48.701 332s supply_price supply_farmPrice supply_trend 332s 0.270 0.226 0.322 332s > print( round( coef( fitsur4r2$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s 92.527 -0.230 0.322 332s > 332s > print( round( coef( fitsuri5e ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income supply_(Intercept) 332s 97.630 -0.258 0.298 89.544 332s supply_income supply_farmPrice supply_trend 332s 0.242 -0.169 0.298 332s > print( round( coef( fitsuri5e, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s 97.630 -0.258 0.298 89.544 0.242 -0.169 332s > print( round( coef( fitsuri5e$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) income farmPrice trend 332s 89.544 0.242 -0.169 0.298 332s > 332s > print( round( coef( fitsur5w ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income supply_(Intercept) 332s 96.442 -0.275 0.328 52.576 332s supply_price supply_farmPrice supply_trend 332s 0.225 0.232 0.328 332s > print( round( coef( fitsur5w, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s 96.442 -0.275 0.328 52.576 0.225 0.232 332s > print( round( coef( fitsur5w$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s 96.442 -0.275 0.328 332s > 332s > 332s > ## *************** coefficients with stats ********************* 332s > print( round( coef( summary( fitsur1r3 ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 99.225 7.5129 13.21 0.000000 332s demand_price -0.268 0.0878 -3.05 0.007262 332s demand_income 0.292 0.0408 7.15 0.000002 332s supply_(Intercept) 62.958 10.9850 5.73 0.000031 332s supply_price 0.144 0.0944 1.53 0.145991 332s supply_farmPrice 0.207 0.0386 5.37 0.000062 332s supply_trend 0.333 0.0644 5.18 0.000092 332s > print( round( coef( summary( fitsur1r3$eq[[ 2 ]] ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 62.958 10.9850 5.73 0.000031 332s price 0.144 0.0944 1.53 0.145991 332s farmPrice 0.207 0.0386 5.37 0.000062 332s trend 0.333 0.0644 5.18 0.000092 332s > 332s > print( round( coef( summary( fitsuri2, useDfSys = FALSE ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 107.368 7.4986 14.32 0.000000 332s demand_price -0.394 0.0912 -4.33 0.000459 332s demand_income 0.338 0.0466 7.25 0.000001 332s supply_(Intercept) 85.045 12.1069 7.02 0.000003 332s supply_income 0.312 0.1233 2.53 0.022132 332s supply_farmPrice -0.197 0.1157 -1.70 0.107654 332s supply_trend 0.338 0.0466 7.25 0.000002 332s > print( round( coef( summary( fitsuri2$eq[[ 1 ]], useDfSys = FALSE ) ), 332s + digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 107.368 7.4986 14.32 0.000000 332s price -0.394 0.0912 -4.33 0.000459 332s income 0.338 0.0466 7.25 0.000001 332s > 332s > print( round( coef( summary( fitsur3 ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 98.841 7.5581 13.08 0.000000 332s demand_price -0.240 0.0860 -2.79 0.008613 332s demand_income 0.267 0.0368 7.25 0.000000 332s supply_(Intercept) 67.428 10.6647 6.32 0.000000 332s supply_price 0.133 0.0953 1.40 0.171250 332s supply_farmPrice 0.179 0.0337 5.33 0.000006 332s supply_trend 0.267 0.0368 7.25 0.000000 332s > print( round( coef( summary( fitsur3 ), modified.regMat = TRUE ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s C1 98.841 7.5581 13.08 0.000000 332s C2 -0.240 0.0860 -2.79 0.008613 332s C3 0.267 0.0368 7.25 0.000000 332s C4 67.428 10.6647 6.32 0.000000 332s C5 0.133 0.0953 1.40 0.171250 332s C6 0.179 0.0337 5.33 0.000006 332s > print( round( coef( summary( fitsur3$eq[[ 2 ]] ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 67.428 10.6647 6.32 0.000000 332s price 0.133 0.0953 1.40 0.171250 332s farmPrice 0.179 0.0337 5.33 0.000006 332s trend 0.267 0.0368 7.25 0.000000 332s > 332s > print( round( coef( summary( fitsuri3we ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 107.806 6.9270 15.56 0.000000 332s demand_price -0.399 0.0843 -4.73 0.000038 332s demand_income 0.338 0.0431 7.84 0.000000 332s supply_(Intercept) 85.107 10.8288 7.86 0.000000 332s supply_income 0.311 0.1101 2.82 0.007950 332s supply_farmPrice -0.196 0.1034 -1.89 0.066671 332s supply_trend 0.338 0.0431 7.84 0.000000 332s > print( round( coef( summary( fitsuri3we ), modified.regMat = TRUE ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s C1 107.806 6.9270 15.56 0.000000 332s C2 -0.399 0.0843 -4.73 0.000038 332s C3 0.338 0.0431 7.84 0.000000 332s C4 85.107 10.8288 7.86 0.000000 332s C5 0.311 0.1101 2.82 0.007950 332s C6 -0.196 0.1034 -1.89 0.066671 332s > print( round( coef( summary( fitsuri3we$eq[[ 1 ]] ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 107.806 6.9270 15.56 0.0e+00 332s price -0.399 0.0843 -4.73 3.8e-05 332s income 0.338 0.0431 7.84 0.0e+00 332s > 332s > print( round( coef( summary( fitsur4r2 ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 92.527 7.2896 12.69 0.00000 332s demand_price -0.230 0.0827 -2.79 0.00855 332s demand_income 0.322 0.0166 19.37 0.00000 332s supply_(Intercept) 48.701 7.4034 6.58 0.00000 332s supply_price 0.270 0.0827 3.26 0.00248 332s supply_farmPrice 0.226 0.0166 13.62 0.00000 332s supply_trend 0.322 0.0166 19.37 0.00000 332s > print( round( coef( summary( fitsur4r2$eq[[ 1 ]] ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 92.527 7.2896 12.69 0.00000 332s price -0.230 0.0827 -2.79 0.00855 332s income 0.322 0.0166 19.37 0.00000 332s > 332s > print( round( coef( summary( fitsur4we ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 96.941 6.8894 14.07 0.000000 332s demand_price -0.281 0.0766 -3.67 0.000796 332s demand_income 0.329 0.0181 18.18 0.000000 332s supply_(Intercept) 52.996 7.0652 7.50 0.000000 332s supply_price 0.219 0.0766 2.85 0.007215 332s supply_farmPrice 0.234 0.0183 12.76 0.000000 332s supply_trend 0.329 0.0181 18.18 0.000000 332s > print( round( coef( summary( fitsur4we$eq[[ 2 ]] ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 52.996 7.0652 7.50 0.00000 332s price 0.219 0.0766 2.85 0.00722 332s farmPrice 0.234 0.0183 12.76 0.00000 332s trend 0.329 0.0181 18.18 0.00000 332s > 332s > print( round( coef( summary( fitsuri5e, useDfSys = FALSE ) ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s demand_(Intercept) 97.630 6.1560 15.86 0.000000 332s demand_price -0.258 0.0709 -3.63 0.002060 332s demand_income 0.298 0.0403 7.38 0.000001 332s supply_(Intercept) 89.544 9.3372 9.59 0.000000 332s supply_income 0.242 0.0709 3.42 0.003516 332s supply_farmPrice -0.169 0.0988 -1.71 0.107123 332s supply_trend 0.298 0.0403 7.38 0.000002 332s > print( round( coef( summary( fitsuri5e, useDfSys = FALSE ), 332s + modified.regMat = TRUE ), digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s C1 97.630 6.1560 15.86 NA 332s C2 -0.258 0.0709 -3.63 NA 332s C3 0.298 0.0403 7.38 NA 332s C4 89.544 9.3372 9.59 NA 332s C5 0.242 0.0709 3.42 NA 332s C6 -0.169 0.0988 -1.71 NA 332s > print( round( coef( summary( fitsuri5e$eq[[ 2 ]], useDfSys = FALSE ) ), 332s + digits = 6 ) ) 332s Estimate Std. Error t value Pr(>|t|) 332s (Intercept) 89.544 9.3372 9.59 0.000000 332s income 0.242 0.0709 3.42 0.003516 332s farmPrice -0.169 0.0988 -1.71 0.107123 332s trend 0.298 0.0403 7.38 0.000002 332s > 332s > 332s > ## *********** variance covariance matrix of the coefficients ******* 332s > print( round( vcov( fitsur1e2 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 56.4403 -0.58751 0.025716 332s demand_price -0.5875 0.00769 -0.001866 332s demand_income 0.0257 -0.00187 0.001650 332s supply_(Intercept) 61.0550 -0.40370 -0.209805 332s supply_price -0.6325 0.00579 0.000546 332s supply_farmPrice 0.0215 -0.00156 0.001379 332s supply_trend 0.0327 -0.00237 0.002095 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 61.055 -0.632489 0.021495 332s demand_price -0.404 0.005792 -0.001559 332s demand_income -0.210 0.000546 0.001379 332s supply_(Intercept) 120.418 -0.954714 -0.221454 332s supply_price -0.955 0.008900 0.000584 332s supply_farmPrice -0.221 0.000584 0.001476 332s supply_trend -0.309 0.000772 0.001950 332s supply_trend 332s demand_(Intercept) 0.032652 332s demand_price -0.002369 332s demand_income 0.002095 332s supply_(Intercept) -0.308674 332s supply_price 0.000772 332s supply_farmPrice 0.001950 332s supply_trend 0.004100 332s > print( round( vcov( fitsur1e2$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s (Intercept) 56.4403 -0.58751 0.02572 332s price -0.5875 0.00769 -0.00187 332s income 0.0257 -0.00187 0.00165 332s > 332s > print( round( vcov( fitsur1r3 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 56.4432 -0.58772 0.025901 332s demand_price -0.5877 0.00771 -0.001879 332s demand_income 0.0259 -0.00188 0.001662 332s supply_(Intercept) 60.8607 -0.40086 -0.210729 332s supply_price -0.6307 0.00577 0.000548 332s supply_farmPrice 0.0216 -0.00157 0.001385 332s supply_trend 0.0328 -0.00238 0.002104 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 60.861 -0.630659 0.021589 332s demand_price -0.401 0.005771 -0.001566 332s demand_income -0.211 0.000548 0.001385 332s supply_(Intercept) 120.671 -0.955395 -0.223176 332s supply_price -0.955 0.008902 0.000589 332s supply_farmPrice -0.223 0.000589 0.001487 332s supply_trend -0.310 0.000776 0.001959 332s supply_trend 332s demand_(Intercept) 0.032796 332s demand_price -0.002379 332s demand_income 0.002104 332s supply_(Intercept) -0.310422 332s supply_price 0.000776 332s supply_farmPrice 0.001959 332s supply_trend 0.004149 332s > print( round( vcov( fitsur1r3$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) price farmPrice trend 332s (Intercept) 120.671 -0.955395 -0.223176 -0.310422 332s price -0.955 0.008902 0.000589 0.000776 332s farmPrice -0.223 0.000589 0.001487 0.001959 332s trend -0.310 0.000776 0.001959 0.004149 332s > 332s > print( round( vcov( fitsur2e ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 48.5631 -0.50188 0.018400 332s demand_price -0.5019 0.00632 -0.001335 332s demand_income 0.0184 -0.00134 0.001180 332s supply_(Intercept) 53.2014 -0.39283 -0.140738 332s supply_price -0.5462 0.00510 0.000373 332s supply_farmPrice 0.0147 -0.00107 0.000942 332s supply_trend 0.0184 -0.00134 0.001180 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 53.201 -0.546194 0.014689 332s demand_price -0.393 0.005097 -0.001066 332s demand_income -0.141 0.000373 0.000942 332s supply_(Intercept) 91.607 -0.766739 -0.136644 332s supply_price -0.767 0.007271 0.000368 332s supply_farmPrice -0.137 0.000368 0.000931 332s supply_trend -0.141 0.000373 0.000942 332s supply_trend 332s demand_(Intercept) 0.018400 332s demand_price -0.001335 332s demand_income 0.001180 332s supply_(Intercept) -0.140738 332s supply_price 0.000373 332s supply_farmPrice 0.000942 332s supply_trend 0.001180 332s > print( round( vcov( fitsur2e$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s (Intercept) 48.5631 -0.50188 0.01840 332s price -0.5019 0.00632 -0.00134 332s income 0.0184 -0.00134 0.00118 332s > 332s > print( round( vcov( fitsur3 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 57.1254 -0.58989 0.02116 332s demand_price -0.5899 0.00739 -0.00153 332s demand_income 0.0212 -0.00153 0.00136 332s supply_(Intercept) 64.5952 -0.48211 -0.16560 332s supply_price -0.6626 0.00619 0.00044 332s supply_farmPrice 0.0173 -0.00126 0.00111 332s supply_trend 0.0212 -0.00153 0.00136 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 64.595 -0.662552 0.017322 332s demand_price -0.482 0.006195 -0.001257 332s demand_income -0.166 0.000440 0.001111 332s supply_(Intercept) 113.736 -0.956493 -0.165927 332s supply_price -0.956 0.009084 0.000448 332s supply_farmPrice -0.166 0.000448 0.001133 332s supply_trend -0.166 0.000440 0.001111 332s supply_trend 332s demand_(Intercept) 0.02116 332s demand_price -0.00153 332s demand_income 0.00136 332s supply_(Intercept) -0.16560 332s supply_price 0.00044 332s supply_farmPrice 0.00111 332s supply_trend 0.00136 332s > print( round( vcov( fitsur3, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s C1 57.1254 -0.58989 0.02116 64.595 -0.662552 0.017322 332s C2 -0.5899 0.00739 -0.00153 -0.482 0.006195 -0.001257 332s C3 0.0212 -0.00153 0.00136 -0.166 0.000440 0.001111 332s C4 64.5952 -0.48211 -0.16560 113.736 -0.956493 -0.165927 332s C5 -0.6626 0.00619 0.00044 -0.956 0.009084 0.000448 332s C6 0.0173 -0.00126 0.00111 -0.166 0.000448 0.001133 332s > print( round( vcov( fitsur3$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) price farmPrice trend 332s (Intercept) 113.736 -0.956493 -0.165927 -0.16560 332s price -0.956 0.009084 0.000448 0.00044 332s farmPrice -0.166 0.000448 0.001133 0.00111 332s trend -0.166 0.000440 0.001111 0.00136 332s > 332s > print( round( vcov( fitsur3w ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 56.7267 -0.58513 0.020348 332s demand_price -0.5851 0.00729 -0.001476 332s demand_income 0.0203 -0.00148 0.001305 332s supply_(Intercept) 64.8820 -0.48999 -0.160451 332s supply_price -0.6648 0.00623 0.000426 332s supply_farmPrice 0.0168 -0.00122 0.001077 332s supply_trend 0.0203 -0.00148 0.001305 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 64.882 -0.664819 0.016795 332s demand_price -0.490 0.006231 -0.001219 332s demand_income -0.160 0.000426 0.001077 332s supply_(Intercept) 113.543 -0.959668 -0.161181 332s supply_price -0.960 0.009129 0.000435 332s supply_farmPrice -0.161 0.000435 0.001100 332s supply_trend -0.160 0.000426 0.001077 332s supply_trend 332s demand_(Intercept) 0.020348 332s demand_price -0.001476 332s demand_income 0.001305 332s supply_(Intercept) -0.160451 332s supply_price 0.000426 332s supply_farmPrice 0.001077 332s supply_trend 0.001305 332s > print( round( vcov( fitsur3w, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s C1 56.7267 -0.58513 0.020348 64.882 -0.664819 0.016795 332s C2 -0.5851 0.00729 -0.001476 -0.490 0.006231 -0.001219 332s C3 0.0203 -0.00148 0.001305 -0.160 0.000426 0.001077 332s C4 64.8820 -0.48999 -0.160451 113.543 -0.959668 -0.161181 332s C5 -0.6648 0.00623 0.000426 -0.960 0.009129 0.000435 332s C6 0.0168 -0.00122 0.001077 -0.161 0.000435 0.001100 332s > print( round( vcov( fitsur3w$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s (Intercept) 56.7267 -0.58513 0.02035 332s price -0.5851 0.00729 -0.00148 332s income 0.0203 -0.00148 0.00130 332s > 332s > print( round( vcov( fitsur4r2 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 53.1384 -0.593514 0.065746 332s demand_price -0.5935 0.006838 -0.000927 332s demand_income 0.0657 -0.000927 0.000276 332s supply_(Intercept) 53.3903 -0.599312 0.069540 332s supply_price -0.5935 0.006838 -0.000927 332s supply_farmPrice 0.0570 -0.000775 0.000210 332s supply_trend 0.0657 -0.000927 0.000276 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 53.3903 -0.593514 0.057048 332s demand_price -0.5993 0.006838 -0.000775 332s demand_income 0.0695 -0.000927 0.000210 332s supply_(Intercept) 54.8108 -0.599312 0.048653 332s supply_price -0.5993 0.006838 -0.000775 332s supply_farmPrice 0.0487 -0.000775 0.000276 332s supply_trend 0.0695 -0.000927 0.000210 332s supply_trend 332s demand_(Intercept) 0.065746 332s demand_price -0.000927 332s demand_income 0.000276 332s supply_(Intercept) 0.069540 332s supply_price -0.000927 332s supply_farmPrice 0.000210 332s supply_trend 0.000276 332s > print( round( vcov( fitsur4r2$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s (Intercept) 53.1384 -0.593514 0.065746 332s price -0.5935 0.006838 -0.000927 332s income 0.0657 -0.000927 0.000276 332s > 332s > print( round( vcov( fitsur5e ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 47.8867 -0.516747 0.040579 332s demand_price -0.5167 0.005886 -0.000738 332s demand_income 0.0406 -0.000738 0.000340 332s supply_(Intercept) 48.2187 -0.526670 0.047594 332s supply_price -0.5167 0.005886 -0.000738 332s supply_farmPrice 0.0334 -0.000562 0.000234 332s supply_trend 0.0406 -0.000738 0.000340 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 48.2187 -0.516747 0.033361 332s demand_price -0.5267 0.005886 -0.000562 332s demand_income 0.0476 -0.000738 0.000234 332s supply_(Intercept) 50.4739 -0.526670 0.020109 332s supply_price -0.5267 0.005886 -0.000562 332s supply_farmPrice 0.0201 -0.000562 0.000348 332s supply_trend 0.0476 -0.000738 0.000234 332s supply_trend 332s demand_(Intercept) 0.040579 332s demand_price -0.000738 332s demand_income 0.000340 332s supply_(Intercept) 0.047594 332s supply_price -0.000738 332s supply_farmPrice 0.000234 332s supply_trend 0.000340 332s > print( round( vcov( fitsur5e, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s C1 47.8867 -0.516747 0.040579 48.2187 -0.516747 0.033361 332s C2 -0.5167 0.005886 -0.000738 -0.5267 0.005886 -0.000562 332s C3 0.0406 -0.000738 0.000340 0.0476 -0.000738 0.000234 332s C4 48.2187 -0.526670 0.047594 50.4739 -0.526670 0.020109 332s C5 -0.5167 0.005886 -0.000738 -0.5267 0.005886 -0.000562 332s C6 0.0334 -0.000562 0.000234 0.0201 -0.000562 0.000348 332s > print( round( vcov( fitsur5e$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) price farmPrice trend 332s (Intercept) 50.4739 -0.526670 0.020109 0.047594 332s price -0.5267 0.005886 -0.000562 -0.000738 332s farmPrice 0.0201 -0.000562 0.000348 0.000234 332s trend 0.0476 -0.000738 0.000234 0.000340 332s > 332s > print( round( vcov( fitsuri1r3 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 54.5505 -0.55698 0.013891 332s demand_price -0.5570 0.00770 -0.002185 332s demand_income 0.0139 -0.00218 0.002098 332s supply_(Intercept) -2.7032 -0.08733 0.115993 332s supply_income 0.2249 -0.00185 -0.000411 332s supply_farmPrice -0.1721 0.00238 -0.000675 332s supply_trend -0.2597 0.00359 -0.001019 332s supply_(Intercept) supply_income supply_farmPrice 332s demand_(Intercept) -2.7032 0.224902 -0.172110 332s demand_price -0.0873 -0.001848 0.002379 332s demand_income 0.1160 -0.000411 -0.000675 332s supply_(Intercept) 11.4659 -0.058750 -0.051728 332s supply_income -0.0587 0.001787 -0.001018 332s supply_farmPrice -0.0517 -0.001018 0.001368 332s supply_trend -0.0578 -0.001631 0.001794 332s supply_trend 332s demand_(Intercept) -0.25970 332s demand_price 0.00359 332s demand_income -0.00102 332s supply_(Intercept) -0.05784 332s supply_income -0.00163 332s supply_farmPrice 0.00179 332s supply_trend 0.00416 332s > print( round( vcov( fitsuri1r3$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s (Intercept) 54.5505 -0.55698 0.01389 332s price -0.5570 0.00770 -0.00218 332s income 0.0139 -0.00218 0.00210 332s > 332s > print( round( vcov( fitsuri2 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 56.2287 -0.59260 0.033216 332s demand_price -0.5926 0.00831 -0.002451 332s demand_income 0.0332 -0.00245 0.002173 332s supply_(Intercept) 5.9548 0.14141 -0.203885 332s supply_income -0.2516 0.00201 0.000518 332s supply_farmPrice 0.1910 -0.00323 0.001351 332s supply_trend 0.0332 -0.00245 0.002173 332s supply_(Intercept) supply_income supply_farmPrice 332s demand_(Intercept) 5.955 -0.251647 0.19097 332s demand_price 0.141 0.002011 -0.00323 332s demand_income -0.204 0.000518 0.00135 332s supply_(Intercept) 146.577 -0.828954 -0.64122 332s supply_income -0.829 0.015214 -0.00683 332s supply_farmPrice -0.641 -0.006835 0.01339 332s supply_trend -0.204 0.000518 0.00135 332s supply_trend 332s demand_(Intercept) 0.033216 332s demand_price -0.002451 332s demand_income 0.002173 332s supply_(Intercept) -0.203885 332s supply_income 0.000518 332s supply_farmPrice 0.001351 332s supply_trend 0.002173 332s > print( round( vcov( fitsuri2$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) income farmPrice trend 332s (Intercept) 146.577 -0.828954 -0.64122 -0.203885 332s income -0.829 0.015214 -0.00683 0.000518 332s farmPrice -0.641 -0.006835 0.01339 0.001351 332s trend -0.204 0.000518 0.00135 0.002173 332s > 332s > print( round( vcov( fitsuri3e ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 47.9834 -0.50592 0.028570 332s demand_price -0.5059 0.00710 -0.002098 332s demand_income 0.0286 -0.00210 0.001859 332s supply_(Intercept) 4.9860 0.11975 -0.172089 332s supply_income -0.2118 0.00170 0.000428 332s supply_farmPrice 0.1609 -0.00273 0.001147 332s supply_trend 0.0286 -0.00210 0.001859 332s supply_(Intercept) supply_income supply_farmPrice 332s demand_(Intercept) 4.986 -0.211763 0.16090 332s demand_price 0.120 0.001700 -0.00273 332s demand_income -0.172 0.000428 0.00115 332s supply_(Intercept) 117.261 -0.661134 -0.51405 332s supply_income -0.661 0.012132 -0.00545 332s supply_farmPrice -0.514 -0.005450 0.01070 332s supply_trend -0.172 0.000428 0.00115 332s supply_trend 332s demand_(Intercept) 0.028570 332s demand_price -0.002098 332s demand_income 0.001859 332s supply_(Intercept) -0.172089 332s supply_income 0.000428 332s supply_farmPrice 0.001147 332s supply_trend 0.001859 332s > print( round( vcov( fitsuri3e, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s C1 47.9834 -0.50592 0.028570 4.986 -0.211763 0.16090 332s C2 -0.5059 0.00710 -0.002098 0.120 0.001700 -0.00273 332s C3 0.0286 -0.00210 0.001859 -0.172 0.000428 0.00115 332s C4 4.9860 0.11975 -0.172089 117.261 -0.661134 -0.51405 332s C5 -0.2118 0.00170 0.000428 -0.661 0.012132 -0.00545 332s C6 0.1609 -0.00273 0.001147 -0.514 -0.005450 0.01070 332s > print( round( vcov( fitsuri3e$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s (Intercept) 47.9834 -0.5059 0.02857 332s price -0.5059 0.0071 -0.00210 332s income 0.0286 -0.0021 0.00186 332s > 332s > print( round( vcov( fitsurio4e ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 47.0268 -0.525375 0.058300 332s demand_price -0.5254 0.006074 -0.000842 332s demand_income 0.0583 -0.000842 0.000266 332s supply_(Intercept) 47.2346 -0.530682 0.061997 332s supply_price -0.5254 0.006074 -0.000842 332s supply_farmPrice 0.0508 -0.000704 0.000201 332s supply_trend 0.0583 -0.000842 0.000266 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 47.2346 -0.525375 0.050751 332s demand_price -0.5307 0.006074 -0.000704 332s demand_income 0.0620 -0.000842 0.000201 332s supply_(Intercept) 48.6183 -0.530682 0.042182 332s supply_price -0.5307 0.006074 -0.000704 332s supply_farmPrice 0.0422 -0.000704 0.000270 332s supply_trend 0.0620 -0.000842 0.000201 332s supply_trend 332s demand_(Intercept) 0.058300 332s demand_price -0.000842 332s demand_income 0.000266 332s supply_(Intercept) 0.061997 332s supply_price -0.000842 332s supply_farmPrice 0.000201 332s supply_trend 0.000266 332s > print( round( vcov( fitsurio4e$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) price farmPrice trend 332s (Intercept) 48.6183 -0.530682 0.042182 0.061997 332s price -0.5307 0.006074 -0.000704 -0.000842 332s farmPrice 0.0422 -0.000704 0.000270 0.000201 332s trend 0.0620 -0.000842 0.000201 0.000266 332s > print( round( vcov( fitsuri4e ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 37.8960 -0.36274 -0.01487 332s demand_price -0.3627 0.00503 -0.00144 332s demand_income -0.0149 -0.00144 0.00163 332s supply_(Intercept) 19.0822 -0.20611 0.01617 332s supply_income -0.3627 0.00503 -0.00144 332s supply_farmPrice 0.1707 -0.00279 0.00111 332s supply_trend -0.0149 -0.00144 0.00163 332s supply_(Intercept) supply_income supply_farmPrice 332s demand_(Intercept) 19.0822 -0.36274 0.17073 332s demand_price -0.2061 0.00503 -0.00279 332s demand_income 0.0162 -0.00144 0.00111 332s supply_(Intercept) 87.1827 -0.20611 -0.68294 332s supply_income -0.2061 0.00503 -0.00279 332s supply_farmPrice -0.6829 -0.00279 0.00976 332s supply_trend 0.0162 -0.00144 0.00111 332s supply_trend 332s demand_(Intercept) -0.01487 332s demand_price -0.00144 332s demand_income 0.00163 332s supply_(Intercept) 0.01617 332s supply_income -0.00144 332s supply_farmPrice 0.00111 332s supply_trend 0.00163 332s > print( round( vcov( fitsuri4e$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) income farmPrice trend 332s (Intercept) 87.1827 -0.20611 -0.68294 0.01617 332s income -0.2061 0.00503 -0.00279 -0.00144 332s farmPrice -0.6829 -0.00279 0.00976 0.00111 332s trend 0.0162 -0.00144 0.00111 0.00163 332s > 332s > print( round( vcov( fitsurio5r2 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 51.3196 -0.579747 0.070528 332s demand_price -0.5797 0.006646 -0.000872 332s demand_income 0.0705 -0.000872 0.000171 332s supply_(Intercept) 51.5518 -0.583025 0.072036 332s supply_price -0.5797 0.006646 -0.000872 332s supply_farmPrice 0.0617 -0.000751 0.000138 332s supply_trend 0.0705 -0.000872 0.000171 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 51.5518 -0.579747 0.061658 332s demand_price -0.5830 0.006646 -0.000751 332s demand_income 0.0720 -0.000872 0.000138 332s supply_(Intercept) 52.2109 -0.583025 0.058794 332s supply_price -0.5830 0.006646 -0.000751 332s supply_farmPrice 0.0588 -0.000751 0.000154 332s supply_trend 0.0720 -0.000872 0.000138 332s supply_trend 332s demand_(Intercept) 0.070528 332s demand_price -0.000872 332s demand_income 0.000171 332s supply_(Intercept) 0.072036 332s supply_price -0.000872 332s supply_farmPrice 0.000138 332s supply_trend 0.000171 332s > print( round( vcov( fitsurio5r2, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s C1 51.3196 -0.579747 0.070528 51.5518 -0.579747 0.061658 332s C2 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 332s C3 0.0705 -0.000872 0.000171 0.0720 -0.000872 0.000138 332s C4 51.5518 -0.583025 0.072036 52.2109 -0.583025 0.058794 332s C5 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 332s C6 0.0617 -0.000751 0.000138 0.0588 -0.000751 0.000154 332s > print( round( vcov( fitsurio5r2$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s (Intercept) 51.3196 -0.579747 0.070528 332s price -0.5797 0.006646 -0.000872 332s income 0.0705 -0.000872 0.000171 332s > print( round( vcov( fitsuri5r2 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 45.6881 -0.44008 -0.01517 332s demand_price -0.4401 0.00605 -0.00170 332s demand_income -0.0152 -0.00170 0.00190 332s supply_(Intercept) 22.8172 -0.23903 0.01186 332s supply_income -0.4401 0.00605 -0.00170 332s supply_farmPrice 0.2104 -0.00345 0.00138 332s supply_trend -0.0152 -0.00170 0.00190 332s supply_(Intercept) supply_income supply_farmPrice 332s demand_(Intercept) 22.8172 -0.44008 0.21042 332s demand_price -0.2390 0.00605 -0.00345 332s demand_income 0.0119 -0.00170 0.00138 332s supply_(Intercept) 108.8722 -0.23903 -0.87024 332s supply_income -0.2390 0.00605 -0.00345 332s supply_farmPrice -0.8702 -0.00345 0.01234 332s supply_trend 0.0119 -0.00170 0.00138 332s supply_trend 332s demand_(Intercept) -0.01517 332s demand_price -0.00170 332s demand_income 0.00190 332s supply_(Intercept) 0.01186 332s supply_income -0.00170 332s supply_farmPrice 0.00138 332s supply_trend 0.00190 332s > print( round( vcov( fitsuri5r2, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s C1 45.6881 -0.44008 -0.01517 22.8172 -0.44008 0.21042 332s C2 -0.4401 0.00605 -0.00170 -0.2390 0.00605 -0.00345 332s C3 -0.0152 -0.00170 0.00190 0.0119 -0.00170 0.00138 332s C4 22.8172 -0.23903 0.01186 108.8722 -0.23903 -0.87024 332s C5 -0.4401 0.00605 -0.00170 -0.2390 0.00605 -0.00345 332s C6 0.2104 -0.00345 0.00138 -0.8702 -0.00345 0.01234 332s > print( round( vcov( fitsuri5r2$eq[[ 1 ]] ), digits = 6 ) ) 332s (Intercept) price income 332s (Intercept) 45.6881 -0.44008 -0.0152 332s price -0.4401 0.00605 -0.0017 332s income -0.0152 -0.00170 0.0019 332s > 332s > print( round( vcov( fitsurio5wr2 ), digits = 6 ) ) 332s demand_(Intercept) demand_price demand_income 332s demand_(Intercept) 51.3196 -0.579747 0.070528 332s demand_price -0.5797 0.006646 -0.000872 332s demand_income 0.0705 -0.000872 0.000171 332s supply_(Intercept) 51.5518 -0.583025 0.072036 332s supply_price -0.5797 0.006646 -0.000872 332s supply_farmPrice 0.0617 -0.000751 0.000138 332s supply_trend 0.0705 -0.000872 0.000171 332s supply_(Intercept) supply_price supply_farmPrice 332s demand_(Intercept) 51.5518 -0.579747 0.061658 332s demand_price -0.5830 0.006646 -0.000751 332s demand_income 0.0720 -0.000872 0.000138 332s supply_(Intercept) 52.2109 -0.583025 0.058794 332s supply_price -0.5830 0.006646 -0.000751 332s supply_farmPrice 0.0588 -0.000751 0.000154 332s supply_trend 0.0720 -0.000872 0.000138 332s supply_trend 332s demand_(Intercept) 0.070528 332s demand_price -0.000872 332s demand_income 0.000171 332s supply_(Intercept) 0.072036 332s supply_price -0.000872 332s supply_farmPrice 0.000138 332s supply_trend 0.000171 332s > print( round( vcov( fitsurio5wr2, modified.regMat = TRUE ), digits = 6 ) ) 332s C1 C2 C3 C4 C5 C6 332s C1 51.3196 -0.579747 0.070528 51.5518 -0.579747 0.061658 332s C2 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 332s C3 0.0705 -0.000872 0.000171 0.0720 -0.000872 0.000138 332s C4 51.5518 -0.583025 0.072036 52.2109 -0.583025 0.058794 332s C5 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 332s C6 0.0617 -0.000751 0.000138 0.0588 -0.000751 0.000154 332s > print( round( vcov( fitsurio5wr2$eq[[ 2 ]] ), digits = 6 ) ) 332s (Intercept) price farmPrice trend 332s (Intercept) 52.2109 -0.583025 0.058794 0.072036 332s price -0.5830 0.006646 -0.000751 -0.000872 332s farmPrice 0.0588 -0.000751 0.000154 0.000138 332s trend 0.0720 -0.000872 0.000138 0.000171 332s > 332s > 332s > ## *********** confidence intervals of coefficients ************* 332s > print( confint( fitsur1e2, useDfSys = TRUE ) ) 332s 2.5 % 97.5 % 332s demand_(Intercept) 83.927 114.497 332s demand_price -0.445 -0.088 332s demand_income 0.208 0.373 332s supply_(Intercept) 40.751 85.403 332s supply_price -0.048 0.336 332s supply_farmPrice 0.128 0.285 332s supply_trend 0.202 0.463 332s > print( confint( fitsur1e2$eq[[ 2 ]], level = 0.9, useDfSys = TRUE ) ) 332s 5 % 95 % 332s (Intercept) 44.506 81.648 332s price -0.016 0.304 332s farmPrice 0.141 0.271 332s trend 0.224 0.441 332s > 332s > print( confint( fitsur1we2, useDfSys = TRUE ) ) 332s 2.5 % 97.5 % 332s demand_(Intercept) 83.927 114.497 332s demand_price -0.445 -0.088 332s demand_income 0.208 0.373 332s supply_(Intercept) 40.751 85.403 332s supply_price -0.048 0.336 332s supply_farmPrice 0.128 0.285 332s supply_trend 0.202 0.463 332s > print( confint( fitsur1we2$eq[[ 1 ]], level = 0.9, useDfSys = TRUE ) ) 332s 5 % 95 % 332s (Intercept) 86.498 111.926 332s price -0.415 -0.118 332s income 0.222 0.360 332s > 332s > print( confint( fitsur2e, level = 0.9 ) ) 332s 5 % 95 % 332s demand_(Intercept) 84.618 112.942 332s demand_price -0.397 -0.074 332s demand_income 0.193 0.333 332s supply_(Intercept) 48.153 87.055 332s supply_price -0.040 0.306 332s supply_farmPrice 0.116 0.240 332s supply_trend 0.193 0.333 332s > print( confint( fitsur2e$eq[[ 1 ]], level = 0.99 ) ) 332s 0.5 % 99.5 % 332s (Intercept) 79.767 117.793 332s price -0.452 -0.018 332s income 0.169 0.357 332s > 332s > print( confint( fitsur3, level = 0.99 ) ) 332s 0.5 % 99.5 % 332s demand_(Intercept) 83.481 114.201 332s demand_price -0.415 -0.065 332s demand_income 0.192 0.342 332s supply_(Intercept) 45.755 89.102 332s supply_price -0.060 0.327 332s supply_farmPrice 0.111 0.248 332s supply_trend 0.192 0.342 332s > print( confint( fitsur3$eq[[ 2 ]], level = 0.5 ) ) 332s 25 % 75 % 332s (Intercept) 60.157 74.699 332s price 0.068 0.198 332s farmPrice 0.157 0.202 332s trend 0.242 0.292 332s > 332s > print( confint( fitsur4r3, level = 0.5 ) ) 332s 25 % 75 % 332s demand_(Intercept) 78.344 108.052 332s demand_price -0.406 -0.070 332s demand_income 0.289 0.358 332s supply_(Intercept) 34.267 64.468 332s supply_price 0.094 0.430 332s supply_farmPrice 0.192 0.262 332s supply_trend 0.289 0.358 332s > print( confint( fitsur4r3$eq[[ 1 ]], level = 0.25 ) ) 332s 37.5 % 62.5 % 332s (Intercept) 90.848 95.548 332s price -0.265 -0.211 332s income 0.318 0.329 332s > 332s > print( confint( fitsur5, level = 0.25 ) ) 332s 37.5 % 62.5 % 332s demand_(Intercept) 81.670 111.985 332s demand_price -0.450 -0.109 332s demand_income 0.287 0.371 332s supply_(Intercept) 37.377 68.500 332s supply_price 0.050 0.391 332s supply_farmPrice 0.190 0.276 332s supply_trend 0.287 0.371 332s > print( confint( fitsur5$eq[[ 2 ]], level = 0.975 ) ) 332s 1.3 % 98.8 % 332s (Intercept) 34.986 70.891 332s price 0.024 0.417 332s farmPrice 0.183 0.282 332s trend 0.280 0.377 332s > 332s > print( confint( fitsuri1r3, level = 0.975 ) ) 332s 1.3 % 98.8 % 332s demand_(Intercept) 77.960 109.125 332s demand_price -0.414 -0.043 332s demand_income 0.213 0.406 332s supply_(Intercept) 82.005 96.361 332s supply_income 0.574 0.753 332s supply_farmPrice -0.550 -0.393 332s supply_trend -0.932 -0.659 332s > print( confint( fitsuri1r3$eq[[ 1 ]], level = 0.999 ) ) 332s 0.1 % 100 % 332s (Intercept) 64.257 122.828 332s price -0.576 0.119 332s income 0.128 0.491 332s > 332s > print( confint( fitsuri2, level = 0.999 ) ) 332s 0.1 % 100 % 332s demand_(Intercept) 92.129 122.607 332s demand_price -0.580 -0.209 332s demand_income 0.243 0.433 332s supply_(Intercept) 60.441 109.649 332s supply_income 0.062 0.563 332s supply_farmPrice -0.432 0.038 332s supply_trend 0.243 0.433 332s > print( confint( fitsuri2$eq[[ 2 ]], level = 0.1 ) ) 332s 45 % 55 % 332s (Intercept) 83.512 86.578 332s income 0.297 0.328 332s farmPrice -0.212 -0.183 332s trend 0.332 0.344 332s > 332s > print( confint( fitsuri3e, level = 0.1 ) ) 332s 45 % 55 % 332s demand_(Intercept) 93.728 121.882 332s demand_price -0.570 -0.227 332s demand_income 0.250 0.426 332s supply_(Intercept) 63.100 107.114 332s supply_income 0.087 0.534 332s supply_farmPrice -0.406 0.014 332s supply_trend 0.250 0.426 332s > print( confint( fitsuri3e$eq[[ 1 ]], level = 0.01 ) ) 332s 49.5 % 50.5 % 332s (Intercept) 107.718 107.893 332s price -0.400 -0.398 332s income 0.337 0.338 332s > 332s > print( confint( fitsurio4, level = 0.01 ) ) 332s 49.5 % 50.5 % 332s demand_(Intercept) 77.496 107.356 332s demand_price -0.400 -0.055 332s demand_income 0.283 0.358 332s supply_(Intercept) 33.588 63.871 332s supply_price 0.100 0.445 332s supply_farmPrice 0.185 0.262 332s supply_trend 0.283 0.358 332s > print( confint( fitsurio4$eq[[ 2 ]], level = 0.33 ) ) 332s 33.5 % 66.5 % 332s (Intercept) 45.524 51.935 332s price 0.236 0.309 332s farmPrice 0.215 0.231 332s trend 0.312 0.328 332s > print( confint( fitsuri4, level = 0.01 ) ) 332s 49.5 % 50.5 % 332s demand_(Intercept) 84.345 111.726 332s demand_price -0.422 -0.107 332s demand_income 0.212 0.389 332s supply_(Intercept) 68.817 111.192 332s supply_income 0.078 0.393 332s supply_farmPrice -0.392 0.058 332s supply_trend 0.212 0.389 332s > print( confint( fitsuri4$eq[[ 2 ]], level = 0.33 ) ) 332s 33.5 % 66.5 % 332s (Intercept) 85.519 94.490 332s income 0.202 0.269 332s farmPrice -0.214 -0.119 332s trend 0.282 0.319 332s > 332s > print( confint( fitsurio4w, level = 0.01 ) ) 332s 49.5 % 50.5 % 332s demand_(Intercept) 77.496 107.356 332s demand_price -0.400 -0.055 332s demand_income 0.283 0.358 332s supply_(Intercept) 33.587 63.871 332s supply_price 0.100 0.445 332s supply_farmPrice 0.185 0.262 332s supply_trend 0.283 0.358 332s > print( confint( fitsurio4w$eq[[ 1 ]], level = 0.33 ) ) 332s 33.5 % 66.5 % 332s (Intercept) 89.266 95.587 332s price -0.264 -0.191 332s income 0.312 0.328 332s > 332s > print( confint( fitsurio5r2, level = 0.33 ) ) 332s 33.5 % 66.5 % 332s demand_(Intercept) 63.491 92.577 332s demand_price -0.230 0.101 332s demand_income 0.274 0.327 332s supply_(Intercept) 19.527 48.865 332s supply_price 0.270 0.601 332s supply_farmPrice 0.182 0.232 332s supply_trend 0.274 0.327 332s > print( confint( fitsurio5r2$eq[[ 1 ]] ) ) 332s 2.5 % 97.5 % 332s (Intercept) 63.491 92.577 332s price -0.230 0.101 332s income 0.274 0.327 332s > print( confint( fitsuri5r2, level = 0.33 ) ) 332s 33.5 % 66.5 % 332s demand_(Intercept) 84.498 111.942 332s demand_price -0.425 -0.109 332s demand_income 0.213 0.390 332s supply_(Intercept) 69.034 111.399 332s supply_income 0.075 0.391 332s supply_farmPrice -0.392 0.059 332s supply_trend 0.213 0.390 332s > print( confint( fitsuri5r2$eq[[ 1 ]] ) ) 332s 2.5 % 97.5 % 332s (Intercept) 84.498 111.942 332s price -0.425 -0.109 332s income 0.213 0.390 332s > 332s > 332s > ## *********** fitted values ************* 332s > print( fitted( fitsur1e2 ) ) 332s demand supply 332s 1 97.9 98.1 332s 2 99.8 99.2 332s 3 99.7 99.4 332s 4 99.9 99.7 332s 5 102.1 101.7 332s 6 101.9 101.7 332s 7 102.3 101.7 332s 8 102.6 103.5 332s 9 101.6 102.4 332s 10 100.7 100.3 332s 11 96.2 96.8 332s 12 95.2 95.4 332s 13 96.4 96.8 332s 14 99.2 98.7 332s 15 103.8 102.9 332s 16 103.5 104.2 332s 17 104.2 104.0 332s 18 101.8 103.1 332s 19 103.2 103.0 332s 20 105.9 105.2 332s > print( fitted( fitsur1e2$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 98.1 99.2 99.4 99.7 101.7 101.7 101.7 103.5 102.4 100.3 96.8 95.4 96.8 332s 14 15 16 17 18 19 20 332s 98.7 102.9 104.2 104.0 103.1 103.0 105.2 332s > 332s > print( fitted( fitsur2e ) ) 332s demand supply 332s 1 98.2 98.7 332s 2 99.9 99.7 332s 3 99.9 99.8 332s 4 100.0 100.0 332s 5 102.0 101.7 332s 6 101.8 101.7 332s 7 102.1 101.7 332s 8 102.5 103.2 332s 9 101.5 102.2 332s 10 100.7 100.3 332s 11 96.6 97.3 332s 12 95.8 96.1 332s 13 96.8 97.3 332s 14 99.4 98.9 332s 15 103.5 102.4 332s 16 103.3 103.6 332s 17 103.8 103.3 332s 18 101.8 102.7 332s 19 103.0 102.6 332s 20 105.5 104.5 332s > print( fitted( fitsur2e$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 98.2 99.9 99.9 100.0 102.0 101.8 102.1 102.5 101.5 100.7 96.6 95.8 96.8 332s 14 15 16 17 18 19 20 332s 99.4 103.5 103.3 103.8 101.8 103.0 105.5 332s > 332s > print( fitted( fitsur2we ) ) 332s demand supply 332s 1 98.2 98.7 332s 2 99.9 99.7 332s 3 99.9 99.8 332s 4 100.0 100.1 332s 5 102.0 101.7 332s 6 101.8 101.7 332s 7 102.1 101.7 332s 8 102.5 103.2 332s 9 101.5 102.2 332s 10 100.7 100.3 332s 11 96.7 97.4 332s 12 95.8 96.2 332s 13 96.8 97.4 332s 14 99.4 99.0 332s 15 103.5 102.4 332s 16 103.2 103.6 332s 17 103.8 103.3 332s 18 101.8 102.7 332s 19 103.0 102.6 332s 20 105.5 104.5 332s > print( fitted( fitsur2we$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 98.7 99.7 99.8 100.1 101.7 101.7 101.7 103.2 102.2 100.3 97.4 96.2 97.4 332s 14 15 16 17 18 19 20 332s 99.0 102.4 103.6 103.3 102.7 102.6 104.5 332s > 332s > print( fitted( fitsur3 ) ) 332s demand supply 332s 1 98.1 98.6 332s 2 99.9 99.6 332s 3 99.9 99.8 332s 4 100.0 100.0 332s 5 102.0 101.7 332s 6 101.8 101.7 332s 7 102.2 101.7 332s 8 102.5 103.2 332s 9 101.5 102.2 332s 10 100.7 100.3 332s 11 96.6 97.3 332s 12 95.7 96.1 332s 13 96.8 97.3 332s 14 99.3 98.9 332s 15 103.6 102.5 332s 16 103.3 103.7 332s 17 103.8 103.3 332s 18 101.8 102.7 332s 19 103.0 102.6 332s 20 105.6 104.6 332s > print( fitted( fitsur3$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 98.6 99.6 99.8 100.0 101.7 101.7 101.7 103.2 102.2 100.3 97.3 96.1 97.3 332s 14 15 16 17 18 19 20 332s 98.9 102.5 103.7 103.3 102.7 102.6 104.6 332s > 332s > print( fitted( fitsur4r3 ) ) 332s demand supply 332s 1 97.6 98.2 332s 2 99.9 99.8 332s 3 99.8 99.9 332s 4 100.0 100.3 332s 5 102.1 101.8 332s 6 102.0 101.9 332s 7 102.5 102.1 332s 8 103.1 104.3 332s 9 101.4 102.2 332s 10 100.2 99.3 332s 11 95.3 95.7 332s 12 94.5 94.7 332s 13 96.0 96.6 332s 14 99.0 98.2 332s 15 103.9 102.4 332s 16 103.7 104.2 332s 17 103.8 102.6 332s 18 102.2 103.4 332s 19 103.8 103.5 332s 20 107.2 106.7 332s > print( fitted( fitsur4r3$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 97.6 99.9 99.8 100.0 102.1 102.0 102.5 103.1 101.4 100.2 95.3 94.5 96.0 332s 14 15 16 17 18 19 20 332s 99.0 103.9 103.7 103.8 102.2 103.8 107.2 332s > 332s > print( fitted( fitsur5 ) ) 332s demand supply 332s 1 97.5 98.2 332s 2 99.7 99.6 332s 3 99.7 99.8 332s 4 99.9 100.1 332s 5 102.2 101.9 332s 6 102.0 102.0 332s 7 102.5 102.1 332s 8 102.9 104.2 332s 9 101.6 102.4 332s 10 100.5 99.7 332s 11 95.5 95.9 332s 12 94.5 94.6 332s 13 95.8 96.4 332s 14 99.0 98.2 332s 15 104.1 102.6 332s 16 103.8 104.3 332s 17 104.3 103.3 332s 18 102.0 103.3 332s 19 103.6 103.3 332s 20 106.8 106.1 332s > print( fitted( fitsur5$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 98.2 99.6 99.8 100.1 101.9 102.0 102.1 104.2 102.4 99.7 95.9 94.6 96.4 332s 14 15 16 17 18 19 20 332s 98.2 102.6 104.3 103.3 103.3 103.3 106.1 332s > 332s > print( fitted( fitsuri1r3 ) ) 332s demand supply 332s 1 97.7 100.2 332s 2 99.9 105.7 332s 3 99.9 104.3 332s 4 100.1 104.9 332s 5 102.1 99.2 332s 6 101.9 100.1 332s 7 102.4 102.3 332s 8 103.0 102.6 332s 9 101.4 94.9 332s 10 100.2 92.8 332s 11 95.5 92.1 332s 12 94.8 98.3 332s 13 96.2 101.6 332s 14 99.0 99.8 332s 15 103.7 97.5 332s 16 103.6 96.7 332s 17 103.6 87.6 332s 18 102.1 100.6 332s 19 103.7 105.5 332s 20 107.0 113.8 332s > print( fitted( fitsuri1r3$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 97.7 99.9 99.9 100.1 102.1 101.9 102.4 103.0 101.4 100.2 95.5 94.8 96.2 332s 14 15 16 17 18 19 20 332s 99.0 103.7 103.6 103.6 102.1 103.7 107.0 332s > 332s > print( fitted( fitsuri1wr3 ) ) 332s demand supply 332s 1 97.7 100.2 332s 2 99.9 105.7 332s 3 99.9 104.3 332s 4 100.1 104.9 332s 5 102.1 99.2 332s 6 101.9 100.1 332s 7 102.4 102.3 332s 8 103.0 102.6 332s 9 101.4 94.9 332s 10 100.2 92.8 332s 11 95.5 92.1 332s 12 94.8 98.3 332s 13 96.2 101.6 332s 14 99.0 99.8 332s 15 103.7 97.5 332s 16 103.6 96.7 332s 17 103.6 87.6 332s 18 102.1 100.6 332s 19 103.7 105.5 332s 20 107.0 113.8 332s > print( fitted( fitsuri1wr3$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 100.2 105.7 104.3 104.9 99.2 100.1 102.3 102.6 94.9 92.8 92.1 98.3 101.6 332s 14 15 16 17 18 19 20 332s 99.8 97.5 96.7 87.6 100.6 105.5 113.8 332s > 332s > print( fitted( fitsuri2 ) ) 332s demand supply 332s 1 97.4 93.4 332s 2 99.2 96.7 332s 3 99.3 96.7 332s 4 99.4 97.7 332s 5 102.5 96.1 332s 6 102.1 97.1 332s 7 102.4 98.8 332s 8 102.5 99.8 332s 9 102.0 96.8 332s 10 101.4 96.4 332s 11 96.0 96.3 332s 12 94.4 99.6 332s 13 95.4 101.9 332s 14 99.1 102.0 332s 15 104.7 102.2 332s 16 104.1 102.6 332s 17 105.8 99.1 332s 18 101.6 105.5 332s 19 103.1 108.5 332s 20 105.6 113.2 332s > print( fitted( fitsuri2$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 93.4 96.7 96.7 97.7 96.1 97.1 98.8 99.8 96.8 96.4 96.3 99.6 101.9 332s 14 15 16 17 18 19 20 332s 102.0 102.2 102.6 99.1 105.5 108.5 113.2 332s > 332s > print( fitted( fitsuri3e ) ) 332s demand supply 332s 1 97.4 93.4 332s 2 99.2 96.7 332s 3 99.3 96.7 332s 4 99.3 97.7 332s 5 102.5 96.1 332s 6 102.1 97.2 332s 7 102.4 98.8 332s 8 102.5 99.8 332s 9 102.0 96.9 332s 10 101.5 96.4 332s 11 96.1 96.3 332s 12 94.4 99.6 332s 13 95.4 101.9 332s 14 99.1 102.0 332s 15 104.7 102.2 332s 16 104.1 102.6 332s 17 105.9 99.1 332s 18 101.6 105.5 332s 19 103.1 108.4 332s 20 105.5 113.1 332s > print( fitted( fitsuri3e$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 97.4 99.2 99.3 99.3 102.5 102.1 102.4 102.5 102.0 101.5 96.1 94.4 95.4 332s 14 15 16 17 18 19 20 332s 99.1 104.7 104.1 105.9 101.6 103.1 105.5 332s > 332s > print( fitted( fitsurio4 ) ) 332s demand supply 332s 1 97.6 98.2 332s 2 100.0 99.9 332s 3 99.9 100.0 332s 4 100.1 100.4 332s 5 102.1 101.8 332s 6 102.0 101.9 332s 7 102.5 102.1 332s 8 103.1 104.3 332s 9 101.4 102.1 332s 10 100.1 99.2 332s 11 95.3 95.7 332s 12 94.6 94.8 332s 13 96.1 96.7 332s 14 99.0 98.3 332s 15 103.8 102.3 332s 16 103.7 104.1 332s 17 103.6 102.4 332s 18 102.2 103.5 332s 19 103.8 103.6 332s 20 107.3 106.8 332s > print( fitted( fitsurio4$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 98.2 99.9 100.0 100.4 101.8 101.9 102.1 104.3 102.1 99.2 95.7 94.8 96.7 332s 14 15 16 17 18 19 20 332s 98.3 102.3 104.1 102.4 103.5 103.6 106.8 332s > print( fitted( fitsuri4 ) ) 332s demand supply 332s 1 97.8 94.5 332s 2 99.8 97.1 332s 3 99.7 97.2 332s 4 99.9 98.0 332s 5 102.1 96.5 332s 6 101.9 97.4 332s 7 102.3 98.8 332s 8 102.7 99.5 332s 9 101.6 97.3 332s 10 100.6 97.2 332s 11 96.0 97.5 332s 12 95.0 100.3 332s 13 96.2 102.0 332s 14 99.1 102.0 332s 15 103.9 101.7 332s 16 103.6 102.1 332s 17 104.1 99.4 332s 18 101.9 104.6 332s 19 103.3 106.9 332s 20 106.2 110.4 332s > print( fitted( fitsuri4$eq[[ 2 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 94.5 97.1 97.2 98.0 96.5 97.4 98.8 99.5 97.3 97.2 97.5 100.3 102.0 332s 14 15 16 17 18 19 20 332s 102.0 101.7 102.1 99.4 104.6 106.9 110.4 332s > 332s > print( fitted( fitsurio5r2 ) ) 332s demand supply 332s 1 97.8 98.5 332s 2 100.6 100.7 332s 3 100.4 100.6 332s 4 100.8 101.2 332s 5 101.7 101.3 332s 6 101.8 101.7 332s 7 102.5 102.2 332s 8 103.7 104.9 332s 9 100.8 101.4 332s 10 98.9 97.7 332s 11 94.6 94.8 332s 12 94.8 95.0 332s 13 96.8 97.6 332s 14 98.9 98.2 332s 15 102.9 101.3 332s 16 103.3 103.6 332s 17 101.4 99.8 332s 18 102.7 104.0 332s 19 104.5 104.4 332s 20 108.9 108.9 332s > print( fitted( fitsurio5r2$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 97.8 100.6 100.4 100.8 101.7 101.8 102.5 103.7 100.8 98.9 94.6 94.8 96.8 332s 14 15 16 17 18 19 20 332s 98.9 102.9 103.3 101.4 102.7 104.5 108.9 332s > print( fitted( fitsuri5r2 ) ) 332s demand supply 332s 1 97.8 94.6 332s 2 99.8 97.1 332s 3 99.7 97.2 332s 4 99.9 98.0 332s 5 102.1 96.5 332s 6 101.9 97.4 332s 7 102.3 98.8 332s 8 102.7 99.5 332s 9 101.6 97.3 332s 10 100.6 97.2 332s 11 96.0 97.5 332s 12 95.0 100.3 332s 13 96.2 102.0 332s 14 99.1 102.0 332s 15 103.9 101.7 332s 16 103.6 102.0 332s 17 104.2 99.4 332s 18 101.9 104.6 332s 19 103.3 106.9 332s 20 106.2 110.4 332s > print( fitted( fitsuri5r2$eq[[ 1 ]] ) ) 332s 1 2 3 4 5 6 7 8 9 10 11 12 13 332s 97.8 99.8 99.7 99.9 102.1 101.9 102.3 102.7 101.6 100.6 96.0 95.0 96.2 332s 14 15 16 17 18 19 20 332s 99.1 103.9 103.6 104.2 101.9 103.3 106.2 332s > 332s > 332s > ## *********** predicted values ************* 332s > predictData <- Kmenta 332s > predictData$consump <- NULL 332s > predictData$price <- Kmenta$price * 0.9 332s > predictData$income <- Kmenta$income * 1.1 332s > 332s > print( predict( fitsur1e2, se.fit = TRUE, interval = "prediction", 332s + useDfSys = TRUE ) ) 332s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 332s 1 97.9 0.607 93.7 102.1 98.1 0.780 332s 2 99.8 0.569 95.6 104.0 99.2 0.793 332s 3 99.7 0.537 95.6 103.9 99.4 0.728 332s 4 99.9 0.575 95.7 104.1 99.7 0.755 332s 5 102.1 0.493 97.9 106.3 101.7 0.652 332s 6 101.9 0.458 97.8 106.0 101.7 0.605 332s 7 102.3 0.475 98.1 106.4 101.7 0.592 332s 8 102.6 0.593 98.4 106.8 103.5 0.835 332s 9 101.6 0.523 97.4 105.8 102.4 0.717 332s 10 100.7 0.788 96.4 105.1 100.3 0.980 332s 11 96.2 0.898 91.8 100.7 96.8 1.081 332s 12 95.2 0.898 90.8 99.7 95.4 1.159 332s 13 96.4 0.816 92.0 100.7 96.8 1.019 332s 14 99.2 0.495 95.1 103.4 98.7 0.710 332s 15 103.8 0.724 99.5 108.1 102.9 0.816 332s 16 103.5 0.586 99.3 107.7 104.2 0.830 332s 17 104.2 1.240 99.4 108.9 104.0 1.540 332s 18 101.8 0.533 97.7 106.0 103.1 0.770 332s 19 103.2 0.666 98.9 107.4 103.0 0.862 332s 20 105.9 1.240 101.1 110.7 105.2 1.517 332s supply.lwr supply.upr 332s 1 92.6 104 332s 2 93.7 105 332s 3 94.0 105 332s 4 94.2 105 332s 5 96.3 107 332s 6 96.3 107 332s 7 96.4 107 332s 8 98.0 109 332s 9 97.0 108 332s 10 94.7 106 332s 11 91.2 103 332s 12 89.7 101 332s 13 91.2 102 332s 14 93.3 104 332s 15 97.4 108 332s 16 98.7 110 332s 17 97.9 110 332s 18 97.7 109 332s 19 97.5 109 332s 20 99.2 111 332s > print( predict( fitsur1e2$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 332s + useDfSys = TRUE ) ) 332s fit se.fit lwr upr 332s 1 98.1 0.780 92.6 104 332s 2 99.2 0.793 93.7 105 332s 3 99.4 0.728 94.0 105 332s 4 99.7 0.755 94.2 105 332s 5 101.7 0.652 96.3 107 332s 6 101.7 0.605 96.3 107 332s 7 101.7 0.592 96.4 107 332s 8 103.5 0.835 98.0 109 332s 9 102.4 0.717 97.0 108 332s 10 100.3 0.980 94.7 106 332s 11 96.8 1.081 91.2 103 332s 12 95.4 1.159 89.7 101 332s 13 96.8 1.019 91.2 102 332s 14 98.7 0.710 93.3 104 332s 15 102.9 0.816 97.4 108 332s 16 104.2 0.830 98.7 110 332s 17 104.0 1.540 97.9 110 332s 18 103.1 0.770 97.7 109 332s 19 103.0 0.862 97.5 109 332s 20 105.2 1.517 99.2 111 332s > 332s > print( predict( fitsur2e, se.pred = TRUE, interval = "confidence", 332s + level = 0.999, newdata = predictData ) ) 332s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 332s 1 103 2.23 99.8 106 97.4 2.80 332s 2 105 2.22 102.0 108 98.3 2.71 332s 3 105 2.23 101.8 108 98.4 2.72 332s 4 105 2.23 102.1 108 98.7 2.70 332s 5 107 2.42 102.3 111 100.4 2.83 332s 6 107 2.39 102.5 111 100.4 2.79 332s 7 107 2.37 103.0 111 100.4 2.75 332s 8 108 2.34 103.8 112 101.8 2.70 332s 9 106 2.44 101.7 111 100.9 2.87 332s 10 105 2.54 99.8 111 99.1 3.05 332s 11 101 2.39 96.5 105 96.1 3.05 332s 12 100 2.24 97.0 103 94.8 2.96 332s 13 101 2.17 99.1 104 96.0 2.83 332s 14 104 2.30 100.5 108 97.6 2.85 332s 15 108 2.58 102.9 114 101.2 2.91 332s 16 108 2.49 103.4 113 102.3 2.83 332s 17 108 2.85 101.3 115 102.1 3.26 332s 18 107 2.31 103.2 111 101.3 2.70 332s 19 108 2.36 104.3 113 101.2 2.68 332s 20 112 2.52 106.4 117 103.0 2.66 332s supply.lwr supply.upr 332s 1 93.6 101.1 332s 2 95.5 101.1 332s 3 95.5 101.3 332s 4 96.0 101.3 332s 5 96.4 104.4 332s 6 96.7 104.1 332s 7 97.1 103.7 332s 8 99.2 104.5 332s 9 96.5 105.3 332s 10 93.4 104.8 332s 11 90.3 101.8 332s 12 89.7 99.9 332s 13 91.9 100.0 332s 14 93.4 101.8 332s 15 96.4 105.9 332s 16 98.3 106.4 332s 17 95.1 109.2 332s 18 98.6 103.9 332s 19 98.9 103.5 332s 20 101.0 105.1 332s > print( predict( fitsur2e$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 332s + level = 0.999, newdata = predictData ) ) 332s fit se.pred lwr upr 332s 1 103 2.23 99.8 106 332s 2 105 2.22 102.0 108 332s 3 105 2.23 101.8 108 332s 4 105 2.23 102.1 108 332s 5 107 2.42 102.3 111 332s 6 107 2.39 102.5 111 332s 7 107 2.37 103.0 111 332s 8 108 2.34 103.8 112 332s 9 106 2.44 101.7 111 332s 10 105 2.54 99.8 111 332s 11 101 2.39 96.5 105 332s 12 100 2.24 97.0 103 332s 13 101 2.17 99.1 104 332s 14 104 2.30 100.5 108 332s 15 108 2.58 102.9 114 332s 16 108 2.49 103.4 113 332s 17 108 2.85 101.3 115 332s 18 107 2.31 103.2 111 332s 19 108 2.36 104.3 113 332s 20 112 2.52 106.4 117 332s > 332s > print( predict( fitsur3, se.pred = TRUE, interval = "prediction", 332s + level = 0.975 ) ) 332s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 332s 1 98.1 2.13 93.1 103 98.6 2.67 332s 2 99.9 2.13 94.9 105 99.6 2.69 332s 3 99.9 2.12 94.9 105 99.8 2.68 332s 4 100.0 2.13 95.0 105 100.0 2.69 332s 5 102.0 2.11 97.0 107 101.7 2.67 332s 6 101.8 2.10 96.9 107 101.7 2.66 332s 7 102.2 2.11 97.2 107 101.7 2.66 332s 8 102.5 2.14 97.5 108 103.2 2.72 332s 9 101.5 2.12 96.5 106 102.2 2.69 332s 10 100.7 2.20 95.5 106 100.3 2.78 332s 11 96.6 2.23 91.3 102 97.3 2.80 332s 12 95.7 2.22 90.5 101 96.1 2.81 332s 13 96.8 2.19 91.6 102 97.3 2.77 332s 14 99.3 2.11 94.4 104 98.9 2.69 332s 15 103.6 2.17 98.5 109 102.5 2.71 332s 16 103.3 2.13 98.3 108 103.7 2.69 332s 17 103.8 2.39 98.2 109 103.3 2.99 332s 18 101.8 2.12 96.8 107 102.7 2.69 332s 19 103.0 2.16 98.0 108 102.6 2.71 332s 20 105.6 2.39 100.0 111 104.6 2.97 332s supply.lwr supply.upr 332s 1 92.4 105 332s 2 93.3 106 332s 3 93.5 106 332s 4 93.7 106 332s 5 95.4 108 332s 6 95.5 108 332s 7 95.5 108 332s 8 96.8 110 332s 9 95.9 109 332s 10 93.8 107 332s 11 90.7 104 332s 12 89.5 103 332s 13 90.8 104 332s 14 92.6 105 332s 15 96.1 109 332s 16 97.3 110 332s 17 96.3 110 332s 18 96.4 109 332s 19 96.3 109 332s 20 97.6 112 332s > print( predict( fitsur3$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 332s + level = 0.975 ) ) 332s fit se.pred lwr upr 332s 1 98.6 2.67 92.4 105 332s 2 99.6 2.69 93.3 106 332s 3 99.8 2.68 93.5 106 332s 4 100.0 2.69 93.7 106 332s 5 101.7 2.67 95.4 108 332s 6 101.7 2.66 95.5 108 332s 7 101.7 2.66 95.5 108 332s 8 103.2 2.72 96.8 110 332s 9 102.2 2.69 95.9 109 332s 10 100.3 2.78 93.8 107 332s 11 97.3 2.80 90.7 104 332s 12 96.1 2.81 89.5 103 332s 13 97.3 2.77 90.8 104 332s 14 98.9 2.69 92.6 105 332s 15 102.5 2.71 96.1 109 332s 16 103.7 2.69 97.3 110 332s 17 103.3 2.99 96.3 110 332s 18 102.7 2.69 96.4 109 332s 19 102.6 2.71 96.3 109 332s 20 104.6 2.97 97.6 112 332s > 332s > print( predict( fitsur4r3, se.fit = TRUE, interval = "confidence", 332s + level = 0.25 ) ) 332s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 332s 1 97.6 0.474 97.4 97.7 98.2 0.571 332s 2 99.9 0.558 99.7 100.1 99.8 0.699 332s 3 99.8 0.523 99.6 100.0 99.9 0.651 332s 4 100.0 0.567 99.9 100.2 100.3 0.701 332s 5 102.1 0.476 102.0 102.3 101.8 0.620 332s 6 102.0 0.443 101.8 102.1 101.9 0.574 332s 7 102.5 0.440 102.3 102.6 102.1 0.559 332s 8 103.1 0.532 102.9 103.3 104.3 0.646 332s 9 101.4 0.520 101.3 101.6 102.2 0.692 332s 10 100.2 0.774 100.0 100.4 99.3 0.939 332s 11 95.3 0.612 95.1 95.5 95.7 0.732 332s 12 94.5 0.525 94.4 94.7 94.7 0.687 332s 13 96.0 0.603 95.8 96.2 96.6 0.791 332s 14 99.0 0.444 98.8 99.1 98.2 0.580 332s 15 103.9 0.643 103.7 104.1 102.4 0.759 332s 16 103.7 0.494 103.6 103.9 104.2 0.634 332s 17 103.8 1.191 103.4 104.1 102.6 1.456 332s 18 102.2 0.510 102.0 102.3 103.4 0.622 332s 19 103.8 0.570 103.6 104.0 103.5 0.714 332s 20 107.2 0.973 106.9 107.6 106.7 1.183 332s supply.lwr supply.upr 332s 1 98.0 98.4 332s 2 99.6 100.0 332s 3 99.7 100.1 332s 4 100.1 100.5 332s 5 101.6 102.0 332s 6 101.7 102.1 332s 7 101.9 102.3 332s 8 104.1 104.5 332s 9 102.0 102.4 332s 10 99.0 99.6 332s 11 95.5 95.9 332s 12 94.5 94.9 332s 13 96.4 96.9 332s 14 98.1 98.4 332s 15 102.1 102.6 332s 16 104.0 104.4 332s 17 102.1 103.1 332s 18 103.2 103.6 332s 19 103.3 103.7 332s 20 106.3 107.1 332s > print( predict( fitsur4r3$eq[[ 1 ]], se.fit = TRUE, interval = "confidence", 332s + level = 0.25 ) ) 332s fit se.fit lwr upr 332s 1 97.6 0.474 97.4 97.7 332s 2 99.9 0.558 99.7 100.1 332s 3 99.8 0.523 99.6 100.0 332s 4 100.0 0.567 99.9 100.2 332s 5 102.1 0.476 102.0 102.3 332s 6 102.0 0.443 101.8 102.1 332s 7 102.5 0.440 102.3 102.6 332s 8 103.1 0.532 102.9 103.3 332s 9 101.4 0.520 101.3 101.6 332s 10 100.2 0.774 100.0 100.4 332s 11 95.3 0.612 95.1 95.5 332s 12 94.5 0.525 94.4 94.7 332s 13 96.0 0.603 95.8 96.2 332s 14 99.0 0.444 98.8 99.1 332s 15 103.9 0.643 103.7 104.1 332s 16 103.7 0.494 103.6 103.9 332s 17 103.8 1.191 103.4 104.1 332s 18 102.2 0.510 102.0 102.3 332s 19 103.8 0.570 103.6 104.0 332s 20 107.2 0.973 106.9 107.6 332s > 332s > print( predict( fitsur4we, se.fit = TRUE, interval = "confidence", 332s + level = 0.25 ) ) 332s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 332s 1 97.5 0.445 97.3 97.6 98.2 0.519 332s 2 99.7 0.514 99.6 99.9 99.6 0.636 332s 3 99.7 0.482 99.5 99.8 99.8 0.591 332s 4 99.9 0.523 99.7 100.0 100.1 0.636 332s 5 102.2 0.438 102.1 102.4 102.0 0.568 332s 6 102.0 0.408 101.9 102.2 102.0 0.523 332s 7 102.5 0.409 102.3 102.6 102.1 0.508 332s 8 102.9 0.503 102.8 103.1 104.2 0.603 332s 9 101.6 0.479 101.4 101.7 102.4 0.631 332s 10 100.5 0.724 100.3 100.8 99.7 0.856 332s 11 95.5 0.612 95.3 95.7 95.9 0.694 332s 12 94.4 0.520 94.3 94.6 94.6 0.677 332s 13 95.8 0.565 95.6 96.0 96.3 0.748 332s 14 99.0 0.414 98.8 99.1 98.2 0.540 332s 15 104.1 0.592 103.9 104.3 102.6 0.690 332s 16 103.8 0.458 103.7 104.0 104.3 0.581 332s 17 104.3 1.100 104.0 104.7 103.3 1.334 332s 18 102.0 0.477 101.9 102.2 103.3 0.564 332s 19 103.6 0.545 103.4 103.8 103.2 0.651 332s 20 106.8 0.958 106.5 107.1 106.1 1.091 332s supply.lwr supply.upr 332s 1 98.0 98.3 332s 2 99.4 99.8 332s 3 99.6 99.9 332s 4 99.9 100.3 332s 5 101.8 102.1 332s 6 101.8 102.2 332s 7 101.9 102.2 332s 8 104.0 104.4 332s 9 102.2 102.6 332s 10 99.5 100.0 332s 11 95.7 96.1 332s 12 94.4 94.8 332s 13 96.1 96.6 332s 14 98.0 98.4 332s 15 102.4 102.9 332s 16 104.1 104.5 332s 17 102.9 103.8 332s 18 103.1 103.5 332s 19 103.0 103.5 332s 20 105.8 106.5 332s > print( predict( fitsur4we$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 332s + level = 0.25 ) ) 332s fit se.fit lwr upr 332s 1 98.2 0.519 98.0 98.3 332s 2 99.6 0.636 99.4 99.8 332s 3 99.8 0.591 99.6 99.9 332s 4 100.1 0.636 99.9 100.3 332s 5 102.0 0.568 101.8 102.1 332s 6 102.0 0.523 101.8 102.2 332s 7 102.1 0.508 101.9 102.2 332s 8 104.2 0.603 104.0 104.4 332s 9 102.4 0.631 102.2 102.6 332s 10 99.7 0.856 99.5 100.0 332s 11 95.9 0.694 95.7 96.1 332s 12 94.6 0.677 94.4 94.8 332s 13 96.3 0.748 96.1 96.6 332s 14 98.2 0.540 98.0 98.4 332s 15 102.6 0.690 102.4 102.9 332s 16 104.3 0.581 104.1 104.5 332s 17 103.3 1.334 102.9 103.8 332s 18 103.3 0.564 103.1 103.5 332s 19 103.2 0.651 103.0 103.5 332s 20 106.1 1.091 105.8 106.5 332s > 332s > print( predict( fitsur5, se.fit = TRUE, se.pred = TRUE, 332s + interval = "prediction", level = 0.5, newdata = predictData ) ) 332s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 332s 1 103.2 0.911 2.14 101.7 105 96.0 332s 2 105.9 0.786 2.09 104.4 107 97.3 332s 3 105.7 0.824 2.11 104.3 107 97.5 332s 4 106.0 0.780 2.09 104.6 107 97.8 332s 5 108.2 1.233 2.30 106.7 110 99.8 332s 6 108.1 1.143 2.25 106.6 110 99.8 332s 7 108.7 1.076 2.22 107.2 110 99.8 332s 8 109.4 0.919 2.15 108.0 111 101.9 332s 9 107.5 1.295 2.33 105.9 109 100.3 332s 10 106.0 1.568 2.49 104.3 108 97.7 332s 11 100.5 1.292 2.33 98.9 102 93.8 332s 12 99.7 0.921 2.15 98.3 101 92.4 332s 13 101.5 0.720 2.07 100.1 103 94.1 332s 14 104.7 1.054 2.21 103.2 106 96.1 332s 15 110.1 1.485 2.44 108.5 112 100.5 332s 16 110.0 1.284 2.33 108.4 112 102.1 332s 17 109.9 2.013 2.80 108.0 112 101.4 332s 18 108.4 0.906 2.14 106.9 110 101.0 332s 19 110.2 0.911 2.14 108.8 112 100.9 332s 20 114.2 0.898 2.14 112.7 116 103.6 332s supply.se.fit supply.se.pred supply.lwr supply.upr 332s 1 0.916 2.68 94.1 97.8 332s 2 0.715 2.62 95.5 99.1 332s 3 0.760 2.63 95.7 99.3 332s 4 0.708 2.62 96.0 99.6 332s 5 1.213 2.80 97.9 101.7 332s 6 1.100 2.75 97.9 101.7 332s 7 0.982 2.70 98.0 101.7 332s 8 0.825 2.65 100.1 103.7 332s 9 1.339 2.85 98.4 102.2 332s 10 1.631 3.00 95.7 99.8 332s 11 1.375 2.87 91.9 95.8 332s 12 1.025 2.72 90.6 94.3 332s 13 0.831 2.65 92.3 95.9 332s 14 1.033 2.72 94.2 97.9 332s 15 1.434 2.90 98.5 102.5 332s 16 1.249 2.81 100.2 104.1 332s 17 2.163 3.32 99.1 103.6 332s 18 0.809 2.65 99.2 102.8 332s 19 0.712 2.62 99.1 102.7 332s 20 0.572 2.58 101.9 105.4 332s > print( predict( fitsur5$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 332s + interval = "prediction", level = 0.5, newdata = predictData ) ) 332s fit se.fit se.pred lwr upr 332s 1 96.0 0.916 2.68 94.1 97.8 332s 2 97.3 0.715 2.62 95.5 99.1 332s 3 97.5 0.760 2.63 95.7 99.3 332s 4 97.8 0.708 2.62 96.0 99.6 332s 5 99.8 1.213 2.80 97.9 101.7 332s 6 99.8 1.100 2.75 97.9 101.7 332s 7 99.8 0.982 2.70 98.0 101.7 332s 8 101.9 0.825 2.65 100.1 103.7 332s 9 100.3 1.339 2.85 98.4 102.2 332s 10 97.7 1.631 3.00 95.7 99.8 332s 11 93.8 1.375 2.87 91.9 95.8 332s 12 92.4 1.025 2.72 90.6 94.3 332s 13 94.1 0.831 2.65 92.3 95.9 332s 14 96.1 1.033 2.72 94.2 97.9 332s 15 100.5 1.434 2.90 98.5 102.5 332s 16 102.1 1.249 2.81 100.2 104.1 332s 17 101.4 2.163 3.32 99.1 103.6 332s 18 101.0 0.809 2.65 99.2 102.8 332s 19 100.9 0.712 2.62 99.1 102.7 332s 20 103.6 0.572 2.58 101.9 105.4 332s > 332s > print( predict( fitsuri1r3, se.fit = TRUE, se.pred = TRUE, 332s + interval = "confidence", level = 0.99 ) ) 332s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 332s 1 97.7 0.653 2.09 95.8 99.6 100.2 332s 2 99.9 0.578 2.07 98.3 101.6 105.7 332s 3 99.9 0.548 2.06 98.3 101.4 104.3 332s 4 100.1 0.583 2.07 98.4 101.8 104.9 332s 5 102.1 0.509 2.05 100.6 103.5 99.2 332s 6 101.9 0.474 2.04 100.6 103.3 100.1 332s 7 102.4 0.496 2.04 101.0 103.9 102.3 332s 8 103.0 0.615 2.08 101.2 104.8 102.6 332s 9 101.4 0.531 2.05 99.9 103.0 94.9 332s 10 100.2 0.785 2.13 98.0 102.5 92.8 332s 11 95.5 0.971 2.21 92.7 98.3 92.1 332s 12 94.8 0.996 2.22 91.9 97.7 98.3 332s 13 96.2 0.880 2.17 93.7 98.8 101.6 332s 14 99.0 0.521 2.05 97.5 100.5 99.8 332s 15 103.7 0.752 2.12 101.6 105.9 97.5 332s 16 103.6 0.622 2.08 101.8 105.4 96.7 332s 17 103.6 1.241 2.34 100.0 107.2 87.6 332s 18 102.1 0.546 2.06 100.5 103.7 100.6 332s 19 103.7 0.696 2.10 101.6 105.7 105.5 332s 20 107.0 1.299 2.37 103.2 110.7 113.8 332s supply.se.fit supply.se.pred supply.lwr supply.upr 332s 1 0.599 1.72 98.4 101.9 332s 2 0.604 1.72 103.9 107.4 332s 3 0.539 1.70 102.7 105.8 332s 4 0.536 1.70 103.4 106.5 332s 5 0.486 1.69 97.8 100.6 332s 6 0.448 1.68 98.8 101.4 332s 7 0.444 1.67 101.0 103.6 332s 8 0.522 1.70 101.1 104.1 332s 9 0.542 1.70 93.3 96.5 332s 10 0.579 1.72 91.1 94.5 332s 11 0.812 1.81 89.7 94.5 332s 12 0.865 1.83 95.8 100.9 332s 13 0.747 1.78 99.4 103.8 332s 14 0.507 1.69 98.3 101.3 332s 15 0.509 1.69 96.0 98.9 332s 16 0.596 1.72 95.0 98.5 332s 17 0.975 1.89 84.7 90.4 332s 18 0.500 1.69 99.1 102.0 332s 19 0.649 1.74 103.6 107.3 332s 20 1.124 1.97 110.5 117.1 332s > print( predict( fitsuri1r3$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 332s + interval = "confidence", level = 0.99 ) ) 332s fit se.fit se.pred lwr upr 332s 1 97.7 0.653 2.09 95.8 99.6 332s 2 99.9 0.578 2.07 98.3 101.6 332s 3 99.9 0.548 2.06 98.3 101.4 332s 4 100.1 0.583 2.07 98.4 101.8 332s 5 102.1 0.509 2.05 100.6 103.5 332s 6 101.9 0.474 2.04 100.6 103.3 332s 7 102.4 0.496 2.04 101.0 103.9 332s 8 103.0 0.615 2.08 101.2 104.8 332s 9 101.4 0.531 2.05 99.9 103.0 332s 10 100.2 0.785 2.13 98.0 102.5 332s 11 95.5 0.971 2.21 92.7 98.3 332s 12 94.8 0.996 2.22 91.9 97.7 332s 13 96.2 0.880 2.17 93.7 98.8 332s 14 99.0 0.521 2.05 97.5 100.5 332s 15 103.7 0.752 2.12 101.6 105.9 332s 16 103.6 0.622 2.08 101.8 105.4 332s 17 103.6 1.241 2.34 100.0 107.2 332s 18 102.1 0.546 2.06 100.5 103.7 332s 19 103.7 0.696 2.10 101.6 105.7 332s 20 107.0 1.299 2.37 103.2 110.7 332s > 332s > print( predict( fitsuri2, se.fit = TRUE, interval = "prediction", 332s + level = 0.9, newdata = predictData ) ) 332s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 332s 1 104 0.960 100.5 108 96.1 1.37 332s 2 107 1.011 102.9 110 99.7 1.69 332s 3 107 1.032 102.8 110 99.8 1.61 332s 4 107 1.019 103.0 111 100.8 1.76 332s 5 110 1.547 105.4 114 99.2 2.00 332s 6 109 1.468 105.3 114 100.3 1.94 332s 7 110 1.465 105.7 114 102.1 2.12 332s 8 110 1.423 106.1 114 103.2 2.60 332s 9 109 1.543 104.8 113 99.9 1.80 332s 10 108 1.699 103.6 112 99.1 1.35 332s 11 102 1.299 98.2 106 98.6 2.25 332s 12 101 0.939 97.2 105 102.0 3.10 332s 13 102 0.731 98.7 106 104.5 3.01 332s 14 106 1.164 102.1 110 104.9 2.27 332s 15 112 1.896 107.3 117 105.4 2.20 332s 16 112 1.733 107.1 116 105.9 2.40 332s 17 113 2.316 107.4 118 102.1 2.02 332s 18 109 1.316 105.2 113 108.8 2.75 332s 19 111 1.497 106.8 115 111.9 3.73 332s 20 114 1.918 109.7 119 117.2 5.62 332s supply.lwr supply.upr 332s 1 86.2 106 332s 2 89.7 110 332s 3 89.7 110 332s 4 90.7 111 332s 5 89.0 109 332s 6 90.1 110 332s 7 91.8 112 332s 8 92.6 114 332s 9 89.7 110 332s 10 89.2 109 332s 11 88.2 109 332s 12 91.0 113 332s 13 93.6 115 332s 14 94.5 115 332s 15 95.0 116 332s 16 95.4 116 332s 17 91.9 112 332s 18 98.1 119 332s 19 100.4 123 332s 20 103.6 131 332s > print( predict( fitsuri2$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 332s + level = 0.9, newdata = predictData ) ) 332s fit se.fit lwr upr 332s 1 96.1 1.37 86.2 106 332s 2 99.7 1.69 89.7 110 332s 3 99.8 1.61 89.7 110 332s 4 100.8 1.76 90.7 111 332s 5 99.2 2.00 89.0 109 332s 6 100.3 1.94 90.1 110 332s 7 102.1 2.12 91.8 112 332s 8 103.2 2.60 92.6 114 332s 9 99.9 1.80 89.7 110 332s 10 99.1 1.35 89.2 109 332s 11 98.6 2.25 88.2 109 332s 12 102.0 3.10 91.0 113 332s 13 104.5 3.01 93.6 115 332s 14 104.9 2.27 94.5 115 332s 15 105.4 2.20 95.0 116 332s 16 105.9 2.40 95.4 116 332s 17 102.1 2.02 91.9 112 332s 18 108.8 2.75 98.1 119 332s 19 111.9 3.73 100.4 123 332s 20 117.2 5.62 103.6 131 332s > 332s > print( predict( fitsuri2w, se.fit = TRUE, interval = "prediction", 332s + level = 0.9, newdata = predictData ) ) 332s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 332s 1 104 0.960 100.5 108 96.1 1.37 332s 2 107 1.011 102.9 110 99.7 1.69 332s 3 107 1.032 102.8 110 99.8 1.61 332s 4 107 1.019 103.0 111 100.8 1.76 332s 5 110 1.547 105.4 114 99.2 2.00 332s 6 109 1.468 105.3 114 100.3 1.94 332s 7 110 1.465 105.7 114 102.1 2.12 332s 8 110 1.423 106.1 114 103.2 2.60 332s 9 109 1.543 104.8 113 99.9 1.80 332s 10 108 1.699 103.6 112 99.1 1.35 332s 11 102 1.299 98.2 106 98.6 2.25 332s 12 101 0.939 97.2 105 102.0 3.10 332s 13 102 0.731 98.7 106 104.5 3.01 332s 14 106 1.164 102.1 110 104.9 2.27 332s 15 112 1.896 107.3 117 105.4 2.20 332s 16 112 1.733 107.1 116 105.9 2.40 332s 17 113 2.316 107.4 118 102.1 2.02 332s 18 109 1.316 105.2 113 108.8 2.75 332s 19 111 1.497 106.8 115 111.9 3.73 332s 20 114 1.918 109.7 119 117.2 5.62 332s supply.lwr supply.upr 332s 1 86.2 106 332s 2 89.7 110 332s 3 89.7 110 332s 4 90.7 111 332s 5 89.0 109 332s 6 90.1 110 332s 7 91.8 112 332s 8 92.6 114 332s 9 89.7 110 332s 10 89.2 109 332s 11 88.2 109 332s 12 91.0 113 332s 13 93.6 115 332s 14 94.5 115 332s 15 95.0 116 332s 16 95.4 116 332s 17 91.9 112 332s 18 98.1 119 332s 19 100.4 123 332s 20 103.6 131 332s > print( predict( fitsuri2w$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 332s + level = 0.9, newdata = predictData ) ) 332s fit se.fit lwr upr 332s 1 96.1 1.37 86.2 106 332s 2 99.7 1.69 89.7 110 332s 3 99.8 1.61 89.7 110 332s 4 100.8 1.76 90.7 111 332s 5 99.2 2.00 89.0 109 332s 6 100.3 1.94 90.1 110 332s 7 102.1 2.12 91.8 112 332s 8 103.2 2.60 92.6 114 332s 9 99.9 1.80 89.7 110 332s 10 99.1 1.35 89.2 109 332s 11 98.6 2.25 88.2 109 332s 12 102.0 3.10 91.0 113 332s 13 104.5 3.01 93.6 115 332s 14 104.9 2.27 94.5 115 332s 15 105.4 2.20 95.0 116 332s 16 105.9 2.40 95.4 116 332s 17 102.1 2.02 91.9 112 332s 18 108.8 2.75 98.1 119 332s 19 111.9 3.73 100.4 123 332s 20 117.2 5.62 103.6 131 332s > 332s > print( predict( fitsuri3e, interval = "prediction", level = 0.925 ) ) 332s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 332s 1 97.4 93.5 101.2 93.4 82.5 104 332s 2 99.2 95.4 103.0 96.7 86.0 107 332s 3 99.3 95.5 103.0 96.7 86.0 107 332s 4 99.3 95.5 103.1 97.7 87.0 108 332s 5 102.5 98.7 106.2 96.1 85.1 107 332s 6 102.1 98.4 105.9 97.2 86.3 108 332s 7 102.4 98.6 106.2 98.8 88.1 110 332s 8 102.5 98.7 106.3 99.8 88.9 111 332s 9 102.0 98.2 105.8 96.9 85.9 108 332s 10 101.5 97.6 105.4 96.4 85.5 107 332s 11 96.1 92.1 100.1 96.3 84.9 108 332s 12 94.4 90.4 98.4 99.6 87.9 111 332s 13 95.4 91.4 99.3 101.9 90.4 113 332s 14 99.1 95.3 102.8 102.0 91.1 113 332s 15 104.7 100.8 108.6 102.2 91.4 113 332s 16 104.1 100.3 107.9 102.6 91.8 113 332s 17 105.9 101.6 110.2 99.1 88.1 110 332s 18 101.6 97.9 105.4 105.5 94.6 116 332s 19 103.1 99.2 106.9 108.4 97.1 120 332s 20 105.5 101.3 109.8 113.1 100.7 126 332s > print( predict( fitsuri3e$eq[[ 1 ]], interval = "prediction", level = 0.925 ) ) 332s fit lwr upr 332s 1 97.4 93.5 101.2 332s 2 99.2 95.4 103.0 332s 3 99.3 95.5 103.0 332s 4 99.3 95.5 103.1 332s 5 102.5 98.7 106.2 332s 6 102.1 98.4 105.9 332s 7 102.4 98.6 106.2 332s 8 102.5 98.7 106.3 332s 9 102.0 98.2 105.8 332s 10 101.5 97.6 105.4 332s 11 96.1 92.1 100.1 332s 12 94.4 90.4 98.4 332s 13 95.4 91.4 99.3 332s 14 99.1 95.3 102.8 332s 15 104.7 100.8 108.6 332s 16 104.1 100.3 107.9 332s 17 105.9 101.6 110.2 332s 18 101.6 97.9 105.4 332s 19 103.1 99.2 106.9 332s 20 105.5 101.3 109.8 332s > 332s > print( predict( fitsurio4, interval = "confidence", newdata = predictData ) ) 332s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 332s 1 102.7 100.8 105 95.5 93.6 97.4 332s 2 105.5 103.8 107 97.0 95.5 98.5 332s 3 105.3 103.6 107 97.2 95.6 98.8 332s 4 105.6 104.0 107 97.5 96.0 99.0 332s 5 107.5 105.0 110 99.1 96.5 101.6 332s 6 107.5 105.1 110 99.2 96.9 101.5 332s 7 108.1 105.9 110 99.3 97.2 101.4 332s 8 108.9 107.1 111 101.5 99.7 103.2 332s 9 106.7 104.0 109 99.5 96.7 102.3 332s 10 105.1 101.8 108 96.7 93.4 100.1 332s 11 99.8 97.2 102 93.1 90.4 95.9 332s 12 99.3 97.4 101 92.1 90.1 94.1 332s 13 101.1 99.7 103 93.9 92.3 95.5 332s 14 104.1 101.9 106 95.6 93.5 97.7 332s 15 109.3 106.2 112 99.7 96.7 102.7 332s 16 109.3 106.6 112 101.4 98.8 104.0 332s 17 108.7 104.5 113 100.0 95.5 104.5 332s 18 107.9 106.0 110 100.6 98.9 102.3 332s 19 109.8 107.9 112 100.7 99.2 102.2 332s 20 114.0 112.3 116 103.7 102.5 104.9 332s > print( predict( fitsurio4$eq[[ 2 ]], interval = "confidence", 332s + newdata = predictData ) ) 332s fit lwr upr 332s 1 95.5 93.6 97.4 332s 2 97.0 95.5 98.5 332s 3 97.2 95.6 98.8 332s 4 97.5 96.0 99.0 332s 5 99.1 96.5 101.6 332s 6 99.2 96.9 101.5 332s 7 99.3 97.2 101.4 332s 8 101.5 99.7 103.2 332s 9 99.5 96.7 102.3 332s 10 96.7 93.4 100.1 332s 11 93.1 90.4 95.9 332s 12 92.1 90.1 94.1 332s 13 93.9 92.3 95.5 332s 14 95.6 93.5 97.7 332s 15 99.7 96.7 102.7 332s 16 101.4 98.8 104.0 332s 17 100.0 95.5 104.5 332s 18 100.6 98.9 102.3 332s 19 100.7 99.2 102.2 332s 20 103.7 102.5 104.9 332s > print( predict( fitsuri4, interval = "confidence", newdata = predictData ) ) 332s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 332s 1 103.1 101.3 105 96.6 93.9 99.3 332s 2 105.5 103.7 107 99.4 96.2 102.5 332s 3 105.4 103.5 107 99.4 96.4 102.5 332s 4 105.6 103.8 107 100.3 97.1 103.5 332s 5 107.7 105.0 110 98.9 94.9 102.9 332s 6 107.6 105.0 110 99.8 96.1 103.5 332s 7 108.1 105.5 111 101.2 97.6 104.9 332s 8 108.7 106.1 111 102.0 97.7 106.4 332s 9 107.0 104.3 110 99.6 96.0 103.2 332s 10 105.7 102.7 109 99.3 96.6 102.0 332s 11 100.7 98.3 103 99.3 95.0 103.5 332s 12 99.9 98.2 102 102.1 95.8 108.4 332s 13 101.5 100.2 103 104.0 97.9 110.1 332s 14 104.5 102.4 107 104.1 99.8 108.4 332s 15 109.5 106.1 113 104.2 100.8 107.5 332s 16 109.4 106.3 112 104.5 100.9 108.2 332s 17 109.3 105.3 113 101.7 97.7 105.6 332s 18 107.8 105.4 110 107.0 103.1 110.9 332s 19 109.5 106.7 112 109.5 104.4 114.6 332s 20 113.0 109.4 117 113.4 106.3 120.6 332s > print( predict( fitsuri4$eq[[ 2 ]], interval = "confidence", 332s + newdata = predictData ) ) 332s fit lwr upr 332s 1 96.6 93.9 99.3 332s 2 99.4 96.2 102.5 332s 3 99.4 96.4 102.5 332s 4 100.3 97.1 103.5 332s 5 98.9 94.9 102.9 332s 6 99.8 96.1 103.5 332s 7 101.2 97.6 104.9 332s 8 102.0 97.7 106.4 332s 9 99.6 96.0 103.2 332s 10 99.3 96.6 102.0 332s 11 99.3 95.0 103.5 332s 12 102.1 95.8 108.4 332s 13 104.0 97.9 110.1 332s 14 104.1 99.8 108.4 332s 15 104.2 100.8 107.5 332s 16 104.5 100.9 108.2 332s 17 101.7 97.7 105.6 332s 18 107.0 103.1 110.9 332s 19 109.5 104.4 114.6 332s 20 113.4 106.3 120.6 332s > 332s > print( predict( fitsurio5r2 ) ) 332s demand.pred supply.pred 332s 1 97.8 98.5 332s 2 100.6 100.7 332s 3 100.4 100.6 332s 4 100.8 101.2 332s 5 101.7 101.3 332s 6 101.8 101.7 332s 7 102.5 102.2 332s 8 103.7 104.9 332s 9 100.8 101.4 332s 10 98.9 97.7 332s 11 94.6 94.8 332s 12 94.8 95.0 332s 13 96.8 97.6 332s 14 98.9 98.2 332s 15 102.9 101.3 332s 16 103.3 103.6 332s 17 101.4 99.8 332s 18 102.7 104.0 332s 19 104.5 104.4 332s 20 108.9 108.9 332s > print( predict( fitsurio5r2$eq[[ 1 ]] ) ) 332s fit 332s 1 97.8 332s 2 100.6 332s 3 100.4 332s 4 100.8 332s 5 101.7 332s 6 101.8 332s 7 102.5 332s 8 103.7 332s 9 100.8 332s 10 98.9 332s 11 94.6 332s 12 94.8 332s 13 96.8 332s 14 98.9 332s 15 102.9 332s 16 103.3 332s 17 101.4 332s 18 102.7 332s 19 104.5 332s 20 108.9 332s > print( predict( fitsuri5r2 ) ) 332s demand.pred supply.pred 332s 1 97.8 94.6 332s 2 99.8 97.1 332s 3 99.7 97.2 332s 4 99.9 98.0 332s 5 102.1 96.5 332s 6 101.9 97.4 332s 7 102.3 98.8 332s 8 102.7 99.5 332s 9 101.6 97.3 332s 10 100.6 97.2 332s 11 96.0 97.5 332s 12 95.0 100.3 332s 13 96.2 102.0 332s 14 99.1 102.0 332s 15 103.9 101.7 332s 16 103.6 102.0 332s 17 104.2 99.4 332s 18 101.9 104.6 332s 19 103.3 106.9 332s 20 106.2 110.4 332s > print( predict( fitsuri5r2$eq[[ 1 ]] ) ) 332s fit 332s 1 97.8 332s 2 99.8 332s 3 99.7 332s 4 99.9 332s 5 102.1 332s 6 101.9 332s 7 102.3 332s 8 102.7 332s 9 101.6 332s 10 100.6 332s 11 96.0 332s 12 95.0 332s 13 96.2 332s 14 99.1 332s 15 103.9 332s 16 103.6 332s 17 104.2 332s 18 101.9 332s 19 103.3 332s 20 106.2 332s > 332s > # predict just one observation 332s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 332s + trend = 25 ) 332s > 332s > print( predict( fitsur1e2, newdata = smallData ) ) 332s demand.pred supply.pred 332s 1 108 115 332s > print( predict( fitsur1e2$eq[[ 1 ]], newdata = smallData ) ) 332s fit 332s 1 108 332s > 332s > print( predict( fitsur2e, se.fit = TRUE, level = 0.9, 332s + newdata = smallData ) ) 332s demand.pred demand.se.fit supply.pred supply.se.fit 332s 1 108 2.21 113 3 332s > print( predict( fitsur2e$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 332s + newdata = smallData ) ) 332s fit se.pred 332s 1 108 3.03 332s > 332s > print( predict( fitsur3, interval = "prediction", level = 0.975, 332s + newdata = smallData ) ) 332s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 332s 1 108 100 115 113 103 123 332s > print( predict( fitsur3$eq[[ 1 ]], interval = "confidence", level = 0.8, 332s + newdata = smallData ) ) 332s fit lwr upr 332s 1 108 105 111 332s > 332s > print( predict( fitsur4r3, se.fit = TRUE, interval = "confidence", 332s + level = 0.999, newdata = smallData ) ) 332s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 332s 1 111 2.06 103 118 119 2.22 332s supply.lwr supply.upr 332s 1 111 127 332s > print( predict( fitsur4r3$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 332s + level = 0.75, newdata = smallData ) ) 332s fit se.pred lwr upr 332s 1 119 3.41 115 123 332s > 332s > print( predict( fitsur5, se.fit = TRUE, interval = "prediction", 332s + newdata = smallData ) ) 332s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 332s 1 110 2.15 104 116 118 2.29 332s supply.lwr supply.upr 332s 1 111 125 332s > print( predict( fitsur5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 332s + newdata = smallData ) ) 332s fit se.pred lwr upr 332s 1 110 2.9 105 114 332s > 332s > print( predict( fitsurio5r2, se.fit = TRUE, se.pred = TRUE, 332s + interval = "prediction", level = 0.5, newdata = smallData ) ) 332s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 332s 1 115 1.98 3.09 113 117 123 332s supply.se.fit supply.se.pred supply.lwr supply.upr 332s 1 2.17 3.82 121 126 332s > print( predict( fitsurio5r2$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 332s + interval = "confidence", level = 0.25, newdata = smallData ) ) 332s fit se.fit se.pred lwr upr 332s 1 115 1.98 3.09 114 115 332s > print( predict( fitsuri5r2, se.fit = TRUE, se.pred = TRUE, 332s + interval = "prediction", level = 0.5, newdata = smallData ) ) 332s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 332s 1 109 2.35 3.06 107 111 113 332s supply.se.fit supply.se.pred supply.lwr supply.upr 332s 1 3.91 6.87 108 117 332s > print( predict( fitsuri5r2$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 332s + interval = "confidence", level = 0.25, newdata = smallData ) ) 332s fit se.fit se.pred lwr upr 332s 1 109 2.35 3.06 108 109 332s > 332s > print( predict( fitsuri5wr2, se.fit = TRUE, se.pred = TRUE, 332s + interval = "prediction", level = 0.5, newdata = smallData ) ) 332s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 332s 1 109 2.35 3.06 107 111 113 332s supply.se.fit supply.se.pred supply.lwr supply.upr 332s 1 3.91 6.87 108 117 332s > print( predict( fitsuri5wr2$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 332s + interval = "confidence", level = 0.25, newdata = smallData ) ) 332s fit se.fit se.pred lwr upr 332s 1 109 2.35 3.06 108 109 332s > 332s > 332s > ## ************ correlation of predicted values *************** 332s > print( correlation.systemfit( fitsur1e2, 2, 1 ) ) 332s [,1] 332s [1,] 0.849 332s [2,] 0.856 332s [3,] 0.864 332s [4,] 0.882 332s [5,] 0.844 332s [6,] 0.861 332s [7,] 0.875 332s [8,] 0.877 332s [9,] 0.884 332s [10,] 0.918 332s [11,] 0.903 332s [12,] 0.884 332s [13,] 0.880 332s [14,] 0.863 332s [15,] 0.896 332s [16,] 0.897 332s [17,] 0.914 332s [18,] 0.839 332s [19,] 0.867 332s [20,] 0.902 332s > 332s > print( correlation.systemfit( fitsur2e, 1, 2 ) ) 332s [,1] 332s [1,] 0.942 332s [2,] 0.944 332s [3,] 0.942 332s [4,] 0.941 332s [5,] 0.902 332s [6,] 0.909 332s [7,] 0.917 332s [8,] 0.903 332s [9,] 0.910 332s [10,] 0.941 332s [11,] 0.923 332s [12,] 0.902 332s [13,] 0.901 332s [14,] 0.893 332s [15,] 0.925 332s [16,] 0.952 332s [17,] 0.944 332s [18,] 0.935 332s [19,] 0.930 332s [20,] 0.938 332s > 332s > print( correlation.systemfit( fitsur3, 2, 1 ) ) 332s [,1] 332s [1,] 0.939 332s [2,] 0.943 332s [3,] 0.941 332s [4,] 0.940 332s [5,] 0.902 332s [6,] 0.909 332s [7,] 0.918 332s [8,] 0.903 332s [9,] 0.910 332s [10,] 0.941 332s [11,] 0.922 332s [12,] 0.900 332s [13,] 0.899 332s [14,] 0.892 332s [15,] 0.923 332s [16,] 0.952 332s [17,] 0.943 332s [18,] 0.936 332s [19,] 0.929 332s [20,] 0.937 332s > 332s > print( correlation.systemfit( fitsur3w, 2, 1 ) ) 332s [,1] 332s [1,] 0.940 332s [2,] 0.946 332s [3,] 0.944 332s [4,] 0.944 332s [5,] 0.908 332s [6,] 0.914 332s [7,] 0.922 332s [8,] 0.907 332s [9,] 0.914 332s [10,] 0.944 332s [11,] 0.926 332s [12,] 0.904 332s [13,] 0.903 332s [14,] 0.897 332s [15,] 0.926 332s [16,] 0.954 332s [17,] 0.946 332s [18,] 0.940 332s [19,] 0.932 332s [20,] 0.940 332s > 332s > print( correlation.systemfit( fitsur4r3, 1, 2 ) ) 332s [,1] 332s [1,] 0.963 332s [2,] 0.971 332s [3,] 0.971 332s [4,] 0.973 332s [5,] 0.940 332s [6,] 0.944 332s [7,] 0.947 332s [8,] 0.942 332s [9,] 0.947 332s [10,] 0.973 332s [11,] 0.910 332s [12,] 0.858 332s [13,] 0.914 332s [14,] 0.923 332s [15,] 0.977 332s [16,] 0.964 332s [17,] 0.978 332s [18,] 0.969 332s [19,] 0.946 332s [20,] 0.941 332s > 332s > print( correlation.systemfit( fitsur5, 2, 1 ) ) 332s [,1] 332s [1,] 0.938 332s [2,] 0.948 332s [3,] 0.948 332s [4,] 0.951 332s [5,] 0.892 332s [6,] 0.897 332s [7,] 0.903 332s [8,] 0.900 332s [9,] 0.907 332s [10,] 0.952 332s [11,] 0.853 332s [12,] 0.784 332s [13,] 0.858 332s [14,] 0.867 332s [15,] 0.961 332s [16,] 0.935 332s [17,] 0.961 332s [18,] 0.944 332s [19,] 0.907 332s [20,] 0.904 332s > 332s > print( correlation.systemfit( fitsuri1r3, 1, 2 ) ) 332s [,1] 332s [1,] -0.662 332s [2,] -0.656 332s [3,] -0.664 332s [4,] -0.689 332s [5,] -0.629 332s [6,] -0.664 332s [7,] -0.696 332s [8,] -0.675 332s [9,] -0.722 332s [10,] -0.757 332s [11,] -0.759 332s [12,] -0.732 332s [13,] -0.710 332s [14,] -0.669 332s [15,] -0.728 332s [16,] -0.737 332s [17,] -0.741 332s [18,] -0.583 332s [19,] -0.684 332s [20,] -0.746 332s > 332s > print( correlation.systemfit( fitsuri2, 2, 1 ) ) 332s [,1] 332s [1,] 0.360 332s [2,] 0.337 332s [3,] 0.337 332s [4,] 0.336 332s [5,] 0.286 332s [6,] 0.299 332s [7,] 0.317 332s [8,] 0.275 332s [9,] 0.322 332s [10,] 0.318 332s [11,] 0.334 332s [12,] 0.334 332s [13,] 0.318 332s [14,] 0.286 332s [15,] 0.358 332s [16,] 0.432 332s [17,] 0.367 332s [18,] 0.362 332s [19,] 0.333 332s [20,] 0.335 332s > 332s > print( correlation.systemfit( fitsuri2w, 1, 2 ) ) 332s [,1] 332s [1,] 0.360 332s [2,] 0.337 332s [3,] 0.337 332s [4,] 0.336 332s [5,] 0.286 332s [6,] 0.299 332s [7,] 0.317 332s [8,] 0.275 332s [9,] 0.322 332s [10,] 0.318 332s [11,] 0.334 332s [12,] 0.334 332s [13,] 0.318 332s [14,] 0.286 332s [15,] 0.358 332s [16,] 0.432 332s [17,] 0.367 332s [18,] 0.362 332s [19,] 0.333 332s [20,] 0.335 332s > 332s > print( correlation.systemfit( fitsuri3e, 1, 2 ) ) 332s [,1] 332s [1,] 0.368 332s [2,] 0.345 332s [3,] 0.344 332s [4,] 0.344 332s [5,] 0.292 332s [6,] 0.305 332s [7,] 0.323 332s [8,] 0.280 332s [9,] 0.329 332s [10,] 0.325 332s [11,] 0.340 332s [12,] 0.340 332s [13,] 0.324 332s [14,] 0.291 332s [15,] 0.366 332s [16,] 0.441 332s [17,] 0.375 332s [18,] 0.369 332s [19,] 0.340 332s [20,] 0.342 332s > 332s > print( correlation.systemfit( fitsurio4, 2, 1 ) ) 332s [,1] 332s [1,] 0.961 332s [2,] 0.971 332s [3,] 0.971 332s [4,] 0.973 332s [5,] 0.940 332s [6,] 0.944 332s [7,] 0.947 332s [8,] 0.939 332s [9,] 0.947 332s [10,] 0.972 332s [11,] 0.904 332s [12,] 0.861 332s [13,] 0.917 332s [14,] 0.922 332s [15,] 0.976 332s [16,] 0.964 332s [17,] 0.978 332s [18,] 0.967 332s [19,] 0.942 332s [20,] 0.934 332s > print( correlation.systemfit( fitsuri4, 2, 1 ) ) 332s [,1] 332s [1,] 0.0384 332s [2,] 0.1213 332s [3,] 0.0975 332s [4,] 0.1381 332s [5,] 0.1295 332s [6,] 0.0937 332s [7,] 0.0630 332s [8,] 0.1056 332s [9,] 0.2180 332s [10,] 0.4042 332s [11,] 0.1074 332s [12,] 0.0337 332s [13,] 0.0760 332s [14,] 0.0701 332s [15,] 0.0680 332s [16,] 0.1263 332s [17,] 0.3859 332s [18,] 0.2715 332s [19,] 0.2850 332s [20,] 0.3967 332s > 332s > print( correlation.systemfit( fitsurio5r2, 1, 2 ) ) 332s [,1] 332s [1,] 0.986 332s [2,] 0.991 332s [3,] 0.991 332s [4,] 0.991 332s [5,] 0.981 332s [6,] 0.983 332s [7,] 0.984 332s [8,] 0.980 332s [9,] 0.982 332s [10,] 0.991 332s [11,] 0.968 332s [12,] 0.947 332s [13,] 0.970 332s [14,] 0.975 332s [15,] 0.991 332s [16,] 0.989 332s [17,] 0.992 332s [18,] 0.990 332s [19,] 0.982 332s [20,] 0.978 332s > print( correlation.systemfit( fitsuri5r2, 1, 2 ) ) 332s [,1] 332s [1,] 0.0440 332s [2,] 0.1279 332s [3,] 0.1045 332s [4,] 0.1451 332s [5,] 0.1375 332s [6,] 0.1021 332s [7,] 0.0719 332s [8,] 0.1124 332s [9,] 0.2252 332s [10,] 0.4097 332s [11,] 0.1145 332s [12,] 0.0410 332s [13,] 0.0834 332s [14,] 0.0778 332s [15,] 0.0750 332s [16,] 0.1344 332s [17,] 0.3900 332s [18,] 0.2789 332s [19,] 0.2897 332s [20,] 0.4005 332s > 332s > 332s > ## ************ Log-Likelihood values *************** 332s > print( logLik( fitsur1e2 ) ) 332s 'log Lik.' -50.9 (df=10) 332s > print( logLik( fitsur1e2, residCovDiag = TRUE ) ) 332s 'log Lik.' -85.4 (df=10) 332s > 332s > print( logLik( fitsur2e ) ) 332s 'log Lik.' -52 (df=9) 332s > print( logLik( fitsur2e, residCovDiag = TRUE ) ) 332s 'log Lik.' -86.5 (df=9) 332s > 332s > print( logLik( fitsur3 ) ) 332s 'log Lik.' -52.2 (df=9) 332s > print( logLik( fitsur3, residCovDiag = TRUE ) ) 332s 'log Lik.' -86.4 (df=9) 332s > 332s > print( logLik( fitsur4r3 ) ) 332s 'log Lik.' -58.4 (df=8) 332s > print( logLik( fitsur4r3, residCovDiag = TRUE ) ) 332s 'log Lik.' -85.5 (df=8) 332s > 332s > print( logLik( fitsur5 ) ) 332s 'log Lik.' -58.5 (df=8) 332s > print( logLik( fitsur5, residCovDiag = TRUE ) ) 332s 'log Lik.' -84.6 (df=8) 332s > 332s > print( logLik( fitsur5w ) ) 332s 'log Lik.' -58.5 (df=8) 332s > print( logLik( fitsur5w, residCovDiag = TRUE ) ) 332s 'log Lik.' -84.7 (df=8) 332s > 332s > print( logLik( fitsuri1r3 ) ) 332s 'log Lik.' -67.8 (df=10) 332s > print( logLik( fitsuri1r3, residCovDiag = TRUE ) ) 332s 'log Lik.' -76.2 (df=10) 332s > 332s > print( logLik( fitsuri2 ) ) 332s 'log Lik.' -99.9 (df=9) 332s > print( logLik( fitsuri2, residCovDiag = TRUE ) ) 332s 'log Lik.' -101 (df=9) 332s > 332s > print( logLik( fitsuri3e ) ) 332s 'log Lik.' -99.9 (df=9) 332s > print( logLik( fitsuri3e, residCovDiag = TRUE ) ) 332s 'log Lik.' -102 (df=9) 332s > 332s > print( logLik( fitsurio4 ) ) 332s 'log Lik.' -58.5 (df=8) 332s > print( logLik( fitsurio4, residCovDiag = TRUE ) ) 332s 'log Lik.' -85.9 (df=8) 332s > 332s > print( logLik( fitsuri4 ) ) 332s 'log Lik.' -101 (df=8) 332s > print( logLik( fitsuri4, residCovDiag = TRUE ) ) 332s 'log Lik.' -101 (df=8) 332s > 332s > print( logLik( fitsuri4w ) ) 332s 'log Lik.' -101 (df=8) 332s > print( logLik( fitsuri4w, residCovDiag = TRUE ) ) 332s 'log Lik.' -101 (df=8) 332s > 332s > print( logLik( fitsurio5r2 ) ) 332s 'log Lik.' -59.8 (df=8) 332s > print( logLik( fitsurio5r2, residCovDiag = TRUE ) ) 332s 'log Lik.' -93.1 (df=8) 332s > 332s > print( logLik( fitsuri5r2 ) ) 332s 'log Lik.' -101 (df=8) 332s > print( logLik( fitsuri5r2, residCovDiag = TRUE ) ) 332s 'log Lik.' -101 (df=8) 332s > 332s > 332s > ## *********** likelihood ratio tests ************* 332s > # testing first restriction 332s > # non-iterating, methodResidCov = 1 332s > print( lrtest( fitsur2, fitsur1 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur2 332s Model 2: fitsur1 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -52.2 332s 2 10 -51.6 1 1.19 0.28 332s > print( lrtest( fitsur3, fitsur1 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur3 332s Model 2: fitsur1 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -52.2 332s 2 10 -51.6 1 1.19 0.28 332s > # non-iterating, methodResidCov = 0 332s > print( lrtest( fitsur2e, fitsur1e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur2e 332s Model 2: fitsur1e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -52.0 332s 2 10 -51.6 1 0.7 0.4 332s > print( lrtest( fitsur3e, fitsur1e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur3e 332s Model 2: fitsur1e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -52.0 332s 2 10 -51.6 1 0.7 0.4 332s > # iterating, methodResidCov = 1 332s > print( lrtest( fitsuri2, fitsuri1 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri2 332s Model 2: fitsuri1 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 10 -67.8 1 64.3 1.1e-15 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsuri3, fitsuri1 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri3 332s Model 2: fitsuri1 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 10 -67.8 1 64.3 1.1e-15 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > # iterating, methodResidCov = 0 332s > print( lrtest( fitsuri2e, fitsuri1e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri2e 332s Model 2: fitsuri1e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 10 -67.8 1 64.3 1.1e-15 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsuri3e, fitsuri1e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri3e 332s Model 2: fitsuri1e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 10 -67.8 1 64.3 1.1e-15 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > # non-iterating, methodResidCov = 1, WSUR 332s > print( lrtest( fitsur3w, fitsur1w ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur3w 332s Model 2: fitsur1w 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -52.1 332s 2 10 -51.6 1 0.87 0.35 332s > 332s > # testing second restriction 332s > # non-iterating, methodResidCov = 1 332s > print( lrtest( fitsur4, fitsur2 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur4 332s Model 2: fitsur2 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 9 -52.2 1 12.7 0.00037 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsur4, fitsur3 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur4 332s Model 2: fitsur3 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 9 -52.2 1 12.7 0.00037 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsur5, fitsur2 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur5 332s Model 2: fitsur2 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 9 -52.2 1 12.7 0.00037 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsur5, fitsur3 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur5 332s Model 2: fitsur3 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 9 -52.2 1 12.7 0.00037 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > # non-iterating, methodResidCov = 0 332s > print( lrtest( fitsur4e, fitsur2e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur4e 332s Model 2: fitsur2e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.6 332s 2 9 -52.0 1 13.2 0.00028 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsur4e, fitsur3e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur4e 332s Model 2: fitsur3e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.6 332s 2 9 -52.0 1 13.2 0.00028 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsur5e, fitsur2e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur5e 332s Model 2: fitsur2e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.6 332s 2 9 -52.0 1 13.2 0.00028 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsur5e, fitsur3e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur5e 332s Model 2: fitsur3e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.6 332s 2 9 -52.0 1 13.2 0.00028 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > # iterating, methodResidCov = 1 332s > print( lrtest( fitsurio4, fitsuri2 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsurio4 332s Model 2: fitsuri2 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 9 -99.9 1 82.9 <2e-16 *** 332s Warning message: 332s In lrtest.systemfit(fitsurio4, fitsuri2) : 332s model '2' has a smaller log-likelihood value than the more restricted model '1' 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsurio4, fitsuri3 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsurio4 332s Model 2: fitsuri3 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 9 -99.9 1 82.9 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s Warning message: 332s In lrtest.systemfit(fitsurio4, fitsuri3) : 332s > print( lrtest( fitsurio5, fitsuri2 ) ) 332s model '2' has a smaller log-likelihood value than the more restricted model '1' 332s Likelihood ratio test 332s 332s Model 1: fitsurio5 332s Model 2: fitsuri2 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 9 -99.9 1 82.9 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsurio5, fitsuri3 ) ) 332s Warning message: 332s In lrtest.systemfit(fitsurio5, fitsuri2) : 332s model '2' has a smaller log-likelihood value than the more restricted model '1' 332s Likelihood ratio test 332s 332s Model 1: fitsurio5 332s Model 2: fitsuri3 332s Warning message: 332s In lrtest.systemfit(fitsurio5, fitsuri3) : 332s model '2' has a smaller log-likelihood value than the more restricted model '1' 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 9 -99.9 1 82.9 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > # corrected 332s > print( lrtest( fitsuri2, fitsuri4 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri2 332s Model 2: fitsuri4 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 8 -100.9 -1 1.9 0.17 332s > print( lrtest( fitsuri3, fitsuri4 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri3 332s Model 2: fitsuri4 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 8 -100.9 -1 1.9 0.17 332s > print( lrtest( fitsuri2, fitsuri5 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri2 332s Model 2: fitsuri5 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 8 -100.9 -1 1.9 0.17 332s > print( lrtest( fitsuri3, fitsuri5 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri3 332s Model 2: fitsuri5 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 8 -100.9 -1 1.9 0.17 332s > 332s > # iterating, methodResidCov = 0 332s > print( lrtest( fitsurio4e, fitsuri2e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsurio4e 332s Model 2: fitsuri2e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.4 332s 2 9 -99.9 1 83 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsurio4e, fitsuri3e ) ) 332s Warning message: 332s In lrtest.systemfit(fitsurio4e, fitsuri2e) : 332s model '2' has a smaller log-likelihood value than the more restricted model '1' 332s Likelihood ratio test 332s 332s Model 1: fitsurio4e 332s Model 2: fitsuri3e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.4 332s 2 9 -99.9 1 83 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsurio5e, fitsuri2e ) ) 332s Warning message: 332s In lrtest.systemfit(fitsurio4e, fitsuri3e) : 332s model '2' has a smaller log-likelihood value than the more restricted model '1' 332s Likelihood ratio test 332s 332s Model 1: fitsurio5e 332s Model 2: fitsuri2e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.4 332s 2 9 -99.9 1 83 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsurio5e, fitsuri3e ) ) 332s Warning message: 332s In lrtest.systemfit(fitsurio5e, fitsuri2e) : 332s model '2' has a smaller log-likelihood value than the more restricted model '1' 332s Warning message: 332s In lrtest.systemfit(fitsurio5e, fitsuri3e) : 332s model '2' has a smaller log-likelihood value than the more restricted model '1' 332s Likelihood ratio test 332s 332s Model 1: fitsurio5e 332s Model 2: fitsuri3e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.4 332s 2 9 -99.9 1 83 <2e-16 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > # corrected 332s > print( lrtest( fitsuri2e, fitsuri4e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri2e 332s Model 2: fitsuri4e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 8 -100.9 -1 1.9 0.17 332s > print( lrtest( fitsuri3e, fitsuri4e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri3e 332s Model 2: fitsuri4e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 8 -100.9 -1 1.9 0.17 332s > print( lrtest( fitsuri2e, fitsuri5e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri2e 332s Model 2: fitsuri5e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 8 -100.9 -1 1.9 0.17 332s > print( lrtest( fitsuri3e, fitsuri5e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri3e 332s Model 2: fitsuri5e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 8 -100.9 -1 1.9 0.17 332s > 332s > # non-iterating, methodResidCov = 0, WSUR 332s > print( lrtest( fitsur4we, fitsur2we ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur4we 332s Model 2: fitsur2we 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.6 332s 2 9 -51.8 1 13.5 0.00024 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > 332s > # iterating, methodResidCov = 1, WSUR 332s > print( lrtest( fitsuri2w, fitsuri4w ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsuri2w 332s Model 2: fitsuri4w 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 9 -99.9 332s 2 8 -100.9 -1 1.9 0.17 332s > 332s > # testing both of the restrictions 332s > # non-iterating, methodResidCov = 1 332s > print( lrtest( fitsur4, fitsur1 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur4 332s Model 2: fitsur1 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 10 -51.6 2 13.8 0.00098 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsur5, fitsur1 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur5 332s Model 2: fitsur1 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 10 -51.6 2 13.8 0.00098 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > # non-iterating, methodResidCov = 0 332s > print( lrtest( fitsur4e, fitsur1e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur4e 332s Model 2: fitsur1e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.6 332s 2 10 -51.6 2 13.9 0.00095 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsur5e, fitsur1e ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsur5e 332s Model 2: fitsur1e 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.6 332s 2 10 -51.6 2 13.9 0.00095 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > # iterating, methodResidCov = 1 332s > print( lrtest( fitsurio4, fitsuri1 ) ) 332s Likelihood ratio test 332s 332s Model 1: fitsurio4 332s Model 2: fitsuri1 332s #Df LogLik Df Chisq Pr(>Chisq) 332s 1 8 -58.5 332s 2 10 -67.8 2 18.6 9e-05 *** 332s --- 332s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 332s > print( lrtest( fitsurio5, fitsuri1 ) ) 332s Warning message: 332s In lrtest.systemfit(fitsurio4, fitsuri1) : 332s model '2' has a smaller log-likelihood value than the more restricted model '1' 333s Likelihood ratio test 333s 333s Model 1: fitsurio5 333s Model 2: fitsuri1 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -58.5 333s 2 10 -67.8 2 18.6 9e-05 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > # corrected 333s > print( lrtest( fitsuri1, fitsuri4 ) ) 333s Warning message: 333s In lrtest.systemfit(fitsurio5, fitsuri1) : 333s model '2' has a smaller log-likelihood value than the more restricted model '1' 333s Likelihood ratio test 333s 333s Model 1: fitsuri1 333s Model 2: fitsuri4 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 10 -67.8 333s 2 8 -100.9 -2 66.2 4.2e-15 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > print( lrtest( fitsuri1, fitsuri5 ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsuri1 333s Model 2: fitsuri5 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 10 -67.8 333s 2 8 -100.9 -2 66.2 4.2e-15 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > # iterating, methodResidCov = 0 333s > print( lrtest( fitsurio4e, fitsuri1e ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsurio4e 333s Model 2: fitsuri1e 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -58.4 333s 2 10 -67.8 2 18.7 8.9e-05 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > print( lrtest( fitsurio5e, fitsuri1e ) ) 333s Warning message: 333s In lrtest.systemfit(fitsurio4e, fitsuri1e) : 333s model '2' has a smaller log-likelihood value than the more restricted model '1' 333s Likelihood ratio test 333s 333s Model 1: fitsurio5e 333s Model 2: fitsuri1e 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -58.4 333s 2 10 -67.8 2 18.7 8.9e-05 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > # corrected 333s > print( lrtest( fitsuri1e, fitsuri4e ) ) 333s Warning message: 333s In lrtest.systemfit(fitsurio5e, fitsuri1e) : 333s model '2' has a smaller log-likelihood value than the more restricted model '1' 333s Likelihood ratio test 333s 333s Model 1: fitsuri1e 333s Model 2: fitsuri4e 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 10 -67.8 333s 2 8 -100.9 -2 66.2 4.2e-15 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > print( lrtest( fitsuri1e, fitsuri5e ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsuri1e 333s Model 2: fitsuri5e 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 10 -67.8 333s 2 8 -100.9 -2 66.2 4.2e-15 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > # non-iterating, methodResidCov = 1, WSUR 333s > print( lrtest( fitsur5w, fitsur1w ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsur5w 333s Model 2: fitsur1w 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -58.5 333s 2 10 -51.6 2 13.8 0.001 ** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > # testing the two restrictions with one call 333s > # non-iterating, methodResidCov = 1 333s > print( lrtest( fitsur4, fitsur2, fitsur1 ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsur4 333s Model 2: fitsur2 333s Model 3: fitsur1 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -58.5 333s 2 9 -52.2 1 12.66 0.00037 *** 333s 3 10 -51.6 1 1.19 0.27520 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > print( lrtest( fitsur5, fitsur3, fitsur1 ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsur5 333s Model 2: fitsur3 333s Model 3: fitsur1 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -58.5 333s 2 9 -52.2 1 12.66 0.00037 *** 333s 3 10 -51.6 1 1.19 0.27520 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > print( lrtest( fitsur1, fitsur3, fitsur5 ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsur1 333s Model 2: fitsur3 333s Model 3: fitsur5 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 10 -51.6 333s 2 9 -52.2 -1 1.19 0.27520 333s 3 8 -58.5 -1 12.66 0.00037 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > print( lrtest( object = fitsur5, fitsur3, fitsur1 ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsur5 333s Model 2: fitsur3 333s Model 3: fitsur1 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -58.5 333s 2 9 -52.2 1 12.66 0.00037 *** 333s 3 10 -51.6 1 1.19 0.27520 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > print( lrtest( fitsur3, object = fitsur5, fitsur1 ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsur5 333s Model 2: fitsur3 333s Model 3: fitsur1 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -58.5 333s 2 9 -52.2 1 12.66 0.00037 *** 333s 3 10 -51.6 1 1.19 0.27520 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > print( lrtest( fitsur3, fitsur1, object = fitsur5 ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsur5 333s Model 2: fitsur3 333s Model 3: fitsur1 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -58.5 333s 2 9 -52.2 1 12.66 0.00037 *** 333s 3 10 -51.6 1 1.19 0.27520 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > # iterating, methodResidCov = 0 333s > print( lrtest( fitsuri4e, fitsuri2e, fitsuri1e ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsuri4e 333s Model 2: fitsuri2e 333s Model 3: fitsuri1e 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -100.9 333s 2 9 -99.9 1 1.9 0.17 333s 3 10 -67.8 1 64.3 1.1e-15 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > print( lrtest( fitsuri5e, fitsuri3e, fitsuri1e ) ) 333s Likelihood ratio test 333s 333s Model 1: fitsuri5e 333s Model 2: fitsuri3e 333s Model 3: fitsuri1e 333s #Df LogLik Df Chisq Pr(>Chisq) 333s 1 8 -100.9 333s 2 9 -99.9 1 1.9 0.17 333s 3 10 -67.8 1 64.3 1.1e-15 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > ## ************** F tests **************** 333s > # testing first restriction 333s > print( linearHypothesis( fitsur1, restrm ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 1.24 0.27 333s > linearHypothesis( fitsur1, restrict ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 1.24 0.27 333s > 333s > print( linearHypothesis( fitsur1r2, restrm ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1r2 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 1.65 0.21 333s > linearHypothesis( fitsur1r2, restrict ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1r2 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 1.65 0.21 333s > 333s > print( linearHypothesis( fitsuri1e2, restrm ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1e2 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 140 2.1e-13 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1e2, restrict ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1e2 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 140 2.1e-13 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsuri1r3, restrm ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1r3 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 141 1.9e-13 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1r3, restrict ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1r3 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 141 1.9e-13 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsur1we2, restrm ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1we2 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 1.65 0.21 333s > linearHypothesis( fitsur1we2, restrict ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1we2 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 1.65 0.21 333s > 333s > print( linearHypothesis( fitsuri1wr3, restrm ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1wr3 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 141 1.9e-13 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1wr3, restrict ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1wr3 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 141 1.9e-13 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > # testing second restriction 333s > restrOnly2m <- matrix(0,1,7) 333s > restrOnly2q <- 0.5 333s > restrOnly2m[1,2] <- -1 333s > restrOnly2m[1,5] <- 1 333s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 333s > restrictOnly2i <- "- demand_price + supply_income = 0.5" 333s > # first restriction not imposed 333s > print( linearHypothesis( fitsur1e2, restrOnly2m, restrOnly2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1e2 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 2.36 0.13 333s > linearHypothesis( fitsur1e2, restrictOnly2 ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1e2 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 2.36 0.13 333s > 333s > print( linearHypothesis( fitsuri1, restrOnly2m, restrOnly2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 12.2 0.0014 ** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1, restrictOnly2i ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1 333s 333s Res.Df Df F Pr(>F) 333s 1 34 333s 2 33 1 12.2 0.0014 ** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > # first restriction imposed 333s > print( linearHypothesis( fitsur2, restrOnly2m, restrOnly2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur2 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 5.5 0.025 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsur2, restrictOnly2 ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur2 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 5.5 0.025 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsur3, restrOnly2m, restrOnly2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur3 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 5.5 0.025 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsur3, restrictOnly2 ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur3 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 5.5 0.025 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsuri2e, restrOnly2m, restrOnly2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri2e 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 2.35 0.13 333s > linearHypothesis( fitsuri2e, restrictOnly2i ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri2e 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 2.35 0.13 333s > 333s > print( linearHypothesis( fitsuri3e, restrOnly2m, restrOnly2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri3e 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 2.35 0.13 333s > linearHypothesis( fitsuri3e, restrictOnly2i ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri3e 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 2.35 0.13 333s > 333s > print( linearHypothesis( fitsur2we, restrOnly2m, restrOnly2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur2we 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 6.26 0.017 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsur2we, restrictOnly2 ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur2we 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 6.26 0.017 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsuri3we, restrOnly2m, restrOnly2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri3we 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 2.35 0.13 333s > linearHypothesis( fitsuri3we, restrictOnly2i ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri3we 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 34 1 2.35 0.13 333s > 333s > # testing both of the restrictions 333s > print( linearHypothesis( fitsur1r3, restr2m, restr2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1r3 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 33 2 2.6 0.089 . 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsur1r3, restrict2 ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1r3 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 33 2 2.6 0.089 . 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsuri1e2, restr2m, restr2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1e2 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 33 2 89.1 5e-14 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1e2, restrict2i ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1e2 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 33 2 89.1 5e-14 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsur1w, restr2m, restr2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1w 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 33 2 1.8 0.18 333s > linearHypothesis( fitsur1w, restrict2 ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1w 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 33 2 1.8 0.18 333s > 333s > print( linearHypothesis( fitsuri1wr3, restr2m, restr2q ) ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1wr3 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 33 2 89.6 4.6e-14 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1wr3, restrict2i ) 333s Linear hypothesis test (Theil's F test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1wr3 333s 333s Res.Df Df F Pr(>F) 333s 1 35 333s 2 33 2 89.6 4.6e-14 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > 333s > ## ************** Wald tests **************** 333s > # testing first restriction 333s > print( linearHypothesis( fitsur1, restrm, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 0.81 0.37 333s > linearHypothesis( fitsur1, restrict, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 0.81 0.37 333s > 333s > print( linearHypothesis( fitsur1r2, restrm, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1r2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 1.12 0.29 333s > linearHypothesis( fitsur1r2, restrict, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1r2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 1.12 0.29 333s > 333s > print( linearHypothesis( fitsuri1e2, restrm, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1e2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 147 <2e-16 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1e2, restrict, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1e2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 147 <2e-16 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsuri1r3, restrm, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1r3 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 147 <2e-16 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1r3, restrict, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsuri1r3 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 147 <2e-16 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsur1w, restrm, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1w 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 0.81 0.37 333s > linearHypothesis( fitsur1w, restrict, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s 333s Model 1: restricted model 333s Model 2: fitsur1w 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 0.81 0.37 333s > 333s > # testing second restriction 333s > # first restriction not imposed 333s > print( linearHypothesis( fitsur1e2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1e2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 1.6 0.21 333s > linearHypothesis( fitsur1e2, restrictOnly2, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1e2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 1.6 0.21 333s > 333s > print( linearHypothesis( fitsuri1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 12.2 0.00047 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1, restrictOnly2i, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 34 333s 2 33 1 12.2 0.00047 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > # first restriction imposed 333s > print( linearHypothesis( fitsur2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 3.95 0.047 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsur2, restrictOnly2, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 3.95 0.047 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsur3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur3 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 3.95 0.047 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsur3, restrictOnly2, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur3 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 3.95 0.047 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsuri2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri2e 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 2.76 0.096 . 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri2e, restrictOnly2i, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri2e 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 2.76 0.096 . 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsuri3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri3e 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 2.76 0.096 . 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri3e, restrictOnly2i, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri3e 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 2.76 0.096 . 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsuri2w, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri2w 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 2.2 0.14 333s > linearHypothesis( fitsuri2w, restrictOnly2i, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri2w 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 2.2 0.14 333s > 333s > print( linearHypothesis( fitsur3w, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur3w 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 4.26 0.039 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsur3w, restrictOnly2, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur3w 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 34 1 4.26 0.039 * 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > 333s > # testing both of the restrictions 333s > print( linearHypothesis( fitsur1r3, restr2m, restr2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1r3 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 33 2 3.51 0.17 333s > linearHypothesis( fitsur1r3, restrict2, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1r3 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 33 2 3.51 0.17 333s > 333s > print( linearHypothesis( fitsuri1e2, restr2m, restr2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1e2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 33 2 188 <2e-16 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1e2, restrict2i, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1e2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 33 2 188 <2e-16 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > print( linearHypothesis( fitsur1we2, restr2m, restr2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1we2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 33 2 3.66 0.16 333s > linearHypothesis( fitsur1we2, restrict2, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_price = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsur1we2 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 33 2 3.66 0.16 333s > 333s > print( linearHypothesis( fitsuri1wr3, restr2m, restr2q, test = "Chisq" ) ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1wr3 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 33 2 187 <2e-16 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > linearHypothesis( fitsuri1wr3, restrict2i, test = "Chisq" ) 333s Linear hypothesis test (Chi^2 statistic of a Wald test) 333s 333s Hypothesis: 333s demand_income - supply_trend = 0 333s - demand_price + supply_income = 0.5 333s 333s Model 1: restricted model 333s Model 2: fitsuri1wr3 333s 333s Res.Df Df Chisq Pr(>Chisq) 333s 1 35 333s 2 33 2 187 <2e-16 *** 333s --- 333s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 333s > 333s > 333s > ## ****************** model frame ************************** 333s > print( mf <- model.frame( fitsur1e2 ) ) 333s consump price income farmPrice trend 333s 1 98.5 100.3 87.4 98.0 1 333s 2 99.2 104.3 97.6 99.1 2 333s 3 102.2 103.4 96.7 99.1 3 333s 4 101.5 104.5 98.2 98.1 4 333s 5 104.2 98.0 99.8 110.8 5 333s 6 103.2 99.5 100.5 108.2 6 333s 7 104.0 101.1 103.2 105.6 7 333s 8 99.9 104.8 107.8 109.8 8 333s 9 100.3 96.4 96.6 108.7 9 333s 10 102.8 91.2 88.9 100.6 10 333s 11 95.4 93.1 75.1 81.0 11 333s 12 92.4 98.8 76.9 68.6 12 333s 13 94.5 102.9 84.6 70.9 13 333s 14 98.8 98.8 90.6 81.4 14 333s 15 105.8 95.1 103.1 102.3 15 333s 16 100.2 98.5 105.1 105.0 16 333s 17 103.5 86.5 96.4 110.5 17 333s 18 99.9 104.0 104.4 92.5 18 333s 19 105.2 105.8 110.7 89.3 19 333s 20 106.2 113.5 127.1 93.0 20 333s > print( mf1 <- model.frame( fitsur1e2$eq[[ 1 ]] ) ) 333s consump price income 333s 1 98.5 100.3 87.4 333s 2 99.2 104.3 97.6 333s 3 102.2 103.4 96.7 333s 4 101.5 104.5 98.2 333s 5 104.2 98.0 99.8 333s 6 103.2 99.5 100.5 333s 7 104.0 101.1 103.2 333s 8 99.9 104.8 107.8 333s 9 100.3 96.4 96.6 333s 10 102.8 91.2 88.9 333s 11 95.4 93.1 75.1 333s 12 92.4 98.8 76.9 333s 13 94.5 102.9 84.6 333s 14 98.8 98.8 90.6 333s 15 105.8 95.1 103.1 333s 16 100.2 98.5 105.1 333s 17 103.5 86.5 96.4 333s 18 99.9 104.0 104.4 333s 19 105.2 105.8 110.7 333s 20 106.2 113.5 127.1 333s > print( attributes( mf1 )$terms ) 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s > print( mf2 <- model.frame( fitsur1e2$eq[[ 2 ]] ) ) 333s consump price farmPrice trend 333s 1 98.5 100.3 98.0 1 333s 2 99.2 104.3 99.1 2 333s 3 102.2 103.4 99.1 3 333s 4 101.5 104.5 98.1 4 333s 5 104.2 98.0 110.8 5 333s 6 103.2 99.5 108.2 6 333s 7 104.0 101.1 105.6 7 333s 8 99.9 104.8 109.8 8 333s 9 100.3 96.4 108.7 9 333s 10 102.8 91.2 100.6 10 333s 11 95.4 93.1 81.0 11 333s 12 92.4 98.8 68.6 12 333s 13 94.5 102.9 70.9 13 333s 14 98.8 98.8 81.4 14 333s 15 105.8 95.1 102.3 15 333s 16 100.2 98.5 105.0 16 333s 17 103.5 86.5 110.5 17 333s 18 99.9 104.0 92.5 18 333s 19 105.2 105.8 89.3 19 333s 20 106.2 113.5 93.0 20 333s > print( attributes( mf2 )$terms ) 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s > 333s > print( all.equal( mf, model.frame( fitsur1w ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsur1w$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsur2e ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsur2e$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsur3 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf2, model.frame( fitsur3$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsur4r3 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsur4r3$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsur4we ) ) ) 333s [1] TRUE 333s > print( all.equal( mf2, model.frame( fitsur4we$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsur5 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf2, model.frame( fitsur5$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsuri1r3 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsuri1r3$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsuri2 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsuri2$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsuri3e ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsuri3e$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsurio4 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf2, model.frame( fitsurio4$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mf, model.frame( fitsuri4 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsuri4$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsurio5r2 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsurio5r2$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mf, model.frame( fitsuri5r2 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsuri5r2$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > print( all.equal( mf, model.frame( fitsuri5wr2 ) ) ) 333s [1] TRUE 333s > print( all.equal( mf1, model.frame( fitsuri5wr2$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > 333s > ## **************** model matrix ************************ 333s > # with x (returnModelMatrix) = TRUE 333s > print( !is.null( fitsur1e2$eq[[ 1 ]]$x ) ) 333s [1] TRUE 333s > print( mm <- model.matrix( fitsur1e2 ) ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s demand_1 1 100.3 87.4 0 333s demand_2 1 104.3 97.6 0 333s demand_3 1 103.4 96.7 0 333s demand_4 1 104.5 98.2 0 333s demand_5 1 98.0 99.8 0 333s demand_6 1 99.5 100.5 0 333s demand_7 1 101.1 103.2 0 333s demand_8 1 104.8 107.8 0 333s demand_9 1 96.4 96.6 0 333s demand_10 1 91.2 88.9 0 333s demand_11 1 93.1 75.1 0 333s demand_12 1 98.8 76.9 0 333s demand_13 1 102.9 84.6 0 333s demand_14 1 98.8 90.6 0 333s demand_15 1 95.1 103.1 0 333s demand_16 1 98.5 105.1 0 333s demand_17 1 86.5 96.4 0 333s demand_18 1 104.0 104.4 0 333s demand_19 1 105.8 110.7 0 333s demand_20 1 113.5 127.1 0 333s supply_1 0 0.0 0.0 1 333s supply_2 0 0.0 0.0 1 333s supply_3 0 0.0 0.0 1 333s supply_4 0 0.0 0.0 1 333s supply_5 0 0.0 0.0 1 333s supply_6 0 0.0 0.0 1 333s supply_7 0 0.0 0.0 1 333s supply_8 0 0.0 0.0 1 333s supply_9 0 0.0 0.0 1 333s supply_10 0 0.0 0.0 1 333s supply_11 0 0.0 0.0 1 333s supply_12 0 0.0 0.0 1 333s supply_13 0 0.0 0.0 1 333s supply_14 0 0.0 0.0 1 333s supply_15 0 0.0 0.0 1 333s supply_16 0 0.0 0.0 1 333s supply_17 0 0.0 0.0 1 333s supply_18 0 0.0 0.0 1 333s supply_19 0 0.0 0.0 1 333s supply_20 0 0.0 0.0 1 333s supply_price supply_farmPrice supply_trend 333s demand_1 0.0 0.0 0 333s demand_2 0.0 0.0 0 333s demand_3 0.0 0.0 0 333s demand_4 0.0 0.0 0 333s demand_5 0.0 0.0 0 333s demand_6 0.0 0.0 0 333s demand_7 0.0 0.0 0 333s demand_8 0.0 0.0 0 333s demand_9 0.0 0.0 0 333s demand_10 0.0 0.0 0 333s demand_11 0.0 0.0 0 333s demand_12 0.0 0.0 0 333s demand_13 0.0 0.0 0 333s demand_14 0.0 0.0 0 333s demand_15 0.0 0.0 0 333s demand_16 0.0 0.0 0 333s demand_17 0.0 0.0 0 333s demand_18 0.0 0.0 0 333s demand_19 0.0 0.0 0 333s demand_20 0.0 0.0 0 333s supply_1 100.3 98.0 1 333s supply_2 104.3 99.1 2 333s supply_3 103.4 99.1 3 333s supply_4 104.5 98.1 4 333s supply_5 98.0 110.8 5 333s supply_6 99.5 108.2 6 333s supply_7 101.1 105.6 7 333s supply_8 104.8 109.8 8 333s supply_9 96.4 108.7 9 333s supply_10 91.2 100.6 10 333s supply_11 93.1 81.0 11 333s supply_12 98.8 68.6 12 333s supply_13 102.9 70.9 13 333s supply_14 98.8 81.4 14 333s supply_15 95.1 102.3 15 333s supply_16 98.5 105.0 16 333s supply_17 86.5 110.5 17 333s supply_18 104.0 92.5 18 333s supply_19 105.8 89.3 19 333s supply_20 113.5 93.0 20 333s > print( mm1 <- model.matrix( fitsur1e2$eq[[ 1 ]] ) ) 333s (Intercept) price income 333s 1 1 100.3 87.4 333s 2 1 104.3 97.6 333s 3 1 103.4 96.7 333s 4 1 104.5 98.2 333s 5 1 98.0 99.8 333s 6 1 99.5 100.5 333s 7 1 101.1 103.2 333s 8 1 104.8 107.8 333s 9 1 96.4 96.6 333s 10 1 91.2 88.9 333s 11 1 93.1 75.1 333s 12 1 98.8 76.9 333s 13 1 102.9 84.6 333s 14 1 98.8 90.6 333s 15 1 95.1 103.1 333s 16 1 98.5 105.1 333s 17 1 86.5 96.4 333s 18 1 104.0 104.4 333s 19 1 105.8 110.7 333s 20 1 113.5 127.1 333s attr(,"assign") 333s [1] 0 1 2 333s > print( mm2 <- model.matrix( fitsur1e2$eq[[ 2 ]] ) ) 333s (Intercept) price farmPrice trend 333s 1 1 100.3 98.0 1 333s 2 1 104.3 99.1 2 333s 3 1 103.4 99.1 3 333s 4 1 104.5 98.1 4 333s 5 1 98.0 110.8 5 333s 6 1 99.5 108.2 6 333s 7 1 101.1 105.6 7 333s 8 1 104.8 109.8 8 333s 9 1 96.4 108.7 9 333s 10 1 91.2 100.6 10 333s 11 1 93.1 81.0 11 333s 12 1 98.8 68.6 12 333s 13 1 102.9 70.9 13 333s 14 1 98.8 81.4 14 333s 15 1 95.1 102.3 15 333s 16 1 98.5 105.0 16 333s 17 1 86.5 110.5 17 333s 18 1 104.0 92.5 18 333s 19 1 105.8 89.3 19 333s 20 1 113.5 93.0 20 333s attr(,"assign") 333s [1] 0 1 2 3 333s > 333s > # with x (returnModelMatrix) = FALSE 333s > print( all.equal( mm, model.matrix( fitsur1r2 ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur1r2$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur1r2$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > print( !is.null( fitsur1r2$eq[[ 1 ]]$x ) ) 333s [1] FALSE 333s > 333s > # with x (returnModelMatrix) = TRUE 333s > print( !is.null( fitsur2e$eq[[ 1 ]]$x ) ) 333s [1] TRUE 333s > print( all.equal( mm, model.matrix( fitsur2e ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur2e$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur2e$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > 333s > # with x (returnModelMatrix) = FALSE 333s > print( all.equal( mm, model.matrix( fitsur2 ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur2$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur2$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > print( !is.null( fitsur2$eq[[ 1 ]]$x ) ) 333s [1] FALSE 333s > 333s > # with x (returnModelMatrix) = TRUE 333s > print( !is.null( fitsur2we$eq[[ 1 ]]$x ) ) 333s [1] TRUE 333s > print( all.equal( mm, model.matrix( fitsur2we ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur2we$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur2we$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > 333s > # with x (returnModelMatrix) = FALSE 333s > print( all.equal( mm, model.matrix( fitsur2 ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur2$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur2$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > print( !is.null( fitsuri2$eq[[ 1 ]]$x ) ) 333s [1] FALSE 333s > 333s > # with x (returnModelMatrix) = TRUE 333s > print( !is.null( fitsur3e$eq[[ 1 ]]$x ) ) 333s [1] TRUE 333s > print( all.equal( mm, model.matrix( fitsur3e ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur3e$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur3e$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > 333s > # with x (returnModelMatrix) = FALSE 333s > print( all.equal( mm, model.matrix( fitsur3 ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur3$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur3$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > print( !is.null( fitsur3$eq[[ 1 ]]$x ) ) 333s [1] FALSE 333s > 333s > # with x (returnModelMatrix) = TRUE 333s > print( !is.null( fitsur3w$eq[[ 1 ]]$x ) ) 333s [1] TRUE 333s > print( all.equal( mm, model.matrix( fitsur3w ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur3w$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur3w$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > 333s > # with x (returnModelMatrix) = FALSE 333s > print( all.equal( mm, model.matrix( fitsur3 ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur3$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur3$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > print( !is.null( fitsuri3$eq[[ 1 ]]$x ) ) 333s [1] FALSE 333s > 333s > # with x (returnModelMatrix) = TRUE 333s > print( !is.null( fitsur4r3$eq[[ 1 ]]$x ) ) 333s [1] TRUE 333s > print( all.equal( mm, model.matrix( fitsur4r3 ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur4r3$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur4r3$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > 333s > # with x (returnModelMatrix) = FALSE 333s > print( all.equal( mm, model.matrix( fitsur4we ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur4we$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm2, model.matrix( fitsur4we$eq[[ 2 ]] ) ) ) 333s [1] TRUE 333s > print( !is.null( fitsur4we$eq[[ 1 ]]$x ) ) 333s [1] FALSE 333s > 333s > # with x (returnModelMatrix) = TRUE 333s > print( !is.null( fitsurio5r2$eq[[ 1 ]]$x ) ) 333s [1] TRUE 333s > print( !is.null( fitsur5$eq[[ 1 ]]$x ) ) 333s [1] TRUE 333s > print( all.equal( mm, model.matrix( fitsurio5r2 ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsurio5r2$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > print( all.equal( mm, model.matrix( fitsur5 ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur5$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > #print( all.equal( mm2, model.matrix( fitsuri5r2$eq[[ 2 ]] ) ) ) 333s > 333s > # with x (returnModelMatrix) = FALSE 333s > print( all.equal( mm, model.matrix( fitsurio5 ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsurio5$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > 333s > # with x (returnModelMatrix) = FALSE 333s > print( all.equal( mm, model.matrix( fitsur5w ) ) ) 333s [1] TRUE 333s > print( all.equal( mm1, model.matrix( fitsur5w$eq[[ 1 ]] ) ) ) 333s [1] TRUE 333s > #print( all.equal( mm2, model.matrix( fitsuri5r2$eq[[ 1 ]] ) ) ) 333s > print( !is.null( fitsurio5$eq[[ 1 ]]$x ) ) 333s [1] FALSE 333s > print( !is.null( fitsur5w$eq[[ 1 ]]$x ) ) 333s [1] FALSE 333s > 333s > 333s > ## **************** formulas ************************ 333s > formula( fitsur1e2 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s 333s > formula( fitsur1e2$eq[[ 2 ]] ) 333s consump ~ price + farmPrice + trend 333s > 333s > formula( fitsur2e ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s 333s > formula( fitsur2e$eq[[ 1 ]] ) 333s consump ~ price + income 333s > 333s > formula( fitsur2we ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s 333s > formula( fitsur2we$eq[[ 1 ]] ) 333s consump ~ price + income 333s > 333s > formula( fitsur3 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s 333s > formula( fitsur3$eq[[ 2 ]] ) 333s consump ~ price + farmPrice + trend 333s > 333s > formula( fitsur4r3 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s 333s > formula( fitsur4r3$eq[[ 1 ]] ) 333s consump ~ price + income 333s > 333s > formula( fitsur5 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s 333s > formula( fitsur5$eq[[ 2 ]] ) 333s consump ~ price + farmPrice + trend 333s > 333s > formula( fitsuri1r3 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s price ~ income + farmPrice + trend 333s 333s > formula( fitsuri1r3$eq[[ 1 ]] ) 333s consump ~ price + income 333s > 333s > formula( fitsuri2 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s price ~ income + farmPrice + trend 333s 333s > formula( fitsuri2$eq[[ 2 ]] ) 333s price ~ income + farmPrice + trend 333s > 333s > formula( fitsuri3e ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s price ~ income + farmPrice + trend 333s 333s > formula( fitsuri3e$eq[[ 1 ]] ) 333s consump ~ price + income 333s > 333s > formula( fitsurio4 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s 333s > formula( fitsurio4$eq[[ 2 ]] ) 333s consump ~ price + farmPrice + trend 333s > formula( fitsuri4 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s price ~ income + farmPrice + trend 333s 333s > formula( fitsuri4$eq[[ 2 ]] ) 333s price ~ income + farmPrice + trend 333s > 333s > formula( fitsurio5r2 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s 333s > formula( fitsurio5r2$eq[[ 1 ]] ) 333s consump ~ price + income 333s > formula( fitsuri5r2 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s price ~ income + farmPrice + trend 333s 333s > formula( fitsuri5r2$eq[[ 1 ]] ) 333s consump ~ price + income 333s > 333s > formula( fitsuri5wr2 ) 333s $demand 333s consump ~ price + income 333s 333s $supply 333s price ~ income + farmPrice + trend 333s 333s > formula( fitsuri5wr2$eq[[ 1 ]] ) 333s consump ~ price + income 333s > 333s > 333s > ## **************** model terms ******************* 333s > terms( fitsur1e2 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsur1e2$eq[[ 2 ]] ) 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s > 333s > terms( fitsur2e ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsur2e$eq[[ 1 ]] ) 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s > 333s > terms( fitsur3 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsur3$eq[[ 2 ]] ) 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s > 333s > terms( fitsur3w ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsur3w$eq[[ 2 ]] ) 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s > 333s > terms( fitsur4r3 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsur4r3$eq[[ 1 ]] ) 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s > 333s > terms( fitsur4we ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsur4we$eq[[ 1 ]] ) 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s > 333s > terms( fitsur5 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsur5$eq[[ 2 ]] ) 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s > 333s > terms( fitsuri1r3 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s price ~ income + farmPrice + trend 333s attr(,"variables") 333s list(price, income, farmPrice, trend) 333s attr(,"factors") 333s income farmPrice trend 333s price 0 0 0 333s income 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "income" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(price, income, farmPrice, trend) 333s attr(,"dataClasses") 333s price income farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsuri1r3$eq[[ 1 ]] ) 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s > 333s > terms( fitsuri2 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s price ~ income + farmPrice + trend 333s attr(,"variables") 333s list(price, income, farmPrice, trend) 333s attr(,"factors") 333s income farmPrice trend 333s price 0 0 0 333s income 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "income" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(price, income, farmPrice, trend) 333s attr(,"dataClasses") 333s price income farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsuri2$eq[[ 2 ]] ) 333s price ~ income + farmPrice + trend 333s attr(,"variables") 333s list(price, income, farmPrice, trend) 333s attr(,"factors") 333s income farmPrice trend 333s price 0 0 0 333s income 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "income" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(price, income, farmPrice, trend) 333s attr(,"dataClasses") 333s price income farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s > 333s > terms( fitsuri3e ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s price ~ income + farmPrice + trend 333s attr(,"variables") 333s list(price, income, farmPrice, trend) 333s attr(,"factors") 333s income farmPrice trend 333s price 0 0 0 333s income 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "income" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(price, income, farmPrice, trend) 333s attr(,"dataClasses") 333s price income farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsuri3e$eq[[ 1 ]] ) 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s > 333s > terms( fitsurio4 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsurio4$eq[[ 2 ]] ) 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s > terms( fitsuri4 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s price ~ income + farmPrice + trend 333s attr(,"variables") 333s list(price, income, farmPrice, trend) 333s attr(,"factors") 333s income farmPrice trend 333s price 0 0 0 333s income 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "income" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(price, income, farmPrice, trend) 333s attr(,"dataClasses") 333s price income farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsuri4$eq[[ 2 ]] ) 333s price ~ income + farmPrice + trend 333s attr(,"variables") 333s list(price, income, farmPrice, trend) 333s attr(,"factors") 333s income farmPrice trend 333s price 0 0 0 333s income 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "income" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(price, income, farmPrice, trend) 333s attr(,"dataClasses") 333s price income farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s > 333s > terms( fitsurio5r2 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s consump ~ price + farmPrice + trend 333s attr(,"variables") 333s list(consump, price, farmPrice, trend) 333s attr(,"factors") 333s price farmPrice trend 333s consump 0 0 0 333s price 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "price" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, farmPrice, trend) 333s attr(,"dataClasses") 333s consump price farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsurio5r2$eq[[ 1 ]] ) 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s > terms( fitsuri5r2 ) 333s $demand 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s 333s $supply 333s price ~ income + farmPrice + trend 333s attr(,"variables") 333s list(price, income, farmPrice, trend) 333s attr(,"factors") 333s income farmPrice trend 333s price 0 0 0 333s income 1 0 0 333s farmPrice 0 1 0 333s trend 0 0 1 333s attr(,"term.labels") 333s [1] "income" "farmPrice" "trend" 333s attr(,"order") 333s [1] 1 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(price, income, farmPrice, trend) 333s attr(,"dataClasses") 333s price income farmPrice trend 333s "numeric" "numeric" "numeric" "numeric" 333s 333s > terms( fitsuri5r2$eq[[ 1 ]] ) 333s consump ~ price + income 333s attr(,"variables") 333s list(consump, price, income) 333s attr(,"factors") 333s price income 333s consump 0 0 333s price 1 0 333s income 0 1 333s attr(,"term.labels") 333s [1] "price" "income" 333s attr(,"order") 333s [1] 1 1 333s attr(,"intercept") 333s [1] 1 333s attr(,"response") 333s [1] 1 333s attr(,".Environment") 333s 333s attr(,"predvars") 333s list(consump, price, income) 333s attr(,"dataClasses") 333s consump price income 333s "numeric" "numeric" "numeric" 333s > 333s > 333s > ## **************** estfun ************************ 333s > library( "sandwich" ) 333s > 333s > estfun( fitsur1 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s demand_1 0.9083 91.12 79.38 -0.6496 333s demand_2 -0.7320 -76.32 -71.44 0.5235 333s demand_3 3.2023 331.23 309.66 -2.2902 333s demand_4 2.1435 224.00 210.49 -1.5330 333s demand_5 2.7516 269.66 274.61 -1.9679 333s demand_6 1.7015 169.22 171.00 -1.2169 333s demand_7 2.2068 223.03 227.74 -1.5783 333s demand_8 -3.5946 -376.58 -387.50 2.5708 333s demand_9 -1.6348 -157.67 -157.92 1.1692 333s demand_10 2.7103 247.26 240.95 -1.9384 333s demand_11 -0.8810 -82.01 -66.16 0.6301 333s demand_12 -3.4554 -341.39 -265.72 2.4712 333s demand_13 -2.2246 -228.93 -188.20 1.5910 333s demand_14 -0.5461 -53.93 -49.48 0.3906 333s demand_15 2.4619 234.17 253.82 -1.7607 333s demand_16 -4.3873 -431.94 -461.11 3.1378 333s demand_17 -0.9942 -85.99 -95.84 0.7110 333s demand_18 -2.5012 -260.17 -261.13 1.7888 333s demand_19 2.5805 272.93 285.66 -1.8455 333s demand_20 0.2846 32.30 36.17 -0.2036 333s supply_1 -0.4396 -44.11 -38.42 0.3959 333s supply_2 -0.0184 -1.92 -1.79 0.0166 333s supply_3 -2.5916 -268.06 -250.60 2.3337 333s supply_4 -1.7132 -179.04 -168.24 1.5428 333s supply_5 -2.3049 -225.88 -230.03 2.0756 333s supply_6 -1.3780 -137.06 -138.49 1.2410 333s supply_7 -2.0596 -208.16 -212.55 1.8547 333s supply_8 3.4200 358.29 368.68 -3.0798 333s supply_9 1.9576 188.80 189.10 -1.7628 333s supply_10 -2.3620 -215.48 -209.98 2.1270 333s supply_11 1.1852 110.32 89.01 -1.0673 333s supply_12 2.6183 258.69 201.34 -2.3578 333s supply_13 1.9874 204.52 168.14 -1.7897 333s supply_14 -0.1072 -10.59 -9.72 0.0966 333s supply_15 -2.6839 -255.29 -276.71 2.4169 333s supply_16 3.8259 376.66 402.10 -3.4452 333s supply_17 0.5270 45.59 50.80 -0.4746 333s supply_18 3.0021 312.27 313.42 -2.7035 333s supply_19 -2.0184 -213.48 -223.44 1.8176 333s supply_20 -0.8466 -96.08 -107.60 0.7623 333s supply_price supply_farmPrice supply_trend 333s demand_1 -65.17 -63.66 -0.6496 333s demand_2 54.58 51.88 1.0470 333s demand_3 -236.89 -226.96 -6.8707 333s demand_4 -160.20 -150.38 -6.1319 333s demand_5 -192.86 -218.05 -9.8397 333s demand_6 -121.02 -131.66 -7.3012 333s demand_7 -159.51 -166.67 -11.0480 333s demand_8 269.33 282.28 20.5665 333s demand_9 112.76 127.09 10.5227 333s demand_10 -176.84 -195.00 -19.3840 333s demand_11 58.65 51.04 6.9309 333s demand_12 244.16 169.53 29.6547 333s demand_13 163.73 112.80 20.6833 333s demand_14 38.57 31.79 5.4681 333s demand_15 -167.48 -180.12 -26.4104 333s demand_16 308.92 329.47 50.2044 333s demand_17 61.50 78.57 12.0871 333s demand_18 186.07 165.47 32.1991 333s demand_19 -195.20 -164.81 -35.0650 333s demand_20 -23.10 -18.93 -4.0710 333s supply_1 39.72 38.80 0.3959 333s supply_2 1.73 1.64 0.0331 333s supply_3 241.39 231.27 7.0012 333s supply_4 161.23 151.34 6.1710 333s supply_5 203.41 229.98 10.3781 333s supply_6 123.42 134.27 7.4457 333s supply_7 187.45 195.86 12.9829 333s supply_8 -322.64 -338.16 -24.6380 333s supply_9 -170.02 -191.62 -15.8653 333s supply_10 194.04 213.98 21.2699 333s supply_11 -99.35 -86.45 -11.7402 333s supply_12 -232.95 -161.74 -28.2933 333s supply_13 -184.18 -126.89 -23.2663 333s supply_14 9.54 7.86 1.3521 333s supply_15 229.90 247.25 36.2539 333s supply_16 -339.19 -361.75 -55.1237 333s supply_17 -41.05 -52.44 -8.0678 333s supply_18 -281.20 -250.07 -48.6623 333s supply_19 192.24 162.31 34.5341 333s supply_20 86.52 70.90 15.2466 333s > round( colSums( estfun( fitsur1 ) ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s 0 0 0 0 333s supply_price supply_farmPrice supply_trend 333s 0 0 0 333s > 333s > estfun( fitsur1e2 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s demand_1 1.09034 109.386 95.295 -0.80605 333s demand_2 -1.05992 -110.511 -103.448 0.78356 333s demand_3 4.28760 443.488 414.611 -3.16968 333s demand_4 2.85253 298.107 280.119 -2.10878 333s demand_5 3.80226 372.625 379.466 -2.81088 333s demand_6 2.36197 234.912 237.378 -1.74612 333s demand_7 3.06088 309.351 315.883 -2.26280 333s demand_8 -4.81806 -504.754 -519.386 3.56182 333s demand_9 -2.17915 -210.170 -210.506 1.61097 333s demand_10 3.70159 337.689 329.071 -2.73646 333s demand_11 -1.39799 -130.132 -104.989 1.03349 333s demand_12 -4.96091 -490.143 -381.494 3.66743 333s demand_13 -3.24623 -334.063 -274.631 2.39983 333s demand_14 -0.81794 -80.776 -74.105 0.60467 333s demand_15 3.49861 332.784 360.707 -2.58640 333s demand_16 -5.83443 -574.406 -613.199 4.31320 333s demand_17 -1.15650 -100.035 -111.487 0.85496 333s demand_18 -3.36717 -350.239 -351.532 2.48923 333s demand_19 3.59870 380.631 398.376 -2.66040 333s demand_20 0.58382 66.257 74.203 -0.43160 333s supply_1 -0.54811 -54.988 -47.905 0.47751 333s supply_2 0.00819 0.854 0.799 -0.00713 333s supply_3 -3.61236 -373.644 -349.315 3.14703 333s supply_4 -2.38151 -248.882 -233.865 2.07474 333s supply_5 -3.32295 -325.653 -331.631 2.89490 333s supply_6 -2.00948 -199.855 -201.953 1.75063 333s supply_7 -2.95622 -298.773 -305.081 2.57541 333s supply_8 4.67628 489.901 504.103 -4.07390 333s supply_9 2.65680 256.238 256.647 -2.31456 333s supply_10 -3.31875 -302.763 -295.037 2.89124 333s supply_11 1.84429 171.676 138.506 -1.60672 333s supply_12 3.95003 390.267 303.757 -3.44120 333s supply_13 3.01568 310.338 255.127 -2.62722 333s supply_14 -0.02452 -2.421 -2.221 0.02136 333s supply_15 -3.84791 -366.010 -396.720 3.35224 333s supply_16 5.24831 516.701 551.597 -4.57224 333s supply_17 0.59732 51.667 57.582 -0.52037 333s supply_18 4.17631 434.404 436.007 -3.63834 333s supply_19 -2.86060 -302.562 -316.668 2.49211 333s supply_20 -1.29079 -146.492 -164.060 1.12452 333s supply_price supply_farmPrice supply_trend 333s demand_1 -80.865 -78.993 -0.8060 333s demand_2 81.697 77.651 1.5671 333s demand_3 -327.856 -314.115 -9.5090 333s demand_4 -220.380 -206.871 -8.4351 333s demand_5 -275.469 -311.446 -14.0544 333s demand_6 -173.662 -188.931 -10.4767 333s demand_7 -228.692 -238.952 -15.8396 333s demand_8 373.147 391.088 28.4946 333s demand_9 155.372 175.113 14.4987 333s demand_10 -249.642 -275.288 -27.3646 333s demand_11 96.202 83.712 11.3683 333s demand_12 362.346 251.586 44.0092 333s demand_13 246.962 170.148 31.1978 333s demand_14 59.715 49.220 8.4654 333s demand_15 -246.016 -264.589 -38.7961 333s demand_16 424.638 452.886 69.0111 333s demand_17 73.953 94.473 14.5344 333s demand_18 258.920 230.254 44.8061 333s demand_19 -281.388 -237.573 -50.5475 333s demand_20 -48.982 -40.138 -8.6319 333s supply_1 47.905 46.796 0.4775 333s supply_2 -0.744 -0.707 -0.0143 333s supply_3 325.513 311.871 9.4411 333s supply_4 216.822 203.532 8.2989 333s supply_5 283.704 320.755 14.4745 333s supply_6 174.111 189.418 10.5038 333s supply_7 260.286 271.963 18.0279 333s supply_8 -426.794 -447.314 -32.5912 333s supply_9 -223.230 -251.593 -20.8310 333s supply_10 263.762 290.859 28.9124 333s supply_11 -149.561 -130.144 -17.6739 333s supply_12 -339.994 -236.066 -41.2944 333s supply_13 -270.361 -186.270 -34.1538 333s supply_14 2.109 1.739 0.2990 333s supply_15 318.862 342.934 50.2836 333s supply_16 -450.142 -480.085 -73.1559 333s supply_17 -45.011 -57.501 -8.8464 333s supply_18 -378.445 -336.546 -65.4901 333s supply_19 263.588 222.545 47.3500 333s supply_20 127.621 104.580 22.4903 333s > round( colSums( estfun( fitsur1e2 ) ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s 0 0 0 0 333s supply_price supply_farmPrice supply_trend 333s 0 0 0 333s > 333s > estfun( fitsur1r3 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s demand_1 1.07229 107.575 93.718 -0.79049 333s demand_2 -1.02096 -106.450 -99.646 0.75265 333s demand_3 4.16424 430.729 402.682 -3.06988 333s demand_4 2.77231 289.723 272.240 -2.04374 333s demand_5 3.68037 360.680 367.301 -2.71316 333s demand_6 2.28513 227.270 229.656 -1.68460 333s demand_7 2.96157 299.314 305.634 -2.18327 333s demand_8 -4.67889 -490.175 -504.385 3.44927 333s demand_9 -2.11749 -204.223 -204.549 1.56101 333s demand_10 3.58740 327.271 318.920 -2.64463 333s demand_11 -1.33464 -124.235 -100.231 0.98389 333s demand_12 -4.78276 -472.541 -367.794 3.52584 333s demand_13 -3.12449 -321.535 -264.332 2.30337 333s demand_14 -0.78522 -77.545 -71.141 0.57886 333s demand_15 3.37652 321.171 348.119 -2.48917 333s demand_16 -5.67080 -558.296 -596.001 4.18051 333s demand_17 -1.14172 -98.757 -110.062 0.84168 333s demand_18 -3.26836 -339.962 -341.217 2.40943 333s demand_19 3.47995 368.071 385.231 -2.56542 333s demand_20 0.54555 61.914 69.339 -0.40218 333s supply_1 -0.53834 -54.008 -47.051 0.47031 333s supply_2 0.00335 0.349 0.327 -0.00293 333s supply_3 -3.49682 -361.694 -338.143 3.05492 333s supply_4 -2.30621 -241.013 -226.470 2.01477 333s supply_5 -3.20507 -314.100 -319.866 2.80004 333s supply_6 -1.93606 -192.553 -194.574 1.69139 333s supply_7 -2.85248 -288.289 -294.376 2.49200 333s supply_8 4.53460 475.059 488.830 -3.96155 333s supply_9 2.57840 248.676 249.073 -2.25256 333s supply_10 -3.20906 -292.756 -285.286 2.80352 333s supply_11 1.76494 164.289 132.547 -1.54190 333s supply_12 3.79168 374.622 291.580 -3.31251 333s supply_13 2.89330 297.744 244.773 -2.52766 333s supply_14 -0.03625 -3.580 -3.284 0.03167 333s supply_15 -3.71220 -353.101 -382.728 3.24307 333s supply_16 5.08854 500.972 534.805 -4.44548 333s supply_17 0.59312 51.303 57.176 -0.51816 333s supply_18 4.04346 420.584 422.137 -3.53247 333s supply_19 -2.76240 -292.176 -305.797 2.41330 333s supply_20 -1.23648 -140.329 -157.157 1.08023 333s supply_price supply_farmPrice supply_trend 333s demand_1 -79.304 -77.47 -0.79049 333s demand_2 78.475 74.59 1.50531 333s demand_3 -317.533 -304.22 -9.20963 333s demand_4 -213.583 -200.49 -8.17496 333s demand_5 -265.893 -300.62 -13.56581 333s demand_6 -167.543 -182.27 -10.10759 333s demand_7 -220.654 -230.55 -15.28289 333s demand_8 361.356 378.73 27.59420 333s demand_9 150.553 169.68 14.04907 333s demand_10 -241.264 -266.05 -26.44627 333s demand_11 91.586 79.70 10.82281 333s demand_12 348.357 241.87 42.31014 333s demand_13 237.035 163.31 29.94383 333s demand_14 57.166 47.12 8.10410 333s demand_15 -236.767 -254.64 -37.33751 333s demand_16 411.575 438.95 66.88809 333s demand_17 72.803 93.01 14.30850 333s demand_18 250.619 222.87 43.36977 333s demand_19 -271.341 -229.09 -48.74290 333s demand_20 -45.643 -37.40 -8.04353 333s supply_1 47.183 46.09 0.47031 333s supply_2 -0.305 -0.29 -0.00585 333s supply_3 315.985 302.74 9.16476 333s supply_4 210.555 197.65 8.05908 333s supply_5 274.406 310.24 14.00018 333s supply_6 168.219 183.01 10.14835 333s supply_7 251.857 263.16 17.44401 333s supply_8 -415.024 -434.98 -31.69241 333s supply_9 -217.250 -244.85 -20.27300 333s supply_10 255.760 282.03 28.03523 333s supply_11 -143.528 -124.89 -16.96088 333s supply_12 -327.279 -227.24 -39.75013 333s supply_13 -260.117 -179.21 -32.85963 333s supply_14 3.128 2.58 0.44339 333s supply_15 308.478 331.77 48.64611 333s supply_16 -437.662 -466.78 -71.12773 333s supply_17 -44.820 -57.26 -8.80876 333s supply_18 -367.434 -326.75 -63.58452 333s supply_19 255.253 215.51 45.85274 333s supply_20 122.595 100.46 21.60450 333s > round( colSums( estfun( fitsur1r3 ) ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s 0 0 0 0 333s supply_price supply_farmPrice supply_trend 333s 0 0 0 333s > 333s > estfun( fitsur1w ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s demand_1 0.9083 91.12 79.38 -0.6496 333s demand_2 -0.7320 -76.32 -71.44 0.5235 333s demand_3 3.2023 331.23 309.66 -2.2902 333s demand_4 2.1435 224.00 210.49 -1.5330 333s demand_5 2.7516 269.66 274.61 -1.9679 333s demand_6 1.7015 169.22 171.00 -1.2169 333s demand_7 2.2068 223.03 227.74 -1.5783 333s demand_8 -3.5946 -376.58 -387.50 2.5708 333s demand_9 -1.6348 -157.67 -157.92 1.1692 333s demand_10 2.7103 247.26 240.95 -1.9384 333s demand_11 -0.8810 -82.01 -66.16 0.6301 333s demand_12 -3.4554 -341.39 -265.72 2.4712 333s demand_13 -2.2246 -228.93 -188.20 1.5910 333s demand_14 -0.5461 -53.93 -49.48 0.3906 333s demand_15 2.4619 234.17 253.82 -1.7607 333s demand_16 -4.3873 -431.94 -461.11 3.1378 333s demand_17 -0.9942 -85.99 -95.84 0.7110 333s demand_18 -2.5012 -260.17 -261.13 1.7888 333s demand_19 2.5805 272.93 285.66 -1.8455 333s demand_20 0.2846 32.30 36.17 -0.2036 333s supply_1 -0.4396 -44.11 -38.42 0.3959 333s supply_2 -0.0184 -1.92 -1.79 0.0166 333s supply_3 -2.5916 -268.06 -250.60 2.3337 333s supply_4 -1.7132 -179.04 -168.24 1.5428 333s supply_5 -2.3049 -225.88 -230.03 2.0756 333s supply_6 -1.3780 -137.06 -138.49 1.2410 333s supply_7 -2.0596 -208.16 -212.55 1.8547 333s supply_8 3.4200 358.29 368.68 -3.0798 333s supply_9 1.9576 188.80 189.10 -1.7628 333s supply_10 -2.3620 -215.48 -209.98 2.1270 333s supply_11 1.1852 110.32 89.01 -1.0673 333s supply_12 2.6183 258.69 201.34 -2.3578 333s supply_13 1.9874 204.52 168.14 -1.7897 333s supply_14 -0.1072 -10.59 -9.72 0.0966 333s supply_15 -2.6839 -255.29 -276.71 2.4169 333s supply_16 3.8259 376.66 402.10 -3.4452 333s supply_17 0.5270 45.59 50.80 -0.4746 333s supply_18 3.0021 312.27 313.42 -2.7035 333s supply_19 -2.0184 -213.48 -223.44 1.8176 333s supply_20 -0.8466 -96.08 -107.60 0.7623 333s supply_price supply_farmPrice supply_trend 333s demand_1 -65.17 -63.66 -0.6496 333s demand_2 54.58 51.88 1.0470 333s demand_3 -236.89 -226.96 -6.8707 333s demand_4 -160.20 -150.38 -6.1319 333s demand_5 -192.86 -218.05 -9.8397 333s demand_6 -121.02 -131.66 -7.3012 333s demand_7 -159.51 -166.67 -11.0480 333s demand_8 269.33 282.28 20.5665 333s demand_9 112.76 127.09 10.5227 333s demand_10 -176.84 -195.00 -19.3840 333s demand_11 58.65 51.04 6.9309 333s demand_12 244.16 169.53 29.6547 333s demand_13 163.73 112.80 20.6833 333s demand_14 38.57 31.79 5.4681 333s demand_15 -167.48 -180.12 -26.4104 333s demand_16 308.92 329.47 50.2044 333s demand_17 61.50 78.57 12.0871 333s demand_18 186.07 165.47 32.1991 333s demand_19 -195.20 -164.81 -35.0650 333s demand_20 -23.10 -18.93 -4.0710 333s supply_1 39.72 38.80 0.3959 333s supply_2 1.73 1.64 0.0331 333s supply_3 241.39 231.27 7.0012 333s supply_4 161.23 151.34 6.1710 333s supply_5 203.41 229.98 10.3781 333s supply_6 123.42 134.27 7.4457 333s supply_7 187.45 195.86 12.9829 333s supply_8 -322.64 -338.16 -24.6380 333s supply_9 -170.02 -191.62 -15.8653 333s supply_10 194.04 213.98 21.2699 333s supply_11 -99.35 -86.45 -11.7402 333s supply_12 -232.95 -161.74 -28.2933 333s supply_13 -184.18 -126.89 -23.2663 333s supply_14 9.54 7.86 1.3521 333s supply_15 229.90 247.25 36.2539 333s supply_16 -339.19 -361.75 -55.1237 333s supply_17 -41.05 -52.44 -8.0678 333s supply_18 -281.20 -250.07 -48.6623 333s supply_19 192.24 162.31 34.5341 333s supply_20 86.52 70.90 15.2466 333s > round( colSums( estfun( fitsur1w ) ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s 0 0 0 0 333s supply_price supply_farmPrice supply_trend 333s 0 0 0 333s > 333s > estfun( fitsuri1e ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s demand_1 0.5467 54.84 47.78 0.5219 333s demand_2 -0.5182 -54.03 -50.58 -0.4947 333s demand_3 1.5799 163.41 152.77 1.5082 333s demand_4 0.9787 102.28 96.11 0.9343 333s demand_5 1.4899 146.02 148.70 1.4224 333s demand_6 0.8875 88.27 89.19 0.8472 333s demand_7 1.0809 109.24 111.55 1.0319 333s demand_8 -2.1165 -221.73 -228.15 -2.0205 333s demand_9 -0.7383 -71.21 -71.32 -0.7049 333s demand_10 1.7668 161.19 157.07 1.6867 333s demand_11 -0.0682 -6.35 -5.12 -0.0651 333s demand_12 -1.6133 -159.40 -124.07 -1.5402 333s demand_13 -1.1570 -119.06 -97.88 -1.1045 333s demand_14 -0.1925 -19.01 -17.44 -0.1838 333s demand_15 1.4026 133.41 144.61 1.3390 333s demand_16 -2.3128 -227.70 -243.08 -2.2080 333s demand_17 -0.0876 -7.58 -8.44 -0.0836 333s demand_18 -1.4924 -155.23 -155.81 -1.4247 333s demand_19 1.0702 113.20 118.47 1.0217 333s demand_20 -0.5064 -57.47 -64.36 -0.4834 333s supply_1 0.1054 10.57 9.21 0.1789 333s supply_2 -0.8882 -92.60 -86.68 -1.5080 333s supply_3 -0.5218 -53.97 -50.46 -0.8859 333s supply_4 -0.2644 -27.63 -25.96 -0.4489 333s supply_5 -0.7666 -75.13 -76.51 -1.3016 333s supply_6 -0.4056 -40.34 -40.77 -0.6887 333s supply_7 -0.8114 -82.00 -83.74 -1.3777 333s supply_8 1.4243 149.22 153.54 2.4183 333s supply_9 1.0270 99.05 99.21 1.7438 333s supply_10 -1.0278 -93.77 -91.37 -1.7451 333s supply_11 0.6336 58.98 47.58 1.0758 333s supply_12 0.2724 26.92 20.95 0.4626 333s supply_13 0.8434 86.79 71.35 1.4319 333s supply_14 -0.7107 -70.19 -64.39 -1.2067 333s supply_15 -1.5343 -145.94 -158.18 -2.6050 333s supply_16 1.1276 111.01 118.51 1.9145 333s supply_17 -0.6907 -59.75 -66.58 -1.1727 333s supply_18 2.2394 232.94 233.79 3.8022 333s supply_19 0.1792 18.96 19.84 0.3043 333s supply_20 -0.2309 -26.21 -29.35 -0.3921 333s supply_income supply_farmPrice supply_trend 333s demand_1 45.61 51.15 0.522 333s demand_2 -48.28 -49.03 -0.989 333s demand_3 145.85 149.47 4.525 333s demand_4 91.75 91.66 3.737 333s demand_5 141.95 157.60 7.112 333s demand_6 85.15 91.67 5.083 333s demand_7 106.49 108.97 7.223 333s demand_8 -217.81 -221.85 -16.164 333s demand_9 -68.09 -76.62 -6.344 333s demand_10 149.95 169.69 16.867 333s demand_11 -4.89 -5.28 -0.717 333s demand_12 -118.44 -105.66 -18.482 333s demand_13 -93.44 -78.31 -14.359 333s demand_14 -16.65 -14.96 -2.573 333s demand_15 138.05 136.98 20.085 333s demand_16 -232.06 -231.84 -35.327 333s demand_17 -8.06 -9.24 -1.421 333s demand_18 -148.74 -131.79 -25.645 333s demand_19 113.10 91.24 19.412 333s demand_20 -61.44 -44.96 -9.668 333s supply_1 15.64 17.53 0.179 333s supply_2 -147.18 -149.44 -3.016 333s supply_3 -85.67 -87.79 -2.658 333s supply_4 -44.08 -44.04 -1.796 333s supply_5 -129.90 -144.21 -6.508 333s supply_6 -69.22 -74.52 -4.132 333s supply_7 -142.17 -145.48 -9.644 333s supply_8 260.69 265.53 19.346 333s supply_9 168.45 189.55 15.694 333s supply_10 -155.14 -175.56 -17.451 333s supply_11 80.79 87.14 11.833 333s supply_12 35.57 31.73 5.551 333s supply_13 121.14 101.52 18.615 333s supply_14 -109.33 -98.23 -16.894 333s supply_15 -268.57 -266.49 -39.075 333s supply_16 201.22 201.03 30.633 333s supply_17 -113.05 -129.59 -19.937 333s supply_18 396.95 351.71 68.440 333s supply_19 33.69 27.18 5.782 333s supply_20 -49.83 -36.46 -7.841 333s > round( colSums( estfun( fitsuri1e ) ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s 0 0 0 0 333s supply_income supply_farmPrice supply_trend 333s 0 0 0 333s > 333s > estfun( fitsuri1wr3 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s demand_1 0.5102 51.19 44.59 0.4867 333s demand_2 -0.4886 -50.94 -47.68 -0.4661 333s demand_3 1.4782 152.90 142.94 1.4102 333s demand_4 0.9143 95.55 89.79 0.8722 333s demand_5 1.3982 137.03 139.54 1.3339 333s demand_6 0.8327 82.82 83.69 0.7944 333s demand_7 1.0134 102.42 104.59 0.9668 333s demand_8 -1.9849 -207.94 -213.97 -1.8935 333s demand_9 -0.6897 -66.52 -66.63 -0.6580 333s demand_10 1.6602 151.46 147.60 1.5838 333s demand_11 -0.0636 -5.92 -4.77 -0.0606 333s demand_12 -1.5152 -149.71 -116.52 -1.4455 333s demand_13 -1.0888 -112.05 -92.11 -1.0387 333s demand_14 -0.1809 -17.86 -16.39 -0.1726 333s demand_15 1.3190 125.46 135.99 1.2583 333s demand_16 -2.1651 -213.16 -227.55 -2.0655 333s demand_17 -0.0731 -6.33 -7.05 -0.0698 333s demand_18 -1.4001 -145.63 -146.17 -1.3357 333s demand_19 1.0017 105.95 110.89 0.9556 333s demand_20 -0.4780 -54.25 -60.76 -0.4560 333s supply_1 0.0755 7.57 6.60 0.1193 333s supply_2 -0.8526 -88.90 -83.22 -1.3478 333s supply_3 -0.5074 -52.48 -49.07 -0.8021 333s supply_4 -0.2631 -27.49 -25.83 -0.4159 333s supply_5 -0.7425 -72.77 -74.10 -1.1737 333s supply_6 -0.3998 -39.77 -40.18 -0.6320 333s supply_7 -0.7750 -78.33 -79.98 -1.2251 333s supply_8 1.3178 138.06 142.06 2.0831 333s supply_9 0.9476 91.39 91.54 1.4979 333s supply_10 -0.9683 -88.34 -86.08 -1.5306 333s supply_11 0.6060 56.40 45.51 0.9578 333s supply_12 0.2813 27.79 21.63 0.4446 333s supply_13 0.8170 84.07 69.12 1.2914 333s supply_14 -0.6451 -63.71 -58.44 -1.0197 333s supply_15 -1.4315 -136.17 -147.59 -2.2629 333s supply_16 1.0615 104.50 111.56 1.6779 333s supply_17 -0.6453 -55.82 -62.21 -1.0200 333s supply_18 2.1183 220.33 221.15 3.3484 333s supply_19 0.1946 20.58 21.54 0.3076 333s supply_20 -0.1888 -21.42 -23.99 -0.2984 333s supply_income supply_farmPrice supply_trend 333s demand_1 42.54 47.70 0.487 333s demand_2 -45.49 -46.19 -0.932 333s demand_3 136.37 139.75 4.231 333s demand_4 85.65 85.57 3.489 333s demand_5 133.12 147.79 6.669 333s demand_6 79.84 85.95 4.766 333s demand_7 99.77 102.09 6.768 333s demand_8 -204.12 -207.91 -15.148 333s demand_9 -63.56 -71.52 -5.922 333s demand_10 140.80 159.34 15.838 333s demand_11 -4.55 -4.91 -0.667 333s demand_12 -111.16 -99.16 -17.346 333s demand_13 -87.88 -73.64 -13.503 333s demand_14 -15.63 -14.05 -2.416 333s demand_15 129.73 128.72 18.874 333s demand_16 -217.08 -216.88 -33.048 333s demand_17 -6.73 -7.71 -1.186 333s demand_18 -139.45 -123.55 -24.042 333s demand_19 105.78 85.33 18.156 333s demand_20 -57.96 -42.41 -9.120 333s supply_1 10.43 11.69 0.119 333s supply_2 -131.54 -133.56 -2.696 333s supply_3 -77.56 -79.49 -2.406 333s supply_4 -40.84 -40.80 -1.663 333s supply_5 -117.13 -130.04 -5.868 333s supply_6 -63.52 -68.39 -3.792 333s supply_7 -126.43 -129.37 -8.575 333s supply_8 224.56 228.72 16.665 333s supply_9 144.70 162.82 13.481 333s supply_10 -136.07 -153.98 -15.306 333s supply_11 71.93 77.58 10.536 333s supply_12 34.19 30.50 5.335 333s supply_13 109.25 91.56 16.788 333s supply_14 -92.38 -83.00 -14.276 333s supply_15 -233.30 -231.49 -33.943 333s supply_16 176.34 176.17 26.846 333s supply_17 -98.33 -112.71 -17.341 333s supply_18 349.57 309.73 60.271 333s supply_19 34.05 27.47 5.845 333s supply_20 -37.92 -27.75 -5.967 333s > round( colSums( estfun( fitsuri1wr3 ) ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s 0 0 0 0 333s supply_income supply_farmPrice supply_trend 333s 0 0 0 333s > 333s > estfun( fitsurS1 ) 333s eq1_consump eq2_(Intercept) eq2_consump eq2_trend 333s eq1_1 7.162 0.02160 2.127 0.0216 333s eq1_2 15.562 0.04659 4.621 0.0932 333s eq1_3 6.026 0.01752 1.789 0.0525 333s eq1_4 10.524 0.03079 3.125 0.1232 333s eq1_5 -14.099 -0.04017 -4.187 -0.2008 333s eq1_6 -7.426 -0.02136 -2.205 -0.1282 333s eq1_7 -5.141 -0.01468 -1.527 -0.1028 333s eq1_8 15.138 0.04500 4.495 0.3600 333s eq1_9 -7.596 -0.02248 -2.256 -0.2023 333s eq1_10 -28.217 -0.08150 -8.379 -0.8150 333s eq1_11 -3.498 -0.01088 -1.039 -0.1197 333s eq1_12 17.457 0.05609 5.184 0.6731 333s eq1_13 22.800 0.07162 6.771 0.9311 333s eq1_14 2.479 0.00746 0.736 0.1044 333s eq1_15 -26.446 -0.07423 -7.853 -1.1135 333s eq1_16 -2.054 -0.00609 -0.610 -0.0974 333s eq1_17 -42.973 -0.12327 -12.761 -2.0956 333s eq1_18 13.132 0.03902 3.900 0.7024 333s eq1_19 4.307 0.01216 1.279 0.2310 333s eq1_20 22.866 0.06392 6.790 1.2784 333s eq2_1 -1.322 -0.02928 -2.884 -0.0293 333s eq2_2 -0.971 -0.02136 -2.118 -0.0427 333s eq2_3 -5.293 -0.11298 -11.542 -0.3389 333s eq2_4 -4.273 -0.09180 -9.318 -0.3672 333s eq2_5 1.836 0.03840 4.003 0.1920 333s eq2_6 2.119 0.04477 4.622 0.2686 333s eq2_7 -0.532 -0.01115 -1.160 -0.0781 333s eq2_8 10.068 0.21978 21.956 1.7582 333s eq2_9 9.192 0.19974 20.044 1.7977 333s eq2_10 -0.465 -0.00986 -1.014 -0.0986 333s eq2_11 -2.679 -0.06122 -5.843 -0.6735 333s eq2_12 -6.257 -0.14762 -13.644 -1.7715 333s eq2_13 -7.360 -0.16978 -16.050 -2.2072 333s eq2_14 -5.865 -0.12951 -12.790 -1.8131 333s eq2_15 -0.730 -0.01505 -1.593 -0.2258 333s eq2_16 11.188 0.24342 24.396 3.8947 333s eq2_17 11.047 0.23271 24.091 3.9561 333s eq2_18 3.346 0.07302 7.297 1.3144 333s eq2_19 -7.478 -0.15498 -16.307 -2.9445 333s eq2_20 -5.570 -0.11434 -12.146 -2.2868 333s > round( colSums( estfun( fitsurS1 ) ), digits = 7 ) 333s eq1_consump eq2_(Intercept) eq2_consump eq2_trend 333s 0 0 0 0 333s > 333s > estfun( fitsurS2 ) 333s eq1_price eq2_trend 333s eq1_1 -5.42871 -0.000114 333s eq1_2 -13.14782 -0.000531 333s eq1_3 -4.34907 -0.000266 333s eq1_4 -8.39779 -0.000677 333s eq1_5 12.19030 0.001310 333s eq1_6 6.97176 0.000886 333s eq1_7 5.14513 0.000750 333s eq1_8 -12.72321 -0.002046 333s eq1_9 7.04895 0.001385 333s eq1_10 22.20478 0.005126 333s eq1_11 3.65437 0.000909 333s eq1_12 -15.21951 -0.003893 333s eq1_13 -20.44077 -0.005438 333s eq1_14 -1.31641 -0.000393 333s eq1_15 21.18383 0.007035 333s eq1_16 2.54257 0.000870 333s eq1_17 31.47441 0.013026 333s eq1_18 -10.84129 -0.003951 333s eq1_19 -2.78655 -0.001054 333s eq1_20 -19.91341 -0.007390 333s eq2_1 0.42448 0.037215 333s eq2_2 0.40866 0.068949 333s eq2_3 0.38411 0.097989 333s eq2_4 0.34891 0.117463 333s eq2_5 0.30591 0.137281 333s eq2_6 0.27161 0.144126 333s eq2_7 0.24474 0.149098 333s eq2_8 0.19771 0.132796 333s eq2_9 0.15083 0.123801 333s eq2_10 0.12174 0.117373 333s eq2_11 0.06024 0.062610 333s eq2_12 0.01611 0.017205 333s eq2_13 -0.00856 -0.009507 333s eq2_14 -0.02284 -0.028474 333s eq2_15 -0.02363 -0.032773 333s eq2_16 -0.08383 -0.119831 333s eq2_17 -0.09018 -0.155889 333s eq2_18 -0.16161 -0.245985 333s eq2_19 -0.17473 -0.276076 333s eq2_20 -0.22123 -0.342915 333s > round( colSums( estfun( fitsurS2 ) ), digits = 7 ) 333s eq1_price eq2_trend 333s 0 0 333s > 333s > estfun( fitsurS3 ) 333s eq1_trend eq2_trend 333s eq1_1 2.069 -2.039 333s eq1_2 3.833 -3.777 333s eq1_3 5.448 -5.369 333s eq1_4 6.531 -6.436 333s eq1_5 7.634 -7.523 333s eq1_6 8.015 -7.899 333s eq1_7 8.293 -8.173 333s eq1_8 7.389 -7.281 333s eq1_9 6.890 -6.790 333s eq1_10 6.535 -6.440 333s eq1_11 3.493 -3.443 333s eq1_12 0.972 -0.958 333s eq1_13 -0.510 0.503 333s eq1_14 -1.562 1.539 333s eq1_15 -1.798 1.772 333s eq1_16 -6.634 6.537 333s eq1_17 -8.634 8.509 333s eq1_18 -13.639 13.441 333s eq1_19 -15.308 15.085 333s eq1_20 -19.019 18.743 333s eq2_1 -2.082 2.089 333s eq2_2 -4.012 4.027 333s eq2_3 -5.472 5.491 333s eq2_4 -6.736 6.760 333s eq2_5 -6.873 6.897 333s eq2_6 -7.460 7.486 333s eq2_7 -7.809 7.837 333s eq2_8 -8.276 8.305 333s eq2_9 -6.161 6.182 333s eq2_10 -4.039 4.053 333s eq2_11 -3.098 3.109 333s eq2_12 -2.949 2.960 333s eq2_13 -2.261 2.269 333s eq2_14 1.160 -1.164 333s eq2_15 4.921 -4.939 333s eq2_16 6.677 -6.701 333s eq2_17 14.428 -14.479 333s eq2_18 11.167 -11.207 333s eq2_19 14.155 -14.205 333s eq2_20 14.719 -14.771 333s > round( colSums( estfun( fitsurS3 ) ), digits = 7 ) 333s eq1_trend eq2_trend 333s 0 0 333s > 333s > try( estfun( fitsurS4 ) ) 333s Error in estfun.systemfit(fitsurS4) : 333s returning the estimation function for models with restrictions has not yet been implemented. 333s > 333s > estfun( fitsurS5 ) 333s eq1_(Intercept) eq2_(Intercept) 333s eq1_1 -0.17267 0.01074 333s eq1_2 -0.12244 0.00761 333s eq1_3 0.09050 -0.00563 333s eq1_4 0.04335 -0.00270 333s eq1_5 0.23912 -0.01487 333s eq1_6 0.16778 -0.01043 333s eq1_7 0.22144 -0.01377 333s eq1_8 -0.07143 0.00444 333s eq1_9 -0.03923 0.00244 333s eq1_10 0.13751 -0.00855 333s eq1_11 -0.39091 0.02431 333s eq1_12 -0.60636 0.03770 333s eq1_13 -0.45531 0.02831 333s eq1_14 -0.15321 0.00953 333s eq1_15 0.35053 -0.02180 333s eq1_16 -0.04817 0.00300 333s eq1_17 0.18774 -0.01167 333s eq1_18 -0.06935 0.00431 333s eq1_19 0.30946 -0.01924 333s eq1_20 0.38165 -0.02373 333s eq2_1 -0.00135 0.00874 333s eq2_2 -0.01889 0.12205 333s eq2_3 -0.01520 0.09821 333s eq2_4 -0.01996 0.12901 333s eq2_5 0.00898 -0.05802 333s eq2_6 0.00251 -0.01619 333s eq2_7 -0.00466 0.03010 333s eq2_8 -0.02111 0.13640 333s eq2_9 0.01590 -0.10273 333s eq2_10 0.03911 -0.25276 333s eq2_11 0.03085 -0.19937 333s eq2_12 0.00542 -0.03502 333s eq2_13 -0.01285 0.08306 333s eq2_14 0.00562 -0.03631 333s eq2_15 0.02180 -0.14088 333s eq2_16 0.00698 -0.04508 333s eq2_17 0.06016 -0.38875 333s eq2_18 -0.01778 0.11492 333s eq2_19 -0.02558 0.16532 333s eq2_20 -0.05994 0.38731 333s > round( colSums( estfun( fitsurS5 ) ), digits = 7 ) 333s eq1_(Intercept) eq2_(Intercept) 333s 0 0 333s > 333s > 333s > ## **************** bread ************************ 333s > round( bread( fitsur1 ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s [1,] 2258.680 -23.5779 1.0971 2354.23 333s [2,] -23.578 0.3134 -0.0796 -15.01 333s [3,] 1.097 -0.0796 0.0704 -8.66 333s [4,] 2354.232 -15.0109 -8.6593 4911.36 333s [5,] -24.454 0.2225 0.0225 -38.45 333s [6,] 0.887 -0.0644 0.0569 -9.51 333s [7,] 1.348 -0.0978 0.0864 -12.94 333s supply_price supply_farmPrice supply_trend 333s [1,] -24.4536 0.8871 1.3477 333s [2,] 0.2225 -0.0644 -0.0978 333s [3,] 0.0225 0.0569 0.0864 333s [4,] -38.4456 -9.5077 -12.9352 333s [5,] 0.3567 0.0252 0.0320 333s [6,] 0.0252 0.0636 0.0807 333s [7,] 0.0320 0.0807 0.1845 333s > 333s > round( bread( fitsur1e2 ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s [1,] 2257.61 -23.5004 1.0286 2442.20 333s [2,] -23.50 0.3077 -0.0746 -16.15 333s [3,] 1.03 -0.0746 0.0660 -8.39 333s [4,] 2442.20 -16.1480 -8.3922 4816.72 333s [5,] -25.30 0.2317 0.0218 -38.19 333s [6,] 0.86 -0.0624 0.0552 -8.86 333s [7,] 1.31 -0.0948 0.0838 -12.35 333s supply_price supply_farmPrice supply_trend 333s [1,] -25.2995 0.8598 1.3061 333s [2,] 0.2317 -0.0624 -0.0948 333s [3,] 0.0218 0.0552 0.0838 333s [4,] -38.1886 -8.8582 -12.3470 333s [5,] 0.3560 0.0234 0.0309 333s [6,] 0.0234 0.0590 0.0780 333s [7,] 0.0309 0.0780 0.1640 333s > 333s > round( bread( fitsur1r3 ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s [1,] 2257.728 -23.5088 1.0361 2434.43 333s [2,] -23.509 0.3083 -0.0752 -16.03 333s [3,] 1.036 -0.0752 0.0665 -8.43 333s [4,] 2434.429 -16.0346 -8.4292 4826.83 333s [5,] -25.226 0.2308 0.0219 -38.22 333s [6,] 0.864 -0.0627 0.0554 -8.93 333s [7,] 1.312 -0.0952 0.0842 -12.42 333s supply_price supply_farmPrice supply_trend 333s [1,] -25.2264 0.8636 1.3118 333s [2,] 0.2308 -0.0627 -0.0952 333s [3,] 0.0219 0.0554 0.0842 333s [4,] -38.2158 -8.9270 -12.4169 333s [5,] 0.3561 0.0235 0.0310 333s [6,] 0.0235 0.0595 0.0784 333s [7,] 0.0310 0.0784 0.1660 333s > 333s > round( bread( fitsur1w ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s [1,] 2258.680 -23.5779 1.0971 2354.23 333s [2,] -23.578 0.3134 -0.0796 -15.01 333s [3,] 1.097 -0.0796 0.0704 -8.66 333s [4,] 2354.232 -15.0109 -8.6593 4911.36 333s [5,] -24.454 0.2225 0.0225 -38.45 333s [6,] 0.887 -0.0644 0.0569 -9.51 333s [7,] 1.348 -0.0978 0.0864 -12.94 333s supply_price supply_farmPrice supply_trend 333s [1,] -24.4536 0.8871 1.3477 333s [2,] 0.2225 -0.0644 -0.0978 333s [3,] 0.0225 0.0569 0.0864 333s [4,] -38.4456 -9.5077 -12.9352 333s [5,] 0.3567 0.0252 0.0320 333s [6,] 0.0252 0.0636 0.0807 333s [7,] 0.0320 0.0807 0.1845 333s > 333s > round( bread( fitsuri1e ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s [1,] 1876.862 -19.2519 0.5677 -81.89 333s [2,] -19.252 0.2661 -0.0755 -2.81 333s [3,] 0.568 -0.0755 0.0716 3.68 333s [4,] -81.887 -2.8102 3.6811 363.96 333s [5,] 7.186 -0.0595 -0.0127 -1.84 333s [6,] -5.538 0.0766 -0.0217 -1.67 333s [7,] -8.357 0.1155 -0.0328 -1.82 333s supply_income supply_farmPrice supply_trend 333s [1,] 7.1857 -5.5385 -8.3572 333s [2,] -0.0595 0.0766 0.1155 333s [3,] -0.0127 -0.0217 -0.0328 333s [4,] -1.8380 -1.6714 -1.8169 333s [5,] 0.0569 -0.0327 -0.0527 333s [6,] -0.0327 0.0441 0.0571 333s [7,] -0.0527 0.0571 0.1367 333s > 333s > round( bread( fitsuri1wr3 ), digits = 7 ) 333s demand_(Intercept) demand_price demand_income supply_(Intercept) 333s [1,] 2182.020 -22.2793 0.5557 -108.13 333s [2,] -22.279 0.3080 -0.0874 -3.49 333s [3,] 0.556 -0.0874 0.0839 4.64 333s [4,] -108.127 -3.4932 4.6397 458.64 333s [5,] 8.996 -0.0739 -0.0164 -2.35 333s [6,] -6.884 0.0952 -0.0270 -2.07 333s [7,] -10.388 0.1436 -0.0408 -2.31 333s supply_income supply_farmPrice supply_trend 333s [1,] 8.9961 -6.8844 -10.3882 333s [2,] -0.0739 0.0952 0.1436 333s [3,] -0.0164 -0.0270 -0.0408 333s [4,] -2.3500 -2.0691 -2.3134 333s [5,] 0.0715 -0.0407 -0.0653 333s [6,] -0.0407 0.0547 0.0717 333s [7,] -0.0653 0.0717 0.1662 333s > 333s > round( bread( fitsurS1 ), digits = 7 ) 333s eq1_consump eq2_(Intercept) eq2_consump eq2_trend 333s [1,] 0.00876 0.0 -4.02e-03 0.000 333s [2,] 0.00000 91218.4 -9.08e+02 48.892 333s [3,] -0.00402 -908.0 9.09e+00 -0.866 333s [4,] 0.00000 48.9 -8.66e-01 3.664 333s > 333s > round( bread( fitsurS2 ), digits = 7 ) 333s eq1_price eq2_trend 333s [1,] 0.00903 -0.00752 333s [2,] -0.00752 34.11430 333s > 333s > round( bread( fitsurS3 ), digits = 7 ) 333s eq1_trend eq2_trend 333s [1,] 34.1 34.0 333s [2,] 34.0 34.5 333s > 333s > try( bread( fitsurS4 ) ) 333s > 333s Error in bread.systemfit(fitsurS4) : 333s returning the 'bread' for models with restrictions has not yet been implemented. 333s BEGIN TEST test_w2sls.R 333s 333s R version 4.3.2 (2023-10-31) -- "Eye Holes" 333s Copyright (C) 2023 The R Foundation for Statistical Computing 333s Platform: x86_64-pc-linux-gnu (64-bit) 333s 333s R is free software and comes with ABSOLUTELY NO WARRANTY. 333s You are welcome to redistribute it under certain conditions. 333s Type 'license()' or 'licence()' for distribution details. 333s 333s R is a collaborative project with many contributors. 333s Type 'contributors()' for more information and 333s 'citation()' on how to cite R or R packages in publications. 333s 333s Type 'demo()' for some demos, 'help()' for on-line help, or 333s 'help.start()' for an HTML browser interface to help. 333s Type 'q()' to quit R. 333s 333s > library( systemfit ) 333s Loading required package: Matrix 334s Loading required package: car 334s Loading required package: carData 334s Loading required package: lmtest 334s Loading required package: zoo 334s 334s Attaching package: ‘zoo’ 334s 334s The following objects are masked from ‘package:base’: 334s 334s as.Date, as.Date.numeric 334s 334s 334s Please cite the 'systemfit' package as: 334s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 334s 334s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 334s https://r-forge.r-project.org/projects/systemfit/ 334s > options( digits = 3 ) 334s > 334s > data( "Kmenta" ) 334s > useMatrix <- FALSE 334s > 334s > demand <- consump ~ price + income 334s > supply <- consump ~ price + farmPrice + trend 334s > inst <- ~ income + farmPrice + trend 334s > inst1 <- ~ income + farmPrice 334s > instlist <- list( inst1, inst ) 334s > system <- list( demand = demand, supply = supply ) 334s > restrm <- matrix(0,1,7) # restriction matrix "R" 334s > restrm[1,3] <- 1 334s > restrm[1,7] <- -1 334s > restrict <- "demand_income - supply_trend = 0" 334s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 334s > restr2m[1,3] <- 1 334s > restr2m[1,7] <- -1 334s > restr2m[2,2] <- -1 334s > restr2m[2,5] <- 1 334s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 334s > restrict2 <- c( "demand_income - supply_trend = 0", 334s + "- demand_price + supply_price = 0.5" ) 334s > tc <- matrix(0,7,6) 334s > tc[1,1] <- 1 334s > tc[2,2] <- 1 334s > tc[3,3] <- 1 334s > tc[4,4] <- 1 334s > tc[5,5] <- 1 334s > tc[6,6] <- 1 334s > tc[7,3] <- 1 334s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 334s > restr3m[1,2] <- -1 334s > restr3m[1,5] <- 1 334s > restr3q <- c( 0.5 ) # restriction vector "q" 2 334s > restrict3 <- "- C2 + C5 = 0.5" 334s > 334s > 334s > ## ********************* W2SLS ***************** 334s > fitw2sls1 <- systemfit( system, "W2SLS", data = Kmenta, inst = inst, 334s + useMatrix = useMatrix ) 334s > print( summary( fitw2sls1 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 33 162 4.36 0.697 0.548 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 65.7 3.87 1.97 0.755 0.726 334s supply 20 16 96.6 6.04 2.46 0.640 0.572 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.87 0.00 334s supply 0.00 6.04 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.87 4.36 334s supply 4.36 6.04 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.902 334s supply 0.902 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 334s price -0.2436 0.0965 -2.52 0.022 * 334s income 0.3140 0.0469 6.69 3.8e-06 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.966 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 334s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 334s price 0.2401 0.0999 2.40 0.0288 * 334s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 334s trend 0.2529 0.0997 2.54 0.0219 * 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.458 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 334s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 334s 334s > 334s > ## ********************* W2SLS (EViews-like) ***************** 334s > fitw2sls1e <- systemfit( system, "W2SLS", data = Kmenta, inst = inst, 334s + methodResidCov = "noDfCor", x = TRUE, 334s + useMatrix = useMatrix ) 334s > print( summary( fitw2sls1e, useDfSys = TRUE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 33 162 2.97 0.697 0.525 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 65.7 3.87 1.97 0.755 0.726 334s supply 20 16 96.6 6.04 2.46 0.640 0.572 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.29 0.00 334s supply 0.00 4.83 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.29 3.59 334s supply 3.59 4.83 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.902 334s supply 0.902 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 334s price -0.2436 0.0890 -2.74 0.0099 ** 334s income 0.3140 0.0433 7.25 2.5e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.966 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 334s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 334s price 0.2401 0.0894 2.69 0.0112 * 334s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 334s trend 0.2529 0.0891 2.84 0.0077 ** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.458 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 334s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 334s 334s > 334s > ## ********************* W2SLS with restriction ******************* 334s > fitw2sls2 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 334s + inst = inst, useMatrix = useMatrix ) 334s > print( summary( fitw2sls2 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 165 3.41 0.692 0.565 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 66.8 3.93 1.98 0.751 0.721 334s supply 20 16 98.4 6.15 2.48 0.633 0.564 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.97 0.00 334s supply 0.00 6.13 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.93 4.56 334s supply 4.56 6.15 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.927 334s supply 0.927 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 94.3832 8.0090 11.78 1.5e-13 *** 334s price -0.2302 0.0946 -2.43 0.02 * 334s income 0.3028 0.0430 7.05 3.9e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.983 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 66.838 MSE: 3.932 Root MSE: 1.983 334s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 48.0494 11.8001 4.07 0.00026 *** 334s price 0.2430 0.1006 2.42 0.02122 * 334s farmPrice 0.2625 0.0459 5.72 2.0e-06 *** 334s trend 0.3028 0.0430 7.05 3.9e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.48 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 98.445 MSE: 6.153 Root MSE: 2.48 334s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 334s 334s > # the same with symbolically specified restrictions 334s > fitw2sls2Sym <- systemfit( system, "W2SLS", data = Kmenta, 334s + restrict.matrix = restrict, inst = inst, useMatrix = useMatrix ) 334s > all.equal( fitw2sls2, fitw2sls2Sym ) 334s [1] "Component “call”: target, current do not match when deparsed" 334s > 334s > ## ********************* W2SLS with restriction (EViews-like) ************** 334s > fitw2sls2e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 334s + inst = inst, methodResidCov = "noDfCor", x = TRUE, 334s + useMatrix = useMatrix ) 334s > print( summary( fitw2sls2e, useDfSys = TRUE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 165 2.33 0.692 0.535 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 66.9 3.94 1.98 0.750 0.721 334s supply 20 16 98.4 6.15 2.48 0.633 0.564 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.37 0.00 334s supply 0.00 4.91 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.35 3.76 334s supply 3.76 4.92 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.926 334s supply 0.926 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 94.3706 7.3834 12.78 1.6e-14 *** 334s price -0.2295 0.0871 -2.63 0.013 * 334s income 0.3022 0.0394 7.67 6.4e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.984 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 66.906 MSE: 3.936 Root MSE: 1.984 334s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 48.0661 10.5574 4.55 6.5e-05 *** 334s price 0.2430 0.0900 2.70 0.011 * 334s farmPrice 0.2624 0.0411 6.39 2.7e-07 *** 334s trend 0.3022 0.0394 7.67 6.4e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.48 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 98.408 MSE: 6.15 Root MSE: 2.48 334s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 334s 334s > nobs( fitw2sls2e ) 334s [1] 40 334s > 334s > ## ********************* W2SLS with restriction via restrict.regMat ******************* 334s > fitw2sls3 <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 334s + inst = inst, x = TRUE, useMatrix = useMatrix ) 334s > print( summary( fitw2sls3 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 165 3.41 0.692 0.565 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 66.8 3.93 1.98 0.751 0.721 334s supply 20 16 98.4 6.15 2.48 0.633 0.564 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.97 0.00 334s supply 0.00 6.13 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.93 4.56 334s supply 4.56 6.15 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.927 334s supply 0.927 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 94.3832 8.0090 11.78 1.5e-13 *** 334s price -0.2302 0.0946 -2.43 0.02 * 334s income 0.3028 0.0430 7.05 3.9e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.983 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 66.838 MSE: 3.932 Root MSE: 1.983 334s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 48.0494 11.8001 4.07 0.00026 *** 334s price 0.2430 0.1006 2.42 0.02122 * 334s farmPrice 0.2625 0.0459 5.72 2.0e-06 *** 334s trend 0.3028 0.0430 7.05 3.9e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.48 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 98.445 MSE: 6.153 Root MSE: 2.48 334s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 334s 334s > 334s > ## ********************* W2SLS with restriction via restrict.regMat (EViews-like) ************** 334s > fitw2sls3e <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 334s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 334s > print( summary( fitw2sls3e, useDfSys = TRUE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 165 2.33 0.692 0.535 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 66.9 3.94 1.98 0.750 0.721 334s supply 20 16 98.4 6.15 2.48 0.633 0.564 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.37 0.00 334s supply 0.00 4.91 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.35 3.76 334s supply 3.76 4.92 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.926 334s supply 0.926 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 94.3706 7.3834 12.78 1.6e-14 *** 334s price -0.2295 0.0871 -2.63 0.013 * 334s income 0.3022 0.0394 7.67 6.4e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.984 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 66.906 MSE: 3.936 Root MSE: 1.984 334s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 48.0661 10.5574 4.55 6.5e-05 *** 334s price 0.2430 0.0900 2.70 0.011 * 334s farmPrice 0.2624 0.0411 6.39 2.7e-07 *** 334s trend 0.3022 0.0394 7.67 6.4e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.48 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 98.408 MSE: 6.15 Root MSE: 2.48 334s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 334s 334s > 334s > ## ***************** W2SLS with 2 restrictions ******************** 334s > fitw2sls4 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr2m, 334s + restrict.rhs = restr2q, inst = inst, x = TRUE, 334s + useMatrix = useMatrix ) 334s > print( summary( fitw2sls4 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 35 166 3.57 0.69 0.575 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 65.9 3.88 1.97 0.754 0.725 334s supply 20 16 100.3 6.27 2.50 0.626 0.556 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.89 0.00 334s supply 0.00 6.25 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.88 4.55 334s supply 4.55 6.27 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.924 334s supply 0.924 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 95.3043 6.3056 15.11 < 2e-16 *** 334s price -0.2428 0.0684 -3.55 0.0011 ** 334s income 0.3063 0.0394 7.78 3.9e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.969 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 65.931 MSE: 3.878 Root MSE: 1.969 334s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 46.4229 8.3296 5.57 2.8e-06 *** 334s price 0.2572 0.0684 3.76 0.00062 *** 334s farmPrice 0.2642 0.0455 5.80 1.4e-06 *** 334s trend 0.3063 0.0394 7.78 3.9e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.503 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 100.255 MSE: 6.266 Root MSE: 2.503 334s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 334s 334s > # the same with symbolically specified restrictions 334s > fitw2sls4Sym <- systemfit( system, "W2SLS", data = Kmenta, 334s + restrict.matrix = restrict2, inst = inst, x = TRUE, 334s + useMatrix = useMatrix ) 334s > all.equal( fitw2sls4, fitw2sls4Sym ) 334s [1] "Component “call”: target, current do not match when deparsed" 334s > 334s > ## ***************** W2SLS with 2 restrictions (EViews-like) ************** 334s > fitw2sls4e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr2m, 334s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 334s + useMatrix = useMatrix ) 334s > print( summary( fitw2sls4e, useDfSys = TRUE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 35 166 2.44 0.69 0.546 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 65.9 3.88 1.97 0.754 0.725 334s supply 20 16 100.2 6.26 2.50 0.626 0.556 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.3 0 334s supply 0.0 5 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.30 3.75 334s supply 3.75 5.01 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.923 334s supply 0.923 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 95.3470 5.7579 16.56 < 2e-16 *** 334s price -0.2428 0.0621 -3.91 0.00041 *** 334s income 0.3059 0.0360 8.49 5.1e-10 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.97 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 65.945 MSE: 3.879 Root MSE: 1.97 334s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 46.4366 7.5360 6.16 4.7e-07 *** 334s price 0.2572 0.0621 4.14 0.00021 *** 334s farmPrice 0.2642 0.0407 6.48 1.8e-07 *** 334s trend 0.3059 0.0360 8.49 5.1e-10 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.503 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 100.225 MSE: 6.264 Root MSE: 2.503 334s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 334s 334s > 334s > ## ***************** W2SLS with 2 restrictions via R and restrict.regMat ****************** 334s > fitw2sls5 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr3m, 334s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 334s + x = TRUE, useMatrix = useMatrix ) 334s > print( summary( fitw2sls5 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 35 166 3.57 0.69 0.575 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 65.9 3.88 1.97 0.754 0.725 334s supply 20 16 100.3 6.27 2.50 0.626 0.556 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.89 0.00 334s supply 0.00 6.25 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.88 4.55 334s supply 4.55 6.27 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.924 334s supply 0.924 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 95.3043 6.3056 15.11 < 2e-16 *** 334s price -0.2428 0.0684 -3.55 0.0011 ** 334s income 0.3063 0.0394 7.78 3.9e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.969 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 65.931 MSE: 3.878 Root MSE: 1.969 334s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 46.4229 8.3296 5.57 2.8e-06 *** 334s price 0.2572 0.0684 3.76 0.00062 *** 334s farmPrice 0.2642 0.0455 5.80 1.4e-06 *** 334s trend 0.3063 0.0394 7.78 3.9e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.503 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 100.255 MSE: 6.266 Root MSE: 2.503 334s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 334s 334s > # the same with symbolically specified restrictions 334s > fitw2sls5Sym <- systemfit( system, "W2SLS", data = Kmenta, 334s + restrict.matrix = restrict3, restrict.regMat = tc, inst = inst, 334s + x = TRUE, useMatrix = useMatrix ) 334s > all.equal( fitw2sls5, fitw2sls5Sym ) 334s [1] "Component “call”: target, current do not match when deparsed" 334s > 334s > ## ***************** W2SLS with 2 restrictions via R and restrict.regMat (EViews-like) ************** 334s > fitw2sls5e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr3m, 334s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 334s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 334s > print( summary( fitw2sls5e, useDfSys = TRUE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 35 166 2.44 0.69 0.546 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 65.9 3.88 1.97 0.754 0.725 334s supply 20 16 100.2 6.26 2.50 0.626 0.556 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.3 0 334s supply 0.0 5 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.30 3.75 334s supply 3.75 5.01 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.923 334s supply 0.923 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 95.3470 5.7579 16.56 < 2e-16 *** 334s price -0.2428 0.0621 -3.91 0.00041 *** 334s income 0.3059 0.0360 8.49 5.1e-10 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.97 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 65.945 MSE: 3.879 Root MSE: 1.97 334s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 46.4366 7.5360 6.16 4.7e-07 *** 334s price 0.2572 0.0621 4.14 0.00021 *** 334s farmPrice 0.2642 0.0407 6.48 1.8e-07 *** 334s trend 0.3059 0.0360 8.49 5.1e-10 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.503 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 100.225 MSE: 6.264 Root MSE: 2.503 334s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 334s 334s > 334s > ## ****** 2SLS estimation with different instruments ********************** 334s > fitw2slsd1 <- systemfit( system, "W2SLS", data = Kmenta, inst = instlist, 334s + useMatrix = useMatrix ) 334s > print( summary( fitw2slsd1 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 33 164 9.25 0.694 0.512 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 67.4 3.97 1.99 0.748 0.719 334s supply 20 16 96.6 6.04 2.46 0.640 0.572 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.97 0.00 334s supply 0.00 6.04 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.97 3.84 334s supply 3.84 6.04 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.784 334s supply 0.784 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 334s price -0.4116 0.1448 -2.84 0.011 * 334s income 0.3617 0.0564 6.41 6.4e-06 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.992 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 334s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 334s price 0.2401 0.0999 2.40 0.0288 * 334s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 334s trend 0.2529 0.0997 2.54 0.0219 * 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.458 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 334s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 334s 334s > 334s > ## ****** 2SLS estimation with different instruments (EViews-like)****************** 334s > fitw2slsd1e <- systemfit( system, "W2SLS", data = Kmenta, inst = instlist, 334s + methodResidCov = "noDfCor", x = TRUE, 334s + useMatrix = useMatrix ) 334s > print( summary( fitw2slsd1e, useDfSys = TRUE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 33 164 6.29 0.694 0.5 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 67.4 3.97 1.99 0.748 0.719 334s supply 20 16 96.6 6.04 2.46 0.640 0.572 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.37 0.00 334s supply 0.00 4.83 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.37 3.16 334s supply 3.16 4.83 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.784 334s supply 0.784 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 334s price -0.412 0.134 -3.08 0.0041 ** 334s income 0.362 0.052 6.95 6.0e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.992 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 334s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 334s price 0.2401 0.0894 2.69 0.0112 * 334s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 334s trend 0.2529 0.0891 2.84 0.0077 ** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.458 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 334s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 334s 334s > 334s > ## **** W2SLS estimation with different instruments and restriction ******** 334s > fitw2slsd2 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 334s + inst = instlist, useMatrix = useMatrix ) 334s > print( summary( fitw2slsd2 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 166 5.11 0.69 0.557 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 64.8 3.81 1.95 0.758 0.730 334s supply 20 16 101.4 6.34 2.52 0.622 0.551 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.79 0.00 334s supply 0.00 6.27 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.81 4.36 334s supply 4.36 6.34 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.888 334s supply 0.888 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 104.5695 10.6344 9.83 1.8e-11 *** 334s price -0.3653 0.1327 -2.75 0.0094 ** 334s income 0.3369 0.0485 6.95 5.1e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.952 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 64.776 MSE: 3.81 Root MSE: 1.952 334s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.73 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 47.0356 11.9466 3.94 0.00039 *** 334s price 0.2450 0.1017 2.41 0.02156 * 334s farmPrice 0.2672 0.0465 5.74 1.9e-06 *** 334s trend 0.3369 0.0485 6.95 5.1e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.518 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 101.426 MSE: 6.339 Root MSE: 2.518 334s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 334s 334s > 334s > ## **** W2SLS estimation with different instruments and restriction (EViews-like)* 334s > fitw2slsd2e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 334s + inst = instlist, methodResidCov = "noDfCor", x = TRUE, 334s + useMatrix = useMatrix ) 334s > print( summary( fitw2slsd2e, useDfSys = TRUE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 166 3.45 0.69 0.535 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 64.7 3.81 1.95 0.759 0.730 334s supply 20 16 101.3 6.33 2.52 0.622 0.551 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.22 0.00 334s supply 0.00 5.02 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.24 3.60 334s supply 3.60 5.06 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.888 334s supply 0.888 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 334s price -0.3630 0.1220 -2.98 0.0053 ** 334s income 0.3357 0.0444 7.57 8.6e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.951 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 64.715 MSE: 3.807 Root MSE: 1.951 334s Multiple R-Squared: 0.759 Adjusted R-Squared: 0.73 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 47.0706 10.6890 4.40 0.0001 *** 334s price 0.2449 0.0910 2.69 0.0109 * 334s farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 334s trend 0.3357 0.0444 7.57 8.6e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.516 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 101.299 MSE: 6.331 Root MSE: 2.516 334s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 334s 334s > 334s > ## ** W2SLS estimation with different instruments and restriction via restrict.regMat **** 334s > fitw2slsd3 <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 334s + inst = instlist, x = TRUE, useMatrix = useMatrix ) 334s > print( summary( fitw2slsd3 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 166 5.11 0.69 0.557 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 64.8 3.81 1.95 0.758 0.730 334s supply 20 16 101.4 6.34 2.52 0.622 0.551 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.79 0.00 334s supply 0.00 6.27 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.81 4.36 334s supply 4.36 6.34 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.888 334s supply 0.888 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 104.5695 10.6344 9.83 1.8e-11 *** 334s price -0.3653 0.1327 -2.75 0.0094 ** 334s income 0.3369 0.0485 6.95 5.1e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.952 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 64.776 MSE: 3.81 Root MSE: 1.952 334s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.73 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 47.0356 11.9466 3.94 0.00039 *** 334s price 0.2450 0.1017 2.41 0.02156 * 334s farmPrice 0.2672 0.0465 5.74 1.9e-06 *** 334s trend 0.3369 0.0485 6.95 5.1e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.518 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 101.426 MSE: 6.339 Root MSE: 2.518 334s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 334s 334s > 334s > ## W2SLS estimation with different instruments and restriction via restrict.regMat (EViews-like) 334s > fitw2slsd3e <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 334s + inst = instlist, methodResidCov = "noDfCor", useMatrix = useMatrix ) 334s > print( summary( fitw2slsd3e, useDfSys = TRUE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 166 3.45 0.69 0.535 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 64.7 3.81 1.95 0.759 0.730 334s supply 20 16 101.3 6.33 2.52 0.622 0.551 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.22 0.00 334s supply 0.00 5.02 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.24 3.60 334s supply 3.60 5.06 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.888 334s supply 0.888 1.000 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 334s price -0.3630 0.1220 -2.98 0.0053 ** 334s income 0.3357 0.0444 7.57 8.6e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.951 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 64.715 MSE: 3.807 Root MSE: 1.951 334s Multiple R-Squared: 0.759 Adjusted R-Squared: 0.73 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 47.0706 10.6890 4.40 0.0001 *** 334s price 0.2449 0.0910 2.69 0.0109 * 334s farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 334s trend 0.3357 0.0444 7.57 8.6e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.516 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 101.299 MSE: 6.331 Root MSE: 2.516 334s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 334s 334s > 334s > 334s > ## *********** estimations with a single regressor ************ 334s > fitw2slsS1 <- systemfit( 334s + list( consump ~ price - 1, price ~ consump + trend ), "W2SLS", 334s + data = Kmenta, inst = ~ farmPrice + trend + income, useMatrix = useMatrix ) 334s > print( summary( fitw2slsS1 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 36 1544 179 -0.65 0.852 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s eq1 20 19 861 45.3 6.73 -2.213 -2.213 334s eq2 20 17 682 40.1 6.33 -0.022 -0.143 334s 334s The covariance matrix of the residuals used for estimation 334s eq1 eq2 334s eq1 45.3 0.0 334s eq2 0.0 40.1 334s 334s The covariance matrix of the residuals 334s eq1 eq2 334s eq1 45.3 -40.5 334s eq2 -40.5 40.1 334s 334s The correlations of the residuals 334s eq1 eq2 334s eq1 1.00 -0.95 334s eq2 -0.95 1.00 334s 334s 334s W2SLS estimates for 'eq1' (equation 1) 334s Model Formula: consump ~ price - 1 334s Instruments: ~farmPrice + trend + income 334s 334s Estimate Std. Error t value Pr(>|t|) 334s price 1.006 0.015 66.9 <2e-16 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 6.734 on 19 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 19 334s SSR: 861.48 MSE: 45.341 Root MSE: 6.734 334s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 334s 334s 334s W2SLS estimates for 'eq2' (equation 2) 334s Model Formula: price ~ consump + trend 334s Instruments: ~farmPrice + trend + income 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 55.5365 46.2668 1.20 0.25 334s consump 0.4453 0.4622 0.96 0.35 334s trend -0.0426 0.2496 -0.17 0.87 334s 334s Residual standard error: 6.335 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 682.257 MSE: 40.133 Root MSE: 6.335 334s Multiple R-Squared: -0.022 Adjusted R-Squared: -0.143 334s 334s > fitw2slsS2 <- systemfit( 334s + list( consump ~ price - 1, consump ~ trend - 1 ), "W2SLS", 334s + data = Kmenta, inst = ~ farmPrice + price + income, useMatrix = useMatrix ) 334s > print( summary( fitw2slsS2 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 38 47456 111148 -87.5 -5.28 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s eq1 20 19 861 45.3 6.73 -2.21 -2.21 334s eq2 20 19 46595 2452.3 49.52 -172.79 -172.79 334s 334s The covariance matrix of the residuals used for estimation 334s eq1 eq2 334s eq1 45.3 0 334s eq2 0.0 2452 334s 334s The covariance matrix of the residuals 334s eq1 eq2 334s eq1 45.34 -6.33 334s eq2 -6.33 2452.34 334s 334s The correlations of the residuals 334s eq1 eq2 334s eq1 1.0000 -0.0448 334s eq2 -0.0448 1.0000 334s 334s 334s W2SLS estimates for 'eq1' (equation 1) 334s Model Formula: consump ~ price - 1 334s Instruments: ~farmPrice + price + income 334s 334s Estimate Std. Error t value Pr(>|t|) 334s price 1.006 0.015 66.9 <2e-16 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 6.733 on 19 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 19 334s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 334s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 334s 334s 334s W2SLS estimates for 'eq2' (equation 2) 334s Model Formula: consump ~ trend - 1 334s Instruments: ~farmPrice + price + income 334s 334s Estimate Std. Error t value Pr(>|t|) 334s trend 7.578 0.934 8.11 1.4e-07 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 49.521 on 19 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 19 334s SSR: 46594.549 MSE: 2452.345 Root MSE: 49.521 334s Multiple R-Squared: -172.786 Adjusted R-Squared: -172.786 334s 334s > fitw2slsS3 <- systemfit( 334s + list( consump ~ trend - 1, price ~ trend - 1 ), "W2SLS", 334s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 334s > print( summary( fitw2slsS3 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 38 97978 687515 -104 -10.6 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s eq1 20 19 50950 2682 51.8 -189.0 -189.0 334s eq2 20 19 47028 2475 49.8 -69.5 -69.5 334s 334s The covariance matrix of the residuals used for estimation 334s eq1 eq2 334s eq1 2682 0 334s eq2 0 2475 334s 334s The covariance matrix of the residuals 334s eq1 eq2 334s eq1 2682 2439 334s eq2 2439 2475 334s 334s The correlations of the residuals 334s eq1 eq2 334s eq1 1.000 0.989 334s eq2 0.989 1.000 334s 334s 334s W2SLS estimates for 'eq1' (equation 1) 334s Model Formula: consump ~ trend - 1 334s Instruments: ~income + farmPrice 334s 334s Estimate Std. Error t value Pr(>|t|) 334s trend 8.65 1.05 8.27 1e-07 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 51.784 on 19 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 19 334s SSR: 50949.985 MSE: 2681.578 Root MSE: 51.784 334s Multiple R-Squared: -189.031 Adjusted R-Squared: -189.031 334s 334s 334s W2SLS estimates for 'eq2' (equation 2) 334s Model Formula: price ~ trend - 1 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s trend 7.318 0.929 7.88 2.1e-07 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 49.751 on 19 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 19 334s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 334s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 334s 334s > fitw2slsS4 <- systemfit( 334s + list( consump ~ trend - 1, price ~ trend - 1 ), "W2SLS", 334s + data = Kmenta, inst = ~ farmPrice + trend + income, 334s + restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), useMatrix = useMatrix ) 334s > print( summary( fitw2slsS4 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 39 93548 111736 -99 -1.03 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s eq1 20 19 46514 2448 49.5 -172.5 -172.5 334s eq2 20 19 47034 2475 49.8 -69.5 -69.5 334s 334s The covariance matrix of the residuals used for estimation 334s eq1 eq2 334s eq1 2448 0 334s eq2 0 2475 334s 334s The covariance matrix of the residuals 334s eq1 eq2 334s eq1 2448 2439 334s eq2 2439 2475 334s 334s The correlations of the residuals 334s eq1 eq2 334s eq1 1.000 0.988 334s eq2 0.988 1.000 334s 334s 334s W2SLS estimates for 'eq1' (equation 1) 334s Model Formula: consump ~ trend - 1 334s Instruments: ~farmPrice + trend + income 334s 334s Estimate Std. Error t value Pr(>|t|) 334s trend 7.362 0.655 11.2 8.4e-14 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 49.478 on 19 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 19 334s SSR: 46514.224 MSE: 2448.117 Root MSE: 49.478 334s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 334s 334s 334s W2SLS estimates for 'eq2' (equation 2) 334s Model Formula: price ~ trend - 1 334s Instruments: ~farmPrice + trend + income 334s 334s Estimate Std. Error t value Pr(>|t|) 334s trend 7.362 0.655 11.2 8.4e-14 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 49.754 on 19 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 19 334s SSR: 47033.528 MSE: 2475.449 Root MSE: 49.754 334s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 334s 334s > fitw2slsS5 <- systemfit( 334s + list( consump ~ 1, price ~ 1 ), "W2SLS", 334s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 334s > print( summary( fitw2slsS5 ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 38 935 491 0 0 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s eq1 20 19 268 14.1 3.76 0 0 334s eq2 20 19 667 35.1 5.93 0 0 334s 334s The covariance matrix of the residuals used for estimation 334s eq1 eq2 334s eq1 14.1 0.0 334s eq2 0.0 35.1 334s 334s The covariance matrix of the residuals 334s eq1 eq2 334s eq1 14.11 2.18 334s eq2 2.18 35.12 334s 334s The correlations of the residuals 334s eq1 eq2 334s eq1 1.0000 0.0981 334s eq2 0.0981 1.0000 334s 334s 334s W2SLS estimates for 'eq1' (equation 1) 334s Model Formula: consump ~ 1 334s Instruments: ~income + farmPrice 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 100.90 0.84 120 <2e-16 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 3.756 on 19 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 19 334s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 334s Multiple R-Squared: 0 Adjusted R-Squared: 0 334s 334s 334s W2SLS estimates for 'eq2' (equation 2) 334s Model Formula: price ~ 1 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 100.02 1.33 75.5 <2e-16 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 5.926 on 19 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 19 334s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 334s Multiple R-Squared: 0 Adjusted R-Squared: 0 334s 334s > 334s > 334s > ## **************** shorter summaries ********************** 334s > print( summary( fitw2sls1e, residCov = FALSE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 33 162 2.97 0.697 0.525 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 65.7 3.87 1.97 0.755 0.726 334s supply 20 16 96.6 6.04 2.46 0.640 0.572 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 94.6333 7.3027 12.96 3.1e-10 *** 334s price -0.2436 0.0890 -2.74 0.014 * 334s income 0.3140 0.0433 7.25 1.3e-06 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.966 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 334s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 49.5324 10.7425 4.61 0.00029 *** 334s price 0.2401 0.0894 2.69 0.01623 * 334s farmPrice 0.2556 0.0423 6.05 1.7e-05 *** 334s trend 0.2529 0.0891 2.84 0.01188 * 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.458 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 334s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 334s 334s > 334s > print( summary( fitw2sls2, residCov = FALSE, equations = FALSE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 165 3.41 0.692 0.565 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 66.8 3.93 1.98 0.751 0.721 334s supply 20 16 98.4 6.15 2.48 0.633 0.564 334s 334s 334s Coefficients: 334s Estimate Std. Error t value Pr(>|t|) 334s demand_(Intercept) 94.3832 8.0090 11.78 1.5e-13 *** 334s demand_price -0.2302 0.0946 -2.43 0.02042 * 334s demand_income 0.3028 0.0430 7.05 3.9e-08 *** 334s supply_(Intercept) 48.0494 11.8001 4.07 0.00026 *** 334s supply_price 0.2430 0.1006 2.42 0.02122 * 334s supply_farmPrice 0.2625 0.0459 5.72 2.0e-06 *** 334s supply_trend 0.3028 0.0430 7.05 3.9e-08 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s > 334s > print( summary( fitw2sls3, useDfSys = FALSE ), equations = FALSE ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 165 3.41 0.692 0.565 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 66.8 3.93 1.98 0.751 0.721 334s supply 20 16 98.4 6.15 2.48 0.633 0.564 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.97 0.00 334s supply 0.00 6.13 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.93 4.56 334s supply 4.56 6.15 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.927 334s supply 0.927 1.000 334s 334s 334s Coefficients: 334s Estimate Std. Error t value Pr(>|t|) 334s demand_(Intercept) 94.3832 8.0090 11.78 1.3e-09 *** 334s demand_price -0.2302 0.0946 -2.43 0.02634 * 334s demand_income 0.3028 0.0430 7.05 2.0e-06 *** 334s supply_(Intercept) 48.0494 11.8001 4.07 0.00089 *** 334s supply_price 0.2430 0.1006 2.42 0.02802 * 334s supply_farmPrice 0.2625 0.0459 5.72 3.2e-05 *** 334s supply_trend 0.3028 0.0430 7.05 2.8e-06 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s > 334s > print( summary( fitw2sls4e ), residCov = FALSE ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 35 166 2.44 0.69 0.546 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 65.9 3.88 1.97 0.754 0.725 334s supply 20 16 100.2 6.26 2.50 0.626 0.556 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 95.3470 5.7579 16.56 < 2e-16 *** 334s price -0.2428 0.0621 -3.91 0.00041 *** 334s income 0.3059 0.0360 8.49 5.1e-10 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.97 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 65.945 MSE: 3.879 Root MSE: 1.97 334s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 46.4366 7.5360 6.16 4.7e-07 *** 334s price 0.2572 0.0621 4.14 0.00021 *** 334s farmPrice 0.2642 0.0407 6.48 1.8e-07 *** 334s trend 0.3059 0.0360 8.49 5.1e-10 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.503 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 100.225 MSE: 6.264 Root MSE: 2.503 334s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 334s 334s > 334s > print( summary( fitw2sls5, useDfSys = FALSE, residCov = FALSE ) ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 35 166 3.57 0.69 0.575 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 65.9 3.88 1.97 0.754 0.725 334s supply 20 16 100.3 6.27 2.50 0.626 0.556 334s 334s 334s W2SLS estimates for 'demand' (equation 1) 334s Model Formula: consump ~ price + income 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 95.3043 6.3056 15.11 2.7e-11 *** 334s price -0.2428 0.0684 -3.55 0.0025 ** 334s income 0.3063 0.0394 7.78 5.4e-07 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 1.969 on 17 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 17 334s SSR: 65.931 MSE: 3.878 Root MSE: 1.969 334s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 334s 334s 334s W2SLS estimates for 'supply' (equation 2) 334s Model Formula: consump ~ price + farmPrice + trend 334s Instruments: ~income + farmPrice + trend 334s 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 46.4229 8.3296 5.57 4.2e-05 *** 334s price 0.2572 0.0684 3.76 0.0017 ** 334s farmPrice 0.2642 0.0455 5.80 2.7e-05 *** 334s trend 0.3063 0.0394 7.78 8.0e-07 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s 334s Residual standard error: 2.503 on 16 degrees of freedom 334s Number of observations: 20 Degrees of Freedom: 16 334s SSR: 100.255 MSE: 6.266 Root MSE: 2.503 334s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 334s 334s > 334s > print( summary( fitw2slsd1, useDfSys = TRUE ), residCov = FALSE, 334s + equations = FALSE ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 33 164 9.25 0.694 0.512 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 67.4 3.97 1.99 0.748 0.719 334s supply 20 16 96.6 6.04 2.46 0.640 0.572 334s 334s 334s Coefficients: 334s Estimate Std. Error t value Pr(>|t|) 334s demand_(Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 334s demand_price -0.4116 0.1448 -2.84 0.00764 ** 334s demand_income 0.3617 0.0564 6.41 2.9e-07 *** 334s supply_(Intercept) 49.5324 12.0105 4.12 0.00024 *** 334s supply_price 0.2401 0.0999 2.40 0.02208 * 334s supply_farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 334s supply_trend 0.2529 0.0997 2.54 0.01605 * 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s > 334s > print( summary( fitw2slsd2e, equations = TRUE ), equations = FALSE ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 166 3.45 0.69 0.535 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 64.7 3.81 1.95 0.759 0.730 334s supply 20 16 101.3 6.33 2.52 0.622 0.551 334s 334s The covariance matrix of the residuals used for estimation 334s demand supply 334s demand 3.22 0.00 334s supply 0.00 5.02 334s 334s The covariance matrix of the residuals 334s demand supply 334s demand 3.24 3.60 334s supply 3.60 5.06 334s 334s The correlations of the residuals 334s demand supply 334s demand 1.000 0.888 334s supply 0.888 1.000 334s 334s 334s Coefficients: 334s Estimate Std. Error t value Pr(>|t|) 334s demand_(Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 334s demand_price -0.3630 0.1220 -2.98 0.0053 ** 334s demand_income 0.3357 0.0444 7.57 8.6e-09 *** 334s supply_(Intercept) 47.0706 10.6890 4.40 0.0001 *** 334s supply_price 0.2449 0.0910 2.69 0.0109 * 334s supply_farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 334s supply_trend 0.3357 0.0444 7.57 8.6e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s > 334s > print( summary( fitw2slsd3e, equations = FALSE ), residCov = FALSE ) 334s 334s systemfit results 334s method: W2SLS 334s 334s N DF SSR detRCov OLS-R2 McElroy-R2 334s system 40 34 166 3.45 0.69 0.535 334s 334s N DF SSR MSE RMSE R2 Adj R2 334s demand 20 17 64.7 3.81 1.95 0.759 0.730 334s supply 20 16 101.3 6.33 2.52 0.622 0.551 334s 334s 334s Coefficients: 334s Estimate Std. Error t value Pr(>|t|) 334s demand_(Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 334s demand_price -0.3630 0.1220 -2.98 0.0053 ** 334s demand_income 0.3357 0.0444 7.57 8.6e-09 *** 334s supply_(Intercept) 47.0706 10.6890 4.40 0.0001 *** 334s supply_price 0.2449 0.0910 2.69 0.0109 * 334s supply_farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 334s supply_trend 0.3357 0.0444 7.57 8.6e-09 *** 334s --- 334s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 334s > 334s > 334s > ## ****************** residuals ************************** 334s > print( residuals( fitw2sls1e ) ) 334s demand supply 334s 1 0.843 -0.4348 334s 2 -0.698 -1.2131 334s 3 2.359 1.7090 334s 4 1.490 0.7956 334s 5 2.139 1.5942 334s 6 1.277 0.6595 334s 7 1.571 1.4346 334s 8 -3.066 -4.8724 334s 9 -1.125 -2.3975 334s 10 2.492 3.1427 334s 11 -0.108 0.0689 334s 12 -2.292 -1.3978 334s 13 -1.598 -1.1136 334s 14 -0.271 1.1684 334s 15 1.958 3.4865 334s 16 -3.430 -3.8285 334s 17 -0.313 0.6793 334s 18 -2.151 -2.7713 334s 19 1.592 2.6668 334s 20 -0.668 0.6235 334s > print( residuals( fitw2sls1e$eq[[ 1 ]] ) ) 334s 1 2 3 4 5 6 7 8 9 10 11 334s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 334s 12 13 14 15 16 17 18 19 20 334s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 334s > 334s > print( residuals( fitw2sls2 ) ) 334s demand supply 334s 1 0.726 0.0287 334s 2 -0.754 -0.8185 334s 3 2.304 2.0561 334s 4 1.437 1.0966 334s 5 2.191 1.7764 334s 6 1.317 0.8056 334s 7 1.620 1.5441 334s 8 -3.015 -4.8526 334s 9 -1.087 -2.3957 334s 10 2.513 3.1658 334s 11 -0.265 0.1722 334s 12 -2.506 -1.2753 334s 13 -1.781 -1.0688 334s 14 -0.332 1.1028 334s 15 2.086 3.2370 334s 16 -3.325 -4.1563 334s 17 -0.144 0.2984 334s 18 -2.128 -3.1286 334s 19 1.662 2.2767 334s 20 -0.518 0.1355 334s > print( residuals( fitw2sls2$eq[[ 2 ]] ) ) 334s 1 2 3 4 5 6 7 8 9 10 334s 0.0287 -0.8185 2.0561 1.0966 1.7764 0.8056 1.5441 -4.8526 -2.3957 3.1658 334s 11 12 13 14 15 16 17 18 19 20 334s 0.1722 -1.2753 -1.0688 1.1028 3.2370 -4.1563 0.2984 -3.1286 2.2767 0.1355 334s > 334s > print( residuals( fitw2sls3 ) ) 334s demand supply 334s 1 0.726 0.0287 334s 2 -0.754 -0.8185 334s 3 2.304 2.0561 334s 4 1.437 1.0966 334s 5 2.191 1.7764 334s 6 1.317 0.8056 334s 7 1.620 1.5441 334s 8 -3.015 -4.8526 334s 9 -1.087 -2.3957 334s 10 2.513 3.1658 334s 11 -0.265 0.1722 334s 12 -2.506 -1.2753 334s 13 -1.781 -1.0688 334s 14 -0.332 1.1028 334s 15 2.086 3.2370 334s 16 -3.325 -4.1563 334s 17 -0.144 0.2984 334s 18 -2.128 -3.1286 334s 19 1.662 2.2767 334s 20 -0.518 0.1355 334s > print( residuals( fitw2sls3$eq[[ 1 ]] ) ) 334s 1 2 3 4 5 6 7 8 9 10 11 334s 0.726 -0.754 2.304 1.437 2.191 1.317 1.620 -3.015 -1.087 2.513 -0.265 334s 12 13 14 15 16 17 18 19 20 334s -2.506 -1.781 -0.332 2.086 -3.325 -0.144 -2.128 1.662 -0.518 334s > 334s > print( residuals( fitw2sls4e ) ) 334s demand supply 334s 1 0.761 0.0514 334s 2 -0.700 -0.8567 334s 3 2.350 2.0266 334s 4 1.492 1.0504 334s 5 2.159 1.7988 334s 6 1.301 0.8085 334s 7 1.616 1.5253 334s 8 -2.986 -4.9339 334s 9 -1.130 -2.3600 334s 10 2.429 3.2858 334s 11 -0.284 0.2948 334s 12 -2.458 -1.2168 334s 13 -1.705 -1.0756 334s 14 -0.327 1.1348 334s 15 2.007 3.2835 334s 16 -3.368 -4.1646 334s 17 -0.312 0.4480 334s 18 -2.099 -3.2018 334s 19 1.694 2.1807 334s 20 -0.439 -0.0794 334s > print( residuals( fitw2sls4e$eq[[ 2 ]] ) ) 334s 1 2 3 4 5 6 7 8 9 10 334s 0.0514 -0.8567 2.0266 1.0504 1.7988 0.8085 1.5253 -4.9339 -2.3600 3.2858 334s 11 12 13 14 15 16 17 18 19 20 334s 0.2948 -1.2168 -1.0756 1.1348 3.2835 -4.1646 0.4480 -3.2018 2.1807 -0.0794 334s > 334s > print( residuals( fitw2sls5 ) ) 334s demand supply 334s 1 0.765 0.0551 334s 2 -0.701 -0.8537 334s 3 2.350 2.0293 334s 4 1.491 1.0527 334s 5 2.158 1.8003 334s 6 1.300 0.8097 334s 7 1.614 1.5262 334s 8 -2.991 -4.9339 334s 9 -1.129 -2.3600 334s 10 2.433 3.2862 334s 11 -0.275 0.2958 334s 12 -2.450 -1.2157 334s 13 -1.700 -1.0752 334s 14 -0.324 1.1344 334s 15 2.005 3.2816 334s 16 -3.371 -4.1672 334s 17 -0.311 0.4452 334s 18 -2.102 -3.2047 334s 19 1.688 2.1776 334s 20 -0.451 -0.0835 334s > print( residuals( fitw2sls5$eq[[ 1 ]] ) ) 334s 1 2 3 4 5 6 7 8 9 10 11 334s 0.765 -0.701 2.350 1.491 2.158 1.300 1.614 -2.991 -1.129 2.433 -0.275 334s 12 13 14 15 16 17 18 19 20 334s -2.450 -1.700 -0.324 2.005 -3.371 -0.311 -2.102 1.688 -0.451 334s > 334s > print( residuals( fitw2slsd1 ) ) 334s demand supply 334s 1 1.3775 -0.4348 334s 2 0.0125 -1.2131 334s 3 2.9728 1.7090 334s 4 2.2121 0.7956 334s 5 1.6920 1.5942 334s 6 1.0407 0.6595 334s 7 1.4768 1.4346 334s 8 -2.7583 -4.8724 334s 9 -1.6807 -2.3975 334s 10 1.4265 3.1427 334s 11 -0.2029 0.0689 334s 12 -1.5123 -1.3978 334s 13 -0.4958 -1.1136 334s 14 -0.1528 1.1684 334s 15 0.8692 3.4865 334s 16 -4.0547 -3.8285 334s 17 -2.5309 0.6793 334s 18 -1.8070 -2.7713 334s 19 1.9299 2.6668 334s 20 0.1853 0.6235 334s > print( residuals( fitw2slsd1$eq[[ 2 ]] ) ) 334s 1 2 3 4 5 6 7 8 9 10 334s -0.4348 -1.2131 1.7090 0.7956 1.5942 0.6595 1.4346 -4.8724 -2.3975 3.1427 334s 11 12 13 14 15 16 17 18 19 20 334s 0.0689 -1.3978 -1.1136 1.1684 3.4865 -3.8285 0.6793 -2.7713 2.6668 0.6235 334s > 334s > print( residuals( fitw2slsd2e ) ) 334s demand supply 334s 1 1.100 0.3346 334s 2 -0.192 -0.5581 334s 3 2.785 2.2852 334s 4 2.012 1.2953 334s 5 1.849 1.8966 334s 6 1.145 0.9020 334s 7 1.573 1.6164 334s 8 -2.722 -4.8395 334s 9 -1.531 -2.3946 334s 10 1.629 3.1810 334s 11 -0.448 0.2403 334s 12 -1.988 -1.1944 334s 13 -0.972 -1.0393 334s 14 -0.271 1.0594 334s 15 1.251 3.0723 334s 16 -3.782 -4.3726 334s 17 -1.904 0.0471 334s 18 -1.823 -3.3644 334s 19 1.992 2.0193 334s 20 0.298 -0.1866 334s > print( residuals( fitw2slsd2e$eq[[ 1 ]] ) ) 334s 1 2 3 4 5 6 7 8 9 10 11 334s 1.100 -0.192 2.785 2.012 1.849 1.145 1.573 -2.722 -1.531 1.629 -0.448 334s 12 13 14 15 16 17 18 19 20 334s -1.988 -0.972 -0.271 1.251 -3.782 -1.904 -1.823 1.992 0.298 334s > 334s > print( residuals( fitw2slsd3e ) ) 334s demand supply 334s 1 1.100 0.3346 334s 2 -0.192 -0.5581 334s 3 2.785 2.2852 334s 4 2.012 1.2953 334s 5 1.849 1.8966 334s 6 1.145 0.9020 334s 7 1.573 1.6164 334s 8 -2.722 -4.8395 334s 9 -1.531 -2.3946 334s 10 1.629 3.1810 334s 11 -0.448 0.2403 334s 12 -1.988 -1.1944 334s 13 -0.972 -1.0393 334s 14 -0.271 1.0594 334s 15 1.251 3.0723 334s 16 -3.782 -4.3726 334s 17 -1.904 0.0471 334s 18 -1.823 -3.3644 334s 19 1.992 2.0193 334s 20 0.298 -0.1866 334s > print( residuals( fitw2slsd3e$eq[[ 2 ]] ) ) 334s 1 2 3 4 5 6 7 8 9 10 334s 0.3346 -0.5581 2.2852 1.2953 1.8966 0.9020 1.6164 -4.8395 -2.3946 3.1810 334s 11 12 13 14 15 16 17 18 19 20 334s 0.2403 -1.1944 -1.0393 1.0594 3.0723 -4.3726 0.0471 -3.3644 2.0193 -0.1866 334s > 334s > 334s > ## *************** coefficients ********************* 334s > print( round( coef( fitw2sls1e ), digits = 6 ) ) 334s demand_(Intercept) demand_price demand_income supply_(Intercept) 334s 94.633 -0.244 0.314 49.532 334s supply_price supply_farmPrice supply_trend 334s 0.240 0.256 0.253 334s > print( round( coef( fitw2sls1e$eq[[ 2 ]] ), digits = 6 ) ) 334s (Intercept) price farmPrice trend 334s 49.532 0.240 0.256 0.253 334s > 334s > print( round( coef( fitw2slsd2e ), digits = 6 ) ) 334s demand_(Intercept) demand_price demand_income supply_(Intercept) 334s 104.464 -0.363 0.336 47.071 334s supply_price supply_farmPrice supply_trend 334s 0.245 0.267 0.336 334s > print( round( coef( fitw2slsd2e$eq[[ 1 ]] ), digits = 6 ) ) 334s (Intercept) price income 334s 104.464 -0.363 0.336 334s > 334s > print( round( coef( fitw2slsd3e ), digits = 6 ) ) 334s demand_(Intercept) demand_price demand_income supply_(Intercept) 334s 104.464 -0.363 0.336 47.071 334s supply_price supply_farmPrice supply_trend 334s 0.245 0.267 0.336 334s > print( round( coef( fitw2slsd3e, modified.regMat = TRUE ), digits = 6 ) ) 334s C1 C2 C3 C4 C5 C6 334s 104.464 -0.363 0.336 47.071 0.245 0.267 334s > print( round( coef( fitw2slsd3e$eq[[ 2 ]] ), digits = 6 ) ) 334s (Intercept) price farmPrice trend 334s 47.071 0.245 0.267 0.336 334s > 334s > print( round( coef( fitw2sls4 ), digits = 6 ) ) 334s demand_(Intercept) demand_price demand_income supply_(Intercept) 334s 95.304 -0.243 0.306 46.423 334s supply_price supply_farmPrice supply_trend 334s 0.257 0.264 0.306 334s > print( round( coef( fitw2sls4$eq[[ 1 ]] ), digits = 6 ) ) 334s (Intercept) price income 334s 95.304 -0.243 0.306 334s > 334s > print( round( coef( fitw2sls5 ), digits = 6 ) ) 334s demand_(Intercept) demand_price demand_income supply_(Intercept) 334s 95.304 -0.243 0.306 46.423 334s supply_price supply_farmPrice supply_trend 334s 0.257 0.264 0.306 334s > print( round( coef( fitw2sls5, modified.regMat = TRUE ), digits = 6 ) ) 334s C1 C2 C3 C4 C5 C6 334s 95.304 -0.243 0.306 46.423 0.257 0.264 334s > print( round( coef( fitw2sls5$eq[[ 2 ]] ), digits = 6 ) ) 334s (Intercept) price farmPrice trend 334s 46.423 0.257 0.264 0.306 334s > 334s > 334s > ## *************** coefficients with stats ********************* 334s > print( round( coef( summary( fitw2sls1e, useDfSys = FALSE ) ), digits = 6 ) ) 334s Estimate Std. Error t value Pr(>|t|) 334s demand_(Intercept) 94.633 7.3027 12.96 0.000000 334s demand_price -0.244 0.0890 -2.74 0.014016 334s demand_income 0.314 0.0433 7.25 0.000001 334s supply_(Intercept) 49.532 10.7425 4.61 0.000289 334s supply_price 0.240 0.0894 2.69 0.016234 334s supply_farmPrice 0.256 0.0423 6.05 0.000017 334s supply_trend 0.253 0.0891 2.84 0.011883 334s > print( round( coef( summary( fitw2sls1e$eq[[ 2 ]], useDfSys = FALSE ) ), 334s + digits = 6 ) ) 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 49.532 10.7425 4.61 0.000289 334s price 0.240 0.0894 2.69 0.016234 334s farmPrice 0.256 0.0423 6.05 0.000017 334s trend 0.253 0.0891 2.84 0.011883 334s > 334s > print( round( coef( summary( fitw2slsd2e ) ), digits = 6 ) ) 334s Estimate Std. Error t value Pr(>|t|) 334s demand_(Intercept) 104.464 9.7929 10.67 0.00000 334s demand_price -0.363 0.1220 -2.98 0.00534 334s demand_income 0.336 0.0444 7.57 0.00000 334s supply_(Intercept) 47.071 10.6890 4.40 0.00010 334s supply_price 0.245 0.0910 2.69 0.01093 334s supply_farmPrice 0.267 0.0416 6.41 0.00000 334s supply_trend 0.336 0.0444 7.57 0.00000 334s > print( round( coef( summary( fitw2slsd2e$eq[[ 1 ]] ) ), digits = 6 ) ) 334s Estimate Std. Error t value Pr(>|t|) 334s (Intercept) 104.464 9.7929 10.67 0.00000 334s price -0.363 0.1220 -2.98 0.00534 334s income 0.336 0.0444 7.57 0.00000 334s > 334s > print( round( coef( summary( fitw2slsd3e, useDfSys = FALSE ) ), digits = 6 ) ) 334s Estimate Std. Error t value Pr(>|t|) 335s demand_(Intercept) 104.464 9.7929 10.67 0.000000 335s demand_price -0.363 0.1220 -2.98 0.008475 335s demand_income 0.336 0.0444 7.57 0.000001 335s supply_(Intercept) 47.071 10.6890 4.40 0.000444 335s supply_price 0.245 0.0910 2.69 0.016014 335s supply_farmPrice 0.267 0.0416 6.41 0.000009 335s supply_trend 0.336 0.0444 7.57 0.000001 335s > print( round( coef( summary( fitw2slsd3e, useDfSys = FALSE ), 335s + modified.regMat = TRUE ), digits = 6 ) ) 335s Estimate Std. Error t value Pr(>|t|) 335s C1 104.464 9.7929 10.67 NA 335s C2 -0.363 0.1220 -2.98 NA 335s C3 0.336 0.0444 7.57 NA 335s C4 47.071 10.6890 4.40 NA 335s C5 0.245 0.0910 2.69 NA 335s C6 0.267 0.0416 6.41 NA 335s > print( round( coef( summary( fitw2slsd3e$eq[[ 2 ]], useDfSys = FALSE ) ), 335s + digits = 6 ) ) 335s Estimate Std. Error t value Pr(>|t|) 335s (Intercept) 47.071 10.6890 4.40 0.000444 335s price 0.245 0.0910 2.69 0.016014 335s farmPrice 0.267 0.0416 6.41 0.000009 335s trend 0.336 0.0444 7.57 0.000001 335s > 335s > print( round( coef( summary( fitw2sls4 ) ), digits = 6 ) ) 335s Estimate Std. Error t value Pr(>|t|) 335s demand_(Intercept) 95.304 6.3056 15.11 0.000000 335s demand_price -0.243 0.0684 -3.55 0.001128 335s demand_income 0.306 0.0394 7.78 0.000000 335s supply_(Intercept) 46.423 8.3296 5.57 0.000003 335s supply_price 0.257 0.0684 3.76 0.000622 335s supply_farmPrice 0.264 0.0455 5.80 0.000001 335s supply_trend 0.306 0.0394 7.78 0.000000 335s > print( round( coef( summary( fitw2sls4$eq[[ 1 ]] ) ), digits = 6 ) ) 335s Estimate Std. Error t value Pr(>|t|) 335s (Intercept) 95.304 6.3056 15.11 0.00000 335s price -0.243 0.0684 -3.55 0.00113 335s income 0.306 0.0394 7.78 0.00000 335s > 335s > print( round( coef( summary( fitw2sls5 ) ), digits = 6 ) ) 335s Estimate Std. Error t value Pr(>|t|) 335s demand_(Intercept) 95.304 6.3056 15.11 0.000000 335s demand_price -0.243 0.0684 -3.55 0.001128 335s demand_income 0.306 0.0394 7.78 0.000000 335s supply_(Intercept) 46.423 8.3296 5.57 0.000003 335s supply_price 0.257 0.0684 3.76 0.000622 335s supply_farmPrice 0.264 0.0455 5.80 0.000001 335s supply_trend 0.306 0.0394 7.78 0.000000 335s > print( round( coef( summary( fitw2sls5 ), modified.regMat = TRUE ), digits = 6 ) ) 335s Estimate Std. Error t value Pr(>|t|) 335s C1 95.304 6.3056 15.11 0.000000 335s C2 -0.243 0.0684 -3.55 0.001128 335s C3 0.306 0.0394 7.78 0.000000 335s C4 46.423 8.3296 5.57 0.000003 335s C5 0.257 0.0684 3.76 0.000622 335s C6 0.264 0.0455 5.80 0.000001 335s > print( round( coef( summary( fitw2sls5$eq[[ 2 ]] ) ), digits = 6 ) ) 335s Estimate Std. Error t value Pr(>|t|) 335s (Intercept) 46.423 8.3296 5.57 0.000003 335s price 0.257 0.0684 3.76 0.000622 335s farmPrice 0.264 0.0455 5.80 0.000001 335s trend 0.306 0.0394 7.78 0.000000 335s > 335s > 335s > ## *********** variance covariance matrix of the coefficients ******* 335s > print( round( vcov( fitw2sls1e ), digits = 6 ) ) 335s demand_(Intercept) demand_price demand_income 335s demand_(Intercept) 53.3287 -0.57241 0.04191 335s demand_price -0.5724 0.00791 -0.00225 335s demand_income 0.0419 -0.00225 0.00187 335s supply_(Intercept) 0.0000 0.00000 0.00000 335s supply_price 0.0000 0.00000 0.00000 335s supply_farmPrice 0.0000 0.00000 0.00000 335s supply_trend 0.0000 0.00000 0.00000 335s supply_(Intercept) supply_price supply_farmPrice 335s demand_(Intercept) 0.000 0.000000 0.000000 335s demand_price 0.000 0.000000 0.000000 335s demand_income 0.000 0.000000 0.000000 335s supply_(Intercept) 115.402 -0.876328 -0.259055 335s supply_price -0.876 0.007989 0.000749 335s supply_farmPrice -0.259 0.000749 0.001786 335s supply_trend -0.236 0.000463 0.001101 335s supply_trend 335s demand_(Intercept) 0.000000 335s demand_price 0.000000 335s demand_income 0.000000 335s supply_(Intercept) -0.236183 335s supply_price 0.000463 335s supply_farmPrice 0.001101 335s supply_trend 0.007945 335s > print( round( vcov( fitw2sls1e$eq[[ 2 ]] ), digits = 6 ) ) 335s (Intercept) price farmPrice trend 335s (Intercept) 115.402 -0.876328 -0.259055 -0.236183 335s price -0.876 0.007989 0.000749 0.000463 335s farmPrice -0.259 0.000749 0.001786 0.001101 335s trend -0.236 0.000463 0.001101 0.007945 335s > 335s > print( round( vcov( fitw2sls2 ), digits = 6 ) ) 335s demand_(Intercept) demand_price demand_income 335s demand_(Intercept) 64.14482 -0.679629 0.041312 335s demand_price -0.67963 0.008954 -0.002214 335s demand_income 0.04131 -0.002214 0.001847 335s supply_(Intercept) -1.22810 0.065809 -0.054894 335s supply_price 0.00241 -0.000129 0.000108 335s supply_farmPrice 0.00573 -0.000307 0.000256 335s supply_trend 0.04131 -0.002214 0.001847 335s supply_(Intercept) supply_price supply_farmPrice 335s demand_(Intercept) -1.2281 0.002409 0.005727 335s demand_price 0.0658 -0.000129 -0.000307 335s demand_income -0.0549 0.000108 0.000256 335s supply_(Intercept) 139.2416 -1.098376 -0.294954 335s supply_price -1.0984 0.010116 0.000884 335s supply_farmPrice -0.2950 0.000884 0.002109 335s supply_trend -0.0549 0.000108 0.000256 335s supply_trend 335s demand_(Intercept) 0.041312 335s demand_price -0.002214 335s demand_income 0.001847 335s supply_(Intercept) -0.054894 335s supply_price 0.000108 335s supply_farmPrice 0.000256 335s supply_trend 0.001847 335s > print( round( vcov( fitw2sls2$eq[[ 1 ]] ), digits = 6 ) ) 335s (Intercept) price income 335s (Intercept) 64.1448 -0.67963 0.04131 335s price -0.6796 0.00895 -0.00221 335s income 0.0413 -0.00221 0.00185 335s > 335s > print( round( vcov( fitw2sls3e ), digits = 6 ) ) 335s demand_(Intercept) demand_price demand_income 335s demand_(Intercept) 54.51421 -0.577209 0.034718 335s demand_price -0.57721 0.007585 -0.001860 335s demand_income 0.03472 -0.001860 0.001552 335s supply_(Intercept) -1.03208 0.055305 -0.046132 335s supply_price 0.00202 -0.000108 0.000090 335s supply_farmPrice 0.00481 -0.000258 0.000215 335s supply_trend 0.03472 -0.001860 0.001552 335s supply_(Intercept) supply_price supply_farmPrice 335s demand_(Intercept) -1.0321 0.002024 0.004813 335s demand_price 0.0553 -0.000108 -0.000258 335s demand_income -0.0461 0.000090 0.000215 335s supply_(Intercept) 111.4592 -0.878830 -0.236271 335s supply_price -0.8788 0.008093 0.000708 335s supply_farmPrice -0.2363 0.000708 0.001689 335s supply_trend -0.0461 0.000090 0.000215 335s supply_trend 335s demand_(Intercept) 0.034718 335s demand_price -0.001860 335s demand_income 0.001552 335s supply_(Intercept) -0.046132 335s supply_price 0.000090 335s supply_farmPrice 0.000215 335s supply_trend 0.001552 335s > print( round( vcov( fitw2sls3e, modified.regMat = TRUE ), digits = 6 ) ) 335s C1 C2 C3 C4 C5 C6 335s C1 54.51421 -0.577209 0.034718 -1.0321 0.002024 0.004813 335s C2 -0.57721 0.007585 -0.001860 0.0553 -0.000108 -0.000258 335s C3 0.03472 -0.001860 0.001552 -0.0461 0.000090 0.000215 335s C4 -1.03208 0.055305 -0.046132 111.4592 -0.878830 -0.236271 335s C5 0.00202 -0.000108 0.000090 -0.8788 0.008093 0.000708 335s C6 0.00481 -0.000258 0.000215 -0.2363 0.000708 0.001689 335s > print( round( vcov( fitw2sls3e$eq[[ 2 ]] ), digits = 6 ) ) 335s (Intercept) price farmPrice trend 335s (Intercept) 111.4592 -0.878830 -0.236271 -0.046132 335s price -0.8788 0.008093 0.000708 0.000090 335s farmPrice -0.2363 0.000708 0.001689 0.000215 335s trend -0.0461 0.000090 0.000215 0.001552 335s > 335s > print( round( vcov( fitw2sls4 ), digits = 6 ) ) 335s demand_(Intercept) demand_price demand_income 335s demand_(Intercept) 39.7610 -0.358128 -0.03842 335s demand_price -0.3581 0.004681 -0.00113 335s demand_income -0.0384 -0.001129 0.00155 335s supply_(Intercept) 39.6949 -0.480685 0.08595 335s supply_price -0.3581 0.004681 -0.00113 335s supply_farmPrice -0.0359 0.000252 0.00011 335s supply_trend -0.0384 -0.001129 0.00155 335s supply_(Intercept) supply_price supply_farmPrice 335s demand_(Intercept) 39.6949 -0.358128 -0.035932 335s demand_price -0.4807 0.004681 0.000252 335s demand_income 0.0859 -0.001129 0.000110 335s supply_(Intercept) 69.3817 -0.480685 -0.226588 335s supply_price -0.4807 0.004681 0.000252 335s supply_farmPrice -0.2266 0.000252 0.002072 335s supply_trend 0.0859 -0.001129 0.000110 335s supply_trend 335s demand_(Intercept) -0.03842 335s demand_price -0.00113 335s demand_income 0.00155 335s supply_(Intercept) 0.08595 335s supply_price -0.00113 335s supply_farmPrice 0.00011 335s supply_trend 0.00155 335s > print( round( vcov( fitw2sls4$eq[[ 1 ]] ), digits = 6 ) ) 335s (Intercept) price income 335s (Intercept) 39.7610 -0.35813 -0.03842 335s price -0.3581 0.00468 -0.00113 335s income -0.0384 -0.00113 0.00155 335s > 335s > print( round( vcov( fitw2sls5 ), digits = 6 ) ) 335s demand_(Intercept) demand_price demand_income 335s demand_(Intercept) 39.7610 -0.358128 -0.03842 335s demand_price -0.3581 0.004681 -0.00113 335s demand_income -0.0384 -0.001129 0.00155 335s supply_(Intercept) 39.6949 -0.480685 0.08595 335s supply_price -0.3581 0.004681 -0.00113 335s supply_farmPrice -0.0359 0.000252 0.00011 335s supply_trend -0.0384 -0.001129 0.00155 335s supply_(Intercept) supply_price supply_farmPrice 335s demand_(Intercept) 39.6949 -0.358128 -0.035932 335s demand_price -0.4807 0.004681 0.000252 335s demand_income 0.0859 -0.001129 0.000110 335s supply_(Intercept) 69.3817 -0.480685 -0.226588 335s supply_price -0.4807 0.004681 0.000252 335s supply_farmPrice -0.2266 0.000252 0.002072 335s supply_trend 0.0859 -0.001129 0.000110 335s supply_trend 335s demand_(Intercept) -0.03842 335s demand_price -0.00113 335s demand_income 0.00155 335s supply_(Intercept) 0.08595 335s supply_price -0.00113 335s supply_farmPrice 0.00011 335s supply_trend 0.00155 335s > print( round( vcov( fitw2sls5, modified.regMat = TRUE ), digits = 6 ) ) 335s C1 C2 C3 C4 C5 C6 335s C1 39.7610 -0.358128 -0.03842 39.6949 -0.358128 -0.035932 335s C2 -0.3581 0.004681 -0.00113 -0.4807 0.004681 0.000252 335s C3 -0.0384 -0.001129 0.00155 0.0859 -0.001129 0.000110 335s C4 39.6949 -0.480685 0.08595 69.3817 -0.480685 -0.226588 335s C5 -0.3581 0.004681 -0.00113 -0.4807 0.004681 0.000252 335s C6 -0.0359 0.000252 0.00011 -0.2266 0.000252 0.002072 335s > print( round( vcov( fitw2sls5$eq[[ 2 ]] ), digits = 6 ) ) 335s (Intercept) price farmPrice trend 335s (Intercept) 69.3817 -0.480685 -0.226588 0.08595 335s price -0.4807 0.004681 0.000252 -0.00113 335s farmPrice -0.2266 0.000252 0.002072 0.00011 335s trend 0.0859 -0.001129 0.000110 0.00155 335s > 335s > print( round( vcov( fitw2slsd1 ), digits = 6 ) ) 335s demand_(Intercept) demand_price demand_income 335s demand_(Intercept) 124.179 -1.51767 0.28519 335s demand_price -1.518 0.02098 -0.00595 335s demand_income 0.285 -0.00595 0.00318 335s supply_(Intercept) 0.000 0.00000 0.00000 335s supply_price 0.000 0.00000 0.00000 335s supply_farmPrice 0.000 0.00000 0.00000 335s supply_trend 0.000 0.00000 0.00000 335s supply_(Intercept) supply_price supply_farmPrice 335s demand_(Intercept) 0.000 0.000000 0.000000 335s demand_price 0.000 0.000000 0.000000 335s demand_income 0.000 0.000000 0.000000 335s supply_(Intercept) 144.253 -1.095410 -0.323818 335s supply_price -1.095 0.009987 0.000936 335s supply_farmPrice -0.324 0.000936 0.002233 335s supply_trend -0.295 0.000579 0.001377 335s supply_trend 335s demand_(Intercept) 0.000000 335s demand_price 0.000000 335s demand_income 0.000000 335s supply_(Intercept) -0.295229 335s supply_price 0.000579 335s supply_farmPrice 0.001377 335s supply_trend 0.009931 335s > print( round( vcov( fitw2slsd1$eq[[ 1 ]] ), digits = 6 ) ) 335s (Intercept) price income 335s (Intercept) 124.179 -1.51767 0.28519 335s price -1.518 0.02098 -0.00595 335s income 0.285 -0.00595 0.00318 335s > 335s > print( round( vcov( fitw2slsd2e ), digits = 6 ) ) 335s demand_(Intercept) demand_price demand_income 335s demand_(Intercept) 95.9017 -1.129212 0.176368 335s demand_price -1.1292 0.014881 -0.003682 335s demand_income 0.1764 -0.003682 0.001968 335s supply_(Intercept) -5.2430 0.109460 -0.058492 335s supply_price 0.0103 -0.000215 0.000115 335s supply_farmPrice 0.0245 -0.000510 0.000273 335s supply_trend 0.1764 -0.003682 0.001968 335s supply_(Intercept) supply_price supply_farmPrice 335s demand_(Intercept) -5.2430 0.010284 0.024451 335s demand_price 0.1095 -0.000215 -0.000510 335s demand_income -0.0585 0.000115 0.000273 335s supply_(Intercept) 114.2555 -0.898881 -0.243056 335s supply_price -0.8989 0.008273 0.000727 335s supply_farmPrice -0.2431 0.000727 0.001733 335s supply_trend -0.0585 0.000115 0.000273 335s supply_trend 335s demand_(Intercept) 0.176368 335s demand_price -0.003682 335s demand_income 0.001968 335s supply_(Intercept) -0.058492 335s supply_price 0.000115 335s supply_farmPrice 0.000273 335s supply_trend 0.001968 335s > print( round( vcov( fitw2slsd2e$eq[[ 2 ]] ), digits = 6 ) ) 335s (Intercept) price farmPrice trend 335s (Intercept) 114.2555 -0.898881 -0.243056 -0.058492 335s price -0.8989 0.008273 0.000727 0.000115 335s farmPrice -0.2431 0.000727 0.001733 0.000273 335s trend -0.0585 0.000115 0.000273 0.001968 335s > 335s > print( round( vcov( fitw2slsd3 ), digits = 6 ) ) 335s demand_(Intercept) demand_price demand_income 335s demand_(Intercept) 113.0903 -1.334011 0.210445 335s demand_price -1.3340 0.017622 -0.004394 335s demand_income 0.2104 -0.004394 0.002348 335s supply_(Intercept) -6.2560 0.130609 -0.069794 335s supply_price 0.0123 -0.000256 0.000137 335s supply_farmPrice 0.0292 -0.000609 0.000325 335s supply_trend 0.2104 -0.004394 0.002348 335s supply_(Intercept) supply_price supply_farmPrice 335s demand_(Intercept) -6.2560 0.012271 0.029175 335s demand_price 0.1306 -0.000256 -0.000609 335s demand_income -0.0698 0.000137 0.000325 335s supply_(Intercept) 142.7207 -1.123408 -0.303360 335s supply_price -1.1234 0.010341 0.000908 335s supply_farmPrice -0.3034 0.000908 0.002165 335s supply_trend -0.0698 0.000137 0.000325 335s supply_trend 335s demand_(Intercept) 0.210445 335s demand_price -0.004394 335s demand_income 0.002348 335s supply_(Intercept) -0.069794 335s supply_price 0.000137 335s supply_farmPrice 0.000325 335s supply_trend 0.002348 335s > print( round( vcov( fitw2slsd3, modified.regMat = TRUE ), digits = 6 ) ) 335s C1 C2 C3 C4 C5 C6 335s C1 113.0903 -1.334011 0.210445 -6.2560 0.012271 0.029175 335s C2 -1.3340 0.017622 -0.004394 0.1306 -0.000256 -0.000609 335s C3 0.2104 -0.004394 0.002348 -0.0698 0.000137 0.000325 335s C4 -6.2560 0.130609 -0.069794 142.7207 -1.123408 -0.303360 335s C5 0.0123 -0.000256 0.000137 -1.1234 0.010341 0.000908 335s C6 0.0292 -0.000609 0.000325 -0.3034 0.000908 0.002165 335s > print( round( vcov( fitw2slsd3$eq[[ 1 ]] ), digits = 6 ) ) 335s (Intercept) price income 335s (Intercept) 113.09 -1.33401 0.21044 335s price -1.33 0.01762 -0.00439 335s income 0.21 -0.00439 0.00235 335s > 335s > 335s > ## *********** confidence intervals of coefficients ************* 335s > print( confint( fitw2sls1e, useDfSys = TRUE ) ) 335s 2.5 % 97.5 % 335s demand_(Intercept) 79.776 109.491 335s demand_price -0.425 -0.063 335s demand_income 0.226 0.402 335s supply_(Intercept) 27.677 71.388 335s supply_price 0.058 0.422 335s supply_farmPrice 0.170 0.342 335s supply_trend 0.072 0.434 335s > print( confint( fitw2sls1e$eq[[ 1 ]], level = 0.9, useDfSys = TRUE ) ) 335s 5 % 95 % 335s (Intercept) 82.275 106.992 335s price -0.394 -0.093 335s income 0.241 0.387 335s > 335s > print( confint( fitw2sls2, level = 0.9 ) ) 335s 5 % 95 % 335s demand_(Intercept) 78.107 110.660 335s demand_price -0.422 -0.038 335s demand_income 0.215 0.390 335s supply_(Intercept) 24.069 72.030 335s supply_price 0.039 0.447 335s supply_farmPrice 0.169 0.356 335s supply_trend 0.215 0.390 335s > print( confint( fitw2sls2$eq[[ 2 ]], level = 0.99 ) ) 335s 0.5 % 99.5 % 335s (Intercept) 15.854 80.245 335s price -0.031 0.517 335s farmPrice 0.137 0.388 335s trend 0.186 0.420 335s > 335s > print( confint( fitw2sls3, level = 0.99 ) ) 335s 0.5 % 99.5 % 335s demand_(Intercept) 78.107 110.660 335s demand_price -0.422 -0.038 335s demand_income 0.215 0.390 335s supply_(Intercept) 24.069 72.030 335s supply_price 0.039 0.447 335s supply_farmPrice 0.169 0.356 335s supply_trend 0.215 0.390 335s > print( confint( fitw2sls3$eq[[ 1 ]], level = 0.5 ) ) 335s 25 % 75 % 335s (Intercept) 88.923 99.844 335s price -0.295 -0.166 335s income 0.274 0.332 335s > 335s > print( confint( fitw2sls4e, level = 0.5, useDfSys = TRUE ) ) 335s 25 % 75 % 335s demand_(Intercept) 83.658 107.036 335s demand_price -0.369 -0.117 335s demand_income 0.233 0.379 335s supply_(Intercept) 31.138 61.736 335s supply_price 0.131 0.383 335s supply_farmPrice 0.181 0.347 335s supply_trend 0.233 0.379 335s > print( confint( fitw2sls4e$eq[[ 2 ]], level = 0.25, useDfSys = TRUE ) ) 335s 37.5 % 62.5 % 335s (Intercept) 44.016 48.857 335s price 0.237 0.277 335s farmPrice 0.251 0.277 335s trend 0.294 0.317 335s > 335s > print( confint( fitw2sls5, level = 0.25 ) ) 335s 37.5 % 62.5 % 335s demand_(Intercept) 82.503 108.105 335s demand_price -0.382 -0.104 335s demand_income 0.226 0.386 335s supply_(Intercept) 29.513 63.333 335s supply_price 0.118 0.396 335s supply_farmPrice 0.172 0.357 335s supply_trend 0.226 0.386 335s > print( confint( fitw2sls5$eq[[ 1 ]], level = 0.975 ) ) 335s 1.3 % 98.8 % 335s (Intercept) 80.537 110.072 335s price -0.403 -0.083 335s income 0.214 0.399 335s > 335s > print( confint( fitw2slsd1, level = 0.975 ) ) 335s 1.3 % 98.8 % 335s demand_(Intercept) 83.279 130.300 335s demand_price -0.717 -0.106 335s demand_income 0.243 0.481 335s supply_(Intercept) 24.071 74.994 335s supply_price 0.028 0.452 335s supply_farmPrice 0.155 0.356 335s supply_trend 0.042 0.464 335s > print( confint( fitw2slsd1$eq[[ 2 ]], level = 0.999 ) ) 335s 0.1 % 100 % 335s (Intercept) 1.310 97.755 335s price -0.161 0.641 335s farmPrice 0.066 0.445 335s trend -0.147 0.653 335s > 335s > print( confint( fitw2slsd2e, level = 0.999, useDfSys = TRUE ) ) 335s 0.1 % 100 % 335s demand_(Intercept) 84.562 124.365 335s demand_price -0.611 -0.115 335s demand_income 0.246 0.426 335s supply_(Intercept) 25.348 68.793 335s supply_price 0.060 0.430 335s supply_farmPrice 0.182 0.352 335s supply_trend 0.246 0.426 335s > print( confint( fitw2slsd2e$eq[[ 1 ]], level = 0.01, useDfSys = TRUE ) ) 335s 49.5 % 50.5 % 335s (Intercept) 104.340 104.587 335s price -0.365 -0.362 335s income 0.335 0.336 335s > 335s > print( confint( fitw2slsd3e, level = 0.01, useDfSys = TRUE ) ) 335s 49.5 % 50.5 % 335s demand_(Intercept) 84.562 124.365 335s demand_price -0.611 -0.115 335s demand_income 0.246 0.426 335s supply_(Intercept) 25.348 68.793 335s supply_price 0.060 0.430 335s supply_farmPrice 0.182 0.352 335s supply_trend 0.246 0.426 335s > print( confint( fitw2slsd3e$eq[[ 2 ]], useDfSys = TRUE ) ) 335s 2.5 % 97.5 % 335s (Intercept) 25.348 68.793 335s price 0.060 0.430 335s farmPrice 0.182 0.352 335s trend 0.246 0.426 335s > 335s > 335s > ## *********** fitted values ************* 335s > print( fitted( fitw2sls1e ) ) 335s demand supply 335s 1 97.6 98.9 335s 2 99.9 100.4 335s 3 99.8 100.5 335s 4 100.0 100.7 335s 5 102.1 102.6 335s 6 102.0 102.6 335s 7 102.4 102.6 335s 8 103.0 104.8 335s 9 101.5 102.7 335s 10 100.3 99.7 335s 11 95.5 95.4 335s 12 94.7 93.8 335s 13 96.1 95.6 335s 14 99.0 97.6 335s 15 103.8 102.3 335s 16 103.7 104.1 335s 17 103.8 102.8 335s 18 102.1 102.7 335s 19 103.6 102.6 335s 20 106.9 105.6 335s > print( fitted( fitw2sls1e$eq[[ 1 ]] ) ) 335s 1 2 3 4 5 6 7 8 9 10 11 12 13 335s 97.6 99.9 99.8 100.0 102.1 102.0 102.4 103.0 101.5 100.3 95.5 94.7 96.1 335s 14 15 16 17 18 19 20 335s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 335s > 335s > print( fitted( fitw2sls2 ) ) 335s demand supply 335s 1 97.8 98.5 335s 2 99.9 100.0 335s 3 99.9 100.1 335s 4 100.1 100.4 335s 5 102.0 102.5 335s 6 101.9 102.4 335s 7 102.4 102.4 335s 8 102.9 104.8 335s 9 101.4 102.7 335s 10 100.3 99.7 335s 11 95.7 95.3 335s 12 94.9 93.7 335s 13 96.3 95.6 335s 14 99.1 97.7 335s 15 103.7 102.6 335s 16 103.5 104.4 335s 17 103.7 103.2 335s 18 102.1 103.1 335s 19 103.6 102.9 335s 20 106.8 106.1 335s > print( fitted( fitw2sls2$eq[[ 2 ]] ) ) 335s 1 2 3 4 5 6 7 8 9 10 11 12 13 335s 98.5 100.0 100.1 100.4 102.5 102.4 102.4 104.8 102.7 99.7 95.3 93.7 95.6 335s 14 15 16 17 18 19 20 335s 97.7 102.6 104.4 103.2 103.1 102.9 106.1 335s > 335s > print( fitted( fitw2sls3 ) ) 335s demand supply 335s 1 97.8 98.5 335s 2 99.9 100.0 335s 3 99.9 100.1 335s 4 100.1 100.4 335s 5 102.0 102.5 335s 6 101.9 102.4 335s 7 102.4 102.4 335s 8 102.9 104.8 335s 9 101.4 102.7 335s 10 100.3 99.7 335s 11 95.7 95.3 335s 12 94.9 93.7 335s 13 96.3 95.6 335s 14 99.1 97.7 335s 15 103.7 102.6 335s 16 103.5 104.4 335s 17 103.7 103.2 335s 18 102.1 103.1 335s 19 103.6 102.9 335s 20 106.8 106.1 335s > print( fitted( fitw2sls3$eq[[ 1 ]] ) ) 335s 1 2 3 4 5 6 7 8 9 10 11 12 13 335s 97.8 99.9 99.9 100.1 102.0 101.9 102.4 102.9 101.4 100.3 95.7 94.9 96.3 335s 14 15 16 17 18 19 20 335s 99.1 103.7 103.5 103.7 102.1 103.6 106.8 335s > 335s > print( fitted( fitw2sls4e ) ) 335s demand supply 335s 1 97.7 98.4 335s 2 99.9 100.0 335s 3 99.8 100.1 335s 4 100.0 100.5 335s 5 102.1 102.4 335s 6 101.9 102.4 335s 7 102.4 102.5 335s 8 102.9 104.8 335s 9 101.5 102.7 335s 10 100.4 99.5 335s 11 95.7 95.1 335s 12 94.9 93.6 335s 13 96.2 95.6 335s 14 99.1 97.6 335s 15 103.8 102.5 335s 16 103.6 104.4 335s 17 103.8 103.1 335s 18 102.0 103.1 335s 19 103.5 103.0 335s 20 106.7 106.3 335s > print( fitted( fitw2sls4e$eq[[ 2 ]] ) ) 335s 1 2 3 4 5 6 7 8 9 10 11 12 13 335s 98.4 100.0 100.1 100.5 102.4 102.4 102.5 104.8 102.7 99.5 95.1 93.6 95.6 335s 14 15 16 17 18 19 20 335s 97.6 102.5 104.4 103.1 103.1 103.0 106.3 335s > 335s > print( fitted( fitw2sls5 ) ) 335s demand supply 335s 1 97.7 98.4 335s 2 99.9 100.0 335s 3 99.8 100.1 335s 4 100.0 100.5 335s 5 102.1 102.4 335s 6 101.9 102.4 335s 7 102.4 102.5 335s 8 102.9 104.8 335s 9 101.5 102.7 335s 10 100.4 99.5 335s 11 95.7 95.1 335s 12 94.9 93.6 335s 13 96.2 95.6 335s 14 99.1 97.6 335s 15 103.8 102.5 335s 16 103.6 104.4 335s 17 103.8 103.1 335s 18 102.0 103.1 335s 19 103.5 103.0 335s 20 106.7 106.3 335s > print( fitted( fitw2sls5$eq[[ 1 ]] ) ) 335s 1 2 3 4 5 6 7 8 9 10 11 12 13 335s 97.7 99.9 99.8 100.0 102.1 101.9 102.4 102.9 101.5 100.4 95.7 94.9 96.2 335s 14 15 16 17 18 19 20 335s 99.1 103.8 103.6 103.8 102.0 103.5 106.7 335s > 335s > print( fitted( fitw2slsd1 ) ) 335s demand supply 335s 1 97.1 98.9 335s 2 99.2 100.4 335s 3 99.2 100.5 335s 4 99.3 100.7 335s 5 102.5 102.6 335s 6 102.2 102.6 335s 7 102.5 102.6 335s 8 102.7 104.8 335s 9 102.0 102.7 335s 10 101.4 99.7 335s 11 95.6 95.4 335s 12 93.9 93.8 335s 13 95.0 95.6 335s 14 98.9 97.6 335s 15 104.9 102.3 335s 16 104.3 104.1 335s 17 106.1 102.8 335s 18 101.7 102.7 335s 19 103.3 102.6 335s 20 106.0 105.6 335s > print( fitted( fitw2slsd1$eq[[ 2 ]] ) ) 335s 1 2 3 4 5 6 7 8 9 10 11 12 13 335s 98.9 100.4 100.5 100.7 102.6 102.6 102.6 104.8 102.7 99.7 95.4 93.8 95.6 335s 14 15 16 17 18 19 20 335s 97.6 102.3 104.1 102.8 102.7 102.6 105.6 335s > 335s > print( fitted( fitw2slsd2e ) ) 335s demand supply 335s 1 97.4 98.2 335s 2 99.4 99.7 335s 3 99.4 99.9 335s 4 99.5 100.2 335s 5 102.4 102.3 335s 6 102.1 102.3 335s 7 102.4 102.4 335s 8 102.6 104.7 335s 9 101.9 102.7 335s 10 101.2 99.6 335s 11 95.9 95.2 335s 12 94.4 93.6 335s 13 95.5 95.6 335s 14 99.0 97.7 335s 15 104.5 102.7 335s 16 104.0 104.6 335s 17 105.4 103.5 335s 18 101.8 103.3 335s 19 103.2 103.2 335s 20 105.9 106.4 335s > print( fitted( fitw2slsd2e$eq[[ 1 ]] ) ) 335s 1 2 3 4 5 6 7 8 9 10 11 12 13 335s 97.4 99.4 99.4 99.5 102.4 102.1 102.4 102.6 101.9 101.2 95.9 94.4 95.5 335s 14 15 16 17 18 19 20 335s 99.0 104.5 104.0 105.4 101.8 103.2 105.9 335s > 335s > print( fitted( fitw2slsd3e ) ) 335s demand supply 335s 1 97.4 98.2 335s 2 99.4 99.7 335s 3 99.4 99.9 335s 4 99.5 100.2 335s 5 102.4 102.3 335s 6 102.1 102.3 335s 7 102.4 102.4 335s 8 102.6 104.7 335s 9 101.9 102.7 335s 10 101.2 99.6 335s 11 95.9 95.2 335s 12 94.4 93.6 335s 13 95.5 95.6 335s 14 99.0 97.7 335s 15 104.5 102.7 335s 16 104.0 104.6 335s 17 105.4 103.5 335s 18 101.8 103.3 335s 19 103.2 103.2 335s 20 105.9 106.4 335s > print( fitted( fitw2slsd3e$eq[[ 2 ]] ) ) 335s 1 2 3 4 5 6 7 8 9 10 11 12 13 335s 98.2 99.7 99.9 100.2 102.3 102.3 102.4 104.7 102.7 99.6 95.2 93.6 95.6 335s 14 15 16 17 18 19 20 335s 97.7 102.7 104.6 103.5 103.3 103.2 106.4 335s > 335s > 335s > ## *********** predicted values ************* 335s > predictData <- Kmenta 335s > predictData$consump <- NULL 335s > predictData$price <- Kmenta$price * 0.9 335s > predictData$income <- Kmenta$income * 1.1 335s > 335s > print( predict( fitw2sls1e, se.fit = TRUE, interval = "prediction", 335s + useDfSys = TRUE ) ) 335s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 335s 1 97.6 0.609 93.5 101.8 98.9 0.965 335s 2 99.9 0.553 95.7 104.0 100.4 0.952 335s 3 99.8 0.520 95.7 103.9 100.5 0.861 335s 4 100.0 0.558 95.9 104.2 100.7 0.839 335s 5 102.1 0.476 98.0 106.2 102.6 0.818 335s 6 102.0 0.437 97.9 106.1 102.6 0.723 335s 7 102.4 0.454 98.3 106.5 102.6 0.658 335s 8 103.0 0.567 98.8 107.1 104.8 0.889 335s 9 101.5 0.502 97.3 105.6 102.7 0.723 335s 10 100.3 0.758 96.0 104.6 99.7 0.915 335s 11 95.5 0.888 91.2 99.9 95.4 1.098 335s 12 94.7 0.928 90.3 99.1 93.8 1.277 335s 13 96.1 0.844 91.8 100.5 95.6 1.137 335s 14 99.0 0.477 94.9 103.1 97.6 0.820 335s 15 103.8 0.731 99.6 108.1 102.3 0.804 335s 16 103.7 0.587 99.5 107.8 104.1 0.837 335s 17 103.8 1.243 99.1 108.6 102.8 1.489 335s 18 102.1 0.506 97.9 106.2 102.7 0.884 335s 19 103.6 0.641 99.4 107.8 102.6 1.010 335s 20 106.9 1.204 102.2 111.6 105.6 1.550 335s supply.lwr supply.upr 335s 1 93.5 104.3 335s 2 95.0 105.8 335s 3 95.2 105.8 335s 4 95.4 106.0 335s 5 97.4 107.9 335s 6 97.4 107.8 335s 7 97.4 107.7 335s 8 99.5 110.1 335s 9 97.5 108.0 335s 10 94.3 105.0 335s 11 89.9 100.8 335s 12 88.2 99.5 335s 13 90.1 101.2 335s 14 92.3 102.9 335s 15 97.1 107.6 335s 16 98.8 109.3 335s 17 97.0 108.7 335s 18 97.4 108.0 335s 19 97.2 108.0 335s 20 99.7 111.5 335s > print( predict( fitw2sls1e$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 335s + useDfSys = TRUE ) ) 335s fit se.fit lwr upr 335s 1 97.6 0.609 93.5 101.8 335s 2 99.9 0.553 95.7 104.0 335s 3 99.8 0.520 95.7 103.9 335s 4 100.0 0.558 95.9 104.2 335s 5 102.1 0.476 98.0 106.2 335s 6 102.0 0.437 97.9 106.1 335s 7 102.4 0.454 98.3 106.5 335s 8 103.0 0.567 98.8 107.1 335s 9 101.5 0.502 97.3 105.6 335s 10 100.3 0.758 96.0 104.6 335s 11 95.5 0.888 91.2 99.9 335s 12 94.7 0.928 90.3 99.1 335s 13 96.1 0.844 91.8 100.5 335s 14 99.0 0.477 94.9 103.1 335s 15 103.8 0.731 99.6 108.1 335s 16 103.7 0.587 99.5 107.8 335s 17 103.8 1.243 99.1 108.6 335s 18 102.1 0.506 97.9 106.2 335s 19 103.6 0.641 99.4 107.8 335s 20 106.9 1.204 102.2 111.6 335s > 335s > print( predict( fitw2sls2, se.pred = TRUE, interval = "confidence", 335s + level = 0.999, newdata = predictData ) ) 335s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 335s 1 102.7 2.22 99.1 106 96.0 2.75 335s 2 105.3 2.22 101.7 109 97.5 2.64 335s 3 105.2 2.23 101.5 109 97.6 2.65 335s 4 105.4 2.22 101.9 109 97.9 2.62 335s 5 107.3 2.51 101.8 113 100.1 2.83 335s 6 107.3 2.46 102.0 112 100.0 2.77 335s 7 107.8 2.44 102.7 113 100.0 2.71 335s 8 108.6 2.40 103.7 113 102.2 2.65 335s 9 106.6 2.52 101.0 112 100.4 2.87 335s 10 105.1 2.65 98.8 111 97.4 3.10 335s 11 100.1 2.41 95.2 105 93.0 3.18 335s 12 99.5 2.21 96.0 103 91.3 3.15 335s 13 101.2 2.12 98.5 104 93.1 2.95 335s 14 104.1 2.31 99.8 108 95.3 2.91 335s 15 109.0 2.73 102.3 116 100.2 2.92 335s 16 109.0 2.61 102.9 115 102.0 2.80 335s 17 108.6 3.08 100.1 117 101.1 3.37 335s 18 107.6 2.35 103.0 112 100.5 2.65 335s 19 109.3 2.44 104.2 114 100.4 2.64 335s 20 113.2 2.66 106.8 120 103.3 2.58 335s supply.lwr supply.upr 335s 1 91.7 100.3 335s 2 94.2 100.7 335s 3 94.2 101.0 335s 4 94.8 101.0 335s 5 95.1 105.0 335s 6 95.6 104.4 335s 7 96.1 103.9 335s 8 98.8 105.6 335s 9 95.2 105.6 335s 10 90.7 104.1 335s 11 85.9 100.1 335s 12 84.3 98.3 335s 13 87.3 98.9 335s 14 89.7 100.8 335s 15 94.7 105.8 335s 16 97.3 106.6 335s 17 92.9 109.4 335s 18 97.1 103.9 335s 19 97.1 103.6 335s 20 100.7 105.9 335s > print( predict( fitw2sls2$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 335s + level = 0.999, newdata = predictData ) ) 335s fit se.pred lwr upr 335s 1 96.0 2.75 91.7 100.3 335s 2 97.5 2.64 94.2 100.7 335s 3 97.6 2.65 94.2 101.0 335s 4 97.9 2.62 94.8 101.0 335s 5 100.1 2.83 95.1 105.0 335s 6 100.0 2.77 95.6 104.4 335s 7 100.0 2.71 96.1 103.9 335s 8 102.2 2.65 98.8 105.6 335s 9 100.4 2.87 95.2 105.6 335s 10 97.4 3.10 90.7 104.1 335s 11 93.0 3.18 85.9 100.1 335s 12 91.3 3.15 84.3 98.3 335s 13 93.1 2.95 87.3 98.9 335s 14 95.3 2.91 89.7 100.8 335s 15 100.2 2.92 94.7 105.8 335s 16 102.0 2.80 97.3 106.6 335s 17 101.1 3.37 92.9 109.4 335s 18 100.5 2.65 97.1 103.9 335s 19 100.4 2.64 97.1 103.6 335s 20 103.3 2.58 100.7 105.9 335s > 335s > print( predict( fitw2sls3, se.pred = TRUE, interval = "prediction", 335s + level = 0.975 ) ) 335s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 335s 1 97.8 2.08 92.9 103 98.5 2.57 335s 2 99.9 2.07 95.1 105 100.0 2.61 335s 3 99.9 2.06 95.0 105 100.1 2.59 335s 4 100.1 2.07 95.2 105 100.4 2.60 335s 5 102.0 2.05 97.2 107 102.5 2.63 335s 6 101.9 2.04 97.1 107 102.4 2.60 335s 7 102.4 2.04 97.6 107 102.4 2.58 335s 8 102.9 2.08 98.0 108 104.8 2.68 335s 9 101.4 2.06 96.6 106 102.7 2.61 335s 10 100.3 2.15 95.3 105 99.7 2.69 335s 11 95.7 2.19 90.6 101 95.3 2.77 335s 12 94.9 2.20 89.8 100 93.7 2.86 335s 13 96.3 2.16 91.2 101 95.6 2.79 335s 14 99.1 2.05 94.3 104 97.7 2.64 335s 15 103.7 2.13 98.7 109 102.6 2.60 335s 16 103.5 2.08 98.7 108 104.4 2.59 335s 17 103.7 2.39 98.1 109 103.2 2.91 335s 18 102.1 2.06 97.2 107 103.1 2.59 335s 19 103.6 2.10 98.6 108 102.9 2.64 335s 20 106.8 2.37 101.2 112 106.1 2.90 335s supply.lwr supply.upr 335s 1 92.4 104 335s 2 93.9 106 335s 3 94.0 106 335s 4 94.3 106 335s 5 96.3 109 335s 6 96.3 109 335s 7 96.4 109 335s 8 98.5 111 335s 9 96.6 109 335s 10 93.4 106 335s 11 88.8 102 335s 12 87.0 100 335s 13 89.1 102 335s 14 91.5 104 335s 15 96.5 109 335s 16 98.3 110 335s 17 96.4 110 335s 18 97.0 109 335s 19 96.8 109 335s 20 99.3 113 335s > print( predict( fitw2sls3$eq[[ 1 ]], se.pred = TRUE, interval = "prediction", 335s + level = 0.975 ) ) 335s fit se.pred lwr upr 335s 1 97.8 2.08 92.9 103 335s 2 99.9 2.07 95.1 105 335s 3 99.9 2.06 95.0 105 335s 4 100.1 2.07 95.2 105 335s 5 102.0 2.05 97.2 107 335s 6 101.9 2.04 97.1 107 335s 7 102.4 2.04 97.6 107 335s 8 102.9 2.08 98.0 108 335s 9 101.4 2.06 96.6 106 335s 10 100.3 2.15 95.3 105 335s 11 95.7 2.19 90.6 101 335s 12 94.9 2.20 89.8 100 335s 13 96.3 2.16 91.2 101 335s 14 99.1 2.05 94.3 104 335s 15 103.7 2.13 98.7 109 335s 16 103.5 2.08 98.7 108 335s 17 103.7 2.39 98.1 109 335s 18 102.1 2.06 97.2 107 335s 19 103.6 2.10 98.6 108 335s 20 106.8 2.37 101.2 112 335s > 335s > print( predict( fitw2sls4e, se.fit = TRUE, interval = "confidence", 335s + level = 0.25, useDfSys = TRUE ) ) 335s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 335s 1 97.7 0.552 97.5 97.9 98.4 0.611 335s 2 99.9 0.484 99.7 100.0 100.0 0.700 335s 3 99.8 0.465 99.7 100.0 100.1 0.652 335s 4 100.0 0.488 99.9 100.2 100.5 0.664 335s 5 102.1 0.443 101.9 102.2 102.4 0.769 335s 6 101.9 0.425 101.8 102.1 102.4 0.695 335s 7 102.4 0.447 102.2 102.5 102.5 0.639 335s 8 102.9 0.547 102.7 103.1 104.8 0.821 335s 9 101.5 0.458 101.3 101.6 102.7 0.716 335s 10 100.4 0.648 100.2 100.6 99.5 0.743 335s 11 95.7 0.847 95.4 96.0 95.1 0.944 335s 12 94.9 0.823 94.6 95.1 93.6 1.254 335s 13 96.2 0.695 96.0 96.5 95.6 1.154 335s 14 99.1 0.467 98.9 99.2 97.6 0.814 335s 15 103.8 0.590 103.6 104.0 102.5 0.675 335s 16 103.6 0.520 103.4 103.8 104.4 0.659 335s 17 103.8 0.919 103.5 104.1 103.1 1.196 335s 18 102.0 0.487 101.9 102.2 103.1 0.587 335s 19 103.5 0.615 103.3 103.7 103.0 0.664 335s 20 106.7 1.126 106.3 107.0 106.3 0.909 335s supply.lwr supply.upr 335s 1 98.2 98.6 335s 2 99.8 100.3 335s 3 99.9 100.3 335s 4 100.2 100.7 335s 5 102.2 102.7 335s 6 102.2 102.7 335s 7 102.3 102.7 335s 8 104.6 105.1 335s 9 102.5 102.9 335s 10 99.3 99.8 335s 11 94.8 95.4 335s 12 93.2 94.0 335s 13 95.2 96.0 335s 14 97.4 97.9 335s 15 102.3 102.7 335s 16 104.2 104.6 335s 17 102.7 103.5 335s 18 102.9 103.3 335s 19 102.8 103.3 335s 20 106.0 106.6 335s > print( predict( fitw2sls4e$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 335s + level = 0.25, useDfSys = TRUE ) ) 335s fit se.fit lwr upr 335s 1 98.4 0.611 98.2 98.6 335s 2 100.0 0.700 99.8 100.3 335s 3 100.1 0.652 99.9 100.3 335s 4 100.5 0.664 100.2 100.7 335s 5 102.4 0.769 102.2 102.7 335s 6 102.4 0.695 102.2 102.7 335s 7 102.5 0.639 102.3 102.7 335s 8 104.8 0.821 104.6 105.1 335s 9 102.7 0.716 102.5 102.9 335s 10 99.5 0.743 99.3 99.8 335s 11 95.1 0.944 94.8 95.4 335s 12 93.6 1.254 93.2 94.0 335s 13 95.6 1.154 95.2 96.0 335s 14 97.6 0.814 97.4 97.9 335s 15 102.5 0.675 102.3 102.7 335s 16 104.4 0.659 104.2 104.6 335s 17 103.1 1.196 102.7 103.5 335s 18 103.1 0.587 102.9 103.3 335s 19 103.0 0.664 102.8 103.3 335s 20 106.3 0.909 106.0 106.6 335s > 335s > print( predict( fitw2sls5, se.fit = TRUE, se.pred = TRUE, 335s + interval = "prediction", level = 0.5, newdata = predictData ) ) 335s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 335s 1 102.8 0.781 2.12 101.4 104 95.8 335s 2 105.4 0.812 2.13 104.0 107 97.4 335s 3 105.3 0.824 2.13 103.8 107 97.5 335s 4 105.6 0.820 2.13 104.1 107 97.8 335s 5 107.5 1.186 2.30 106.0 109 99.9 335s 6 107.4 1.133 2.27 105.9 109 99.9 335s 7 108.0 1.141 2.28 106.4 110 99.9 335s 8 108.7 1.143 2.28 107.2 110 102.1 335s 9 106.8 1.179 2.30 105.2 108 100.2 335s 10 105.3 1.307 2.36 103.7 107 97.2 335s 11 100.3 1.108 2.26 98.7 102 92.7 335s 12 99.6 0.841 2.14 98.2 101 91.1 335s 13 101.3 0.638 2.07 99.9 103 93.0 335s 14 104.3 0.914 2.17 102.8 106 95.1 335s 15 109.3 1.440 2.44 107.6 111 100.1 335s 16 109.2 1.333 2.38 107.6 111 101.9 335s 17 108.9 1.742 2.63 107.1 111 100.9 335s 18 107.8 1.049 2.23 106.2 109 100.5 335s 19 109.5 1.216 2.31 107.9 111 100.3 335s 20 113.3 1.669 2.58 111.6 115 103.4 335s supply.se.fit supply.se.pred supply.lwr supply.upr 335s 1 0.825 2.64 94.1 97.6 335s 2 0.696 2.60 95.6 99.1 335s 3 0.712 2.60 95.7 99.2 335s 4 0.674 2.59 96.0 99.5 335s 5 1.087 2.73 98.1 101.8 335s 6 0.979 2.69 98.0 101.7 335s 7 0.874 2.65 98.1 101.7 335s 8 0.871 2.65 100.3 103.9 335s 9 1.143 2.75 98.4 102.1 335s 10 1.338 2.84 95.3 99.1 335s 11 1.483 2.91 90.8 94.7 335s 12 1.645 3.00 89.1 93.1 335s 13 1.440 2.89 91.0 94.9 335s 14 1.247 2.80 93.2 97.0 335s 15 1.222 2.79 98.2 102.0 335s 16 1.104 2.74 100.0 103.7 335s 17 1.808 3.09 98.7 103.0 335s 18 0.861 2.65 98.7 102.3 335s 19 0.861 2.65 98.5 102.1 335s 20 0.666 2.59 101.6 105.2 335s > print( predict( fitw2sls5$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 335s + interval = "prediction", level = 0.5, newdata = predictData ) ) 335s fit se.fit se.pred lwr upr 335s 1 102.8 0.781 2.12 101.4 104 335s 2 105.4 0.812 2.13 104.0 107 335s 3 105.3 0.824 2.13 103.8 107 335s 4 105.6 0.820 2.13 104.1 107 335s 5 107.5 1.186 2.30 106.0 109 335s 6 107.4 1.133 2.27 105.9 109 335s 7 108.0 1.141 2.28 106.4 110 335s 8 108.7 1.143 2.28 107.2 110 335s 9 106.8 1.179 2.30 105.2 108 335s 10 105.3 1.307 2.36 103.7 107 335s 11 100.3 1.108 2.26 98.7 102 335s 12 99.6 0.841 2.14 98.2 101 335s 13 101.3 0.638 2.07 99.9 103 335s 14 104.3 0.914 2.17 102.8 106 335s 15 109.3 1.440 2.44 107.6 111 335s 16 109.2 1.333 2.38 107.6 111 335s 17 108.9 1.742 2.63 107.1 111 335s 18 107.8 1.049 2.23 106.2 109 335s 19 109.5 1.216 2.31 107.9 111 335s 20 113.3 1.669 2.58 111.6 115 335s > 335s > print( predict( fitw2slsd1, se.fit = TRUE, se.pred = TRUE, 335s + interval = "confidence", level = 0.99 ) ) 335s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 335s 1 97.1 0.751 2.13 94.9 99.3 98.9 335s 2 99.2 0.757 2.13 97.0 101.4 100.4 335s 3 99.2 0.692 2.11 97.2 101.2 100.5 335s 4 99.3 0.766 2.13 97.1 101.5 100.7 335s 5 102.5 0.595 2.08 100.8 104.3 102.6 335s 6 102.2 0.503 2.05 100.7 103.7 102.6 335s 7 102.5 0.503 2.05 101.1 104.0 102.6 335s 8 102.7 0.653 2.10 100.8 104.5 104.8 335s 9 102.0 0.655 2.10 100.1 103.9 102.7 335s 10 101.4 1.074 2.26 98.3 104.5 99.7 335s 11 95.6 0.978 2.22 92.8 98.5 95.4 335s 12 93.9 1.134 2.29 90.7 97.2 93.8 335s 13 95.0 1.162 2.31 91.7 98.4 95.6 335s 14 98.9 0.530 2.06 97.4 100.4 97.6 335s 15 104.9 1.061 2.26 101.9 108.0 102.3 335s 16 104.3 0.757 2.13 102.1 106.5 104.1 335s 17 106.1 1.963 2.80 100.4 111.7 102.8 335s 18 101.7 0.597 2.08 100.0 103.5 102.7 335s 19 103.3 0.736 2.12 101.2 105.4 102.6 335s 20 106.0 1.430 2.45 101.9 110.2 105.6 335s supply.se.fit supply.se.pred supply.lwr supply.upr 335s 1 1.079 2.68 95.8 102.1 335s 2 1.064 2.68 97.3 103.5 335s 3 0.962 2.64 97.6 103.3 335s 4 0.938 2.63 98.0 103.4 335s 5 0.914 2.62 100.0 105.3 335s 6 0.808 2.59 100.2 104.9 335s 7 0.736 2.57 100.4 104.7 335s 8 0.994 2.65 101.9 107.7 335s 9 0.808 2.59 100.4 105.1 335s 10 1.023 2.66 96.7 102.7 335s 11 1.228 2.75 91.8 99.0 335s 12 1.428 2.84 89.7 98.0 335s 13 1.272 2.77 91.9 99.4 335s 14 0.917 2.62 94.9 100.3 335s 15 0.899 2.62 99.7 104.9 335s 16 0.936 2.63 101.3 106.8 335s 17 1.665 2.97 98.0 107.7 335s 18 0.988 2.65 99.8 105.6 335s 19 1.129 2.70 99.3 105.9 335s 20 1.733 3.01 100.5 110.7 335s > print( predict( fitw2slsd1$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 335s + interval = "confidence", level = 0.99 ) ) 335s fit se.fit se.pred lwr upr 335s 1 98.9 1.079 2.68 95.8 102.1 335s 2 100.4 1.064 2.68 97.3 103.5 335s 3 100.5 0.962 2.64 97.6 103.3 335s 4 100.7 0.938 2.63 98.0 103.4 335s 5 102.6 0.914 2.62 100.0 105.3 335s 6 102.6 0.808 2.59 100.2 104.9 335s 7 102.6 0.736 2.57 100.4 104.7 335s 8 104.8 0.994 2.65 101.9 107.7 335s 9 102.7 0.808 2.59 100.4 105.1 335s 10 99.7 1.023 2.66 96.7 102.7 335s 11 95.4 1.228 2.75 91.8 99.0 335s 12 93.8 1.428 2.84 89.7 98.0 335s 13 95.6 1.272 2.77 91.9 99.4 335s 14 97.6 0.917 2.62 94.9 100.3 335s 15 102.3 0.899 2.62 99.7 104.9 335s 16 104.1 0.936 2.63 101.3 106.8 335s 17 102.8 1.665 2.97 98.0 107.7 335s 18 102.7 0.988 2.65 99.8 105.6 335s 19 102.6 1.129 2.70 99.3 105.9 335s 20 105.6 1.733 3.01 100.5 110.7 335s > 335s > print( predict( fitw2slsd2e, se.fit = TRUE, interval = "prediction", 335s + level = 0.9, newdata = predictData, useDfSys = TRUE ) ) 335s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 335s 1 104 1.214 100.1 108 95.7 1.100 335s 2 106 1.169 102.6 110 97.2 0.835 335s 3 106 1.216 102.5 110 97.3 0.864 335s 4 107 1.169 102.7 110 97.6 0.789 335s 5 109 1.897 104.7 114 99.9 1.242 335s 6 109 1.773 104.6 114 99.9 1.115 335s 7 110 1.718 105.2 114 99.9 0.983 335s 8 110 1.552 105.8 114 102.2 0.843 335s 9 109 1.939 104.0 113 100.4 1.310 335s 10 107 2.229 102.5 112 97.4 1.683 335s 11 102 1.655 97.5 106 92.9 1.794 335s 12 101 1.125 96.8 104 91.2 1.750 335s 13 102 0.879 98.5 106 93.1 1.449 335s 14 106 1.480 101.5 110 95.3 1.383 335s 15 111 2.331 106.3 117 100.4 1.395 335s 16 111 2.064 106.3 116 102.2 1.175 335s 17 112 3.001 105.7 118 101.4 2.074 335s 18 109 1.475 104.9 113 100.7 0.861 335s 19 111 1.589 106.5 115 100.6 0.829 335s 20 114 1.756 109.9 119 103.6 0.680 335s supply.lwr supply.upr 335s 1 91.1 100.3 335s 2 92.7 101.7 335s 3 92.8 101.8 335s 4 93.2 102.1 335s 5 95.2 104.7 335s 6 95.3 104.6 335s 7 95.3 104.5 335s 8 97.7 106.7 335s 9 95.6 105.2 335s 10 92.3 102.5 335s 11 87.7 98.1 335s 12 86.0 96.4 335s 13 88.1 98.0 335s 14 90.4 100.1 335s 15 95.5 105.3 335s 16 97.5 106.9 335s 17 95.8 106.9 335s 18 96.2 105.2 335s 19 96.1 105.1 335s 20 99.2 108.0 335s > print( predict( fitw2slsd2e$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 335s + level = 0.9, newdata = predictData, useDfSys = TRUE ) ) 335s fit se.fit lwr upr 335s 1 104 1.214 100.1 108 335s 2 106 1.169 102.6 110 335s 3 106 1.216 102.5 110 335s 4 107 1.169 102.7 110 335s 5 109 1.897 104.7 114 335s 6 109 1.773 104.6 114 335s 7 110 1.718 105.2 114 335s 8 110 1.552 105.8 114 335s 9 109 1.939 104.0 113 335s 10 107 2.229 102.5 112 335s 11 102 1.655 97.5 106 335s 12 101 1.125 96.8 104 335s 13 102 0.879 98.5 106 335s 14 106 1.480 101.5 110 335s 15 111 2.331 106.3 117 335s 16 111 2.064 106.3 116 335s 17 112 3.001 105.7 118 335s 18 109 1.475 104.9 113 335s 19 111 1.589 106.5 115 335s 20 114 1.756 109.9 119 335s > 335s > print( predict( fitw2slsd3e, se.fit = TRUE, se.pred = TRUE, 335s + interval = "prediction", level = 0.01, useDfSys = TRUE ) ) 335s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 335s 1 97.4 0.622 2.05 97.4 97.4 98.2 335s 2 99.4 0.654 2.06 99.4 99.4 99.7 335s 3 99.4 0.598 2.04 99.4 99.4 99.9 335s 4 99.5 0.663 2.06 99.5 99.5 100.2 335s 5 102.4 0.515 2.02 102.4 102.4 102.3 335s 6 102.1 0.442 2.00 102.1 102.1 102.3 335s 7 102.4 0.444 2.00 102.4 102.4 102.4 335s 8 102.6 0.587 2.04 102.6 102.6 104.7 335s 9 101.9 0.573 2.03 101.9 101.9 102.7 335s 10 101.2 0.948 2.17 101.2 101.2 99.6 335s 11 95.9 0.849 2.13 95.9 95.9 95.2 335s 12 94.4 0.914 2.15 94.4 94.4 93.6 335s 13 95.5 0.943 2.17 95.5 95.5 95.6 335s 14 99.0 0.464 2.01 99.0 99.1 97.7 335s 15 104.5 0.883 2.14 104.5 104.6 102.7 335s 16 104.0 0.631 2.05 104.0 104.0 104.6 335s 17 105.4 1.665 2.56 105.4 105.5 103.5 335s 18 101.8 0.538 2.02 101.7 101.8 103.3 335s 19 103.2 0.661 2.06 103.2 103.3 103.2 335s 20 105.9 1.284 2.34 105.9 106.0 106.4 335s supply.se.fit supply.se.pred supply.lwr supply.upr 335s 1 0.652 2.60 98.1 98.2 335s 2 0.740 2.62 99.7 99.8 335s 3 0.682 2.61 99.8 99.9 335s 4 0.708 2.61 100.2 100.2 335s 5 0.782 2.63 102.3 102.4 335s 6 0.699 2.61 102.3 102.4 335s 7 0.648 2.60 102.3 102.4 335s 8 0.906 2.67 104.7 104.8 335s 9 0.736 2.62 102.7 102.8 335s 10 0.931 2.68 99.6 99.7 335s 11 1.107 2.75 95.2 95.2 335s 12 1.287 2.83 93.6 93.7 335s 13 1.157 2.77 95.5 95.6 335s 14 0.829 2.65 97.7 97.7 335s 15 0.717 2.62 102.7 102.8 335s 16 0.676 2.61 104.6 104.6 335s 17 1.392 2.88 103.4 103.5 335s 18 0.699 2.61 103.3 103.3 335s 19 0.822 2.65 103.2 103.2 335s 20 1.376 2.87 106.4 106.5 335s > print( predict( fitw2slsd3e$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 335s + interval = "prediction", level = 0.01, useDfSys = TRUE ) ) 335s fit se.fit se.pred lwr upr 335s 1 98.2 0.652 2.60 98.1 98.2 335s 2 99.7 0.740 2.62 99.7 99.8 335s 3 99.9 0.682 2.61 99.8 99.9 335s 4 100.2 0.708 2.61 100.2 100.2 335s 5 102.3 0.782 2.63 102.3 102.4 335s 6 102.3 0.699 2.61 102.3 102.4 335s 7 102.4 0.648 2.60 102.3 102.4 335s 8 104.7 0.906 2.67 104.7 104.8 335s 9 102.7 0.736 2.62 102.7 102.8 335s 10 99.6 0.931 2.68 99.6 99.7 335s 11 95.2 1.107 2.75 95.2 95.2 335s 12 93.6 1.287 2.83 93.6 93.7 335s 13 95.6 1.157 2.77 95.5 95.6 335s 14 97.7 0.829 2.65 97.7 97.7 335s 15 102.7 0.717 2.62 102.7 102.8 335s 16 104.6 0.676 2.61 104.6 104.6 335s 17 103.5 1.392 2.88 103.4 103.5 335s 18 103.3 0.699 2.61 103.3 103.3 335s 19 103.2 0.822 2.65 103.2 103.2 335s 20 106.4 1.376 2.87 106.4 106.5 335s > 335s > # predict just one observation 335s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 335s + trend = 25 ) 335s > 335s > print( predict( fitw2sls1e, newdata = smallData ) ) 335s demand.pred supply.pred 335s 1 110 118 335s > print( predict( fitw2sls1e$eq[[ 1 ]], newdata = smallData ) ) 335s fit 335s 1 110 335s > 335s > print( predict( fitw2sls2, se.fit = TRUE, level = 0.9, 335s + newdata = smallData ) ) 335s demand.pred demand.se.fit supply.pred supply.se.fit 335s 1 110 2.52 119 3.53 335s > print( predict( fitw2sls2$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 335s + newdata = smallData ) ) 335s fit se.pred 335s 1 110 3.21 335s > 335s > print( predict( fitw2sls3, interval = "prediction", level = 0.975, 335s + newdata = smallData ) ) 335s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 335s 1 110 102 117 119 109 129 335s > print( predict( fitw2sls3$eq[[ 1 ]], interval = "confidence", level = 0.8, 335s + newdata = smallData ) ) 335s fit lwr upr 335s 1 110 107 113 335s > 335s > print( predict( fitw2sls4e, se.fit = TRUE, interval = "confidence", 335s + level = 0.999, newdata = smallData ) ) 335s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 335s 1 110 2.08 102 117 119 2.11 335s supply.lwr supply.upr 335s 1 112 127 335s > print( predict( fitw2sls4e$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 335s + level = 0.75, newdata = smallData ) ) 335s fit se.pred lwr upr 335s 1 119 3.27 115 123 335s > 335s > print( predict( fitw2sls5, se.fit = TRUE, interval = "prediction", 335s + newdata = smallData ) ) 335s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 335s 1 110 2.26 104 116 119 2.33 335s supply.lwr supply.upr 335s 1 112 126 335s > print( predict( fitw2sls5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 335s + newdata = smallData ) ) 335s fit se.pred lwr upr 335s 1 110 3 105 114 335s > 335s > print( predict( fitw2slsd2e, se.fit = TRUE, se.pred = TRUE, 335s + interval = "prediction", level = 0.5, newdata = smallData ) ) 335s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 335s 1 108 2.71 3.34 105 110 119 335s supply.se.fit supply.se.pred supply.lwr supply.upr 335s 1 3.22 4.08 117 122 335s > print( predict( fitw2slsd2e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 335s + interval = "confidence", level = 0.25, newdata = smallData ) ) 335s fit se.fit se.pred lwr upr 335s 1 108 2.71 3.34 107 109 335s > 335s > 335s > ## ************ correlation of predicted values *************** 335s > print( correlation.systemfit( fitw2sls1e, 1, 2 ) ) 335s [,1] 335s [1,] 0 335s [2,] 0 335s [3,] 0 335s [4,] 0 335s [5,] 0 335s [6,] 0 335s [7,] 0 335s [8,] 0 335s [9,] 0 335s [10,] 0 335s [11,] 0 335s [12,] 0 335s [13,] 0 335s [14,] 0 335s [15,] 0 335s [16,] 0 335s [17,] 0 335s [18,] 0 335s [19,] 0 335s [20,] 0 335s > 335s > print( correlation.systemfit( fitw2sls2, 2, 1 ) ) 335s [,1] 335s [1,] 0.413453 335s [2,] 0.153759 335s [3,] 0.152962 335s [4,] 0.112671 335s [5,] -0.071442 335s [6,] -0.053943 335s [7,] -0.050961 335s [8,] -0.005442 335s [9,] -0.000476 335s [10,] -0.001894 335s [11,] 0.047351 335s [12,] 0.064973 335s [13,] 0.024591 335s [14,] -0.028036 335s [15,] 0.175326 335s [16,] 0.254878 335s [17,] 0.104540 335s [18,] 0.065579 335s [19,] 0.147008 335s [20,] 0.124593 335s > 335s > print( correlation.systemfit( fitw2sls3, 1, 2 ) ) 335s [,1] 335s [1,] 0.413453 335s [2,] 0.153759 335s [3,] 0.152962 335s [4,] 0.112671 335s [5,] -0.071442 335s [6,] -0.053943 335s [7,] -0.050961 335s [8,] -0.005442 335s [9,] -0.000476 335s [10,] -0.001894 335s [11,] 0.047351 335s [12,] 0.064973 335s [13,] 0.024591 335s [14,] -0.028036 335s [15,] 0.175326 335s [16,] 0.254878 335s [17,] 0.104540 335s [18,] 0.065579 335s [19,] 0.147008 335s [20,] 0.124593 335s > 335s > print( correlation.systemfit( fitw2sls4e, 2, 1 ) ) 335s [,1] 335s [1,] 0.38438 335s [2,] 0.30697 335s [3,] 0.26690 335s [4,] 0.30163 335s [5,] -0.02768 335s [6,] -0.05086 335s [7,] -0.05895 335s [8,] 0.10102 335s [9,] 0.10072 335s [10,] 0.45547 335s [11,] 0.10817 335s [12,] 0.00552 335s [13,] 0.04219 335s [14,] -0.04054 335s [15,] 0.42100 335s [16,] 0.24974 335s [17,] 0.65722 335s [18,] 0.24286 335s [19,] 0.34336 335s [20,] 0.54717 335s > 335s > print( correlation.systemfit( fitw2sls5, 1, 2 ) ) 335s [,1] 335s [1,] 0.38030 335s [2,] 0.30892 335s [3,] 0.26808 335s [4,] 0.30325 335s [5,] -0.02730 335s [6,] -0.05035 335s [7,] -0.05831 335s [8,] 0.10036 335s [9,] 0.10045 335s [10,] 0.45492 335s [11,] 0.10525 335s [12,] 0.00394 335s [13,] 0.04171 335s [14,] -0.04037 335s [15,] 0.41958 335s [16,] 0.24706 335s [17,] 0.65619 335s [18,] 0.23872 335s [19,] 0.33729 335s [20,] 0.54239 335s > 335s > print( correlation.systemfit( fitw2slsd1, 2, 1 ) ) 335s [,1] 335s [1,] 0 335s [2,] 0 335s [3,] 0 335s [4,] 0 335s [5,] 0 335s [6,] 0 335s [7,] 0 335s [8,] 0 335s [9,] 0 335s [10,] 0 335s [11,] 0 335s [12,] 0 335s [13,] 0 335s [14,] 0 335s [15,] 0 335s [16,] 0 335s [17,] 0 335s [18,] 0 335s [19,] 0 335s [20,] 0 335s > 335s > print( correlation.systemfit( fitw2slsd2e, 1, 2 ) ) 335s [,1] 335s [1,] 0.482214 335s [2,] 0.253368 335s [3,] 0.242824 335s [4,] 0.195411 335s [5,] -0.107828 335s [6,] -0.074958 335s [7,] -0.055696 335s [8,] -0.002037 335s [9,] -0.000921 335s [10,] -0.008040 335s [11,] 0.040999 335s [12,] 0.075418 335s [13,] 0.029702 335s [14,] -0.030775 335s [15,] 0.229063 335s [16,] 0.318607 335s [17,] 0.156734 335s [18,] -0.023016 335s [19,] 0.068128 335s [20,] 0.047481 335s > 335s > print( correlation.systemfit( fitw2slsd3e, 2, 1 ) ) 335s [,1] 335s [1,] 0.482214 335s [2,] 0.253368 335s [3,] 0.242824 335s [4,] 0.195411 335s [5,] -0.107828 335s [6,] -0.074958 335s [7,] -0.055696 335s [8,] -0.002037 335s [9,] -0.000921 335s [10,] -0.008040 335s [11,] 0.040999 335s [12,] 0.075418 335s [13,] 0.029702 335s [14,] -0.030775 335s [15,] 0.229063 335s [16,] 0.318607 335s [17,] 0.156734 335s [18,] -0.023016 335s [19,] 0.068128 335s [20,] 0.047481 335s > 335s > 335s > ## ************ LOG-Likelihood values *************** 335s > print( logLik( fitw2sls1e ) ) 335s 'log Lik.' -67.6 (df=9) 335s > print( logLik( fitw2sls1e, residCovDiag = TRUE ) ) 335s 'log Lik.' -84.4 (df=9) 335s > 335s > print( logLik( fitw2sls2 ) ) 335s 'log Lik.' -65.2 (df=8) 335s > print( logLik( fitw2sls2, residCovDiag = TRUE ) ) 335s 'log Lik.' -84.8 (df=8) 335s > 335s > print( logLik( fitw2sls3 ) ) 335s 'log Lik.' -65.2 (df=8) 335s > print( logLik( fitw2sls3, residCovDiag = TRUE ) ) 335s 'log Lik.' -84.8 (df=8) 335s > 335s > print( logLik( fitw2sls4e ) ) 335s 'log Lik.' -65.7 (df=7) 335s > print( logLik( fitw2sls4e, residCovDiag = TRUE ) ) 335s 'log Lik.' -84.8 (df=7) 335s > 335s > print( logLik( fitw2sls5 ) ) 335s 'log Lik.' -65.6 (df=7) 335s > print( logLik( fitw2sls5, residCovDiag = TRUE ) ) 335s 'log Lik.' -84.8 (df=7) 335s > 335s > print( logLik( fitw2slsd1 ) ) 335s 'log Lik.' -75.1 (df=9) 335s > print( logLik( fitw2slsd1, residCovDiag = TRUE ) ) 335s 'log Lik.' -84.7 (df=9) 335s > 335s > print( logLik( fitw2slsd2e ) ) 335s 'log Lik.' -69.1 (df=8) 335s > print( logLik( fitw2slsd2e, residCovDiag = TRUE ) ) 335s 'log Lik.' -84.7 (df=8) 335s > 335s > print( logLik( fitw2slsd3e ) ) 335s 'log Lik.' -69.1 (df=8) 335s > print( logLik( fitw2slsd3e, residCovDiag = TRUE ) ) 335s 'log Lik.' -84.7 (df=8) 335s > 335s > 335s > ## ************** F tests **************** 335s > # testing first restriction 335s > print( linearHypothesis( fitw2sls1, restrm ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1 335s 335s Res.Df Df F Pr(>F) 335s 1 34 335s 2 33 1 0.31 0.58 335s > linearHypothesis( fitw2sls1, restrict ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1 335s 335s Res.Df Df F Pr(>F) 335s 1 34 335s 2 33 1 0.31 0.58 335s > 335s > print( linearHypothesis( fitw2slsd1e, restrm ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1e 335s 335s Res.Df Df F Pr(>F) 335s 1 34 335s 2 33 1 0.92 0.35 335s > linearHypothesis( fitw2slsd1e, restrict ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1e 335s 335s Res.Df Df F Pr(>F) 335s 1 34 335s 2 33 1 0.92 0.35 335s > 335s > # testing second restriction 335s > restrOnly2m <- matrix(0,1,7) 335s > restrOnly2q <- 0.5 335s > restrOnly2m[1,2] <- -1 335s > restrOnly2m[1,5] <- 1 335s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 335s > # first restriction not imposed 335s > print( linearHypothesis( fitw2sls1e, restrOnly2m, restrOnly2q ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1e 335s 335s Res.Df Df F Pr(>F) 335s 1 34 335s 2 33 1 0.01 0.91 335s > linearHypothesis( fitw2sls1e, restrictOnly2 ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1e 335s 335s Res.Df Df F Pr(>F) 335s 1 34 335s 2 33 1 0.01 0.91 335s > 335s > print( linearHypothesis( fitw2slsd1, restrOnly2m, restrOnly2q ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1 335s 335s Res.Df Df F Pr(>F) 335s 1 34 335s 2 33 1 0.74 0.39 335s > linearHypothesis( fitw2slsd1, restrictOnly2 ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1 335s 335s Res.Df Df F Pr(>F) 335s 1 34 335s 2 33 1 0.74 0.39 335s > 335s > # first restriction imposed 335s > print( linearHypothesis( fitw2sls2, restrOnly2m, restrOnly2q ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls2 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 34 1 0.04 0.85 335s > linearHypothesis( fitw2sls2, restrictOnly2 ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls2 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 34 1 0.04 0.85 335s > 335s > print( linearHypothesis( fitw2sls3, restrOnly2m, restrOnly2q ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls3 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 34 1 0.04 0.85 335s > linearHypothesis( fitw2sls3, restrictOnly2 ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls3 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 34 1 0.04 0.85 335s > 335s > print( linearHypothesis( fitw2slsd2e, restrOnly2m, restrOnly2q ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd2e 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 34 1 0.42 0.52 335s > linearHypothesis( fitw2slsd2e, restrictOnly2 ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd2e 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 34 1 0.42 0.52 335s > 335s > print( linearHypothesis( fitw2slsd3e, restrOnly2m, restrOnly2q ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd3e 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 34 1 0.42 0.52 335s > linearHypothesis( fitw2slsd3e, restrictOnly2 ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd3e 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 34 1 0.42 0.52 335s > 335s > # testing both of the restrictions 335s > print( linearHypothesis( fitw2sls1e, restr2m, restr2q ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1e 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 33 2 0.18 0.84 335s > linearHypothesis( fitw2sls1e, restrict2 ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1e 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 33 2 0.18 0.84 335s > 335s > print( linearHypothesis( fitw2slsd1, restr2m, restr2q ) ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 33 2 0.65 0.53 335s > linearHypothesis( fitw2slsd1, restrict2 ) 335s Linear hypothesis test (Theil's F test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1 335s 335s Res.Df Df F Pr(>F) 335s 1 35 335s 2 33 2 0.65 0.53 335s > 335s > 335s > ## ************** Wald tests **************** 335s > # testing first restriction 335s > print( linearHypothesis( fitw2sls1, restrm, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 34 335s 2 33 1 0.31 0.58 335s > linearHypothesis( fitw2sls1, restrict, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 34 335s 2 33 1 0.31 0.58 335s > 335s > print( linearHypothesis( fitw2slsd1e, restrm, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 34 335s 2 33 1 1.11 0.29 335s > linearHypothesis( fitw2slsd1e, restrict, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 34 335s 2 33 1 1.11 0.29 335s > 335s > # testing second restriction 335s > # first restriction not imposed 335s > print( linearHypothesis( fitw2sls1e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 34 335s 2 33 1 0.02 0.9 335s > linearHypothesis( fitw2sls1e, restrictOnly2, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 34 335s 2 33 1 0.02 0.9 335s > 335s > print( linearHypothesis( fitw2slsd1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 34 335s 2 33 1 0.74 0.39 335s > linearHypothesis( fitw2slsd1, restrictOnly2, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 34 335s 2 33 1 0.74 0.39 335s > # first restriction imposed 335s > print( linearHypothesis( fitw2sls2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls2 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 34 1 0.04 0.85 335s > linearHypothesis( fitw2sls2, restrictOnly2, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls2 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 34 1 0.04 0.85 335s > 335s > print( linearHypothesis( fitw2sls3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls3 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 34 1 0.04 0.85 335s > linearHypothesis( fitw2sls3, restrictOnly2, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls3 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 34 1 0.04 0.85 335s > 335s > print( linearHypothesis( fitw2slsd2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd2e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 34 1 0.49 0.48 335s > linearHypothesis( fitw2slsd2e, restrictOnly2, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd2e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 34 1 0.49 0.48 335s > 335s > print( linearHypothesis( fitw2slsd3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd3e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 34 1 0.49 0.48 335s > linearHypothesis( fitw2slsd3e, restrictOnly2, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd3e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 34 1 0.49 0.48 335s > 335s > # testing both of the restrictions 335s > print( linearHypothesis( fitw2sls1e, restr2m, restr2q, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 33 2 0.43 0.81 335s > linearHypothesis( fitw2sls1e, restrict2, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2sls1e 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 33 2 0.43 0.81 335s > 335s > print( linearHypothesis( fitw2slsd1, restr2m, restr2q, test = "Chisq" ) ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 33 2 1.3 0.52 335s > linearHypothesis( fitw2slsd1, restrict2, test = "Chisq" ) 335s Linear hypothesis test (Chi^2 statistic of a Wald test) 335s 335s Hypothesis: 335s demand_income - supply_trend = 0 335s - demand_price + supply_price = 0.5 335s 335s Model 1: restricted model 335s Model 2: fitw2slsd1 335s 335s Res.Df Df Chisq Pr(>Chisq) 335s 1 35 335s 2 33 2 1.3 0.52 335s > 335s > 335s > ## ****************** model frame ************************** 335s > print( mf <- model.frame( fitw2sls1e ) ) 335s consump price income farmPrice trend 335s 1 98.5 100.3 87.4 98.0 1 335s 2 99.2 104.3 97.6 99.1 2 335s 3 102.2 103.4 96.7 99.1 3 335s 4 101.5 104.5 98.2 98.1 4 335s 5 104.2 98.0 99.8 110.8 5 335s 6 103.2 99.5 100.5 108.2 6 335s 7 104.0 101.1 103.2 105.6 7 335s 8 99.9 104.8 107.8 109.8 8 335s 9 100.3 96.4 96.6 108.7 9 335s 10 102.8 91.2 88.9 100.6 10 335s 11 95.4 93.1 75.1 81.0 11 335s 12 92.4 98.8 76.9 68.6 12 335s 13 94.5 102.9 84.6 70.9 13 335s 14 98.8 98.8 90.6 81.4 14 335s 15 105.8 95.1 103.1 102.3 15 335s 16 100.2 98.5 105.1 105.0 16 335s 17 103.5 86.5 96.4 110.5 17 335s 18 99.9 104.0 104.4 92.5 18 335s 19 105.2 105.8 110.7 89.3 19 335s 20 106.2 113.5 127.1 93.0 20 335s > print( mf1 <- model.frame( fitw2sls1e$eq[[ 1 ]] ) ) 335s consump price income 335s 1 98.5 100.3 87.4 335s 2 99.2 104.3 97.6 335s 3 102.2 103.4 96.7 335s 4 101.5 104.5 98.2 335s 5 104.2 98.0 99.8 335s 6 103.2 99.5 100.5 335s 7 104.0 101.1 103.2 335s 8 99.9 104.8 107.8 335s 9 100.3 96.4 96.6 335s 10 102.8 91.2 88.9 335s 11 95.4 93.1 75.1 335s 12 92.4 98.8 76.9 335s 13 94.5 102.9 84.6 335s 14 98.8 98.8 90.6 335s 15 105.8 95.1 103.1 335s 16 100.2 98.5 105.1 335s 17 103.5 86.5 96.4 335s 18 99.9 104.0 104.4 335s 19 105.2 105.8 110.7 335s 20 106.2 113.5 127.1 335s > print( attributes( mf1 )$terms ) 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s > print( mf2 <- model.frame( fitw2sls1e$eq[[ 2 ]] ) ) 335s consump price farmPrice trend 335s 1 98.5 100.3 98.0 1 335s 2 99.2 104.3 99.1 2 335s 3 102.2 103.4 99.1 3 335s 4 101.5 104.5 98.1 4 335s 5 104.2 98.0 110.8 5 335s 6 103.2 99.5 108.2 6 335s 7 104.0 101.1 105.6 7 335s 8 99.9 104.8 109.8 8 335s 9 100.3 96.4 108.7 9 335s 10 102.8 91.2 100.6 10 335s 11 95.4 93.1 81.0 11 335s 12 92.4 98.8 68.6 12 335s 13 94.5 102.9 70.9 13 335s 14 98.8 98.8 81.4 14 335s 15 105.8 95.1 102.3 15 335s 16 100.2 98.5 105.0 16 335s 17 103.5 86.5 110.5 17 335s 18 99.9 104.0 92.5 18 335s 19 105.2 105.8 89.3 19 335s 20 106.2 113.5 93.0 20 335s > print( attributes( mf2 )$terms ) 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s > 335s > print( all.equal( mf, model.frame( fitw2sls2 ) ) ) 335s [1] TRUE 335s > print( all.equal( mf2, model.frame( fitw2sls2$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > 335s > print( all.equal( mf, model.frame( fitw2sls3 ) ) ) 335s [1] TRUE 335s > print( all.equal( mf1, model.frame( fitw2sls3$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > 335s > print( all.equal( mf, model.frame( fitw2sls4e ) ) ) 335s [1] TRUE 335s > print( all.equal( mf2, model.frame( fitw2sls4e$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > 335s > print( all.equal( mf, model.frame( fitw2sls5 ) ) ) 335s [1] TRUE 335s > print( all.equal( mf1, model.frame( fitw2sls5$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > 335s > print( all.equal( mf, model.frame( fitw2slsd1 ) ) ) 335s [1] TRUE 335s > print( all.equal( mf2, model.frame( fitw2slsd1$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > 335s > print( all.equal( mf, model.frame( fitw2slsd2e ) ) ) 335s [1] TRUE 335s > print( all.equal( mf1, model.frame( fitw2slsd2e$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > 335s > print( all.equal( mf, model.frame( fitw2slsd3e ) ) ) 335s [1] TRUE 335s > print( all.equal( mf2, model.frame( fitw2slsd3e$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > 335s > fitw2sls1e$eq[[ 1 ]]$modelInst 335s income farmPrice trend 335s 1 87.4 98.0 1 335s 2 97.6 99.1 2 335s 3 96.7 99.1 3 335s 4 98.2 98.1 4 335s 5 99.8 110.8 5 335s 6 100.5 108.2 6 335s 7 103.2 105.6 7 335s 8 107.8 109.8 8 335s 9 96.6 108.7 9 335s 10 88.9 100.6 10 335s 11 75.1 81.0 11 335s 12 76.9 68.6 12 335s 13 84.6 70.9 13 335s 14 90.6 81.4 14 335s 15 103.1 102.3 15 335s 16 105.1 105.0 16 335s 17 96.4 110.5 17 335s 18 104.4 92.5 18 335s 19 110.7 89.3 19 335s 20 127.1 93.0 20 335s > fitw2sls1e$eq[[ 2 ]]$modelInst 335s income farmPrice trend 335s 1 87.4 98.0 1 335s 2 97.6 99.1 2 335s 3 96.7 99.1 3 335s 4 98.2 98.1 4 335s 5 99.8 110.8 5 335s 6 100.5 108.2 6 335s 7 103.2 105.6 7 335s 8 107.8 109.8 8 335s 9 96.6 108.7 9 335s 10 88.9 100.6 10 335s 11 75.1 81.0 11 335s 12 76.9 68.6 12 335s 13 84.6 70.9 13 335s 14 90.6 81.4 14 335s 15 103.1 102.3 15 335s 16 105.1 105.0 16 335s 17 96.4 110.5 17 335s 18 104.4 92.5 18 335s 19 110.7 89.3 19 335s 20 127.1 93.0 20 335s > 335s > fitw2sls4Sym$eq[[ 1 ]]$modelInst 335s income farmPrice trend 335s 1 87.4 98.0 1 335s 2 97.6 99.1 2 335s 3 96.7 99.1 3 335s 4 98.2 98.1 4 335s 5 99.8 110.8 5 335s 6 100.5 108.2 6 335s 7 103.2 105.6 7 335s 8 107.8 109.8 8 335s 9 96.6 108.7 9 335s 10 88.9 100.6 10 335s 11 75.1 81.0 11 335s 12 76.9 68.6 12 335s 13 84.6 70.9 13 335s 14 90.6 81.4 14 335s 15 103.1 102.3 15 335s 16 105.1 105.0 16 335s 17 96.4 110.5 17 335s 18 104.4 92.5 18 335s 19 110.7 89.3 19 335s 20 127.1 93.0 20 335s > fitw2sls4Sym$eq[[ 2 ]]$modelInst 335s income farmPrice trend 335s 1 87.4 98.0 1 335s 2 97.6 99.1 2 335s 3 96.7 99.1 3 335s 4 98.2 98.1 4 335s 5 99.8 110.8 5 335s 6 100.5 108.2 6 335s 7 103.2 105.6 7 335s 8 107.8 109.8 8 335s 9 96.6 108.7 9 335s 10 88.9 100.6 10 335s 11 75.1 81.0 11 335s 12 76.9 68.6 12 335s 13 84.6 70.9 13 335s 14 90.6 81.4 14 335s 15 103.1 102.3 15 335s 16 105.1 105.0 16 335s 17 96.4 110.5 17 335s 18 104.4 92.5 18 335s 19 110.7 89.3 19 335s 20 127.1 93.0 20 335s > 335s > fitw2sls5$eq[[ 1 ]]$modelInst 335s income farmPrice trend 335s 1 87.4 98.0 1 335s 2 97.6 99.1 2 335s 3 96.7 99.1 3 335s 4 98.2 98.1 4 335s 5 99.8 110.8 5 335s 6 100.5 108.2 6 335s 7 103.2 105.6 7 335s 8 107.8 109.8 8 335s 9 96.6 108.7 9 335s 10 88.9 100.6 10 335s 11 75.1 81.0 11 335s 12 76.9 68.6 12 335s 13 84.6 70.9 13 335s 14 90.6 81.4 14 335s 15 103.1 102.3 15 335s 16 105.1 105.0 16 335s 17 96.4 110.5 17 335s 18 104.4 92.5 18 335s 19 110.7 89.3 19 335s 20 127.1 93.0 20 335s > fitw2sls5$eq[[ 2 ]]$modelInst 335s income farmPrice trend 335s 1 87.4 98.0 1 335s 2 97.6 99.1 2 335s 3 96.7 99.1 3 335s 4 98.2 98.1 4 335s 5 99.8 110.8 5 335s 6 100.5 108.2 6 335s 7 103.2 105.6 7 335s 8 107.8 109.8 8 335s 9 96.6 108.7 9 335s 10 88.9 100.6 10 335s 11 75.1 81.0 11 335s 12 76.9 68.6 12 335s 13 84.6 70.9 13 335s 14 90.6 81.4 14 335s 15 103.1 102.3 15 335s 16 105.1 105.0 16 335s 17 96.4 110.5 17 335s 18 104.4 92.5 18 335s 19 110.7 89.3 19 335s 20 127.1 93.0 20 335s > 335s > 335s > ## **************** model matrix ************************ 335s > # with x (returnModelMatrix) = TRUE 335s > print( !is.null( fitw2sls1e$eq[[ 1 ]]$x ) ) 335s [1] TRUE 335s > print( mm <- model.matrix( fitw2sls1e ) ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s demand_1 1 100.3 87.4 0 335s demand_2 1 104.3 97.6 0 335s demand_3 1 103.4 96.7 0 335s demand_4 1 104.5 98.2 0 335s demand_5 1 98.0 99.8 0 335s demand_6 1 99.5 100.5 0 335s demand_7 1 101.1 103.2 0 335s demand_8 1 104.8 107.8 0 335s demand_9 1 96.4 96.6 0 335s demand_10 1 91.2 88.9 0 335s demand_11 1 93.1 75.1 0 335s demand_12 1 98.8 76.9 0 335s demand_13 1 102.9 84.6 0 335s demand_14 1 98.8 90.6 0 335s demand_15 1 95.1 103.1 0 335s demand_16 1 98.5 105.1 0 335s demand_17 1 86.5 96.4 0 335s demand_18 1 104.0 104.4 0 335s demand_19 1 105.8 110.7 0 335s demand_20 1 113.5 127.1 0 335s supply_1 0 0.0 0.0 1 335s supply_2 0 0.0 0.0 1 335s supply_3 0 0.0 0.0 1 335s supply_4 0 0.0 0.0 1 335s supply_5 0 0.0 0.0 1 335s supply_6 0 0.0 0.0 1 335s supply_7 0 0.0 0.0 1 335s supply_8 0 0.0 0.0 1 335s supply_9 0 0.0 0.0 1 335s supply_10 0 0.0 0.0 1 335s supply_11 0 0.0 0.0 1 335s supply_12 0 0.0 0.0 1 335s supply_13 0 0.0 0.0 1 335s supply_14 0 0.0 0.0 1 335s supply_15 0 0.0 0.0 1 335s supply_16 0 0.0 0.0 1 335s supply_17 0 0.0 0.0 1 335s supply_18 0 0.0 0.0 1 335s supply_19 0 0.0 0.0 1 335s supply_20 0 0.0 0.0 1 335s supply_price supply_farmPrice supply_trend 335s demand_1 0.0 0.0 0 335s demand_2 0.0 0.0 0 335s demand_3 0.0 0.0 0 335s demand_4 0.0 0.0 0 335s demand_5 0.0 0.0 0 335s demand_6 0.0 0.0 0 335s demand_7 0.0 0.0 0 335s demand_8 0.0 0.0 0 335s demand_9 0.0 0.0 0 335s demand_10 0.0 0.0 0 335s demand_11 0.0 0.0 0 335s demand_12 0.0 0.0 0 335s demand_13 0.0 0.0 0 335s demand_14 0.0 0.0 0 335s demand_15 0.0 0.0 0 335s demand_16 0.0 0.0 0 335s demand_17 0.0 0.0 0 335s demand_18 0.0 0.0 0 335s demand_19 0.0 0.0 0 335s demand_20 0.0 0.0 0 335s supply_1 100.3 98.0 1 335s supply_2 104.3 99.1 2 335s supply_3 103.4 99.1 3 335s supply_4 104.5 98.1 4 335s supply_5 98.0 110.8 5 335s supply_6 99.5 108.2 6 335s supply_7 101.1 105.6 7 335s supply_8 104.8 109.8 8 335s supply_9 96.4 108.7 9 335s supply_10 91.2 100.6 10 335s supply_11 93.1 81.0 11 335s supply_12 98.8 68.6 12 335s supply_13 102.9 70.9 13 335s supply_14 98.8 81.4 14 335s supply_15 95.1 102.3 15 335s supply_16 98.5 105.0 16 335s supply_17 86.5 110.5 17 335s supply_18 104.0 92.5 18 335s supply_19 105.8 89.3 19 335s supply_20 113.5 93.0 20 335s > print( mm1 <- model.matrix( fitw2sls1e$eq[[ 1 ]] ) ) 335s (Intercept) price income 335s 1 1 100.3 87.4 335s 2 1 104.3 97.6 335s 3 1 103.4 96.7 335s 4 1 104.5 98.2 335s 5 1 98.0 99.8 335s 6 1 99.5 100.5 335s 7 1 101.1 103.2 335s 8 1 104.8 107.8 335s 9 1 96.4 96.6 335s 10 1 91.2 88.9 335s 11 1 93.1 75.1 335s 12 1 98.8 76.9 335s 13 1 102.9 84.6 335s 14 1 98.8 90.6 335s 15 1 95.1 103.1 335s 16 1 98.5 105.1 335s 17 1 86.5 96.4 335s 18 1 104.0 104.4 335s 19 1 105.8 110.7 335s 20 1 113.5 127.1 335s attr(,"assign") 335s [1] 0 1 2 335s > print( mm2 <- model.matrix( fitw2sls1e$eq[[ 2 ]] ) ) 335s (Intercept) price farmPrice trend 335s 1 1 100.3 98.0 1 335s 2 1 104.3 99.1 2 335s 3 1 103.4 99.1 3 335s 4 1 104.5 98.1 4 335s 5 1 98.0 110.8 5 335s 6 1 99.5 108.2 6 335s 7 1 101.1 105.6 7 335s 8 1 104.8 109.8 8 335s 9 1 96.4 108.7 9 335s 10 1 91.2 100.6 10 335s 11 1 93.1 81.0 11 335s 12 1 98.8 68.6 12 335s 13 1 102.9 70.9 13 335s 14 1 98.8 81.4 14 335s 15 1 95.1 102.3 15 335s 16 1 98.5 105.0 16 335s 17 1 86.5 110.5 17 335s 18 1 104.0 92.5 18 335s 19 1 105.8 89.3 19 335s 20 1 113.5 93.0 20 335s attr(,"assign") 335s [1] 0 1 2 3 335s > 335s > # with x (returnModelMatrix) = FALSE 335s > print( all.equal( mm, model.matrix( fitw2sls1 ) ) ) 335s [1] TRUE 335s > print( all.equal( mm1, model.matrix( fitw2sls1$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > print( all.equal( mm2, model.matrix( fitw2sls1$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > print( !is.null( fitw2sls1$eq[[ 1 ]]$x ) ) 335s [1] FALSE 335s > 335s > # with x (returnModelMatrix) = TRUE 335s > print( !is.null( fitw2sls2e$eq[[ 1 ]]$x ) ) 335s [1] TRUE 335s > print( all.equal( mm, model.matrix( fitw2sls2e ) ) ) 335s [1] TRUE 335s > print( all.equal( mm1, model.matrix( fitw2sls2e$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > print( all.equal( mm2, model.matrix( fitw2sls2e$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > 335s > # with x (returnModelMatrix) = FALSE 335s > print( all.equal( mm, model.matrix( fitw2sls2Sym ) ) ) 335s [1] TRUE 335s > print( all.equal( mm1, model.matrix( fitw2sls2Sym$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > print( all.equal( mm2, model.matrix( fitw2sls2Sym$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > print( !is.null( fitw2sls2Sym$eq[[ 1 ]]$x ) ) 335s [1] FALSE 335s > 335s > # with x (returnModelMatrix) = TRUE 335s > print( !is.null( fitw2slsd3$eq[[ 1 ]]$x ) ) 335s [1] TRUE 335s > print( all.equal( mm, model.matrix( fitw2slsd3 ) ) ) 335s [1] TRUE 335s > print( all.equal( mm1, model.matrix( fitw2slsd3$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > print( all.equal( mm2, model.matrix( fitw2slsd3$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > 335s > # with x (returnModelMatrix) = FALSE 335s > print( all.equal( mm, model.matrix( fitw2slsd3e ) ) ) 335s [1] TRUE 335s > print( all.equal( mm1, model.matrix( fitw2slsd3e$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > print( all.equal( mm2, model.matrix( fitw2slsd3e$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > print( !is.null( fitw2slsd3e$eq[[ 1 ]]$x ) ) 335s [1] FALSE 335s > 335s > # with x (returnModelMatrix) = TRUE 335s > print( !is.null( fitw2sls4$eq[[ 1 ]]$x ) ) 335s [1] TRUE 335s > print( all.equal( mm, model.matrix( fitw2sls4 ) ) ) 335s [1] TRUE 335s > print( all.equal( mm1, model.matrix( fitw2sls4$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > print( all.equal( mm2, model.matrix( fitw2sls4$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > 335s > # with x (returnModelMatrix) = FALSE 335s > print( all.equal( mm, model.matrix( fitw2sls4e ) ) ) 335s [1] TRUE 335s > print( all.equal( mm1, model.matrix( fitw2sls4e$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > print( all.equal( mm2, model.matrix( fitw2sls4e$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > print( !is.null( fitw2sls4e$eq[[ 1 ]]$x ) ) 335s [1] FALSE 335s > 335s > # with x (returnModelMatrix) = TRUE 335s > print( !is.null( fitw2sls5$eq[[ 1 ]]$x ) ) 335s [1] TRUE 335s > print( all.equal( mm, model.matrix( fitw2sls5 ) ) ) 335s [1] TRUE 335s > print( all.equal( mm1, model.matrix( fitw2sls5$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > print( all.equal( mm2, model.matrix( fitw2sls5$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > 335s > # with x (returnModelMatrix) = FALSE 335s > print( all.equal( mm, model.matrix( fitw2sls5e ) ) ) 335s [1] TRUE 335s > print( all.equal( mm1, model.matrix( fitw2sls5e$eq[[ 1 ]] ) ) ) 335s [1] TRUE 335s > print( all.equal( mm2, model.matrix( fitw2sls5e$eq[[ 2 ]] ) ) ) 335s [1] TRUE 335s > print( !is.null( fitw2sls5e$eq[[ 1 ]]$x ) ) 335s [1] FALSE 335s > 335s > # matrices of instrumental variables 335s > model.matrix( fitw2sls1, which = "z" ) 335s demand_(Intercept) demand_income demand_farmPrice demand_trend 335s demand_1 1 87.4 98.0 1 335s demand_2 1 97.6 99.1 2 335s demand_3 1 96.7 99.1 3 335s demand_4 1 98.2 98.1 4 335s demand_5 1 99.8 110.8 5 335s demand_6 1 100.5 108.2 6 335s demand_7 1 103.2 105.6 7 335s demand_8 1 107.8 109.8 8 335s demand_9 1 96.6 108.7 9 335s demand_10 1 88.9 100.6 10 335s demand_11 1 75.1 81.0 11 335s demand_12 1 76.9 68.6 12 335s demand_13 1 84.6 70.9 13 335s demand_14 1 90.6 81.4 14 335s demand_15 1 103.1 102.3 15 335s demand_16 1 105.1 105.0 16 335s demand_17 1 96.4 110.5 17 335s demand_18 1 104.4 92.5 18 335s demand_19 1 110.7 89.3 19 335s demand_20 1 127.1 93.0 20 335s supply_1 0 0.0 0.0 0 335s supply_2 0 0.0 0.0 0 335s supply_3 0 0.0 0.0 0 335s supply_4 0 0.0 0.0 0 335s supply_5 0 0.0 0.0 0 335s supply_6 0 0.0 0.0 0 335s supply_7 0 0.0 0.0 0 335s supply_8 0 0.0 0.0 0 335s supply_9 0 0.0 0.0 0 335s supply_10 0 0.0 0.0 0 335s supply_11 0 0.0 0.0 0 335s supply_12 0 0.0 0.0 0 335s supply_13 0 0.0 0.0 0 335s supply_14 0 0.0 0.0 0 335s supply_15 0 0.0 0.0 0 335s supply_16 0 0.0 0.0 0 335s supply_17 0 0.0 0.0 0 335s supply_18 0 0.0 0.0 0 335s supply_19 0 0.0 0.0 0 335s supply_20 0 0.0 0.0 0 335s supply_(Intercept) supply_income supply_farmPrice supply_trend 335s demand_1 0 0.0 0.0 0 335s demand_2 0 0.0 0.0 0 335s demand_3 0 0.0 0.0 0 335s demand_4 0 0.0 0.0 0 335s demand_5 0 0.0 0.0 0 335s demand_6 0 0.0 0.0 0 335s demand_7 0 0.0 0.0 0 335s demand_8 0 0.0 0.0 0 335s demand_9 0 0.0 0.0 0 335s demand_10 0 0.0 0.0 0 335s demand_11 0 0.0 0.0 0 335s demand_12 0 0.0 0.0 0 335s demand_13 0 0.0 0.0 0 335s demand_14 0 0.0 0.0 0 335s demand_15 0 0.0 0.0 0 335s demand_16 0 0.0 0.0 0 335s demand_17 0 0.0 0.0 0 335s demand_18 0 0.0 0.0 0 335s demand_19 0 0.0 0.0 0 335s demand_20 0 0.0 0.0 0 335s supply_1 1 87.4 98.0 1 335s supply_2 1 97.6 99.1 2 335s supply_3 1 96.7 99.1 3 335s supply_4 1 98.2 98.1 4 335s supply_5 1 99.8 110.8 5 335s supply_6 1 100.5 108.2 6 335s supply_7 1 103.2 105.6 7 335s supply_8 1 107.8 109.8 8 335s supply_9 1 96.6 108.7 9 335s supply_10 1 88.9 100.6 10 335s supply_11 1 75.1 81.0 11 335s supply_12 1 76.9 68.6 12 335s supply_13 1 84.6 70.9 13 335s supply_14 1 90.6 81.4 14 335s supply_15 1 103.1 102.3 15 335s supply_16 1 105.1 105.0 16 335s supply_17 1 96.4 110.5 17 335s supply_18 1 104.4 92.5 18 335s supply_19 1 110.7 89.3 19 335s supply_20 1 127.1 93.0 20 335s > model.matrix( fitw2sls1$eq[[ 1 ]], which = "z" ) 335s (Intercept) income farmPrice trend 335s 1 1 87.4 98.0 1 335s 2 1 97.6 99.1 2 335s 3 1 96.7 99.1 3 335s 4 1 98.2 98.1 4 335s 5 1 99.8 110.8 5 335s 6 1 100.5 108.2 6 335s 7 1 103.2 105.6 7 335s 8 1 107.8 109.8 8 335s 9 1 96.6 108.7 9 335s 10 1 88.9 100.6 10 335s 11 1 75.1 81.0 11 335s 12 1 76.9 68.6 12 335s 13 1 84.6 70.9 13 335s 14 1 90.6 81.4 14 335s 15 1 103.1 102.3 15 335s 16 1 105.1 105.0 16 335s 17 1 96.4 110.5 17 335s 18 1 104.4 92.5 18 335s 19 1 110.7 89.3 19 335s 20 1 127.1 93.0 20 335s attr(,"assign") 335s [1] 0 1 2 3 335s > model.matrix( fitw2sls1$eq[[ 2 ]], which = "z" ) 335s (Intercept) income farmPrice trend 335s 1 1 87.4 98.0 1 335s 2 1 97.6 99.1 2 335s 3 1 96.7 99.1 3 335s 4 1 98.2 98.1 4 335s 5 1 99.8 110.8 5 335s 6 1 100.5 108.2 6 335s 7 1 103.2 105.6 7 335s 8 1 107.8 109.8 8 335s 9 1 96.6 108.7 9 335s 10 1 88.9 100.6 10 335s 11 1 75.1 81.0 11 335s 12 1 76.9 68.6 12 335s 13 1 84.6 70.9 13 335s 14 1 90.6 81.4 14 335s 15 1 103.1 102.3 15 335s 16 1 105.1 105.0 16 335s 17 1 96.4 110.5 17 335s 18 1 104.4 92.5 18 335s 19 1 110.7 89.3 19 335s 20 1 127.1 93.0 20 335s attr(,"assign") 335s [1] 0 1 2 3 335s > 335s > # matrices of fitted regressors 335s > model.matrix( fitw2sls5e, which = "xHat" ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s demand_1 1 99.6 87.4 0 335s demand_2 1 105.1 97.6 0 335s demand_3 1 103.8 96.7 0 335s demand_4 1 104.5 98.2 0 335s demand_5 1 98.7 99.8 0 335s demand_6 1 99.6 100.5 0 335s demand_7 1 102.0 103.2 0 335s demand_8 1 102.2 107.8 0 335s demand_9 1 94.6 96.6 0 335s demand_10 1 92.7 88.9 0 335s demand_11 1 92.4 75.1 0 335s demand_12 1 98.9 76.9 0 335s demand_13 1 102.2 84.6 0 335s demand_14 1 100.3 90.6 0 335s demand_15 1 97.6 103.1 0 335s demand_16 1 96.9 105.1 0 335s demand_17 1 87.7 96.4 0 335s demand_18 1 101.1 104.4 0 335s demand_19 1 106.1 110.7 0 335s demand_20 1 114.4 127.1 0 335s supply_1 0 0.0 0.0 1 335s supply_2 0 0.0 0.0 1 335s supply_3 0 0.0 0.0 1 335s supply_4 0 0.0 0.0 1 335s supply_5 0 0.0 0.0 1 335s supply_6 0 0.0 0.0 1 335s supply_7 0 0.0 0.0 1 335s supply_8 0 0.0 0.0 1 335s supply_9 0 0.0 0.0 1 335s supply_10 0 0.0 0.0 1 335s supply_11 0 0.0 0.0 1 335s supply_12 0 0.0 0.0 1 335s supply_13 0 0.0 0.0 1 335s supply_14 0 0.0 0.0 1 335s supply_15 0 0.0 0.0 1 335s supply_16 0 0.0 0.0 1 335s supply_17 0 0.0 0.0 1 335s supply_18 0 0.0 0.0 1 335s supply_19 0 0.0 0.0 1 335s supply_20 0 0.0 0.0 1 335s supply_price supply_farmPrice supply_trend 335s demand_1 0.0 0.0 0 335s demand_2 0.0 0.0 0 335s demand_3 0.0 0.0 0 335s demand_4 0.0 0.0 0 335s demand_5 0.0 0.0 0 335s demand_6 0.0 0.0 0 335s demand_7 0.0 0.0 0 335s demand_8 0.0 0.0 0 335s demand_9 0.0 0.0 0 335s demand_10 0.0 0.0 0 335s demand_11 0.0 0.0 0 335s demand_12 0.0 0.0 0 335s demand_13 0.0 0.0 0 335s demand_14 0.0 0.0 0 335s demand_15 0.0 0.0 0 335s demand_16 0.0 0.0 0 335s demand_17 0.0 0.0 0 335s demand_18 0.0 0.0 0 335s demand_19 0.0 0.0 0 335s demand_20 0.0 0.0 0 335s supply_1 99.6 98.0 1 335s supply_2 105.1 99.1 2 335s supply_3 103.8 99.1 3 335s supply_4 104.5 98.1 4 335s supply_5 98.7 110.8 5 335s supply_6 99.6 108.2 6 335s supply_7 102.0 105.6 7 335s supply_8 102.2 109.8 8 335s supply_9 94.6 108.7 9 335s supply_10 92.7 100.6 10 335s supply_11 92.4 81.0 11 335s supply_12 98.9 68.6 12 335s supply_13 102.2 70.9 13 335s supply_14 100.3 81.4 14 335s supply_15 97.6 102.3 15 335s supply_16 96.9 105.0 16 335s supply_17 87.7 110.5 17 335s supply_18 101.1 92.5 18 335s supply_19 106.1 89.3 19 335s supply_20 114.4 93.0 20 335s > model.matrix( fitw2sls5e$eq[[ 1 ]], which = "xHat" ) 335s (Intercept) price income 335s 1 1 99.6 87.4 335s 2 1 105.1 97.6 335s 3 1 103.8 96.7 335s 4 1 104.5 98.2 335s 5 1 98.7 99.8 335s 6 1 99.6 100.5 335s 7 1 102.0 103.2 335s 8 1 102.2 107.8 335s 9 1 94.6 96.6 335s 10 1 92.7 88.9 335s 11 1 92.4 75.1 335s 12 1 98.9 76.9 335s 13 1 102.2 84.6 335s 14 1 100.3 90.6 335s 15 1 97.6 103.1 335s 16 1 96.9 105.1 335s 17 1 87.7 96.4 335s 18 1 101.1 104.4 335s 19 1 106.1 110.7 335s 20 1 114.4 127.1 335s > model.matrix( fitw2sls5e$eq[[ 2 ]], which = "xHat" ) 335s (Intercept) price farmPrice trend 335s 1 1 99.6 98.0 1 335s 2 1 105.1 99.1 2 335s 3 1 103.8 99.1 3 335s 4 1 104.5 98.1 4 335s 5 1 98.7 110.8 5 335s 6 1 99.6 108.2 6 335s 7 1 102.0 105.6 7 335s 8 1 102.2 109.8 8 335s 9 1 94.6 108.7 9 335s 10 1 92.7 100.6 10 335s 11 1 92.4 81.0 11 335s 12 1 98.9 68.6 12 335s 13 1 102.2 70.9 13 335s 14 1 100.3 81.4 14 335s 15 1 97.6 102.3 15 335s 16 1 96.9 105.0 16 335s 17 1 87.7 110.5 17 335s 18 1 101.1 92.5 18 335s 19 1 106.1 89.3 19 335s 20 1 114.4 93.0 20 335s > 335s > 335s > ## **************** formulas ************************ 335s > formula( fitw2sls1e ) 335s $demand 335s consump ~ price + income 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s 335s > formula( fitw2sls1e$eq[[ 1 ]] ) 335s consump ~ price + income 335s > 335s > formula( fitw2sls2 ) 335s $demand 335s consump ~ price + income 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s 335s > formula( fitw2sls2$eq[[ 2 ]] ) 335s consump ~ price + farmPrice + trend 335s > 335s > formula( fitw2sls3 ) 335s $demand 335s consump ~ price + income 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s 335s > formula( fitw2sls3$eq[[ 1 ]] ) 335s consump ~ price + income 335s > 335s > formula( fitw2sls4e ) 335s $demand 335s consump ~ price + income 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s 335s > formula( fitw2sls4e$eq[[ 2 ]] ) 335s consump ~ price + farmPrice + trend 335s > 335s > formula( fitw2sls5 ) 335s $demand 335s consump ~ price + income 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s 335s > formula( fitw2sls5$eq[[ 1 ]] ) 335s consump ~ price + income 335s > 335s > formula( fitw2slsd1 ) 335s $demand 335s consump ~ price + income 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s 335s > formula( fitw2slsd1$eq[[ 2 ]] ) 335s consump ~ price + farmPrice + trend 335s > 335s > formula( fitw2slsd2e ) 335s $demand 335s consump ~ price + income 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s 335s > formula( fitw2slsd2e$eq[[ 1 ]] ) 335s consump ~ price + income 335s > 335s > formula( fitw2slsd3e ) 335s $demand 335s consump ~ price + income 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s 335s > formula( fitw2slsd3e$eq[[ 2 ]] ) 335s consump ~ price + farmPrice + trend 335s > 335s > 335s > ## **************** model terms ******************* 335s > terms( fitw2sls1e ) 335s $demand 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s 335s > terms( fitw2sls1e$eq[[ 1 ]] ) 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s > 335s > terms( fitw2sls2 ) 335s $demand 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s 335s > terms( fitw2sls2$eq[[ 2 ]] ) 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s > 335s > terms( fitw2sls3 ) 335s $demand 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s 335s > terms( fitw2sls3$eq[[ 1 ]] ) 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s > 335s > terms( fitw2sls4e ) 335s $demand 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s 335s > terms( fitw2sls4e$eq[[ 2 ]] ) 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s > 335s > terms( fitw2sls5 ) 335s $demand 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s 335s > terms( fitw2sls5$eq[[ 1 ]] ) 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s > 335s > terms( fitw2slsd1 ) 335s $demand 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s 335s > terms( fitw2slsd1$eq[[ 2 ]] ) 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s > 335s > terms( fitw2slsd2e ) 335s $demand 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s 335s > terms( fitw2slsd2e$eq[[ 1 ]] ) 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s > 335s > terms( fitw2slsd3e ) 335s $demand 335s consump ~ price + income 335s attr(,"variables") 335s list(consump, price, income) 335s attr(,"factors") 335s price income 335s consump 0 0 335s price 1 0 335s income 0 1 335s attr(,"term.labels") 335s [1] "price" "income" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, income) 335s attr(,"dataClasses") 335s consump price income 335s "numeric" "numeric" "numeric" 335s 335s $supply 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s 335s > terms( fitw2slsd3e$eq[[ 2 ]] ) 335s consump ~ price + farmPrice + trend 335s attr(,"variables") 335s list(consump, price, farmPrice, trend) 335s attr(,"factors") 335s price farmPrice trend 335s consump 0 0 0 335s price 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "price" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 1 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(consump, price, farmPrice, trend) 335s attr(,"dataClasses") 335s consump price farmPrice trend 335s "numeric" "numeric" "numeric" "numeric" 335s > 335s > 335s > ## **************** terms of instruments ******************* 335s > fitw2sls1e$eq[[ 1 ]]$termsInst 335s ~income + farmPrice + trend 335s attr(,"variables") 335s list(income, farmPrice, trend) 335s attr(,"factors") 335s income farmPrice trend 335s income 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "income" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 0 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(income, farmPrice, trend) 335s attr(,"dataClasses") 335s income farmPrice trend 335s "numeric" "numeric" "numeric" 335s > 335s > fitw2sls2$eq[[ 2 ]]$termsInst 335s ~income + farmPrice + trend 335s attr(,"variables") 335s list(income, farmPrice, trend) 335s attr(,"factors") 335s income farmPrice trend 335s income 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "income" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 0 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(income, farmPrice, trend) 335s attr(,"dataClasses") 335s income farmPrice trend 335s "numeric" "numeric" "numeric" 335s > 335s > fitw2sls3$eq[[ 1 ]]$termsInst 335s ~income + farmPrice + trend 335s attr(,"variables") 335s list(income, farmPrice, trend) 335s attr(,"factors") 335s income farmPrice trend 335s income 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "income" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 0 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(income, farmPrice, trend) 335s attr(,"dataClasses") 335s income farmPrice trend 335s "numeric" "numeric" "numeric" 335s > 335s > fitw2sls4e$eq[[ 2 ]]$termsInst 335s ~income + farmPrice + trend 335s attr(,"variables") 335s list(income, farmPrice, trend) 335s attr(,"factors") 335s income farmPrice trend 335s income 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "income" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 0 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(income, farmPrice, trend) 335s attr(,"dataClasses") 335s income farmPrice trend 335s "numeric" "numeric" "numeric" 335s > 335s > fitw2sls5$eq[[ 1 ]]$termsInst 335s ~income + farmPrice + trend 335s attr(,"variables") 335s list(income, farmPrice, trend) 335s attr(,"factors") 335s income farmPrice trend 335s income 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "income" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 0 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(income, farmPrice, trend) 335s attr(,"dataClasses") 335s income farmPrice trend 335s "numeric" "numeric" "numeric" 335s > 335s > fitw2slsd1$eq[[ 2 ]]$termsInst 335s ~income + farmPrice + trend 335s attr(,"variables") 335s list(income, farmPrice, trend) 335s attr(,"factors") 335s income farmPrice trend 335s income 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "income" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 0 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(income, farmPrice, trend) 335s attr(,"dataClasses") 335s income farmPrice trend 335s "numeric" "numeric" "numeric" 335s > 335s > fitw2slsd2e$eq[[ 1 ]]$termsInst 335s ~income + farmPrice 335s attr(,"variables") 335s list(income, farmPrice) 335s attr(,"factors") 335s income farmPrice 335s income 1 0 335s farmPrice 0 1 335s attr(,"term.labels") 335s [1] "income" "farmPrice" 335s attr(,"order") 335s [1] 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 0 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(income, farmPrice) 335s attr(,"dataClasses") 335s income farmPrice 335s "numeric" "numeric" 335s > 335s > fitw2slsd3e$eq[[ 2 ]]$termsInst 335s ~income + farmPrice + trend 335s attr(,"variables") 335s list(income, farmPrice, trend) 335s attr(,"factors") 335s income farmPrice trend 335s income 1 0 0 335s farmPrice 0 1 0 335s trend 0 0 1 335s attr(,"term.labels") 335s [1] "income" "farmPrice" "trend" 335s attr(,"order") 335s [1] 1 1 1 335s attr(,"intercept") 335s [1] 1 335s attr(,"response") 335s [1] 0 335s attr(,".Environment") 335s 335s attr(,"predvars") 335s list(income, farmPrice, trend) 335s attr(,"dataClasses") 335s income farmPrice trend 335s "numeric" "numeric" "numeric" 335s > 335s > 335s > ## **************** estfun ************************ 335s > library( "sandwich" ) 335s > 335s > estfun( fitw2sls1 ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s demand_1 0.17426 17.362 15.231 0.0000 335s demand_2 -0.12666 -13.314 -12.362 0.0000 335s demand_3 0.63211 65.603 61.125 0.0000 335s demand_4 0.38686 40.439 37.990 0.0000 335s demand_5 0.59421 58.619 59.302 0.0000 335s demand_6 0.34231 34.111 34.403 0.0000 335s demand_7 0.46340 47.253 47.822 0.0000 335s demand_8 -0.95225 -97.353 -102.653 0.0000 335s demand_9 -0.40681 -38.486 -39.297 0.0000 335s demand_10 0.73846 68.469 65.649 0.0000 335s demand_11 -0.07078 -6.540 -5.315 0.0000 335s demand_12 -0.58541 -57.907 -45.018 0.0000 335s demand_13 -0.46025 -47.020 -38.937 0.0000 335s demand_14 0.02562 2.569 2.322 0.0000 335s demand_15 0.66403 64.824 68.462 0.0000 335s demand_16 -0.98546 -95.483 -103.572 0.0000 335s demand_17 -0.00533 -0.468 -0.514 0.0000 335s demand_18 -0.74266 -75.053 -77.534 0.0000 335s demand_19 0.43017 45.625 47.620 0.0000 335s demand_20 -0.11583 -13.250 -14.722 0.0000 335s supply_1 0.00000 0.000 0.000 -0.0444 335s supply_2 0.00000 0.000 0.000 -0.2348 335s supply_3 0.00000 0.000 0.000 0.2691 335s supply_4 0.00000 0.000 0.000 0.1308 335s supply_5 0.00000 0.000 0.000 0.2381 335s supply_6 0.00000 0.000 0.000 0.1015 335s supply_7 0.00000 0.000 0.000 0.2015 335s supply_8 0.00000 0.000 0.000 -0.7062 335s supply_9 0.00000 0.000 0.000 -0.3238 335s supply_10 0.00000 0.000 0.000 0.4611 335s supply_11 0.00000 0.000 0.000 0.0385 335s supply_12 0.00000 0.000 0.000 -0.2360 335s supply_13 0.00000 0.000 0.000 -0.1548 335s supply_14 0.00000 0.000 0.000 0.1330 335s supply_15 0.00000 0.000 0.000 0.4778 335s supply_16 0.00000 0.000 0.000 -0.5719 335s supply_17 0.00000 0.000 0.000 0.0648 335s supply_18 0.00000 0.000 0.000 -0.3413 335s supply_19 0.00000 0.000 0.000 0.4299 335s supply_20 0.00000 0.000 0.000 0.0672 335s supply_price supply_farmPrice supply_trend 335s demand_1 0.00 0.00 0.0000 335s demand_2 0.00 0.00 0.0000 335s demand_3 0.00 0.00 0.0000 335s demand_4 0.00 0.00 0.0000 335s demand_5 0.00 0.00 0.0000 335s demand_6 0.00 0.00 0.0000 335s demand_7 0.00 0.00 0.0000 335s demand_8 0.00 0.00 0.0000 335s demand_9 0.00 0.00 0.0000 335s demand_10 0.00 0.00 0.0000 335s demand_11 0.00 0.00 0.0000 335s demand_12 0.00 0.00 0.0000 335s demand_13 0.00 0.00 0.0000 335s demand_14 0.00 0.00 0.0000 335s demand_15 0.00 0.00 0.0000 335s demand_16 0.00 0.00 0.0000 335s demand_17 0.00 0.00 0.0000 335s demand_18 0.00 0.00 0.0000 335s demand_19 0.00 0.00 0.0000 335s demand_20 0.00 0.00 0.0000 335s supply_1 -4.42 -4.35 -0.0444 335s supply_2 -24.68 -23.27 -0.4696 335s supply_3 27.93 26.67 0.8073 335s supply_4 13.67 12.83 0.5230 335s supply_5 23.49 26.38 1.1905 335s supply_6 10.12 10.99 0.6093 335s supply_7 20.55 21.28 1.4107 335s supply_8 -72.20 -77.54 -5.6498 335s supply_9 -30.64 -35.20 -2.9145 335s supply_10 42.75 46.39 4.6109 335s supply_11 3.56 3.12 0.4235 335s supply_12 -23.35 -16.19 -2.8326 335s supply_13 -15.81 -10.97 -2.0121 335s supply_14 13.34 10.83 1.8621 335s supply_15 46.64 48.88 7.1671 335s supply_16 -55.42 -60.05 -9.1508 335s supply_17 5.68 7.16 1.1011 335s supply_18 -34.49 -31.57 -6.1438 335s supply_19 45.59 38.39 8.1674 335s supply_20 7.69 6.25 1.3448 335s > round( colSums( estfun( fitw2sls1 ) ), digits = 7 ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s 0 0 0 0 335s supply_price supply_farmPrice supply_trend 335s 0 0 0 335s > 335s > estfun( fitw2sls1e ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s demand_1 0.20502 20.43 17.918 0.0000 335s demand_2 -0.14901 -15.66 -14.543 0.0000 335s demand_3 0.74366 77.18 71.912 0.0000 335s demand_4 0.45513 47.57 44.694 0.0000 335s demand_5 0.69907 68.96 69.767 0.0000 335s demand_6 0.40272 40.13 40.474 0.0000 335s demand_7 0.54517 55.59 56.262 0.0000 335s demand_8 -1.12030 -114.53 -120.768 0.0000 335s demand_9 -0.47860 -45.28 -46.232 0.0000 335s demand_10 0.86877 80.55 77.234 0.0000 335s demand_11 -0.08327 -7.69 -6.253 0.0000 335s demand_12 -0.68871 -68.13 -52.962 0.0000 335s demand_13 -0.54147 -55.32 -45.808 0.0000 335s demand_14 0.03015 3.02 2.731 0.0000 335s demand_15 0.78121 76.26 80.543 0.0000 335s demand_16 -1.15937 -112.33 -121.850 0.0000 335s demand_17 -0.00627 -0.55 -0.605 0.0000 335s demand_18 -0.87372 -88.30 -91.217 0.0000 335s demand_19 0.50608 53.68 56.023 0.0000 335s demand_20 -0.13627 -15.59 -17.320 0.0000 335s supply_1 0.00000 0.00 0.000 -0.0554 335s supply_2 0.00000 0.00 0.000 -0.2935 335s supply_3 0.00000 0.00 0.000 0.3364 335s supply_4 0.00000 0.00 0.000 0.1634 335s supply_5 0.00000 0.00 0.000 0.2976 335s supply_6 0.00000 0.00 0.000 0.1269 335s supply_7 0.00000 0.00 0.000 0.2519 335s supply_8 0.00000 0.00 0.000 -0.8828 335s supply_9 0.00000 0.00 0.000 -0.4048 335s supply_10 0.00000 0.00 0.000 0.5764 335s supply_11 0.00000 0.00 0.000 0.0481 335s supply_12 0.00000 0.00 0.000 -0.2951 335s supply_13 0.00000 0.00 0.000 -0.1935 335s supply_14 0.00000 0.00 0.000 0.1663 335s supply_15 0.00000 0.00 0.000 0.5973 335s supply_16 0.00000 0.00 0.000 -0.7149 335s supply_17 0.00000 0.00 0.000 0.0810 335s supply_18 0.00000 0.00 0.000 -0.4267 335s supply_19 0.00000 0.00 0.000 0.5373 335s supply_20 0.00000 0.00 0.000 0.0841 335s supply_price supply_farmPrice supply_trend 335s demand_1 0.00 0.00 0.0000 335s demand_2 0.00 0.00 0.0000 335s demand_3 0.00 0.00 0.0000 335s demand_4 0.00 0.00 0.0000 335s demand_5 0.00 0.00 0.0000 335s demand_6 0.00 0.00 0.0000 335s demand_7 0.00 0.00 0.0000 335s demand_8 0.00 0.00 0.0000 335s demand_9 0.00 0.00 0.0000 335s demand_10 0.00 0.00 0.0000 335s demand_11 0.00 0.00 0.0000 335s demand_12 0.00 0.00 0.0000 335s demand_13 0.00 0.00 0.0000 335s demand_14 0.00 0.00 0.0000 335s demand_15 0.00 0.00 0.0000 335s demand_16 0.00 0.00 0.0000 335s demand_17 0.00 0.00 0.0000 335s demand_18 0.00 0.00 0.0000 335s demand_19 0.00 0.00 0.0000 335s demand_20 0.00 0.00 0.0000 335s supply_1 -5.52 -5.43 -0.0554 335s supply_2 -30.85 -29.09 -0.5870 335s supply_3 34.91 33.33 1.0091 335s supply_4 17.09 16.03 0.6538 335s supply_5 29.36 32.98 1.4882 335s supply_6 12.65 13.73 0.7616 335s supply_7 25.69 26.60 1.7633 335s supply_8 -90.25 -96.93 -7.0623 335s supply_9 -38.30 -44.00 -3.6431 335s supply_10 53.44 57.98 5.7636 335s supply_11 4.45 3.90 0.5294 335s supply_12 -29.19 -20.24 -3.5407 335s supply_13 -19.77 -13.72 -2.5151 335s supply_14 16.67 13.53 2.3277 335s supply_15 58.30 61.10 8.9588 335s supply_16 -69.27 -75.07 -11.4386 335s supply_17 7.10 8.95 1.3763 335s supply_18 -43.12 -39.47 -7.6797 335s supply_19 56.99 47.98 10.2092 335s supply_20 9.62 7.82 1.6810 335s > round( colSums( estfun( fitw2sls1e ) ), digits = 7 ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s 0 0 0 0 335s supply_price supply_farmPrice supply_trend 335s 0 0 0 335s > 335s > estfun( fitw2slsd1e ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s demand_1 -0.2141 -20.39 -18.71 0.0000 335s demand_2 -0.5971 -59.32 -58.28 0.0000 335s demand_3 0.3342 33.06 32.31 0.0000 335s demand_4 0.0923 9.21 9.06 0.0000 335s demand_5 0.3748 36.34 37.40 0.0000 335s demand_6 0.1317 12.91 13.23 0.0000 335s demand_7 0.2982 29.80 30.78 0.0000 335s demand_8 -1.3110 -132.05 -141.32 0.0000 335s demand_9 -0.5322 -51.18 -51.41 0.0000 335s demand_10 0.8995 85.57 79.97 0.0000 335s demand_11 0.1399 13.25 10.51 0.0000 335s demand_12 -0.4189 -41.49 -32.21 0.0000 335s demand_13 -0.2903 -29.54 -24.56 0.0000 335s demand_14 0.2709 27.46 24.55 0.0000 335s demand_15 0.9535 96.13 98.30 0.0000 335s demand_16 -0.9012 -90.95 -94.71 0.0000 335s demand_17 0.3566 34.08 34.37 0.0000 335s demand_18 -0.5159 -53.75 -53.86 0.0000 335s demand_19 0.8239 88.84 91.20 0.0000 335s demand_20 0.1054 12.00 13.39 0.0000 335s supply_1 0.0000 0.00 0.00 -0.0554 335s supply_2 0.0000 0.00 0.00 -0.2935 335s supply_3 0.0000 0.00 0.00 0.3364 335s supply_4 0.0000 0.00 0.00 0.1634 335s supply_5 0.0000 0.00 0.00 0.2976 335s supply_6 0.0000 0.00 0.00 0.1269 335s supply_7 0.0000 0.00 0.00 0.2519 335s supply_8 0.0000 0.00 0.00 -0.8828 335s supply_9 0.0000 0.00 0.00 -0.4048 335s supply_10 0.0000 0.00 0.00 0.5764 335s supply_11 0.0000 0.00 0.00 0.0481 335s supply_12 0.0000 0.00 0.00 -0.2951 335s supply_13 0.0000 0.00 0.00 -0.1935 335s supply_14 0.0000 0.00 0.00 0.1663 335s supply_15 0.0000 0.00 0.00 0.5973 335s supply_16 0.0000 0.00 0.00 -0.7149 335s supply_17 0.0000 0.00 0.00 0.0810 335s supply_18 0.0000 0.00 0.00 -0.4267 335s supply_19 0.0000 0.00 0.00 0.5373 335s supply_20 0.0000 0.00 0.00 0.0841 335s supply_price supply_farmPrice supply_trend 335s demand_1 0.00 0.00 0.0000 335s demand_2 0.00 0.00 0.0000 335s demand_3 0.00 0.00 0.0000 335s demand_4 0.00 0.00 0.0000 335s demand_5 0.00 0.00 0.0000 335s demand_6 0.00 0.00 0.0000 335s demand_7 0.00 0.00 0.0000 335s demand_8 0.00 0.00 0.0000 335s demand_9 0.00 0.00 0.0000 335s demand_10 0.00 0.00 0.0000 335s demand_11 0.00 0.00 0.0000 335s demand_12 0.00 0.00 0.0000 335s demand_13 0.00 0.00 0.0000 335s demand_14 0.00 0.00 0.0000 335s demand_15 0.00 0.00 0.0000 335s demand_16 0.00 0.00 0.0000 335s demand_17 0.00 0.00 0.0000 335s demand_18 0.00 0.00 0.0000 335s demand_19 0.00 0.00 0.0000 335s demand_20 0.00 0.00 0.0000 335s supply_1 -5.52 -5.43 -0.0554 335s supply_2 -30.85 -29.09 -0.5870 335s supply_3 34.91 33.33 1.0091 335s supply_4 17.09 16.03 0.6538 335s supply_5 29.36 32.98 1.4882 335s supply_6 12.65 13.73 0.7616 335s supply_7 25.69 26.60 1.7633 335s supply_8 -90.25 -96.93 -7.0623 335s supply_9 -38.30 -44.00 -3.6431 335s supply_10 53.44 57.98 5.7636 335s supply_11 4.45 3.90 0.5294 335s supply_12 -29.19 -20.24 -3.5407 335s supply_13 -19.77 -13.72 -2.5151 335s supply_14 16.67 13.53 2.3277 335s supply_15 58.30 61.10 8.9588 335s supply_16 -69.27 -75.07 -11.4386 335s supply_17 7.10 8.95 1.3763 335s supply_18 -43.12 -39.47 -7.6797 335s supply_19 56.99 47.98 10.2092 335s supply_20 9.62 7.82 1.6810 335s > round( colSums( estfun( fitw2slsd1e ) ), digits = 7 ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s 0 0 0 0 335s supply_price supply_farmPrice supply_trend 335s 0 0 0 335s > 335s > 335s > ## **************** bread ************************ 335s > bread( fitw2sls1 ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s [1,] 2509.59 -26.937 1.9721 0.0 335s [2,] -26.94 0.372 -0.1057 0.0 335s [3,] 1.97 -0.106 0.0881 0.0 335s [4,] 0.00 0.000 0.0000 5770.1 335s [5,] 0.00 0.000 0.0000 -43.8 335s [6,] 0.00 0.000 0.0000 -13.0 335s [7,] 0.00 0.000 0.0000 -11.8 335s supply_price supply_farmPrice supply_trend 335s [1,] 0.0000 0.0000 0.0000 335s [2,] 0.0000 0.0000 0.0000 335s [3,] 0.0000 0.0000 0.0000 335s [4,] -43.8164 -12.9527 -11.8092 335s [5,] 0.3995 0.0374 0.0232 335s [6,] 0.0374 0.0893 0.0551 335s [7,] 0.0232 0.0551 0.3972 335s > 335s > bread( fitw2sls1e ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s [1,] 2133.15 -22.8963 1.6763 0.00 335s [2,] -22.90 0.3165 -0.0898 0.00 335s [3,] 1.68 -0.0898 0.0749 0.00 335s [4,] 0.00 0.0000 0.0000 4616.09 335s [5,] 0.00 0.0000 0.0000 -35.05 335s [6,] 0.00 0.0000 0.0000 -10.36 335s [7,] 0.00 0.0000 0.0000 -9.45 335s supply_price supply_farmPrice supply_trend 335s [1,] 0.0000 0.0000 0.0000 335s [2,] 0.0000 0.0000 0.0000 335s [3,] 0.0000 0.0000 0.0000 335s [4,] -35.0531 -10.3622 -9.4473 335s [5,] 0.3196 0.0300 0.0185 335s [6,] 0.0300 0.0714 0.0441 335s [7,] 0.0185 0.0441 0.3178 335s > 335s > bread( fitw2slsd1e ) 335s demand_(Intercept) demand_price demand_income supply_(Intercept) 335s [1,] 4222.1 -51.601 9.696 0.00 335s [2,] -51.6 0.713 -0.202 0.00 335s [3,] 9.7 -0.202 0.108 0.00 335s [4,] 0.0 0.000 0.000 4616.09 335s [5,] 0.0 0.000 0.000 -35.05 335s [6,] 0.0 0.000 0.000 -10.36 335s [7,] 0.0 0.000 0.000 -9.45 335s supply_price supply_farmPrice supply_trend 335s [1,] 0.0000 0.0000 0.0000 335s [2,] 0.0000 0.0000 0.0000 335s [3,] 0.0000 0.0000 0.0000 335s [4,] -35.0531 -10.3622 -9.4473 335s [5,] 0.3196 0.0300 0.0185 335s [6,] 0.0300 0.0714 0.0441 335s [7,] 0.0185 0.0441 0.3178 335s > 335s BEGIN TEST test_wls.R 335s 335s R version 4.3.2 (2023-10-31) -- "Eye Holes" 335s Copyright (C) 2023 The R Foundation for Statistical Computing 335s Platform: x86_64-pc-linux-gnu (64-bit) 335s 335s R is free software and comes with ABSOLUTELY NO WARRANTY. 335s You are welcome to redistribute it under certain conditions. 335s Type 'license()' or 'licence()' for distribution details. 335s 335s R is a collaborative project with many contributors. 335s Type 'contributors()' for more information and 335s 'citation()' on how to cite R or R packages in publications. 335s 335s Type 'demo()' for some demos, 'help()' for on-line help, or 335s 'help.start()' for an HTML browser interface to help. 335s Type 'q()' to quit R. 335s 335s Loading required package: Matrix 335s > library( systemfit ) 336s Loading required package: car 336s Loading required package: carData 336s Loading required package: lmtest 336s Loading required package: zoo 336s 336s Attaching package: ‘zoo’ 336s 336s The following objects are masked from ‘package:base’: 336s 336s as.Date, as.Date.numeric 336s 336s 336s Please cite the 'systemfit' package as: 336s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 336s 336s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 336s https://r-forge.r-project.org/projects/systemfit/ 336s > options( digits = 3 ) 336s > 336s > data( "Kmenta" ) 336s > useMatrix <- FALSE 336s > 336s > demand <- consump ~ price + income 336s > supply <- consump ~ price + farmPrice + trend 336s > system <- list( demand = demand, supply = supply ) 336s > restrm <- matrix(0,1,7) # restriction matrix "R" 336s > restrm[1,3] <- 1 336s > restrm[1,7] <- -1 336s > restrict <- "demand_income - supply_trend = 0" 336s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 336s > restr2m[1,3] <- 1 336s > restr2m[1,7] <- -1 336s > restr2m[2,2] <- -1 336s > restr2m[2,5] <- 1 336s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 336s > restrict2 <- c( "demand_income - supply_trend = 0", 336s + "- demand_price + supply_price = 0.5" ) 336s > tc <- matrix(0,7,6) 336s > tc[1,1] <- 1 336s > tc[2,2] <- 1 336s > tc[3,3] <- 1 336s > tc[4,4] <- 1 336s > tc[5,5] <- 1 336s > tc[6,6] <- 1 336s > tc[7,3] <- 1 336s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 336s > restr3m[1,2] <- -1 336s > restr3m[1,5] <- 1 336s > restr3q <- c( 0.5 ) # restriction vector "q" 2 336s > restrict3 <- "- C2 + C5 = 0.5" 336s > 336s > 336s > ## ******* single-equation OLS estimations ********************* 336s > lmDemand <- lm( demand, data = Kmenta ) 336s > lmSupply <- lm( supply, data = Kmenta ) 336s > 336s > ## *************** WLS estimation ************************ 336s > fitwls1 <- systemfit( system, "WLS", data = Kmenta, useMatrix = useMatrix ) 336s > print( summary( fitwls1 ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 33 156 4.43 0.709 0.558 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.3 3.73 1.93 0.764 0.736 336s supply 20 16 92.6 5.78 2.40 0.655 0.590 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.73 0.00 336s supply 0.00 5.78 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.73 4.14 336s supply 4.14 5.78 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.891 336s supply 0.891 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 336s price -0.3163 0.0907 -3.49 0.0028 ** 336s income 0.3346 0.0454 7.37 1.1e-06 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.93 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 336s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 336s price 0.1604 0.0949 1.69 0.11039 336s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 336s trend 0.2483 0.0975 2.55 0.02157 * 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.405 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 336s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 336s 336s > all.equal( coef( fitwls1 ), c( coef( lmDemand ), coef( lmSupply ) ), 336s + check.attributes = FALSE ) 336s [1] TRUE 336s > all.equal( coef( summary( fitwls1 ) ), 336s + rbind( coef( summary( lmDemand ) ), coef( summary( lmSupply ) ) ), 336s + check.attributes = FALSE ) 336s [1] TRUE 336s > all.equal( vcov( fitwls1 ), 336s + as.matrix( bdiag( vcov( lmDemand ), vcov( lmSupply ) ) ), 336s + check.attributes = FALSE ) 336s [1] TRUE 336s > 336s > ## *************** WLS estimation (EViews-like) ************************ 336s > fitwls1e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 336s + x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwls1e, useDfSys = TRUE ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 33 156 3.02 0.709 0.537 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.3 3.73 1.93 0.764 0.736 336s supply 20 16 92.6 5.78 2.40 0.655 0.590 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.17 0.00 336s supply 0.00 4.63 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.17 3.41 336s supply 3.41 4.63 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.891 336s supply 0.891 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.8954 6.9325 14.41 8.9e-16 *** 336s price -0.3163 0.0836 -3.78 0.00062 *** 336s income 0.3346 0.0419 7.99 3.2e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.93 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 336s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 58.2754 10.2527 5.68 2.4e-06 *** 336s price 0.1604 0.0849 1.89 0.0676 . 336s farmPrice 0.2481 0.0413 6.01 9.5e-07 *** 336s trend 0.2483 0.0872 2.85 0.0075 ** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.405 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 336s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 336s 336s > all.equal( coef( fitwls1e ), c( coef( lmDemand ), coef( lmSupply ) ), 336s + check.attributes = FALSE ) 336s [1] TRUE 336s > 336s > ## ************** WLS with cross-equation restriction *************** 336s > fitwls2 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 336s + x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwls2 ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 2.35 0.703 0.622 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.8 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.98 2.44 0.643 0.576 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.78 0.00 336s supply 0.00 5.94 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.75 4.48 336s supply 4.48 5.98 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.946 336s supply 0.946 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.6582 7.5640 13.18 6.4e-15 *** 336s price -0.2991 0.0887 -3.37 0.0019 ** 336s income 0.3194 0.0415 7.70 6.0e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.936 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.75 MSE: 3.75 Root MSE: 1.936 336s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.1877 11.3165 4.97 1.9e-05 *** 336s price 0.1643 0.0960 1.71 0.096 . 336s farmPrice 0.2580 0.0451 5.71 2.0e-06 *** 336s trend 0.3194 0.0415 7.70 6.0e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.445 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 95.627 MSE: 5.977 Root MSE: 2.445 336s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 336s 336s > # the same with symbolically specified restrictions 336s > fitwls2Sym <- systemfit( system, "WLS", data = Kmenta, 336s + restrict.matrix = restrict, x = TRUE, 336s + useMatrix = useMatrix ) 336s > all.equal( fitwls2, fitwls2Sym ) 336s [1] "Component “call”: target, current do not match when deparsed" 336s > 336s > ## ************** WLS with cross-equation restriction (EViews-like) ******* 336s > fitwls2e <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 336s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 336s > print( summary( fitwls2e ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 1.61 0.703 0.589 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.8 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.97 2.44 0.644 0.577 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.21 0.00 336s supply 0.00 4.75 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.19 3.69 336s supply 3.69 4.78 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.946 336s supply 0.946 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.6461 6.9734 14.29 6.7e-16 *** 336s price -0.2982 0.0816 -3.65 0.00086 *** 336s income 0.3186 0.0381 8.37 8.9e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.937 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.794 MSE: 3.753 Root MSE: 1.937 336s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.2104 10.1248 5.55 3.3e-06 *** 336s price 0.1642 0.0859 1.91 0.064 . 336s farmPrice 0.2579 0.0404 6.38 2.7e-07 *** 336s trend 0.3186 0.0381 8.37 8.9e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.444 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 95.561 MSE: 5.973 Root MSE: 2.444 336s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 336s 336s > 336s > ## ******* WLS with cross-equation restriction via restrict.regMat ********** 336s > fitwls3 <- systemfit( system,"WLS", data = Kmenta, restrict.regMat = tc, 336s + x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwls3 ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 2.35 0.703 0.622 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.8 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.98 2.44 0.643 0.576 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.78 0.00 336s supply 0.00 5.94 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.75 4.48 336s supply 4.48 5.98 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.946 336s supply 0.946 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.6582 7.5640 13.18 6.4e-15 *** 336s price -0.2991 0.0887 -3.37 0.0019 ** 336s income 0.3194 0.0415 7.70 6.0e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.936 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.75 MSE: 3.75 Root MSE: 1.936 336s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.1877 11.3165 4.97 1.9e-05 *** 336s price 0.1643 0.0960 1.71 0.096 . 336s farmPrice 0.2580 0.0451 5.71 2.0e-06 *** 336s trend 0.3194 0.0415 7.70 6.0e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.445 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 95.627 MSE: 5.977 Root MSE: 2.445 336s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 336s 336s > 336s > ## ******* WLS with cross-equation restriction via restrict.regMat (EViews-like) ***** 336s > fitwls3e <- systemfit( system,"WLS", data = Kmenta, restrict.regMat = tc, 336s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 336s > print( summary( fitwls3e ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 1.61 0.703 0.589 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.8 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.97 2.44 0.644 0.577 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.21 0.00 336s supply 0.00 4.75 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.19 3.69 336s supply 3.69 4.78 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.946 336s supply 0.946 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.6461 6.9734 14.29 6.7e-16 *** 336s price -0.2982 0.0816 -3.65 0.00086 *** 336s income 0.3186 0.0381 8.37 8.9e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.937 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.794 MSE: 3.753 Root MSE: 1.937 336s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.2104 10.1248 5.55 3.3e-06 *** 336s price 0.1642 0.0859 1.91 0.064 . 336s farmPrice 0.2579 0.0404 6.38 2.7e-07 *** 336s trend 0.3186 0.0381 8.37 8.9e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.444 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 95.561 MSE: 5.973 Root MSE: 2.444 336s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 336s 336s > 336s > ## ***** WLS with 2 cross-equation restrictions *************** 336s > fitwls4 <- systemfit( system,"WLS", data = Kmenta, restrict.matrix = restr2m, 336s + restrict.rhs = restr2q, useMatrix = useMatrix ) 336s > print( summary( fitwls4 ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 2.51 0.702 0.619 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.6 3.74 1.94 0.763 0.735 336s supply 20 16 96.3 6.02 2.45 0.641 0.574 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.76 0.00 336s supply 0.00 5.99 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.74 4.47 336s supply 4.47 6.02 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.943 336s supply 0.943 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9138 6.0474 16.69 < 2e-16 *** 336s price -0.3160 0.0648 -4.87 2.3e-05 *** 336s income 0.3238 0.0385 8.42 6.3e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.636 MSE: 3.743 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9416 7.9687 6.77 7.6e-08 *** 336s price 0.1840 0.0648 2.84 0.0075 ** 336s farmPrice 0.2603 0.0446 5.84 1.3e-06 *** 336s trend 0.3238 0.0385 8.42 6.3e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.453 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.268 MSE: 6.017 Root MSE: 2.453 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > # the same with symbolically specified restrictions 336s > fitwls4Sym <- systemfit( system, "WLS", data = Kmenta, 336s + restrict.matrix = restrict2, useMatrix = useMatrix ) 336s > all.equal( fitwls4, fitwls4Sym ) 336s [1] "Component “call”: target, current do not match when deparsed" 336s > 336s > ## ***** WLS with 2 cross-equation restrictions (EViews-like) ********** 336s > fitwls4e <- systemfit( system,"WLS", data = Kmenta, methodResidCov = "noDfCor", 336s + restrict.matrix = restr2m, restrict.rhs = restr2q, 336s + x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwls4e ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 1.72 0.702 0.586 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.7 3.75 1.94 0.763 0.735 336s supply 20 16 96.2 6.01 2.45 0.641 0.574 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.2 0.00 336s supply 0.0 4.79 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.18 3.69 336s supply 3.69 4.81 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.942 336s supply 0.942 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9762 5.5234 18.28 < 2e-16 *** 336s price -0.3160 0.0589 -5.37 5.3e-06 *** 336s income 0.3233 0.0352 9.18 7.6e-11 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.67 MSE: 3.745 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9630 7.2089 7.49 9.1e-09 *** 336s price 0.1840 0.0589 3.13 0.0036 ** 336s farmPrice 0.2602 0.0399 6.53 1.6e-07 *** 336s trend 0.3233 0.0352 9.18 7.6e-11 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.452 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.215 MSE: 6.013 Root MSE: 2.452 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > 336s > ## *********** WLS with 2 cross-equation restrictions via R and restrict.regMat ****** 336s > fitwls5 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restr3m, 336s + restrict.rhs = restr3q, restrict.regMat = tc, 336s + x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwls5 ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 2.51 0.702 0.619 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.6 3.74 1.94 0.763 0.735 336s supply 20 16 96.3 6.02 2.45 0.641 0.574 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.76 0.00 336s supply 0.00 5.99 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.74 4.47 336s supply 4.47 6.02 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.943 336s supply 0.943 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9138 6.0474 16.69 < 2e-16 *** 336s price -0.3160 0.0648 -4.87 2.3e-05 *** 336s income 0.3238 0.0385 8.42 6.3e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.636 MSE: 3.743 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9416 7.9687 6.77 7.6e-08 *** 336s price 0.1840 0.0648 2.84 0.0075 ** 336s farmPrice 0.2603 0.0446 5.84 1.3e-06 *** 336s trend 0.3238 0.0385 8.42 6.3e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.453 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.268 MSE: 6.017 Root MSE: 2.453 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > # the same with symbolically specified restrictions 336s > fitwls5Sym <- systemfit( system, "WLS", data = Kmenta, 336s + restrict.matrix = restrict3, restrict.regMat = tc, 336s + x = TRUE, useMatrix = useMatrix ) 336s > all.equal( fitwls5, fitwls5Sym ) 336s [1] "Component “call”: target, current do not match when deparsed" 336s > 336s > ## *********** WLS with 2 cross-equation restrictions via R and restrict.regMat (EViews-like) 336s > fitwls5e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 336s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 336s + useMatrix = useMatrix ) 336s > print( summary( fitwls5e ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 1.72 0.702 0.586 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.7 3.75 1.94 0.763 0.735 336s supply 20 16 96.2 6.01 2.45 0.641 0.574 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.2 0.00 336s supply 0.0 4.79 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.18 3.69 336s supply 3.69 4.81 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.942 336s supply 0.942 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9762 5.5234 18.28 < 2e-16 *** 336s price -0.3160 0.0589 -5.37 5.3e-06 *** 336s income 0.3233 0.0352 9.18 7.6e-11 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.67 MSE: 3.745 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9630 7.2089 7.49 9.1e-09 *** 336s price 0.1840 0.0589 3.13 0.0036 ** 336s farmPrice 0.2602 0.0399 6.53 1.6e-07 *** 336s trend 0.3233 0.0352 9.18 7.6e-11 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.452 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.215 MSE: 6.013 Root MSE: 2.452 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > 336s > ## *************** iterated WLS estimation ********************* 336s > fitwlsi1 <- systemfit( system, "WLS", data = Kmenta, 336s + maxit = 100, useMatrix = useMatrix ) 336s > print( summary( fitwlsi1, useDfSys = TRUE ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 33 156 4.43 0.709 0.558 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.3 3.73 1.93 0.764 0.736 336s supply 20 16 92.6 5.78 2.40 0.655 0.590 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.73 0.00 336s supply 0.00 5.78 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.73 4.14 336s supply 4.14 5.78 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.891 336s supply 0.891 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.8954 7.5194 13.29 8.4e-15 *** 336s price -0.3163 0.0907 -3.49 0.0014 ** 336s income 0.3346 0.0454 7.37 1.8e-08 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.93 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 336s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 58.2754 11.4629 5.08 1.4e-05 *** 336s price 0.1604 0.0949 1.69 0.100 336s farmPrice 0.2481 0.0462 5.37 6.1e-06 *** 336s trend 0.2483 0.0975 2.55 0.016 * 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.405 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 336s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 336s 336s > 336s > ## *************** iterated WLS estimation (EViews-like) ************ 336s > fitwlsi1e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 336s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwlsi1e, useDfSys = TRUE ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 33 156 3.02 0.709 0.537 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.3 3.73 1.93 0.764 0.736 336s supply 20 16 92.6 5.78 2.40 0.655 0.590 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.17 0.00 336s supply 0.00 4.63 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.17 3.41 336s supply 3.41 4.63 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.891 336s supply 0.891 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.8954 6.9325 14.41 8.9e-16 *** 336s price -0.3163 0.0836 -3.78 0.00062 *** 336s income 0.3346 0.0419 7.99 3.2e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.93 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 336s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 58.2754 10.2527 5.68 2.4e-06 *** 336s price 0.1604 0.0849 1.89 0.0676 . 336s farmPrice 0.2481 0.0413 6.01 9.5e-07 *** 336s trend 0.2483 0.0872 2.85 0.0075 ** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.405 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 336s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 336s 336s > 336s > ## ****** iterated WLS with cross-equation restriction *************** 336s > fitwlsi2 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 336s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwlsi2 ) ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 2.34 0.703 0.623 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.7 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.98 2.44 0.643 0.576 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.75 0.00 336s supply 0.00 5.98 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.75 4.48 336s supply 4.48 5.98 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.946 336s supply 0.946 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.6607 7.5378 13.22 5.8e-15 *** 336s price -0.2993 0.0884 -3.39 0.0018 ** 336s income 0.3196 0.0414 7.72 5.6e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.936 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.741 MSE: 3.749 Root MSE: 1.936 336s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.1830 11.3487 4.95 2.0e-05 *** 336s price 0.1643 0.0963 1.71 0.097 . 336s farmPrice 0.2580 0.0453 5.70 2.1e-06 *** 336s trend 0.3196 0.0414 7.72 5.6e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.445 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 95.641 MSE: 5.978 Root MSE: 2.445 336s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 336s 336s > 336s > ## ****** iterated WLS with cross-equation restriction (EViews-like) ******** 336s > fitwlsi2e <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 336s + methodResidCov = "noDfCor", maxit = 100, useMatrix = useMatrix ) 336s > print( summary( fitwlsi2e ) ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 1.6 0.703 0.589 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.8 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.97 2.44 0.644 0.577 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.19 0.00 336s supply 0.00 4.78 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.19 3.69 336s supply 3.69 4.78 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.946 336s supply 0.946 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.6484 6.9516 14.33 4.4e-16 *** 336s price -0.2984 0.0814 -3.67 0.00083 *** 336s income 0.3188 0.0380 8.39 8.4e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.937 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.785 MSE: 3.752 Root MSE: 1.937 336s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.2061 10.1500 5.54 3.4e-06 *** 336s price 0.1642 0.0861 1.91 0.065 . 336s farmPrice 0.2579 0.0405 6.37 2.9e-07 *** 336s trend 0.3188 0.0380 8.39 8.4e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.444 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 95.573 MSE: 5.973 Root MSE: 2.444 336s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 336s 336s > 336s > ## ******* iterated WLS with cross-equation restriction via restrict.regMat ********** 336s > fitwlsi3 <- systemfit( system, "WLS", data = Kmenta, restrict.regMat = tc, 336s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwlsi3 ) ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 2.34 0.703 0.623 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.7 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.98 2.44 0.643 0.576 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.75 0.00 336s supply 0.00 5.98 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.75 4.48 336s supply 4.48 5.98 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.946 336s supply 0.946 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.6607 7.5378 13.22 5.8e-15 *** 336s price -0.2993 0.0884 -3.39 0.0018 ** 336s income 0.3196 0.0414 7.72 5.6e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.936 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.741 MSE: 3.749 Root MSE: 1.936 336s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.1830 11.3487 4.95 2.0e-05 *** 336s price 0.1643 0.0963 1.71 0.097 . 336s farmPrice 0.2580 0.0453 5.70 2.1e-06 *** 336s trend 0.3196 0.0414 7.72 5.6e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.445 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 95.641 MSE: 5.978 Root MSE: 2.445 336s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 336s 336s > 336s > ## ******* iterated WLS with cross-equation restriction via restrict.regMat (EViews-like) *** 336s > fitwlsi3e <- systemfit( system, "WLS", data = Kmenta, restrict.regMat = tc, 336s + methodResidCov = "noDfCor", maxit = 100, useMatrix = useMatrix ) 336s > print( summary( fitwlsi3e ) ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 1.6 0.703 0.589 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.8 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.97 2.44 0.644 0.577 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.19 0.00 336s supply 0.00 4.78 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.19 3.69 336s supply 3.69 4.78 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.946 336s supply 0.946 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.6484 6.9516 14.33 4.4e-16 *** 336s price -0.2984 0.0814 -3.67 0.00083 *** 336s income 0.3188 0.0380 8.39 8.4e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.937 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.785 MSE: 3.752 Root MSE: 1.937 336s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.2061 10.1500 5.54 3.4e-06 *** 336s price 0.1642 0.0861 1.91 0.065 . 336s farmPrice 0.2579 0.0405 6.37 2.9e-07 *** 336s trend 0.3188 0.0380 8.39 8.4e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.444 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 95.573 MSE: 5.973 Root MSE: 2.444 336s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 336s 336s > nobs( fitwlsi3e ) 336s [1] 40 336s > 336s > ## ******* iterated WLS with 2 cross-equation restrictions *********** 336s > fitwlsi4 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restr2m, 336s + restrict.rhs = restr2q, maxit = 100, useMatrix = useMatrix ) 336s > print( summary( fitwlsi4 ) ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 2.51 0.702 0.619 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.6 3.74 1.94 0.763 0.735 336s supply 20 16 96.3 6.02 2.45 0.641 0.574 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.74 0.00 336s supply 0.00 6.02 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.74 4.47 336s supply 4.47 6.02 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.943 336s supply 0.943 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9031 6.0396 16.71 < 2e-16 *** 336s price -0.3159 0.0648 -4.88 2.3e-05 *** 336s income 0.3239 0.0384 8.43 6.0e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.63 MSE: 3.743 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9379 7.9718 6.77 7.7e-08 *** 336s price 0.1841 0.0648 2.84 0.0075 ** 336s farmPrice 0.2603 0.0447 5.83 1.3e-06 *** 336s trend 0.3239 0.0384 8.43 6.0e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.453 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.277 MSE: 6.017 Root MSE: 2.453 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > 336s > ## ******* iterated WLS with 2 cross-equation restrictions (EViews-like) ***** 336s > fitwlsi4e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 336s + restrict.matrix = restr2m, restrict.rhs = restr2q, maxit = 100, 336s + x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwlsi4e ) ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 1.72 0.702 0.586 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.7 3.75 1.94 0.763 0.735 336s supply 20 16 96.2 6.01 2.45 0.641 0.574 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.18 0.00 336s supply 0.00 4.81 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.18 3.69 336s supply 3.69 4.81 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.942 336s supply 0.942 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9662 5.5170 18.30 < 2e-16 *** 336s price -0.3160 0.0589 -5.37 5.2e-06 *** 336s income 0.3234 0.0352 9.20 7.3e-11 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.665 MSE: 3.745 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9595 7.2114 7.48 9.2e-09 *** 336s price 0.1840 0.0589 3.13 0.0036 ** 336s farmPrice 0.2602 0.0400 6.51 1.6e-07 *** 336s trend 0.3234 0.0352 9.20 7.3e-11 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.452 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.223 MSE: 6.014 Root MSE: 2.452 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > 336s > ## ***** iterated WLS with 2 cross-equation restrictions via R and restrict.regMat ****** 336s > fitwlsi5 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restr3m, 336s + restrict.rhs = restr3q, restrict.regMat = tc, maxit = 100, 336s + x = TRUE, useMatrix = useMatrix ) 336s > print( summary( fitwlsi5 ) ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 2.51 0.702 0.619 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.6 3.74 1.94 0.763 0.735 336s supply 20 16 96.3 6.02 2.45 0.641 0.574 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.74 0.00 336s supply 0.00 6.02 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.74 4.47 336s supply 4.47 6.02 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.943 336s supply 0.943 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9031 6.0396 16.71 < 2e-16 *** 336s price -0.3159 0.0648 -4.88 2.3e-05 *** 336s income 0.3239 0.0384 8.43 6.0e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.63 MSE: 3.743 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9379 7.9718 6.77 7.7e-08 *** 336s price 0.1841 0.0648 2.84 0.0075 ** 336s farmPrice 0.2603 0.0447 5.83 1.3e-06 *** 336s trend 0.3239 0.0384 8.43 6.0e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.453 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.277 MSE: 6.017 Root MSE: 2.453 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > 336s > ## *** iterated WLS with 2 cross-equation restrictions via R and restrict.regMat (EViews-like) 336s > fitwlsi5e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 336s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 336s + maxit = 100, useMatrix = useMatrix ) 336s > print( summary( fitwlsi5e ) ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 1.72 0.702 0.586 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.7 3.75 1.94 0.763 0.735 336s supply 20 16 96.2 6.01 2.45 0.641 0.574 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.18 0.00 336s supply 0.00 4.81 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.18 3.69 336s supply 3.69 4.81 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.942 336s supply 0.942 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9662 5.5170 18.30 < 2e-16 *** 336s price -0.3160 0.0589 -5.37 5.2e-06 *** 336s income 0.3234 0.0352 9.20 7.3e-11 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.665 MSE: 3.745 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9595 7.2114 7.48 9.2e-09 *** 336s price 0.1840 0.0589 3.13 0.0036 ** 336s farmPrice 0.2602 0.0400 6.51 1.6e-07 *** 336s trend 0.3234 0.0352 9.20 7.3e-11 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.452 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.223 MSE: 6.014 Root MSE: 2.452 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > 336s > 336s > ## *********** estimations with a single regressor ************ 336s > fitwlsS1 <- systemfit( 336s + list( consump ~ price - 1, consump ~ price + trend ), "WLS", 336s + data = Kmenta, useMatrix = useMatrix ) 336s > print( summary( fitwlsS1 ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 36 1121 484 -1.09 -1.05 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s eq1 20 19 861 45.3 6.73 -2.213 -2.213 336s eq2 20 17 259 15.3 3.91 0.032 -0.082 336s 336s The covariance matrix of the residuals used for estimation 336s eq1 eq2 336s eq1 45.3 0.0 336s eq2 0.0 15.3 336s 336s The covariance matrix of the residuals 336s eq1 eq2 336s eq1 45.3 14.4 336s eq2 14.4 15.3 336s 336s The correlations of the residuals 336s eq1 eq2 336s eq1 1.000 0.549 336s eq2 0.549 1.000 336s 336s 336s WLS estimates for 'eq1' (equation 1) 336s Model Formula: consump ~ price - 1 336s 336s Estimate Std. Error t value Pr(>|t|) 336s price 1.006 0.015 66.9 <2e-16 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 6.733 on 19 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 19 336s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 336s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 336s 336s 336s WLS estimates for 'eq2' (equation 2) 336s Model Formula: consump ~ price + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 93.6767 15.2367 6.15 1.1e-05 *** 336s price 0.0622 0.1513 0.41 0.69 336s trend 0.0953 0.1515 0.63 0.54 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 3.907 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 259.497 MSE: 15.265 Root MSE: 3.907 336s Multiple R-Squared: 0.032 Adjusted R-Squared: -0.082 336s 336s > fitwlsS2 <- systemfit( 336s + list( consump ~ price - 1, consump ~ trend - 1 ), "WLS", 336s + data = Kmenta, useMatrix = useMatrix ) 336s > print( summary( fitwlsS2 ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 38 47370 110957 -87.3 -5.28 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s eq1 20 19 861 45.3 6.73 -2.21 -2.21 336s eq2 20 19 46509 2447.8 49.48 -172.47 -172.47 336s 336s The covariance matrix of the residuals used for estimation 336s eq1 eq2 336s eq1 45.3 0 336s eq2 0.0 2448 336s 336s The covariance matrix of the residuals 336s eq1 eq2 336s eq1 45.34 -5.15 336s eq2 -5.15 2447.84 336s 336s The correlations of the residuals 336s eq1 eq2 336s eq1 1.0000 -0.0439 336s eq2 -0.0439 1.0000 336s 336s 336s WLS estimates for 'eq1' (equation 1) 336s Model Formula: consump ~ price - 1 336s 336s Estimate Std. Error t value Pr(>|t|) 336s price 1.006 0.015 66.9 <2e-16 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 6.733 on 19 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 19 336s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 336s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 336s 336s 336s WLS estimates for 'eq2' (equation 2) 336s Model Formula: consump ~ trend - 1 336s 336s Estimate Std. Error t value Pr(>|t|) 336s trend 7.405 0.924 8.02 1.6e-07 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 49.476 on 19 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 19 336s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 336s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 336s 336s > fitwlsS3 <- systemfit( 336s + list( consump ~ trend - 1, price ~ trend - 1 ), "WLS", 336s + data = Kmenta, useMatrix = useMatrix ) 336s > print( summary( fitwlsS3 ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 38 93537 108970 -99 -0.977 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s eq1 20 19 46509 2448 49.5 -172.5 -172.5 336s eq2 20 19 47028 2475 49.8 -69.5 -69.5 336s 336s The covariance matrix of the residuals used for estimation 336s eq1 eq2 336s eq1 2448 0 336s eq2 0 2475 336s 336s The covariance matrix of the residuals 336s eq1 eq2 336s eq1 2448 2439 336s eq2 2439 2475 336s 336s The correlations of the residuals 336s eq1 eq2 336s eq1 1.000 0.988 336s eq2 0.988 1.000 336s 336s 336s WLS estimates for 'eq1' (equation 1) 336s Model Formula: consump ~ trend - 1 336s 336s Estimate Std. Error t value Pr(>|t|) 336s trend 7.405 0.924 8.02 1.6e-07 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 49.476 on 19 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 19 336s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 336s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 336s 336s 336s WLS estimates for 'eq2' (equation 2) 336s Model Formula: price ~ trend - 1 336s 336s Estimate Std. Error t value Pr(>|t|) 336s trend 7.318 0.929 7.88 2.1e-07 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 49.751 on 19 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 19 336s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 336s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 336s 336s > fitwlsS4 <- systemfit( 336s + list( consump ~ trend - 1, price ~ trend - 1 ), "WLS", 336s + data = Kmenta, restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), 336s + useMatrix = useMatrix ) 336s > print( summary( fitwlsS4 ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 39 93548 111736 -99 -1.03 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s eq1 20 19 46514 2448 49.5 -172.5 -172.5 336s eq2 20 19 47034 2475 49.8 -69.5 -69.5 336s 336s The covariance matrix of the residuals used for estimation 336s eq1 eq2 336s eq1 2448 0 336s eq2 0 2475 336s 336s The covariance matrix of the residuals 336s eq1 eq2 336s eq1 2448 2439 336s eq2 2439 2475 336s 336s The correlations of the residuals 336s eq1 eq2 336s eq1 1.000 0.988 336s eq2 0.988 1.000 336s 336s 336s WLS estimates for 'eq1' (equation 1) 336s Model Formula: consump ~ trend - 1 336s 336s Estimate Std. Error t value Pr(>|t|) 336s trend 7.362 0.655 11.2 8.4e-14 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 49.478 on 19 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 19 336s SSR: 46514.224 MSE: 2448.117 Root MSE: 49.478 336s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 336s 336s 336s WLS estimates for 'eq2' (equation 2) 336s Model Formula: price ~ trend - 1 336s 336s Estimate Std. Error t value Pr(>|t|) 336s trend 7.362 0.655 11.2 8.4e-14 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 49.754 on 19 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 19 336s SSR: 47033.528 MSE: 2475.449 Root MSE: 49.754 336s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 336s 336s > fitwlsS5 <- systemfit( 336s + list( consump ~ 1, price ~ 1 ), "WLS", 336s + data = Kmenta, useMatrix = useMatrix ) 336s > print( summary( fitwlsS5) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 38 935 491 0 0 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s eq1 20 19 268 14.1 3.76 0 0 336s eq2 20 19 667 35.1 5.93 0 0 336s 336s The covariance matrix of the residuals used for estimation 336s eq1 eq2 336s eq1 14.1 0.0 336s eq2 0.0 35.1 336s 336s The covariance matrix of the residuals 336s eq1 eq2 336s eq1 14.11 2.18 336s eq2 2.18 35.12 336s 336s The correlations of the residuals 336s eq1 eq2 336s eq1 1.0000 0.0981 336s eq2 0.0981 1.0000 336s 336s 336s WLS estimates for 'eq1' (equation 1) 336s Model Formula: consump ~ 1 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.90 0.84 120 <2e-16 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 3.756 on 19 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 19 336s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 336s Multiple R-Squared: 0 Adjusted R-Squared: 0 336s 336s 336s WLS estimates for 'eq2' (equation 2) 336s Model Formula: price ~ 1 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.02 1.33 75.5 <2e-16 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 5.926 on 19 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 19 336s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 336s Multiple R-Squared: 0 Adjusted R-Squared: 0 336s 336s > 336s > 336s > ## **************** shorter summaries ********************** 336s > print( summary( fitwls1 ), residCov = FALSE, equations = FALSE ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 33 156 4.43 0.709 0.558 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.3 3.73 1.93 0.764 0.736 336s supply 20 16 92.6 5.78 2.40 0.655 0.590 336s 336s 336s Coefficients: 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 336s demand_price -0.3163 0.0907 -3.49 0.00282 ** 336s demand_income 0.3346 0.0454 7.37 1.1e-06 *** 336s supply_(Intercept) 58.2754 11.4629 5.08 0.00011 *** 336s supply_price 0.1604 0.0949 1.69 0.11039 336s supply_farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 336s supply_trend 0.2483 0.0975 2.55 0.02157 * 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s > 336s > print( summary( fitwls2e, useDfSys = FALSE, residCov = FALSE ), 336s + equations = FALSE ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 1.61 0.703 0.589 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.8 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.97 2.44 0.644 0.577 336s 336s 336s Coefficients: 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 99.6461 6.9734 14.29 6.7e-11 *** 336s demand_price -0.2982 0.0816 -3.65 0.002 ** 336s demand_income 0.3186 0.0381 8.37 2.0e-07 *** 336s supply_(Intercept) 56.2104 10.1248 5.55 4.4e-05 *** 336s supply_price 0.1642 0.0859 1.91 0.074 . 336s supply_farmPrice 0.2579 0.0404 6.38 9.1e-06 *** 336s supply_trend 0.3186 0.0381 8.37 3.1e-07 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s > 336s > print( summary( fitwls3 ), residCov = FALSE ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 2.35 0.703 0.622 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.8 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.98 2.44 0.643 0.576 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.6582 7.5640 13.18 6.4e-15 *** 336s price -0.2991 0.0887 -3.37 0.0019 ** 336s income 0.3194 0.0415 7.70 6.0e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.936 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.75 MSE: 3.75 Root MSE: 1.936 336s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.1877 11.3165 4.97 1.9e-05 *** 336s price 0.1643 0.0960 1.71 0.096 . 336s farmPrice 0.2580 0.0451 5.71 2.0e-06 *** 336s trend 0.3194 0.0415 7.70 6.0e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.445 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 95.627 MSE: 5.977 Root MSE: 2.445 336s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 336s 336s > 336s > print( summary( fitwls4e, residCov = FALSE, equations = FALSE ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 1.72 0.702 0.586 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.7 3.75 1.94 0.763 0.735 336s supply 20 16 96.2 6.01 2.45 0.641 0.574 336s 336s 336s Coefficients: 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 100.9762 5.5234 18.28 < 2e-16 *** 336s demand_price -0.3160 0.0589 -5.37 5.3e-06 *** 336s demand_income 0.3233 0.0352 9.18 7.6e-11 *** 336s supply_(Intercept) 53.9630 7.2089 7.49 9.1e-09 *** 336s supply_price 0.1840 0.0589 3.13 0.0036 ** 336s supply_farmPrice 0.2602 0.0399 6.53 1.6e-07 *** 336s supply_trend 0.3233 0.0352 9.18 7.6e-11 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s > 336s > print( summary( fitwls5, useDfSys = FALSE ), residCov = FALSE ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 2.51 0.702 0.619 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.6 3.74 1.94 0.763 0.735 336s supply 20 16 96.3 6.02 2.45 0.641 0.574 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9138 6.0474 16.69 5.6e-12 *** 336s price -0.3160 0.0648 -4.87 0.00014 *** 336s income 0.3238 0.0385 8.42 1.8e-07 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.636 MSE: 3.743 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9416 7.9687 6.77 4.5e-06 *** 336s price 0.1840 0.0648 2.84 0.012 * 336s farmPrice 0.2603 0.0446 5.84 2.5e-05 *** 336s trend 0.3238 0.0385 8.42 2.9e-07 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.453 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.268 MSE: 6.017 Root MSE: 2.453 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > 336s > print( summary( fitwlsi1e, useDfSys = TRUE, equations = FALSE ) ) 336s 336s systemfit results 336s method: WLS 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 33 156 3.02 0.709 0.537 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.3 3.73 1.93 0.764 0.736 336s supply 20 16 92.6 5.78 2.40 0.655 0.590 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.17 0.00 336s supply 0.00 4.63 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.17 3.41 336s supply 3.41 4.63 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.891 336s supply 0.891 1.000 336s 336s 336s Coefficients: 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 99.8954 6.9325 14.41 8.9e-16 *** 336s demand_price -0.3163 0.0836 -3.78 0.00062 *** 336s demand_income 0.3346 0.0419 7.99 3.2e-09 *** 336s supply_(Intercept) 58.2754 10.2527 5.68 2.4e-06 *** 336s supply_price 0.1604 0.0849 1.89 0.06762 . 336s supply_farmPrice 0.2481 0.0413 6.01 9.5e-07 *** 336s supply_trend 0.2483 0.0872 2.85 0.00754 ** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s > 336s > print( summary( fitwlsi2, equations = FALSE, residCov = FALSE ), 336s + residCov = TRUE ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 2.34 0.703 0.623 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.7 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.98 2.44 0.643 0.576 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.75 0.00 336s supply 0.00 5.98 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.75 4.48 336s supply 4.48 5.98 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.946 336s supply 0.946 1.000 336s 336s 336s Coefficients: 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 99.6607 7.5378 13.22 5.8e-15 *** 336s demand_price -0.2993 0.0884 -3.39 0.0018 ** 336s demand_income 0.3196 0.0414 7.72 5.6e-09 *** 336s supply_(Intercept) 56.1830 11.3487 4.95 2.0e-05 *** 336s supply_price 0.1643 0.0963 1.71 0.0972 . 336s supply_farmPrice 0.2580 0.0453 5.70 2.1e-06 *** 336s supply_trend 0.3196 0.0414 7.72 5.6e-09 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s > 336s > print( summary( fitwlsi3e ), equations = FALSE, residCov = FALSE ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 34 159 1.6 0.703 0.589 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.8 3.75 1.94 0.762 0.734 336s supply 20 16 95.6 5.97 2.44 0.644 0.577 336s 336s 336s Coefficients: 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 99.6484 6.9516 14.33 4.4e-16 *** 336s demand_price -0.2984 0.0814 -3.67 0.00083 *** 336s demand_income 0.3188 0.0380 8.39 8.4e-10 *** 336s supply_(Intercept) 56.2061 10.1500 5.54 3.4e-06 *** 336s supply_price 0.1642 0.0861 1.91 0.06502 . 336s supply_farmPrice 0.2579 0.0405 6.37 2.9e-07 *** 336s supply_trend 0.3188 0.0380 8.39 8.4e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s > 336s > print( summary( fitwlsi4, equations = FALSE ), equations = TRUE ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 2.51 0.702 0.619 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.6 3.74 1.94 0.763 0.735 336s supply 20 16 96.3 6.02 2.45 0.641 0.574 336s 336s The covariance matrix of the residuals used for estimation 336s demand supply 336s demand 3.74 0.00 336s supply 0.00 6.02 336s 336s The covariance matrix of the residuals 336s demand supply 336s demand 3.74 4.47 336s supply 4.47 6.02 336s 336s The correlations of the residuals 336s demand supply 336s demand 1.000 0.943 336s supply 0.943 1.000 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9031 6.0396 16.71 < 2e-16 *** 336s price -0.3159 0.0648 -4.88 2.3e-05 *** 336s income 0.3239 0.0384 8.43 6.0e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.63 MSE: 3.743 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9379 7.9718 6.77 7.7e-08 *** 336s price 0.1841 0.0648 2.84 0.0075 ** 336s farmPrice 0.2603 0.0447 5.83 1.3e-06 *** 336s trend 0.3239 0.0384 8.43 6.0e-10 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.453 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.277 MSE: 6.017 Root MSE: 2.453 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > 336s > print( summary( fitwlsi5e, useDfSys = FALSE, residCov = FALSE ) ) 336s 336s systemfit results 336s method: iterated WLS 336s 336s convergence achieved after 3 iterations 336s 336s N DF SSR detRCov OLS-R2 McElroy-R2 336s system 40 35 160 1.72 0.702 0.586 336s 336s N DF SSR MSE RMSE R2 Adj R2 336s demand 20 17 63.7 3.75 1.94 0.763 0.735 336s supply 20 16 96.2 6.01 2.45 0.641 0.574 336s 336s 336s WLS estimates for 'demand' (equation 1) 336s Model Formula: consump ~ price + income 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.9662 5.5170 18.30 1.3e-12 *** 336s price -0.3160 0.0589 -5.37 5.1e-05 *** 336s income 0.3234 0.0352 9.20 5.2e-08 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 1.935 on 17 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 17 336s SSR: 63.665 MSE: 3.745 Root MSE: 1.935 336s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 336s 336s 336s WLS estimates for 'supply' (equation 2) 336s Model Formula: consump ~ price + farmPrice + trend 336s 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.9595 7.2114 7.48 1.3e-06 *** 336s price 0.1840 0.0589 3.13 0.0065 ** 336s farmPrice 0.2602 0.0400 6.51 7.2e-06 *** 336s trend 0.3234 0.0352 9.20 8.7e-08 *** 336s --- 336s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 336s 336s Residual standard error: 2.452 on 16 degrees of freedom 336s Number of observations: 20 Degrees of Freedom: 16 336s SSR: 96.223 MSE: 6.014 Root MSE: 2.452 336s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 336s 336s > 336s > 336s > ## ****************** residuals ************************** 336s > print( residuals( fitwls1 ) ) 336s demand supply 336s 1 1.074 -0.444 336s 2 -0.390 -0.896 336s 3 2.625 1.965 336s 4 1.802 1.134 336s 5 1.946 1.514 336s 6 1.175 0.680 336s 7 1.530 1.569 336s 8 -2.933 -4.407 336s 9 -1.365 -2.599 336s 10 2.031 2.469 336s 11 -0.149 -0.598 336s 12 -1.954 -1.697 336s 13 -1.121 -1.064 336s 14 -0.220 0.970 336s 15 1.487 3.159 336s 16 -3.701 -3.866 336s 17 -1.273 -0.265 336s 18 -2.002 -2.449 336s 19 1.738 3.110 336s 20 -0.299 1.714 336s > print( residuals( fitwls1$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 336s -0.444 -0.896 1.965 1.134 1.514 0.680 1.569 -4.407 -2.599 2.469 -0.598 336s 12 13 14 15 16 17 18 19 20 336s -1.697 -1.064 0.970 3.159 -3.866 -0.265 -2.449 3.110 1.714 336s > 336s > print( residuals( fitwls2e ) ) 336s demand supply 336s 1 0.9069 0.209 336s 2 -0.4660 -0.338 336s 3 2.5495 2.455 336s 4 1.7320 1.560 336s 5 2.0183 1.771 336s 6 1.2321 0.886 336s 7 1.6019 1.724 336s 8 -2.8544 -4.378 336s 9 -1.3158 -2.597 336s 10 2.0517 2.500 336s 11 -0.3823 -0.455 336s 12 -2.2623 -1.525 336s 13 -1.3801 -1.001 336s 14 -0.3081 0.877 336s 15 1.6643 2.806 336s 16 -3.5513 -4.328 336s 17 -1.0466 -0.805 336s 18 -1.9647 -2.952 336s 19 1.8446 2.561 336s 20 -0.0697 1.029 336s > print( residuals( fitwls2e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 336s 0.9069 -0.4660 2.5495 1.7320 2.0183 1.2321 1.6019 -2.8544 -1.3158 2.0517 336s 11 12 13 14 15 16 17 18 19 20 336s -0.3823 -2.2623 -1.3801 -0.3081 1.6643 -3.5513 -1.0466 -1.9647 1.8446 -0.0697 336s > 336s > print( residuals( fitwls3 ) ) 336s demand supply 336s 1 0.9150 0.217 336s 2 -0.4624 -0.332 336s 3 2.5532 2.461 336s 4 1.7354 1.564 336s 5 2.0148 1.773 336s 6 1.2293 0.889 336s 7 1.5984 1.725 336s 8 -2.8582 -4.378 336s 9 -1.3182 -2.597 336s 10 2.0507 2.500 336s 11 -0.3710 -0.453 336s 12 -2.2473 -1.524 336s 13 -1.3675 -1.000 336s 14 -0.3038 0.876 336s 15 1.6557 2.802 336s 16 -3.5586 -4.333 336s 17 -1.0576 -0.811 336s 18 -1.9666 -2.957 336s 19 1.8394 2.555 336s 20 -0.0808 1.022 336s > print( residuals( fitwls3$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 336s 0.217 -0.332 2.461 1.564 1.773 0.889 1.725 -4.378 -2.597 2.500 -0.453 336s 12 13 14 15 16 17 18 19 20 336s -1.524 -1.000 0.876 2.802 -4.333 -0.811 -2.957 2.555 1.022 336s > 336s > print( residuals( fitwls4e ) ) 336s demand supply 336s 1 0.9593 0.244 336s 2 -0.3907 -0.388 336s 3 2.6143 2.417 336s 4 1.8088 1.498 336s 5 1.9718 1.803 336s 6 1.2083 0.892 336s 7 1.5943 1.699 336s 8 -2.8174 -4.491 336s 9 -1.3751 -2.548 336s 10 1.9351 2.667 336s 11 -0.4019 -0.284 336s 12 -2.1883 -1.443 336s 13 -1.2686 -1.010 336s 14 -0.2984 0.921 336s 15 1.5512 2.869 336s 16 -3.6143 -4.342 336s 17 -1.2823 -0.600 336s 18 -1.9253 -3.056 336s 19 1.8860 2.425 336s 20 0.0333 0.728 336s > print( residuals( fitwls4e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 336s 0.9593 -0.3907 2.6143 1.8088 1.9718 1.2083 1.5943 -2.8174 -1.3751 1.9351 336s 11 12 13 14 15 16 17 18 19 20 336s -0.4019 -2.1883 -1.2686 -0.2984 1.5512 -3.6143 -1.2823 -1.9253 1.8860 0.0333 336s > 336s > print( residuals( fitwls5 ) ) 336s demand supply 336s 1 0.9649 0.249 336s 2 -0.3911 -0.384 336s 3 2.6145 2.421 336s 4 1.8081 1.501 336s 5 1.9707 1.805 336s 6 1.2067 0.893 336s 7 1.5910 1.700 336s 8 -2.8235 -4.491 336s 9 -1.3743 -2.548 336s 10 1.9406 2.667 336s 11 -0.3887 -0.282 336s 12 -2.1767 -1.442 336s 13 -1.2616 -1.009 336s 14 -0.2944 0.920 336s 15 1.5485 2.866 336s 16 -3.6185 -4.345 336s 17 -1.2806 -0.604 336s 18 -1.9295 -3.060 336s 19 1.8782 2.420 336s 20 0.0157 0.721 336s > print( residuals( fitwls5$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 336s 0.249 -0.384 2.421 1.501 1.805 0.893 1.700 -4.491 -2.548 2.667 -0.282 336s 12 13 14 15 16 17 18 19 20 336s -1.442 -1.009 0.920 2.866 -4.345 -0.604 -3.060 2.420 0.721 336s > 336s > print( residuals( fitwlsi1e ) ) 336s demand supply 336s 1 1.074 -0.444 336s 2 -0.390 -0.896 336s 3 2.625 1.965 336s 4 1.802 1.134 336s 5 1.946 1.514 336s 6 1.175 0.680 336s 7 1.530 1.569 336s 8 -2.933 -4.407 336s 9 -1.365 -2.599 336s 10 2.031 2.469 336s 11 -0.149 -0.598 336s 12 -1.954 -1.697 336s 13 -1.121 -1.064 336s 14 -0.220 0.970 336s 15 1.487 3.159 336s 16 -3.701 -3.866 336s 17 -1.273 -0.265 336s 18 -2.002 -2.449 336s 19 1.738 3.110 336s 20 -0.299 1.714 336s > print( residuals( fitwlsi1e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 336s 1.074 -0.390 2.625 1.802 1.946 1.175 1.530 -2.933 -1.365 2.031 -0.149 336s 12 13 14 15 16 17 18 19 20 336s -1.954 -1.121 -0.220 1.487 -3.701 -1.273 -2.002 1.738 -0.299 336s > 336s > print( residuals( fitwlsi2 ) ) 336s demand supply 336s 1 0.9167 0.218 336s 2 -0.4616 -0.331 336s 3 2.5539 2.462 336s 4 1.7361 1.565 336s 5 2.0140 1.774 336s 6 1.2288 0.889 336s 7 1.5977 1.726 336s 8 -2.8589 -4.378 336s 9 -1.3187 -2.597 336s 10 2.0505 2.500 336s 11 -0.3686 -0.453 336s 12 -2.2443 -1.523 336s 13 -1.3649 -1.000 336s 14 -0.3029 0.876 336s 15 1.6539 2.802 336s 16 -3.5601 -4.334 336s 17 -1.0599 -0.812 336s 18 -1.9669 -2.958 336s 19 1.8383 2.554 336s 20 -0.0831 1.020 336s > print( residuals( fitwlsi2$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 336s 0.218 -0.331 2.462 1.565 1.774 0.889 1.726 -4.378 -2.597 2.500 -0.453 336s 12 13 14 15 16 17 18 19 20 336s -1.523 -1.000 0.876 2.802 -4.334 -0.812 -2.958 2.554 1.020 336s > 336s > print( residuals( fitwlsi3e ) ) 336s demand supply 336s 1 0.9084 0.211 336s 2 -0.4653 -0.337 336s 3 2.5502 2.456 336s 4 1.7326 1.561 336s 5 2.0176 1.771 336s 6 1.2316 0.887 336s 7 1.6012 1.724 336s 8 -2.8551 -4.378 336s 9 -1.3162 -2.597 336s 10 2.0515 2.500 336s 11 -0.3801 -0.454 336s 12 -2.2594 -1.525 336s 13 -1.3777 -1.001 336s 14 -0.3073 0.877 336s 15 1.6627 2.806 336s 16 -3.5527 -4.329 336s 17 -1.0487 -0.806 336s 18 -1.9651 -2.953 336s 19 1.8436 2.560 336s 20 -0.0718 1.028 336s > print( residuals( fitwlsi3e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 336s 0.9084 -0.4653 2.5502 1.7326 2.0176 1.2316 1.6012 -2.8551 -1.3162 2.0515 336s 11 12 13 14 15 16 17 18 19 20 336s -0.3801 -2.2594 -1.3777 -0.3073 1.6627 -3.5527 -1.0487 -1.9651 1.8436 -0.0718 336s > 336s > print( residuals( fitwlsi4 ) ) 336s demand supply 336s 1 0.9659 0.250 336s 2 -0.3911 -0.383 336s 3 2.6145 2.421 336s 4 1.8080 1.502 336s 5 1.9705 1.805 336s 6 1.2064 0.893 336s 7 1.5905 1.700 336s 8 -2.8246 -4.491 336s 9 -1.3742 -2.547 336s 10 1.9415 2.667 336s 11 -0.3865 -0.282 336s 12 -2.1747 -1.442 336s 13 -1.2604 -1.009 336s 14 -0.2938 0.920 336s 15 1.5480 2.866 336s 16 -3.6192 -4.346 336s 17 -1.2804 -0.604 336s 18 -1.9302 -3.061 336s 19 1.8768 2.420 336s 20 0.0127 0.720 336s > print( residuals( fitwlsi4$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 336s 0.250 -0.383 2.421 1.502 1.805 0.893 1.700 -4.491 -2.547 2.667 -0.282 336s 12 13 14 15 16 17 18 19 20 336s -1.442 -1.009 0.920 2.866 -4.346 -0.604 -3.061 2.420 0.720 336s > 336s > print( residuals( fitwlsi5e ) ) 336s demand supply 336s 1 0.9602 0.245 336s 2 -0.3908 -0.388 336s 3 2.6143 2.418 336s 4 1.8087 1.498 336s 5 1.9716 1.803 336s 6 1.2081 0.892 336s 7 1.5938 1.699 336s 8 -2.8184 -4.491 336s 9 -1.3750 -2.548 336s 10 1.9360 2.667 336s 11 -0.3997 -0.284 336s 12 -2.1865 -1.443 336s 13 -1.2675 -1.010 336s 14 -0.2978 0.921 336s 15 1.5508 2.869 336s 16 -3.6150 -4.342 336s 17 -1.2820 -0.601 336s 18 -1.9260 -3.057 336s 19 1.8848 2.424 336s 20 0.0305 0.727 336s > print( residuals( fitwlsi5e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 336s 0.9602 -0.3908 2.6143 1.8087 1.9716 1.2081 1.5938 -2.8184 -1.3750 1.9360 336s 11 12 13 14 15 16 17 18 19 20 336s -0.3997 -2.1865 -1.2675 -0.2978 1.5508 -3.6150 -1.2820 -1.9260 1.8848 0.0305 336s > 336s > 336s > ## *************** coefficients ********************* 336s > print( round( coef( fitwls1e ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income supply_(Intercept) 336s 99.895 -0.316 0.335 58.275 336s supply_price supply_farmPrice supply_trend 336s 0.160 0.248 0.248 336s > print( round( coef( fitwls1e$eq[[ 1 ]] ), digits = 6 ) ) 336s (Intercept) price income 336s 99.895 -0.316 0.335 336s > 336s > print( round( coef( fitwlsi2 ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income supply_(Intercept) 336s 99.661 -0.299 0.320 56.183 336s supply_price supply_farmPrice supply_trend 336s 0.164 0.258 0.320 336s > print( round( coef( fitwlsi2$eq[[ 2 ]] ), digits = 6 ) ) 336s (Intercept) price farmPrice trend 336s 56.183 0.164 0.258 0.320 336s > 336s > print( round( coef( fitwls3e ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income supply_(Intercept) 336s 99.646 -0.298 0.319 56.210 336s supply_price supply_farmPrice supply_trend 336s 0.164 0.258 0.319 336s > print( round( coef( fitwls3e, modified.regMat = TRUE ), digits = 6 ) ) 336s C1 C2 C3 C4 C5 C6 336s 99.646 -0.298 0.319 56.210 0.164 0.258 336s > print( round( coef( fitwls3e$eq[[ 1 ]] ), digits = 6 ) ) 336s (Intercept) price income 336s 99.646 -0.298 0.319 336s > 336s > print( round( coef( fitwls4 ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income supply_(Intercept) 336s 100.914 -0.316 0.324 53.942 336s supply_price supply_farmPrice supply_trend 336s 0.184 0.260 0.324 336s > print( round( coef( fitwls4$eq[[ 2 ]] ), digits = 6 ) ) 336s (Intercept) price farmPrice trend 336s 53.942 0.184 0.260 0.324 336s > 336s > print( round( coef( fitwlsi5 ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income supply_(Intercept) 336s 100.903 -0.316 0.324 53.938 336s supply_price supply_farmPrice supply_trend 336s 0.184 0.260 0.324 336s > print( round( coef( fitwlsi5, modified.regMat = TRUE ), digits = 6 ) ) 336s C1 C2 C3 C4 C5 C6 336s 100.903 -0.316 0.324 53.938 0.184 0.260 336s > print( round( coef( fitwlsi5$eq[[ 1 ]] ), digits = 6 ) ) 336s (Intercept) price income 336s 100.903 -0.316 0.324 336s > 336s > 336s > ## *************** coefficients with stats ********************* 336s > print( round( coef( summary( fitwls1e ) ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 99.895 6.9325 14.41 0.000000 336s demand_price -0.316 0.0836 -3.78 0.001483 336s demand_income 0.335 0.0419 7.99 0.000000 336s supply_(Intercept) 58.275 10.2527 5.68 0.000034 336s supply_price 0.160 0.0849 1.89 0.077067 336s supply_farmPrice 0.248 0.0413 6.01 0.000018 336s supply_trend 0.248 0.0872 2.85 0.011659 336s > print( round( coef( summary( fitwls1e$eq[[ 1 ]] ) ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.895 6.9325 14.41 0.00000 336s price -0.316 0.0836 -3.78 0.00148 336s income 0.335 0.0419 7.99 0.00000 336s > 336s > print( round( coef( summary( fitwlsi2 ) ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 99.661 7.5378 13.22 0.000000 336s demand_price -0.299 0.0884 -3.39 0.001805 336s demand_income 0.320 0.0414 7.72 0.000000 336s supply_(Intercept) 56.183 11.3487 4.95 0.000020 336s supply_price 0.164 0.0963 1.71 0.097239 336s supply_farmPrice 0.258 0.0453 5.70 0.000002 336s supply_trend 0.320 0.0414 7.72 0.000000 336s > print( round( coef( summary( fitwlsi2$eq[[ 2 ]] ) ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 56.183 11.3487 4.95 0.000020 336s price 0.164 0.0963 1.71 0.097239 336s farmPrice 0.258 0.0453 5.70 0.000002 336s trend 0.320 0.0414 7.72 0.000000 336s > 336s > print( round( coef( summary( fitwls3e ) ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 99.646 6.9734 14.29 0.000000 336s demand_price -0.298 0.0816 -3.65 0.000863 336s demand_income 0.319 0.0381 8.37 0.000000 336s supply_(Intercept) 56.210 10.1248 5.55 0.000003 336s supply_price 0.164 0.0859 1.91 0.064384 336s supply_farmPrice 0.258 0.0404 6.38 0.000000 336s supply_trend 0.319 0.0381 8.37 0.000000 336s > print( round( coef( summary( fitwls3e ), modified.regMat = TRUE ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s C1 99.646 6.9734 14.29 0.000000 336s C2 -0.298 0.0816 -3.65 0.000863 336s C3 0.319 0.0381 8.37 0.000000 336s C4 56.210 10.1248 5.55 0.000003 336s C5 0.164 0.0859 1.91 0.064384 336s C6 0.258 0.0404 6.38 0.000000 336s > print( round( coef( summary( fitwls3e$eq[[ 1 ]] ) ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 99.646 6.9734 14.29 0.000000 336s price -0.298 0.0816 -3.65 0.000863 336s income 0.319 0.0381 8.37 0.000000 336s > 336s > print( round( coef( summary( fitwls4, useDfSys = FALSE ) ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 100.914 6.0474 16.69 0.000000 336s demand_price -0.316 0.0648 -4.87 0.000143 336s demand_income 0.324 0.0385 8.42 0.000000 336s supply_(Intercept) 53.942 7.9687 6.77 0.000005 336s supply_price 0.184 0.0648 2.84 0.011833 336s supply_farmPrice 0.260 0.0446 5.84 0.000025 336s supply_trend 0.324 0.0385 8.42 0.000000 336s > print( round( coef( summary( fitwls4$eq[[ 2 ]], useDfSys = FALSE ) ), 336s + digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 53.942 7.9687 6.77 0.000005 336s price 0.184 0.0648 2.84 0.011833 336s farmPrice 0.260 0.0446 5.84 0.000025 336s trend 0.324 0.0385 8.42 0.000000 336s > 336s > print( round( coef( summary( fitwlsi5, useDfSys = FALSE ) ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s demand_(Intercept) 100.903 6.0396 16.71 0.000000 336s demand_price -0.316 0.0648 -4.88 0.000142 336s demand_income 0.324 0.0384 8.43 0.000000 336s supply_(Intercept) 53.938 7.9718 6.77 0.000005 336s supply_price 0.184 0.0648 2.84 0.011806 336s supply_farmPrice 0.260 0.0447 5.83 0.000026 336s supply_trend 0.324 0.0384 8.43 0.000000 336s > print( round( coef( summary( fitwlsi5, useDfSys = FALSE ), 336s + modified.regMat = TRUE ), digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s C1 100.903 6.0396 16.71 NA 336s C2 -0.316 0.0648 -4.88 NA 336s C3 0.324 0.0384 8.43 NA 336s C4 53.938 7.9718 6.77 NA 336s C5 0.184 0.0648 2.84 NA 336s C6 0.260 0.0447 5.83 NA 336s > print( round( coef( summary( fitwlsi5$eq[[ 1 ]], useDfSys = FALSE ) ), 336s + digits = 6 ) ) 336s Estimate Std. Error t value Pr(>|t|) 336s (Intercept) 100.903 6.0396 16.71 0.000000 336s price -0.316 0.0648 -4.88 0.000142 336s income 0.324 0.0384 8.43 0.000000 336s > 336s > 336s > ## *********** variance covariance matrix of the coefficients ******* 336s > print( round( vcov( fitwls1e ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 48.0597 -0.50558 0.02734 336s demand_price -0.5056 0.00699 -0.00198 336s demand_income 0.0273 -0.00198 0.00175 336s supply_(Intercept) 0.0000 0.00000 0.00000 336s supply_price 0.0000 0.00000 0.00000 336s supply_farmPrice 0.0000 0.00000 0.00000 336s supply_trend 0.0000 0.00000 0.00000 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) 0.000 0.000000 0.000000 336s demand_price 0.000 0.000000 0.000000 336s demand_income 0.000 0.000000 0.000000 336s supply_(Intercept) 105.119 -0.790000 -0.243489 336s supply_price -0.790 0.007202 0.000675 336s supply_farmPrice -0.243 0.000675 0.001707 336s supply_trend -0.223 0.000418 0.001052 336s supply_trend 336s demand_(Intercept) 0.000000 336s demand_price 0.000000 336s demand_income 0.000000 336s supply_(Intercept) -0.223347 336s supply_price 0.000418 336s supply_farmPrice 0.001052 336s supply_trend 0.007608 336s > print( round( vcov( fitwls1e$eq[[ 1 ]] ), digits = 6 ) ) 336s (Intercept) price income 336s (Intercept) 48.0597 -0.50558 0.02734 336s price -0.5056 0.00699 -0.00198 336s income 0.0273 -0.00198 0.00175 336s > 336s > print( round( vcov( fitwls2 ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 57.21413 -0.596328 0.026850 336s demand_price -0.59633 0.007862 -0.001948 336s demand_income 0.02685 -0.001948 0.001722 336s supply_(Intercept) -0.78825 0.057190 -0.050565 336s supply_price 0.00147 -0.000107 0.000095 336s supply_farmPrice 0.00371 -0.000269 0.000238 336s supply_trend 0.02685 -0.001948 0.001722 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) -0.7883 0.001474 0.003714 336s demand_price 0.0572 -0.000107 -0.000269 336s demand_income -0.0506 0.000095 0.000238 336s supply_(Intercept) 128.0635 -1.001596 -0.280017 336s supply_price -1.0016 0.009225 0.000806 336s supply_farmPrice -0.2800 0.000806 0.002038 336s supply_trend -0.0506 0.000095 0.000238 336s supply_trend 336s demand_(Intercept) 0.026850 336s demand_price -0.001948 336s demand_income 0.001722 336s supply_(Intercept) -0.050565 336s supply_price 0.000095 336s supply_farmPrice 0.000238 336s supply_trend 0.001722 336s > print( round( vcov( fitwls2$eq[[ 2 ]] ), digits = 6 ) ) 336s (Intercept) price farmPrice trend 336s (Intercept) 128.0635 -1.001596 -0.280017 -0.050565 336s price -1.0016 0.009225 0.000806 0.000095 336s farmPrice -0.2800 0.000806 0.002038 0.000238 336s trend -0.0506 0.000095 0.000238 0.001722 336s > 336s > print( round( vcov( fitwls3e ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 48.62814 -0.506597 0.022574 336s demand_price -0.50660 0.006662 -0.001638 336s demand_income 0.02257 -0.001638 0.001448 336s supply_(Intercept) -0.66271 0.048082 -0.042512 336s supply_price 0.00124 -0.000090 0.000079 336s supply_farmPrice 0.00312 -0.000227 0.000200 336s supply_trend 0.02257 -0.001638 0.001448 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) -0.6627 0.001239 0.003123 336s demand_price 0.0481 -0.000090 -0.000227 336s demand_income -0.0425 0.000079 0.000200 336s supply_(Intercept) 102.5112 -0.801390 -0.224299 336s supply_price -0.8014 0.007381 0.000645 336s supply_farmPrice -0.2243 0.000645 0.001632 336s supply_trend -0.0425 0.000079 0.000200 336s supply_trend 336s demand_(Intercept) 0.022574 336s demand_price -0.001638 336s demand_income 0.001448 336s supply_(Intercept) -0.042512 336s supply_price 0.000079 336s supply_farmPrice 0.000200 336s supply_trend 0.001448 336s > print( round( vcov( fitwls3e, modified.regMat = TRUE ), digits = 6 ) ) 336s C1 C2 C3 C4 C5 C6 336s C1 48.62814 -0.506597 0.022574 -0.6627 0.001239 0.003123 336s C2 -0.50660 0.006662 -0.001638 0.0481 -0.000090 -0.000227 336s C3 0.02257 -0.001638 0.001448 -0.0425 0.000079 0.000200 336s C4 -0.66271 0.048082 -0.042512 102.5112 -0.801390 -0.224299 336s C5 0.00124 -0.000090 0.000079 -0.8014 0.007381 0.000645 336s C6 0.00312 -0.000227 0.000200 -0.2243 0.000645 0.001632 336s > print( round( vcov( fitwls3e$eq[[ 1 ]] ), digits = 6 ) ) 336s (Intercept) price income 336s (Intercept) 48.6281 -0.50660 0.02257 336s price -0.5066 0.00666 -0.00164 336s income 0.0226 -0.00164 0.00145 336s > 336s > print( round( vcov( fitwls4 ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 36.5710 -0.321554 -0.043279 336s demand_price -0.3216 0.004201 -0.001011 336s demand_income -0.0433 -0.001011 0.001481 336s supply_(Intercept) 35.8467 -0.431417 0.074877 336s supply_price -0.3216 0.004201 -0.001011 336s supply_farmPrice -0.0334 0.000226 0.000111 336s supply_trend -0.0433 -0.001011 0.001481 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) 35.8467 -0.321554 -0.033436 336s demand_price -0.4314 0.004201 0.000226 336s demand_income 0.0749 -0.001011 0.000111 336s supply_(Intercept) 63.5001 -0.431417 -0.215648 336s supply_price -0.4314 0.004201 0.000226 336s supply_farmPrice -0.2156 0.000226 0.001986 336s supply_trend 0.0749 -0.001011 0.000111 336s supply_trend 336s demand_(Intercept) -0.043279 336s demand_price -0.001011 336s demand_income 0.001481 336s supply_(Intercept) 0.074877 336s supply_price -0.001011 336s supply_farmPrice 0.000111 336s supply_trend 0.001481 336s > print( round( vcov( fitwls4$eq[[ 2 ]] ), digits = 6 ) ) 336s (Intercept) price farmPrice trend 336s (Intercept) 63.5001 -0.431417 -0.215648 0.074877 336s price -0.4314 0.004201 0.000226 -0.001011 336s farmPrice -0.2156 0.000226 0.001986 0.000111 336s trend 0.0749 -0.001011 0.000111 0.001481 336s > 336s > print( round( vcov( fitwls5 ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 36.5710 -0.321554 -0.043279 336s demand_price -0.3216 0.004201 -0.001011 336s demand_income -0.0433 -0.001011 0.001481 336s supply_(Intercept) 35.8467 -0.431417 0.074877 336s supply_price -0.3216 0.004201 -0.001011 336s supply_farmPrice -0.0334 0.000226 0.000111 336s supply_trend -0.0433 -0.001011 0.001481 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) 35.8467 -0.321554 -0.033436 336s demand_price -0.4314 0.004201 0.000226 336s demand_income 0.0749 -0.001011 0.000111 336s supply_(Intercept) 63.5001 -0.431417 -0.215648 336s supply_price -0.4314 0.004201 0.000226 336s supply_farmPrice -0.2156 0.000226 0.001986 336s supply_trend 0.0749 -0.001011 0.000111 336s supply_trend 336s demand_(Intercept) -0.043279 336s demand_price -0.001011 336s demand_income 0.001481 336s supply_(Intercept) 0.074877 336s supply_price -0.001011 336s supply_farmPrice 0.000111 336s supply_trend 0.001481 336s > print( round( vcov( fitwls5, modified.regMat = TRUE ), digits = 6 ) ) 336s C1 C2 C3 C4 C5 C6 336s C1 36.5710 -0.321554 -0.043279 35.8467 -0.321554 -0.033436 336s C2 -0.3216 0.004201 -0.001011 -0.4314 0.004201 0.000226 336s C3 -0.0433 -0.001011 0.001481 0.0749 -0.001011 0.000111 336s C4 35.8467 -0.431417 0.074877 63.5001 -0.431417 -0.215648 336s C5 -0.3216 0.004201 -0.001011 -0.4314 0.004201 0.000226 336s C6 -0.0334 0.000226 0.000111 -0.2156 0.000226 0.001986 336s > print( round( vcov( fitwls5$eq[[ 1 ]] ), digits = 6 ) ) 336s (Intercept) price income 336s (Intercept) 36.5710 -0.32155 -0.04328 336s price -0.3216 0.00420 -0.00101 336s income -0.0433 -0.00101 0.00148 336s > 336s > print( round( vcov( fitwlsi1 ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 56.5408 -0.59480 0.03216 336s demand_price -0.5948 0.00822 -0.00233 336s demand_income 0.0322 -0.00233 0.00206 336s supply_(Intercept) 0.0000 0.00000 0.00000 336s supply_price 0.0000 0.00000 0.00000 336s supply_farmPrice 0.0000 0.00000 0.00000 336s supply_trend 0.0000 0.00000 0.00000 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) 0.000 0.000000 0.000000 336s demand_price 0.000 0.000000 0.000000 336s demand_income 0.000 0.000000 0.000000 336s supply_(Intercept) 131.398 -0.987500 -0.304361 336s supply_price -0.988 0.009003 0.000844 336s supply_farmPrice -0.304 0.000844 0.002133 336s supply_trend -0.279 0.000522 0.001316 336s supply_trend 336s demand_(Intercept) 0.000000 336s demand_price 0.000000 336s demand_income 0.000000 336s supply_(Intercept) -0.279183 336s supply_price 0.000522 336s supply_farmPrice 0.001316 336s supply_trend 0.009510 336s > print( round( vcov( fitwlsi1$eq[[ 2 ]] ), digits = 6 ) ) 336s (Intercept) price farmPrice trend 336s (Intercept) 131.398 -0.987500 -0.304361 -0.279183 336s price -0.988 0.009003 0.000844 0.000522 336s farmPrice -0.304 0.000844 0.002133 0.001316 336s trend -0.279 0.000522 0.001316 0.009510 336s > 336s > print( round( vcov( fitwlsi2e ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 48.32515 -0.503487 0.022480 336s demand_price -0.50349 0.006624 -0.001631 336s demand_income 0.02248 -0.001631 0.001442 336s supply_(Intercept) -0.65995 0.047882 -0.042335 336s supply_price 0.00123 -0.000090 0.000079 336s supply_farmPrice 0.00311 -0.000226 0.000199 336s supply_trend 0.02248 -0.001631 0.001442 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) -0.6600 0.001234 0.003110 336s demand_price 0.0479 -0.000090 -0.000226 336s demand_income -0.0423 0.000079 0.000199 336s supply_(Intercept) 103.0226 -0.805456 -0.225388 336s supply_price -0.8055 0.007418 0.000649 336s supply_farmPrice -0.2254 0.000649 0.001640 336s supply_trend -0.0423 0.000079 0.000199 336s supply_trend 336s demand_(Intercept) 0.022480 336s demand_price -0.001631 336s demand_income 0.001442 336s supply_(Intercept) -0.042335 336s supply_price 0.000079 336s supply_farmPrice 0.000199 336s supply_trend 0.001442 336s > print( round( vcov( fitwlsi2e$eq[[ 1 ]] ), digits = 6 ) ) 336s (Intercept) price income 336s (Intercept) 48.3251 -0.50349 0.02248 336s price -0.5035 0.00662 -0.00163 336s income 0.0225 -0.00163 0.00144 336s > 336s > print( round( vcov( fitwlsi3 ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 56.81857 -0.592263 0.026724 336s demand_price -0.59226 0.007812 -0.001939 336s demand_income 0.02672 -0.001939 0.001714 336s supply_(Intercept) -0.78454 0.056921 -0.050327 336s supply_price 0.00147 -0.000106 0.000094 336s supply_farmPrice 0.00370 -0.000268 0.000237 336s supply_trend 0.02672 -0.001939 0.001714 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) -0.7845 0.001467 0.003697 336s demand_price 0.0569 -0.000106 -0.000268 336s demand_income -0.0503 0.000094 0.000237 336s supply_(Intercept) 128.7924 -1.007391 -0.281572 336s supply_price -1.0074 0.009279 0.000811 336s supply_farmPrice -0.2816 0.000811 0.002049 336s supply_trend -0.0503 0.000094 0.000237 336s supply_trend 336s demand_(Intercept) 0.026724 336s demand_price -0.001939 336s demand_income 0.001714 336s supply_(Intercept) -0.050327 336s supply_price 0.000094 336s supply_farmPrice 0.000237 336s supply_trend 0.001714 336s > print( round( vcov( fitwlsi3, modified.regMat = TRUE ), digits = 6 ) ) 336s C1 C2 C3 C4 C5 C6 336s C1 56.81857 -0.592263 0.026724 -0.7845 0.001467 0.003697 336s C2 -0.59226 0.007812 -0.001939 0.0569 -0.000106 -0.000268 336s C3 0.02672 -0.001939 0.001714 -0.0503 0.000094 0.000237 336s C4 -0.78454 0.056921 -0.050327 128.7924 -1.007391 -0.281572 336s C5 0.00147 -0.000106 0.000094 -1.0074 0.009279 0.000811 336s C6 0.00370 -0.000268 0.000237 -0.2816 0.000811 0.002049 336s > print( round( vcov( fitwlsi3$eq[[ 2 ]] ), digits = 6 ) ) 336s (Intercept) price farmPrice trend 336s (Intercept) 128.7924 -1.007391 -0.281572 -0.050327 336s price -1.0074 0.009279 0.000811 0.000094 336s farmPrice -0.2816 0.000811 0.002049 0.000237 336s trend -0.0503 0.000094 0.000237 0.001714 336s > 336s > print( round( vcov( fitwlsi4e ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 30.4377 -0.265752 -0.037918 336s demand_price -0.2658 0.003463 -0.000827 336s demand_income -0.0379 -0.000827 0.001237 336s supply_(Intercept) 29.6762 -0.355820 0.060620 336s supply_price -0.2658 0.003463 -0.000827 336s supply_farmPrice -0.0279 0.000187 0.000094 336s supply_trend -0.0379 -0.000827 0.001237 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) 29.6762 -0.265752 -0.027921 336s demand_price -0.3558 0.003463 0.000187 336s demand_income 0.0606 -0.000827 0.000094 336s supply_(Intercept) 52.0044 -0.355820 -0.173988 336s supply_price -0.3558 0.003463 0.000187 336s supply_farmPrice -0.1740 0.000187 0.001596 336s supply_trend 0.0606 -0.000827 0.000094 336s supply_trend 336s demand_(Intercept) -0.037918 336s demand_price -0.000827 336s demand_income 0.001237 336s supply_(Intercept) 0.060620 336s supply_price -0.000827 336s supply_farmPrice 0.000094 336s supply_trend 0.001237 336s > print( round( vcov( fitwlsi4e$eq[[ 1 ]] ), digits = 6 ) ) 336s (Intercept) price income 336s (Intercept) 30.4377 -0.265752 -0.037918 336s price -0.2658 0.003463 -0.000827 336s income -0.0379 -0.000827 0.001237 336s > 336s > print( round( vcov( fitwlsi5e ), digits = 6 ) ) 336s demand_(Intercept) demand_price demand_income 336s demand_(Intercept) 30.4377 -0.265752 -0.037918 336s demand_price -0.2658 0.003463 -0.000827 336s demand_income -0.0379 -0.000827 0.001237 336s supply_(Intercept) 29.6762 -0.355820 0.060620 336s supply_price -0.2658 0.003463 -0.000827 336s supply_farmPrice -0.0279 0.000187 0.000094 336s supply_trend -0.0379 -0.000827 0.001237 336s supply_(Intercept) supply_price supply_farmPrice 336s demand_(Intercept) 29.6762 -0.265752 -0.027921 336s demand_price -0.3558 0.003463 0.000187 336s demand_income 0.0606 -0.000827 0.000094 336s supply_(Intercept) 52.0044 -0.355820 -0.173988 336s supply_price -0.3558 0.003463 0.000187 336s supply_farmPrice -0.1740 0.000187 0.001596 336s supply_trend 0.0606 -0.000827 0.000094 336s supply_trend 336s demand_(Intercept) -0.037918 336s demand_price -0.000827 336s demand_income 0.001237 336s supply_(Intercept) 0.060620 336s supply_price -0.000827 336s supply_farmPrice 0.000094 336s supply_trend 0.001237 336s > print( round( vcov( fitwlsi5e, modified.regMat = TRUE ), digits = 6 ) ) 336s C1 C2 C3 C4 C5 C6 336s C1 30.4377 -0.265752 -0.037918 29.6762 -0.265752 -0.027921 336s C2 -0.2658 0.003463 -0.000827 -0.3558 0.003463 0.000187 336s C3 -0.0379 -0.000827 0.001237 0.0606 -0.000827 0.000094 336s C4 29.6762 -0.355820 0.060620 52.0044 -0.355820 -0.173988 336s C5 -0.2658 0.003463 -0.000827 -0.3558 0.003463 0.000187 336s C6 -0.0279 0.000187 0.000094 -0.1740 0.000187 0.001596 336s > print( round( vcov( fitwlsi5e$eq[[ 2 ]] ), digits = 6 ) ) 336s (Intercept) price farmPrice trend 336s (Intercept) 52.0044 -0.355820 -0.173988 0.060620 336s price -0.3558 0.003463 0.000187 -0.000827 336s farmPrice -0.1740 0.000187 0.001596 0.000094 336s trend 0.0606 -0.000827 0.000094 0.001237 336s > 336s > 336s > ## *********** confidence intervals of coefficients ************* 336s > print( confint( fitwls1 ) ) 336s 2.5 % 97.5 % 336s demand_(Intercept) 84.031 115.760 336s demand_price -0.508 -0.125 336s demand_income 0.239 0.430 336s supply_(Intercept) 33.975 82.576 336s supply_price -0.041 0.362 336s supply_farmPrice 0.150 0.346 336s supply_trend 0.042 0.455 336s > print( confint( fitwls1$eq[[ 2 ]], level = 0.9 ) ) 336s 5 % 95 % 336s (Intercept) 38.263 78.288 336s price -0.005 0.326 336s farmPrice 0.167 0.329 336s trend 0.078 0.419 336s > 336s > print( confint( fitwls2e, level = 0.9 ) ) 336s 5 % 95 % 336s demand_(Intercept) 85.474 113.818 336s demand_price -0.464 -0.132 336s demand_income 0.241 0.396 336s supply_(Intercept) 35.634 76.786 336s supply_price -0.010 0.339 336s supply_farmPrice 0.176 0.340 336s supply_trend 0.241 0.396 336s > print( confint( fitwls2e$eq[[ 1 ]], level = 0.99 ) ) 336s 0.5 % 99.5 % 336s (Intercept) 80.620 118.672 336s price -0.521 -0.076 336s income 0.215 0.422 336s > 336s > print( confint( fitwls3, level = 0.99 ) ) 336s 0.5 % 99.5 % 336s demand_(Intercept) 84.286 115.030 336s demand_price -0.479 -0.119 336s demand_income 0.235 0.404 336s supply_(Intercept) 33.190 79.186 336s supply_price -0.031 0.359 336s supply_farmPrice 0.166 0.350 336s supply_trend 0.235 0.404 336s > print( confint( fitwls3$eq[[ 2 ]], level = 0.5 ) ) 336s 25 % 75 % 336s (Intercept) 48.472 63.903 336s price 0.099 0.230 336s farmPrice 0.227 0.289 336s trend 0.291 0.348 336s > 336s > print( confint( fitwls4e, level = 0.5 ) ) 336s 25 % 75 % 336s demand_(Intercept) 89.763 112.189 336s demand_price -0.436 -0.197 336s demand_income 0.252 0.395 336s supply_(Intercept) 39.328 68.598 336s supply_price 0.064 0.303 336s supply_farmPrice 0.179 0.341 336s supply_trend 0.252 0.395 336s > print( confint( fitwls4e$eq[[ 1 ]], level = 0.25 ) ) 336s 37.5 % 62.5 % 336s (Intercept) 99.202 102.750 336s price -0.335 -0.297 336s income 0.312 0.335 336s > 336s > print( confint( fitwls5, level = 0.25 ) ) 336s 37.5 % 62.5 % 336s demand_(Intercept) 88.637 113.191 336s demand_price -0.448 -0.184 336s demand_income 0.246 0.402 336s supply_(Intercept) 37.764 70.119 336s supply_price 0.052 0.316 336s supply_farmPrice 0.170 0.351 336s supply_trend 0.246 0.402 336s > print( confint( fitwls5$eq[[ 2 ]], level = 0.975 ) ) 336s 1.3 % 98.8 % 336s (Intercept) 35.279 72.604 336s price 0.032 0.336 336s farmPrice 0.156 0.365 336s trend 0.234 0.414 336s > 336s > print( confint( fitwlsi1e, level = 0.975, useDfSys = TRUE ) ) 336s 1.3 % 98.8 % 336s demand_(Intercept) 85.791 114.000 336s demand_price -0.486 -0.146 336s demand_income 0.249 0.420 336s supply_(Intercept) 37.416 79.135 336s supply_price -0.012 0.333 336s supply_farmPrice 0.164 0.332 336s supply_trend 0.071 0.426 336s > print( confint( fitwlsi1e$eq[[ 1 ]], level = 0.999, useDfSys = TRUE ) ) 336s 0.1 % 100 % 336s (Intercept) 74.863 124.928 336s price -0.618 -0.014 336s income 0.183 0.486 336s > 336s > print( confint( fitwlsi2, level = 0.999 ) ) 336s 0.1 % 100 % 336s demand_(Intercept) 84.342 114.979 336s demand_price -0.479 -0.120 336s demand_income 0.235 0.404 336s supply_(Intercept) 33.120 79.246 336s supply_price -0.031 0.360 336s supply_farmPrice 0.166 0.350 336s supply_trend 0.235 0.404 336s > print( confint( fitwlsi2$eq[[ 2 ]], level = 0.1 ) ) 336s 45 % 55 % 336s (Intercept) 54.746 57.620 336s price 0.152 0.176 336s farmPrice 0.252 0.264 336s trend 0.314 0.325 336s > 336s > print( confint( fitwlsi3e, level = 0.1 ) ) 336s 45 % 55 % 336s demand_(Intercept) 85.521 113.776 336s demand_price -0.464 -0.133 336s demand_income 0.242 0.396 336s supply_(Intercept) 35.579 76.833 336s supply_price -0.011 0.339 336s supply_farmPrice 0.176 0.340 336s supply_trend 0.242 0.396 336s > print( confint( fitwlsi3e$eq[[ 1 ]], level = 0.01 ) ) 336s 49.5 % 50.5 % 336s (Intercept) 99.561 99.736 336s price -0.299 -0.297 336s income 0.318 0.319 336s > 336s > print( confint( fitwlsi4, level = 0.01 ) ) 336s 49.5 % 50.5 % 336s demand_(Intercept) 88.642 113.164 336s demand_price -0.447 -0.184 336s demand_income 0.246 0.402 336s supply_(Intercept) 37.754 70.122 336s supply_price 0.053 0.316 336s supply_farmPrice 0.170 0.351 336s supply_trend 0.246 0.402 336s > print( confint( fitwlsi4$eq[[ 2 ]], level = 0.33 ) ) 336s 33.5 % 66.5 % 336s (Intercept) 50.512 57.364 336s price 0.156 0.212 336s farmPrice 0.241 0.279 336s trend 0.307 0.340 336s > 336s > print( confint( fitwlsi5e, level = 0.33 ) ) 336s 33.5 % 66.5 % 336s demand_(Intercept) 89.766 112.166 336s demand_price -0.435 -0.197 336s demand_income 0.252 0.395 336s supply_(Intercept) 39.320 68.599 336s supply_price 0.065 0.303 336s supply_farmPrice 0.179 0.341 336s supply_trend 0.252 0.395 336s > print( confint( fitwlsi5e$eq[[ 1 ]] ) ) 336s 2.5 % 97.5 % 336s (Intercept) 89.766 112.166 336s price -0.435 -0.197 336s income 0.252 0.395 336s > 336s > 336s > ## *********** fitted values ************* 336s > print( fitted( fitwls1 ) ) 336s demand supply 336s 1 97.4 98.9 336s 2 99.6 100.1 336s 3 99.5 100.2 336s 4 99.7 100.4 336s 5 102.3 102.7 336s 6 102.1 102.6 336s 7 102.5 102.4 336s 8 102.8 104.3 336s 9 101.7 102.9 336s 10 100.8 100.4 336s 11 95.6 96.0 336s 12 94.4 94.1 336s 13 95.7 95.6 336s 14 99.0 97.8 336s 15 104.3 102.6 336s 16 103.9 104.1 336s 17 104.8 103.8 336s 18 101.9 102.4 336s 19 103.5 102.1 336s 20 106.5 104.5 336s > print( fitted( fitwls1$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 98.9 100.1 100.2 100.4 102.7 102.6 102.4 104.3 102.9 100.4 96.0 94.1 95.6 336s 14 15 16 17 18 19 20 336s 97.8 102.6 104.1 103.8 102.4 102.1 104.5 336s > 336s > print( fitted( fitwls2e ) ) 336s demand supply 336s 1 97.6 98.3 336s 2 99.7 99.5 336s 3 99.6 99.7 336s 4 99.8 99.9 336s 5 102.2 102.5 336s 6 102.0 102.4 336s 7 102.4 102.3 336s 8 102.8 104.3 336s 9 101.7 102.9 336s 10 100.8 100.3 336s 11 95.8 95.9 336s 12 94.7 93.9 336s 13 95.9 95.5 336s 14 99.1 97.9 336s 15 104.1 103.0 336s 16 103.8 104.6 336s 17 104.6 104.3 336s 18 101.9 102.9 336s 19 103.4 102.7 336s 20 106.3 105.2 336s > print( fitted( fitwls2e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 97.6 99.7 99.6 99.8 102.2 102.0 102.4 102.8 101.7 100.8 95.8 94.7 95.9 336s 14 15 16 17 18 19 20 336s 99.1 104.1 103.8 104.6 101.9 103.4 106.3 336s > 336s > print( fitted( fitwls3 ) ) 336s demand supply 336s 1 97.6 98.3 336s 2 99.6 99.5 336s 3 99.6 99.7 336s 4 99.8 99.9 336s 5 102.2 102.5 336s 6 102.0 102.4 336s 7 102.4 102.3 336s 8 102.8 104.3 336s 9 101.7 102.9 336s 10 100.8 100.3 336s 11 95.8 95.9 336s 12 94.7 93.9 336s 13 95.9 95.5 336s 14 99.1 97.9 336s 15 104.1 103.0 336s 16 103.8 104.6 336s 17 104.6 104.3 336s 18 101.9 102.9 336s 19 103.4 102.7 336s 20 106.3 105.2 336s > print( fitted( fitwls3$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 98.3 99.5 99.7 99.9 102.5 102.4 102.3 104.3 102.9 100.3 95.9 93.9 95.5 336s 14 15 16 17 18 19 20 336s 97.9 103.0 104.6 104.3 102.9 102.7 105.2 336s > 336s > print( fitted( fitwls4e ) ) 336s demand supply 336s 1 97.5 98.2 336s 2 99.6 99.6 336s 3 99.5 99.7 336s 4 99.7 100.0 336s 5 102.3 102.4 336s 6 102.0 102.4 336s 7 102.4 102.3 336s 8 102.7 104.4 336s 9 101.7 102.9 336s 10 100.9 100.2 336s 11 95.8 95.7 336s 12 94.6 93.9 336s 13 95.8 95.5 336s 14 99.1 97.8 336s 15 104.2 102.9 336s 16 103.8 104.6 336s 17 104.8 104.1 336s 18 101.9 103.0 336s 19 103.3 102.8 336s 20 106.2 105.5 336s > print( fitted( fitwls4e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 97.5 99.6 99.5 99.7 102.3 102.0 102.4 102.7 101.7 100.9 95.8 94.6 95.8 336s 14 15 16 17 18 19 20 336s 99.1 104.2 103.8 104.8 101.9 103.3 106.2 336s > 336s > print( fitted( fitwls5 ) ) 336s demand supply 336s 1 97.5 98.2 336s 2 99.6 99.6 336s 3 99.5 99.7 336s 4 99.7 100.0 336s 5 102.3 102.4 336s 6 102.0 102.3 336s 7 102.4 102.3 336s 8 102.7 104.4 336s 9 101.7 102.9 336s 10 100.9 100.2 336s 11 95.8 95.7 336s 12 94.6 93.9 336s 13 95.8 95.5 336s 14 99.1 97.8 336s 15 104.2 102.9 336s 16 103.8 104.6 336s 17 104.8 104.1 336s 18 101.9 103.0 336s 19 103.3 102.8 336s 20 106.2 105.5 336s > print( fitted( fitwls5$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 98.2 99.6 99.7 100.0 102.4 102.3 102.3 104.4 102.9 100.2 95.7 93.9 95.5 336s 14 15 16 17 18 19 20 336s 97.8 102.9 104.6 104.1 103.0 102.8 105.5 336s > 336s > print( fitted( fitwlsi1e ) ) 336s demand supply 336s 1 97.4 98.9 336s 2 99.6 100.1 336s 3 99.5 100.2 336s 4 99.7 100.4 336s 5 102.3 102.7 336s 6 102.1 102.6 336s 7 102.5 102.4 336s 8 102.8 104.3 336s 9 101.7 102.9 336s 10 100.8 100.4 336s 11 95.6 96.0 336s 12 94.4 94.1 336s 13 95.7 95.6 336s 14 99.0 97.8 336s 15 104.3 102.6 336s 16 103.9 104.1 336s 17 104.8 103.8 336s 18 101.9 102.4 336s 19 103.5 102.1 336s 20 106.5 104.5 336s > print( fitted( fitwlsi1e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 97.4 99.6 99.5 99.7 102.3 102.1 102.5 102.8 101.7 100.8 95.6 94.4 95.7 336s 14 15 16 17 18 19 20 336s 99.0 104.3 103.9 104.8 101.9 103.5 106.5 336s > 336s > print( fitted( fitwlsi2 ) ) 336s demand supply 336s 1 97.6 98.3 336s 2 99.6 99.5 336s 3 99.6 99.7 336s 4 99.8 99.9 336s 5 102.2 102.5 336s 6 102.0 102.4 336s 7 102.4 102.3 336s 8 102.8 104.3 336s 9 101.7 102.9 336s 10 100.8 100.3 336s 11 95.8 95.9 336s 12 94.7 93.9 336s 13 95.9 95.5 336s 14 99.1 97.9 336s 15 104.1 103.0 336s 16 103.8 104.6 336s 17 104.6 104.3 336s 18 101.9 102.9 336s 19 103.4 102.7 336s 20 106.3 105.2 336s > print( fitted( fitwlsi2$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 98.3 99.5 99.7 99.9 102.5 102.4 102.3 104.3 102.9 100.3 95.9 93.9 95.5 336s 14 15 16 17 18 19 20 336s 97.9 103.0 104.6 104.3 102.9 102.7 105.2 336s > 336s > print( fitted( fitwlsi3e ) ) 336s demand supply 336s 1 97.6 98.3 336s 2 99.7 99.5 336s 3 99.6 99.7 336s 4 99.8 99.9 336s 5 102.2 102.5 336s 6 102.0 102.4 336s 7 102.4 102.3 336s 8 102.8 104.3 336s 9 101.7 102.9 336s 10 100.8 100.3 336s 11 95.8 95.9 336s 12 94.7 93.9 336s 13 95.9 95.5 336s 14 99.1 97.9 336s 15 104.1 103.0 336s 16 103.8 104.6 336s 17 104.6 104.3 336s 18 101.9 102.9 336s 19 103.4 102.7 336s 20 106.3 105.2 336s > print( fitted( fitwlsi3e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 97.6 99.7 99.6 99.8 102.2 102.0 102.4 102.8 101.7 100.8 95.8 94.7 95.9 336s 14 15 16 17 18 19 20 336s 99.1 104.1 103.8 104.6 101.9 103.4 106.3 336s > 336s > print( fitted( fitwlsi4 ) ) 336s demand supply 336s 1 97.5 98.2 336s 2 99.6 99.6 336s 3 99.5 99.7 336s 4 99.7 100.0 336s 5 102.3 102.4 336s 6 102.0 102.3 336s 7 102.4 102.3 336s 8 102.7 104.4 336s 9 101.7 102.9 336s 10 100.9 100.2 336s 11 95.8 95.7 336s 12 94.6 93.9 336s 13 95.8 95.5 336s 14 99.1 97.8 336s 15 104.2 102.9 336s 16 103.8 104.6 336s 17 104.8 104.1 336s 18 101.9 103.0 336s 19 103.3 102.8 336s 20 106.2 105.5 336s > print( fitted( fitwlsi4$eq[[ 2 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 98.2 99.6 99.7 100.0 102.4 102.3 102.3 104.4 102.9 100.2 95.7 93.9 95.5 336s 14 15 16 17 18 19 20 336s 97.8 102.9 104.6 104.1 103.0 102.8 105.5 336s > 336s > print( fitted( fitwlsi5e ) ) 336s demand supply 336s 1 97.5 98.2 336s 2 99.6 99.6 336s 3 99.5 99.7 336s 4 99.7 100.0 336s 5 102.3 102.4 336s 6 102.0 102.4 336s 7 102.4 102.3 336s 8 102.7 104.4 336s 9 101.7 102.9 336s 10 100.9 100.2 336s 11 95.8 95.7 336s 12 94.6 93.9 336s 13 95.8 95.5 336s 14 99.1 97.8 336s 15 104.2 102.9 336s 16 103.8 104.6 336s 17 104.8 104.1 336s 18 101.9 103.0 336s 19 103.3 102.8 336s 20 106.2 105.5 336s > print( fitted( fitwlsi5e$eq[[ 1 ]] ) ) 336s 1 2 3 4 5 6 7 8 9 10 11 12 13 336s 97.5 99.6 99.5 99.7 102.3 102.0 102.4 102.7 101.7 100.9 95.8 94.6 95.8 336s 14 15 16 17 18 19 20 336s 99.1 104.2 103.8 104.8 101.9 103.3 106.2 336s > 336s > 336s > ## *********** predicted values ************* 336s > predictData <- Kmenta 336s > predictData$consump <- NULL 336s > predictData$price <- Kmenta$price * 0.9 336s > predictData$income <- Kmenta$income * 1.1 336s > 336s > print( predict( fitwls1, se.fit = TRUE, interval = "prediction" ) ) 337s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 337s 1 97.4 0.643 93.1 101.7 98.9 1.056 337s 2 99.6 0.577 95.3 103.8 100.1 1.037 337s 3 99.5 0.545 95.3 103.8 100.2 0.939 337s 4 99.7 0.582 95.4 104.0 100.4 0.912 337s 5 102.3 0.502 98.1 106.5 102.7 0.895 337s 6 102.1 0.463 97.9 106.3 102.6 0.791 337s 7 102.5 0.484 98.3 106.7 102.4 0.719 337s 8 102.8 0.601 98.6 107.1 104.3 0.963 337s 9 101.7 0.527 97.5 105.9 102.9 0.788 337s 10 100.8 0.788 96.4 105.2 100.4 0.981 337s 11 95.6 0.946 91.0 100.1 96.0 1.185 337s 12 94.4 0.980 89.8 98.9 94.1 1.394 337s 13 95.7 0.880 91.2 100.1 95.6 1.244 337s 14 99.0 0.508 94.8 103.2 97.8 0.896 337s 15 104.3 0.758 99.9 108.7 102.6 0.874 337s 16 103.9 0.616 99.7 108.2 104.1 0.916 337s 17 104.8 1.273 99.9 109.7 103.8 1.605 337s 18 101.9 0.536 97.7 106.2 102.4 0.962 337s 19 103.5 0.680 99.2 107.8 102.1 1.098 337s 20 106.5 1.274 101.7 111.4 104.5 1.664 337s supply.lwr supply.upr 337s 1 93.4 104 337s 2 94.5 106 337s 3 94.7 106 337s 4 94.9 106 337s 5 97.3 108 337s 6 97.2 108 337s 7 97.1 108 337s 8 98.8 110 337s 9 97.6 108 337s 10 94.8 106 337s 11 90.3 102 337s 12 88.2 100 337s 13 89.9 101 337s 14 92.3 103 337s 15 97.2 108 337s 16 98.6 110 337s 17 97.7 110 337s 18 96.9 108 337s 19 96.5 108 337s 20 98.3 111 337s > print( predict( fitwls1$eq[[ 2 ]], se.fit = TRUE, interval = "prediction" ) ) 337s fit se.fit lwr upr 337s 1 98.9 1.056 93.4 104 337s 2 100.1 1.037 94.5 106 337s 3 100.2 0.939 94.7 106 337s 4 100.4 0.912 94.9 106 337s 5 102.7 0.895 97.3 108 337s 6 102.6 0.791 97.2 108 337s 7 102.4 0.719 97.1 108 337s 8 104.3 0.963 98.8 110 337s 9 102.9 0.788 97.6 108 337s 10 100.4 0.981 94.8 106 337s 11 96.0 1.185 90.3 102 337s 12 94.1 1.394 88.2 100 337s 13 95.6 1.244 89.9 101 337s 14 97.8 0.896 92.3 103 337s 15 102.6 0.874 97.2 108 337s 16 104.1 0.916 98.6 110 337s 17 103.8 1.605 97.7 110 337s 18 102.4 0.962 96.9 108 337s 19 102.1 1.098 96.5 108 337s 20 104.5 1.664 98.3 111 337s > 337s > print( predict( fitwls2e, se.pred = TRUE, interval = "confidence", 337s + level = 0.999, newdata = predictData ) ) 337s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 337s 1 103 2.12 100.2 106 96.6 2.65 337s 2 106 2.12 102.7 109 97.8 2.57 337s 3 106 2.13 102.6 109 98.0 2.58 337s 4 106 2.12 102.9 109 98.2 2.56 337s 5 108 2.35 103.5 113 100.9 2.72 337s 6 108 2.31 103.6 113 100.7 2.67 337s 7 109 2.30 104.2 113 100.6 2.62 337s 8 109 2.27 105.0 114 102.6 2.58 337s 9 108 2.36 102.8 112 101.4 2.74 337s 10 106 2.46 100.8 112 98.8 2.92 337s 11 101 2.28 96.7 105 94.4 2.98 337s 12 100 2.12 97.0 103 92.3 2.96 337s 13 102 2.05 99.3 104 93.8 2.81 337s 14 105 2.20 101.2 109 96.3 2.78 337s 15 110 2.53 104.4 116 101.4 2.78 337s 16 110 2.44 104.7 115 102.9 2.69 337s 17 110 2.81 102.9 118 102.9 3.14 337s 18 108 2.23 104.3 112 101.2 2.58 337s 19 110 2.30 105.6 115 100.9 2.57 337s 20 114 2.50 108.1 119 103.3 2.52 337s supply.lwr supply.upr 337s 1 92.9 100.3 337s 2 95.0 100.6 337s 3 95.1 100.9 337s 4 95.5 100.9 337s 5 96.6 105.1 337s 6 96.9 104.6 337s 7 97.2 104.0 337s 8 99.6 105.5 337s 9 96.9 105.9 337s 10 93.1 104.6 337s 11 88.2 100.5 337s 12 86.3 98.4 337s 13 88.8 98.9 337s 14 91.5 101.0 337s 15 96.7 106.2 337s 16 98.9 106.9 337s 17 95.8 110.0 337s 18 98.2 104.1 337s 19 98.1 103.8 337s 20 101.1 105.6 337s > print( predict( fitwls2e$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 337s + level = 0.999, newdata = predictData ) ) 337s fit se.pred lwr upr 337s 1 103 2.12 100.2 106 337s 2 106 2.12 102.7 109 337s 3 106 2.13 102.6 109 337s 4 106 2.12 102.9 109 337s 5 108 2.35 103.5 113 337s 6 108 2.31 103.6 113 337s 7 109 2.30 104.2 113 337s 8 109 2.27 105.0 114 337s 9 108 2.36 102.8 112 337s 10 106 2.46 100.8 112 337s 11 101 2.28 96.7 105 337s 12 100 2.12 97.0 103 337s 13 102 2.05 99.3 104 337s 14 105 2.20 101.2 109 337s 15 110 2.53 104.4 116 337s 16 110 2.44 104.7 115 337s 17 110 2.81 102.9 118 337s 18 108 2.23 104.3 112 337s 19 110 2.30 105.6 115 337s 20 114 2.50 108.1 119 337s > 337s > print( predict( fitwls3, se.pred = TRUE, interval = "prediction", 337s + level = 0.975 ) ) 337s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 337s 1 97.6 2.03 92.8 102.3 98.3 2.54 337s 2 99.6 2.02 94.9 104.4 99.5 2.56 337s 3 99.6 2.01 94.9 104.3 99.7 2.55 337s 4 99.8 2.02 95.0 104.5 99.9 2.56 337s 5 102.2 2.00 97.5 106.9 102.5 2.59 337s 6 102.0 1.99 97.3 106.7 102.4 2.56 337s 7 102.4 1.99 97.7 107.1 102.3 2.54 337s 8 102.8 2.03 98.0 107.5 104.3 2.63 337s 9 101.7 2.01 97.0 106.4 102.9 2.57 337s 10 100.8 2.09 95.9 105.7 100.3 2.64 337s 11 95.8 2.14 90.8 100.8 95.9 2.72 337s 12 94.7 2.14 89.6 99.7 93.9 2.82 337s 13 95.9 2.11 91.0 100.8 95.5 2.75 337s 14 99.1 2.00 94.4 103.8 97.9 2.61 337s 15 104.1 2.07 99.3 109.0 103.0 2.56 337s 16 103.8 2.03 99.0 108.5 104.6 2.55 337s 17 104.6 2.31 99.2 110.0 104.3 2.85 337s 18 101.9 2.01 97.2 106.6 102.9 2.55 337s 19 103.4 2.05 98.6 108.2 102.7 2.59 337s 20 106.3 2.31 100.9 111.7 105.2 2.84 337s supply.lwr supply.upr 337s 1 92.3 104 337s 2 93.5 106 337s 3 93.7 106 337s 4 93.9 106 337s 5 96.4 109 337s 6 96.4 108 337s 7 96.3 108 337s 8 98.1 110 337s 9 96.9 109 337s 10 94.1 107 337s 11 89.5 102 337s 12 87.3 101 337s 13 89.1 102 337s 14 91.8 104 337s 15 97.0 109 337s 16 98.6 111 337s 17 97.6 111 337s 18 96.9 109 337s 19 96.6 109 337s 20 98.6 112 337s > print( predict( fitwls3$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 337s + level = 0.975 ) ) 337s fit se.pred lwr upr 337s 1 98.3 2.54 92.3 104 337s 2 99.5 2.56 93.5 106 337s 3 99.7 2.55 93.7 106 337s 4 99.9 2.56 93.9 106 337s 5 102.5 2.59 96.4 109 337s 6 102.4 2.56 96.4 108 337s 7 102.3 2.54 96.3 108 337s 8 104.3 2.63 98.1 110 337s 9 102.9 2.57 96.9 109 337s 10 100.3 2.64 94.1 107 337s 11 95.9 2.72 89.5 102 337s 12 93.9 2.82 87.3 101 337s 13 95.5 2.75 89.1 102 337s 14 97.9 2.61 91.8 104 337s 15 103.0 2.56 97.0 109 337s 16 104.6 2.55 98.6 111 337s 17 104.3 2.85 97.6 111 337s 18 102.9 2.55 96.9 109 337s 19 102.7 2.59 96.6 109 337s 20 105.2 2.84 98.6 112 337s > 337s > print( predict( fitwls4e, se.fit = TRUE, interval = "confidence", 337s + level = 0.25 ) ) 337s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 337s 1 97.5 0.541 97.4 97.7 98.2 0.598 337s 2 99.6 0.471 99.4 99.7 99.6 0.679 337s 3 99.5 0.454 99.4 99.7 99.7 0.634 337s 4 99.7 0.475 99.5 99.8 100.0 0.643 337s 5 102.3 0.434 102.1 102.4 102.4 0.753 337s 6 102.0 0.418 101.9 102.2 102.4 0.680 337s 7 102.4 0.440 102.3 102.5 102.3 0.625 337s 8 102.7 0.537 102.5 102.9 104.4 0.799 337s 9 101.7 0.447 101.6 101.9 102.9 0.700 337s 10 100.9 0.628 100.7 101.1 100.2 0.716 337s 11 95.8 0.833 95.6 96.1 95.7 0.916 337s 12 94.6 0.807 94.4 94.9 93.9 1.226 337s 13 95.8 0.677 95.6 96.0 95.5 1.130 337s 14 99.1 0.459 98.9 99.2 97.8 0.796 337s 15 104.2 0.572 104.1 104.4 102.9 0.656 337s 16 103.8 0.509 103.7 104.0 104.6 0.644 337s 17 104.8 0.877 104.5 105.1 104.1 1.150 337s 18 101.9 0.478 101.7 102.0 103.0 0.575 337s 19 103.3 0.604 103.1 103.5 102.8 0.649 337s 20 106.2 1.102 105.8 106.6 105.5 0.875 337s supply.lwr supply.upr 337s 1 98.0 98.4 337s 2 99.4 99.8 337s 3 99.5 99.9 337s 4 99.8 100.2 337s 5 102.2 102.7 337s 6 102.1 102.6 337s 7 102.1 102.5 337s 8 104.1 104.6 337s 9 102.7 103.1 337s 10 99.9 100.4 337s 11 95.4 96.0 337s 12 93.5 94.3 337s 13 95.2 95.9 337s 14 97.6 98.1 337s 15 102.7 103.1 337s 16 104.4 104.8 337s 17 103.8 104.5 337s 18 102.8 103.2 337s 19 102.6 103.0 337s 20 105.2 105.8 337s > print( predict( fitwls4e$eq[[ 1 ]], se.fit = TRUE, interval = "confidence", 337s + level = 0.25 ) ) 337s fit se.fit lwr upr 337s 1 97.5 0.541 97.4 97.7 337s 2 99.6 0.471 99.4 99.7 337s 3 99.5 0.454 99.4 99.7 337s 4 99.7 0.475 99.5 99.8 337s 5 102.3 0.434 102.1 102.4 337s 6 102.0 0.418 101.9 102.2 337s 7 102.4 0.440 102.3 102.5 337s 8 102.7 0.537 102.5 102.9 337s 9 101.7 0.447 101.6 101.9 337s 10 100.9 0.628 100.7 101.1 337s 11 95.8 0.833 95.6 96.1 337s 12 94.6 0.807 94.4 94.9 337s 13 95.8 0.677 95.6 96.0 337s 14 99.1 0.459 98.9 99.2 337s 15 104.2 0.572 104.1 104.4 337s 16 103.8 0.509 103.7 104.0 337s 17 104.8 0.877 104.5 105.1 337s 18 101.9 0.478 101.7 102.0 337s 19 103.3 0.604 103.1 103.5 337s 20 106.2 1.102 105.8 106.6 337s > 337s > print( predict( fitwls5, se.fit = TRUE, se.pred = TRUE, 337s + interval = "prediction", level = 0.5, newdata = predictData ) ) 337s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 337s 1 104 0.749 2.07 102.1 105 96.4 337s 2 106 0.784 2.09 104.6 107 97.7 337s 3 106 0.793 2.09 104.5 107 97.8 337s 4 106 0.792 2.09 104.8 108 98.1 337s 5 109 1.136 2.24 107.1 110 100.6 337s 6 108 1.086 2.22 106.9 110 100.5 337s 7 109 1.097 2.22 107.4 110 100.4 337s 8 110 1.107 2.23 108.0 111 102.5 337s 9 108 1.126 2.24 106.4 109 101.1 337s 10 107 1.243 2.30 105.1 108 98.5 337s 11 101 1.066 2.21 99.7 103 94.0 337s 12 100 0.814 2.10 98.8 102 92.0 337s 13 102 0.617 2.03 100.4 103 93.7 337s 14 105 0.874 2.12 103.7 107 96.0 337s 15 111 1.377 2.37 109.0 112 101.2 337s 16 110 1.279 2.32 108.8 112 102.8 337s 17 111 1.656 2.55 108.9 112 102.5 337s 18 109 1.014 2.18 107.0 110 101.1 337s 19 110 1.180 2.27 108.7 112 100.9 337s 20 114 1.635 2.53 112.2 116 103.4 337s supply.se.fit supply.se.pred supply.lwr supply.upr 337s 1 0.799 2.58 94.6 98.1 337s 2 0.679 2.55 95.9 99.4 337s 3 0.692 2.55 96.1 99.6 337s 4 0.657 2.54 96.3 99.8 337s 5 1.051 2.67 98.8 102.5 337s 6 0.947 2.63 98.7 102.3 337s 7 0.845 2.59 98.7 102.2 337s 8 0.849 2.60 100.7 104.2 337s 9 1.100 2.69 99.3 103.0 337s 10 1.276 2.77 96.6 100.4 337s 11 1.422 2.84 92.1 95.9 337s 12 1.595 2.93 90.1 94.0 337s 13 1.401 2.82 91.7 95.6 337s 14 1.201 2.73 94.2 97.9 337s 15 1.169 2.72 99.3 103.0 337s 16 1.060 2.67 100.9 104.6 337s 17 1.727 3.00 100.5 104.6 337s 18 0.831 2.59 99.3 102.8 337s 19 0.834 2.59 99.1 102.6 337s 20 0.653 2.54 101.7 105.2 337s > print( predict( fitwls5$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 337s + interval = "prediction", level = 0.5, newdata = predictData ) ) 337s fit se.fit se.pred lwr upr 337s 1 96.4 0.799 2.58 94.6 98.1 337s 2 97.7 0.679 2.55 95.9 99.4 337s 3 97.8 0.692 2.55 96.1 99.6 337s 4 98.1 0.657 2.54 96.3 99.8 337s 5 100.6 1.051 2.67 98.8 102.5 337s 6 100.5 0.947 2.63 98.7 102.3 337s 7 100.4 0.845 2.59 98.7 102.2 337s 8 102.5 0.849 2.60 100.7 104.2 337s 9 101.1 1.100 2.69 99.3 103.0 337s 10 98.5 1.276 2.77 96.6 100.4 337s 11 94.0 1.422 2.84 92.1 95.9 337s 12 92.0 1.595 2.93 90.1 94.0 337s 13 93.7 1.401 2.82 91.7 95.6 337s 14 96.0 1.201 2.73 94.2 97.9 337s 15 101.2 1.169 2.72 99.3 103.0 337s 16 102.8 1.060 2.67 100.9 104.6 337s 17 102.5 1.727 3.00 100.5 104.6 337s 18 101.1 0.831 2.59 99.3 102.8 337s 19 100.9 0.834 2.59 99.1 102.6 337s 20 103.4 0.653 2.54 101.7 105.2 337s > 337s > print( predict( fitwlsi1e, se.fit = TRUE, se.pred = TRUE, 337s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 337s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 337s 1 97.4 0.593 2.02 95.8 99.0 98.9 337s 2 99.6 0.532 2.00 98.1 101.0 100.1 337s 3 99.5 0.502 1.99 98.2 100.9 100.2 337s 4 99.7 0.537 2.00 98.2 101.2 100.4 337s 5 102.3 0.463 1.98 101.0 103.6 102.7 337s 6 102.1 0.427 1.98 100.9 103.2 102.6 337s 7 102.5 0.446 1.98 101.2 103.7 102.4 337s 8 102.8 0.554 2.01 101.3 104.3 104.3 337s 9 101.7 0.486 1.99 100.4 103.0 102.9 337s 10 100.8 0.727 2.06 98.8 102.8 100.4 337s 11 95.6 0.872 2.12 93.2 98.0 96.0 337s 12 94.4 0.903 2.13 91.9 96.8 94.1 337s 13 95.7 0.811 2.09 93.4 97.9 95.6 337s 14 99.0 0.468 1.99 97.7 100.3 97.8 337s 15 104.3 0.699 2.05 102.4 106.2 102.6 337s 16 103.9 0.568 2.01 102.4 105.5 104.1 337s 17 104.8 1.174 2.26 101.6 108.0 103.8 337s 18 101.9 0.494 1.99 100.6 103.3 102.4 337s 19 103.5 0.627 2.03 101.8 105.2 102.1 337s 20 106.5 1.175 2.26 103.3 109.7 104.5 337s supply.se.fit supply.se.pred supply.lwr supply.upr 337s 1 0.945 2.58 96.3 101.5 337s 2 0.928 2.58 97.5 102.6 337s 3 0.839 2.55 97.9 102.5 337s 4 0.816 2.54 98.1 102.6 337s 5 0.800 2.53 100.5 104.9 337s 6 0.707 2.51 100.6 104.5 337s 7 0.643 2.49 100.7 104.2 337s 8 0.862 2.55 102.0 106.7 337s 9 0.705 2.51 101.0 104.9 337s 10 0.877 2.56 98.0 102.7 337s 11 1.060 2.63 93.1 98.9 337s 12 1.247 2.71 90.7 97.5 337s 13 1.113 2.65 92.6 98.6 337s 14 0.801 2.53 95.6 100.0 337s 15 0.782 2.53 100.5 104.8 337s 16 0.819 2.54 101.9 106.3 337s 17 1.436 2.80 99.9 107.7 337s 18 0.861 2.55 100.0 104.7 337s 19 0.982 2.60 99.4 104.8 337s 20 1.489 2.83 100.4 108.6 337s > print( predict( fitwlsi1e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 337s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 337s fit se.fit se.pred lwr upr 337s 1 97.4 0.593 2.02 95.8 99.0 337s 2 99.6 0.532 2.00 98.1 101.0 337s 3 99.5 0.502 1.99 98.2 100.9 337s 4 99.7 0.537 2.00 98.2 101.2 337s 5 102.3 0.463 1.98 101.0 103.6 337s 6 102.1 0.427 1.98 100.9 103.2 337s 7 102.5 0.446 1.98 101.2 103.7 337s 8 102.8 0.554 2.01 101.3 104.3 337s 9 101.7 0.486 1.99 100.4 103.0 337s 10 100.8 0.727 2.06 98.8 102.8 337s 11 95.6 0.872 2.12 93.2 98.0 337s 12 94.4 0.903 2.13 91.9 96.8 337s 13 95.7 0.811 2.09 93.4 97.9 337s 14 99.0 0.468 1.99 97.7 100.3 337s 15 104.3 0.699 2.05 102.4 106.2 337s 16 103.9 0.568 2.01 102.4 105.5 337s 17 104.8 1.174 2.26 101.6 108.0 337s 18 101.9 0.494 1.99 100.6 103.3 337s 19 103.5 0.627 2.03 101.8 105.2 337s 20 106.5 1.175 2.26 103.3 109.7 337s > 337s > print( predict( fitwlsi2, se.fit = TRUE, interval = "prediction", 337s + level = 0.9, newdata = predictData ) ) 337s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 337s 1 103 0.937 99.7 107 96.6 1.151 337s 2 106 0.942 102.2 110 97.8 0.875 337s 3 106 0.966 102.1 109 98.0 0.909 337s 4 106 0.947 102.4 110 98.2 0.833 337s 5 108 1.448 104.3 112 100.9 1.327 337s 6 108 1.368 104.2 112 100.7 1.192 337s 7 109 1.352 104.7 113 100.6 1.052 337s 8 109 1.293 105.4 113 102.6 0.914 337s 9 108 1.459 103.5 112 101.4 1.400 337s 10 106 1.647 102.0 111 98.8 1.787 337s 11 101 1.300 97.0 105 94.4 1.911 337s 12 100 0.938 96.4 104 92.3 1.880 337s 13 102 0.722 98.2 105 93.8 1.565 337s 14 105 1.121 101.1 109 96.3 1.479 337s 15 110 1.769 105.8 115 101.4 1.481 337s 16 110 1.602 105.8 114 102.9 1.248 337s 17 110 2.210 105.3 115 102.9 2.201 337s 18 108 1.205 104.5 112 101.2 0.911 337s 19 110 1.353 106.1 114 100.9 0.877 337s 20 114 1.714 109.4 118 103.3 0.705 337s supply.lwr supply.upr 337s 1 92.0 101.2 337s 2 93.4 102.2 337s 3 93.6 102.4 337s 4 93.9 102.6 337s 5 96.2 105.6 337s 6 96.1 105.3 337s 7 96.1 105.1 337s 8 98.1 107.0 337s 9 96.6 106.1 337s 10 93.7 103.9 337s 11 89.1 99.6 337s 12 87.1 97.5 337s 13 88.9 98.8 337s 14 91.4 101.1 337s 15 96.6 106.3 337s 16 98.3 107.6 337s 17 97.4 108.5 337s 18 96.8 105.6 337s 19 96.5 105.3 337s 20 99.0 107.7 337s > print( predict( fitwlsi2$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 337s + level = 0.9, newdata = predictData ) ) 337s fit se.fit lwr upr 337s 1 96.6 1.151 92.0 101.2 337s 2 97.8 0.875 93.4 102.2 337s 3 98.0 0.909 93.6 102.4 337s 4 98.2 0.833 93.9 102.6 337s 5 100.9 1.327 96.2 105.6 337s 6 100.7 1.192 96.1 105.3 337s 7 100.6 1.052 96.1 105.1 337s 8 102.6 0.914 98.1 107.0 337s 9 101.4 1.400 96.6 106.1 337s 10 98.8 1.787 93.7 103.9 337s 11 94.4 1.911 89.1 99.6 337s 12 92.3 1.880 87.1 97.5 337s 13 93.8 1.565 88.9 98.8 337s 14 96.3 1.479 91.4 101.1 337s 15 101.4 1.481 96.6 106.3 337s 16 102.9 1.248 98.3 107.6 337s 17 102.9 2.201 97.4 108.5 337s 18 101.2 0.911 96.8 105.6 337s 19 100.9 0.877 96.5 105.3 337s 20 103.3 0.705 99.0 107.7 337s > 337s > print( predict( fitwlsi3e, interval = "prediction", level = 0.925 ) ) 337s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 337s 1 97.6 93.9 101.3 98.3 93.6 103 337s 2 99.7 96.0 103.3 99.5 94.9 104 337s 3 99.6 95.9 103.3 99.7 95.1 104 337s 4 99.8 96.1 103.5 99.9 95.3 105 337s 5 102.2 98.6 105.9 102.5 97.8 107 337s 6 102.0 98.4 105.7 102.4 97.7 107 337s 7 102.4 98.7 106.0 102.3 97.6 107 337s 8 102.8 99.1 106.5 104.3 99.5 109 337s 9 101.7 98.0 105.3 102.9 98.3 108 337s 10 100.8 97.0 104.6 100.3 95.5 105 337s 11 95.8 91.9 99.7 95.9 91.0 101 337s 12 94.7 90.8 98.6 93.9 88.9 99 337s 13 95.9 92.1 99.7 95.5 90.6 100 337s 14 99.1 95.4 102.7 97.9 93.2 103 337s 15 104.1 100.4 107.9 103.0 98.3 108 337s 16 103.8 100.1 107.5 104.6 99.9 109 337s 17 104.6 100.4 108.7 104.3 99.2 109 337s 18 101.9 98.2 105.6 102.9 98.2 108 337s 19 103.4 99.6 107.1 102.7 98.0 107 337s 20 106.3 102.2 110.4 105.2 100.1 110 337s > print( predict( fitwlsi3e$eq[[ 1 ]], interval = "prediction", level = 0.925 ) ) 337s fit lwr upr 337s 1 97.6 93.9 101.3 337s 2 99.7 96.0 103.3 337s 3 99.6 95.9 103.3 337s 4 99.8 96.1 103.5 337s 5 102.2 98.6 105.9 337s 6 102.0 98.4 105.7 337s 7 102.4 98.7 106.0 337s 8 102.8 99.1 106.5 337s 9 101.7 98.0 105.3 337s 10 100.8 97.0 104.6 337s 11 95.8 91.9 99.7 337s 12 94.7 90.8 98.6 337s 13 95.9 92.1 99.7 337s 14 99.1 95.4 102.7 337s 15 104.1 100.4 107.9 337s 16 103.8 100.1 107.5 337s 17 104.6 100.4 108.7 337s 18 101.9 98.2 105.6 337s 19 103.4 99.6 107.1 337s 20 106.3 102.2 110.4 337s > 337s > print( predict( fitwlsi4, interval = "confidence", newdata = predictData ) ) 337s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 337s 1 104 102.0 105 96.4 94.8 98.0 337s 2 106 104.4 108 97.7 96.3 99.0 337s 3 106 104.3 108 97.8 96.4 99.2 337s 4 106 104.6 108 98.1 96.7 99.4 337s 5 109 106.3 111 100.6 98.5 102.8 337s 6 108 106.2 111 100.5 98.6 102.4 337s 7 109 106.7 111 100.4 98.7 102.2 337s 8 110 107.3 112 102.5 100.7 104.2 337s 9 108 105.6 110 101.1 98.9 103.4 337s 10 107 104.1 109 98.5 95.9 101.1 337s 11 101 99.0 103 94.0 91.1 96.9 337s 12 100 98.6 102 92.0 88.8 95.3 337s 13 102 100.5 103 93.7 90.8 96.5 337s 14 105 103.3 107 96.0 93.6 98.5 337s 15 111 107.8 113 101.2 98.8 103.6 337s 16 110 107.8 113 102.8 100.6 104.9 337s 17 111 107.3 114 102.5 99.0 106.0 337s 18 109 106.5 111 101.1 99.4 102.8 337s 19 110 107.9 113 100.9 99.2 102.6 337s 20 114 110.6 117 103.4 102.1 104.7 337s > print( predict( fitwlsi4$eq[[ 2 ]], interval = "confidence", 337s + newdata = predictData ) ) 337s fit lwr upr 337s 1 96.4 94.8 98.0 337s 2 97.7 96.3 99.0 337s 3 97.8 96.4 99.2 337s 4 98.1 96.7 99.4 337s 5 100.6 98.5 102.8 337s 6 100.5 98.6 102.4 337s 7 100.4 98.7 102.2 337s 8 102.5 100.7 104.2 337s 9 101.1 98.9 103.4 337s 10 98.5 95.9 101.1 337s 11 94.0 91.1 96.9 337s 12 92.0 88.8 95.3 337s 13 93.7 90.8 96.5 337s 14 96.0 93.6 98.5 337s 15 101.2 98.8 103.6 337s 16 102.8 100.6 104.9 337s 17 102.5 99.0 106.0 337s 18 101.1 99.4 102.8 337s 19 100.9 99.2 102.6 337s 20 103.4 102.1 104.7 337s > 337s > print( predict( fitwlsi5e, se.fit = TRUE, se.pred = TRUE, 337s + interval = "prediction", level = 0.01 ) ) 337s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 337s 1 97.5 0.540 2.01 97.5 97.6 98.2 337s 2 99.6 0.470 1.99 99.6 99.6 99.6 337s 3 99.5 0.453 1.99 99.5 99.6 99.7 337s 4 99.7 0.474 1.99 99.7 99.7 100.0 337s 5 102.3 0.433 1.98 102.2 102.3 102.4 337s 6 102.0 0.417 1.98 102.0 102.1 102.4 337s 7 102.4 0.439 1.98 102.4 102.4 102.3 337s 8 102.7 0.536 2.01 102.7 102.7 104.4 337s 9 101.7 0.446 1.99 101.7 101.8 102.9 337s 10 100.9 0.627 2.03 100.9 100.9 100.2 337s 11 95.8 0.831 2.11 95.8 95.9 95.7 337s 12 94.6 0.806 2.10 94.6 94.6 93.9 337s 13 95.8 0.676 2.05 95.8 95.8 95.5 337s 14 99.1 0.458 1.99 99.0 99.1 97.8 337s 15 104.2 0.571 2.02 104.2 104.3 102.9 337s 16 103.8 0.508 2.00 103.8 103.9 104.6 337s 17 104.8 0.877 2.12 104.8 104.8 104.1 337s 18 101.9 0.477 1.99 101.8 101.9 103.0 337s 19 103.3 0.602 2.03 103.3 103.4 102.8 337s 20 106.2 1.100 2.23 106.2 106.2 105.5 337s supply.se.fit supply.se.pred supply.lwr supply.upr 337s 1 0.598 2.52 98.2 98.3 337s 2 0.680 2.54 99.5 99.6 337s 3 0.634 2.53 99.7 99.8 337s 4 0.644 2.54 100.0 100.0 337s 5 0.754 2.57 102.4 102.5 337s 6 0.681 2.55 102.3 102.4 337s 7 0.626 2.53 102.3 102.3 337s 8 0.800 2.58 104.4 104.4 337s 9 0.701 2.55 102.9 102.9 337s 10 0.716 2.55 100.1 100.2 337s 11 0.918 2.62 95.7 95.8 337s 12 1.229 2.74 93.8 93.9 337s 13 1.132 2.70 95.5 95.6 337s 14 0.797 2.58 97.8 97.9 337s 15 0.657 2.54 102.9 103.0 337s 16 0.645 2.54 104.5 104.6 337s 17 1.151 2.71 104.1 104.2 337s 18 0.575 2.52 103.0 103.0 337s 19 0.649 2.54 102.8 102.8 337s 20 0.875 2.60 105.5 105.5 337s > print( predict( fitwlsi5e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 337s + interval = "prediction", level = 0.01 ) ) 337s fit se.fit se.pred lwr upr 337s 1 97.5 0.540 2.01 97.5 97.6 337s 2 99.6 0.470 1.99 99.6 99.6 337s 3 99.5 0.453 1.99 99.5 99.6 337s 4 99.7 0.474 1.99 99.7 99.7 337s 5 102.3 0.433 1.98 102.2 102.3 337s 6 102.0 0.417 1.98 102.0 102.1 337s 7 102.4 0.439 1.98 102.4 102.4 337s 8 102.7 0.536 2.01 102.7 102.7 337s 9 101.7 0.446 1.99 101.7 101.8 337s 10 100.9 0.627 2.03 100.9 100.9 337s 11 95.8 0.831 2.11 95.8 95.9 337s 12 94.6 0.806 2.10 94.6 94.6 337s 13 95.8 0.676 2.05 95.8 95.8 337s 14 99.1 0.458 1.99 99.0 99.1 337s 15 104.2 0.571 2.02 104.2 104.3 337s 16 103.8 0.508 2.00 103.8 103.9 337s 17 104.8 0.877 2.12 104.8 104.8 337s 18 101.9 0.477 1.99 101.8 101.9 337s 19 103.3 0.602 2.03 103.3 103.4 337s 20 106.2 1.100 2.23 106.2 106.2 337s > 337s > # predict just one observation 337s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 337s + trend = 25 ) 337s > 337s > print( predict( fitwls1, newdata = smallData ) ) 337s demand.pred supply.pred 337s 1 109 115 337s > print( predict( fitwls1$eq[[ 1 ]], newdata = smallData ) ) 337s fit 337s 1 109 337s > 337s > print( predict( fitwls2e, se.fit = TRUE, level = 0.9, 337s + newdata = smallData ) ) 337s demand.pred demand.se.fit supply.pred supply.se.fit 337s 1 109 2.23 116 3.03 337s > print( predict( fitwls2e$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 337s + newdata = smallData ) ) 337s fit se.pred 337s 1 109 2.96 337s > 337s > print( predict( fitwls3, interval = "prediction", level = 0.975, 337s + newdata = smallData ) ) 337s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 337s 1 109 101 116 116 107 126 337s > print( predict( fitwls3$eq[[ 1 ]], interval = "confidence", level = 0.8, 337s + newdata = smallData ) ) 337s fit lwr upr 337s 1 109 106 112 337s > 337s > print( predict( fitwls4e, se.fit = TRUE, interval = "confidence", 337s + level = 0.999, newdata = smallData ) ) 337s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 337s 1 108 2.02 101 116 117 2.02 337s supply.lwr supply.upr 337s 1 110 124 337s > print( predict( fitwls4e$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 337s + level = 0.75, newdata = smallData ) ) 337s fit se.pred lwr upr 337s 1 117 3.18 113 121 337s > 337s > print( predict( fitwls5, se.fit = TRUE, interval = "prediction", 337s + newdata = smallData ) ) 337s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 337s 1 108 2.2 102 114 117 2.23 337s supply.lwr supply.upr 337s 1 110 124 337s > print( predict( fitwls5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 337s + newdata = smallData ) ) 337s fit se.pred lwr upr 337s 1 108 2.93 104 113 337s > 337s > print( predict( fitwlsi3e, se.fit = TRUE, se.pred = TRUE, 337s + interval = "prediction", level = 0.5, newdata = smallData ) ) 337s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 337s 1 109 2.23 2.95 107 111 116 337s supply.se.fit supply.se.pred supply.lwr supply.upr 337s 1 3.04 3.9 114 119 337s > print( predict( fitwlsi3e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 337s + interval = "confidence", level = 0.25, newdata = smallData ) ) 337s fit se.fit se.pred lwr upr 337s 1 109 2.23 2.95 108 109 337s > 337s > 337s > ## ************ correlation of predicted values *************** 337s > print( correlation.systemfit( fitwls1, 2, 1 ) ) 337s [,1] 337s [1,] 0 337s [2,] 0 337s [3,] 0 337s [4,] 0 337s [5,] 0 337s [6,] 0 337s [7,] 0 337s [8,] 0 337s [9,] 0 337s [10,] 0 337s [11,] 0 337s [12,] 0 337s [13,] 0 337s [14,] 0 337s [15,] 0 337s [16,] 0 337s [17,] 0 337s [18,] 0 337s [19,] 0 337s [20,] 0 337s > 337s > print( correlation.systemfit( fitwls2e, 1, 2 ) ) 337s [,1] 337s [1,] 0.411525 337s [2,] 0.147624 337s [3,] 0.147711 337s [4,] 0.107654 337s [5,] -0.069284 337s [6,] -0.053039 337s [7,] -0.051551 337s [8,] -0.006153 337s [9,] -0.000333 337s [10,] -0.001262 337s [11,] 0.048574 337s [12,] 0.064996 337s [13,] 0.024618 337s [14,] -0.028485 337s [15,] 0.174980 337s [16,] 0.252722 337s [17,] 0.103392 337s [18,] 0.074219 337s [19,] 0.156545 337s [20,] 0.135438 337s > 337s > print( correlation.systemfit( fitwls3, 2, 1 ) ) 337s [,1] 337s [1,] 0.405901 337s [2,] 0.145364 337s [3,] 0.145375 337s [4,] 0.105835 337s [5,] -0.067958 337s [6,] -0.052026 337s [7,] -0.050543 337s [8,] -0.006031 337s [9,] -0.000326 337s [10,] -0.001237 337s [11,] 0.047534 337s [12,] 0.063493 337s [13,] 0.024060 337s [14,] -0.027910 337s [15,] 0.171580 337s [16,] 0.248212 337s [17,] 0.101409 337s [18,] 0.073084 337s [19,] 0.153950 337s [20,] 0.132944 337s > 337s > print( correlation.systemfit( fitwls4e, 1, 2 ) ) 337s [,1] 337s [1,] 0.38162 337s [2,] 0.29173 337s [3,] 0.25421 337s [4,] 0.28598 337s [5,] -0.02775 337s [6,] -0.04974 337s [7,] -0.05850 337s [8,] 0.09388 337s [9,] 0.09469 337s [10,] 0.43814 337s [11,] 0.10559 337s [12,] 0.00876 337s [13,] 0.04090 337s [14,] -0.03984 337s [15,] 0.40767 337s [16,] 0.24571 337s [17,] 0.64160 337s [18,] 0.24037 337s [19,] 0.34075 337s [20,] 0.54270 337s > 337s > print( correlation.systemfit( fitwls5, 2, 1 ) ) 337s [,1] 337s [1,] 0.3775 337s [2,] 0.2936 337s [3,] 0.2553 337s [4,] 0.2875 337s [5,] -0.0274 337s [6,] -0.0492 337s [7,] -0.0578 337s [8,] 0.0932 337s [9,] 0.0944 337s [10,] 0.4375 337s [11,] 0.1027 337s [12,] 0.0072 337s [13,] 0.0404 337s [14,] -0.0396 337s [15,] 0.4062 337s [16,] 0.2430 337s [17,] 0.6406 337s [18,] 0.2362 337s [19,] 0.3347 337s [20,] 0.5378 337s > 337s > print( correlation.systemfit( fitwlsi1e, 1, 2 ) ) 337s [,1] 337s [1,] 0 337s [2,] 0 337s [3,] 0 337s [4,] 0 337s [5,] 0 337s [6,] 0 337s [7,] 0 337s [8,] 0 337s [9,] 0 337s [10,] 0 337s [11,] 0 337s [12,] 0 337s [13,] 0 337s [14,] 0 337s [15,] 0 337s [16,] 0 337s [17,] 0 337s [18,] 0 337s [19,] 0 337s [20,] 0 337s > 337s > print( correlation.systemfit( fitwlsi2, 2, 1 ) ) 337s [,1] 337s [1,] 0.404696 337s [2,] 0.144881 337s [3,] 0.144877 337s [4,] 0.105448 337s [5,] -0.067678 337s [6,] -0.051812 337s [7,] -0.050330 337s [8,] -0.006005 337s [9,] -0.000325 337s [10,] -0.001232 337s [11,] 0.047315 337s [12,] 0.063179 337s [13,] 0.023943 337s [14,] -0.027789 337s [15,] 0.170862 337s [16,] 0.247256 337s [17,] 0.100990 337s [18,] 0.072842 337s [19,] 0.153398 337s [20,] 0.132415 337s > 337s > print( correlation.systemfit( fitwlsi3e, 1, 2 ) ) 337s [,1] 337s [1,] 0.410485 337s [2,] 0.147206 337s [3,] 0.147278 337s [4,] 0.107316 337s [5,] -0.069036 337s [6,] -0.052850 337s [7,] -0.051363 337s [8,] -0.006130 337s [9,] -0.000331 337s [10,] -0.001257 337s [11,] 0.048379 337s [12,] 0.064714 337s [13,] 0.024513 337s [14,] -0.028377 337s [15,] 0.174345 337s [16,] 0.251882 337s [17,] 0.103022 337s [18,] 0.074009 337s [19,] 0.156063 337s [20,] 0.134974 337s > 337s > print( correlation.systemfit( fitwlsi4, 2, 1 ) ) 337s [,1] 337s [1,] 0.37672 337s [2,] 0.29387 337s [3,] 0.25544 337s [4,] 0.28775 337s [5,] -0.02729 337s [6,] -0.04911 337s [7,] -0.05771 337s [8,] 0.09311 337s [9,] 0.09437 337s [10,] 0.43736 337s [11,] 0.10223 337s [12,] 0.00693 337s [13,] 0.04035 337s [14,] -0.03961 337s [15,] 0.40591 337s [16,] 0.24248 337s [17,] 0.64034 337s [18,] 0.23551 337s [19,] 0.33360 337s [20,] 0.53687 337s > 337s > print( correlation.systemfit( fitwlsi5e, 1, 2 ) ) 337s [,1] 337s [1,] 0.38098 337s [2,] 0.29204 337s [3,] 0.25439 337s [4,] 0.28624 337s [5,] -0.02769 337s [6,] -0.04966 337s [7,] -0.05840 337s [8,] 0.09378 337s [9,] 0.09465 337s [10,] 0.43805 337s [11,] 0.10513 337s [12,] 0.00851 337s [13,] 0.04083 337s [14,] -0.03981 337s [15,] 0.40746 337s [16,] 0.24528 337s [17,] 0.64146 337s [18,] 0.23972 337s [19,] 0.33979 337s [20,] 0.54192 337s > 337s > 337s > ## ************ Log-Likelihood values *************** 337s > print( logLik( fitwls1 ) ) 337s 'log Lik.' -67.8 (df=9) 337s > print( logLik( fitwls1, residCovDiag = TRUE ) ) 337s 'log Lik.' -83.6 (df=9) 337s > all.equal( logLik( fitwls1, residCovDiag = TRUE ), 337s + logLik( lmDemand ) + logLik( lmSupply ), 337s + check.attributes = FALSE ) 337s [1] TRUE 337s > 337s > print( logLik( fitwls2e ) ) 337s 'log Lik.' -61.5 (df=8) 337s > print( logLik( fitwls2e, residCovDiag = TRUE ) ) 337s 'log Lik.' -84 (df=8) 337s > 337s > print( logLik( fitwls3 ) ) 337s 'log Lik.' -61.4 (df=8) 337s > print( logLik( fitwls3, residCovDiag = TRUE ) ) 337s 'log Lik.' -84 (df=8) 337s > 337s > print( logLik( fitwls4e ) ) 337s 'log Lik.' -62.2 (df=7) 337s > print( logLik( fitwls4e, residCovDiag = TRUE ) ) 337s 'log Lik.' -84 (df=7) 337s > 337s > print( logLik( fitwls5 ) ) 337s 'log Lik.' -62.1 (df=7) 337s > print( logLik( fitwls5, residCovDiag = TRUE ) ) 337s 'log Lik.' -84 (df=7) 337s > 337s > print( logLik( fitwlsi1e ) ) 337s 'log Lik.' -67.8 (df=9) 337s > print( logLik( fitwlsi1e, residCovDiag = TRUE ) ) 337s 'log Lik.' -83.6 (df=9) 337s > 337s > print( logLik( fitwlsi2 ) ) 337s 'log Lik.' -61.4 (df=8) 337s > print( logLik( fitwlsi2, residCovDiag = TRUE ) ) 337s 'log Lik.' -84 (df=8) 337s > 337s > print( logLik( fitwlsi3e ) ) 337s 'log Lik.' -61.5 (df=8) 337s > print( logLik( fitwlsi3e, residCovDiag = TRUE ) ) 337s 'log Lik.' -84 (df=8) 337s > 337s > print( logLik( fitwlsi4 ) ) 337s 'log Lik.' -62.1 (df=7) 337s > print( logLik( fitwlsi4, residCovDiag = TRUE ) ) 337s 'log Lik.' -84 (df=7) 337s > 337s > print( logLik( fitwlsi5e ) ) 337s 'log Lik.' -62.2 (df=7) 337s > print( logLik( fitwlsi5e, residCovDiag = TRUE ) ) 337s 'log Lik.' -84 (df=7) 337s > 337s > 337s > ## ************** F tests **************** 337s > # testing first restriction 337s > print( linearHypothesis( fitwls1, restrm ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s 337s Model 1: restricted model 337s Model 2: fitwls1 337s 337s Res.Df Df F Pr(>F) 337s 1 34 337s 2 33 1 0.64 0.43 337s > linearHypothesis( fitwls1, restrict ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s 337s Model 1: restricted model 337s Model 2: fitwls1 337s 337s Res.Df Df F Pr(>F) 337s 1 34 337s 2 33 1 0.64 0.43 337s > 337s > print( linearHypothesis( fitwlsi1e, restrm ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1e 337s 337s Res.Df Df F Pr(>F) 337s 1 34 337s 2 33 1 0.66 0.42 337s > linearHypothesis( fitwlsi1e, restrict ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1e 337s 337s Res.Df Df F Pr(>F) 337s 1 34 337s 2 33 1 0.66 0.42 337s > 337s > # testing second restriction 337s > restrOnly2m <- matrix(0,1,7) 337s > restrOnly2q <- 0.5 337s > restrOnly2m[1,2] <- -1 337s > restrOnly2m[1,5] <- 1 337s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 337s > # first restriction not imposed 337s > print( linearHypothesis( fitwls1e, restrOnly2m, restrOnly2q ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls1e 337s 337s Res.Df Df F Pr(>F) 337s 1 34 337s 2 33 1 0.03 0.86 337s > linearHypothesis( fitwls1e, restrictOnly2 ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls1e 337s 337s Res.Df Df F Pr(>F) 337s 1 34 337s 2 33 1 0.03 0.86 337s > 337s > print( linearHypothesis( fitwlsi1, restrOnly2m, restrOnly2q ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1 337s 337s Res.Df Df F Pr(>F) 337s 1 34 337s 2 33 1 0.03 0.86 337s > linearHypothesis( fitwlsi1, restrictOnly2 ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1 337s 337s Res.Df Df F Pr(>F) 337s 1 34 337s 2 33 1 0.03 0.86 337s > 337s > # first restriction imposed 337s > print( linearHypothesis( fitwls2, restrOnly2m, restrOnly2q ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls2 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 34 1 0.08 0.78 337s > linearHypothesis( fitwls2, restrictOnly2 ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls2 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 34 1 0.08 0.78 337s > 337s > print( linearHypothesis( fitwls3, restrOnly2m, restrOnly2q ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls3 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 34 1 0.08 0.78 337s > linearHypothesis( fitwls3, restrictOnly2 ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls3 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 34 1 0.08 0.78 337s > 337s > print( linearHypothesis( fitwlsi2e, restrOnly2m, restrOnly2q ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi2e 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 34 1 0.08 0.77 337s > linearHypothesis( fitwlsi2e, restrictOnly2 ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi2e 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 34 1 0.08 0.77 337s > 337s > print( linearHypothesis( fitwlsi3e, restrOnly2m, restrOnly2q ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi3e 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 34 1 0.08 0.77 337s > linearHypothesis( fitwlsi3e, restrictOnly2 ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi3e 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 34 1 0.08 0.77 337s > 337s > # testing both of the restrictions 337s > print( linearHypothesis( fitwls1e, restr2m, restr2q ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls1e 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 33 2 0.37 0.69 337s > linearHypothesis( fitwls1e, restrict2 ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls1e 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 33 2 0.37 0.69 337s > 337s > print( linearHypothesis( fitwlsi1, restr2m, restr2q ) ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 33 2 0.36 0.7 337s > linearHypothesis( fitwlsi1, restrict2 ) 337s Linear hypothesis test (Theil's F test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1 337s 337s Res.Df Df F Pr(>F) 337s 1 35 337s 2 33 2 0.36 0.7 337s > 337s > 337s > ## ************** Wald tests **************** 337s > # testing first restriction 337s > print( linearHypothesis( fitwls1, restrm, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s 337s Model 1: restricted model 337s Model 2: fitwls1 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 34 337s 2 33 1 0.64 0.42 337s > linearHypothesis( fitwls1, restrict, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s 337s Model 1: restricted model 337s Model 2: fitwls1 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 34 337s 2 33 1 0.64 0.42 337s > 337s > print( linearHypothesis( fitwlsi1e, restrm, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 34 337s 2 33 1 0.8 0.37 337s > linearHypothesis( fitwlsi1e, restrict, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 34 337s 2 33 1 0.8 0.37 337s > 337s > # testing second restriction 337s > # first restriction not imposed 337s > print( linearHypothesis( fitwls1e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls1e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 34 337s 2 33 1 0.04 0.84 337s > linearHypothesis( fitwls1e, restrictOnly2, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls1e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 34 337s 2 33 1 0.04 0.84 337s > 337s > print( linearHypothesis( fitwlsi1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 34 337s 2 33 1 0.03 0.86 337s > linearHypothesis( fitwlsi1, restrictOnly2, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 34 337s 2 33 1 0.03 0.86 337s > 337s > # first restriction imposed 337s > print( linearHypothesis( fitwls2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls2 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 34 1 0.08 0.78 337s > linearHypothesis( fitwls2, restrictOnly2, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls2 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 34 1 0.08 0.78 337s > 337s > print( linearHypothesis( fitwls3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls3 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 34 1 0.08 0.78 337s > linearHypothesis( fitwls3, restrictOnly2, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls3 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 34 1 0.08 0.78 337s > 337s > print( linearHypothesis( fitwlsi2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi2e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 34 1 0.1 0.75 337s > linearHypothesis( fitwlsi2e, restrictOnly2, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi2e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 34 1 0.1 0.75 337s > 337s > print( linearHypothesis( fitwlsi3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi3e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 34 1 0.1 0.75 337s > linearHypothesis( fitwlsi3e, restrictOnly2, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi3e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 34 1 0.1 0.75 337s > 337s > # testing both of the restrictions 337s > print( linearHypothesis( fitwls1e, restr2m, restr2q, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls1e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 33 2 0.9 0.64 337s > linearHypothesis( fitwls1e, restrict2, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwls1e 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 33 2 0.9 0.64 337s > 337s > print( linearHypothesis( fitwlsi1, restr2m, restr2q, test = "Chisq" ) ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 33 2 0.72 0.7 337s > linearHypothesis( fitwlsi1, restrict2, test = "Chisq" ) 337s Linear hypothesis test (Chi^2 statistic of a Wald test) 337s 337s Hypothesis: 337s demand_income - supply_trend = 0 337s - demand_price + supply_price = 0.5 337s 337s Model 1: restricted model 337s Model 2: fitwlsi1 337s 337s Res.Df Df Chisq Pr(>Chisq) 337s 1 35 337s 2 33 2 0.72 0.7 337s > 337s > 337s > ## ****************** model frame ************************** 337s > print( mf <- model.frame( fitwls1 ) ) 337s consump price income farmPrice trend 337s 1 98.5 100.3 87.4 98.0 1 337s 2 99.2 104.3 97.6 99.1 2 337s 3 102.2 103.4 96.7 99.1 3 337s 4 101.5 104.5 98.2 98.1 4 337s 5 104.2 98.0 99.8 110.8 5 337s 6 103.2 99.5 100.5 108.2 6 337s 7 104.0 101.1 103.2 105.6 7 337s 8 99.9 104.8 107.8 109.8 8 337s 9 100.3 96.4 96.6 108.7 9 337s 10 102.8 91.2 88.9 100.6 10 337s 11 95.4 93.1 75.1 81.0 11 337s 12 92.4 98.8 76.9 68.6 12 337s 13 94.5 102.9 84.6 70.9 13 337s 14 98.8 98.8 90.6 81.4 14 337s 15 105.8 95.1 103.1 102.3 15 337s 16 100.2 98.5 105.1 105.0 16 337s 17 103.5 86.5 96.4 110.5 17 337s 18 99.9 104.0 104.4 92.5 18 337s 19 105.2 105.8 110.7 89.3 19 337s 20 106.2 113.5 127.1 93.0 20 337s > print( mf1 <- model.frame( fitwls1$eq[[ 1 ]] ) ) 337s consump price income 337s 1 98.5 100.3 87.4 337s 2 99.2 104.3 97.6 337s 3 102.2 103.4 96.7 337s 4 101.5 104.5 98.2 337s 5 104.2 98.0 99.8 337s 6 103.2 99.5 100.5 337s 7 104.0 101.1 103.2 337s 8 99.9 104.8 107.8 337s 9 100.3 96.4 96.6 337s 10 102.8 91.2 88.9 337s 11 95.4 93.1 75.1 337s 12 92.4 98.8 76.9 337s 13 94.5 102.9 84.6 337s 14 98.8 98.8 90.6 337s 15 105.8 95.1 103.1 337s 16 100.2 98.5 105.1 337s 17 103.5 86.5 96.4 337s 18 99.9 104.0 104.4 337s 19 105.2 105.8 110.7 337s 20 106.2 113.5 127.1 337s > print( attributes( mf1 )$terms ) 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s > print( mf2 <- model.frame( fitwls1$eq[[ 2 ]] ) ) 337s consump price farmPrice trend 337s 1 98.5 100.3 98.0 1 337s 2 99.2 104.3 99.1 2 337s 3 102.2 103.4 99.1 3 337s 4 101.5 104.5 98.1 4 337s 5 104.2 98.0 110.8 5 337s 6 103.2 99.5 108.2 6 337s 7 104.0 101.1 105.6 7 337s 8 99.9 104.8 109.8 8 337s 9 100.3 96.4 108.7 9 337s 10 102.8 91.2 100.6 10 337s 11 95.4 93.1 81.0 11 337s 12 92.4 98.8 68.6 12 337s 13 94.5 102.9 70.9 13 337s 14 98.8 98.8 81.4 14 337s 15 105.8 95.1 102.3 15 337s 16 100.2 98.5 105.0 16 337s 17 103.5 86.5 110.5 17 337s 18 99.9 104.0 92.5 18 337s 19 105.2 105.8 89.3 19 337s 20 106.2 113.5 93.0 20 337s > print( attributes( mf2 )$terms ) 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s > 337s > print( all.equal( mf, model.frame( fitwls2e ) ) ) 337s [1] TRUE 337s > print( all.equal( mf1, model.frame( fitwls2e$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > 337s > print( all.equal( mf, model.frame( fitwls3 ) ) ) 337s [1] TRUE 337s > print( all.equal( mf2, model.frame( fitwls3$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > 337s > print( all.equal( mf, model.frame( fitwls4e ) ) ) 337s [1] TRUE 337s > print( all.equal( mf1, model.frame( fitwls4e$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > 337s > print( all.equal( mf, model.frame( fitwls5 ) ) ) 337s [1] TRUE 337s > print( all.equal( mf2, model.frame( fitwls5$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > 337s > print( all.equal( mf, model.frame( fitwlsi1e ) ) ) 337s [1] TRUE 337s > print( all.equal( mf1, model.frame( fitwlsi1e$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > 337s > print( all.equal( mf, model.frame( fitwlsi2 ) ) ) 337s [1] TRUE 337s > print( all.equal( mf2, model.frame( fitwlsi2$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > 337s > print( all.equal( mf, model.frame( fitwlsi3e ) ) ) 337s [1] TRUE 337s > print( all.equal( mf1, model.frame( fitwlsi3e$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > 337s > print( all.equal( mf, model.frame( fitwlsi4 ) ) ) 337s [1] TRUE 337s > print( all.equal( mf2, model.frame( fitwlsi4$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > 337s > print( all.equal( mf, model.frame( fitwlsi5e ) ) ) 337s [1] TRUE 337s > print( all.equal( mf1, model.frame( fitwlsi5e$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > 337s > 337s > ## **************** model matrix ************************ 337s > # with x (returnModelMatrix) = TRUE 337s > print( !is.null( fitwls1e$eq[[ 1 ]]$x ) ) 337s [1] TRUE 337s > print( mm <- model.matrix( fitwlsi1e ) ) 337s demand_(Intercept) demand_price demand_income supply_(Intercept) 337s demand_1 1 100.3 87.4 0 337s demand_2 1 104.3 97.6 0 337s demand_3 1 103.4 96.7 0 337s demand_4 1 104.5 98.2 0 337s demand_5 1 98.0 99.8 0 337s demand_6 1 99.5 100.5 0 337s demand_7 1 101.1 103.2 0 337s demand_8 1 104.8 107.8 0 337s demand_9 1 96.4 96.6 0 337s demand_10 1 91.2 88.9 0 337s demand_11 1 93.1 75.1 0 337s demand_12 1 98.8 76.9 0 337s demand_13 1 102.9 84.6 0 337s demand_14 1 98.8 90.6 0 337s demand_15 1 95.1 103.1 0 337s demand_16 1 98.5 105.1 0 337s demand_17 1 86.5 96.4 0 337s demand_18 1 104.0 104.4 0 337s demand_19 1 105.8 110.7 0 337s demand_20 1 113.5 127.1 0 337s supply_1 0 0.0 0.0 1 337s supply_2 0 0.0 0.0 1 337s supply_3 0 0.0 0.0 1 337s supply_4 0 0.0 0.0 1 337s supply_5 0 0.0 0.0 1 337s supply_6 0 0.0 0.0 1 337s supply_7 0 0.0 0.0 1 337s supply_8 0 0.0 0.0 1 337s supply_9 0 0.0 0.0 1 337s supply_10 0 0.0 0.0 1 337s supply_11 0 0.0 0.0 1 337s supply_12 0 0.0 0.0 1 337s supply_13 0 0.0 0.0 1 337s supply_14 0 0.0 0.0 1 337s supply_15 0 0.0 0.0 1 337s supply_16 0 0.0 0.0 1 337s supply_17 0 0.0 0.0 1 337s supply_18 0 0.0 0.0 1 337s supply_19 0 0.0 0.0 1 337s supply_20 0 0.0 0.0 1 337s supply_price supply_farmPrice supply_trend 337s demand_1 0.0 0.0 0 337s demand_2 0.0 0.0 0 337s demand_3 0.0 0.0 0 337s demand_4 0.0 0.0 0 337s demand_5 0.0 0.0 0 337s demand_6 0.0 0.0 0 337s demand_7 0.0 0.0 0 337s demand_8 0.0 0.0 0 337s demand_9 0.0 0.0 0 337s demand_10 0.0 0.0 0 337s demand_11 0.0 0.0 0 337s demand_12 0.0 0.0 0 337s demand_13 0.0 0.0 0 337s demand_14 0.0 0.0 0 337s demand_15 0.0 0.0 0 337s demand_16 0.0 0.0 0 337s demand_17 0.0 0.0 0 337s demand_18 0.0 0.0 0 337s demand_19 0.0 0.0 0 337s demand_20 0.0 0.0 0 337s supply_1 100.3 98.0 1 337s supply_2 104.3 99.1 2 337s supply_3 103.4 99.1 3 337s supply_4 104.5 98.1 4 337s supply_5 98.0 110.8 5 337s supply_6 99.5 108.2 6 337s supply_7 101.1 105.6 7 337s supply_8 104.8 109.8 8 337s supply_9 96.4 108.7 9 337s supply_10 91.2 100.6 10 337s supply_11 93.1 81.0 11 337s supply_12 98.8 68.6 12 337s supply_13 102.9 70.9 13 337s supply_14 98.8 81.4 14 337s supply_15 95.1 102.3 15 337s supply_16 98.5 105.0 16 337s supply_17 86.5 110.5 17 337s supply_18 104.0 92.5 18 337s supply_19 105.8 89.3 19 337s supply_20 113.5 93.0 20 337s > print( mm1 <- model.matrix( fitwlsi1e$eq[[ 1 ]] ) ) 337s (Intercept) price income 337s 1 1 100.3 87.4 337s 2 1 104.3 97.6 337s 3 1 103.4 96.7 337s 4 1 104.5 98.2 337s 5 1 98.0 99.8 337s 6 1 99.5 100.5 337s 7 1 101.1 103.2 337s 8 1 104.8 107.8 337s 9 1 96.4 96.6 337s 10 1 91.2 88.9 337s 11 1 93.1 75.1 337s 12 1 98.8 76.9 337s 13 1 102.9 84.6 337s 14 1 98.8 90.6 337s 15 1 95.1 103.1 337s 16 1 98.5 105.1 337s 17 1 86.5 96.4 337s 18 1 104.0 104.4 337s 19 1 105.8 110.7 337s 20 1 113.5 127.1 337s attr(,"assign") 337s [1] 0 1 2 337s > print( mm2 <- model.matrix( fitwlsi1e$eq[[ 2 ]] ) ) 337s (Intercept) price farmPrice trend 337s 1 1 100.3 98.0 1 337s 2 1 104.3 99.1 2 337s 3 1 103.4 99.1 3 337s 4 1 104.5 98.1 4 337s 5 1 98.0 110.8 5 337s 6 1 99.5 108.2 6 337s 7 1 101.1 105.6 7 337s 8 1 104.8 109.8 8 337s 9 1 96.4 108.7 9 337s 10 1 91.2 100.6 10 337s 11 1 93.1 81.0 11 337s 12 1 98.8 68.6 12 337s 13 1 102.9 70.9 13 337s 14 1 98.8 81.4 14 337s 15 1 95.1 102.3 15 337s 16 1 98.5 105.0 16 337s 17 1 86.5 110.5 17 337s 18 1 104.0 92.5 18 337s 19 1 105.8 89.3 19 337s 20 1 113.5 93.0 20 337s attr(,"assign") 337s [1] 0 1 2 3 337s > 337s > # with x (returnModelMatrix) = FALSE 337s > print( all.equal( mm, model.matrix( fitwlsi1 ) ) ) 337s [1] TRUE 337s > print( all.equal( mm1, model.matrix( fitwlsi1$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > print( all.equal( mm2, model.matrix( fitwlsi1$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > print( !is.null( fitwls1$eq[[ 1 ]]$x ) ) 337s [1] FALSE 337s > 337s > # with x (returnModelMatrix) = TRUE 337s > print( !is.null( fitwls2$eq[[ 1 ]]$x ) ) 337s [1] TRUE 337s > print( all.equal( mm, model.matrix( fitwls2 ) ) ) 337s [1] TRUE 337s > print( all.equal( mm1, model.matrix( fitwls2$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > print( all.equal( mm2, model.matrix( fitwls2$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > 337s > # with x (returnModelMatrix) = FALSE 337s > print( all.equal( mm, model.matrix( fitwls2e ) ) ) 337s [1] TRUE 337s > print( all.equal( mm1, model.matrix( fitwls2e$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > print( all.equal( mm2, model.matrix( fitwls2e$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > print( !is.null( fitwls2e$eq[[ 1 ]]$x ) ) 337s [1] FALSE 337s > 337s > # with x (returnModelMatrix) = TRUE 337s > print( !is.null( fitwlsi3$eq[[ 1 ]]$x ) ) 337s [1] TRUE 337s > print( all.equal( mm, model.matrix( fitwlsi3 ) ) ) 337s [1] TRUE 337s > print( all.equal( mm1, model.matrix( fitwlsi3$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > print( all.equal( mm2, model.matrix( fitwlsi3$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > 337s > # with x (returnModelMatrix) = FALSE 337s > print( all.equal( mm, model.matrix( fitwlsi3e ) ) ) 337s [1] TRUE 337s > print( all.equal( mm1, model.matrix( fitwlsi3e$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > print( all.equal( mm2, model.matrix( fitwlsi3e$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > print( !is.null( fitwlsi3e$eq[[ 1 ]]$x ) ) 337s [1] FALSE 337s > 337s > # with x (returnModelMatrix) = TRUE 337s > print( !is.null( fitwls4e$eq[[ 1 ]]$x ) ) 337s [1] TRUE 337s > print( all.equal( mm, model.matrix( fitwls4e ) ) ) 337s [1] TRUE 337s > print( all.equal( mm1, model.matrix( fitwls4e$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > print( all.equal( mm2, model.matrix( fitwls4e$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > 337s > # with x (returnModelMatrix) = FALSE 337s > print( all.equal( mm, model.matrix( fitwls4Sym ) ) ) 337s [1] TRUE 337s > print( all.equal( mm1, model.matrix( fitwls4Sym$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > print( all.equal( mm2, model.matrix( fitwls4Sym$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > print( !is.null( fitwls4Sym$eq[[ 1 ]]$x ) ) 337s [1] FALSE 337s > 337s > # with x (returnModelMatrix) = TRUE 337s > print( !is.null( fitwls5$eq[[ 1 ]]$x ) ) 337s [1] TRUE 337s > print( all.equal( mm, model.matrix( fitwls5 ) ) ) 337s [1] TRUE 337s > print( all.equal( mm1, model.matrix( fitwls5$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > print( all.equal( mm2, model.matrix( fitwls5$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > 337s > # with x (returnModelMatrix) = FALSE 337s > print( all.equal( mm, model.matrix( fitwls5e ) ) ) 337s [1] TRUE 337s > print( all.equal( mm1, model.matrix( fitwls5e$eq[[ 1 ]] ) ) ) 337s [1] TRUE 337s > print( all.equal( mm2, model.matrix( fitwls5e$eq[[ 2 ]] ) ) ) 337s [1] TRUE 337s > print( !is.null( fitwls5e$eq[[ 1 ]]$x ) ) 337s [1] FALSE 337s > 337s > 337s > ## **************** formulas ************************ 337s > formula( fitwls1 ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwls1$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s > 337s > formula( fitwls2e ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwls2e$eq[[ 1 ]] ) 337s consump ~ price + income 337s > 337s > formula( fitwls3 ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwls3$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s > 337s > formula( fitwls4e ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwls4e$eq[[ 1 ]] ) 337s consump ~ price + income 337s > 337s > formula( fitwls5 ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwls5$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s > 337s > formula( fitwlsi1e ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwlsi1e$eq[[ 1 ]] ) 337s consump ~ price + income 337s > 337s > formula( fitwlsi2 ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwlsi2$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s > 337s > formula( fitwlsi3e ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwlsi3e$eq[[ 1 ]] ) 337s consump ~ price + income 337s > 337s > formula( fitwlsi4 ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwlsi4$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s > 337s > formula( fitwlsi5e ) 337s $demand 337s consump ~ price + income 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s 337s > formula( fitwlsi5e$eq[[ 1 ]] ) 337s consump ~ price + income 337s > 337s > 337s > ## **************** model terms ******************* 337s > terms( fitwls1 ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwls1$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s > 337s > terms( fitwls2e ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwls2e$eq[[ 1 ]] ) 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s > 337s > terms( fitwls3 ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwls3$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s > 337s > terms( fitwls4e ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwls4e$eq[[ 1 ]] ) 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s > 337s > terms( fitwls5 ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwls5$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s > 337s > terms( fitwlsi1e ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwlsi1e$eq[[ 1 ]] ) 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s > 337s > terms( fitwlsi2 ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwlsi2$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s > 337s > terms( fitwlsi3e ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwlsi3e$eq[[ 1 ]] ) 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s > 337s > terms( fitwlsi4 ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwlsi4$eq[[ 2 ]] ) 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s > 337s > terms( fitwlsi5e ) 337s $demand 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s 337s $supply 337s consump ~ price + farmPrice + trend 337s attr(,"variables") 337s list(consump, price, farmPrice, trend) 337s attr(,"factors") 337s price farmPrice trend 337s consump 0 0 0 337s price 1 0 0 337s farmPrice 0 1 0 337s trend 0 0 1 337s attr(,"term.labels") 337s [1] "price" "farmPrice" "trend" 337s attr(,"order") 337s [1] 1 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, farmPrice, trend) 337s attr(,"dataClasses") 337s consump price farmPrice trend 337s "numeric" "numeric" "numeric" "numeric" 337s 337s > terms( fitwlsi5e$eq[[ 1 ]] ) 337s consump ~ price + income 337s attr(,"variables") 337s list(consump, price, income) 337s attr(,"factors") 337s price income 337s consump 0 0 337s price 1 0 337s income 0 1 337s attr(,"term.labels") 337s [1] "price" "income" 337s attr(,"order") 337s [1] 1 1 337s attr(,"intercept") 337s [1] 1 337s attr(,"response") 337s [1] 1 337s attr(,".Environment") 337s 337s attr(,"predvars") 337s list(consump, price, income) 337s attr(,"dataClasses") 337s consump price income 337s "numeric" "numeric" "numeric" 337s > 337s > 337s > ## **************** estfun ************************ 337s > library( "sandwich" ) 337s > 337s > estfun( fitwls1 ) 337s demand_(Intercept) demand_price demand_income supply_(Intercept) 337s demand_1 0.2884 28.93 25.21 0.0000 337s demand_2 -0.1048 -10.92 -10.22 0.0000 337s demand_3 0.7045 72.87 68.13 0.0000 337s demand_4 0.4838 50.56 47.51 0.0000 337s demand_5 0.5222 51.18 52.12 0.0000 337s demand_6 0.3153 31.36 31.68 0.0000 337s demand_7 0.4108 41.51 42.39 0.0000 337s demand_8 -0.7872 -82.47 -84.86 0.0000 337s demand_9 -0.3665 -35.35 -35.41 0.0000 337s demand_10 0.5451 49.73 48.46 0.0000 337s demand_11 -0.0400 -3.72 -3.00 0.0000 337s demand_12 -0.5246 -51.83 -40.34 0.0000 337s demand_13 -0.3009 -30.96 -25.45 0.0000 337s demand_14 -0.0591 -5.83 -5.35 0.0000 337s demand_15 0.3991 37.96 41.14 0.0000 337s demand_16 -0.9934 -97.80 -104.40 0.0000 337s demand_17 -0.3417 -29.56 -32.94 0.0000 337s demand_18 -0.5375 -55.90 -56.11 0.0000 337s demand_19 0.4665 49.34 51.65 0.0000 337s demand_20 -0.0802 -9.10 -10.20 0.0000 337s supply_1 0.0000 0.00 0.00 -0.0768 337s supply_2 0.0000 0.00 0.00 -0.1548 337s supply_3 0.0000 0.00 0.00 0.3397 337s supply_4 0.0000 0.00 0.00 0.1961 337s supply_5 0.0000 0.00 0.00 0.2617 337s supply_6 0.0000 0.00 0.00 0.1176 337s supply_7 0.0000 0.00 0.00 0.2712 337s supply_8 0.0000 0.00 0.00 -0.7619 337s supply_9 0.0000 0.00 0.00 -0.4493 337s supply_10 0.0000 0.00 0.00 0.4269 337s supply_11 0.0000 0.00 0.00 -0.1034 337s supply_12 0.0000 0.00 0.00 -0.2934 337s supply_13 0.0000 0.00 0.00 -0.1839 337s supply_14 0.0000 0.00 0.00 0.1677 337s supply_15 0.0000 0.00 0.00 0.5461 337s supply_16 0.0000 0.00 0.00 -0.6683 337s supply_17 0.0000 0.00 0.00 -0.0458 337s supply_18 0.0000 0.00 0.00 -0.4234 337s supply_19 0.0000 0.00 0.00 0.5376 337s supply_20 0.0000 0.00 0.00 0.2963 337s supply_price supply_farmPrice supply_trend 337s demand_1 0.00 0.00 0.0000 337s demand_2 0.00 0.00 0.0000 337s demand_3 0.00 0.00 0.0000 337s demand_4 0.00 0.00 0.0000 337s demand_5 0.00 0.00 0.0000 337s demand_6 0.00 0.00 0.0000 337s demand_7 0.00 0.00 0.0000 337s demand_8 0.00 0.00 0.0000 337s demand_9 0.00 0.00 0.0000 337s demand_10 0.00 0.00 0.0000 337s demand_11 0.00 0.00 0.0000 337s demand_12 0.00 0.00 0.0000 337s demand_13 0.00 0.00 0.0000 337s demand_14 0.00 0.00 0.0000 337s demand_15 0.00 0.00 0.0000 337s demand_16 0.00 0.00 0.0000 337s demand_17 0.00 0.00 0.0000 337s demand_18 0.00 0.00 0.0000 337s demand_19 0.00 0.00 0.0000 337s demand_20 0.00 0.00 0.0000 337s supply_1 -7.70 -7.53 -0.0768 337s supply_2 -16.14 -15.34 -0.3096 337s supply_3 35.14 33.67 1.0192 337s supply_4 20.49 19.24 0.7843 337s supply_5 25.65 29.00 1.3085 337s supply_6 11.70 12.73 0.7057 337s supply_7 27.41 28.64 1.8987 337s supply_8 -79.82 -83.66 -6.0955 337s supply_9 -43.33 -48.84 -4.0437 337s supply_10 38.95 42.95 4.2691 337s supply_11 -9.63 -8.38 -1.1377 337s supply_12 -28.99 -20.13 -3.5213 337s supply_13 -18.93 -13.04 -2.3913 337s supply_14 16.56 13.65 2.3480 337s supply_15 51.95 55.87 8.1920 337s supply_16 -65.79 -70.17 -10.6922 337s supply_17 -3.96 -5.06 -0.7779 337s supply_18 -44.04 -39.16 -7.6205 337s supply_19 56.86 48.01 10.2144 337s supply_20 33.63 27.56 5.9267 337s > round( colSums( estfun( fitwls1 ) ), digits = 7 ) 337s demand_(Intercept) demand_price demand_income supply_(Intercept) 337s 0 0 0 0 337s supply_price supply_farmPrice supply_trend 337s 0 0 0 337s > 337s > estfun( fitwlsi1e ) 337s demand_(Intercept) demand_price demand_income supply_(Intercept) 337s demand_1 0.3393 34.04 29.66 0.0000 337s demand_2 -0.1232 -12.85 -12.03 0.0000 337s demand_3 0.8289 85.73 80.15 0.0000 337s demand_4 0.5692 59.49 55.90 0.0000 337s demand_5 0.6144 60.21 61.32 0.0000 337s demand_6 0.3709 36.89 37.28 0.0000 337s demand_7 0.4832 48.84 49.87 0.0000 337s demand_8 -0.9261 -97.03 -99.84 0.0000 337s demand_9 -0.4312 -41.59 -41.66 0.0000 337s demand_10 0.6413 58.51 57.01 0.0000 337s demand_11 -0.0470 -4.38 -3.53 0.0000 337s demand_12 -0.6172 -60.98 -47.46 0.0000 337s demand_13 -0.3540 -36.43 -29.95 0.0000 337s demand_14 -0.0695 -6.86 -6.29 0.0000 337s demand_15 0.4695 44.66 48.40 0.0000 337s demand_16 -1.1687 -115.06 -122.83 0.0000 337s demand_17 -0.4020 -34.78 -38.76 0.0000 337s demand_18 -0.6323 -65.77 -66.01 0.0000 337s demand_19 0.5489 58.05 60.76 0.0000 337s demand_20 -0.0944 -10.71 -12.00 0.0000 337s supply_1 0.0000 0.00 0.00 -0.0960 337s supply_2 0.0000 0.00 0.00 -0.1935 337s supply_3 0.0000 0.00 0.00 0.4247 337s supply_4 0.0000 0.00 0.00 0.2451 337s supply_5 0.0000 0.00 0.00 0.3271 337s supply_6 0.0000 0.00 0.00 0.1470 337s supply_7 0.0000 0.00 0.00 0.3390 337s supply_8 0.0000 0.00 0.00 -0.9524 337s supply_9 0.0000 0.00 0.00 -0.5616 337s supply_10 0.0000 0.00 0.00 0.5336 337s supply_11 0.0000 0.00 0.00 -0.1293 337s supply_12 0.0000 0.00 0.00 -0.3668 337s supply_13 0.0000 0.00 0.00 -0.2299 337s supply_14 0.0000 0.00 0.00 0.2096 337s supply_15 0.0000 0.00 0.00 0.6827 337s supply_16 0.0000 0.00 0.00 -0.8353 337s supply_17 0.0000 0.00 0.00 -0.0572 337s supply_18 0.0000 0.00 0.00 -0.5292 337s supply_19 0.0000 0.00 0.00 0.6720 337s supply_20 0.0000 0.00 0.00 0.3704 337s supply_price supply_farmPrice supply_trend 337s demand_1 0.00 0.00 0.000 337s demand_2 0.00 0.00 0.000 337s demand_3 0.00 0.00 0.000 337s demand_4 0.00 0.00 0.000 337s demand_5 0.00 0.00 0.000 337s demand_6 0.00 0.00 0.000 337s demand_7 0.00 0.00 0.000 337s demand_8 0.00 0.00 0.000 337s demand_9 0.00 0.00 0.000 337s demand_10 0.00 0.00 0.000 337s demand_11 0.00 0.00 0.000 337s demand_12 0.00 0.00 0.000 337s demand_13 0.00 0.00 0.000 337s demand_14 0.00 0.00 0.000 337s demand_15 0.00 0.00 0.000 337s demand_16 0.00 0.00 0.000 337s demand_17 0.00 0.00 0.000 337s demand_18 0.00 0.00 0.000 337s demand_19 0.00 0.00 0.000 337s demand_20 0.00 0.00 0.000 337s supply_1 -9.63 -9.41 -0.096 337s supply_2 -20.18 -19.18 -0.387 337s supply_3 43.92 42.08 1.274 337s supply_4 25.61 24.04 0.980 337s supply_5 32.06 36.25 1.636 337s supply_6 14.62 15.91 0.882 337s supply_7 34.27 35.80 2.373 337s supply_8 -99.78 -104.58 -7.619 337s supply_9 -54.17 -61.05 -5.055 337s supply_10 48.68 53.68 5.336 337s supply_11 -12.03 -10.47 -1.422 337s supply_12 -36.24 -25.16 -4.402 337s supply_13 -23.66 -16.30 -2.989 337s supply_14 20.70 17.06 2.935 337s supply_15 64.93 69.84 10.240 337s supply_16 -82.24 -87.71 -13.365 337s supply_17 -4.95 -6.32 -0.972 337s supply_18 -55.05 -48.95 -9.526 337s supply_19 71.08 60.01 12.768 337s supply_20 42.04 34.45 7.408 337s > round( colSums( estfun( fitwlsi1e ) ), digits = 7 ) 337s demand_(Intercept) demand_price demand_income supply_(Intercept) 337s 0 0 0 0 337s supply_price supply_farmPrice supply_trend 337s 0 0 0 337s > 337s > 337s > ## **************** bread ************************ 337s > bread( fitwls1 ) 337s demand_(Intercept) demand_price demand_income supply_(Intercept) 337s [1,] 2261.63 -23.7921 1.2865 0.0 337s [2,] -23.79 0.3289 -0.0933 0.0 337s [3,] 1.29 -0.0933 0.0825 0.0 337s [4,] 0.00 0.0000 0.0000 5255.9 337s [5,] 0.00 0.0000 0.0000 -39.5 337s [6,] 0.00 0.0000 0.0000 -12.2 337s [7,] 0.00 0.0000 0.0000 -11.2 337s supply_price supply_farmPrice supply_trend 337s [1,] 0.0000 0.0000 0.0000 337s [2,] 0.0000 0.0000 0.0000 337s [3,] 0.0000 0.0000 0.0000 337s [4,] -39.5000 -12.1744 -11.1673 337s [5,] 0.3601 0.0338 0.0209 337s [6,] 0.0338 0.0853 0.0526 337s [7,] 0.0209 0.0526 0.3804 337s > 337s > bread( fitwlsi1e ) 337s demand_(Intercept) demand_price demand_income supply_(Intercept) 337s [1,] 1922.39 -20.2232 1.0935 0.00 337s [2,] -20.22 0.2796 -0.0793 0.00 337s [3,] 1.09 -0.0793 0.0701 0.00 337s [4,] 0.00 0.0000 0.0000 4204.75 337s [5,] 0.00 0.0000 0.0000 -31.60 337s [6,] 0.00 0.0000 0.0000 -9.74 337s [7,] 0.00 0.0000 0.0000 -8.93 337s supply_price supply_farmPrice supply_trend 337s [1,] 0.0000 0.0000 0.0000 337s [2,] 0.0000 0.0000 0.0000 337s [3,] 0.0000 0.0000 0.0000 337s [4,] -31.6000 -9.7395 -8.9339 337s [5,] 0.2881 0.0270 0.0167 337s [6,] 0.0270 0.0683 0.0421 337s [7,] 0.0167 0.0421 0.3043 337s > 337s autopkgtest [01:37:37]: test run-unit-test: -----------------------] 337s run-unit-test PASS 337s autopkgtest [01:37:37]: test run-unit-test: - - - - - - - - - - results - - - - - - - - - - 337s autopkgtest [01:37:37]: test pkg-r-autopkgtest: preparing testbed 340s Note, using file '/tmp/autopkgtest.isQjql/3-autopkgtest-satdep.dsc' to get the build dependencies 340s Reading package lists... 340s Building dependency tree... 340s Reading state information... 340s Starting pkgProblemResolver with broken count: 0 340s Starting 2 pkgProblemResolver with broken count: 0 340s Done 341s The following NEW packages will be installed: 341s dctrl-tools gfortran gfortran-13 gfortran-13-x86-64-linux-gnu 341s gfortran-x86-64-linux-gnu icu-devtools libblas-dev libbz2-dev 341s libgfortran-13-dev libicu-dev libjpeg-dev libjpeg-turbo8-dev libjpeg8-dev 341s liblapack-dev liblzma-dev libncurses-dev libpcre2-16-0 libpcre2-32-0 341s libpcre2-dev libpcre2-posix3 libpkgconf3 libpng-dev libreadline-dev 341s pkg-config pkg-r-autopkgtest pkgconf pkgconf-bin r-base-dev r-cran-arm 341s r-cran-coda r-cran-mi r-cran-sem zlib1g-dev 341s 0 upgraded, 33 newly installed, 0 to remove and 0 not upgraded. 341s Need to get 36.8 MB of archives. 341s After this operation, 134 MB of additional disk space will be used. 341s Get:1 http://ftpmaster.internal/ubuntu noble/main amd64 dctrl-tools amd64 2.24-3build2 [66.9 kB] 341s Get:2 http://ftpmaster.internal/ubuntu noble/main amd64 libgfortran-13-dev amd64 13.2.0-17ubuntu2 [942 kB] 341s Get:3 http://ftpmaster.internal/ubuntu noble/main amd64 gfortran-13-x86-64-linux-gnu amd64 13.2.0-17ubuntu2 [11.6 MB] 341s Get:4 http://ftpmaster.internal/ubuntu noble/main amd64 gfortran-13 amd64 13.2.0-17ubuntu2 [10.3 kB] 341s Get:5 http://ftpmaster.internal/ubuntu noble/main amd64 gfortran-x86-64-linux-gnu amd64 4:13.2.0-7ubuntu1 [1024 B] 341s Get:6 http://ftpmaster.internal/ubuntu noble/main amd64 gfortran amd64 4:13.2.0-7ubuntu1 [1176 B] 341s Get:7 http://ftpmaster.internal/ubuntu noble/main amd64 icu-devtools amd64 74.2-1ubuntu1 [212 kB] 341s Get:8 http://ftpmaster.internal/ubuntu noble/main amd64 libblas-dev amd64 3.12.0-3 [170 kB] 341s Get:9 http://ftpmaster.internal/ubuntu noble/main amd64 libbz2-dev amd64 1.0.8-5ubuntu1 [33.6 kB] 341s Get:10 http://ftpmaster.internal/ubuntu noble/main amd64 libicu-dev amd64 74.2-1ubuntu1 [11.9 MB] 341s Get:11 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg-turbo8-dev amd64 2.1.5-2ubuntu1 [294 kB] 341s Get:12 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg8-dev amd64 8c-2ubuntu11 [1484 B] 341s Get:13 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg-dev amd64 8c-2ubuntu11 [1482 B] 341s Get:14 http://ftpmaster.internal/ubuntu noble/main amd64 liblapack-dev amd64 3.12.0-3 [5196 kB] 341s Get:15 http://ftpmaster.internal/ubuntu noble/main amd64 libncurses-dev amd64 6.4+20240113-1ubuntu1 [384 kB] 341s Get:16 http://ftpmaster.internal/ubuntu noble/main amd64 libpcre2-16-0 amd64 10.42-4ubuntu1 [211 kB] 341s Get:17 http://ftpmaster.internal/ubuntu noble/main amd64 libpcre2-32-0 amd64 10.42-4ubuntu1 [198 kB] 341s Get:18 http://ftpmaster.internal/ubuntu noble/main amd64 libpcre2-posix3 amd64 10.42-4ubuntu1 [6808 B] 341s Get:19 http://ftpmaster.internal/ubuntu noble/main amd64 libpcre2-dev amd64 10.42-4ubuntu1 [743 kB] 341s Get:20 http://ftpmaster.internal/ubuntu noble/main amd64 libpkgconf3 amd64 1.8.1-2 [31.1 kB] 341s Get:21 http://ftpmaster.internal/ubuntu noble/main amd64 zlib1g-dev amd64 1:1.3.dfsg-3ubuntu1 [896 kB] 341s Get:22 http://ftpmaster.internal/ubuntu noble/main amd64 libpng-dev amd64 1.6.43-1 [264 kB] 341s Get:23 http://ftpmaster.internal/ubuntu noble/main amd64 libreadline-dev amd64 8.2-3 [167 kB] 341s Get:24 http://ftpmaster.internal/ubuntu noble/main amd64 pkgconf-bin amd64 1.8.1-2 [20.7 kB] 341s Get:25 http://ftpmaster.internal/ubuntu noble/main amd64 pkgconf amd64 1.8.1-2 [16.8 kB] 341s Get:26 http://ftpmaster.internal/ubuntu noble/main amd64 pkg-config amd64 1.8.1-2 [7170 B] 341s Get:27 http://ftpmaster.internal/ubuntu noble/main amd64 liblzma-dev amd64 5.4.5-0.3 [205 kB] 341s Get:28 http://ftpmaster.internal/ubuntu noble/universe amd64 r-base-dev all 4.3.2-1build1 [4336 B] 341s Get:29 http://ftpmaster.internal/ubuntu noble/universe amd64 pkg-r-autopkgtest all 20231212ubuntu1 [6448 B] 341s Get:30 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-coda all 0.19-4.1-1 [321 kB] 341s Get:31 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-arm all 1.13-1-1 [407 kB] 341s Get:32 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-mi all 1.1-1 [1840 kB] 341s Get:33 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-sem amd64 3.1.15-1 [631 kB] 341s Fetched 36.8 MB in 0s (110 MB/s) 341s Selecting previously unselected package dctrl-tools. 342s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 95548 files and directories currently installed.) 342s Preparing to unpack .../00-dctrl-tools_2.24-3build2_amd64.deb ... 342s Unpacking dctrl-tools (2.24-3build2) ... 342s Selecting previously unselected package libgfortran-13-dev:amd64. 342s Preparing to unpack .../01-libgfortran-13-dev_13.2.0-17ubuntu2_amd64.deb ... 342s Unpacking libgfortran-13-dev:amd64 (13.2.0-17ubuntu2) ... 342s Selecting previously unselected package gfortran-13-x86-64-linux-gnu. 342s Preparing to unpack .../02-gfortran-13-x86-64-linux-gnu_13.2.0-17ubuntu2_amd64.deb ... 342s Unpacking gfortran-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 342s Selecting previously unselected package gfortran-13. 342s Preparing to unpack .../03-gfortran-13_13.2.0-17ubuntu2_amd64.deb ... 342s Unpacking gfortran-13 (13.2.0-17ubuntu2) ... 342s Selecting previously unselected package gfortran-x86-64-linux-gnu. 342s Preparing to unpack .../04-gfortran-x86-64-linux-gnu_4%3a13.2.0-7ubuntu1_amd64.deb ... 342s Unpacking gfortran-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 342s Selecting previously unselected package gfortran. 342s Preparing to unpack .../05-gfortran_4%3a13.2.0-7ubuntu1_amd64.deb ... 342s Unpacking gfortran (4:13.2.0-7ubuntu1) ... 342s Selecting previously unselected package icu-devtools. 342s Preparing to unpack .../06-icu-devtools_74.2-1ubuntu1_amd64.deb ... 342s Unpacking icu-devtools (74.2-1ubuntu1) ... 342s Selecting previously unselected package libblas-dev:amd64. 342s Preparing to unpack .../07-libblas-dev_3.12.0-3_amd64.deb ... 342s Unpacking libblas-dev:amd64 (3.12.0-3) ... 342s Selecting previously unselected package libbz2-dev:amd64. 342s Preparing to unpack .../08-libbz2-dev_1.0.8-5ubuntu1_amd64.deb ... 342s Unpacking libbz2-dev:amd64 (1.0.8-5ubuntu1) ... 342s Selecting previously unselected package libicu-dev:amd64. 342s Preparing to unpack .../09-libicu-dev_74.2-1ubuntu1_amd64.deb ... 342s Unpacking libicu-dev:amd64 (74.2-1ubuntu1) ... 342s Selecting previously unselected package libjpeg-turbo8-dev:amd64. 342s Preparing to unpack .../10-libjpeg-turbo8-dev_2.1.5-2ubuntu1_amd64.deb ... 342s Unpacking libjpeg-turbo8-dev:amd64 (2.1.5-2ubuntu1) ... 342s Selecting previously unselected package libjpeg8-dev:amd64. 342s Preparing to unpack .../11-libjpeg8-dev_8c-2ubuntu11_amd64.deb ... 342s Unpacking libjpeg8-dev:amd64 (8c-2ubuntu11) ... 342s Selecting previously unselected package libjpeg-dev:amd64. 342s Preparing to unpack .../12-libjpeg-dev_8c-2ubuntu11_amd64.deb ... 342s Unpacking libjpeg-dev:amd64 (8c-2ubuntu11) ... 342s Selecting previously unselected package liblapack-dev:amd64. 342s Preparing to unpack .../13-liblapack-dev_3.12.0-3_amd64.deb ... 342s Unpacking liblapack-dev:amd64 (3.12.0-3) ... 343s Selecting previously unselected package libncurses-dev:amd64. 343s Preparing to unpack .../14-libncurses-dev_6.4+20240113-1ubuntu1_amd64.deb ... 343s Unpacking libncurses-dev:amd64 (6.4+20240113-1ubuntu1) ... 343s Selecting previously unselected package libpcre2-16-0:amd64. 343s Preparing to unpack .../15-libpcre2-16-0_10.42-4ubuntu1_amd64.deb ... 343s Unpacking libpcre2-16-0:amd64 (10.42-4ubuntu1) ... 343s Selecting previously unselected package libpcre2-32-0:amd64. 343s Preparing to unpack .../16-libpcre2-32-0_10.42-4ubuntu1_amd64.deb ... 343s Unpacking libpcre2-32-0:amd64 (10.42-4ubuntu1) ... 343s Selecting previously unselected package libpcre2-posix3:amd64. 343s Preparing to unpack .../17-libpcre2-posix3_10.42-4ubuntu1_amd64.deb ... 343s Unpacking libpcre2-posix3:amd64 (10.42-4ubuntu1) ... 343s Selecting previously unselected package libpcre2-dev:amd64. 343s Preparing to unpack .../18-libpcre2-dev_10.42-4ubuntu1_amd64.deb ... 343s Unpacking libpcre2-dev:amd64 (10.42-4ubuntu1) ... 343s Selecting previously unselected package libpkgconf3:amd64. 343s Preparing to unpack .../19-libpkgconf3_1.8.1-2_amd64.deb ... 343s Unpacking libpkgconf3:amd64 (1.8.1-2) ... 343s Selecting previously unselected package zlib1g-dev:amd64. 343s Preparing to unpack .../20-zlib1g-dev_1%3a1.3.dfsg-3ubuntu1_amd64.deb ... 343s Unpacking zlib1g-dev:amd64 (1:1.3.dfsg-3ubuntu1) ... 343s Selecting previously unselected package libpng-dev:amd64. 343s Preparing to unpack .../21-libpng-dev_1.6.43-1_amd64.deb ... 343s Unpacking libpng-dev:amd64 (1.6.43-1) ... 343s Selecting previously unselected package libreadline-dev:amd64. 343s Preparing to unpack .../22-libreadline-dev_8.2-3_amd64.deb ... 343s Unpacking libreadline-dev:amd64 (8.2-3) ... 343s Selecting previously unselected package pkgconf-bin. 343s Preparing to unpack .../23-pkgconf-bin_1.8.1-2_amd64.deb ... 343s Unpacking pkgconf-bin (1.8.1-2) ... 343s Selecting previously unselected package pkgconf:amd64. 343s Preparing to unpack .../24-pkgconf_1.8.1-2_amd64.deb ... 343s Unpacking pkgconf:amd64 (1.8.1-2) ... 343s Selecting previously unselected package pkg-config:amd64. 343s Preparing to unpack .../25-pkg-config_1.8.1-2_amd64.deb ... 343s Unpacking pkg-config:amd64 (1.8.1-2) ... 343s Selecting previously unselected package liblzma-dev:amd64. 343s Preparing to unpack .../26-liblzma-dev_5.4.5-0.3_amd64.deb ... 343s Unpacking liblzma-dev:amd64 (5.4.5-0.3) ... 343s Selecting previously unselected package r-base-dev. 343s Preparing to unpack .../27-r-base-dev_4.3.2-1build1_all.deb ... 343s Unpacking r-base-dev (4.3.2-1build1) ... 343s Selecting previously unselected package pkg-r-autopkgtest. 343s Preparing to unpack .../28-pkg-r-autopkgtest_20231212ubuntu1_all.deb ... 343s Unpacking pkg-r-autopkgtest (20231212ubuntu1) ... 343s Selecting previously unselected package r-cran-coda. 343s Preparing to unpack .../29-r-cran-coda_0.19-4.1-1_all.deb ... 343s Unpacking r-cran-coda (0.19-4.1-1) ... 343s Selecting previously unselected package r-cran-arm. 343s Preparing to unpack .../30-r-cran-arm_1.13-1-1_all.deb ... 343s Unpacking r-cran-arm (1.13-1-1) ... 343s Selecting previously unselected package r-cran-mi. 343s Preparing to unpack .../31-r-cran-mi_1.1-1_all.deb ... 343s Unpacking r-cran-mi (1.1-1) ... 343s Selecting previously unselected package r-cran-sem. 343s Preparing to unpack .../32-r-cran-sem_3.1.15-1_amd64.deb ... 343s Unpacking r-cran-sem (3.1.15-1) ... 343s Setting up libjpeg-turbo8-dev:amd64 (2.1.5-2ubuntu1) ... 343s Setting up libncurses-dev:amd64 (6.4+20240113-1ubuntu1) ... 343s Setting up libreadline-dev:amd64 (8.2-3) ... 343s Setting up libpcre2-16-0:amd64 (10.42-4ubuntu1) ... 343s Setting up libpcre2-32-0:amd64 (10.42-4ubuntu1) ... 343s Setting up libpkgconf3:amd64 (1.8.1-2) ... 343s Setting up icu-devtools (74.2-1ubuntu1) ... 343s Setting up pkgconf-bin (1.8.1-2) ... 343s Setting up liblzma-dev:amd64 (5.4.5-0.3) ... 343s Setting up zlib1g-dev:amd64 (1:1.3.dfsg-3ubuntu1) ... 343s Setting up libpcre2-posix3:amd64 (10.42-4ubuntu1) ... 343s Setting up libjpeg8-dev:amd64 (8c-2ubuntu11) ... 343s Setting up libgfortran-13-dev:amd64 (13.2.0-17ubuntu2) ... 343s Setting up r-cran-coda (0.19-4.1-1) ... 343s Setting up libicu-dev:amd64 (74.2-1ubuntu1) ... 343s Setting up libblas-dev:amd64 (3.12.0-3) ... 343s update-alternatives: using /usr/lib/x86_64-linux-gnu/blas/libblas.so to provide /usr/lib/x86_64-linux-gnu/libblas.so (libblas.so-x86_64-linux-gnu) in auto mode 343s Setting up dctrl-tools (2.24-3build2) ... 343s Setting up r-cran-arm (1.13-1-1) ... 343s Setting up libbz2-dev:amd64 (1.0.8-5ubuntu1) ... 343s Setting up libpcre2-dev:amd64 (10.42-4ubuntu1) ... 343s Setting up libpng-dev:amd64 (1.6.43-1) ... 343s Setting up libjpeg-dev:amd64 (8c-2ubuntu11) ... 343s Setting up gfortran-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 343s Setting up pkgconf:amd64 (1.8.1-2) ... 343s Setting up r-cran-mi (1.1-1) ... 343s Setting up gfortran-13 (13.2.0-17ubuntu2) ... 343s Setting up liblapack-dev:amd64 (3.12.0-3) ... 343s update-alternatives: using /usr/lib/x86_64-linux-gnu/lapack/liblapack.so to provide /usr/lib/x86_64-linux-gnu/liblapack.so (liblapack.so-x86_64-linux-gnu) in auto mode 343s Setting up pkg-config:amd64 (1.8.1-2) ... 343s Setting up r-cran-sem (3.1.15-1) ... 343s Setting up gfortran-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 343s Setting up gfortran (4:13.2.0-7ubuntu1) ... 343s update-alternatives: using /usr/bin/gfortran to provide /usr/bin/f95 (f95) in auto mode 343s update-alternatives: warning: skip creation of /usr/share/man/man1/f95.1.gz because associated file /usr/share/man/man1/gfortran.1.gz (of link group f95) doesn't exist 343s update-alternatives: using /usr/bin/gfortran to provide /usr/bin/f77 (f77) in auto mode 343s update-alternatives: warning: skip creation of /usr/share/man/man1/f77.1.gz because associated file /usr/share/man/man1/gfortran.1.gz (of link group f77) doesn't exist 343s Setting up r-base-dev (4.3.2-1build1) ... 343s Setting up pkg-r-autopkgtest (20231212ubuntu1) ... 343s Processing triggers for libc-bin (2.39-0ubuntu6) ... 343s Processing triggers for man-db (2.12.0-3) ... 344s Processing triggers for install-info (7.1-3) ... 346s Reading package lists... 346s Building dependency tree... 346s Reading state information... 346s Starting pkgProblemResolver with broken count: 0 346s Starting 2 pkgProblemResolver with broken count: 0 346s Done 347s The following NEW packages will be installed: 347s autopkgtest-satdep 347s 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. 347s Need to get 0 B/692 B of archives. 347s After this operation, 0 B of additional disk space will be used. 347s Get:1 /tmp/autopkgtest.isQjql/4-autopkgtest-satdep.deb autopkgtest-satdep amd64 0 [692 B] 347s Selecting previously unselected package autopkgtest-satdep. 347s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 96437 files and directories currently installed.) 347s Preparing to unpack .../4-autopkgtest-satdep.deb ... 347s Unpacking autopkgtest-satdep (0) ... 347s Setting up autopkgtest-satdep (0) ... 348s (Reading database ... 96437 files and directories currently installed.) 348s Removing autopkgtest-satdep (0) ... 349s autopkgtest [01:37:49]: test pkg-r-autopkgtest: /usr/share/dh-r/pkg-r-autopkgtest 349s autopkgtest [01:37:49]: test pkg-r-autopkgtest: [----------------------- 349s Test: Try to load the R library systemfit 349s 349s R version 4.3.2 (2023-10-31) -- "Eye Holes" 349s Copyright (C) 2023 The R Foundation for Statistical Computing 349s Platform: x86_64-pc-linux-gnu (64-bit) 349s 349s R is free software and comes with ABSOLUTELY NO WARRANTY. 349s You are welcome to redistribute it under certain conditions. 349s Type 'license()' or 'licence()' for distribution details. 349s 349s R is a collaborative project with many contributors. 349s Type 'contributors()' for more information and 349s 'citation()' on how to cite R or R packages in publications. 349s 349s Type 'demo()' for some demos, 'help()' for on-line help, or 349s 'help.start()' for an HTML browser interface to help. 349s Type 'q()' to quit R. 349s 349s > library('systemfit') 349s Loading required package: Matrix 350s Loading required package: car 350s Loading required package: carData 350s Loading required package: lmtest 350s Loading required package: zoo 350s 350s Attaching package: ‘zoo’ 350s 350s The following objects are masked from ‘package:base’: 350s 350s as.Date, as.Date.numeric 350s 350s > 350s > 350s 350s Please cite the 'systemfit' package as: 350s Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/. 350s 350s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 350s https://r-forge.r-project.org/projects/systemfit/ 350s Other tests are currently unsupported! 350s They will be progressively added. 350s autopkgtest [01:37:50]: test pkg-r-autopkgtest: -----------------------] 351s pkg-r-autopkgtest PASS 351s autopkgtest [01:37:51]: test pkg-r-autopkgtest: - - - - - - - - - - results - - - - - - - - - - 351s autopkgtest [01:37:51]: @@@@@@@@@@@@@@@@@@@@ summary 351s run-unit-test PASS 351s pkg-r-autopkgtest PASS 361s Creating nova instance adt-noble-i386-r-cran-systemfit-20240324-013200-juju-7f2275-prod-proposed-migration-environment-2 from image adt/ubuntu-noble-amd64-server-20240323.img (UUID 5df8a563-0957-4fdd-8453-862df650aaf8)...