0s autopkgtest [03:12:48]: starting date and time: 2024-03-23 03:12:48+0000 0s autopkgtest [03:12:48]: git checkout: 4a1cd702 l/adt_testbed: don't blame the testbed for unsolvable build deps 0s autopkgtest [03:12:48]: host juju-7f2275-prod-proposed-migration-environment-2; command line: /home/ubuntu/autopkgtest/runner/autopkgtest --output-dir /tmp/autopkgtest-work.nwo2tcgo/out --timeout-copy=6000 --setup-commands /home/ubuntu/autopkgtest-cloud/worker-config-production/setup-canonical.sh --setup-commands /home/ubuntu/autopkgtest/setup-commands/setup-testbed --apt-pocket=proposed --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@lcy02-10.secgroup --name adt-noble-amd64-r-cran-systemfit-20240323-031248-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/ 81s autopkgtest [03:14:09]: testbed dpkg architecture: amd64 81s autopkgtest [03:14:09]: testbed apt version: 2.7.12 81s autopkgtest [03:14:09]: @@@@@@@@@@@@@@@@@@@@ test bed setup 81s Get:1 http://ftpmaster.internal/ubuntu noble-proposed InRelease [117 kB] 81s Get:2 http://ftpmaster.internal/ubuntu noble-proposed/universe Sources [4001 kB] 81s Get:3 http://ftpmaster.internal/ubuntu noble-proposed/multiverse Sources [57.7 kB] 81s Get:4 http://ftpmaster.internal/ubuntu noble-proposed/main Sources [495 kB] 81s Get:5 http://ftpmaster.internal/ubuntu noble-proposed/restricted Sources [6540 B] 81s Get:6 http://ftpmaster.internal/ubuntu noble-proposed/main amd64 Packages [695 kB] 81s Get:7 http://ftpmaster.internal/ubuntu noble-proposed/main i386 Packages [461 kB] 81s Get:8 http://ftpmaster.internal/ubuntu noble-proposed/main amd64 c-n-f Metadata [3508 B] 81s Get:9 http://ftpmaster.internal/ubuntu noble-proposed/restricted amd64 Packages [30.5 kB] 81s Get:10 http://ftpmaster.internal/ubuntu noble-proposed/restricted i386 Packages [6700 B] 81s Get:11 http://ftpmaster.internal/ubuntu noble-proposed/restricted amd64 c-n-f Metadata [116 B] 81s Get:12 http://ftpmaster.internal/ubuntu noble-proposed/universe amd64 Packages [4407 kB] 81s Get:13 http://ftpmaster.internal/ubuntu noble-proposed/universe i386 Packages [1303 kB] 81s Get:14 http://ftpmaster.internal/ubuntu noble-proposed/universe amd64 c-n-f Metadata [9396 B] 81s Get:15 http://ftpmaster.internal/ubuntu noble-proposed/multiverse i386 Packages [27.6 kB] 81s Get:16 http://ftpmaster.internal/ubuntu noble-proposed/multiverse amd64 Packages [96.8 kB] 81s Get:17 http://ftpmaster.internal/ubuntu noble-proposed/multiverse amd64 c-n-f Metadata [196 B] 85s Fetched 11.7 MB in 2s (7520 kB/s) 85s Reading package lists... 87s Reading package lists... 87s Building dependency tree... 87s Reading state information... 87s Calculating upgrade... 87s The following packages will be upgraded: 87s libbsd0 87s 1 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 87s Need to get 41.2 kB of archives. 87s After this operation, 0 B of additional disk space will be used. 87s Get:1 http://ftpmaster.internal/ubuntu noble/main amd64 libbsd0 amd64 0.12.1-1 [41.2 kB] 87s Fetched 41.2 kB in 0s (2025 kB/s) 87s (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.) 87s Preparing to unpack .../libbsd0_0.12.1-1_amd64.deb ... 87s Unpacking libbsd0:amd64 (0.12.1-1) over (0.11.8-1) ... 87s Setting up libbsd0:amd64 (0.12.1-1) ... 87s Processing triggers for libc-bin (2.39-0ubuntu2) ... 88s Reading package lists... 88s Building dependency tree... 88s Reading state information... 88s 0 upgraded, 0 newly installed, 0 to remove and 248 not upgraded. 89s sh: Attempting to set up Debian/Ubuntu apt sources automatically 89s sh: Distribution appears to be Ubuntu 90s Reading package lists... 90s Building dependency tree... 90s Reading state information... 90s eatmydata is already the newest version (131-1). 90s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 90s Reading package lists... 90s Building dependency tree... 90s Reading state information... 91s dbus is already the newest version (1.14.10-4ubuntu1). 91s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 91s Reading package lists... 91s Building dependency tree... 91s Reading state information... 91s rng-tools-debian is already the newest version (2.4). 91s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 91s Reading package lists... 91s Building dependency tree... 91s Reading state information... 92s The following packages will be REMOVED: 92s cloud-init* python3-configobj* python3-debconf* 92s 0 upgraded, 0 newly installed, 3 to remove and 0 not upgraded. 92s After this operation, 3256 kB disk space will be freed. 92s (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.) 92s Removing cloud-init (24.1.2-0ubuntu1) ... 93s Removing python3-configobj (5.0.8-3) ... 93s Removing python3-debconf (1.5.86) ... 93s Processing triggers for man-db (2.12.0-3) ... 93s (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.) 93s Purging configuration files for cloud-init (24.1.2-0ubuntu1) ... 94s dpkg: warning: while removing cloud-init, directory '/etc/cloud/cloud.cfg.d' not empty so not removed 94s Processing triggers for rsyslog (8.2312.0-3ubuntu3) ... 94s invoke-rc.d: policy-rc.d denied execution of try-restart. 94s Reading package lists... 94s Building dependency tree... 94s Reading state information... 95s linux-generic is already the newest version (6.8.0-11.11+1). 95s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 95s Hit:1 http://ftpmaster.internal/ubuntu noble InRelease 95s Hit:2 http://ftpmaster.internal/ubuntu noble-updates InRelease 95s Hit:3 http://ftpmaster.internal/ubuntu noble-security InRelease 97s Reading package lists... 97s Reading package lists... 97s Building dependency tree... 97s Reading state information... 97s Calculating upgrade... 97s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 97s Reading package lists... 98s Building dependency tree... 98s Reading state information... 98s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 98s autopkgtest [03:14:26]: rebooting testbed after setup commands that affected boot 115s autopkgtest [03:14:43]: testbed running kernel: Linux 6.8.0-11-generic #11-Ubuntu SMP PREEMPT_DYNAMIC Wed Feb 14 00:29:05 UTC 2024 116s autopkgtest [03:14:44]: @@@@@@@@@@@@@@@@@@@@ apt-source r-cran-systemfit 117s Get:1 http://ftpmaster.internal/ubuntu noble/universe r-cran-systemfit 1.1-30-1 (dsc) [2203 B] 117s Get:2 http://ftpmaster.internal/ubuntu noble/universe r-cran-systemfit 1.1-30-1 (tar) [1040 kB] 117s Get:3 http://ftpmaster.internal/ubuntu noble/universe r-cran-systemfit 1.1-30-1 (diff) [2516 B] 117s gpgv: Signature made Wed Jun 28 12:43:54 2023 UTC 117s gpgv: using RSA key F1F007320A035541F0A663CA578A0494D1C646D1 117s gpgv: issuer "tille@debian.org" 117s gpgv: Can't check signature: No public key 117s dpkg-source: warning: cannot verify inline signature for ./r-cran-systemfit_1.1-30-1.dsc: no acceptable signature found 117s autopkgtest [03:14:45]: testing package r-cran-systemfit version 1.1-30-1 117s autopkgtest [03:14:45]: build not needed 119s autopkgtest [03:14:47]: test run-unit-test: preparing testbed 121s Reading package lists... 122s Building dependency tree... 122s Reading state information... 122s Starting pkgProblemResolver with broken count: 0 122s Starting 2 pkgProblemResolver with broken count: 0 122s Done 122s The following additional packages will be installed: 122s fontconfig fontconfig-config fonts-dejavu-core fonts-dejavu-mono 122s fonts-glyphicons-halflings fonts-mathjax libblas3 libcairo2 libdatrie1 122s libdeflate0 libfontconfig1 libgfortran5 libgomp1 libgraphite2-3 122s libharfbuzz0b libice6 libjbig0 libjpeg-turbo8 libjpeg8 libjs-bootstrap 122s libjs-highlight.js libjs-jquery libjs-jquery-datatables libjs-mathjax 122s liblapack3 liblerc4 libnlopt0 libpango-1.0-0 libpangocairo-1.0-0 122s libpangoft2-1.0-0 libpaper-utils libpaper1 libpixman-1-0 libsharpyuv0 libsm6 122s libtcl8.6 libthai-data libthai0 libtiff6 libtk8.6 libwebp7 libxcb-render0 122s libxcb-shm0 libxft2 libxrender1 libxss1 libxt6 littler node-normalize.css 122s r-base-core r-cran-abind r-cran-backports r-cran-bdsmatrix r-cran-bit 122s r-cran-bit64 r-cran-boot r-cran-brio r-cran-broom r-cran-callr r-cran-car 122s r-cran-cardata r-cran-caret r-cran-cellranger r-cran-class r-cran-cli 122s r-cran-clipr r-cran-clock r-cran-codetools r-cran-collapse r-cran-colorspace 122s r-cran-conquer r-cran-cpp11 r-cran-crayon r-cran-curl r-cran-data.table 122s r-cran-desc r-cran-diagram r-cran-diffobj r-cran-digest r-cran-dplyr 122s r-cran-e1071 r-cran-ellipsis r-cran-evaluate r-cran-fansi r-cran-farver 122s r-cran-forcats r-cran-foreach r-cran-foreign r-cran-formula r-cran-fs 122s r-cran-future r-cran-future.apply r-cran-generics r-cran-ggplot2 122s r-cran-globals r-cran-glue r-cran-gower r-cran-gtable r-cran-hardhat 122s r-cran-haven r-cran-highr r-cran-hms r-cran-ipred r-cran-isoband 122s r-cran-iterators r-cran-jsonlite r-cran-kernsmooth r-cran-knitr 122s r-cran-labeling r-cran-lattice r-cran-lava r-cran-lifecycle r-cran-listenv 122s r-cran-littler r-cran-lme4 r-cran-lmtest r-cran-lubridate r-cran-magrittr 122s r-cran-maptools r-cran-mass r-cran-matrix r-cran-matrixmodels 122s r-cran-matrixstats r-cran-maxlik r-cran-mgcv r-cran-minqa r-cran-misctools 122s r-cran-modelmetrics r-cran-munsell r-cran-nlme r-cran-nloptr r-cran-nnet 122s r-cran-numderiv r-cran-openxlsx r-cran-parallelly r-cran-pbkrtest 122s r-cran-pillar r-cran-pkgbuild r-cran-pkgconfig r-cran-pkgkitten 122s r-cran-pkgload r-cran-plm r-cran-plyr r-cran-praise r-cran-prettyunits 122s r-cran-proc r-cran-processx r-cran-prodlim r-cran-progress r-cran-progressr 122s r-cran-proxy r-cran-ps r-cran-purrr r-cran-quantreg r-cran-r.methodss3 122s r-cran-r.oo r-cran-r.utils r-cran-r6 r-cran-rbibutils r-cran-rcolorbrewer 122s r-cran-rcpp r-cran-rcpparmadillo r-cran-rcppeigen r-cran-rdpack r-cran-readr 122s r-cran-readxl r-cran-recipes r-cran-rematch r-cran-rematch2 r-cran-reshape2 122s r-cran-rio r-cran-rlang r-cran-rpart r-cran-rprojroot r-cran-sandwich 122s r-cran-scales r-cran-shape r-cran-sp r-cran-sparsem r-cran-squarem 122s r-cran-statmod r-cran-stringi r-cran-stringr r-cran-survival 122s r-cran-systemfit r-cran-testthat r-cran-tibble r-cran-tidyr 122s r-cran-tidyselect r-cran-timechange r-cran-timedate r-cran-tzdb r-cran-utf8 122s r-cran-vctrs r-cran-viridislite r-cran-vroom r-cran-waldo r-cran-withr 122s r-cran-writexl r-cran-xfun r-cran-yaml r-cran-zip r-cran-zoo unzip 122s x11-common xdg-utils zip 122s Suggested packages: 122s fonts-mathjax-extras fonts-stix libjs-mathjax-doc tcl8.6 tk8.6 122s libjs-html5shiv elpa-ess r-doc-info | r-doc-pdf r-mathlib r-base-html 122s r-cran-roxygen2 r-cran-rmarkdown r-cran-ff r-cran-aer r-cran-bbmle 122s r-cran-cluster r-cran-cmprsk r-cran-coda r-cran-covr r-cran-emmeans 122s r-cran-epir r-cran-gam r-cran-gee r-cran-geepack r-cran-glmnet r-cran-gmm 122s r-cran-hmisc r-cran-irlba r-cran-interp r-cran-ks r-cran-lavaan r-cran-leaps 122s r-cran-lsmeans r-cran-maps r-cran-mclust r-cran-metafor r-cran-modeldata 122s r-cran-multcomp r-cran-network r-cran-ordinal r-cran-psych r-cran-robust 122s r-cran-robustbase r-cran-rsample r-cran-spdep r-cran-spatialreg 122s r-cran-spelling r-cran-survey r-cran-tseries r-cran-bradleyterry2 122s r-cran-ellipse r-cran-mlbench r-cran-party r-cran-pls r-cran-randomforest 122s r-cran-rann r-cran-rstudioapi r-cran-slider r-cran-kernlab r-cran-mvtnorm 122s r-cran-vcd r-cran-shiny r-cran-shinyjs r-cran-png r-cran-jpeg r-cran-viridis 122s r-cran-tinytest r-cran-markdown r-cran-th.data r-cran-magick r-cran-sf 122s r-cran-getopt r-cran-rgeos r-cran-spatstat.geom r-cran-raster 122s r-cran-polyclip r-cran-plotrix r-cran-spatstat.linnet r-cran-spatstat.utils 122s r-cran-spatstat r-cran-clue r-cran-dbi r-cran-formattable r-cran-nanotime 122s r-cran-palmerpenguins r-cran-units r-cran-vdiffr r-cran-inline r-cran-sem 122s r-cran-bench r-cran-blob r-cran-here r-cran-htmltools r-cran-runit 122s Recommended packages: 122s javascript-common r-recommended r-base-dev r-doc-html r-cran-covr 122s r-cran-cliapp r-cran-mockery r-cran-earth r-cran-mda r-cran-mlmetrics 122s r-cran-fastica r-cran-kernlab r-cran-themis r-cran-htmltools 122s r-cran-htmlwidgets r-cran-rmarkdown r-cran-rstudioapi r-cran-whoami 122s r-cran-xts r-cran-bench r-cran-decor r-cran-lobstr r-cran-spelling 122s r-cran-later r-cran-httpuv r-cran-webutils r-cran-nanotime r-cran-gh 122s r-cran-dbi r-cran-dbplyr r-cran-rmysql r-cran-rpostgresql r-cran-rsqlite 122s r-cran-unitizer r-cran-rhpcblasctl r-cran-r.rsp r-cran-markdown 122s r-cran-hexbin r-cran-hmisc r-cran-mapproj r-cran-maps r-cran-multcomp 122s r-cran-profvis r-cran-ragg r-cran-sf r-cran-svglite r-cran-vdiffr 122s r-cran-xml2 r-cran-devtools r-cran-modeldata r-cran-roxygen2 r-cran-usethis 122s r-cran-testit r-cran-mlbench r-cran-httr r-cran-bslib r-cran-formatr 122s r-cran-gridsvg r-cran-jpeg r-cran-magick r-cran-png r-cran-reticulate 122s r-cran-rgl r-cran-sass r-cran-tikzdevice r-cran-tinytex r-cran-webshot 122s node-highlight.js r-cran-ellipse r-cran-fields r-cran-geepack r-bioc-graph 122s r-cran-bookdown r-cran-igraph r-cran-lavasearch2 r-cran-mets r-cran-optimx 122s r-cran-polycor r-cran-lintr r-cran-tidyverse r-cran-base64enc 122s r-cran-r.devices r-cran-runit r-cran-bitops r-cran-mathjaxr r-cran-mockr 122s r-cran-remotes r-cran-aer r-cran-spdep r-cran-urca r-cran-doparallel 122s r-cran-itertools r-cran-logcondens r-cran-webfakes r-cran-pbmcapply 122s r-cran-furrr r-cran-shiny r-cran-commonmark r-cran-cba r-cran-pingr 122s r-cran-gbrd r-cran-ddalpha r-cran-dials r-cran-rann r-cran-rcpproll 122s r-cran-rsample r-cran-rspectra r-cran-splines2 r-cran-dichromat r-cran-gstat 122s r-cran-deldir r-cran-terra r-cran-raster r-cran-setrng r-cran-formattable 122s r-cran-pkgdown r-cran-zeallot r-cran-mime r-cran-renv libfile-mimeinfo-perl 122s libnet-dbus-perl libx11-protocol-perl x11-utils x11-xserver-utils 123s The following NEW packages will be installed: 123s autopkgtest-satdep fontconfig fontconfig-config fonts-dejavu-core 123s fonts-dejavu-mono fonts-glyphicons-halflings fonts-mathjax libblas3 123s libcairo2 libdatrie1 libdeflate0 libfontconfig1 libgfortran5 libgomp1 123s libgraphite2-3 libharfbuzz0b libice6 libjbig0 libjpeg-turbo8 libjpeg8 123s libjs-bootstrap libjs-highlight.js libjs-jquery libjs-jquery-datatables 123s libjs-mathjax liblapack3 liblerc4 libnlopt0 libpango-1.0-0 123s libpangocairo-1.0-0 libpangoft2-1.0-0 libpaper-utils libpaper1 libpixman-1-0 123s libsharpyuv0 libsm6 libtcl8.6 libthai-data libthai0 libtiff6 libtk8.6 123s libwebp7 libxcb-render0 libxcb-shm0 libxft2 libxrender1 libxss1 libxt6 123s littler node-normalize.css r-base-core r-cran-abind r-cran-backports 123s r-cran-bdsmatrix r-cran-bit r-cran-bit64 r-cran-boot r-cran-brio 123s r-cran-broom r-cran-callr r-cran-car r-cran-cardata r-cran-caret 123s r-cran-cellranger r-cran-class r-cran-cli r-cran-clipr r-cran-clock 123s r-cran-codetools r-cran-collapse r-cran-colorspace r-cran-conquer 123s r-cran-cpp11 r-cran-crayon r-cran-curl r-cran-data.table r-cran-desc 123s r-cran-diagram r-cran-diffobj r-cran-digest r-cran-dplyr r-cran-e1071 123s r-cran-ellipsis r-cran-evaluate r-cran-fansi r-cran-farver r-cran-forcats 123s r-cran-foreach r-cran-foreign r-cran-formula r-cran-fs r-cran-future 123s r-cran-future.apply r-cran-generics r-cran-ggplot2 r-cran-globals 123s r-cran-glue r-cran-gower r-cran-gtable r-cran-hardhat r-cran-haven 123s r-cran-highr r-cran-hms r-cran-ipred r-cran-isoband r-cran-iterators 123s r-cran-jsonlite r-cran-kernsmooth r-cran-knitr r-cran-labeling 123s r-cran-lattice r-cran-lava r-cran-lifecycle r-cran-listenv r-cran-littler 123s r-cran-lme4 r-cran-lmtest r-cran-lubridate r-cran-magrittr r-cran-maptools 123s r-cran-mass r-cran-matrix r-cran-matrixmodels r-cran-matrixstats 123s r-cran-maxlik r-cran-mgcv r-cran-minqa r-cran-misctools r-cran-modelmetrics 123s r-cran-munsell r-cran-nlme r-cran-nloptr r-cran-nnet r-cran-numderiv 123s r-cran-openxlsx r-cran-parallelly r-cran-pbkrtest r-cran-pillar 123s r-cran-pkgbuild r-cran-pkgconfig r-cran-pkgkitten r-cran-pkgload r-cran-plm 123s r-cran-plyr r-cran-praise r-cran-prettyunits r-cran-proc r-cran-processx 123s r-cran-prodlim r-cran-progress r-cran-progressr r-cran-proxy r-cran-ps 123s r-cran-purrr r-cran-quantreg r-cran-r.methodss3 r-cran-r.oo r-cran-r.utils 123s r-cran-r6 r-cran-rbibutils r-cran-rcolorbrewer r-cran-rcpp 123s r-cran-rcpparmadillo r-cran-rcppeigen r-cran-rdpack r-cran-readr 123s r-cran-readxl r-cran-recipes r-cran-rematch r-cran-rematch2 r-cran-reshape2 123s r-cran-rio r-cran-rlang r-cran-rpart r-cran-rprojroot r-cran-sandwich 123s r-cran-scales r-cran-shape r-cran-sp r-cran-sparsem r-cran-squarem 123s r-cran-statmod r-cran-stringi r-cran-stringr r-cran-survival 123s r-cran-systemfit r-cran-testthat r-cran-tibble r-cran-tidyr 123s r-cran-tidyselect r-cran-timechange r-cran-timedate r-cran-tzdb r-cran-utf8 123s r-cran-vctrs r-cran-viridislite r-cran-vroom r-cran-waldo r-cran-withr 123s r-cran-writexl r-cran-xfun r-cran-yaml r-cran-zip r-cran-zoo unzip 123s x11-common xdg-utils zip 123s 0 upgraded, 208 newly installed, 0 to remove and 0 not upgraded. 123s Need to get 163 MB/163 MB of archives. 123s After this operation, 334 MB of additional disk space will be used. 123s Get:1 /tmp/autopkgtest.tI0y9z/1-autopkgtest-satdep.deb autopkgtest-satdep amd64 0 [712 B] 123s Get:2 http://ftpmaster.internal/ubuntu noble/main amd64 fonts-dejavu-mono all 2.37-8 [502 kB] 123s Get:3 http://ftpmaster.internal/ubuntu noble/main amd64 fonts-dejavu-core all 2.37-8 [835 kB] 123s Get:4 http://ftpmaster.internal/ubuntu noble/main amd64 fontconfig-config amd64 2.15.0-1ubuntu1 [36.9 kB] 123s Get:5 http://ftpmaster.internal/ubuntu noble/main amd64 libfontconfig1 amd64 2.15.0-1ubuntu1 [139 kB] 123s Get:6 http://ftpmaster.internal/ubuntu noble/main amd64 fontconfig amd64 2.15.0-1ubuntu1 [180 kB] 123s Get:7 http://ftpmaster.internal/ubuntu noble/universe amd64 fonts-glyphicons-halflings all 1.009~3.4.1+dfsg-3 [118 kB] 123s Get:8 http://ftpmaster.internal/ubuntu noble/main amd64 fonts-mathjax all 2.7.9+dfsg-1 [2208 kB] 123s Get:9 http://ftpmaster.internal/ubuntu noble/main amd64 libblas3 amd64 3.12.0-3 [238 kB] 123s Get:10 http://ftpmaster.internal/ubuntu noble/main amd64 libpixman-1-0 amd64 0.42.2-1 [268 kB] 123s Get:11 http://ftpmaster.internal/ubuntu noble/main amd64 libxcb-render0 amd64 1.15-1 [16.3 kB] 123s Get:12 http://ftpmaster.internal/ubuntu noble/main amd64 libxcb-shm0 amd64 1.15-1 [5740 B] 123s Get:13 http://ftpmaster.internal/ubuntu noble/main amd64 libxrender1 amd64 1:0.9.10-1.1 [20.0 kB] 123s Get:14 http://ftpmaster.internal/ubuntu noble/main amd64 libcairo2 amd64 1.18.0-1 [572 kB] 123s Get:15 http://ftpmaster.internal/ubuntu noble/main amd64 libdatrie1 amd64 0.2.13-3 [20.9 kB] 123s Get:16 http://ftpmaster.internal/ubuntu noble/main amd64 libdeflate0 amd64 1.19-1 [43.7 kB] 123s Get:17 http://ftpmaster.internal/ubuntu noble/main amd64 libgfortran5 amd64 14-20240303-1ubuntu1 [924 kB] 123s Get:18 http://ftpmaster.internal/ubuntu noble/main amd64 libgomp1 amd64 14-20240303-1ubuntu1 [147 kB] 123s Get:19 http://ftpmaster.internal/ubuntu noble/main amd64 libgraphite2-3 amd64 1.3.14-2 [83.1 kB] 123s Get:20 http://ftpmaster.internal/ubuntu noble/main amd64 libharfbuzz0b amd64 8.3.0-2 [469 kB] 123s Get:21 http://ftpmaster.internal/ubuntu noble/main amd64 x11-common all 1:7.7+23ubuntu2 [23.4 kB] 123s Get:22 http://ftpmaster.internal/ubuntu noble/main amd64 libice6 amd64 2:1.0.10-1build2 [42.6 kB] 123s Get:23 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg-turbo8 amd64 2.1.5-2ubuntu1 [147 kB] 123s Get:24 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg8 amd64 8c-2ubuntu11 [2148 B] 123s Get:25 http://ftpmaster.internal/ubuntu noble/universe amd64 libjs-bootstrap all 3.4.1+dfsg-3 [129 kB] 123s Get:26 http://ftpmaster.internal/ubuntu noble/universe amd64 libjs-highlight.js all 9.18.5+dfsg1-2 [385 kB] 123s Get:27 http://ftpmaster.internal/ubuntu noble/main amd64 libjs-jquery all 3.6.1+dfsg+~3.5.14-1 [328 kB] 123s Get:28 http://ftpmaster.internal/ubuntu noble/universe amd64 libjs-jquery-datatables all 1.11.5+dfsg-2 [146 kB] 123s Get:29 http://ftpmaster.internal/ubuntu noble/main amd64 liblapack3 amd64 3.12.0-3 [2649 kB] 123s Get:30 http://ftpmaster.internal/ubuntu noble/main amd64 liblerc4 amd64 4.0.0+ds-4ubuntu1 [184 kB] 123s Get:31 http://ftpmaster.internal/ubuntu noble/main amd64 libthai-data all 0.1.29-2 [158 kB] 123s Get:32 http://ftpmaster.internal/ubuntu noble/main amd64 libthai0 amd64 0.1.29-2 [18.8 kB] 123s Get:33 http://ftpmaster.internal/ubuntu noble/main amd64 libpango-1.0-0 amd64 1.51.0+ds-4 [228 kB] 123s Get:34 http://ftpmaster.internal/ubuntu noble/main amd64 libpangoft2-1.0-0 amd64 1.51.0+ds-4 [42.1 kB] 123s Get:35 http://ftpmaster.internal/ubuntu noble/main amd64 libpangocairo-1.0-0 amd64 1.51.0+ds-4 [29.0 kB] 123s Get:36 http://ftpmaster.internal/ubuntu noble/main amd64 libpaper1 amd64 1.1.29 [13.4 kB] 123s Get:37 http://ftpmaster.internal/ubuntu noble/main amd64 libpaper-utils amd64 1.1.29 [8658 B] 123s Get:38 http://ftpmaster.internal/ubuntu noble/main amd64 libsharpyuv0 amd64 1.3.2-0.4 [15.6 kB] 123s Get:39 http://ftpmaster.internal/ubuntu noble/main amd64 libsm6 amd64 2:1.2.3-1build2 [16.7 kB] 123s Get:40 http://ftpmaster.internal/ubuntu noble/main amd64 libtcl8.6 amd64 8.6.13+dfsg-2 [984 kB] 123s Get:41 http://ftpmaster.internal/ubuntu noble/main amd64 libjbig0 amd64 2.1-6.1ubuntu1 [29.3 kB] 123s Get:42 http://ftpmaster.internal/ubuntu noble/main amd64 libwebp7 amd64 1.3.2-0.4 [230 kB] 123s Get:43 http://ftpmaster.internal/ubuntu noble/main amd64 libtiff6 amd64 4.5.1+git230720-3ubuntu1 [232 kB] 123s Get:44 http://ftpmaster.internal/ubuntu noble/main amd64 libxft2 amd64 2.3.6-1 [44.5 kB] 123s Get:45 http://ftpmaster.internal/ubuntu noble/main amd64 libxss1 amd64 1:1.2.3-1build2 [8476 B] 123s Get:46 http://ftpmaster.internal/ubuntu noble/main amd64 libtk8.6 amd64 8.6.14-1 [779 kB] 123s Get:47 http://ftpmaster.internal/ubuntu noble/main amd64 libxt6 amd64 1:1.2.1-1.1 [173 kB] 123s Get:48 http://ftpmaster.internal/ubuntu noble/main amd64 zip amd64 3.0-13 [176 kB] 123s Get:49 http://ftpmaster.internal/ubuntu noble/main amd64 unzip amd64 6.0-28ubuntu3 [174 kB] 123s Get:50 http://ftpmaster.internal/ubuntu noble/main amd64 xdg-utils all 1.1.3-4.1ubuntu3 [62.0 kB] 123s Get:51 http://ftpmaster.internal/ubuntu noble/universe amd64 r-base-core amd64 4.3.2-1build1 [27.0 MB] 123s Get:52 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-littler amd64 0.3.19-1 [94.1 kB] 123s Get:53 http://ftpmaster.internal/ubuntu noble/universe amd64 littler all 0.3.19-1 [2472 B] 123s Get:54 http://ftpmaster.internal/ubuntu noble/universe amd64 node-normalize.css all 8.0.1-5 [10.8 kB] 123s Get:55 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-abind all 1.4-5-2 [63.6 kB] 123s Get:56 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-backports amd64 1.4.1-1 [101 kB] 123s Get:57 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-bdsmatrix amd64 1.3-6-1 [293 kB] 123s Get:58 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-bit amd64 4.0.5-1 [1063 kB] 123s Get:59 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-bit64 amd64 4.0.5-1 [465 kB] 123s Get:60 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-boot all 1.3-30-1 [619 kB] 123s Get:61 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-brio amd64 1.1.4-1 [37.9 kB] 123s Get:62 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-cli amd64 3.6.2-1 [1380 kB] 123s Get:63 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-generics all 0.1.3-1 [81.3 kB] 123s Get:64 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-glue amd64 1.7.0-1 [154 kB] 123s Get:65 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rlang amd64 1.1.3-1 [1663 kB] 123s Get:66 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lifecycle all 1.0.4+dfsg-1 [110 kB] 123s Get:67 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-magrittr amd64 2.0.3-1 [154 kB] 123s Get:68 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-fansi amd64 1.0.5-1 [619 kB] 123s Get:69 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-utf8 amd64 1.2.4-1 [140 kB] 123s Get:70 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-vctrs amd64 0.6.5-1 [1335 kB] 123s Get:71 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pillar all 1.9.0+dfsg-1 [464 kB] 123s Get:72 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-r6 all 2.5.1-1 [99.0 kB] 123s Get:73 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pkgconfig all 2.0.3-2build1 [19.7 kB] 123s Get:74 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-tibble amd64 3.2.1+dfsg-2 [415 kB] 123s Get:75 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-withr all 2.5.0-1 [225 kB] 123s Get:76 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-tidyselect amd64 1.2.0+dfsg-1 [218 kB] 123s Get:77 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-dplyr amd64 1.1.4-1 [1515 kB] 123s Get:78 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-ellipsis amd64 0.3.2-2 [35.6 kB] 123s Get:79 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-purrr amd64 1.0.2-1 [502 kB] 123s Get:80 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-stringi amd64 1.8.3-1 [873 kB] 123s Get:81 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-stringr all 1.5.1-1 [290 kB] 123s Get:82 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-cpp11 all 0.4.7-1 [266 kB] 123s Get:83 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-tidyr amd64 1.3.1-1 [1156 kB] 123s Get:84 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-broom all 1.0.5+dfsg-1 [1729 kB] 123s Get:85 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-ps amd64 1.7.6-1 [313 kB] 123s Get:86 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-processx amd64 3.8.3-1 [346 kB] 123s Get:87 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-callr all 3.7.3-2 [425 kB] 123s Get:88 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-cardata all 3.0.5-1 [1819 kB] 123s Get:89 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-mass amd64 7.3-60.0.1-1 [1119 kB] 123s Get:90 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lattice amd64 0.22-5-1 [1342 kB] 123s Get:91 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-nlme amd64 3.1.164-1 [2260 kB] 123s Get:92 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-matrix amd64 1.6-5-1 [3830 kB] 123s Get:93 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-mgcv amd64 1.9-1-1 [3252 kB] 123s Get:94 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-nnet amd64 7.3-19-2 [112 kB] 123s Get:95 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pkgkitten all 0.2.3-1 [25.1 kB] 123s Get:96 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rcpp amd64 1.0.12-1 [1981 kB] 123s Get:97 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-minqa amd64 1.2.6-1 [116 kB] 123s Get:98 http://ftpmaster.internal/ubuntu noble/universe amd64 libnlopt0 amd64 2.7.1-5build2 [184 kB] 123s Get:99 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-desc all 1.4.3-1 [359 kB] 123s Get:100 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-digest amd64 0.6.34-1 [186 kB] 123s Get:101 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-evaluate all 0.23-1 [90.2 kB] 123s Get:102 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-jsonlite amd64 1.8.8+dfsg-1 [441 kB] 123s Get:103 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-crayon all 1.5.2-1 [164 kB] 123s Get:104 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-fs amd64 1.6.3+dfsg-1 [229 kB] 123s Get:105 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pkgbuild all 1.4.3-1 [209 kB] 123s Get:106 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rprojroot all 2.0.4-1 [124 kB] 123s Get:107 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pkgload all 1.3.4-1 [207 kB] 123s Get:108 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-praise all 1.0.0-4build1 [20.3 kB] 123s Get:109 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-diffobj amd64 0.3.5-1 [1117 kB] 123s Get:110 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rematch2 all 2.1.2-2build1 [46.5 kB] 123s Get:111 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-waldo all 0.5.2-1build1 [120 kB] 123s Get:112 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-testthat amd64 3.2.1-1 [1684 kB] 123s Get:113 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-nloptr amd64 2.0.3-1 [381 kB] 123s Get:114 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rcppeigen amd64 0.3.3.9.4-1 [1189 kB] 123s Get:115 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-statmod amd64 1.5.0-1 [295 kB] 123s Get:116 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lme4 amd64 1.1-35.1-4 [4138 kB] 124s Get:117 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-numderiv all 2016.8-1.1-3 [115 kB] 124s Get:118 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-xfun amd64 0.41+dfsg-1 [415 kB] 124s Get:119 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-highr all 0.10+dfsg-1 [38.3 kB] 124s Get:120 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-yaml amd64 2.3.8-1 [108 kB] 124s Get:121 http://ftpmaster.internal/ubuntu noble/main amd64 libjs-mathjax all 2.7.9+dfsg-1 [5665 kB] 124s Get:122 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-knitr all 1.45+dfsg-1 [917 kB] 124s Get:123 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-pbkrtest all 0.5.2-2 [182 kB] 124s Get:124 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-sparsem amd64 1.81-1 [905 kB] 124s Get:125 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-matrixmodels all 0.5-3-1 [361 kB] 124s Get:126 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-survival amd64 3.5-8-1 [6120 kB] 124s Get:127 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-matrixstats amd64 1.2.0-1 [488 kB] 124s Get:128 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rcpparmadillo amd64 0.12.8.0.0-1 [862 kB] 124s Get:129 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-gtable all 0.3.4+dfsg-1 [191 kB] 124s Get:130 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-isoband amd64 0.2.7-1 [1481 kB] 124s Get:131 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-farver amd64 2.1.1-1 [1353 kB] 124s Get:132 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-labeling all 0.4.3-1 [62.1 kB] 124s Get:133 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-colorspace amd64 2.1-0+dfsg-1 [1541 kB] 124s Get:134 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-munsell all 0.5.0-2build1 [208 kB] 124s Get:135 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rcolorbrewer all 1.1-3-1build1 [55.4 kB] 124s Get:136 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-viridislite all 0.4.2-2 [1088 kB] 124s Get:137 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-scales all 1.3.0-1 [603 kB] 124s Get:138 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-ggplot2 all 3.4.4+dfsg-1 [3411 kB] 124s Get:139 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-class amd64 7.3-22-2 [88.3 kB] 124s Get:140 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-proxy amd64 0.4-27-1 [182 kB] 124s Get:141 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-e1071 amd64 1.7-14-1 [558 kB] 124s Get:142 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-codetools all 0.2-19-1 [90.5 kB] 124s Get:143 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-iterators all 1.0.14-1 [336 kB] 124s Get:144 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-foreach all 1.5.2-1 [124 kB] 124s Get:145 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-data.table amd64 1.14.10+dfsg-1 [1837 kB] 124s Get:146 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-modelmetrics amd64 1.2.2.2-1build1 [128 kB] 124s Get:147 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-plyr amd64 1.8.9-1 [832 kB] 124s Get:148 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-proc amd64 1.18.5-1 [966 kB] 124s Get:149 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-tzdb amd64 0.4.0-2 [521 kB] 124s Get:150 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-clock amd64 0.7.0-1.1 [1765 kB] 124s Get:151 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-gower amd64 1.0.1-1 [207 kB] 124s Get:152 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-hardhat all 1.3.1+dfsg-1 [554 kB] 124s Get:153 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rpart amd64 4.1.23-1 [661 kB] 124s Get:154 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-shape all 1.4.6-1 [770 kB] 124s Get:155 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-diagram all 1.6.5-2 [656 kB] 124s Get:156 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-kernsmooth amd64 2.23-22-1 [91.7 kB] 124s Get:157 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-globals all 0.16.2-1 [117 kB] 124s Get:158 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-listenv all 0.9.1+dfsg-1 [112 kB] 124s Get:159 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-parallelly amd64 1.37.1-1 [365 kB] 124s Get:160 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-future all 1.33.1+dfsg-1 [634 kB] 124s Get:161 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-future.apply all 1.11.1+dfsg-1 [171 kB] 124s Get:162 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-progressr all 0.14.0-1 [338 kB] 124s Get:163 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-squarem all 2021.1-1 [179 kB] 124s Get:164 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lava all 1.7.3+dfsg-1 [2166 kB] 124s Get:165 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-prodlim amd64 2023.08.28-1 [408 kB] 124s Get:166 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-ipred amd64 0.9-14-1 [383 kB] 124s Get:167 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-timechange amd64 0.3.0-1 [178 kB] 124s Get:168 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lubridate amd64 1.9.3+dfsg-1 [1010 kB] 124s Get:169 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-timedate amd64 4032.109-1 [1229 kB] 124s Get:170 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-recipes all 1.0.9+dfsg-1 [1964 kB] 124s Get:171 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-reshape2 amd64 1.4.4-2build1 [114 kB] 124s Get:172 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-caret amd64 6.0-94+dfsg-1 [3434 kB] 124s Get:173 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-conquer amd64 1.3.3-1 [499 kB] 124s Get:174 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-quantreg amd64 5.97-1 [1533 kB] 124s Get:175 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-sp amd64 1:2.1-2+dfsg-1 [1447 kB] 124s Get:176 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-foreign amd64 0.8.86-1 [242 kB] 124s Get:177 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-maptools amd64 1:1.1-8+dfsg-1 [1365 kB] 124s Get:178 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-forcats all 1.0.0-1 [369 kB] 124s Get:179 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-hms all 1.1.3-1 [96.5 kB] 124s Get:180 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-clipr all 0.8.0-1 [53.5 kB] 124s Get:181 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-prettyunits all 1.2.0-1 [162 kB] 124s Get:182 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-progress all 1.2.3-1 [91.9 kB] 124s Get:183 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-vroom amd64 1.6.5-1 [848 kB] 124s Get:184 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-readr amd64 2.1.5-1 [766 kB] 124s Get:185 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-haven amd64 2.5.4-1 [346 kB] 124s Get:186 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-curl amd64 5.2.0+dfsg-1 [188 kB] 124s Get:187 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rematch all 2.0.0-1 [18.3 kB] 124s Get:188 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-cellranger all 1.1.0-3 [102 kB] 124s Get:189 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-readxl amd64 1.4.3-1 [736 kB] 124s Get:190 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-writexl amd64 1.5.0-1 [157 kB] 124s Get:191 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-r.methodss3 all 1.8.2-1 [84.0 kB] 124s Get:192 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-r.oo all 1.26.0-1 [955 kB] 124s Get:193 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-r.utils all 2.12.3-1 [1386 kB] 124s Get:194 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-zip amd64 2.3.1-1 [123 kB] 124s Get:195 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-openxlsx amd64 4.2.5.2-1 [1943 kB] 124s Get:196 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rio all 1.0.1-1 [529 kB] 124s Get:197 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-car all 3.1-2-2 [1692 kB] 124s Get:198 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-collapse amd64 2.0.10-1 [3112 kB] 124s Get:199 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-formula all 1.2-5-1 [158 kB] 124s Get:200 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-zoo amd64 1.8-12-2 [984 kB] 124s Get:201 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-lmtest amd64 0.9.40-1 [396 kB] 124s Get:202 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-misctools all 0.6-28-1 [99.9 kB] 124s Get:203 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-sandwich all 3.1-0-1 [1484 kB] 124s Get:204 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-maxlik all 1.5-2-1 [1550 kB] 124s Get:205 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rbibutils amd64 2.2.16-1 [754 kB] 124s Get:206 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-rdpack all 2.6-1 [742 kB] 124s Get:207 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-plm all 2.6-3-1 [2141 kB] 124s Get:208 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-systemfit all 1.1-30-1 [1174 kB] 125s Preconfiguring packages ... 125s Fetched 163 MB in 2s (97.1 MB/s) 125s Selecting previously unselected package fonts-dejavu-mono. 125s (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.) 126s Preparing to unpack .../000-fonts-dejavu-mono_2.37-8_all.deb ... 126s Unpacking fonts-dejavu-mono (2.37-8) ... 126s Selecting previously unselected package fonts-dejavu-core. 126s Preparing to unpack .../001-fonts-dejavu-core_2.37-8_all.deb ... 126s Unpacking fonts-dejavu-core (2.37-8) ... 126s Selecting previously unselected package fontconfig-config. 126s Preparing to unpack .../002-fontconfig-config_2.15.0-1ubuntu1_amd64.deb ... 126s Unpacking fontconfig-config (2.15.0-1ubuntu1) ... 126s Selecting previously unselected package libfontconfig1:amd64. 126s Preparing to unpack .../003-libfontconfig1_2.15.0-1ubuntu1_amd64.deb ... 126s Unpacking libfontconfig1:amd64 (2.15.0-1ubuntu1) ... 126s Selecting previously unselected package fontconfig. 126s Preparing to unpack .../004-fontconfig_2.15.0-1ubuntu1_amd64.deb ... 126s Unpacking fontconfig (2.15.0-1ubuntu1) ... 126s Selecting previously unselected package fonts-glyphicons-halflings. 126s Preparing to unpack .../005-fonts-glyphicons-halflings_1.009~3.4.1+dfsg-3_all.deb ... 126s Unpacking fonts-glyphicons-halflings (1.009~3.4.1+dfsg-3) ... 126s Selecting previously unselected package fonts-mathjax. 126s Preparing to unpack .../006-fonts-mathjax_2.7.9+dfsg-1_all.deb ... 126s Unpacking fonts-mathjax (2.7.9+dfsg-1) ... 126s Selecting previously unselected package libblas3:amd64. 126s Preparing to unpack .../007-libblas3_3.12.0-3_amd64.deb ... 126s Unpacking libblas3:amd64 (3.12.0-3) ... 126s Selecting previously unselected package libpixman-1-0:amd64. 126s Preparing to unpack .../008-libpixman-1-0_0.42.2-1_amd64.deb ... 126s Unpacking libpixman-1-0:amd64 (0.42.2-1) ... 126s Selecting previously unselected package libxcb-render0:amd64. 126s Preparing to unpack .../009-libxcb-render0_1.15-1_amd64.deb ... 126s Unpacking libxcb-render0:amd64 (1.15-1) ... 126s Selecting previously unselected package libxcb-shm0:amd64. 126s Preparing to unpack .../010-libxcb-shm0_1.15-1_amd64.deb ... 126s Unpacking libxcb-shm0:amd64 (1.15-1) ... 126s Selecting previously unselected package libxrender1:amd64. 126s Preparing to unpack .../011-libxrender1_1%3a0.9.10-1.1_amd64.deb ... 126s Unpacking libxrender1:amd64 (1:0.9.10-1.1) ... 126s Selecting previously unselected package libcairo2:amd64. 126s Preparing to unpack .../012-libcairo2_1.18.0-1_amd64.deb ... 126s Unpacking libcairo2:amd64 (1.18.0-1) ... 126s Selecting previously unselected package libdatrie1:amd64. 126s Preparing to unpack .../013-libdatrie1_0.2.13-3_amd64.deb ... 126s Unpacking libdatrie1:amd64 (0.2.13-3) ... 126s Selecting previously unselected package libdeflate0:amd64. 126s Preparing to unpack .../014-libdeflate0_1.19-1_amd64.deb ... 126s Unpacking libdeflate0:amd64 (1.19-1) ... 126s Selecting previously unselected package libgfortran5:amd64. 126s Preparing to unpack .../015-libgfortran5_14-20240303-1ubuntu1_amd64.deb ... 126s Unpacking libgfortran5:amd64 (14-20240303-1ubuntu1) ... 126s Selecting previously unselected package libgomp1:amd64. 126s Preparing to unpack .../016-libgomp1_14-20240303-1ubuntu1_amd64.deb ... 126s Unpacking libgomp1:amd64 (14-20240303-1ubuntu1) ... 126s Selecting previously unselected package libgraphite2-3:amd64. 126s Preparing to unpack .../017-libgraphite2-3_1.3.14-2_amd64.deb ... 126s Unpacking libgraphite2-3:amd64 (1.3.14-2) ... 126s Selecting previously unselected package libharfbuzz0b:amd64. 126s Preparing to unpack .../018-libharfbuzz0b_8.3.0-2_amd64.deb ... 126s Unpacking libharfbuzz0b:amd64 (8.3.0-2) ... 126s Selecting previously unselected package x11-common. 126s Preparing to unpack .../019-x11-common_1%3a7.7+23ubuntu2_all.deb ... 126s Unpacking x11-common (1:7.7+23ubuntu2) ... 126s Selecting previously unselected package libice6:amd64. 126s Preparing to unpack .../020-libice6_2%3a1.0.10-1build2_amd64.deb ... 126s Unpacking libice6:amd64 (2:1.0.10-1build2) ... 126s Selecting previously unselected package libjpeg-turbo8:amd64. 126s Preparing to unpack .../021-libjpeg-turbo8_2.1.5-2ubuntu1_amd64.deb ... 126s Unpacking libjpeg-turbo8:amd64 (2.1.5-2ubuntu1) ... 126s Selecting previously unselected package libjpeg8:amd64. 126s Preparing to unpack .../022-libjpeg8_8c-2ubuntu11_amd64.deb ... 126s Unpacking libjpeg8:amd64 (8c-2ubuntu11) ... 126s Selecting previously unselected package libjs-bootstrap. 126s Preparing to unpack .../023-libjs-bootstrap_3.4.1+dfsg-3_all.deb ... 126s Unpacking libjs-bootstrap (3.4.1+dfsg-3) ... 126s Selecting previously unselected package libjs-highlight.js. 126s Preparing to unpack .../024-libjs-highlight.js_9.18.5+dfsg1-2_all.deb ... 126s Unpacking libjs-highlight.js (9.18.5+dfsg1-2) ... 126s Selecting previously unselected package libjs-jquery. 126s Preparing to unpack .../025-libjs-jquery_3.6.1+dfsg+~3.5.14-1_all.deb ... 126s Unpacking libjs-jquery (3.6.1+dfsg+~3.5.14-1) ... 127s Selecting previously unselected package libjs-jquery-datatables. 127s Preparing to unpack .../026-libjs-jquery-datatables_1.11.5+dfsg-2_all.deb ... 127s Unpacking libjs-jquery-datatables (1.11.5+dfsg-2) ... 127s Selecting previously unselected package liblapack3:amd64. 127s Preparing to unpack .../027-liblapack3_3.12.0-3_amd64.deb ... 127s Unpacking liblapack3:amd64 (3.12.0-3) ... 127s Selecting previously unselected package liblerc4:amd64. 127s Preparing to unpack .../028-liblerc4_4.0.0+ds-4ubuntu1_amd64.deb ... 127s Unpacking liblerc4:amd64 (4.0.0+ds-4ubuntu1) ... 127s Selecting previously unselected package libthai-data. 127s Preparing to unpack .../029-libthai-data_0.1.29-2_all.deb ... 127s Unpacking libthai-data (0.1.29-2) ... 127s Selecting previously unselected package libthai0:amd64. 127s Preparing to unpack .../030-libthai0_0.1.29-2_amd64.deb ... 127s Unpacking libthai0:amd64 (0.1.29-2) ... 127s Selecting previously unselected package libpango-1.0-0:amd64. 127s Preparing to unpack .../031-libpango-1.0-0_1.51.0+ds-4_amd64.deb ... 127s Unpacking libpango-1.0-0:amd64 (1.51.0+ds-4) ... 127s Selecting previously unselected package libpangoft2-1.0-0:amd64. 127s Preparing to unpack .../032-libpangoft2-1.0-0_1.51.0+ds-4_amd64.deb ... 127s Unpacking libpangoft2-1.0-0:amd64 (1.51.0+ds-4) ... 127s Selecting previously unselected package libpangocairo-1.0-0:amd64. 127s Preparing to unpack .../033-libpangocairo-1.0-0_1.51.0+ds-4_amd64.deb ... 127s Unpacking libpangocairo-1.0-0:amd64 (1.51.0+ds-4) ... 127s Selecting previously unselected package libpaper1:amd64. 127s Preparing to unpack .../034-libpaper1_1.1.29_amd64.deb ... 127s Unpacking libpaper1:amd64 (1.1.29) ... 127s Selecting previously unselected package libpaper-utils. 127s Preparing to unpack .../035-libpaper-utils_1.1.29_amd64.deb ... 127s Unpacking libpaper-utils (1.1.29) ... 127s Selecting previously unselected package libsharpyuv0:amd64. 127s Preparing to unpack .../036-libsharpyuv0_1.3.2-0.4_amd64.deb ... 127s Unpacking libsharpyuv0:amd64 (1.3.2-0.4) ... 127s Selecting previously unselected package libsm6:amd64. 127s Preparing to unpack .../037-libsm6_2%3a1.2.3-1build2_amd64.deb ... 127s Unpacking libsm6:amd64 (2:1.2.3-1build2) ... 127s Selecting previously unselected package libtcl8.6:amd64. 127s Preparing to unpack .../038-libtcl8.6_8.6.13+dfsg-2_amd64.deb ... 127s Unpacking libtcl8.6:amd64 (8.6.13+dfsg-2) ... 127s Selecting previously unselected package libjbig0:amd64. 127s Preparing to unpack .../039-libjbig0_2.1-6.1ubuntu1_amd64.deb ... 127s Unpacking libjbig0:amd64 (2.1-6.1ubuntu1) ... 127s Selecting previously unselected package libwebp7:amd64. 127s Preparing to unpack .../040-libwebp7_1.3.2-0.4_amd64.deb ... 127s Unpacking libwebp7:amd64 (1.3.2-0.4) ... 127s Selecting previously unselected package libtiff6:amd64. 127s Preparing to unpack .../041-libtiff6_4.5.1+git230720-3ubuntu1_amd64.deb ... 127s Unpacking libtiff6:amd64 (4.5.1+git230720-3ubuntu1) ... 127s Selecting previously unselected package libxft2:amd64. 127s Preparing to unpack .../042-libxft2_2.3.6-1_amd64.deb ... 127s Unpacking libxft2:amd64 (2.3.6-1) ... 127s Selecting previously unselected package libxss1:amd64. 127s Preparing to unpack .../043-libxss1_1%3a1.2.3-1build2_amd64.deb ... 127s Unpacking libxss1:amd64 (1:1.2.3-1build2) ... 127s Selecting previously unselected package libtk8.6:amd64. 127s Preparing to unpack .../044-libtk8.6_8.6.14-1_amd64.deb ... 127s Unpacking libtk8.6:amd64 (8.6.14-1) ... 127s Selecting previously unselected package libxt6:amd64. 127s Preparing to unpack .../045-libxt6_1%3a1.2.1-1.1_amd64.deb ... 127s Unpacking libxt6:amd64 (1:1.2.1-1.1) ... 127s Selecting previously unselected package zip. 127s Preparing to unpack .../046-zip_3.0-13_amd64.deb ... 127s Unpacking zip (3.0-13) ... 127s Selecting previously unselected package unzip. 127s Preparing to unpack .../047-unzip_6.0-28ubuntu3_amd64.deb ... 127s Unpacking unzip (6.0-28ubuntu3) ... 127s Selecting previously unselected package xdg-utils. 127s Preparing to unpack .../048-xdg-utils_1.1.3-4.1ubuntu3_all.deb ... 127s Unpacking xdg-utils (1.1.3-4.1ubuntu3) ... 127s Selecting previously unselected package r-base-core. 127s Preparing to unpack .../049-r-base-core_4.3.2-1build1_amd64.deb ... 127s Unpacking r-base-core (4.3.2-1build1) ... 128s Selecting previously unselected package r-cran-littler. 128s Preparing to unpack .../050-r-cran-littler_0.3.19-1_amd64.deb ... 128s Unpacking r-cran-littler (0.3.19-1) ... 128s Selecting previously unselected package littler. 128s Preparing to unpack .../051-littler_0.3.19-1_all.deb ... 128s Unpacking littler (0.3.19-1) ... 128s Selecting previously unselected package node-normalize.css. 128s Preparing to unpack .../052-node-normalize.css_8.0.1-5_all.deb ... 128s Unpacking node-normalize.css (8.0.1-5) ... 128s Selecting previously unselected package r-cran-abind. 128s Preparing to unpack .../053-r-cran-abind_1.4-5-2_all.deb ... 128s Unpacking r-cran-abind (1.4-5-2) ... 128s Selecting previously unselected package r-cran-backports. 128s Preparing to unpack .../054-r-cran-backports_1.4.1-1_amd64.deb ... 128s Unpacking r-cran-backports (1.4.1-1) ... 128s Selecting previously unselected package r-cran-bdsmatrix. 128s Preparing to unpack .../055-r-cran-bdsmatrix_1.3-6-1_amd64.deb ... 128s Unpacking r-cran-bdsmatrix (1.3-6-1) ... 128s Selecting previously unselected package r-cran-bit. 128s Preparing to unpack .../056-r-cran-bit_4.0.5-1_amd64.deb ... 128s Unpacking r-cran-bit (4.0.5-1) ... 128s Selecting previously unselected package r-cran-bit64. 128s Preparing to unpack .../057-r-cran-bit64_4.0.5-1_amd64.deb ... 128s Unpacking r-cran-bit64 (4.0.5-1) ... 128s Selecting previously unselected package r-cran-boot. 128s Preparing to unpack .../058-r-cran-boot_1.3-30-1_all.deb ... 128s Unpacking r-cran-boot (1.3-30-1) ... 128s Selecting previously unselected package r-cran-brio. 128s Preparing to unpack .../059-r-cran-brio_1.1.4-1_amd64.deb ... 128s Unpacking r-cran-brio (1.1.4-1) ... 128s Selecting previously unselected package r-cran-cli. 128s Preparing to unpack .../060-r-cran-cli_3.6.2-1_amd64.deb ... 128s Unpacking r-cran-cli (3.6.2-1) ... 128s Selecting previously unselected package r-cran-generics. 128s Preparing to unpack .../061-r-cran-generics_0.1.3-1_all.deb ... 128s Unpacking r-cran-generics (0.1.3-1) ... 128s Selecting previously unselected package r-cran-glue. 128s Preparing to unpack .../062-r-cran-glue_1.7.0-1_amd64.deb ... 128s Unpacking r-cran-glue (1.7.0-1) ... 128s Selecting previously unselected package r-cran-rlang. 128s Preparing to unpack .../063-r-cran-rlang_1.1.3-1_amd64.deb ... 128s Unpacking r-cran-rlang (1.1.3-1) ... 128s Selecting previously unselected package r-cran-lifecycle. 128s Preparing to unpack .../064-r-cran-lifecycle_1.0.4+dfsg-1_all.deb ... 128s Unpacking r-cran-lifecycle (1.0.4+dfsg-1) ... 128s Selecting previously unselected package r-cran-magrittr. 128s Preparing to unpack .../065-r-cran-magrittr_2.0.3-1_amd64.deb ... 128s Unpacking r-cran-magrittr (2.0.3-1) ... 128s Selecting previously unselected package r-cran-fansi. 128s Preparing to unpack .../066-r-cran-fansi_1.0.5-1_amd64.deb ... 128s Unpacking r-cran-fansi (1.0.5-1) ... 128s Selecting previously unselected package r-cran-utf8. 128s Preparing to unpack .../067-r-cran-utf8_1.2.4-1_amd64.deb ... 128s Unpacking r-cran-utf8 (1.2.4-1) ... 128s Selecting previously unselected package r-cran-vctrs. 128s Preparing to unpack .../068-r-cran-vctrs_0.6.5-1_amd64.deb ... 128s Unpacking r-cran-vctrs (0.6.5-1) ... 129s Selecting previously unselected package r-cran-pillar. 129s Preparing to unpack .../069-r-cran-pillar_1.9.0+dfsg-1_all.deb ... 129s Unpacking r-cran-pillar (1.9.0+dfsg-1) ... 129s Selecting previously unselected package r-cran-r6. 129s Preparing to unpack .../070-r-cran-r6_2.5.1-1_all.deb ... 129s Unpacking r-cran-r6 (2.5.1-1) ... 129s Selecting previously unselected package r-cran-pkgconfig. 129s Preparing to unpack .../071-r-cran-pkgconfig_2.0.3-2build1_all.deb ... 129s Unpacking r-cran-pkgconfig (2.0.3-2build1) ... 129s Selecting previously unselected package r-cran-tibble. 129s Preparing to unpack .../072-r-cran-tibble_3.2.1+dfsg-2_amd64.deb ... 129s Unpacking r-cran-tibble (3.2.1+dfsg-2) ... 129s Selecting previously unselected package r-cran-withr. 129s Preparing to unpack .../073-r-cran-withr_2.5.0-1_all.deb ... 129s Unpacking r-cran-withr (2.5.0-1) ... 129s Selecting previously unselected package r-cran-tidyselect. 129s Preparing to unpack .../074-r-cran-tidyselect_1.2.0+dfsg-1_amd64.deb ... 129s Unpacking r-cran-tidyselect (1.2.0+dfsg-1) ... 129s Selecting previously unselected package r-cran-dplyr. 129s Preparing to unpack .../075-r-cran-dplyr_1.1.4-1_amd64.deb ... 129s Unpacking r-cran-dplyr (1.1.4-1) ... 129s Selecting previously unselected package r-cran-ellipsis. 129s Preparing to unpack .../076-r-cran-ellipsis_0.3.2-2_amd64.deb ... 129s Unpacking r-cran-ellipsis (0.3.2-2) ... 129s Selecting previously unselected package r-cran-purrr. 129s Preparing to unpack .../077-r-cran-purrr_1.0.2-1_amd64.deb ... 129s Unpacking r-cran-purrr (1.0.2-1) ... 129s Selecting previously unselected package r-cran-stringi. 129s Preparing to unpack .../078-r-cran-stringi_1.8.3-1_amd64.deb ... 129s Unpacking r-cran-stringi (1.8.3-1) ... 129s Selecting previously unselected package r-cran-stringr. 129s Preparing to unpack .../079-r-cran-stringr_1.5.1-1_all.deb ... 129s Unpacking r-cran-stringr (1.5.1-1) ... 129s Selecting previously unselected package r-cran-cpp11. 129s Preparing to unpack .../080-r-cran-cpp11_0.4.7-1_all.deb ... 129s Unpacking r-cran-cpp11 (0.4.7-1) ... 129s Selecting previously unselected package r-cran-tidyr. 129s Preparing to unpack .../081-r-cran-tidyr_1.3.1-1_amd64.deb ... 129s Unpacking r-cran-tidyr (1.3.1-1) ... 129s Selecting previously unselected package r-cran-broom. 129s Preparing to unpack .../082-r-cran-broom_1.0.5+dfsg-1_all.deb ... 129s Unpacking r-cran-broom (1.0.5+dfsg-1) ... 129s Selecting previously unselected package r-cran-ps. 129s Preparing to unpack .../083-r-cran-ps_1.7.6-1_amd64.deb ... 129s Unpacking r-cran-ps (1.7.6-1) ... 129s Selecting previously unselected package r-cran-processx. 129s Preparing to unpack .../084-r-cran-processx_3.8.3-1_amd64.deb ... 129s Unpacking r-cran-processx (3.8.3-1) ... 129s Selecting previously unselected package r-cran-callr. 129s Preparing to unpack .../085-r-cran-callr_3.7.3-2_all.deb ... 129s Unpacking r-cran-callr (3.7.3-2) ... 129s Selecting previously unselected package r-cran-cardata. 129s Preparing to unpack .../086-r-cran-cardata_3.0.5-1_all.deb ... 129s Unpacking r-cran-cardata (3.0.5-1) ... 129s Selecting previously unselected package r-cran-mass. 129s Preparing to unpack .../087-r-cran-mass_7.3-60.0.1-1_amd64.deb ... 129s Unpacking r-cran-mass (7.3-60.0.1-1) ... 129s Selecting previously unselected package r-cran-lattice. 129s Preparing to unpack .../088-r-cran-lattice_0.22-5-1_amd64.deb ... 129s Unpacking r-cran-lattice (0.22-5-1) ... 129s Selecting previously unselected package r-cran-nlme. 129s Preparing to unpack .../089-r-cran-nlme_3.1.164-1_amd64.deb ... 129s Unpacking r-cran-nlme (3.1.164-1) ... 129s Selecting previously unselected package r-cran-matrix. 129s Preparing to unpack .../090-r-cran-matrix_1.6-5-1_amd64.deb ... 129s Unpacking r-cran-matrix (1.6-5-1) ... 130s Selecting previously unselected package r-cran-mgcv. 130s Preparing to unpack .../091-r-cran-mgcv_1.9-1-1_amd64.deb ... 130s Unpacking r-cran-mgcv (1.9-1-1) ... 130s Selecting previously unselected package r-cran-nnet. 130s Preparing to unpack .../092-r-cran-nnet_7.3-19-2_amd64.deb ... 130s Unpacking r-cran-nnet (7.3-19-2) ... 130s Selecting previously unselected package r-cran-pkgkitten. 130s Preparing to unpack .../093-r-cran-pkgkitten_0.2.3-1_all.deb ... 130s Unpacking r-cran-pkgkitten (0.2.3-1) ... 130s Selecting previously unselected package r-cran-rcpp. 130s Preparing to unpack .../094-r-cran-rcpp_1.0.12-1_amd64.deb ... 130s Unpacking r-cran-rcpp (1.0.12-1) ... 130s Selecting previously unselected package r-cran-minqa. 130s Preparing to unpack .../095-r-cran-minqa_1.2.6-1_amd64.deb ... 130s Unpacking r-cran-minqa (1.2.6-1) ... 130s Selecting previously unselected package libnlopt0:amd64. 130s Preparing to unpack .../096-libnlopt0_2.7.1-5build2_amd64.deb ... 130s Unpacking libnlopt0:amd64 (2.7.1-5build2) ... 130s Selecting previously unselected package r-cran-desc. 130s Preparing to unpack .../097-r-cran-desc_1.4.3-1_all.deb ... 130s Unpacking r-cran-desc (1.4.3-1) ... 130s Selecting previously unselected package r-cran-digest. 130s Preparing to unpack .../098-r-cran-digest_0.6.34-1_amd64.deb ... 130s Unpacking r-cran-digest (0.6.34-1) ... 130s Selecting previously unselected package r-cran-evaluate. 130s Preparing to unpack .../099-r-cran-evaluate_0.23-1_all.deb ... 130s Unpacking r-cran-evaluate (0.23-1) ... 130s Selecting previously unselected package r-cran-jsonlite. 130s Preparing to unpack .../100-r-cran-jsonlite_1.8.8+dfsg-1_amd64.deb ... 130s Unpacking r-cran-jsonlite (1.8.8+dfsg-1) ... 130s Selecting previously unselected package r-cran-crayon. 130s Preparing to unpack .../101-r-cran-crayon_1.5.2-1_all.deb ... 130s Unpacking r-cran-crayon (1.5.2-1) ... 130s Selecting previously unselected package r-cran-fs. 130s Preparing to unpack .../102-r-cran-fs_1.6.3+dfsg-1_amd64.deb ... 130s Unpacking r-cran-fs (1.6.3+dfsg-1) ... 130s Selecting previously unselected package r-cran-pkgbuild. 130s Preparing to unpack .../103-r-cran-pkgbuild_1.4.3-1_all.deb ... 130s Unpacking r-cran-pkgbuild (1.4.3-1) ... 130s Selecting previously unselected package r-cran-rprojroot. 130s Preparing to unpack .../104-r-cran-rprojroot_2.0.4-1_all.deb ... 130s Unpacking r-cran-rprojroot (2.0.4-1) ... 130s Selecting previously unselected package r-cran-pkgload. 130s Preparing to unpack .../105-r-cran-pkgload_1.3.4-1_all.deb ... 130s Unpacking r-cran-pkgload (1.3.4-1) ... 130s Selecting previously unselected package r-cran-praise. 130s Preparing to unpack .../106-r-cran-praise_1.0.0-4build1_all.deb ... 130s Unpacking r-cran-praise (1.0.0-4build1) ... 130s Selecting previously unselected package r-cran-diffobj. 130s Preparing to unpack .../107-r-cran-diffobj_0.3.5-1_amd64.deb ... 130s Unpacking r-cran-diffobj (0.3.5-1) ... 130s Selecting previously unselected package r-cran-rematch2. 130s Preparing to unpack .../108-r-cran-rematch2_2.1.2-2build1_all.deb ... 130s Unpacking r-cran-rematch2 (2.1.2-2build1) ... 130s Selecting previously unselected package r-cran-waldo. 130s Preparing to unpack .../109-r-cran-waldo_0.5.2-1build1_all.deb ... 130s Unpacking r-cran-waldo (0.5.2-1build1) ... 130s Selecting previously unselected package r-cran-testthat. 130s Preparing to unpack .../110-r-cran-testthat_3.2.1-1_amd64.deb ... 130s Unpacking r-cran-testthat (3.2.1-1) ... 131s Selecting previously unselected package r-cran-nloptr. 131s Preparing to unpack .../111-r-cran-nloptr_2.0.3-1_amd64.deb ... 131s Unpacking r-cran-nloptr (2.0.3-1) ... 131s Selecting previously unselected package r-cran-rcppeigen. 131s Preparing to unpack .../112-r-cran-rcppeigen_0.3.3.9.4-1_amd64.deb ... 131s Unpacking r-cran-rcppeigen (0.3.3.9.4-1) ... 131s Selecting previously unselected package r-cran-statmod. 131s Preparing to unpack .../113-r-cran-statmod_1.5.0-1_amd64.deb ... 131s Unpacking r-cran-statmod (1.5.0-1) ... 131s Selecting previously unselected package r-cran-lme4. 131s Preparing to unpack .../114-r-cran-lme4_1.1-35.1-4_amd64.deb ... 131s Unpacking r-cran-lme4 (1.1-35.1-4) ... 131s Selecting previously unselected package r-cran-numderiv. 131s Preparing to unpack .../115-r-cran-numderiv_2016.8-1.1-3_all.deb ... 131s Unpacking r-cran-numderiv (2016.8-1.1-3) ... 131s Selecting previously unselected package r-cran-xfun. 131s Preparing to unpack .../116-r-cran-xfun_0.41+dfsg-1_amd64.deb ... 131s Unpacking r-cran-xfun (0.41+dfsg-1) ... 131s Selecting previously unselected package r-cran-highr. 131s Preparing to unpack .../117-r-cran-highr_0.10+dfsg-1_all.deb ... 131s Unpacking r-cran-highr (0.10+dfsg-1) ... 131s Selecting previously unselected package r-cran-yaml. 131s Preparing to unpack .../118-r-cran-yaml_2.3.8-1_amd64.deb ... 131s Unpacking r-cran-yaml (2.3.8-1) ... 131s Selecting previously unselected package libjs-mathjax. 131s Preparing to unpack .../119-libjs-mathjax_2.7.9+dfsg-1_all.deb ... 131s Unpacking libjs-mathjax (2.7.9+dfsg-1) ... 132s Selecting previously unselected package r-cran-knitr. 132s Preparing to unpack .../120-r-cran-knitr_1.45+dfsg-1_all.deb ... 132s Unpacking r-cran-knitr (1.45+dfsg-1) ... 132s Selecting previously unselected package r-cran-pbkrtest. 132s Preparing to unpack .../121-r-cran-pbkrtest_0.5.2-2_all.deb ... 132s Unpacking r-cran-pbkrtest (0.5.2-2) ... 132s Selecting previously unselected package r-cran-sparsem. 132s Preparing to unpack .../122-r-cran-sparsem_1.81-1_amd64.deb ... 132s Unpacking r-cran-sparsem (1.81-1) ... 132s Selecting previously unselected package r-cran-matrixmodels. 132s Preparing to unpack .../123-r-cran-matrixmodels_0.5-3-1_all.deb ... 132s Unpacking r-cran-matrixmodels (0.5-3-1) ... 132s Selecting previously unselected package r-cran-survival. 132s Preparing to unpack .../124-r-cran-survival_3.5-8-1_amd64.deb ... 132s Unpacking r-cran-survival (3.5-8-1) ... 132s Selecting previously unselected package r-cran-matrixstats. 132s Preparing to unpack .../125-r-cran-matrixstats_1.2.0-1_amd64.deb ... 132s Unpacking r-cran-matrixstats (1.2.0-1) ... 132s Selecting previously unselected package r-cran-rcpparmadillo. 132s Preparing to unpack .../126-r-cran-rcpparmadillo_0.12.8.0.0-1_amd64.deb ... 132s Unpacking r-cran-rcpparmadillo (0.12.8.0.0-1) ... 132s Selecting previously unselected package r-cran-gtable. 132s Preparing to unpack .../127-r-cran-gtable_0.3.4+dfsg-1_all.deb ... 132s Unpacking r-cran-gtable (0.3.4+dfsg-1) ... 132s Selecting previously unselected package r-cran-isoband. 132s Preparing to unpack .../128-r-cran-isoband_0.2.7-1_amd64.deb ... 132s Unpacking r-cran-isoband (0.2.7-1) ... 132s Selecting previously unselected package r-cran-farver. 132s Preparing to unpack .../129-r-cran-farver_2.1.1-1_amd64.deb ... 132s Unpacking r-cran-farver (2.1.1-1) ... 132s Selecting previously unselected package r-cran-labeling. 132s Preparing to unpack .../130-r-cran-labeling_0.4.3-1_all.deb ... 132s Unpacking r-cran-labeling (0.4.3-1) ... 132s Selecting previously unselected package r-cran-colorspace. 132s Preparing to unpack .../131-r-cran-colorspace_2.1-0+dfsg-1_amd64.deb ... 132s Unpacking r-cran-colorspace (2.1-0+dfsg-1) ... 132s Selecting previously unselected package r-cran-munsell. 132s Preparing to unpack .../132-r-cran-munsell_0.5.0-2build1_all.deb ... 132s Unpacking r-cran-munsell (0.5.0-2build1) ... 133s Selecting previously unselected package r-cran-rcolorbrewer. 133s Preparing to unpack .../133-r-cran-rcolorbrewer_1.1-3-1build1_all.deb ... 133s Unpacking r-cran-rcolorbrewer (1.1-3-1build1) ... 133s Selecting previously unselected package r-cran-viridislite. 133s Preparing to unpack .../134-r-cran-viridislite_0.4.2-2_all.deb ... 133s Unpacking r-cran-viridislite (0.4.2-2) ... 133s Selecting previously unselected package r-cran-scales. 133s Preparing to unpack .../135-r-cran-scales_1.3.0-1_all.deb ... 133s Unpacking r-cran-scales (1.3.0-1) ... 133s Selecting previously unselected package r-cran-ggplot2. 133s Preparing to unpack .../136-r-cran-ggplot2_3.4.4+dfsg-1_all.deb ... 133s Unpacking r-cran-ggplot2 (3.4.4+dfsg-1) ... 133s Selecting previously unselected package r-cran-class. 133s Preparing to unpack .../137-r-cran-class_7.3-22-2_amd64.deb ... 133s Unpacking r-cran-class (7.3-22-2) ... 133s Selecting previously unselected package r-cran-proxy. 133s Preparing to unpack .../138-r-cran-proxy_0.4-27-1_amd64.deb ... 133s Unpacking r-cran-proxy (0.4-27-1) ... 133s Selecting previously unselected package r-cran-e1071. 133s Preparing to unpack .../139-r-cran-e1071_1.7-14-1_amd64.deb ... 133s Unpacking r-cran-e1071 (1.7-14-1) ... 133s Selecting previously unselected package r-cran-codetools. 133s Preparing to unpack .../140-r-cran-codetools_0.2-19-1_all.deb ... 133s Unpacking r-cran-codetools (0.2-19-1) ... 133s Selecting previously unselected package r-cran-iterators. 133s Preparing to unpack .../141-r-cran-iterators_1.0.14-1_all.deb ... 133s Unpacking r-cran-iterators (1.0.14-1) ... 133s Selecting previously unselected package r-cran-foreach. 133s Preparing to unpack .../142-r-cran-foreach_1.5.2-1_all.deb ... 133s Unpacking r-cran-foreach (1.5.2-1) ... 133s Selecting previously unselected package r-cran-data.table. 133s Preparing to unpack .../143-r-cran-data.table_1.14.10+dfsg-1_amd64.deb ... 133s Unpacking r-cran-data.table (1.14.10+dfsg-1) ... 133s Selecting previously unselected package r-cran-modelmetrics. 133s Preparing to unpack .../144-r-cran-modelmetrics_1.2.2.2-1build1_amd64.deb ... 133s Unpacking r-cran-modelmetrics (1.2.2.2-1build1) ... 133s Selecting previously unselected package r-cran-plyr. 133s Preparing to unpack .../145-r-cran-plyr_1.8.9-1_amd64.deb ... 133s Unpacking r-cran-plyr (1.8.9-1) ... 133s Selecting previously unselected package r-cran-proc. 133s Preparing to unpack .../146-r-cran-proc_1.18.5-1_amd64.deb ... 133s Unpacking r-cran-proc (1.18.5-1) ... 133s Selecting previously unselected package r-cran-tzdb. 133s Preparing to unpack .../147-r-cran-tzdb_0.4.0-2_amd64.deb ... 133s Unpacking r-cran-tzdb (0.4.0-2) ... 133s Selecting previously unselected package r-cran-clock. 133s Preparing to unpack .../148-r-cran-clock_0.7.0-1.1_amd64.deb ... 133s Unpacking r-cran-clock (0.7.0-1.1) ... 133s Selecting previously unselected package r-cran-gower. 133s Preparing to unpack .../149-r-cran-gower_1.0.1-1_amd64.deb ... 133s Unpacking r-cran-gower (1.0.1-1) ... 133s Selecting previously unselected package r-cran-hardhat. 133s Preparing to unpack .../150-r-cran-hardhat_1.3.1+dfsg-1_all.deb ... 133s Unpacking r-cran-hardhat (1.3.1+dfsg-1) ... 133s Selecting previously unselected package r-cran-rpart. 133s Preparing to unpack .../151-r-cran-rpart_4.1.23-1_amd64.deb ... 133s Unpacking r-cran-rpart (4.1.23-1) ... 133s Selecting previously unselected package r-cran-shape. 133s Preparing to unpack .../152-r-cran-shape_1.4.6-1_all.deb ... 133s Unpacking r-cran-shape (1.4.6-1) ... 133s Selecting previously unselected package r-cran-diagram. 133s Preparing to unpack .../153-r-cran-diagram_1.6.5-2_all.deb ... 133s Unpacking r-cran-diagram (1.6.5-2) ... 134s Selecting previously unselected package r-cran-kernsmooth. 134s Preparing to unpack .../154-r-cran-kernsmooth_2.23-22-1_amd64.deb ... 134s Unpacking r-cran-kernsmooth (2.23-22-1) ... 134s Selecting previously unselected package r-cran-globals. 134s Preparing to unpack .../155-r-cran-globals_0.16.2-1_all.deb ... 134s Unpacking r-cran-globals (0.16.2-1) ... 134s Selecting previously unselected package r-cran-listenv. 134s Preparing to unpack .../156-r-cran-listenv_0.9.1+dfsg-1_all.deb ... 134s Unpacking r-cran-listenv (0.9.1+dfsg-1) ... 134s Selecting previously unselected package r-cran-parallelly. 134s Preparing to unpack .../157-r-cran-parallelly_1.37.1-1_amd64.deb ... 134s Unpacking r-cran-parallelly (1.37.1-1) ... 134s Selecting previously unselected package r-cran-future. 134s Preparing to unpack .../158-r-cran-future_1.33.1+dfsg-1_all.deb ... 134s Unpacking r-cran-future (1.33.1+dfsg-1) ... 134s Selecting previously unselected package r-cran-future.apply. 134s Preparing to unpack .../159-r-cran-future.apply_1.11.1+dfsg-1_all.deb ... 134s Unpacking r-cran-future.apply (1.11.1+dfsg-1) ... 134s Selecting previously unselected package r-cran-progressr. 134s Preparing to unpack .../160-r-cran-progressr_0.14.0-1_all.deb ... 134s Unpacking r-cran-progressr (0.14.0-1) ... 134s Selecting previously unselected package r-cran-squarem. 134s Preparing to unpack .../161-r-cran-squarem_2021.1-1_all.deb ... 134s Unpacking r-cran-squarem (2021.1-1) ... 134s Selecting previously unselected package r-cran-lava. 134s Preparing to unpack .../162-r-cran-lava_1.7.3+dfsg-1_all.deb ... 134s Unpacking r-cran-lava (1.7.3+dfsg-1) ... 134s Selecting previously unselected package r-cran-prodlim. 134s Preparing to unpack .../163-r-cran-prodlim_2023.08.28-1_amd64.deb ... 134s Unpacking r-cran-prodlim (2023.08.28-1) ... 134s Selecting previously unselected package r-cran-ipred. 134s Preparing to unpack .../164-r-cran-ipred_0.9-14-1_amd64.deb ... 134s Unpacking r-cran-ipred (0.9-14-1) ... 134s Selecting previously unselected package r-cran-timechange. 134s Preparing to unpack .../165-r-cran-timechange_0.3.0-1_amd64.deb ... 134s Unpacking r-cran-timechange (0.3.0-1) ... 134s Selecting previously unselected package r-cran-lubridate. 134s Preparing to unpack .../166-r-cran-lubridate_1.9.3+dfsg-1_amd64.deb ... 134s Unpacking r-cran-lubridate (1.9.3+dfsg-1) ... 134s Selecting previously unselected package r-cran-timedate. 134s Preparing to unpack .../167-r-cran-timedate_4032.109-1_amd64.deb ... 134s Unpacking r-cran-timedate (4032.109-1) ... 134s Selecting previously unselected package r-cran-recipes. 134s Preparing to unpack .../168-r-cran-recipes_1.0.9+dfsg-1_all.deb ... 134s Unpacking r-cran-recipes (1.0.9+dfsg-1) ... 134s Selecting previously unselected package r-cran-reshape2. 134s Preparing to unpack .../169-r-cran-reshape2_1.4.4-2build1_amd64.deb ... 134s Unpacking r-cran-reshape2 (1.4.4-2build1) ... 134s Selecting previously unselected package r-cran-caret. 134s Preparing to unpack .../170-r-cran-caret_6.0-94+dfsg-1_amd64.deb ... 134s Unpacking r-cran-caret (6.0-94+dfsg-1) ... 134s Selecting previously unselected package r-cran-conquer. 134s Preparing to unpack .../171-r-cran-conquer_1.3.3-1_amd64.deb ... 134s Unpacking r-cran-conquer (1.3.3-1) ... 134s Selecting previously unselected package r-cran-quantreg. 134s Preparing to unpack .../172-r-cran-quantreg_5.97-1_amd64.deb ... 134s Unpacking r-cran-quantreg (5.97-1) ... 134s Selecting previously unselected package r-cran-sp. 134s Preparing to unpack .../173-r-cran-sp_1%3a2.1-2+dfsg-1_amd64.deb ... 134s Unpacking r-cran-sp (1:2.1-2+dfsg-1) ... 134s Selecting previously unselected package 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139s Setting up r-cran-lubridate (1.9.3+dfsg-1) ... 139s Setting up r-cran-pkgload (1.3.4-1) ... 139s Setting up r-cran-r.utils (2.12.3-1) ... 139s Setting up r-cran-vroom (1.6.5-1) ... 139s Setting up r-cran-prodlim (2023.08.28-1) ... 139s Setting up r-cran-ggplot2 (3.4.4+dfsg-1) ... 139s Setting up r-cran-cellranger (1.1.0-3) ... 139s Setting up r-cran-rematch2 (2.1.2-2build1) ... 139s Setting up r-cran-rpart (4.1.23-1) ... 139s Setting up r-cran-plm (2.6-3-1) ... 139s Setting up r-cran-ipred (0.9-14-1) ... 139s Setting up r-cran-readr (2.1.5-1) ... 139s Setting up r-cran-waldo (0.5.2-1build1) ... 139s Setting up r-cran-tidyr (1.3.1-1) ... 139s Setting up r-cran-recipes (1.0.9+dfsg-1) ... 139s Setting up r-cran-readxl (1.4.3-1) ... 139s Setting up r-cran-haven (2.5.4-1) ... 139s Setting up r-cran-caret (6.0-94+dfsg-1) ... 139s Setting up r-cran-testthat (3.2.1-1) ... 139s Setting up r-cran-broom (1.0.5+dfsg-1) ... 139s Setting up r-cran-conquer (1.3.3-1) ... 139s Setting up r-cran-rio (1.0.1-1) ... 139s Setting up r-cran-nloptr (2.0.3-1) ... 139s Setting up r-cran-quantreg (5.97-1) ... 139s Setting up r-cran-lme4 (1.1-35.1-4) ... 139s Setting up r-cran-pbkrtest (0.5.2-2) ... 139s Setting up r-cran-car (3.1-2-2) ... 139s Setting up r-cran-systemfit (1.1-30-1) ... 139s Setting up autopkgtest-satdep (0) ... 139s Processing triggers for man-db (2.12.0-3) ... 140s Processing triggers for install-info (7.1-3) ... 140s Processing triggers for libc-bin (2.39-0ubuntu2) ... 148s (Reading database ... 92671 files and directories currently installed.) 148s Removing autopkgtest-satdep (0) ... 148s autopkgtest [03:15:16]: test run-unit-test: [----------------------- 148s BEGIN TEST KleinI.R 149s 149s R version 4.3.2 (2023-10-31) -- "Eye Holes" 149s Copyright (C) 2023 The R Foundation for Statistical Computing 149s Platform: x86_64-pc-linux-gnu (64-bit) 149s 149s R is free software and comes with ABSOLUTELY NO WARRANTY. 149s You are welcome to redistribute it under certain conditions. 149s Type 'license()' or 'licence()' for distribution details. 149s 149s R is a collaborative project with many contributors. 149s Type 'contributors()' for more information and 149s 'citation()' on how to cite R or R packages in publications. 149s 149s Type 'demo()' for some demos, 'help()' for on-line help, or 149s 'help.start()' for an HTML browser interface to help. 149s Type 'q()' to quit R. 149s 149s > library( "systemfit" ) 149s Loading required package: Matrix 150s Loading required package: car 150s Loading required package: carData 150s Loading required package: lmtest 150s Loading required package: zoo 150s 150s Attaching package: ‘zoo’ 150s 150s The following objects are masked from ‘package:base’: 150s 150s as.Date, as.Date.numeric 150s 150s 150s Please cite the 'systemfit' package as: 150s 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/. 150s 150s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 150s https://r-forge.r-project.org/projects/systemfit/ 150s > library( "sandwich" ) 150s > options( warn = 1 ) 150s > options( digits = 3 ) 150s > 150s > data( "KleinI" ) 150s > eqConsump <- consump ~ corpProf + corpProfLag + wages 150s > eqInvest <- invest ~ corpProf + corpProfLag + capitalLag 150s > eqPrivWage <- privWage ~ gnp + gnpLag + trend 150s > inst <- ~ govExp + taxes + govWage + trend + capitalLag + corpProfLag + gnpLag 150s > system <- list( Consumption = eqConsump, Investment = eqInvest, 150s + PrivateWages = eqPrivWage ) 150s > restrict <- c( "Consumption_corpProf + Investment_capitalLag = 0" ) 150s > restrict2 <- c( restrict, "Consumption_corpProfLag - PrivateWages_trend = 0" ) 150s > 150s > for( dataNo in 1:5 ) { 150s + # set some values of some variables to NA 150s + if( dataNo == 2 ) { 150s + KleinI$gnpLag[ 7 ] <- NA 150s + } else if( dataNo == 3 ) { 150s + KleinI$wages[ 10 ] <- NA 150s + } else if( dataNo == 4 ) { 150s + KleinI$corpProf[ 13 ] <- NA 150s + } else if( dataNo == 5 ) { 150s + KleinI$invest[ 16 ] <- NA 150s + } 150s + 150s + # single-equation OLS 150s + lmConsump <- lm( eqConsump, data = KleinI ) 150s + lmInvest <- lm( eqInvest, data = KleinI ) 150s + lmPrivWage <- lm( eqPrivWage, data = KleinI ) 150s + 150s + for( methodNo in 1:5 ) { 150s + method <- c( "OLS", "2SLS", "SUR", "3SLS", "3SLS" )[ methodNo ] 150s + maxit <- ifelse( methodNo == 5, 500, 1 ) 150s + 150s + cat( "> \n> # ", ifelse( maxit == 1, "", "I" ), method, "\n", sep = "" ) 150s + if( method %in% c( "OLS", "WLS", "SUR" ) ) { 150s + kleinModel <- systemfit( system, method = method, data = KleinI, 150s + methodResidCov = ifelse( method == "OLS", "geomean", "noDfCor" ), 150s + maxit = maxit ) 150s + } else { 150s + kleinModel <- systemfit( system, method = method, data = KleinI, 150s + inst = inst, methodResidCov = "noDfCor", maxit = maxit ) 150s + } 150s + cat( "> summary\n" ) 150s + print( summary( kleinModel ) ) 150s + if( method == "OLS" ) { 150s + cat( "compare coef with single-equation OLS\n" ) 150s + print( all.equal( coef( kleinModel ), 150s + c( coef( lmConsump ), coef( lmInvest ), coef( lmPrivWage ) ), 150s + check.attributes = FALSE ) ) 150s + } 150s + cat( "> residuals\n" ) 150s + print( residuals( kleinModel ) ) 150s + cat( "> fitted\n" ) 150s + print( fitted( kleinModel ) ) 150s + cat( "> predict\n" ) 150s + print( predict( kleinModel, se.fit = TRUE, 150s + interval = ifelse( methodNo %in% c( 1, 4 ), "prediction", "confidence" ), 150s + useDfSys = methodNo %in% c( 1, 3, 5 ) ) ) 150s + cat( "> model.frame\n" ) 150s + if( methodNo == 1 ) { 150s + mfOls <- model.frame( kleinModel ) 150s + print( mfOls ) 150s + } else if( methodNo == 2 ) { 150s + mf2sls <- model.frame( kleinModel ) 150s + print( mf2sls ) 150s + cat( "> Frames of instrumental variables\n" ) 150s + for( i in 1:3 ){ 150s + print( kleinModel$eq[[ i ]]$modelInst ) 150s + } 150s + } else if( methodNo == 3 ) { 150s + print( all.equal( mfOls, model.frame( kleinModel ) ) ) 150s + } else { 150s + print( all.equal( mf2sls, model.frame( kleinModel ) ) ) 150s + } 150s + cat( "> model.matrix\n" ) 150s + if( methodNo == 1 ) { 150s + mmOls <- model.matrix( kleinModel ) 150s + print( mmOls ) 150s + } else { 150s + print( all.equal( mmOls, model.matrix( kleinModel ) ) ) 150s + } 150s + if( methodNo == 2 ) { 150s + cat( "> matrix of instrumental variables\n" ) 150s + print( model.matrix( kleinModel, which = "z" ) ) 150s + cat( "> matrix of fitted regressors\n" ) 150s + print( round( model.matrix( kleinModel, which = "xHat" ), digits = 7 ) ) 150s + } 150s + cat( "> nobs\n" ) 150s + print( nobs( kleinModel ) ) 150s + cat( "> linearHypothesis\n" ) 150s + print( linearHypothesis( kleinModel, restrict ) ) 150s + print( linearHypothesis( kleinModel, restrict, test = "F" ) ) 150s + print( linearHypothesis( kleinModel, restrict, test = "Chisq" ) ) 150s + print( linearHypothesis( kleinModel, restrict2 ) ) 150s + print( linearHypothesis( kleinModel, restrict2, test = "F" ) ) 150s + print( linearHypothesis( kleinModel, restrict2, test = "Chisq" ) ) 150s + cat( "> logLik\n" ) 150s + print( logLik( kleinModel ) ) 150s + print( logLik( kleinModel, residCovDiag = TRUE ) ) 150s + if( method == "OLS" ) { 150s + cat( "compare log likelihood value with single-equation OLS\n" ) 150s + print( all.equal( logLik( kleinModel, residCovDiag = TRUE ), 150s + logLik( lmConsump ) + logLik( lmInvest ) + logLik( lmPrivWage ), 150s + check.attributes = FALSE ) ) 150s + } 150s + 150s + cat( "Estimating function\n" ) 150s + print( round( estfun( kleinModel ), digits = 7 ) ) 150s + print( all.equal( colSums( estfun( kleinModel ) ), 150s + rep( 0, ncol( estfun( kleinModel ) ) ), check.attributes = FALSE ) ) 150s + 150s + cat( "> Bread\n" ) 150s + print( bread( kleinModel ) ) 150s + } 150s + } 150s > 150s > # OLS 150s > summary 150s 150s systemfit results 150s method: OLS 150s 150s N DF SSR detRCov OLS-R2 McElroy-R2 150s system 63 51 45.2 0.371 0.977 0.991 150s 150s N DF SSR MSE RMSE R2 Adj R2 150s Consumption 21 17 17.9 1.052 1.026 0.981 0.978 150s Investment 21 17 17.3 1.019 1.009 0.931 0.919 150s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 150s 150s The covariance matrix of the residuals 150s Consumption Investment PrivateWages 150s Consumption 1.0517 0.0611 -0.470 150s Investment 0.0611 1.0190 0.150 150s PrivateWages -0.4704 0.1497 0.589 150s 150s The correlations of the residuals 150s Consumption Investment PrivateWages 150s Consumption 1.0000 0.0591 -0.598 150s Investment 0.0591 1.0000 0.193 150s PrivateWages -0.5979 0.1933 1.000 150s 150s 150s OLS estimates for 'Consumption' (equation 1) 150s Model Formula: consump ~ corpProf + corpProfLag + wages 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 16.2366 1.3027 12.46 5.6e-10 *** 150s corpProf 0.1929 0.0912 2.12 0.049 * 150s corpProfLag 0.0899 0.0906 0.99 0.335 150s wages 0.7962 0.0399 19.93 3.2e-13 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.026 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 150s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 150s 150s 150s OLS estimates for 'Investment' (equation 2) 150s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 10.1258 5.4655 1.85 0.08137 . 150s corpProf 0.4796 0.0971 4.94 0.00012 *** 150s corpProfLag 0.3330 0.1009 3.30 0.00421 ** 150s capitalLag -0.1118 0.0267 -4.18 0.00062 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.009 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 150s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 150s 150s 150s OLS estimates for 'PrivateWages' (equation 3) 150s Model Formula: privWage ~ gnp + gnpLag + trend 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 1.4970 1.2700 1.18 0.25474 150s gnp 0.4395 0.0324 13.56 1.5e-10 *** 150s gnpLag 0.1461 0.0374 3.90 0.00114 ** 150s trend 0.1302 0.0319 4.08 0.00078 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 0.767 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 150s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 150s 150s compare coef with single-equation OLS 150s [1] TRUE 150s > residuals 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 -0.32389 -0.0668 -1.2942 150s 3 -1.25001 -0.0476 0.2957 150s 4 -1.56574 1.2467 1.1877 150s 5 -0.49350 -1.3512 -0.1358 150s 6 0.00761 0.4154 -0.4654 150s 7 0.86910 1.4923 -0.4838 150s 8 1.33848 0.7889 -0.7281 150s 9 1.05498 -0.6317 0.3392 150s 10 -0.58856 1.0830 1.1957 150s 11 0.28231 0.2791 -0.1508 150s 12 -0.22965 0.0369 0.5942 150s 13 -0.32213 0.3659 0.1027 150s 14 0.32228 0.2237 0.4503 150s 15 -0.05801 -0.1728 0.2816 150s 16 -0.03466 0.0101 0.0138 150s 17 1.61650 0.9719 -0.8508 150s 18 -0.43597 0.0516 0.9956 150s 19 0.21005 -2.5656 -0.4688 150s 20 0.98920 -0.6866 -0.3795 150s 21 0.78508 -0.7807 -1.0909 150s 22 -2.17345 -0.6623 0.5917 150s > fitted 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 42.2 -0.133 26.8 150s 3 46.3 1.948 29.0 150s 4 50.8 3.953 32.9 150s 5 51.1 4.351 34.0 150s 6 52.6 4.685 35.9 150s 7 54.2 4.108 37.9 150s 8 54.9 3.411 38.6 150s 9 56.2 3.632 38.9 150s 10 58.4 4.017 40.1 150s 11 54.7 0.721 38.1 150s 12 51.1 -3.437 33.9 150s 13 45.9 -6.566 28.9 150s 14 46.2 -5.324 28.0 150s 15 48.8 -2.827 30.3 150s 16 51.3 -1.310 33.2 150s 17 56.1 1.128 37.7 150s 18 59.1 1.948 40.0 150s 19 57.3 0.666 38.7 150s 20 60.6 1.987 42.0 150s 21 64.2 4.081 46.1 150s 22 71.9 5.562 52.7 150s > predict 150s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 150s 1 NA NA NA NA 150s 2 42.2 0.462 40.0 44.5 150s 3 46.3 0.518 43.9 48.6 150s 4 50.8 0.341 48.6 52.9 150s 5 51.1 0.396 48.9 53.3 150s 6 52.6 0.397 50.4 54.8 150s 7 54.2 0.359 52.0 56.4 150s 8 54.9 0.327 52.7 57.0 150s 9 56.2 0.350 54.1 58.4 150s 10 58.4 0.370 56.2 60.6 150s 11 54.7 0.606 52.3 57.1 150s 12 51.1 0.484 48.9 53.4 150s 13 45.9 0.629 43.5 48.3 150s 14 46.2 0.602 43.8 48.6 150s 15 48.8 0.374 46.6 50.9 150s 16 51.3 0.333 49.2 53.5 150s 17 56.1 0.366 53.9 58.3 150s 18 59.1 0.321 57.0 61.3 150s 19 57.3 0.371 55.1 59.5 150s 20 60.6 0.434 58.4 62.8 150s 21 64.2 0.425 62.0 66.4 150s 22 71.9 0.666 69.4 74.3 150s Investment.pred Investment.se.fit Investment.lwr Investment.upr 150s 1 NA NA NA NA 150s 2 -0.133 0.607 -2.498 2.231 150s 3 1.948 0.499 -0.313 4.208 150s 4 3.953 0.449 1.735 6.171 150s 5 4.351 0.371 2.192 6.510 150s 6 4.685 0.349 2.540 6.829 150s 7 4.108 0.329 1.976 6.239 150s 8 3.411 0.292 1.301 5.521 150s 9 3.632 0.389 1.460 5.804 150s 10 4.017 0.447 1.801 6.233 150s 11 0.721 0.601 -1.638 3.080 150s 12 -3.437 0.507 -5.704 -1.169 150s 13 -6.566 0.616 -8.940 -4.192 150s 14 -5.324 0.694 -7.783 -2.865 150s 15 -2.827 0.373 -4.988 -0.667 150s 16 -1.310 0.320 -3.436 0.816 150s 17 1.128 0.347 -1.015 3.271 150s 18 1.948 0.243 -0.136 4.033 150s 19 0.666 0.312 -1.456 2.787 150s 20 1.987 0.366 -0.169 4.143 150s 21 4.081 0.332 1.948 6.214 150s 22 5.562 0.461 3.334 7.790 150s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 150s 1 NA NA NA NA 150s 2 26.8 0.354 25.1 28.5 150s 3 29.0 0.355 27.3 30.7 150s 4 32.9 0.354 31.2 34.6 150s 5 34.0 0.269 32.4 35.7 150s 6 35.9 0.266 34.2 37.5 150s 7 37.9 0.266 36.3 39.5 150s 8 38.6 0.273 37.0 40.3 150s 9 38.9 0.261 37.2 40.5 150s 10 40.1 0.247 38.5 41.7 150s 11 38.1 0.354 36.4 39.7 150s 12 33.9 0.363 32.2 35.6 150s 13 28.9 0.429 27.1 30.7 150s 14 28.0 0.376 26.3 29.8 150s 15 30.3 0.371 28.6 32.0 150s 16 33.2 0.310 31.5 34.8 150s 17 37.7 0.305 36.0 39.3 150s 18 40.0 0.238 38.4 41.6 150s 19 38.7 0.357 37.0 40.4 150s 20 42.0 0.321 40.3 43.6 150s 21 46.1 0.335 44.4 47.8 150s 22 52.7 0.502 50.9 54.5 150s > model.frame 150s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 150s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 150s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 150s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 150s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 150s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 150s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 150s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 150s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 150s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 150s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 150s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 150s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 150s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 150s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 150s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 150s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 150s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 150s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 150s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 150s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 150s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 150s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 150s trend 150s 1 -11 150s 2 -10 150s 3 -9 150s 4 -8 150s 5 -7 150s 6 -6 150s 7 -5 150s 8 -4 150s 9 -3 150s 10 -2 150s 11 -1 150s 12 0 150s 13 1 150s 14 2 150s 15 3 150s 16 4 150s 17 5 150s 18 6 150s 19 7 150s 20 8 150s 21 9 150s 22 10 150s > model.matrix 150s Consumption_(Intercept) Consumption_corpProf 150s Consumption_2 1 12.4 150s Consumption_3 1 16.9 150s Consumption_4 1 18.4 150s Consumption_5 1 19.4 150s Consumption_6 1 20.1 150s Consumption_7 1 19.6 150s Consumption_8 1 19.8 150s Consumption_9 1 21.1 150s Consumption_10 1 21.7 150s Consumption_11 1 15.6 150s Consumption_12 1 11.4 150s Consumption_13 1 7.0 150s Consumption_14 1 11.2 150s Consumption_15 1 12.3 150s Consumption_16 1 14.0 150s Consumption_17 1 17.6 150s Consumption_18 1 17.3 150s Consumption_19 1 15.3 150s Consumption_20 1 19.0 150s Consumption_21 1 21.1 150s Consumption_22 1 23.5 150s Investment_2 0 0.0 150s Investment_3 0 0.0 150s Investment_4 0 0.0 150s Investment_5 0 0.0 150s Investment_6 0 0.0 150s Investment_7 0 0.0 150s Investment_8 0 0.0 150s Investment_9 0 0.0 150s Investment_10 0 0.0 150s Investment_11 0 0.0 150s Investment_12 0 0.0 150s Investment_13 0 0.0 150s Investment_14 0 0.0 150s Investment_15 0 0.0 150s Investment_16 0 0.0 150s Investment_17 0 0.0 150s Investment_18 0 0.0 150s Investment_19 0 0.0 150s Investment_20 0 0.0 150s Investment_21 0 0.0 150s Investment_22 0 0.0 150s PrivateWages_2 0 0.0 150s PrivateWages_3 0 0.0 150s PrivateWages_4 0 0.0 150s PrivateWages_5 0 0.0 150s PrivateWages_6 0 0.0 150s PrivateWages_7 0 0.0 150s PrivateWages_8 0 0.0 150s PrivateWages_9 0 0.0 150s PrivateWages_10 0 0.0 150s PrivateWages_11 0 0.0 150s PrivateWages_12 0 0.0 150s PrivateWages_13 0 0.0 150s PrivateWages_14 0 0.0 150s PrivateWages_15 0 0.0 150s PrivateWages_16 0 0.0 150s PrivateWages_17 0 0.0 150s PrivateWages_18 0 0.0 150s PrivateWages_19 0 0.0 150s PrivateWages_20 0 0.0 150s PrivateWages_21 0 0.0 150s PrivateWages_22 0 0.0 150s Consumption_corpProfLag Consumption_wages 150s Consumption_2 12.7 28.2 150s Consumption_3 12.4 32.2 150s Consumption_4 16.9 37.0 150s Consumption_5 18.4 37.0 150s Consumption_6 19.4 38.6 150s Consumption_7 20.1 40.7 150s Consumption_8 19.6 41.5 150s Consumption_9 19.8 42.9 150s Consumption_10 21.1 45.3 150s Consumption_11 21.7 42.1 150s Consumption_12 15.6 39.3 150s Consumption_13 11.4 34.3 150s Consumption_14 7.0 34.1 150s Consumption_15 11.2 36.6 150s Consumption_16 12.3 39.3 150s Consumption_17 14.0 44.2 150s Consumption_18 17.6 47.7 150s Consumption_19 17.3 45.9 150s Consumption_20 15.3 49.4 150s Consumption_21 19.0 53.0 150s Consumption_22 21.1 61.8 150s Investment_2 0.0 0.0 150s Investment_3 0.0 0.0 150s Investment_4 0.0 0.0 150s Investment_5 0.0 0.0 150s Investment_6 0.0 0.0 150s Investment_7 0.0 0.0 150s Investment_8 0.0 0.0 150s Investment_9 0.0 0.0 150s Investment_10 0.0 0.0 150s Investment_11 0.0 0.0 150s Investment_12 0.0 0.0 150s Investment_13 0.0 0.0 150s Investment_14 0.0 0.0 150s Investment_15 0.0 0.0 150s Investment_16 0.0 0.0 150s Investment_17 0.0 0.0 150s Investment_18 0.0 0.0 150s Investment_19 0.0 0.0 150s Investment_20 0.0 0.0 150s Investment_21 0.0 0.0 150s Investment_22 0.0 0.0 150s PrivateWages_2 0.0 0.0 150s PrivateWages_3 0.0 0.0 150s PrivateWages_4 0.0 0.0 150s PrivateWages_5 0.0 0.0 150s PrivateWages_6 0.0 0.0 150s PrivateWages_7 0.0 0.0 150s PrivateWages_8 0.0 0.0 150s PrivateWages_9 0.0 0.0 150s PrivateWages_10 0.0 0.0 150s PrivateWages_11 0.0 0.0 150s PrivateWages_12 0.0 0.0 150s PrivateWages_13 0.0 0.0 150s PrivateWages_14 0.0 0.0 150s PrivateWages_15 0.0 0.0 150s PrivateWages_16 0.0 0.0 150s PrivateWages_17 0.0 0.0 150s PrivateWages_18 0.0 0.0 150s PrivateWages_19 0.0 0.0 150s PrivateWages_20 0.0 0.0 150s PrivateWages_21 0.0 0.0 150s PrivateWages_22 0.0 0.0 150s Investment_(Intercept) Investment_corpProf 150s Consumption_2 0 0.0 150s Consumption_3 0 0.0 150s Consumption_4 0 0.0 150s Consumption_5 0 0.0 150s Consumption_6 0 0.0 150s Consumption_7 0 0.0 150s Consumption_8 0 0.0 150s Consumption_9 0 0.0 150s Consumption_10 0 0.0 150s Consumption_11 0 0.0 150s Consumption_12 0 0.0 150s Consumption_13 0 0.0 150s Consumption_14 0 0.0 150s Consumption_15 0 0.0 150s Consumption_16 0 0.0 150s Consumption_17 0 0.0 150s Consumption_18 0 0.0 150s Consumption_19 0 0.0 150s Consumption_20 0 0.0 150s Consumption_21 0 0.0 150s Consumption_22 0 0.0 150s Investment_2 1 12.4 150s Investment_3 1 16.9 150s Investment_4 1 18.4 150s Investment_5 1 19.4 150s Investment_6 1 20.1 150s Investment_7 1 19.6 150s Investment_8 1 19.8 150s Investment_9 1 21.1 150s Investment_10 1 21.7 150s Investment_11 1 15.6 150s Investment_12 1 11.4 150s Investment_13 1 7.0 150s Investment_14 1 11.2 150s Investment_15 1 12.3 150s Investment_16 1 14.0 150s Investment_17 1 17.6 150s Investment_18 1 17.3 150s Investment_19 1 15.3 150s Investment_20 1 19.0 150s Investment_21 1 21.1 150s Investment_22 1 23.5 150s PrivateWages_2 0 0.0 150s PrivateWages_3 0 0.0 150s PrivateWages_4 0 0.0 150s PrivateWages_5 0 0.0 150s PrivateWages_6 0 0.0 150s PrivateWages_7 0 0.0 150s PrivateWages_8 0 0.0 150s PrivateWages_9 0 0.0 150s PrivateWages_10 0 0.0 150s PrivateWages_11 0 0.0 150s PrivateWages_12 0 0.0 150s PrivateWages_13 0 0.0 150s PrivateWages_14 0 0.0 150s PrivateWages_15 0 0.0 150s PrivateWages_16 0 0.0 150s PrivateWages_17 0 0.0 150s PrivateWages_18 0 0.0 150s PrivateWages_19 0 0.0 150s PrivateWages_20 0 0.0 150s PrivateWages_21 0 0.0 150s PrivateWages_22 0 0.0 150s Investment_corpProfLag Investment_capitalLag 150s Consumption_2 0.0 0 150s Consumption_3 0.0 0 150s Consumption_4 0.0 0 150s Consumption_5 0.0 0 150s Consumption_6 0.0 0 150s Consumption_7 0.0 0 150s Consumption_8 0.0 0 150s Consumption_9 0.0 0 150s Consumption_10 0.0 0 150s Consumption_11 0.0 0 150s Consumption_12 0.0 0 150s Consumption_13 0.0 0 150s Consumption_14 0.0 0 150s Consumption_15 0.0 0 150s Consumption_16 0.0 0 150s Consumption_17 0.0 0 150s Consumption_18 0.0 0 150s Consumption_19 0.0 0 150s Consumption_20 0.0 0 150s Consumption_21 0.0 0 150s Consumption_22 0.0 0 150s Investment_2 12.7 183 150s Investment_3 12.4 183 150s Investment_4 16.9 184 150s Investment_5 18.4 190 150s Investment_6 19.4 193 150s Investment_7 20.1 198 150s Investment_8 19.6 203 150s Investment_9 19.8 208 150s Investment_10 21.1 211 150s Investment_11 21.7 216 150s Investment_12 15.6 217 150s Investment_13 11.4 213 150s Investment_14 7.0 207 150s Investment_15 11.2 202 150s Investment_16 12.3 199 150s Investment_17 14.0 198 150s Investment_18 17.6 200 150s Investment_19 17.3 202 150s Investment_20 15.3 200 150s Investment_21 19.0 201 150s Investment_22 21.1 204 150s PrivateWages_2 0.0 0 150s PrivateWages_3 0.0 0 150s PrivateWages_4 0.0 0 150s PrivateWages_5 0.0 0 150s PrivateWages_6 0.0 0 150s PrivateWages_7 0.0 0 150s PrivateWages_8 0.0 0 150s PrivateWages_9 0.0 0 150s PrivateWages_10 0.0 0 150s PrivateWages_11 0.0 0 150s PrivateWages_12 0.0 0 150s PrivateWages_13 0.0 0 150s PrivateWages_14 0.0 0 150s PrivateWages_15 0.0 0 150s PrivateWages_16 0.0 0 150s PrivateWages_17 0.0 0 150s PrivateWages_18 0.0 0 150s PrivateWages_19 0.0 0 150s PrivateWages_20 0.0 0 150s PrivateWages_21 0.0 0 150s PrivateWages_22 0.0 0 150s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 150s Consumption_2 0 0.0 0.0 150s Consumption_3 0 0.0 0.0 150s Consumption_4 0 0.0 0.0 150s Consumption_5 0 0.0 0.0 150s Consumption_6 0 0.0 0.0 150s Consumption_7 0 0.0 0.0 150s Consumption_8 0 0.0 0.0 150s Consumption_9 0 0.0 0.0 150s Consumption_10 0 0.0 0.0 150s Consumption_11 0 0.0 0.0 150s Consumption_12 0 0.0 0.0 150s Consumption_13 0 0.0 0.0 150s Consumption_14 0 0.0 0.0 150s Consumption_15 0 0.0 0.0 150s Consumption_16 0 0.0 0.0 150s Consumption_17 0 0.0 0.0 150s Consumption_18 0 0.0 0.0 150s Consumption_19 0 0.0 0.0 150s Consumption_20 0 0.0 0.0 150s Consumption_21 0 0.0 0.0 150s Consumption_22 0 0.0 0.0 150s Investment_2 0 0.0 0.0 150s Investment_3 0 0.0 0.0 150s Investment_4 0 0.0 0.0 150s Investment_5 0 0.0 0.0 150s Investment_6 0 0.0 0.0 150s Investment_7 0 0.0 0.0 150s Investment_8 0 0.0 0.0 150s Investment_9 0 0.0 0.0 150s Investment_10 0 0.0 0.0 150s Investment_11 0 0.0 0.0 150s Investment_12 0 0.0 0.0 150s Investment_13 0 0.0 0.0 150s Investment_14 0 0.0 0.0 150s Investment_15 0 0.0 0.0 150s Investment_16 0 0.0 0.0 150s Investment_17 0 0.0 0.0 150s Investment_18 0 0.0 0.0 150s Investment_19 0 0.0 0.0 150s Investment_20 0 0.0 0.0 150s Investment_21 0 0.0 0.0 150s Investment_22 0 0.0 0.0 150s PrivateWages_2 1 45.6 44.9 150s PrivateWages_3 1 50.1 45.6 150s PrivateWages_4 1 57.2 50.1 150s PrivateWages_5 1 57.1 57.2 150s PrivateWages_6 1 61.0 57.1 150s PrivateWages_7 1 64.0 61.0 150s PrivateWages_8 1 64.4 64.0 150s PrivateWages_9 1 64.5 64.4 150s PrivateWages_10 1 67.0 64.5 150s PrivateWages_11 1 61.2 67.0 150s PrivateWages_12 1 53.4 61.2 150s PrivateWages_13 1 44.3 53.4 150s PrivateWages_14 1 45.1 44.3 150s PrivateWages_15 1 49.7 45.1 150s PrivateWages_16 1 54.4 49.7 150s PrivateWages_17 1 62.7 54.4 150s PrivateWages_18 1 65.0 62.7 150s PrivateWages_19 1 60.9 65.0 150s PrivateWages_20 1 69.5 60.9 150s PrivateWages_21 1 75.7 69.5 150s PrivateWages_22 1 88.4 75.7 150s PrivateWages_trend 150s Consumption_2 0 150s Consumption_3 0 150s Consumption_4 0 150s Consumption_5 0 150s Consumption_6 0 150s Consumption_7 0 150s Consumption_8 0 150s Consumption_9 0 150s Consumption_10 0 150s Consumption_11 0 150s Consumption_12 0 150s Consumption_13 0 150s Consumption_14 0 150s Consumption_15 0 150s Consumption_16 0 150s Consumption_17 0 150s Consumption_18 0 150s Consumption_19 0 150s Consumption_20 0 150s Consumption_21 0 150s Consumption_22 0 150s Investment_2 0 150s Investment_3 0 150s Investment_4 0 150s Investment_5 0 150s Investment_6 0 150s Investment_7 0 150s Investment_8 0 150s Investment_9 0 150s Investment_10 0 150s Investment_11 0 150s Investment_12 0 150s Investment_13 0 150s Investment_14 0 150s Investment_15 0 150s Investment_16 0 150s Investment_17 0 150s Investment_18 0 150s Investment_19 0 150s Investment_20 0 150s Investment_21 0 150s Investment_22 0 150s PrivateWages_2 -10 150s PrivateWages_3 -9 150s PrivateWages_4 -8 150s PrivateWages_5 -7 150s PrivateWages_6 -6 150s PrivateWages_7 -5 150s PrivateWages_8 -4 150s PrivateWages_9 -3 150s PrivateWages_10 -2 150s PrivateWages_11 -1 150s PrivateWages_12 0 150s PrivateWages_13 1 150s PrivateWages_14 2 150s PrivateWages_15 3 150s PrivateWages_16 4 150s PrivateWages_17 5 150s PrivateWages_18 6 150s PrivateWages_19 7 150s PrivateWages_20 8 150s PrivateWages_21 9 150s PrivateWages_22 10 150s > nobs 150s [1] 63 150s > linearHypothesis 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 0.82 0.37 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 0.73 0.4 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 52 150s 2 51 1 0.73 0.39 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.42 0.66 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.37 0.69 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 53 150s 2 51 2 0.74 0.69 150s > logLik 150s 'log Lik.' -72.3 (df=13) 150s 'log Lik.' -77.9 (df=13) 150s compare log likelihood value with single-equation OLS 150s [1] TRUE 150s Estimating function 150s Consumption_(Intercept) Consumption_corpProf 150s Consumption_2 -0.32389 -4.016 150s Consumption_3 -1.25001 -21.125 150s Consumption_4 -1.56574 -28.810 150s Consumption_5 -0.49350 -9.574 150s Consumption_6 0.00761 0.153 150s Consumption_7 0.86910 17.034 150s Consumption_8 1.33848 26.502 150s Consumption_9 1.05498 22.260 150s Consumption_10 -0.58856 -12.772 150s Consumption_11 0.28231 4.404 150s Consumption_12 -0.22965 -2.618 150s Consumption_13 -0.32213 -2.255 150s Consumption_14 0.32228 3.610 150s Consumption_15 -0.05801 -0.714 150s Consumption_16 -0.03466 -0.485 150s Consumption_17 1.61650 28.450 150s Consumption_18 -0.43597 -7.542 150s Consumption_19 0.21005 3.214 150s Consumption_20 0.98920 18.795 150s Consumption_21 0.78508 16.565 150s Consumption_22 -2.17345 -51.076 150s Investment_2 0.00000 0.000 150s Investment_3 0.00000 0.000 150s Investment_4 0.00000 0.000 150s Investment_5 0.00000 0.000 150s Investment_6 0.00000 0.000 150s Investment_7 0.00000 0.000 150s Investment_8 0.00000 0.000 150s Investment_9 0.00000 0.000 150s Investment_10 0.00000 0.000 150s Investment_11 0.00000 0.000 150s Investment_12 0.00000 0.000 150s Investment_13 0.00000 0.000 150s Investment_14 0.00000 0.000 150s Investment_15 0.00000 0.000 150s Investment_16 0.00000 0.000 150s Investment_17 0.00000 0.000 150s Investment_18 0.00000 0.000 150s Investment_19 0.00000 0.000 150s Investment_20 0.00000 0.000 150s Investment_21 0.00000 0.000 150s Investment_22 0.00000 0.000 150s PrivateWages_2 0.00000 0.000 150s PrivateWages_3 0.00000 0.000 150s PrivateWages_4 0.00000 0.000 150s PrivateWages_5 0.00000 0.000 150s PrivateWages_6 0.00000 0.000 150s PrivateWages_7 0.00000 0.000 150s PrivateWages_8 0.00000 0.000 150s PrivateWages_9 0.00000 0.000 150s PrivateWages_10 0.00000 0.000 150s PrivateWages_11 0.00000 0.000 150s PrivateWages_12 0.00000 0.000 150s PrivateWages_13 0.00000 0.000 150s PrivateWages_14 0.00000 0.000 150s PrivateWages_15 0.00000 0.000 150s PrivateWages_16 0.00000 0.000 150s PrivateWages_17 0.00000 0.000 150s PrivateWages_18 0.00000 0.000 150s PrivateWages_19 0.00000 0.000 150s PrivateWages_20 0.00000 0.000 150s PrivateWages_21 0.00000 0.000 150s PrivateWages_22 0.00000 0.000 150s Consumption_corpProfLag Consumption_wages 150s Consumption_2 -4.113 -9.134 150s Consumption_3 -15.500 -40.250 150s Consumption_4 -26.461 -57.932 150s Consumption_5 -9.080 -18.260 150s Consumption_6 0.148 0.294 150s Consumption_7 17.469 35.372 150s Consumption_8 26.234 55.547 150s Consumption_9 20.889 45.259 150s Consumption_10 -12.419 -26.662 150s Consumption_11 6.126 11.885 150s Consumption_12 -3.583 -9.025 150s Consumption_13 -3.672 -11.049 150s Consumption_14 2.256 10.990 150s Consumption_15 -0.650 -2.123 150s Consumption_16 -0.426 -1.362 150s Consumption_17 22.631 71.449 150s Consumption_18 -7.673 -20.796 150s Consumption_19 3.634 9.641 150s Consumption_20 15.135 48.867 150s Consumption_21 14.916 41.609 150s Consumption_22 -45.860 -134.319 150s Investment_2 0.000 0.000 150s Investment_3 0.000 0.000 150s Investment_4 0.000 0.000 150s Investment_5 0.000 0.000 150s Investment_6 0.000 0.000 150s Investment_7 0.000 0.000 150s Investment_8 0.000 0.000 150s Investment_9 0.000 0.000 150s Investment_10 0.000 0.000 150s Investment_11 0.000 0.000 150s Investment_12 0.000 0.000 150s Investment_13 0.000 0.000 150s Investment_14 0.000 0.000 150s Investment_15 0.000 0.000 150s Investment_16 0.000 0.000 150s Investment_17 0.000 0.000 150s Investment_18 0.000 0.000 150s Investment_19 0.000 0.000 150s Investment_20 0.000 0.000 150s Investment_21 0.000 0.000 150s Investment_22 0.000 0.000 150s PrivateWages_2 0.000 0.000 150s PrivateWages_3 0.000 0.000 150s PrivateWages_4 0.000 0.000 150s PrivateWages_5 0.000 0.000 150s PrivateWages_6 0.000 0.000 150s PrivateWages_7 0.000 0.000 150s PrivateWages_8 0.000 0.000 150s PrivateWages_9 0.000 0.000 150s PrivateWages_10 0.000 0.000 150s PrivateWages_11 0.000 0.000 150s PrivateWages_12 0.000 0.000 150s PrivateWages_13 0.000 0.000 150s PrivateWages_14 0.000 0.000 150s PrivateWages_15 0.000 0.000 150s PrivateWages_16 0.000 0.000 150s PrivateWages_17 0.000 0.000 150s PrivateWages_18 0.000 0.000 150s PrivateWages_19 0.000 0.000 150s PrivateWages_20 0.000 0.000 150s PrivateWages_21 0.000 0.000 150s PrivateWages_22 0.000 0.000 150s Investment_(Intercept) Investment_corpProf 150s Consumption_2 0.0000 0.000 150s Consumption_3 0.0000 0.000 150s Consumption_4 0.0000 0.000 150s Consumption_5 0.0000 0.000 150s Consumption_6 0.0000 0.000 150s Consumption_7 0.0000 0.000 150s Consumption_8 0.0000 0.000 150s Consumption_9 0.0000 0.000 150s Consumption_10 0.0000 0.000 150s Consumption_11 0.0000 0.000 150s Consumption_12 0.0000 0.000 150s Consumption_13 0.0000 0.000 150s Consumption_14 0.0000 0.000 150s Consumption_15 0.0000 0.000 150s Consumption_16 0.0000 0.000 150s Consumption_17 0.0000 0.000 150s Consumption_18 0.0000 0.000 150s Consumption_19 0.0000 0.000 150s Consumption_20 0.0000 0.000 150s Consumption_21 0.0000 0.000 150s Consumption_22 0.0000 0.000 150s Investment_2 -0.0668 -0.828 150s Investment_3 -0.0476 -0.804 150s Investment_4 1.2467 22.939 150s Investment_5 -1.3512 -26.213 150s Investment_6 0.4154 8.350 150s Investment_7 1.4923 29.248 150s Investment_8 0.7889 15.620 150s Investment_9 -0.6317 -13.329 150s Investment_10 1.0830 23.500 150s Investment_11 0.2791 4.353 150s Investment_12 0.0369 0.420 150s Investment_13 0.3659 2.561 150s Investment_14 0.2237 2.505 150s Investment_15 -0.1728 -2.126 150s Investment_16 0.0101 0.141 150s Investment_17 0.9719 17.105 150s Investment_18 0.0516 0.893 150s Investment_19 -2.5656 -39.254 150s Investment_20 -0.6866 -13.045 150s Investment_21 -0.7807 -16.474 150s Investment_22 -0.6623 -15.565 150s PrivateWages_2 0.0000 0.000 150s PrivateWages_3 0.0000 0.000 150s PrivateWages_4 0.0000 0.000 150s PrivateWages_5 0.0000 0.000 150s PrivateWages_6 0.0000 0.000 150s PrivateWages_7 0.0000 0.000 150s PrivateWages_8 0.0000 0.000 150s PrivateWages_9 0.0000 0.000 150s PrivateWages_10 0.0000 0.000 150s PrivateWages_11 0.0000 0.000 150s PrivateWages_12 0.0000 0.000 150s PrivateWages_13 0.0000 0.000 150s PrivateWages_14 0.0000 0.000 150s PrivateWages_15 0.0000 0.000 150s PrivateWages_16 0.0000 0.000 150s PrivateWages_17 0.0000 0.000 150s PrivateWages_18 0.0000 0.000 150s PrivateWages_19 0.0000 0.000 150s PrivateWages_20 0.0000 0.000 150s PrivateWages_21 0.0000 0.000 150s PrivateWages_22 0.0000 0.000 150s Investment_corpProfLag Investment_capitalLag 150s Consumption_2 0.000 0.00 150s Consumption_3 0.000 0.00 150s Consumption_4 0.000 0.00 150s Consumption_5 0.000 0.00 150s Consumption_6 0.000 0.00 150s Consumption_7 0.000 0.00 150s Consumption_8 0.000 0.00 150s Consumption_9 0.000 0.00 150s Consumption_10 0.000 0.00 150s Consumption_11 0.000 0.00 150s Consumption_12 0.000 0.00 150s Consumption_13 0.000 0.00 150s Consumption_14 0.000 0.00 150s Consumption_15 0.000 0.00 150s Consumption_16 0.000 0.00 150s Consumption_17 0.000 0.00 150s Consumption_18 0.000 0.00 150s Consumption_19 0.000 0.00 150s Consumption_20 0.000 0.00 150s Consumption_21 0.000 0.00 150s Consumption_22 0.000 0.00 150s Investment_2 -0.848 -12.21 150s Investment_3 -0.590 -8.69 150s Investment_4 21.069 230.01 150s Investment_5 -24.862 -256.32 150s Investment_6 8.059 80.05 150s Investment_7 29.994 295.17 150s Investment_8 15.463 160.46 150s Investment_9 -12.507 -131.14 150s Investment_10 22.850 228.07 150s Investment_11 6.056 60.20 150s Investment_12 0.575 7.99 150s Investment_13 4.172 78.05 150s Investment_14 1.566 46.33 150s Investment_15 -1.936 -34.91 150s Investment_16 0.124 2.01 150s Investment_17 13.606 192.14 150s Investment_18 0.908 10.31 150s Investment_19 -44.385 -517.74 150s Investment_20 -10.505 -137.25 150s Investment_21 -14.834 -157.09 150s Investment_22 -13.975 -135.45 150s PrivateWages_2 0.000 0.00 150s PrivateWages_3 0.000 0.00 150s PrivateWages_4 0.000 0.00 150s PrivateWages_5 0.000 0.00 150s PrivateWages_6 0.000 0.00 150s PrivateWages_7 0.000 0.00 150s PrivateWages_8 0.000 0.00 150s PrivateWages_9 0.000 0.00 150s PrivateWages_10 0.000 0.00 150s PrivateWages_11 0.000 0.00 150s PrivateWages_12 0.000 0.00 150s PrivateWages_13 0.000 0.00 150s PrivateWages_14 0.000 0.00 150s PrivateWages_15 0.000 0.00 150s PrivateWages_16 0.000 0.00 150s PrivateWages_17 0.000 0.00 150s PrivateWages_18 0.000 0.00 150s PrivateWages_19 0.000 0.00 150s PrivateWages_20 0.000 0.00 150s PrivateWages_21 0.000 0.00 150s PrivateWages_22 0.000 0.00 150s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 150s Consumption_2 0.0000 0.000 0.000 150s Consumption_3 0.0000 0.000 0.000 150s Consumption_4 0.0000 0.000 0.000 150s Consumption_5 0.0000 0.000 0.000 150s Consumption_6 0.0000 0.000 0.000 150s Consumption_7 0.0000 0.000 0.000 150s Consumption_8 0.0000 0.000 0.000 150s Consumption_9 0.0000 0.000 0.000 150s Consumption_10 0.0000 0.000 0.000 150s Consumption_11 0.0000 0.000 0.000 150s Consumption_12 0.0000 0.000 0.000 150s Consumption_13 0.0000 0.000 0.000 150s Consumption_14 0.0000 0.000 0.000 150s Consumption_15 0.0000 0.000 0.000 150s Consumption_16 0.0000 0.000 0.000 150s Consumption_17 0.0000 0.000 0.000 150s Consumption_18 0.0000 0.000 0.000 150s Consumption_19 0.0000 0.000 0.000 150s Consumption_20 0.0000 0.000 0.000 150s Consumption_21 0.0000 0.000 0.000 150s Consumption_22 0.0000 0.000 0.000 150s Investment_2 0.0000 0.000 0.000 150s Investment_3 0.0000 0.000 0.000 150s Investment_4 0.0000 0.000 0.000 150s Investment_5 0.0000 0.000 0.000 150s Investment_6 0.0000 0.000 0.000 150s Investment_7 0.0000 0.000 0.000 150s Investment_8 0.0000 0.000 0.000 150s Investment_9 0.0000 0.000 0.000 150s Investment_10 0.0000 0.000 0.000 150s Investment_11 0.0000 0.000 0.000 150s Investment_12 0.0000 0.000 0.000 150s Investment_13 0.0000 0.000 0.000 150s Investment_14 0.0000 0.000 0.000 150s Investment_15 0.0000 0.000 0.000 150s Investment_16 0.0000 0.000 0.000 150s Investment_17 0.0000 0.000 0.000 150s Investment_18 0.0000 0.000 0.000 150s Investment_19 0.0000 0.000 0.000 150s Investment_20 0.0000 0.000 0.000 150s Investment_21 0.0000 0.000 0.000 150s Investment_22 0.0000 0.000 0.000 150s PrivateWages_2 -1.2942 -59.015 -58.109 150s PrivateWages_3 0.2957 14.813 13.482 150s PrivateWages_4 1.1877 67.938 59.505 150s PrivateWages_5 -0.1358 -7.755 -7.768 150s PrivateWages_6 -0.4654 -28.390 -26.575 150s PrivateWages_7 -0.4838 -30.965 -29.514 150s PrivateWages_8 -0.7281 -46.892 -46.601 150s PrivateWages_9 0.3392 21.881 21.847 150s PrivateWages_10 1.1957 80.111 77.122 150s PrivateWages_11 -0.1508 -9.230 -10.105 150s PrivateWages_12 0.5942 31.729 36.364 150s PrivateWages_13 0.1027 4.549 5.483 150s PrivateWages_14 0.4503 20.307 19.947 150s PrivateWages_15 0.2816 13.993 12.698 150s PrivateWages_16 0.0138 0.748 0.684 150s PrivateWages_17 -0.8508 -53.343 -46.282 150s PrivateWages_18 0.9956 64.717 62.427 150s PrivateWages_19 -0.4688 -28.547 -30.469 150s PrivateWages_20 -0.3795 -26.378 -23.114 150s PrivateWages_21 -1.0909 -82.582 -75.818 150s PrivateWages_22 0.5917 52.309 44.794 150s PrivateWages_trend 150s Consumption_2 0.000 150s Consumption_3 0.000 150s Consumption_4 0.000 150s Consumption_5 0.000 150s Consumption_6 0.000 150s Consumption_7 0.000 150s Consumption_8 0.000 150s Consumption_9 0.000 150s Consumption_10 0.000 150s Consumption_11 0.000 150s Consumption_12 0.000 150s Consumption_13 0.000 150s Consumption_14 0.000 150s Consumption_15 0.000 150s Consumption_16 0.000 150s Consumption_17 0.000 150s Consumption_18 0.000 150s Consumption_19 0.000 150s Consumption_20 0.000 150s Consumption_21 0.000 150s Consumption_22 0.000 150s Investment_2 0.000 150s Investment_3 0.000 150s Investment_4 0.000 150s Investment_5 0.000 150s Investment_6 0.000 150s Investment_7 0.000 150s Investment_8 0.000 150s Investment_9 0.000 150s Investment_10 0.000 150s Investment_11 0.000 150s Investment_12 0.000 150s Investment_13 0.000 150s Investment_14 0.000 150s Investment_15 0.000 150s Investment_16 0.000 150s Investment_17 0.000 150s Investment_18 0.000 150s Investment_19 0.000 150s Investment_20 0.000 150s Investment_21 0.000 150s Investment_22 0.000 150s PrivateWages_2 12.942 150s PrivateWages_3 -2.661 150s PrivateWages_4 -9.502 150s PrivateWages_5 0.951 150s PrivateWages_6 2.792 150s PrivateWages_7 2.419 150s PrivateWages_8 2.913 150s PrivateWages_9 -1.018 150s PrivateWages_10 -2.391 150s PrivateWages_11 0.151 150s PrivateWages_12 0.000 150s PrivateWages_13 0.103 150s PrivateWages_14 0.901 150s PrivateWages_15 0.845 150s PrivateWages_16 0.055 150s PrivateWages_17 -4.254 150s PrivateWages_18 5.974 150s PrivateWages_19 -3.281 150s PrivateWages_20 -3.036 150s PrivateWages_21 -9.818 150s PrivateWages_22 5.917 150s [1] TRUE 150s > Bread 150s Consumption_(Intercept) Consumption_corpProf 150s Consumption_(Intercept) 101.65 0.030 150s Consumption_corpProf 0.03 0.498 150s Consumption_corpProfLag -1.06 -0.316 150s Consumption_wages -1.97 -0.079 150s Investment_(Intercept) 0.00 0.000 150s Investment_corpProf 0.00 0.000 150s Investment_corpProfLag 0.00 0.000 150s Investment_capitalLag 0.00 0.000 150s PrivateWages_(Intercept) 0.00 0.000 150s PrivateWages_gnp 0.00 0.000 150s PrivateWages_gnpLag 0.00 0.000 150s PrivateWages_trend 0.00 0.000 150s Consumption_corpProfLag Consumption_wages 150s Consumption_(Intercept) -1.0607 -1.9718 150s Consumption_corpProf -0.3157 -0.0790 150s Consumption_corpProfLag 0.4922 -0.0402 150s Consumption_wages -0.0402 0.0956 150s Investment_(Intercept) 0.0000 0.0000 150s Investment_corpProf 0.0000 0.0000 150s Investment_corpProfLag 0.0000 0.0000 150s Investment_capitalLag 0.0000 0.0000 150s PrivateWages_(Intercept) 0.0000 0.0000 150s PrivateWages_gnp 0.0000 0.0000 150s PrivateWages_gnpLag 0.0000 0.0000 150s PrivateWages_trend 0.0000 0.0000 150s Investment_(Intercept) Investment_corpProf 150s Consumption_(Intercept) 0.00 0.0000 150s Consumption_corpProf 0.00 0.0000 150s Consumption_corpProfLag 0.00 0.0000 150s Consumption_wages 0.00 0.0000 150s Investment_(Intercept) 1846.89 -17.9709 150s Investment_corpProf -17.97 0.5831 150s Investment_corpProfLag 14.67 -0.5008 150s Investment_capitalLag -8.88 0.0814 150s PrivateWages_(Intercept) 0.00 0.0000 150s PrivateWages_gnp 0.00 0.0000 150s PrivateWages_gnpLag 0.00 0.0000 150s PrivateWages_trend 0.00 0.0000 150s Investment_corpProfLag Investment_capitalLag 150s Consumption_(Intercept) 0.0000 0.0000 150s Consumption_corpProf 0.0000 0.0000 150s Consumption_corpProfLag 0.0000 0.0000 150s Consumption_wages 0.0000 0.0000 150s Investment_(Intercept) 14.6742 -8.8813 150s Investment_corpProf -0.5008 0.0814 150s Investment_corpProfLag 0.6289 -0.0824 150s Investment_capitalLag -0.0824 0.0442 150s PrivateWages_(Intercept) 0.0000 0.0000 150s PrivateWages_gnp 0.0000 0.0000 150s PrivateWages_gnpLag 0.0000 0.0000 150s PrivateWages_trend 0.0000 0.0000 150s PrivateWages_(Intercept) PrivateWages_gnp 150s Consumption_(Intercept) 0.000 0.0000 150s Consumption_corpProf 0.000 0.0000 150s Consumption_corpProfLag 0.000 0.0000 150s Consumption_wages 0.000 0.0000 150s Investment_(Intercept) 0.000 0.0000 150s Investment_corpProf 0.000 0.0000 150s Investment_corpProfLag 0.000 0.0000 150s Investment_capitalLag 0.000 0.0000 150s PrivateWages_(Intercept) 172.668 -0.5919 150s PrivateWages_gnp -0.592 0.1124 150s PrivateWages_gnpLag -2.313 -0.1062 150s PrivateWages_trend 1.993 -0.0274 150s PrivateWages_gnpLag PrivateWages_trend 150s Consumption_(Intercept) 0.00000 0.00000 150s Consumption_corpProf 0.00000 0.00000 150s Consumption_corpProfLag 0.00000 0.00000 150s Consumption_wages 0.00000 0.00000 150s Investment_(Intercept) 0.00000 0.00000 150s Investment_corpProf 0.00000 0.00000 150s Investment_corpProfLag 0.00000 0.00000 150s Investment_capitalLag 0.00000 0.00000 150s PrivateWages_(Intercept) -2.31299 1.99284 150s PrivateWages_gnp -0.10624 -0.02738 150s PrivateWages_gnpLag 0.14992 -0.00601 150s PrivateWages_trend -0.00601 0.10900 150s > 150s > # 2SLS 150s > summary 150s 150s systemfit results 150s method: 2SLS 150s 150s N DF SSR detRCov OLS-R2 McElroy-R2 150s system 63 51 61 0.288 0.969 0.992 150s 150s N DF SSR MSE RMSE R2 Adj R2 150s Consumption 21 17 21.9 1.290 1.136 0.977 0.973 150s Investment 21 17 29.0 1.709 1.307 0.885 0.865 150s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 150s 150s The covariance matrix of the residuals 150s Consumption Investment PrivateWages 150s Consumption 1.044 0.438 -0.385 150s Investment 0.438 1.383 0.193 150s PrivateWages -0.385 0.193 0.476 150s 150s The correlations of the residuals 150s Consumption Investment PrivateWages 150s Consumption 1.000 0.364 -0.546 150s Investment 0.364 1.000 0.237 150s PrivateWages -0.546 0.237 1.000 150s 150s 150s 2SLS estimates for 'Consumption' (equation 1) 150s Model Formula: consump ~ corpProf + corpProfLag + wages 150s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 150s gnpLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 16.5548 1.3208 12.53 5.2e-10 *** 150s corpProf 0.0173 0.1180 0.15 0.89 150s corpProfLag 0.2162 0.1073 2.02 0.06 . 150s wages 0.8102 0.0402 20.13 2.7e-13 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.136 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 21.925 MSE: 1.29 Root MSE: 1.136 150s Multiple R-Squared: 0.977 Adjusted R-Squared: 0.973 150s 150s 150s 2SLS estimates for 'Investment' (equation 2) 150s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 150s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 150s gnpLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 20.2782 7.5427 2.69 0.01555 * 150s corpProf 0.1502 0.1732 0.87 0.39792 150s corpProfLag 0.6159 0.1628 3.78 0.00148 ** 150s capitalLag -0.1578 0.0361 -4.37 0.00042 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.307 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 29.047 MSE: 1.709 Root MSE: 1.307 150s Multiple R-Squared: 0.885 Adjusted R-Squared: 0.865 150s 150s 150s 2SLS estimates for 'PrivateWages' (equation 3) 150s Model Formula: privWage ~ gnp + gnpLag + trend 150s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 150s gnpLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 1.5003 1.1478 1.31 0.20857 150s gnp 0.4389 0.0356 12.32 6.8e-10 *** 150s gnpLag 0.1467 0.0388 3.78 0.00150 ** 150s trend 0.1304 0.0291 4.47 0.00033 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 0.767 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 150s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 150s 150s > residuals 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 -0.46263 -1.320 -1.2940 150s 3 -0.61635 0.257 0.2981 150s 4 -1.30423 0.860 1.1918 150s 5 -0.24588 -1.594 -0.1361 150s 6 0.22948 0.259 -0.4634 150s 7 0.88538 1.207 -0.4824 150s 8 1.44189 0.969 -0.7284 150s 9 1.34190 0.113 0.3387 150s 10 -0.39403 1.796 1.1965 150s 11 -0.62564 -0.953 -0.1552 150s 12 -1.06543 -0.807 0.5882 150s 13 -1.33021 -0.895 0.0955 150s 14 0.61059 1.306 0.4487 150s 15 -0.14208 -0.151 0.2822 150s 16 0.00315 0.142 0.0145 150s 17 2.00337 1.749 -0.8478 150s 18 -0.60552 -0.192 0.9950 150s 19 -0.24771 -3.291 -0.4734 150s 20 1.38510 0.285 -0.3766 150s 21 1.03204 -0.104 -1.0893 150s 22 -1.89319 0.363 0.5974 150s > fitted 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 42.4 1.120 26.8 150s 3 45.6 1.643 29.0 150s 4 50.5 4.340 32.9 150s 5 50.8 4.594 34.0 150s 6 52.4 4.841 35.9 150s 7 54.2 4.393 37.9 150s 8 54.8 3.231 38.6 150s 9 56.0 2.887 38.9 150s 10 58.2 3.304 40.1 150s 11 55.6 1.953 38.1 150s 12 52.0 -2.593 33.9 150s 13 46.9 -5.305 28.9 150s 14 45.9 -6.406 28.1 150s 15 48.8 -2.849 30.3 150s 16 51.3 -1.442 33.2 150s 17 55.7 0.351 37.6 150s 18 59.3 2.192 40.0 150s 19 57.7 1.391 38.7 150s 20 60.2 1.015 42.0 150s 21 64.0 3.404 46.1 150s 22 71.6 4.537 52.7 150s > predict 150s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 150s 1 NA NA NA NA 150s 2 42.4 0.471 41.4 43.4 150s 3 45.6 0.577 44.4 46.8 150s 4 50.5 0.354 49.8 51.3 150s 5 50.8 0.405 50.0 51.7 150s 6 52.4 0.404 51.5 53.2 150s 7 54.2 0.359 53.5 55.0 150s 8 54.8 0.328 54.1 55.4 150s 9 56.0 0.368 55.2 56.7 150s 10 58.2 0.377 57.4 59.0 150s 11 55.6 0.728 54.1 57.2 150s 12 52.0 0.604 50.7 53.2 150s 13 46.9 0.765 45.3 48.5 150s 14 45.9 0.615 44.6 47.2 150s 15 48.8 0.374 48.1 49.6 150s 16 51.3 0.333 50.6 52.0 150s 17 55.7 0.409 54.8 56.6 150s 18 59.3 0.326 58.6 60.0 150s 19 57.7 0.414 56.9 58.6 150s 20 60.2 0.478 59.2 61.2 150s 21 64.0 0.446 63.0 64.9 150s 22 71.6 0.689 70.1 73.0 150s Investment.pred Investment.se.fit Investment.lwr Investment.upr 150s 1 NA NA NA NA 150s 2 1.120 0.865 -0.706 2.946 150s 3 1.643 0.594 0.390 2.895 150s 4 4.340 0.545 3.190 5.490 150s 5 4.594 0.443 3.660 5.527 150s 6 4.841 0.411 3.973 5.709 150s 7 4.393 0.399 3.550 5.235 150s 8 3.231 0.348 2.497 3.965 150s 9 2.887 0.542 1.744 4.030 150s 10 3.304 0.593 2.054 4.555 150s 11 1.953 0.855 0.148 3.757 150s 12 -2.593 0.679 -4.026 -1.160 150s 13 -5.305 0.876 -7.152 -3.457 150s 14 -6.406 0.916 -8.338 -4.473 150s 15 -2.849 0.435 -3.765 -1.932 150s 16 -1.442 0.376 -2.236 -0.649 150s 17 0.351 0.510 -0.724 1.426 150s 18 2.192 0.299 1.560 2.823 150s 19 1.391 0.464 0.411 2.371 150s 20 1.015 0.576 -0.201 2.230 150s 21 3.404 0.471 2.410 4.398 150s 22 4.537 0.675 3.114 5.961 150s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 150s 1 NA NA NA NA 150s 2 26.8 0.318 26.1 27.5 150s 3 29.0 0.330 28.3 29.7 150s 4 32.9 0.346 32.2 33.6 150s 5 34.0 0.242 33.5 34.5 150s 6 35.9 0.248 35.3 36.4 150s 7 37.9 0.244 37.4 38.4 150s 8 38.6 0.246 38.1 39.1 150s 9 38.9 0.235 38.4 39.4 150s 10 40.1 0.224 39.6 40.6 150s 11 38.1 0.350 37.3 38.8 150s 12 33.9 0.382 33.1 34.7 150s 13 28.9 0.454 27.9 29.9 150s 14 28.1 0.342 27.3 28.8 150s 15 30.3 0.335 29.6 31.0 150s 16 33.2 0.280 32.6 33.8 150s 17 37.6 0.291 37.0 38.3 150s 18 40.0 0.215 39.6 40.5 150s 19 38.7 0.356 37.9 39.4 150s 20 42.0 0.304 41.3 42.6 150s 21 46.1 0.306 45.4 46.7 150s 22 52.7 0.489 51.7 53.7 150s > model.frame 150s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 150s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 150s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 150s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 150s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 150s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 150s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 150s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 150s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 150s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 150s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 150s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 150s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 150s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 150s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 150s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 150s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 150s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 150s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 150s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 150s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 150s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 150s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 150s trend 150s 1 -11 150s 2 -10 150s 3 -9 150s 4 -8 150s 5 -7 150s 6 -6 150s 7 -5 150s 8 -4 150s 9 -3 150s 10 -2 150s 11 -1 150s 12 0 150s 13 1 150s 14 2 150s 15 3 150s 16 4 150s 17 5 150s 18 6 150s 19 7 150s 20 8 150s 21 9 150s 22 10 150s > Frames of instrumental variables 150s govExp taxes govWage trend capitalLag corpProfLag gnpLag 150s 1 2.4 3.4 2.2 -11 180 NA NA 150s 2 3.9 7.7 2.7 -10 183 12.7 44.9 150s 3 3.2 3.9 2.9 -9 183 12.4 45.6 150s 4 2.8 4.7 2.9 -8 184 16.9 50.1 150s 5 3.5 3.8 3.1 -7 190 18.4 57.2 150s 6 3.3 5.5 3.2 -6 193 19.4 57.1 150s 7 3.3 7.0 3.3 -5 198 20.1 61.0 150s 8 4.0 6.7 3.6 -4 203 19.6 64.0 150s 9 4.2 4.2 3.7 -3 208 19.8 64.4 150s 10 4.1 4.0 4.0 -2 211 21.1 64.5 150s 11 5.2 7.7 4.2 -1 216 21.7 67.0 150s 12 5.9 7.5 4.8 0 217 15.6 61.2 150s 13 4.9 8.3 5.3 1 213 11.4 53.4 150s 14 3.7 5.4 5.6 2 207 7.0 44.3 150s 15 4.0 6.8 6.0 3 202 11.2 45.1 150s 16 4.4 7.2 6.1 4 199 12.3 49.7 150s 17 2.9 8.3 7.4 5 198 14.0 54.4 150s 18 4.3 6.7 6.7 6 200 17.6 62.7 150s 19 5.3 7.4 7.7 7 202 17.3 65.0 150s 20 6.6 8.9 7.8 8 200 15.3 60.9 150s 21 7.4 9.6 8.0 9 201 19.0 69.5 150s 22 13.8 11.6 8.5 10 204 21.1 75.7 150s govExp taxes govWage trend capitalLag corpProfLag gnpLag 150s 1 2.4 3.4 2.2 -11 180 NA NA 150s 2 3.9 7.7 2.7 -10 183 12.7 44.9 150s 3 3.2 3.9 2.9 -9 183 12.4 45.6 150s 4 2.8 4.7 2.9 -8 184 16.9 50.1 150s 5 3.5 3.8 3.1 -7 190 18.4 57.2 150s 6 3.3 5.5 3.2 -6 193 19.4 57.1 150s 7 3.3 7.0 3.3 -5 198 20.1 61.0 150s 8 4.0 6.7 3.6 -4 203 19.6 64.0 150s 9 4.2 4.2 3.7 -3 208 19.8 64.4 150s 10 4.1 4.0 4.0 -2 211 21.1 64.5 150s 11 5.2 7.7 4.2 -1 216 21.7 67.0 150s 12 5.9 7.5 4.8 0 217 15.6 61.2 150s 13 4.9 8.3 5.3 1 213 11.4 53.4 150s 14 3.7 5.4 5.6 2 207 7.0 44.3 150s 15 4.0 6.8 6.0 3 202 11.2 45.1 150s 16 4.4 7.2 6.1 4 199 12.3 49.7 150s 17 2.9 8.3 7.4 5 198 14.0 54.4 150s 18 4.3 6.7 6.7 6 200 17.6 62.7 150s 19 5.3 7.4 7.7 7 202 17.3 65.0 150s 20 6.6 8.9 7.8 8 200 15.3 60.9 150s 21 7.4 9.6 8.0 9 201 19.0 69.5 150s 22 13.8 11.6 8.5 10 204 21.1 75.7 150s govExp taxes govWage trend capitalLag corpProfLag gnpLag 150s 1 2.4 3.4 2.2 -11 180 NA NA 150s 2 3.9 7.7 2.7 -10 183 12.7 44.9 150s 3 3.2 3.9 2.9 -9 183 12.4 45.6 150s 4 2.8 4.7 2.9 -8 184 16.9 50.1 150s 5 3.5 3.8 3.1 -7 190 18.4 57.2 150s 6 3.3 5.5 3.2 -6 193 19.4 57.1 150s 7 3.3 7.0 3.3 -5 198 20.1 61.0 150s 8 4.0 6.7 3.6 -4 203 19.6 64.0 150s 9 4.2 4.2 3.7 -3 208 19.8 64.4 150s 10 4.1 4.0 4.0 -2 211 21.1 64.5 150s 11 5.2 7.7 4.2 -1 216 21.7 67.0 150s 12 5.9 7.5 4.8 0 217 15.6 61.2 150s 13 4.9 8.3 5.3 1 213 11.4 53.4 150s 14 3.7 5.4 5.6 2 207 7.0 44.3 150s 15 4.0 6.8 6.0 3 202 11.2 45.1 150s 16 4.4 7.2 6.1 4 199 12.3 49.7 150s 17 2.9 8.3 7.4 5 198 14.0 54.4 150s 18 4.3 6.7 6.7 6 200 17.6 62.7 150s 19 5.3 7.4 7.7 7 202 17.3 65.0 150s 20 6.6 8.9 7.8 8 200 15.3 60.9 150s 21 7.4 9.6 8.0 9 201 19.0 69.5 150s 22 13.8 11.6 8.5 10 204 21.1 75.7 150s > model.matrix 150s [1] TRUE 150s > matrix of instrumental variables 150s Consumption_(Intercept) Consumption_govExp Consumption_taxes 150s Consumption_2 1 3.9 7.7 150s Consumption_3 1 3.2 3.9 150s Consumption_4 1 2.8 4.7 150s Consumption_5 1 3.5 3.8 150s Consumption_6 1 3.3 5.5 150s Consumption_7 1 3.3 7.0 150s Consumption_8 1 4.0 6.7 150s Consumption_9 1 4.2 4.2 150s Consumption_10 1 4.1 4.0 150s Consumption_11 1 5.2 7.7 150s Consumption_12 1 5.9 7.5 150s Consumption_13 1 4.9 8.3 150s Consumption_14 1 3.7 5.4 150s Consumption_15 1 4.0 6.8 150s Consumption_16 1 4.4 7.2 150s Consumption_17 1 2.9 8.3 150s Consumption_18 1 4.3 6.7 150s Consumption_19 1 5.3 7.4 150s Consumption_20 1 6.6 8.9 150s Consumption_21 1 7.4 9.6 150s Consumption_22 1 13.8 11.6 150s Investment_2 0 0.0 0.0 150s Investment_3 0 0.0 0.0 150s Investment_4 0 0.0 0.0 150s Investment_5 0 0.0 0.0 150s Investment_6 0 0.0 0.0 150s Investment_7 0 0.0 0.0 150s Investment_8 0 0.0 0.0 150s Investment_9 0 0.0 0.0 150s Investment_10 0 0.0 0.0 150s Investment_11 0 0.0 0.0 150s Investment_12 0 0.0 0.0 150s Investment_13 0 0.0 0.0 150s Investment_14 0 0.0 0.0 150s Investment_15 0 0.0 0.0 150s Investment_16 0 0.0 0.0 150s Investment_17 0 0.0 0.0 150s Investment_18 0 0.0 0.0 150s Investment_19 0 0.0 0.0 150s Investment_20 0 0.0 0.0 150s Investment_21 0 0.0 0.0 150s Investment_22 0 0.0 0.0 150s PrivateWages_2 0 0.0 0.0 150s PrivateWages_3 0 0.0 0.0 150s PrivateWages_4 0 0.0 0.0 150s PrivateWages_5 0 0.0 0.0 150s PrivateWages_6 0 0.0 0.0 150s PrivateWages_7 0 0.0 0.0 150s PrivateWages_8 0 0.0 0.0 150s PrivateWages_9 0 0.0 0.0 150s PrivateWages_10 0 0.0 0.0 150s PrivateWages_11 0 0.0 0.0 150s PrivateWages_12 0 0.0 0.0 150s PrivateWages_13 0 0.0 0.0 150s PrivateWages_14 0 0.0 0.0 150s PrivateWages_15 0 0.0 0.0 150s PrivateWages_16 0 0.0 0.0 150s PrivateWages_17 0 0.0 0.0 150s PrivateWages_18 0 0.0 0.0 150s PrivateWages_19 0 0.0 0.0 150s PrivateWages_20 0 0.0 0.0 150s PrivateWages_21 0 0.0 0.0 150s PrivateWages_22 0 0.0 0.0 150s Consumption_govWage Consumption_trend Consumption_capitalLag 150s Consumption_2 2.7 -10 183 150s Consumption_3 2.9 -9 183 150s Consumption_4 2.9 -8 184 150s Consumption_5 3.1 -7 190 150s Consumption_6 3.2 -6 193 150s Consumption_7 3.3 -5 198 150s Consumption_8 3.6 -4 203 150s Consumption_9 3.7 -3 208 150s Consumption_10 4.0 -2 211 150s Consumption_11 4.2 -1 216 150s Consumption_12 4.8 0 217 150s Consumption_13 5.3 1 213 150s Consumption_14 5.6 2 207 150s Consumption_15 6.0 3 202 150s Consumption_16 6.1 4 199 150s Consumption_17 7.4 5 198 150s Consumption_18 6.7 6 200 150s Consumption_19 7.7 7 202 150s Consumption_20 7.8 8 200 150s Consumption_21 8.0 9 201 150s Consumption_22 8.5 10 204 150s Investment_2 0.0 0 0 150s Investment_3 0.0 0 0 150s Investment_4 0.0 0 0 150s Investment_5 0.0 0 0 150s Investment_6 0.0 0 0 150s Investment_7 0.0 0 0 150s Investment_8 0.0 0 0 150s Investment_9 0.0 0 0 150s Investment_10 0.0 0 0 150s Investment_11 0.0 0 0 150s Investment_12 0.0 0 0 150s Investment_13 0.0 0 0 150s Investment_14 0.0 0 0 150s Investment_15 0.0 0 0 150s Investment_16 0.0 0 0 150s Investment_17 0.0 0 0 150s Investment_18 0.0 0 0 150s Investment_19 0.0 0 0 150s Investment_20 0.0 0 0 150s Investment_21 0.0 0 0 150s Investment_22 0.0 0 0 150s PrivateWages_2 0.0 0 0 150s PrivateWages_3 0.0 0 0 150s PrivateWages_4 0.0 0 0 150s PrivateWages_5 0.0 0 0 150s PrivateWages_6 0.0 0 0 150s PrivateWages_7 0.0 0 0 150s PrivateWages_8 0.0 0 0 150s PrivateWages_9 0.0 0 0 150s PrivateWages_10 0.0 0 0 150s PrivateWages_11 0.0 0 0 150s PrivateWages_12 0.0 0 0 150s PrivateWages_13 0.0 0 0 150s PrivateWages_14 0.0 0 0 150s PrivateWages_15 0.0 0 0 150s PrivateWages_16 0.0 0 0 150s PrivateWages_17 0.0 0 0 150s PrivateWages_18 0.0 0 0 150s PrivateWages_19 0.0 0 0 150s PrivateWages_20 0.0 0 0 150s PrivateWages_21 0.0 0 0 150s PrivateWages_22 0.0 0 0 150s Consumption_corpProfLag Consumption_gnpLag 150s Consumption_2 12.7 44.9 150s Consumption_3 12.4 45.6 150s Consumption_4 16.9 50.1 150s Consumption_5 18.4 57.2 150s Consumption_6 19.4 57.1 150s Consumption_7 20.1 61.0 150s Consumption_8 19.6 64.0 150s Consumption_9 19.8 64.4 150s Consumption_10 21.1 64.5 150s Consumption_11 21.7 67.0 150s Consumption_12 15.6 61.2 150s Consumption_13 11.4 53.4 150s Consumption_14 7.0 44.3 150s Consumption_15 11.2 45.1 150s Consumption_16 12.3 49.7 150s Consumption_17 14.0 54.4 150s Consumption_18 17.6 62.7 150s Consumption_19 17.3 65.0 150s Consumption_20 15.3 60.9 150s Consumption_21 19.0 69.5 150s Consumption_22 21.1 75.7 150s Investment_2 0.0 0.0 150s Investment_3 0.0 0.0 150s Investment_4 0.0 0.0 150s Investment_5 0.0 0.0 150s Investment_6 0.0 0.0 150s Investment_7 0.0 0.0 150s Investment_8 0.0 0.0 150s Investment_9 0.0 0.0 150s Investment_10 0.0 0.0 150s Investment_11 0.0 0.0 150s Investment_12 0.0 0.0 150s Investment_13 0.0 0.0 150s Investment_14 0.0 0.0 150s Investment_15 0.0 0.0 150s Investment_16 0.0 0.0 150s Investment_17 0.0 0.0 150s Investment_18 0.0 0.0 150s Investment_19 0.0 0.0 150s Investment_20 0.0 0.0 150s Investment_21 0.0 0.0 150s Investment_22 0.0 0.0 150s PrivateWages_2 0.0 0.0 150s PrivateWages_3 0.0 0.0 150s PrivateWages_4 0.0 0.0 150s PrivateWages_5 0.0 0.0 150s PrivateWages_6 0.0 0.0 150s PrivateWages_7 0.0 0.0 150s PrivateWages_8 0.0 0.0 150s PrivateWages_9 0.0 0.0 150s PrivateWages_10 0.0 0.0 150s PrivateWages_11 0.0 0.0 150s PrivateWages_12 0.0 0.0 150s PrivateWages_13 0.0 0.0 150s PrivateWages_14 0.0 0.0 150s PrivateWages_15 0.0 0.0 150s PrivateWages_16 0.0 0.0 150s PrivateWages_17 0.0 0.0 150s PrivateWages_18 0.0 0.0 150s PrivateWages_19 0.0 0.0 150s PrivateWages_20 0.0 0.0 150s PrivateWages_21 0.0 0.0 150s PrivateWages_22 0.0 0.0 150s Investment_(Intercept) Investment_govExp Investment_taxes 150s Consumption_2 0 0.0 0.0 150s Consumption_3 0 0.0 0.0 150s Consumption_4 0 0.0 0.0 150s Consumption_5 0 0.0 0.0 150s Consumption_6 0 0.0 0.0 150s Consumption_7 0 0.0 0.0 150s Consumption_8 0 0.0 0.0 150s Consumption_9 0 0.0 0.0 150s Consumption_10 0 0.0 0.0 150s Consumption_11 0 0.0 0.0 150s Consumption_12 0 0.0 0.0 150s Consumption_13 0 0.0 0.0 150s Consumption_14 0 0.0 0.0 150s Consumption_15 0 0.0 0.0 150s Consumption_16 0 0.0 0.0 150s Consumption_17 0 0.0 0.0 150s Consumption_18 0 0.0 0.0 150s Consumption_19 0 0.0 0.0 150s Consumption_20 0 0.0 0.0 150s Consumption_21 0 0.0 0.0 150s Consumption_22 0 0.0 0.0 150s Investment_2 1 3.9 7.7 150s Investment_3 1 3.2 3.9 150s Investment_4 1 2.8 4.7 150s Investment_5 1 3.5 3.8 150s Investment_6 1 3.3 5.5 150s Investment_7 1 3.3 7.0 150s Investment_8 1 4.0 6.7 150s Investment_9 1 4.2 4.2 150s Investment_10 1 4.1 4.0 150s Investment_11 1 5.2 7.7 150s Investment_12 1 5.9 7.5 150s Investment_13 1 4.9 8.3 150s Investment_14 1 3.7 5.4 150s Investment_15 1 4.0 6.8 150s Investment_16 1 4.4 7.2 150s Investment_17 1 2.9 8.3 150s Investment_18 1 4.3 6.7 150s Investment_19 1 5.3 7.4 150s Investment_20 1 6.6 8.9 150s Investment_21 1 7.4 9.6 150s Investment_22 1 13.8 11.6 150s PrivateWages_2 0 0.0 0.0 150s PrivateWages_3 0 0.0 0.0 150s PrivateWages_4 0 0.0 0.0 150s PrivateWages_5 0 0.0 0.0 150s PrivateWages_6 0 0.0 0.0 150s PrivateWages_7 0 0.0 0.0 150s PrivateWages_8 0 0.0 0.0 150s PrivateWages_9 0 0.0 0.0 150s PrivateWages_10 0 0.0 0.0 150s PrivateWages_11 0 0.0 0.0 150s PrivateWages_12 0 0.0 0.0 150s PrivateWages_13 0 0.0 0.0 150s PrivateWages_14 0 0.0 0.0 150s PrivateWages_15 0 0.0 0.0 150s PrivateWages_16 0 0.0 0.0 150s PrivateWages_17 0 0.0 0.0 150s PrivateWages_18 0 0.0 0.0 150s PrivateWages_19 0 0.0 0.0 150s PrivateWages_20 0 0.0 0.0 150s PrivateWages_21 0 0.0 0.0 150s PrivateWages_22 0 0.0 0.0 150s Investment_govWage Investment_trend Investment_capitalLag 150s Consumption_2 0.0 0 0 150s Consumption_3 0.0 0 0 150s Consumption_4 0.0 0 0 150s Consumption_5 0.0 0 0 150s Consumption_6 0.0 0 0 150s Consumption_7 0.0 0 0 150s Consumption_8 0.0 0 0 150s Consumption_9 0.0 0 0 150s Consumption_10 0.0 0 0 150s Consumption_11 0.0 0 0 150s Consumption_12 0.0 0 0 150s Consumption_13 0.0 0 0 150s Consumption_14 0.0 0 0 150s Consumption_15 0.0 0 0 150s Consumption_16 0.0 0 0 150s Consumption_17 0.0 0 0 150s Consumption_18 0.0 0 0 150s Consumption_19 0.0 0 0 150s Consumption_20 0.0 0 0 150s Consumption_21 0.0 0 0 150s Consumption_22 0.0 0 0 150s Investment_2 2.7 -10 183 150s Investment_3 2.9 -9 183 150s Investment_4 2.9 -8 184 150s Investment_5 3.1 -7 190 150s Investment_6 3.2 -6 193 150s Investment_7 3.3 -5 198 150s Investment_8 3.6 -4 203 150s Investment_9 3.7 -3 208 150s Investment_10 4.0 -2 211 150s Investment_11 4.2 -1 216 150s Investment_12 4.8 0 217 150s Investment_13 5.3 1 213 150s Investment_14 5.6 2 207 150s Investment_15 6.0 3 202 150s Investment_16 6.1 4 199 150s Investment_17 7.4 5 198 150s Investment_18 6.7 6 200 150s Investment_19 7.7 7 202 150s Investment_20 7.8 8 200 150s Investment_21 8.0 9 201 150s Investment_22 8.5 10 204 150s PrivateWages_2 0.0 0 0 150s PrivateWages_3 0.0 0 0 150s PrivateWages_4 0.0 0 0 150s PrivateWages_5 0.0 0 0 150s PrivateWages_6 0.0 0 0 150s PrivateWages_7 0.0 0 0 150s PrivateWages_8 0.0 0 0 150s PrivateWages_9 0.0 0 0 150s PrivateWages_10 0.0 0 0 150s PrivateWages_11 0.0 0 0 150s PrivateWages_12 0.0 0 0 150s PrivateWages_13 0.0 0 0 150s PrivateWages_14 0.0 0 0 150s PrivateWages_15 0.0 0 0 150s PrivateWages_16 0.0 0 0 150s PrivateWages_17 0.0 0 0 150s PrivateWages_18 0.0 0 0 150s PrivateWages_19 0.0 0 0 150s PrivateWages_20 0.0 0 0 150s PrivateWages_21 0.0 0 0 150s PrivateWages_22 0.0 0 0 150s Investment_corpProfLag Investment_gnpLag 150s Consumption_2 0.0 0.0 150s Consumption_3 0.0 0.0 150s Consumption_4 0.0 0.0 150s Consumption_5 0.0 0.0 150s Consumption_6 0.0 0.0 150s Consumption_7 0.0 0.0 150s Consumption_8 0.0 0.0 150s Consumption_9 0.0 0.0 150s Consumption_10 0.0 0.0 150s Consumption_11 0.0 0.0 150s Consumption_12 0.0 0.0 150s Consumption_13 0.0 0.0 150s Consumption_14 0.0 0.0 150s Consumption_15 0.0 0.0 150s Consumption_16 0.0 0.0 150s Consumption_17 0.0 0.0 150s Consumption_18 0.0 0.0 150s Consumption_19 0.0 0.0 150s Consumption_20 0.0 0.0 150s Consumption_21 0.0 0.0 150s Consumption_22 0.0 0.0 150s Investment_2 12.7 44.9 150s Investment_3 12.4 45.6 150s Investment_4 16.9 50.1 150s Investment_5 18.4 57.2 150s Investment_6 19.4 57.1 150s Investment_7 20.1 61.0 150s Investment_8 19.6 64.0 150s Investment_9 19.8 64.4 150s Investment_10 21.1 64.5 150s Investment_11 21.7 67.0 150s Investment_12 15.6 61.2 150s Investment_13 11.4 53.4 150s Investment_14 7.0 44.3 150s Investment_15 11.2 45.1 150s Investment_16 12.3 49.7 150s Investment_17 14.0 54.4 150s Investment_18 17.6 62.7 150s Investment_19 17.3 65.0 150s Investment_20 15.3 60.9 150s Investment_21 19.0 69.5 150s Investment_22 21.1 75.7 150s PrivateWages_2 0.0 0.0 150s PrivateWages_3 0.0 0.0 150s PrivateWages_4 0.0 0.0 150s PrivateWages_5 0.0 0.0 150s PrivateWages_6 0.0 0.0 150s PrivateWages_7 0.0 0.0 150s PrivateWages_8 0.0 0.0 150s PrivateWages_9 0.0 0.0 150s PrivateWages_10 0.0 0.0 150s PrivateWages_11 0.0 0.0 150s PrivateWages_12 0.0 0.0 150s PrivateWages_13 0.0 0.0 150s PrivateWages_14 0.0 0.0 150s PrivateWages_15 0.0 0.0 150s PrivateWages_16 0.0 0.0 150s PrivateWages_17 0.0 0.0 150s PrivateWages_18 0.0 0.0 150s PrivateWages_19 0.0 0.0 150s PrivateWages_20 0.0 0.0 150s PrivateWages_21 0.0 0.0 150s PrivateWages_22 0.0 0.0 150s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 150s Consumption_2 0 0.0 0.0 150s Consumption_3 0 0.0 0.0 150s Consumption_4 0 0.0 0.0 150s Consumption_5 0 0.0 0.0 150s Consumption_6 0 0.0 0.0 150s Consumption_7 0 0.0 0.0 150s Consumption_8 0 0.0 0.0 150s Consumption_9 0 0.0 0.0 150s Consumption_10 0 0.0 0.0 150s Consumption_11 0 0.0 0.0 150s Consumption_12 0 0.0 0.0 150s Consumption_13 0 0.0 0.0 150s Consumption_14 0 0.0 0.0 150s Consumption_15 0 0.0 0.0 150s Consumption_16 0 0.0 0.0 150s Consumption_17 0 0.0 0.0 150s Consumption_18 0 0.0 0.0 150s Consumption_19 0 0.0 0.0 150s Consumption_20 0 0.0 0.0 150s Consumption_21 0 0.0 0.0 150s Consumption_22 0 0.0 0.0 150s Investment_2 0 0.0 0.0 150s Investment_3 0 0.0 0.0 150s Investment_4 0 0.0 0.0 150s Investment_5 0 0.0 0.0 150s Investment_6 0 0.0 0.0 150s Investment_7 0 0.0 0.0 150s Investment_8 0 0.0 0.0 150s Investment_9 0 0.0 0.0 150s Investment_10 0 0.0 0.0 150s Investment_11 0 0.0 0.0 150s Investment_12 0 0.0 0.0 150s Investment_13 0 0.0 0.0 150s Investment_14 0 0.0 0.0 150s Investment_15 0 0.0 0.0 150s Investment_16 0 0.0 0.0 150s Investment_17 0 0.0 0.0 150s Investment_18 0 0.0 0.0 150s Investment_19 0 0.0 0.0 150s Investment_20 0 0.0 0.0 150s Investment_21 0 0.0 0.0 150s Investment_22 0 0.0 0.0 150s PrivateWages_2 1 3.9 7.7 150s PrivateWages_3 1 3.2 3.9 150s PrivateWages_4 1 2.8 4.7 150s PrivateWages_5 1 3.5 3.8 150s PrivateWages_6 1 3.3 5.5 150s PrivateWages_7 1 3.3 7.0 150s PrivateWages_8 1 4.0 6.7 150s PrivateWages_9 1 4.2 4.2 150s PrivateWages_10 1 4.1 4.0 150s PrivateWages_11 1 5.2 7.7 150s PrivateWages_12 1 5.9 7.5 150s PrivateWages_13 1 4.9 8.3 150s PrivateWages_14 1 3.7 5.4 150s PrivateWages_15 1 4.0 6.8 150s PrivateWages_16 1 4.4 7.2 150s PrivateWages_17 1 2.9 8.3 150s PrivateWages_18 1 4.3 6.7 150s PrivateWages_19 1 5.3 7.4 150s PrivateWages_20 1 6.6 8.9 150s PrivateWages_21 1 7.4 9.6 150s PrivateWages_22 1 13.8 11.6 150s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 150s Consumption_2 0.0 0 0 150s Consumption_3 0.0 0 0 150s Consumption_4 0.0 0 0 150s Consumption_5 0.0 0 0 150s Consumption_6 0.0 0 0 150s Consumption_7 0.0 0 0 150s Consumption_8 0.0 0 0 150s Consumption_9 0.0 0 0 150s Consumption_10 0.0 0 0 150s Consumption_11 0.0 0 0 150s Consumption_12 0.0 0 0 150s Consumption_13 0.0 0 0 150s Consumption_14 0.0 0 0 150s Consumption_15 0.0 0 0 150s Consumption_16 0.0 0 0 150s Consumption_17 0.0 0 0 150s Consumption_18 0.0 0 0 150s Consumption_19 0.0 0 0 150s Consumption_20 0.0 0 0 150s Consumption_21 0.0 0 0 150s Consumption_22 0.0 0 0 150s Investment_2 0.0 0 0 150s Investment_3 0.0 0 0 150s Investment_4 0.0 0 0 150s Investment_5 0.0 0 0 150s Investment_6 0.0 0 0 150s Investment_7 0.0 0 0 150s Investment_8 0.0 0 0 150s Investment_9 0.0 0 0 150s Investment_10 0.0 0 0 150s Investment_11 0.0 0 0 150s Investment_12 0.0 0 0 150s Investment_13 0.0 0 0 150s Investment_14 0.0 0 0 150s Investment_15 0.0 0 0 150s Investment_16 0.0 0 0 150s Investment_17 0.0 0 0 150s Investment_18 0.0 0 0 150s Investment_19 0.0 0 0 150s Investment_20 0.0 0 0 150s Investment_21 0.0 0 0 150s Investment_22 0.0 0 0 150s PrivateWages_2 2.7 -10 183 150s PrivateWages_3 2.9 -9 183 150s PrivateWages_4 2.9 -8 184 150s PrivateWages_5 3.1 -7 190 150s PrivateWages_6 3.2 -6 193 150s PrivateWages_7 3.3 -5 198 150s PrivateWages_8 3.6 -4 203 150s PrivateWages_9 3.7 -3 208 150s PrivateWages_10 4.0 -2 211 150s PrivateWages_11 4.2 -1 216 150s PrivateWages_12 4.8 0 217 150s PrivateWages_13 5.3 1 213 150s PrivateWages_14 5.6 2 207 150s PrivateWages_15 6.0 3 202 150s PrivateWages_16 6.1 4 199 150s PrivateWages_17 7.4 5 198 150s PrivateWages_18 6.7 6 200 150s PrivateWages_19 7.7 7 202 150s PrivateWages_20 7.8 8 200 150s PrivateWages_21 8.0 9 201 150s PrivateWages_22 8.5 10 204 150s PrivateWages_corpProfLag PrivateWages_gnpLag 150s Consumption_2 0.0 0.0 150s Consumption_3 0.0 0.0 150s Consumption_4 0.0 0.0 150s Consumption_5 0.0 0.0 150s Consumption_6 0.0 0.0 150s Consumption_7 0.0 0.0 150s Consumption_8 0.0 0.0 150s Consumption_9 0.0 0.0 150s Consumption_10 0.0 0.0 150s Consumption_11 0.0 0.0 150s Consumption_12 0.0 0.0 150s Consumption_13 0.0 0.0 150s Consumption_14 0.0 0.0 150s Consumption_15 0.0 0.0 150s Consumption_16 0.0 0.0 150s Consumption_17 0.0 0.0 150s Consumption_18 0.0 0.0 150s Consumption_19 0.0 0.0 150s Consumption_20 0.0 0.0 150s Consumption_21 0.0 0.0 150s Consumption_22 0.0 0.0 150s Investment_2 0.0 0.0 150s Investment_3 0.0 0.0 150s Investment_4 0.0 0.0 150s Investment_5 0.0 0.0 150s Investment_6 0.0 0.0 150s Investment_7 0.0 0.0 150s Investment_8 0.0 0.0 150s Investment_9 0.0 0.0 150s Investment_10 0.0 0.0 150s Investment_11 0.0 0.0 150s Investment_12 0.0 0.0 150s Investment_13 0.0 0.0 150s Investment_14 0.0 0.0 150s Investment_15 0.0 0.0 150s Investment_16 0.0 0.0 150s Investment_17 0.0 0.0 150s Investment_18 0.0 0.0 150s Investment_19 0.0 0.0 150s Investment_20 0.0 0.0 150s Investment_21 0.0 0.0 150s Investment_22 0.0 0.0 150s PrivateWages_2 12.7 44.9 150s PrivateWages_3 12.4 45.6 150s PrivateWages_4 16.9 50.1 150s PrivateWages_5 18.4 57.2 150s PrivateWages_6 19.4 57.1 150s PrivateWages_7 20.1 61.0 150s PrivateWages_8 19.6 64.0 150s PrivateWages_9 19.8 64.4 150s PrivateWages_10 21.1 64.5 150s PrivateWages_11 21.7 67.0 150s PrivateWages_12 15.6 61.2 150s PrivateWages_13 11.4 53.4 150s PrivateWages_14 7.0 44.3 150s PrivateWages_15 11.2 45.1 150s PrivateWages_16 12.3 49.7 150s PrivateWages_17 14.0 54.4 150s PrivateWages_18 17.6 62.7 150s PrivateWages_19 17.3 65.0 150s PrivateWages_20 15.3 60.9 150s PrivateWages_21 19.0 69.5 150s PrivateWages_22 21.1 75.7 150s > matrix of fitted regressors 150s Consumption_(Intercept) Consumption_corpProf 150s Consumption_2 1 13.26 150s Consumption_3 1 16.58 150s Consumption_4 1 19.28 150s Consumption_5 1 20.96 150s Consumption_6 1 19.77 150s Consumption_7 1 18.24 150s Consumption_8 1 17.57 150s Consumption_9 1 19.54 150s Consumption_10 1 20.38 150s Consumption_11 1 17.18 150s Consumption_12 1 12.71 150s Consumption_13 1 9.00 150s Consumption_14 1 9.05 150s Consumption_15 1 12.67 150s Consumption_16 1 14.42 150s Consumption_17 1 14.71 150s Consumption_18 1 19.80 150s Consumption_19 1 19.21 150s Consumption_20 1 17.42 150s Consumption_21 1 20.31 150s Consumption_22 1 22.66 150s Investment_2 0 0.00 150s Investment_3 0 0.00 150s Investment_4 0 0.00 150s Investment_5 0 0.00 150s Investment_6 0 0.00 150s Investment_7 0 0.00 150s Investment_8 0 0.00 150s Investment_9 0 0.00 150s Investment_10 0 0.00 150s Investment_11 0 0.00 150s Investment_12 0 0.00 150s Investment_13 0 0.00 150s Investment_14 0 0.00 150s Investment_15 0 0.00 150s Investment_16 0 0.00 150s Investment_17 0 0.00 150s Investment_18 0 0.00 150s Investment_19 0 0.00 150s Investment_20 0 0.00 150s Investment_21 0 0.00 150s Investment_22 0 0.00 150s PrivateWages_2 0 0.00 150s PrivateWages_3 0 0.00 150s PrivateWages_4 0 0.00 150s PrivateWages_5 0 0.00 150s PrivateWages_6 0 0.00 150s PrivateWages_7 0 0.00 150s PrivateWages_8 0 0.00 150s PrivateWages_9 0 0.00 150s PrivateWages_10 0 0.00 150s PrivateWages_11 0 0.00 150s PrivateWages_12 0 0.00 150s PrivateWages_13 0 0.00 150s PrivateWages_14 0 0.00 150s PrivateWages_15 0 0.00 150s PrivateWages_16 0 0.00 150s PrivateWages_17 0 0.00 150s PrivateWages_18 0 0.00 150s PrivateWages_19 0 0.00 150s PrivateWages_20 0 0.00 150s PrivateWages_21 0 0.00 150s PrivateWages_22 0 0.00 150s Consumption_corpProfLag Consumption_wages 150s Consumption_2 12.7 29.4 150s Consumption_3 12.4 31.8 150s Consumption_4 16.9 35.8 150s Consumption_5 18.4 39.1 150s Consumption_6 19.4 39.1 150s Consumption_7 20.1 39.4 150s Consumption_8 19.6 40.2 150s Consumption_9 19.8 42.3 150s Consumption_10 21.1 44.0 150s Consumption_11 21.7 43.7 150s Consumption_12 15.6 39.5 150s Consumption_13 11.4 35.1 150s Consumption_14 7.0 32.8 150s Consumption_15 11.2 37.5 150s Consumption_16 12.3 40.1 150s Consumption_17 14.0 41.7 150s Consumption_18 17.6 47.9 150s Consumption_19 17.3 49.3 150s Consumption_20 15.3 48.4 150s Consumption_21 19.0 53.4 150s Consumption_22 21.1 60.7 150s Investment_2 0.0 0.0 150s Investment_3 0.0 0.0 150s Investment_4 0.0 0.0 150s Investment_5 0.0 0.0 150s Investment_6 0.0 0.0 150s Investment_7 0.0 0.0 150s Investment_8 0.0 0.0 150s Investment_9 0.0 0.0 150s Investment_10 0.0 0.0 150s Investment_11 0.0 0.0 150s Investment_12 0.0 0.0 150s Investment_13 0.0 0.0 150s Investment_14 0.0 0.0 150s Investment_15 0.0 0.0 150s Investment_16 0.0 0.0 150s Investment_17 0.0 0.0 150s Investment_18 0.0 0.0 150s Investment_19 0.0 0.0 150s Investment_20 0.0 0.0 150s Investment_21 0.0 0.0 150s Investment_22 0.0 0.0 150s PrivateWages_2 0.0 0.0 150s PrivateWages_3 0.0 0.0 150s PrivateWages_4 0.0 0.0 150s PrivateWages_5 0.0 0.0 150s PrivateWages_6 0.0 0.0 150s PrivateWages_7 0.0 0.0 150s PrivateWages_8 0.0 0.0 150s PrivateWages_9 0.0 0.0 150s PrivateWages_10 0.0 0.0 150s PrivateWages_11 0.0 0.0 150s PrivateWages_12 0.0 0.0 150s PrivateWages_13 0.0 0.0 150s PrivateWages_14 0.0 0.0 150s PrivateWages_15 0.0 0.0 150s PrivateWages_16 0.0 0.0 150s PrivateWages_17 0.0 0.0 150s PrivateWages_18 0.0 0.0 150s PrivateWages_19 0.0 0.0 150s PrivateWages_20 0.0 0.0 150s PrivateWages_21 0.0 0.0 150s PrivateWages_22 0.0 0.0 150s Investment_(Intercept) Investment_corpProf 150s Consumption_2 0 0.00 150s Consumption_3 0 0.00 150s Consumption_4 0 0.00 150s Consumption_5 0 0.00 150s Consumption_6 0 0.00 150s Consumption_7 0 0.00 150s Consumption_8 0 0.00 150s Consumption_9 0 0.00 150s Consumption_10 0 0.00 150s Consumption_11 0 0.00 150s Consumption_12 0 0.00 150s Consumption_13 0 0.00 150s Consumption_14 0 0.00 150s Consumption_15 0 0.00 150s Consumption_16 0 0.00 150s Consumption_17 0 0.00 150s Consumption_18 0 0.00 150s Consumption_19 0 0.00 150s Consumption_20 0 0.00 150s Consumption_21 0 0.00 150s Consumption_22 0 0.00 150s Investment_2 1 13.26 150s Investment_3 1 16.58 150s Investment_4 1 19.28 150s Investment_5 1 20.96 150s Investment_6 1 19.77 150s Investment_7 1 18.24 150s Investment_8 1 17.57 150s Investment_9 1 19.54 150s Investment_10 1 20.38 150s Investment_11 1 17.18 150s Investment_12 1 12.71 150s Investment_13 1 9.00 150s Investment_14 1 9.05 150s Investment_15 1 12.67 150s Investment_16 1 14.42 150s Investment_17 1 14.71 150s Investment_18 1 19.80 150s Investment_19 1 19.21 150s Investment_20 1 17.42 150s Investment_21 1 20.31 150s Investment_22 1 22.66 150s PrivateWages_2 0 0.00 150s PrivateWages_3 0 0.00 150s PrivateWages_4 0 0.00 150s PrivateWages_5 0 0.00 150s PrivateWages_6 0 0.00 150s PrivateWages_7 0 0.00 150s PrivateWages_8 0 0.00 150s PrivateWages_9 0 0.00 150s PrivateWages_10 0 0.00 150s PrivateWages_11 0 0.00 150s PrivateWages_12 0 0.00 150s PrivateWages_13 0 0.00 150s PrivateWages_14 0 0.00 150s PrivateWages_15 0 0.00 150s PrivateWages_16 0 0.00 150s PrivateWages_17 0 0.00 150s PrivateWages_18 0 0.00 150s PrivateWages_19 0 0.00 150s PrivateWages_20 0 0.00 150s PrivateWages_21 0 0.00 150s PrivateWages_22 0 0.00 150s Investment_corpProfLag Investment_capitalLag 150s Consumption_2 0.0 0 150s Consumption_3 0.0 0 150s Consumption_4 0.0 0 150s Consumption_5 0.0 0 150s Consumption_6 0.0 0 150s Consumption_7 0.0 0 150s Consumption_8 0.0 0 150s Consumption_9 0.0 0 150s Consumption_10 0.0 0 150s Consumption_11 0.0 0 150s Consumption_12 0.0 0 150s Consumption_13 0.0 0 150s Consumption_14 0.0 0 150s Consumption_15 0.0 0 150s Consumption_16 0.0 0 150s Consumption_17 0.0 0 150s Consumption_18 0.0 0 150s Consumption_19 0.0 0 150s Consumption_20 0.0 0 150s Consumption_21 0.0 0 150s Consumption_22 0.0 0 150s Investment_2 12.7 183 150s Investment_3 12.4 183 150s Investment_4 16.9 184 150s Investment_5 18.4 190 150s Investment_6 19.4 193 150s Investment_7 20.1 198 150s Investment_8 19.6 203 150s Investment_9 19.8 208 150s Investment_10 21.1 211 150s Investment_11 21.7 216 150s Investment_12 15.6 217 150s Investment_13 11.4 213 150s Investment_14 7.0 207 150s Investment_15 11.2 202 150s Investment_16 12.3 199 150s Investment_17 14.0 198 150s Investment_18 17.6 200 150s Investment_19 17.3 202 150s Investment_20 15.3 200 150s Investment_21 19.0 201 150s Investment_22 21.1 204 150s PrivateWages_2 0.0 0 150s PrivateWages_3 0.0 0 150s PrivateWages_4 0.0 0 150s PrivateWages_5 0.0 0 150s PrivateWages_6 0.0 0 150s PrivateWages_7 0.0 0 150s PrivateWages_8 0.0 0 150s PrivateWages_9 0.0 0 150s PrivateWages_10 0.0 0 150s PrivateWages_11 0.0 0 150s PrivateWages_12 0.0 0 150s PrivateWages_13 0.0 0 150s PrivateWages_14 0.0 0 150s PrivateWages_15 0.0 0 150s PrivateWages_16 0.0 0 150s PrivateWages_17 0.0 0 150s PrivateWages_18 0.0 0 150s PrivateWages_19 0.0 0 150s PrivateWages_20 0.0 0 150s PrivateWages_21 0.0 0 150s PrivateWages_22 0.0 0 150s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 150s Consumption_2 0 0.0 0.0 150s Consumption_3 0 0.0 0.0 150s Consumption_4 0 0.0 0.0 150s Consumption_5 0 0.0 0.0 150s Consumption_6 0 0.0 0.0 150s Consumption_7 0 0.0 0.0 150s Consumption_8 0 0.0 0.0 150s Consumption_9 0 0.0 0.0 150s Consumption_10 0 0.0 0.0 150s Consumption_11 0 0.0 0.0 150s Consumption_12 0 0.0 0.0 150s Consumption_13 0 0.0 0.0 150s Consumption_14 0 0.0 0.0 150s Consumption_15 0 0.0 0.0 150s Consumption_16 0 0.0 0.0 150s Consumption_17 0 0.0 0.0 150s Consumption_18 0 0.0 0.0 150s Consumption_19 0 0.0 0.0 150s Consumption_20 0 0.0 0.0 150s Consumption_21 0 0.0 0.0 150s Consumption_22 0 0.0 0.0 150s Investment_2 0 0.0 0.0 150s Investment_3 0 0.0 0.0 150s Investment_4 0 0.0 0.0 150s Investment_5 0 0.0 0.0 150s Investment_6 0 0.0 0.0 150s Investment_7 0 0.0 0.0 150s Investment_8 0 0.0 0.0 150s Investment_9 0 0.0 0.0 150s Investment_10 0 0.0 0.0 150s Investment_11 0 0.0 0.0 150s Investment_12 0 0.0 0.0 150s Investment_13 0 0.0 0.0 150s Investment_14 0 0.0 0.0 150s Investment_15 0 0.0 0.0 150s Investment_16 0 0.0 0.0 150s Investment_17 0 0.0 0.0 150s Investment_18 0 0.0 0.0 150s Investment_19 0 0.0 0.0 150s Investment_20 0 0.0 0.0 150s Investment_21 0 0.0 0.0 150s Investment_22 0 0.0 0.0 150s PrivateWages_2 1 47.7 44.9 150s PrivateWages_3 1 49.3 45.6 150s PrivateWages_4 1 56.8 50.1 150s PrivateWages_5 1 60.7 57.2 150s PrivateWages_6 1 61.2 57.1 150s PrivateWages_7 1 61.3 61.0 150s PrivateWages_8 1 60.9 64.0 150s PrivateWages_9 1 62.4 64.4 150s PrivateWages_10 1 64.4 64.5 150s PrivateWages_11 1 64.4 67.0 150s PrivateWages_12 1 54.9 61.2 150s PrivateWages_13 1 47.1 53.4 150s PrivateWages_14 1 41.6 44.3 150s PrivateWages_15 1 51.0 45.1 150s PrivateWages_16 1 55.7 49.7 150s PrivateWages_17 1 57.3 54.4 150s PrivateWages_18 1 67.7 62.7 150s PrivateWages_19 1 68.2 65.0 150s PrivateWages_20 1 66.9 60.9 150s PrivateWages_21 1 75.3 69.5 150s PrivateWages_22 1 86.5 75.7 150s PrivateWages_trend 150s Consumption_2 0 150s Consumption_3 0 150s Consumption_4 0 150s Consumption_5 0 150s Consumption_6 0 150s Consumption_7 0 150s Consumption_8 0 150s Consumption_9 0 150s Consumption_10 0 150s Consumption_11 0 150s Consumption_12 0 150s Consumption_13 0 150s Consumption_14 0 150s Consumption_15 0 150s Consumption_16 0 150s Consumption_17 0 150s Consumption_18 0 150s Consumption_19 0 150s Consumption_20 0 150s Consumption_21 0 150s Consumption_22 0 150s Investment_2 0 150s Investment_3 0 150s Investment_4 0 150s Investment_5 0 150s Investment_6 0 150s Investment_7 0 150s Investment_8 0 150s Investment_9 0 150s Investment_10 0 150s Investment_11 0 150s Investment_12 0 150s Investment_13 0 150s Investment_14 0 150s Investment_15 0 150s Investment_16 0 150s Investment_17 0 150s Investment_18 0 150s Investment_19 0 150s Investment_20 0 150s Investment_21 0 150s Investment_22 0 150s PrivateWages_2 -10 150s PrivateWages_3 -9 150s PrivateWages_4 -8 150s PrivateWages_5 -7 150s PrivateWages_6 -6 150s PrivateWages_7 -5 150s PrivateWages_8 -4 150s PrivateWages_9 -3 150s PrivateWages_10 -2 150s PrivateWages_11 -1 150s PrivateWages_12 0 150s PrivateWages_13 1 150s PrivateWages_14 2 150s PrivateWages_15 3 150s PrivateWages_16 4 150s PrivateWages_17 5 150s PrivateWages_18 6 150s PrivateWages_19 7 150s PrivateWages_20 8 150s PrivateWages_21 9 150s PrivateWages_22 10 150s > nobs 150s [1] 63 150s > linearHypothesis 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 1.08 0.3 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 1.29 0.26 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 52 150s 2 51 1 1.29 0.26 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.54 0.58 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.65 0.53 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 53 150s 2 51 2 1.3 0.52 150s > logLik 150s 'log Lik.' -76.3 (df=13) 150s 'log Lik.' -85.5 (df=13) 150s Estimating function 150s Consumption_(Intercept) Consumption_corpProf 150s Consumption_2 -1.455 -19.28 150s Consumption_3 -0.246 -4.08 150s Consumption_4 -0.309 -5.96 150s Consumption_5 -1.952 -40.92 150s Consumption_6 -0.199 -3.93 150s Consumption_7 2.000 36.47 150s Consumption_8 2.547 44.76 150s Consumption_9 1.829 35.74 150s Consumption_10 0.665 13.55 150s Consumption_11 -1.947 -33.46 150s Consumption_12 -1.232 -15.65 150s Consumption_13 -2.039 -18.35 150s Consumption_14 1.714 15.52 150s Consumption_15 -0.877 -11.11 150s Consumption_16 -0.684 -9.87 150s Consumption_17 4.077 59.98 150s Consumption_18 -0.793 -15.70 150s Consumption_19 -3.072 -59.01 150s Consumption_20 2.230 38.84 150s Consumption_21 0.744 15.11 150s Consumption_22 -1.000 -22.66 150s Investment_2 0.000 0.00 150s Investment_3 0.000 0.00 150s Investment_4 0.000 0.00 150s Investment_5 0.000 0.00 150s Investment_6 0.000 0.00 150s Investment_7 0.000 0.00 150s Investment_8 0.000 0.00 150s Investment_9 0.000 0.00 150s Investment_10 0.000 0.00 150s Investment_11 0.000 0.00 150s Investment_12 0.000 0.00 150s Investment_13 0.000 0.00 150s Investment_14 0.000 0.00 150s Investment_15 0.000 0.00 150s Investment_16 0.000 0.00 150s Investment_17 0.000 0.00 150s Investment_18 0.000 0.00 150s Investment_19 0.000 0.00 150s Investment_20 0.000 0.00 150s Investment_21 0.000 0.00 150s Investment_22 0.000 0.00 150s PrivateWages_2 0.000 0.00 150s PrivateWages_3 0.000 0.00 150s PrivateWages_4 0.000 0.00 150s PrivateWages_5 0.000 0.00 150s PrivateWages_6 0.000 0.00 150s PrivateWages_7 0.000 0.00 150s PrivateWages_8 0.000 0.00 150s PrivateWages_9 0.000 0.00 150s PrivateWages_10 0.000 0.00 150s PrivateWages_11 0.000 0.00 150s PrivateWages_12 0.000 0.00 150s PrivateWages_13 0.000 0.00 150s PrivateWages_14 0.000 0.00 150s PrivateWages_15 0.000 0.00 150s PrivateWages_16 0.000 0.00 150s PrivateWages_17 0.000 0.00 150s PrivateWages_18 0.000 0.00 150s PrivateWages_19 0.000 0.00 150s PrivateWages_20 0.000 0.00 150s PrivateWages_21 0.000 0.00 150s PrivateWages_22 0.000 0.00 150s Consumption_corpProfLag Consumption_wages 150s Consumption_2 -18.47 -42.77 150s Consumption_3 -3.05 -7.82 150s Consumption_4 -5.22 -11.05 150s Consumption_5 -35.93 -76.29 150s Consumption_6 -3.85 -7.77 150s Consumption_7 40.20 78.70 150s Consumption_8 49.93 102.36 150s Consumption_9 36.21 77.42 150s Consumption_10 14.03 29.28 150s Consumption_11 -42.26 -85.10 150s Consumption_12 -19.22 -48.63 150s Consumption_13 -23.25 -71.64 150s Consumption_14 12.00 56.20 150s Consumption_15 -9.82 -32.89 150s Consumption_16 -8.42 -27.47 150s Consumption_17 57.07 170.01 150s Consumption_18 -13.96 -37.97 150s Consumption_19 -53.15 -151.48 150s Consumption_20 34.12 107.90 150s Consumption_21 14.14 39.73 150s Consumption_22 -21.10 -60.72 150s Investment_2 0.00 0.00 150s Investment_3 0.00 0.00 150s Investment_4 0.00 0.00 150s Investment_5 0.00 0.00 150s Investment_6 0.00 0.00 150s Investment_7 0.00 0.00 150s Investment_8 0.00 0.00 150s Investment_9 0.00 0.00 150s Investment_10 0.00 0.00 150s Investment_11 0.00 0.00 150s Investment_12 0.00 0.00 150s Investment_13 0.00 0.00 150s Investment_14 0.00 0.00 150s Investment_15 0.00 0.00 150s Investment_16 0.00 0.00 150s Investment_17 0.00 0.00 150s Investment_18 0.00 0.00 150s Investment_19 0.00 0.00 150s Investment_20 0.00 0.00 150s Investment_21 0.00 0.00 150s Investment_22 0.00 0.00 150s PrivateWages_2 0.00 0.00 150s PrivateWages_3 0.00 0.00 150s PrivateWages_4 0.00 0.00 150s PrivateWages_5 0.00 0.00 150s PrivateWages_6 0.00 0.00 150s PrivateWages_7 0.00 0.00 150s PrivateWages_8 0.00 0.00 150s PrivateWages_9 0.00 0.00 150s PrivateWages_10 0.00 0.00 150s PrivateWages_11 0.00 0.00 150s PrivateWages_12 0.00 0.00 150s PrivateWages_13 0.00 0.00 150s PrivateWages_14 0.00 0.00 150s PrivateWages_15 0.00 0.00 150s PrivateWages_16 0.00 0.00 150s PrivateWages_17 0.00 0.00 150s PrivateWages_18 0.00 0.00 150s PrivateWages_19 0.00 0.00 150s PrivateWages_20 0.00 0.00 150s PrivateWages_21 0.00 0.00 150s PrivateWages_22 0.00 0.00 150s Investment_(Intercept) Investment_corpProf 150s Consumption_2 0.0000 0.000 150s Consumption_3 0.0000 0.000 150s Consumption_4 0.0000 0.000 150s Consumption_5 0.0000 0.000 150s Consumption_6 0.0000 0.000 150s Consumption_7 0.0000 0.000 150s Consumption_8 0.0000 0.000 150s Consumption_9 0.0000 0.000 150s Consumption_10 0.0000 0.000 150s Consumption_11 0.0000 0.000 150s Consumption_12 0.0000 0.000 150s Consumption_13 0.0000 0.000 150s Consumption_14 0.0000 0.000 150s Consumption_15 0.0000 0.000 150s Consumption_16 0.0000 0.000 150s Consumption_17 0.0000 0.000 150s Consumption_18 0.0000 0.000 150s Consumption_19 0.0000 0.000 150s Consumption_20 0.0000 0.000 150s Consumption_21 0.0000 0.000 150s Consumption_22 0.0000 0.000 150s Investment_2 -1.4484 -19.199 150s Investment_3 0.3058 5.070 150s Investment_4 0.7275 14.029 150s Investment_5 -1.8279 -38.314 150s Investment_6 0.3088 6.104 150s Investment_7 1.4119 25.751 150s Investment_8 1.3034 22.906 150s Investment_9 0.3472 6.785 150s Investment_10 1.9947 40.642 150s Investment_11 -1.1903 -20.449 150s Investment_12 -1.0029 -12.742 150s Investment_13 -1.1958 -10.762 150s Investment_14 1.6279 14.739 150s Investment_15 -0.2072 -2.625 150s Investment_16 0.0790 1.140 150s Investment_17 2.1831 32.118 150s Investment_18 -0.5667 -11.219 150s Investment_19 -3.8778 -74.479 150s Investment_20 0.5228 9.107 150s Investment_21 0.0154 0.312 150s Investment_22 0.4893 11.087 150s PrivateWages_2 0.0000 0.000 150s PrivateWages_3 0.0000 0.000 150s PrivateWages_4 0.0000 0.000 150s PrivateWages_5 0.0000 0.000 150s PrivateWages_6 0.0000 0.000 150s PrivateWages_7 0.0000 0.000 150s PrivateWages_8 0.0000 0.000 150s PrivateWages_9 0.0000 0.000 150s PrivateWages_10 0.0000 0.000 150s PrivateWages_11 0.0000 0.000 150s PrivateWages_12 0.0000 0.000 150s PrivateWages_13 0.0000 0.000 150s PrivateWages_14 0.0000 0.000 150s PrivateWages_15 0.0000 0.000 150s PrivateWages_16 0.0000 0.000 150s PrivateWages_17 0.0000 0.000 150s PrivateWages_18 0.0000 0.000 150s PrivateWages_19 0.0000 0.000 150s PrivateWages_20 0.0000 0.000 150s PrivateWages_21 0.0000 0.000 150s PrivateWages_22 0.0000 0.000 150s Investment_corpProfLag Investment_capitalLag 150s Consumption_2 0.000 0.0 150s Consumption_3 0.000 0.0 150s Consumption_4 0.000 0.0 150s Consumption_5 0.000 0.0 150s Consumption_6 0.000 0.0 150s Consumption_7 0.000 0.0 150s Consumption_8 0.000 0.0 150s Consumption_9 0.000 0.0 150s Consumption_10 0.000 0.0 150s Consumption_11 0.000 0.0 150s Consumption_12 0.000 0.0 150s Consumption_13 0.000 0.0 150s Consumption_14 0.000 0.0 150s Consumption_15 0.000 0.0 150s Consumption_16 0.000 0.0 150s Consumption_17 0.000 0.0 150s Consumption_18 0.000 0.0 150s Consumption_19 0.000 0.0 150s Consumption_20 0.000 0.0 150s Consumption_21 0.000 0.0 150s Consumption_22 0.000 0.0 150s Investment_2 -18.395 -264.8 150s Investment_3 3.792 55.8 150s Investment_4 12.295 134.2 150s Investment_5 -33.634 -346.8 150s Investment_6 5.991 59.5 150s Investment_7 28.378 279.3 150s Investment_8 25.548 265.1 150s Investment_9 6.875 72.1 150s Investment_10 42.088 420.1 150s Investment_11 -25.829 -256.7 150s Investment_12 -15.646 -217.3 150s Investment_13 -13.632 -255.1 150s Investment_14 11.395 337.1 150s Investment_15 -2.320 -41.8 150s Investment_16 0.972 15.7 150s Investment_17 30.564 431.6 150s Investment_18 -9.974 -113.2 150s Investment_19 -67.085 -782.5 150s Investment_20 7.999 104.5 150s Investment_21 0.292 3.1 150s Investment_22 10.325 100.1 150s PrivateWages_2 0.000 0.0 150s PrivateWages_3 0.000 0.0 150s PrivateWages_4 0.000 0.0 150s PrivateWages_5 0.000 0.0 150s PrivateWages_6 0.000 0.0 150s PrivateWages_7 0.000 0.0 150s PrivateWages_8 0.000 0.0 150s PrivateWages_9 0.000 0.0 150s PrivateWages_10 0.000 0.0 150s PrivateWages_11 0.000 0.0 150s PrivateWages_12 0.000 0.0 150s PrivateWages_13 0.000 0.0 150s PrivateWages_14 0.000 0.0 150s PrivateWages_15 0.000 0.0 150s PrivateWages_16 0.000 0.0 150s PrivateWages_17 0.000 0.0 150s PrivateWages_18 0.000 0.0 150s PrivateWages_19 0.000 0.0 150s PrivateWages_20 0.000 0.0 150s PrivateWages_21 0.000 0.0 150s PrivateWages_22 0.000 0.0 150s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 150s Consumption_2 0.0000 0.00 0.00 150s Consumption_3 0.0000 0.00 0.00 150s Consumption_4 0.0000 0.00 0.00 150s Consumption_5 0.0000 0.00 0.00 150s Consumption_6 0.0000 0.00 0.00 150s Consumption_7 0.0000 0.00 0.00 150s Consumption_8 0.0000 0.00 0.00 150s Consumption_9 0.0000 0.00 0.00 150s Consumption_10 0.0000 0.00 0.00 150s Consumption_11 0.0000 0.00 0.00 150s Consumption_12 0.0000 0.00 0.00 150s Consumption_13 0.0000 0.00 0.00 150s Consumption_14 0.0000 0.00 0.00 150s Consumption_15 0.0000 0.00 0.00 150s Consumption_16 0.0000 0.00 0.00 150s Consumption_17 0.0000 0.00 0.00 150s Consumption_18 0.0000 0.00 0.00 150s Consumption_19 0.0000 0.00 0.00 150s Consumption_20 0.0000 0.00 0.00 150s Consumption_21 0.0000 0.00 0.00 150s Consumption_22 0.0000 0.00 0.00 150s Investment_2 0.0000 0.00 0.00 150s Investment_3 0.0000 0.00 0.00 150s Investment_4 0.0000 0.00 0.00 150s Investment_5 0.0000 0.00 0.00 150s Investment_6 0.0000 0.00 0.00 150s Investment_7 0.0000 0.00 0.00 150s Investment_8 0.0000 0.00 0.00 150s Investment_9 0.0000 0.00 0.00 150s Investment_10 0.0000 0.00 0.00 150s Investment_11 0.0000 0.00 0.00 150s Investment_12 0.0000 0.00 0.00 150s Investment_13 0.0000 0.00 0.00 150s Investment_14 0.0000 0.00 0.00 150s Investment_15 0.0000 0.00 0.00 150s Investment_16 0.0000 0.00 0.00 150s Investment_17 0.0000 0.00 0.00 150s Investment_18 0.0000 0.00 0.00 150s Investment_19 0.0000 0.00 0.00 150s Investment_20 0.0000 0.00 0.00 150s Investment_21 0.0000 0.00 0.00 150s Investment_22 0.0000 0.00 0.00 150s PrivateWages_2 -2.1987 -104.79 -98.72 150s PrivateWages_3 0.6372 31.43 29.06 150s PrivateWages_4 1.3519 76.84 67.73 150s PrivateWages_5 -1.7306 -105.10 -98.99 150s PrivateWages_6 -0.5521 -33.79 -31.52 150s PrivateWages_7 0.7059 43.27 43.06 150s PrivateWages_8 0.8269 50.32 52.92 150s PrivateWages_9 1.2718 79.33 81.90 150s PrivateWages_10 2.3392 150.64 150.88 150s PrivateWages_11 -1.5500 -99.78 -103.85 150s PrivateWages_12 -0.0625 -3.43 -3.82 150s PrivateWages_13 -1.1474 -54.08 -61.27 150s PrivateWages_14 1.9682 81.95 87.19 150s PrivateWages_15 -0.2753 -14.03 -12.42 150s PrivateWages_16 -0.5389 -30.00 -26.78 150s PrivateWages_17 1.5156 86.87 82.45 150s PrivateWages_18 -0.1787 -12.09 -11.21 150s PrivateWages_19 -3.6814 -251.10 -239.29 150s PrivateWages_20 0.7597 50.83 46.27 150s PrivateWages_21 -0.9040 -68.05 -62.83 150s PrivateWages_22 1.4431 124.79 109.24 150s PrivateWages_trend 150s Consumption_2 0.000 150s Consumption_3 0.000 150s Consumption_4 0.000 150s Consumption_5 0.000 150s Consumption_6 0.000 150s Consumption_7 0.000 150s Consumption_8 0.000 150s Consumption_9 0.000 150s Consumption_10 0.000 150s Consumption_11 0.000 150s Consumption_12 0.000 150s Consumption_13 0.000 150s Consumption_14 0.000 150s Consumption_15 0.000 150s Consumption_16 0.000 150s Consumption_17 0.000 150s Consumption_18 0.000 150s Consumption_19 0.000 150s Consumption_20 0.000 150s Consumption_21 0.000 150s Consumption_22 0.000 150s Investment_2 0.000 150s Investment_3 0.000 150s Investment_4 0.000 150s Investment_5 0.000 150s Investment_6 0.000 150s Investment_7 0.000 150s Investment_8 0.000 150s Investment_9 0.000 150s Investment_10 0.000 150s Investment_11 0.000 150s Investment_12 0.000 150s Investment_13 0.000 150s Investment_14 0.000 150s Investment_15 0.000 150s Investment_16 0.000 150s Investment_17 0.000 150s Investment_18 0.000 150s Investment_19 0.000 150s Investment_20 0.000 150s Investment_21 0.000 150s Investment_22 0.000 150s PrivateWages_2 21.987 150s PrivateWages_3 -5.735 150s PrivateWages_4 -10.815 150s PrivateWages_5 12.114 150s PrivateWages_6 3.312 150s PrivateWages_7 -3.529 150s PrivateWages_8 -3.307 150s PrivateWages_9 -3.815 150s PrivateWages_10 -4.678 150s PrivateWages_11 1.550 150s PrivateWages_12 0.000 150s PrivateWages_13 -1.147 150s PrivateWages_14 3.936 150s PrivateWages_15 -0.826 150s PrivateWages_16 -2.156 150s PrivateWages_17 7.578 150s PrivateWages_18 -1.072 150s PrivateWages_19 -25.769 150s PrivateWages_20 6.078 150s PrivateWages_21 -8.136 150s PrivateWages_22 14.431 150s [1] TRUE 150s > Bread 150s Consumption_(Intercept) Consumption_corpProf 150s Consumption_(Intercept) 105.265 -0.9259 150s Consumption_corpProf -0.926 0.8409 150s Consumption_corpProfLag -0.287 -0.5775 150s Consumption_wages -1.975 -0.0921 150s Investment_(Intercept) 0.000 0.0000 150s Investment_corpProf 0.000 0.0000 150s Investment_corpProfLag 0.000 0.0000 150s Investment_capitalLag 0.000 0.0000 150s PrivateWages_(Intercept) 0.000 0.0000 150s PrivateWages_gnp 0.000 0.0000 150s PrivateWages_gnpLag 0.000 0.0000 150s PrivateWages_trend 0.000 0.0000 150s Consumption_corpProfLag Consumption_wages 150s Consumption_(Intercept) -0.287 -1.9751 150s Consumption_corpProf -0.578 -0.0921 150s Consumption_corpProfLag 0.694 -0.0320 150s Consumption_wages -0.032 0.0978 150s Investment_(Intercept) 0.000 0.0000 150s Investment_corpProf 0.000 0.0000 150s Investment_corpProfLag 0.000 0.0000 150s Investment_capitalLag 0.000 0.0000 150s PrivateWages_(Intercept) 0.000 0.0000 150s PrivateWages_gnp 0.000 0.0000 150s PrivateWages_gnpLag 0.000 0.0000 150s PrivateWages_trend 0.000 0.0000 150s Investment_(Intercept) Investment_corpProf 150s Consumption_(Intercept) 0.0 0.000 150s Consumption_corpProf 0.0 0.000 150s Consumption_corpProfLag 0.0 0.000 150s Consumption_wages 0.0 0.000 150s Investment_(Intercept) 2591.3 -42.124 150s Investment_corpProf -42.1 1.367 150s Investment_corpProfLag 35.4 -1.174 150s Investment_capitalLag -12.3 0.191 150s PrivateWages_(Intercept) 0.0 0.000 150s PrivateWages_gnp 0.0 0.000 150s PrivateWages_gnpLag 0.0 0.000 150s PrivateWages_trend 0.0 0.000 150s Investment_corpProfLag Investment_capitalLag 150s Consumption_(Intercept) 0.000 0.0000 150s Consumption_corpProf 0.000 0.0000 150s Consumption_corpProfLag 0.000 0.0000 150s Consumption_wages 0.000 0.0000 150s Investment_(Intercept) 35.417 -12.2536 150s Investment_corpProf -1.174 0.1908 150s Investment_corpProfLag 1.207 -0.1763 150s Investment_capitalLag -0.176 0.0594 150s PrivateWages_(Intercept) 0.000 0.0000 150s PrivateWages_gnp 0.000 0.0000 150s PrivateWages_gnpLag 0.000 0.0000 150s PrivateWages_trend 0.000 0.0000 150s PrivateWages_(Intercept) PrivateWages_gnp 150s Consumption_(Intercept) 0.000 0.0000 150s Consumption_corpProf 0.000 0.0000 150s Consumption_corpProfLag 0.000 0.0000 150s Consumption_wages 0.000 0.0000 150s Investment_(Intercept) 0.000 0.0000 150s Investment_corpProf 0.000 0.0000 150s Investment_corpProfLag 0.000 0.0000 150s Investment_capitalLag 0.000 0.0000 150s PrivateWages_(Intercept) 174.205 -0.8839 150s PrivateWages_gnp -0.884 0.1679 150s PrivateWages_gnpLag -2.037 -0.1586 150s PrivateWages_trend 2.064 -0.0409 150s PrivateWages_gnpLag PrivateWages_trend 150s Consumption_(Intercept) 0.00000 0.00000 150s Consumption_corpProf 0.00000 0.00000 150s Consumption_corpProfLag 0.00000 0.00000 150s Consumption_wages 0.00000 0.00000 150s Investment_(Intercept) 0.00000 0.00000 150s Investment_corpProf 0.00000 0.00000 150s Investment_corpProfLag 0.00000 0.00000 150s Investment_capitalLag 0.00000 0.00000 150s PrivateWages_(Intercept) -2.03709 2.06394 150s PrivateWages_gnp -0.15864 -0.04088 150s PrivateWages_gnpLag 0.19944 0.00675 150s PrivateWages_trend 0.00675 0.11229 150s > 150s > # SUR 150s > summary 150s 150s systemfit results 150s method: SUR 150s 150s N DF SSR detRCov OLS-R2 McElroy-R2 150s system 63 51 46.5 0.158 0.977 0.993 150s 150s N DF SSR MSE RMSE R2 Adj R2 150s Consumption 21 17 18.1 1.065 1.032 0.981 0.977 150s Investment 21 17 17.6 1.036 1.018 0.930 0.918 150s PrivateWages 21 17 10.8 0.633 0.796 0.986 0.984 150s 150s The covariance matrix of the residuals used for estimation 150s Consumption Investment PrivateWages 150s Consumption 0.8514 0.0495 -0.381 150s Investment 0.0495 0.8249 0.121 150s PrivateWages -0.3808 0.1212 0.476 150s 150s The covariance matrix of the residuals 150s Consumption Investment PrivateWages 150s Consumption 0.8618 0.0766 -0.437 150s Investment 0.0766 0.8384 0.203 150s PrivateWages -0.4368 0.2027 0.513 150s 150s The correlations of the residuals 150s Consumption Investment PrivateWages 150s Consumption 1.0000 0.0901 -0.657 150s Investment 0.0901 1.0000 0.309 150s PrivateWages -0.6572 0.3092 1.000 150s 150s 150s SUR estimates for 'Consumption' (equation 1) 150s Model Formula: consump ~ corpProf + corpProfLag + wages 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 15.9805 1.1687 13.67 1.3e-10 *** 150s corpProf 0.2302 0.0767 3.00 0.008 ** 150s corpProfLag 0.0673 0.0769 0.87 0.394 150s wages 0.7962 0.0353 22.58 4.1e-14 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.032 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 18.098 MSE: 1.065 Root MSE: 1.032 150s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 150s 150s 150s SUR estimates for 'Investment' (equation 2) 150s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 12.9293 4.8014 2.69 0.01540 * 150s corpProf 0.4429 0.0861 5.15 8.1e-05 *** 150s corpProfLag 0.3655 0.0894 4.09 0.00077 *** 150s capitalLag -0.1253 0.0235 -5.34 5.4e-05 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.018 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 17.606 MSE: 1.036 Root MSE: 1.018 150s Multiple R-Squared: 0.93 Adjusted R-Squared: 0.918 150s 150s 150s SUR estimates for 'PrivateWages' (equation 3) 150s Model Formula: privWage ~ gnp + gnpLag + trend 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 1.6347 1.1173 1.46 0.16 150s gnp 0.4098 0.0273 15.04 3.0e-11 *** 150s gnpLag 0.1744 0.0312 5.59 3.2e-05 *** 150s trend 0.1558 0.0276 5.65 2.9e-05 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 0.796 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 10.763 MSE: 0.633 Root MSE: 0.796 150s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 150s 150s > residuals 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 -0.24064 -0.3522 -1.0960 150s 3 -1.34080 -0.1605 0.5818 150s 4 -1.61038 1.0687 1.5313 150s 5 -0.54147 -1.4707 -0.0220 150s 6 -0.04372 0.3299 -0.2587 150s 7 0.85234 1.4346 -0.3243 150s 8 1.30302 0.8306 -0.6674 150s 9 0.97574 -0.4918 0.3660 150s 10 -0.66060 1.2434 1.2682 150s 11 0.45069 0.2647 -0.3467 150s 12 -0.04295 0.0795 0.3057 150s 13 -0.06686 0.3369 -0.2602 150s 14 0.32177 0.4080 0.3434 150s 15 -0.00441 -0.1533 0.2628 150s 16 -0.01931 0.0158 -0.0216 150s 17 1.53656 1.0372 -0.7988 150s 18 -0.42317 0.0176 0.8550 150s 19 0.29041 -2.6364 -0.8217 150s 20 0.88685 -0.5822 -0.3869 150s 21 0.68839 -0.7015 -1.1838 150s 22 -2.31147 -0.5183 0.6742 150s > fitted 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 42.1 0.152 26.6 150s 3 46.3 2.060 28.7 150s 4 50.8 4.131 32.6 150s 5 51.1 4.471 33.9 150s 6 52.6 4.770 35.7 150s 7 54.2 4.165 37.7 150s 8 54.9 3.369 38.6 150s 9 56.3 3.492 38.8 150s 10 58.5 3.857 40.0 150s 11 54.5 0.735 38.2 150s 12 50.9 -3.479 34.2 150s 13 45.7 -6.537 29.3 150s 14 46.2 -5.508 28.2 150s 15 48.7 -2.847 30.3 150s 16 51.3 -1.316 33.2 150s 17 56.2 1.063 37.6 150s 18 59.1 1.982 40.1 150s 19 57.2 0.736 39.0 150s 20 60.7 1.882 42.0 150s 21 64.3 4.002 46.2 150s 22 72.0 5.418 52.6 150s > predict 150s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 150s 1 NA NA NA NA 150s 2 42.1 0.415 41.3 43.0 150s 3 46.3 0.449 45.4 47.2 150s 4 50.8 0.300 50.2 51.4 150s 5 51.1 0.348 50.4 51.8 150s 6 52.6 0.350 51.9 53.3 150s 7 54.2 0.317 53.6 54.9 150s 8 54.9 0.289 54.3 55.5 150s 9 56.3 0.309 55.7 56.9 150s 10 58.5 0.328 57.8 59.1 150s 11 54.5 0.516 53.5 55.6 150s 12 50.9 0.414 50.1 51.8 150s 13 45.7 0.544 44.6 46.8 150s 14 46.2 0.527 45.1 47.2 150s 15 48.7 0.332 48.0 49.4 150s 16 51.3 0.295 50.7 51.9 150s 17 56.2 0.319 55.5 56.8 150s 18 59.1 0.286 58.5 59.7 150s 19 57.2 0.323 56.6 57.9 150s 20 60.7 0.381 59.9 61.5 150s 21 64.3 0.381 63.5 65.1 150s 22 72.0 0.597 70.8 73.2 150s Investment.pred Investment.se.fit Investment.lwr Investment.upr 150s 1 NA NA NA NA 150s 2 0.152 0.536 -0.924 1.229 150s 3 2.060 0.446 1.166 2.955 150s 4 4.131 0.397 3.334 4.929 150s 5 4.471 0.329 3.809 5.132 150s 6 4.770 0.311 4.145 5.395 150s 7 4.165 0.294 3.575 4.756 150s 8 3.369 0.263 2.842 3.897 150s 9 3.492 0.347 2.796 4.188 150s 10 3.857 0.398 3.058 4.656 150s 11 0.735 0.539 -0.346 1.816 150s 12 -3.479 0.454 -4.390 -2.569 150s 13 -6.537 0.552 -7.646 -5.428 150s 14 -5.508 0.617 -6.747 -4.269 150s 15 -2.847 0.335 -3.519 -2.175 150s 16 -1.316 0.287 -1.892 -0.739 150s 17 1.063 0.311 0.439 1.686 150s 18 1.982 0.218 1.545 2.420 150s 19 0.736 0.279 0.176 1.296 150s 20 1.882 0.327 1.227 2.538 150s 21 4.002 0.297 3.405 4.598 150s 22 5.418 0.412 4.591 6.245 150s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 150s 1 NA NA NA NA 150s 2 26.6 0.313 26.0 27.2 150s 3 28.7 0.310 28.1 29.3 150s 4 32.6 0.305 32.0 33.2 150s 5 33.9 0.236 33.4 34.4 150s 6 35.7 0.233 35.2 36.1 150s 7 37.7 0.234 37.3 38.2 150s 8 38.6 0.239 38.1 39.0 150s 9 38.8 0.229 38.4 39.3 150s 10 40.0 0.219 39.6 40.5 150s 11 38.2 0.301 37.6 38.9 150s 12 34.2 0.308 33.6 34.8 150s 13 29.3 0.370 28.5 30.0 150s 14 28.2 0.332 27.5 28.8 150s 15 30.3 0.324 29.7 31.0 150s 16 33.2 0.271 32.7 33.8 150s 17 37.6 0.263 37.1 38.1 150s 18 40.1 0.211 39.7 40.6 150s 19 39.0 0.306 38.4 39.6 150s 20 42.0 0.280 41.4 42.5 150s 21 46.2 0.298 45.6 46.8 150s 22 52.6 0.445 51.7 53.5 150s > model.frame 150s [1] TRUE 150s > model.matrix 150s [1] TRUE 150s > nobs 150s [1] 63 150s > linearHypothesis 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 1.44 0.24 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 1.69 0.2 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 52 150s 2 51 1 1.69 0.19 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.77 0.47 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.91 0.41 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 53 150s 2 51 2 1.83 0.4 150s > logLik 150s 'log Lik.' -70 (df=18) 150s 'log Lik.' -79 (df=18) 150s Estimating function 150s Consumption_(Intercept) Consumption_corpProf 150s Consumption_2 -0.46275 -5.7381 150s Consumption_3 -2.57830 -43.5733 150s Consumption_4 -3.09670 -56.9792 150s Consumption_5 -1.04122 -20.1997 150s Consumption_6 -0.08406 -1.6897 150s Consumption_7 1.63901 32.1246 150s Consumption_8 2.50567 49.6122 150s Consumption_9 1.87631 39.5902 150s Consumption_10 -1.27032 -27.5659 150s Consumption_11 0.86667 13.5200 150s Consumption_12 -0.08259 -0.9415 150s Consumption_13 -0.12857 -0.9000 150s Consumption_14 0.61874 6.9299 150s Consumption_15 -0.00847 -0.1042 150s Consumption_16 -0.03714 -0.5200 150s Consumption_17 2.95475 52.0036 150s Consumption_18 -0.81375 -14.0778 150s Consumption_19 0.55845 8.5443 150s Consumption_20 1.70539 32.4023 150s Consumption_21 1.32376 27.9312 150s Consumption_22 -4.44487 -104.4543 150s Investment_2 0.12481 1.5477 150s Investment_3 0.05687 0.9611 150s Investment_4 -0.37877 -6.9693 150s Investment_5 0.52122 10.1116 150s Investment_6 -0.11690 -2.3498 150s Investment_7 -0.50845 -9.9656 150s Investment_8 -0.29439 -5.8289 150s Investment_9 0.17430 3.6777 150s Investment_10 -0.44066 -9.5623 150s Investment_11 -0.09381 -1.4634 150s Investment_12 -0.02816 -0.3210 150s Investment_13 -0.11941 -0.8359 150s Investment_14 -0.14460 -1.6195 150s Investment_15 0.05435 0.6685 150s Investment_16 -0.00559 -0.0783 150s Investment_17 -0.36761 -6.4700 150s Investment_18 -0.00622 -0.1077 150s Investment_19 0.93438 14.2960 150s Investment_20 0.20633 3.9202 150s Investment_21 0.24863 5.2460 150s Investment_22 0.18369 4.3168 150s PrivateWages_2 -1.78352 -22.1156 150s PrivateWages_3 0.94670 15.9992 150s PrivateWages_4 2.49170 45.8473 150s PrivateWages_5 -0.03583 -0.6950 150s PrivateWages_6 -0.42104 -8.4630 150s PrivateWages_7 -0.52776 -10.3441 150s PrivateWages_8 -1.08598 -21.5024 150s PrivateWages_9 0.59560 12.5672 150s PrivateWages_10 2.06359 44.7800 150s PrivateWages_11 -0.56422 -8.8019 150s PrivateWages_12 0.49749 5.6714 150s PrivateWages_13 -0.42337 -2.9636 150s PrivateWages_14 0.55874 6.2579 150s PrivateWages_15 0.42760 5.2595 150s PrivateWages_16 -0.03516 -0.4922 150s PrivateWages_17 -1.29986 -22.8775 150s PrivateWages_18 1.39131 24.0696 150s PrivateWages_19 -1.33711 -20.4578 150s PrivateWages_20 -0.62964 -11.9631 150s PrivateWages_21 -1.92625 -40.6439 150s PrivateWages_22 1.09700 25.7794 150s Consumption_corpProfLag Consumption_wages 150s Consumption_2 -5.8769 -13.049 150s Consumption_3 -31.9709 -83.021 150s Consumption_4 -52.3342 -114.578 150s Consumption_5 -19.1585 -38.525 150s Consumption_6 -1.6308 -3.245 150s Consumption_7 32.9441 66.708 150s Consumption_8 49.1110 103.985 150s Consumption_9 37.1510 80.494 150s Consumption_10 -26.8037 -57.545 150s Consumption_11 18.8066 36.487 150s Consumption_12 -1.2884 -3.246 150s Consumption_13 -1.4658 -4.410 150s Consumption_14 4.3312 21.099 150s Consumption_15 -0.0949 -0.310 150s Consumption_16 -0.4568 -1.460 150s Consumption_17 41.3665 130.600 150s Consumption_18 -14.3220 -38.816 150s Consumption_19 9.6612 25.633 150s Consumption_20 26.0924 84.246 150s Consumption_21 25.1514 70.159 150s Consumption_22 -93.7867 -274.693 150s Investment_2 1.5851 3.520 150s Investment_3 0.7052 1.831 150s Investment_4 -6.4012 -14.014 150s Investment_5 9.5904 19.285 150s Investment_6 -2.2679 -4.513 150s Investment_7 -10.2199 -20.694 150s Investment_8 -5.7700 -12.217 150s Investment_9 3.4511 7.477 150s Investment_10 -9.2979 -19.962 150s Investment_11 -2.0356 -3.949 150s Investment_12 -0.4393 -1.107 150s Investment_13 -1.3613 -4.096 150s Investment_14 -1.0122 -4.931 150s Investment_15 0.6087 1.989 150s Investment_16 -0.0688 -0.220 150s Investment_17 -5.1466 -16.248 150s Investment_18 -0.1095 -0.297 150s Investment_19 16.1648 42.888 150s Investment_20 3.1568 10.193 150s Investment_21 4.7239 13.177 150s Investment_22 3.8759 11.352 150s PrivateWages_2 -22.6507 -50.295 150s PrivateWages_3 11.7391 30.484 150s PrivateWages_4 42.1098 92.193 150s PrivateWages_5 -0.6592 -1.326 150s PrivateWages_6 -8.1683 -16.252 150s PrivateWages_7 -10.6080 -21.480 150s PrivateWages_8 -21.2852 -45.068 150s PrivateWages_9 11.7929 25.551 150s PrivateWages_10 43.5418 93.481 150s PrivateWages_11 -12.2437 -23.754 150s PrivateWages_12 7.7609 19.551 150s PrivateWages_13 -4.8264 -14.521 150s PrivateWages_14 3.9112 19.053 150s PrivateWages_15 4.7891 15.650 150s PrivateWages_16 -0.4325 -1.382 150s PrivateWages_17 -18.1980 -57.454 150s PrivateWages_18 24.4870 66.365 150s PrivateWages_19 -23.1320 -61.373 150s PrivateWages_20 -9.6335 -31.104 150s PrivateWages_21 -36.5988 -102.091 150s PrivateWages_22 23.1466 67.794 150s Investment_(Intercept) Investment_corpProf 150s Consumption_2 0.08529 1.0576 150s Consumption_3 0.47520 8.0308 150s Consumption_4 0.57074 10.5016 150s Consumption_5 0.19190 3.7229 150s Consumption_6 0.01549 0.3114 150s Consumption_7 -0.30208 -5.9207 150s Consumption_8 -0.46181 -9.1438 150s Consumption_9 -0.34582 -7.2967 150s Consumption_10 0.23413 5.0806 150s Consumption_11 -0.15973 -2.4918 150s Consumption_12 0.01522 0.1735 150s Consumption_13 0.02370 0.1659 150s Consumption_14 -0.11404 -1.2772 150s Consumption_15 0.00156 0.0192 150s Consumption_16 0.00685 0.0958 150s Consumption_17 -0.54458 -9.5846 150s Consumption_18 0.14998 2.5946 150s Consumption_19 -0.10293 -1.5748 150s Consumption_20 -0.31431 -5.9719 150s Consumption_21 -0.24398 -5.1479 150s Consumption_22 0.81921 19.2515 150s Investment_2 -0.46650 -5.7846 150s Investment_3 -0.21255 -3.5922 150s Investment_4 1.41568 26.0484 150s Investment_5 -1.94810 -37.7932 150s Investment_6 0.43694 8.7825 150s Investment_7 1.90038 37.2474 150s Investment_8 1.10030 21.7860 150s Investment_9 -0.65146 -13.7457 150s Investment_10 1.64701 35.7401 150s Investment_11 0.35062 5.4696 150s Investment_12 0.10525 1.1998 150s Investment_13 0.44632 3.1242 150s Investment_14 0.54045 6.0530 150s Investment_15 -0.20313 -2.4985 150s Investment_16 0.02090 0.2926 150s Investment_17 1.37398 24.1820 150s Investment_18 0.02326 0.4024 150s Investment_19 -3.49233 -53.4327 150s Investment_20 -0.77116 -14.6521 150s Investment_21 -0.92927 -19.6075 150s Investment_22 -0.68657 -16.1344 150s PrivateWages_2 0.67977 8.4291 150s PrivateWages_3 -0.36082 -6.0979 150s PrivateWages_4 -0.94969 -17.4742 150s PrivateWages_5 0.01365 0.2649 150s PrivateWages_6 0.16048 3.2256 150s PrivateWages_7 0.20115 3.9426 150s PrivateWages_8 0.41391 8.1954 150s PrivateWages_9 -0.22701 -4.7899 150s PrivateWages_10 -0.78652 -17.0674 150s PrivateWages_11 0.21505 3.3548 150s PrivateWages_12 -0.18961 -2.1616 150s PrivateWages_13 0.16136 1.1295 150s PrivateWages_14 -0.21296 -2.3851 150s PrivateWages_15 -0.16298 -2.0046 150s PrivateWages_16 0.01340 0.1876 150s PrivateWages_17 0.49543 8.7195 150s PrivateWages_18 -0.53028 -9.1739 150s PrivateWages_19 0.50963 7.7973 150s PrivateWages_20 0.23998 4.5596 150s PrivateWages_21 0.73417 15.4910 150s PrivateWages_22 -0.41811 -9.8256 150s Investment_corpProfLag Investment_capitalLag 150s Consumption_2 1.0831 15.590 150s Consumption_3 5.8924 86.771 150s Consumption_4 9.6455 105.301 150s Consumption_5 3.5310 36.404 150s Consumption_6 0.3006 2.986 150s Consumption_7 -6.0718 -59.751 150s Consumption_8 -9.0514 -93.932 150s Consumption_9 -6.8471 -71.791 150s Consumption_10 4.9401 49.307 150s Consumption_11 -3.4662 -34.454 150s Consumption_12 0.2375 3.299 150s Consumption_13 0.2701 5.055 150s Consumption_14 -0.7983 -23.617 150s Consumption_15 0.0175 0.315 150s Consumption_16 0.0842 1.362 150s Consumption_17 -7.6241 -107.663 150s Consumption_18 2.6396 29.966 150s Consumption_19 -1.7806 -20.770 150s Consumption_20 -4.8090 -62.831 150s Consumption_21 -4.6355 -49.088 150s Consumption_22 17.2854 167.529 150s Investment_2 -5.9246 -85.277 150s Investment_3 -2.6357 -38.812 150s Investment_4 23.9249 261.192 150s Investment_5 -35.8451 -369.555 150s Investment_6 8.4767 84.199 150s Investment_7 38.1976 375.895 150s Investment_8 21.5660 223.802 150s Investment_9 -12.8988 -135.242 150s Investment_10 34.7519 346.860 150s Investment_11 7.6084 75.628 150s Investment_12 1.6419 22.807 150s Investment_13 5.0880 95.199 150s Investment_14 3.7831 111.927 150s Investment_15 -2.2751 -41.032 150s Investment_16 0.2571 4.159 150s Investment_17 19.2357 271.636 150s Investment_18 0.4094 4.648 150s Investment_19 -60.4174 -704.753 150s Investment_20 -11.7988 -154.156 150s Investment_21 -17.6560 -186.968 150s Investment_22 -14.4866 -140.403 150s PrivateWages_2 8.6331 124.262 150s PrivateWages_3 -4.4742 -65.887 150s PrivateWages_4 -16.0497 -175.217 150s PrivateWages_5 0.2512 2.590 150s PrivateWages_6 3.1132 30.924 150s PrivateWages_7 4.0431 39.788 150s PrivateWages_8 8.1126 84.189 150s PrivateWages_9 -4.4947 -47.127 150s PrivateWages_10 -16.5955 -165.640 150s PrivateWages_11 4.6666 46.386 150s PrivateWages_12 -2.9580 -41.089 150s PrivateWages_13 1.8395 34.418 150s PrivateWages_14 -1.4907 -44.104 150s PrivateWages_15 -1.8253 -32.921 150s PrivateWages_16 0.1648 2.667 150s PrivateWages_17 6.9360 97.946 150s PrivateWages_18 -9.3330 -105.950 150s PrivateWages_19 8.8165 102.843 150s PrivateWages_20 3.6717 47.972 150s PrivateWages_21 13.9492 147.715 150s PrivateWages_22 -8.8221 -85.503 150s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 150s Consumption_2 -0.39158 -17.856 -17.582 150s Consumption_3 -2.18178 -109.307 -99.489 150s Consumption_4 -2.62045 -149.890 -131.285 150s Consumption_5 -0.88109 -50.310 -50.398 150s Consumption_6 -0.07113 -4.339 -4.062 150s Consumption_7 1.38694 88.764 84.604 150s Consumption_8 2.12032 136.548 135.700 150s Consumption_9 1.58775 102.410 102.251 150s Consumption_10 -1.07495 -72.022 -69.335 150s Consumption_11 0.73338 44.883 49.136 150s Consumption_12 -0.06989 -3.732 -4.277 150s Consumption_13 -0.10880 -4.820 -5.810 150s Consumption_14 0.52359 23.614 23.195 150s Consumption_15 -0.00717 -0.356 -0.323 150s Consumption_16 -0.03143 -1.710 -1.562 150s Consumption_17 2.50033 156.771 136.018 150s Consumption_18 -0.68860 -44.759 -43.175 150s Consumption_19 0.47257 28.779 30.717 150s Consumption_20 1.44311 100.296 87.885 150s Consumption_21 1.12017 84.797 77.852 150s Consumption_22 -3.76128 -332.497 -284.729 150s Investment_2 0.21842 9.960 9.807 150s Investment_3 0.09952 4.986 4.538 150s Investment_4 -0.66282 -37.913 -33.207 150s Investment_5 0.91210 52.081 52.172 150s Investment_6 -0.20458 -12.479 -11.681 150s Investment_7 -0.88976 -56.944 -54.275 150s Investment_8 -0.51516 -33.176 -32.970 150s Investment_9 0.30501 19.673 19.643 150s Investment_10 -0.77113 -51.666 -49.738 150s Investment_11 -0.16416 -10.047 -10.999 150s Investment_12 -0.04928 -2.631 -3.016 150s Investment_13 -0.20897 -9.257 -11.159 150s Investment_14 -0.25304 -11.412 -11.210 150s Investment_15 0.09511 4.727 4.289 150s Investment_16 -0.00978 -0.532 -0.486 150s Investment_17 -0.64330 -40.335 -34.995 150s Investment_18 -0.01089 -0.708 -0.683 150s Investment_19 1.63511 99.578 106.282 150s Investment_20 0.36106 25.094 21.989 150s Investment_21 0.43508 32.936 30.238 150s Investment_22 0.32145 28.416 24.334 150s PrivateWages_2 -3.89912 -177.800 -175.070 150s PrivateWages_3 2.06967 103.690 94.377 150s PrivateWages_4 5.44735 311.588 272.912 150s PrivateWages_5 -0.07832 -4.472 -4.480 150s PrivateWages_6 -0.92048 -56.150 -52.560 150s PrivateWages_7 -1.15379 -73.843 -70.381 150s PrivateWages_8 -2.37416 -152.896 -151.946 150s PrivateWages_9 1.30210 83.986 83.855 150s PrivateWages_10 4.51142 302.265 290.986 150s PrivateWages_11 -1.23351 -75.491 -82.645 150s PrivateWages_12 1.08762 58.079 66.562 150s PrivateWages_13 -0.92556 -41.002 -49.425 150s PrivateWages_14 1.22152 55.091 54.114 150s PrivateWages_15 0.93482 46.461 42.160 150s PrivateWages_16 -0.07687 -4.182 -3.820 150s PrivateWages_17 -2.84174 -178.177 -154.591 150s PrivateWages_18 3.04167 197.708 190.713 150s PrivateWages_19 -2.92319 -178.022 -190.007 150s PrivateWages_20 -1.37651 -95.667 -83.829 150s PrivateWages_21 -4.21116 -318.785 -292.676 150s PrivateWages_22 2.39825 212.005 181.548 150s PrivateWages_trend 150s Consumption_2 3.9158 150s Consumption_3 19.6360 150s Consumption_4 20.9636 150s Consumption_5 6.1676 150s Consumption_6 0.4268 150s Consumption_7 -6.9347 150s Consumption_8 -8.4813 150s Consumption_9 -4.7633 150s Consumption_10 2.1499 150s Consumption_11 -0.7334 150s Consumption_12 0.0000 150s Consumption_13 -0.1088 150s Consumption_14 1.0472 150s Consumption_15 -0.0215 150s Consumption_16 -0.1257 150s Consumption_17 12.5017 150s Consumption_18 -4.1316 150s Consumption_19 3.3080 150s Consumption_20 11.5449 150s Consumption_21 10.0816 150s Consumption_22 -37.6128 150s Investment_2 -2.1842 150s Investment_3 -0.8957 150s Investment_4 5.3026 150s Investment_5 -6.3847 150s Investment_6 1.2275 150s Investment_7 4.4488 150s Investment_8 2.0606 150s Investment_9 -0.9150 150s Investment_10 1.5423 150s Investment_11 0.1642 150s Investment_12 0.0000 150s Investment_13 -0.2090 150s Investment_14 -0.5061 150s Investment_15 0.2853 150s Investment_16 -0.0391 150s Investment_17 -3.2165 150s Investment_18 -0.0653 150s Investment_19 11.4458 150s Investment_20 2.8885 150s Investment_21 3.9157 150s Investment_22 3.2145 150s PrivateWages_2 38.9912 150s PrivateWages_3 -18.6270 150s PrivateWages_4 -43.5788 150s PrivateWages_5 0.5483 150s PrivateWages_6 5.5229 150s PrivateWages_7 5.7689 150s PrivateWages_8 9.4967 150s PrivateWages_9 -3.9063 150s PrivateWages_10 -9.0228 150s PrivateWages_11 1.2335 150s PrivateWages_12 0.0000 150s PrivateWages_13 -0.9256 150s PrivateWages_14 2.4431 150s PrivateWages_15 2.8045 150s PrivateWages_16 -0.3075 150s PrivateWages_17 -14.2087 150s PrivateWages_18 18.2500 150s PrivateWages_19 -20.4623 150s PrivateWages_20 -11.0121 150s PrivateWages_21 -37.9005 150s PrivateWages_22 23.9825 150s [1] TRUE 150s > Bread 150s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 150s [1,] 86.0484 -0.02454 -0.83573 150s [2,] -0.0245 0.37055 -0.22831 150s [3,] -0.8357 -0.22831 0.37290 150s [4,] -1.6729 -0.06016 -0.03411 150s [5,] 10.1786 -0.46129 0.72764 150s [6,] -0.1293 0.03988 -0.03792 150s [7,] -0.0505 -0.03436 0.04602 150s [8,] -0.0350 0.00175 -0.00419 150s [9,] -37.4223 0.06800 1.80971 150s [10,] 0.4074 -0.06333 0.04058 150s [11,] 0.2037 0.06442 -0.07324 150s [12,] 0.2057 0.03217 0.03109 150s Consumption_wages Investment_(Intercept) Investment_corpProf 150s [1,] -1.67e+00 10.179 -0.12933 150s [2,] -6.02e-02 -0.461 0.03988 150s [3,] -3.41e-02 0.728 -0.03792 150s [4,] 7.83e-02 -0.341 0.00185 150s [5,] -3.41e-01 1452.346 -13.96098 150s [6,] 1.85e-03 -13.961 0.46676 150s [7,] -2.96e-03 11.230 -0.39879 150s [8,] 1.79e-03 -6.973 0.06288 150s [9,] 1.32e-01 19.427 -0.13338 150s [10,] -5.46e-05 0.416 0.01516 150s [11,] -2.23e-03 -0.760 -0.01340 150s [12,] -3.03e-02 -0.736 0.00571 150s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 150s [1,] -0.05046 -0.03501 -37.4223 150s [2,] -0.03436 0.00175 0.0680 150s [3,] 0.04602 -0.00419 1.8097 150s [4,] -0.00296 0.00179 0.1325 150s [5,] 11.22954 -6.97254 19.4266 150s [6,] -0.39879 0.06288 -0.1334 150s [7,] 0.50387 -0.06357 -0.5157 150s [8,] -0.06357 0.03467 -0.0417 150s [9,] -0.51574 -0.04172 78.6495 150s [10,] -0.00784 -0.00271 -0.3339 150s [11,] 0.01702 0.00353 -0.9859 150s [12,] -0.01390 0.00432 0.8712 150s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 150s [1,] 4.07e-01 0.20374 0.20573 150s [2,] -6.33e-02 0.06442 0.03217 150s [3,] 4.06e-02 -0.07324 0.03109 150s [4,] -5.46e-05 -0.00223 -0.03033 150s [5,] 4.16e-01 -0.75990 -0.73581 150s [6,] 1.52e-02 -0.01340 0.00571 150s [7,] -7.84e-03 0.01702 -0.01390 150s [8,] -2.71e-03 0.00353 0.00432 150s [9,] -3.34e-01 -0.98593 0.87119 150s [10,] 4.68e-02 -0.04271 -0.01162 150s [11,] -4.27e-02 0.06124 -0.00299 150s [12,] -1.16e-02 -0.00299 0.04791 150s > 150s > # 3SLS 150s > summary 150s 150s systemfit results 150s method: 3SLS 150s 150s N DF SSR detRCov OLS-R2 McElroy-R2 150s system 63 51 73.6 0.283 0.963 0.995 150s 150s N DF SSR MSE RMSE R2 Adj R2 150s Consumption 21 17 18.7 1.102 1.050 0.980 0.977 150s Investment 21 17 44.0 2.586 1.608 0.826 0.795 150s PrivateWages 21 17 10.9 0.642 0.801 0.986 0.984 150s 150s The covariance matrix of the residuals used for estimation 150s Consumption Investment PrivateWages 150s Consumption 1.044 0.438 -0.385 150s Investment 0.438 1.383 0.193 150s PrivateWages -0.385 0.193 0.476 150s 150s The covariance matrix of the residuals 150s Consumption Investment PrivateWages 150s Consumption 0.892 0.411 -0.394 150s Investment 0.411 2.093 0.403 150s PrivateWages -0.394 0.403 0.520 150s 150s The correlations of the residuals 150s Consumption Investment PrivateWages 150s Consumption 1.000 0.301 -0.578 150s Investment 0.301 1.000 0.386 150s PrivateWages -0.578 0.386 1.000 150s 150s 150s 3SLS estimates for 'Consumption' (equation 1) 150s Model Formula: consump ~ corpProf + corpProfLag + wages 150s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 150s gnpLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 16.4408 1.3045 12.60 4.7e-10 *** 150s corpProf 0.1249 0.1081 1.16 0.26 150s corpProfLag 0.1631 0.1004 1.62 0.12 150s wages 0.7901 0.0379 20.83 1.5e-13 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.05 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 18.727 MSE: 1.102 Root MSE: 1.05 150s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 150s 150s 150s 3SLS estimates for 'Investment' (equation 2) 150s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 150s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 150s gnpLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 28.1778 6.7938 4.15 0.00067 *** 150s corpProf -0.0131 0.1619 -0.08 0.93655 150s corpProfLag 0.7557 0.1529 4.94 0.00012 *** 150s capitalLag -0.1948 0.0325 -5.99 1.5e-05 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.608 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 43.954 MSE: 2.586 Root MSE: 1.608 150s Multiple R-Squared: 0.826 Adjusted R-Squared: 0.795 150s 150s 150s 3SLS estimates for 'PrivateWages' (equation 3) 150s Model Formula: privWage ~ gnp + gnpLag + trend 150s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 150s gnpLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 1.7972 1.1159 1.61 0.13 150s gnp 0.4005 0.0318 12.59 4.8e-10 *** 150s gnpLag 0.1813 0.0342 5.31 5.8e-05 *** 150s trend 0.1497 0.0279 5.36 5.2e-05 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 0.801 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 10.921 MSE: 0.642 Root MSE: 0.801 150s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 150s 150s > residuals 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 -0.4416 -2.1951 -1.20287 150s 3 -1.0150 0.1515 0.51834 150s 4 -1.5289 0.4406 1.50936 150s 5 -0.4985 -1.8667 -0.08743 150s 6 -0.0132 0.0713 -0.28089 150s 7 0.7759 1.0294 -0.33908 150s 8 1.3004 1.1011 -0.69282 150s 9 1.0993 0.5853 0.34494 150s 10 -0.5839 2.2952 1.27590 150s 11 -0.1917 -1.3443 -0.40414 150s 12 -0.5598 -0.9944 0.22151 150s 13 -0.6746 -1.3404 -0.36962 150s 14 0.5767 1.9316 0.31006 150s 15 -0.0211 -0.1217 0.27309 150s 16 0.0539 0.1847 0.00716 150s 17 1.8555 2.0937 -0.71866 150s 18 -0.4596 -0.3216 0.90582 150s 19 0.0613 -3.6314 -0.81881 150s 20 1.2602 0.7582 -0.26942 150s 21 0.9500 0.2428 -1.06125 150s 22 -1.9451 0.9302 0.87883 150s > fitted 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 42.3 1.99510 26.7 150s 3 46.0 1.74850 28.8 150s 4 50.7 4.75942 32.6 150s 5 51.1 4.86672 34.0 150s 6 52.6 5.02874 35.7 150s 7 54.3 4.57056 37.7 150s 8 54.9 3.09893 38.6 150s 9 56.2 2.41471 38.9 150s 10 58.4 2.80476 40.0 150s 11 55.2 2.34425 38.3 150s 12 51.5 -2.40558 34.3 150s 13 46.3 -4.85959 29.4 150s 14 45.9 -7.03164 28.2 150s 15 48.7 -2.87827 30.3 150s 16 51.2 -1.48466 33.2 150s 17 55.8 0.00629 37.5 150s 18 59.2 2.32164 40.1 150s 19 57.4 1.73138 39.0 150s 20 60.3 0.54175 41.9 150s 21 64.1 3.05716 46.1 150s 22 71.6 3.96979 52.4 150s > predict 150s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 150s 1 NA NA NA NA 150s 2 42.3 0.464 39.9 44.8 150s 3 46.0 0.541 43.5 48.5 150s 4 50.7 0.337 48.4 53.1 150s 5 51.1 0.385 48.7 53.5 150s 6 52.6 0.386 50.3 55.0 150s 7 54.3 0.349 52.0 56.7 150s 8 54.9 0.320 52.6 57.2 150s 9 56.2 0.355 53.9 58.5 150s 10 58.4 0.370 56.0 60.7 150s 11 55.2 0.682 52.6 57.8 150s 12 51.5 0.563 48.9 54.0 150s 13 46.3 0.719 43.6 49.0 150s 14 45.9 0.597 43.4 48.5 150s 15 48.7 0.370 46.4 51.1 150s 16 51.2 0.327 48.9 53.6 150s 17 55.8 0.391 53.5 58.2 150s 18 59.2 0.316 56.8 61.5 150s 19 57.4 0.389 55.1 59.8 150s 20 60.3 0.459 57.9 62.8 150s 21 64.1 0.438 61.7 66.4 150s 22 71.6 0.674 69.0 74.3 150s Investment.pred Investment.se.fit Investment.lwr Investment.upr 150s 1 NA NA NA NA 150s 2 1.99510 0.792 -1.787 5.777 150s 3 1.74850 0.585 -1.861 5.358 150s 4 4.75942 0.510 1.200 8.319 150s 5 4.86672 0.423 1.359 8.375 150s 6 5.02874 0.400 1.533 8.525 150s 7 4.57056 0.391 1.079 8.062 150s 8 3.09893 0.345 -0.371 6.568 150s 9 2.41471 0.511 -1.145 5.974 150s 10 2.80476 0.560 -0.788 6.397 150s 11 2.34425 0.839 -1.482 6.170 150s 12 -2.40558 0.673 -6.083 1.272 150s 13 -4.85959 0.862 -8.708 -1.011 150s 14 -7.03164 0.874 -10.893 -3.171 150s 15 -2.87827 0.433 -6.392 0.635 150s 16 -1.48466 0.375 -4.968 1.999 150s 17 0.00629 0.491 -3.541 3.554 150s 18 2.32164 0.294 -1.127 5.771 150s 19 1.73138 0.446 -1.789 5.252 150s 20 0.54175 0.547 -3.042 4.125 150s 21 3.05716 0.454 -0.468 6.582 150s 22 3.96979 0.642 0.317 7.623 150s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 150s 1 NA NA NA NA 150s 2 26.7 0.314 24.9 28.5 150s 3 28.8 0.318 27.0 30.6 150s 4 32.6 0.325 30.8 34.4 150s 5 34.0 0.235 32.2 35.7 150s 6 35.7 0.241 33.9 37.4 150s 7 37.7 0.238 36.0 39.5 150s 8 38.6 0.237 36.8 40.4 150s 9 38.9 0.227 37.1 40.6 150s 10 40.0 0.219 38.3 41.8 150s 11 38.3 0.317 36.5 40.1 150s 12 34.3 0.344 32.4 36.1 150s 13 29.4 0.419 27.5 31.3 150s 14 28.2 0.334 26.4 30.0 150s 15 30.3 0.320 28.5 32.1 150s 16 33.2 0.268 31.4 35.0 150s 17 37.5 0.269 35.7 39.3 150s 18 40.1 0.212 38.3 41.8 150s 19 39.0 0.331 37.2 40.8 150s 20 41.9 0.287 40.1 43.7 150s 21 46.1 0.301 44.3 47.9 150s 22 52.4 0.471 50.5 54.4 150s > model.frame 150s [1] TRUE 150s > model.matrix 150s [1] TRUE 150s > nobs 150s [1] 63 150s > linearHypothesis 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 0.29 0.59 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 0.39 0.54 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 52 150s 2 51 1 0.39 0.53 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.3 0.74 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.4 0.67 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 53 150s 2 51 2 0.8 0.67 150s > logLik 150s 'log Lik.' -76.1 (df=18) 150s 'log Lik.' -89.1 (df=18) 150s Estimating function 150s Consumption_(Intercept) Consumption_corpProf 150s Consumption_2 -3.2451 -43.02 150s Consumption_3 -1.3384 -22.19 150s Consumption_4 -1.4130 -27.25 150s Consumption_5 -5.0390 -105.62 150s Consumption_6 -0.8531 -16.86 150s Consumption_7 4.3438 79.23 150s Consumption_8 5.6608 99.48 150s Consumption_9 3.7666 73.61 150s Consumption_10 1.2798 26.08 150s Consumption_11 -3.5695 -61.32 150s Consumption_12 -1.8656 -23.70 150s Consumption_13 -3.4193 -30.77 150s Consumption_14 4.0738 36.88 150s Consumption_15 -1.6814 -21.31 150s Consumption_16 -1.4312 -20.64 150s Consumption_17 9.0552 133.22 150s Consumption_18 -1.9716 -39.03 150s Consumption_19 -6.7338 -129.33 150s Consumption_20 4.8735 84.89 150s Consumption_21 1.6324 33.15 150s Consumption_22 -2.1249 -48.14 150s Investment_2 2.1466 28.45 150s Investment_3 -0.1448 -2.40 150s Investment_4 -0.4444 -8.57 150s Investment_5 1.8148 38.04 150s Investment_6 -0.0658 -1.30 150s Investment_7 -0.9944 -18.14 150s Investment_8 -1.0536 -18.52 150s Investment_9 -0.5553 -10.85 150s Investment_10 -2.2390 -45.62 150s Investment_11 1.3010 22.35 150s Investment_12 0.9607 12.21 150s Investment_13 1.2918 11.63 150s Investment_14 -1.8711 -16.94 150s Investment_15 0.1149 1.46 150s Investment_16 -0.1869 -2.70 150s Investment_17 -2.0208 -29.73 150s Investment_18 0.2841 5.62 150s Investment_19 3.5191 67.59 150s Investment_20 -0.7250 -12.63 150s Investment_21 -0.2285 -4.64 150s Investment_22 -0.9035 -20.47 150s PrivateWages_2 -4.3513 -57.68 150s PrivateWages_3 1.7756 29.44 150s PrivateWages_4 3.5512 68.47 150s PrivateWages_5 -3.3088 -69.35 150s PrivateWages_6 -0.7761 -15.34 150s PrivateWages_7 1.5988 29.16 150s PrivateWages_8 1.5583 27.38 150s PrivateWages_9 2.5665 50.15 150s PrivateWages_10 4.9740 101.35 150s PrivateWages_11 -3.5972 -61.80 150s PrivateWages_12 -0.7986 -10.15 150s PrivateWages_13 -3.2258 -29.03 150s PrivateWages_14 3.6395 32.95 150s PrivateWages_15 -0.5056 -6.41 150s PrivateWages_16 -1.0680 -15.40 150s PrivateWages_17 3.0850 45.39 150s PrivateWages_18 -0.3546 -7.02 150s PrivateWages_19 -8.0362 -154.35 150s PrivateWages_20 1.6465 28.68 150s PrivateWages_21 -1.9137 -38.86 150s PrivateWages_22 3.5407 80.22 150s Consumption_corpProfLag Consumption_wages 150s Consumption_2 -41.21 -95.43 150s Consumption_3 -16.60 -42.49 150s Consumption_4 -23.88 -50.52 150s Consumption_5 -92.72 -196.89 150s Consumption_6 -16.55 -33.39 150s Consumption_7 87.31 170.95 150s Consumption_8 110.95 227.47 150s Consumption_9 74.58 159.45 150s Consumption_10 27.00 56.34 150s Consumption_11 -77.46 -155.98 150s Consumption_12 -29.10 -73.65 150s Consumption_13 -38.98 -120.13 150s Consumption_14 28.52 133.55 150s Consumption_15 -18.83 -63.05 150s Consumption_16 -17.60 -57.45 150s Consumption_17 126.77 377.63 150s Consumption_18 -34.70 -94.39 150s Consumption_19 -116.49 -332.00 150s Consumption_20 74.56 235.83 150s Consumption_21 31.02 87.12 150s Consumption_22 -44.84 -129.02 150s Investment_2 27.26 63.12 150s Investment_3 -1.80 -4.60 150s Investment_4 -7.51 -15.89 150s Investment_5 33.39 70.91 150s Investment_6 -1.28 -2.57 150s Investment_7 -19.99 -39.13 150s Investment_8 -20.65 -42.34 150s Investment_9 -10.99 -23.51 150s Investment_10 -47.24 -98.56 150s Investment_11 28.23 56.85 150s Investment_12 14.99 37.92 150s Investment_13 14.73 45.38 150s Investment_14 -13.10 -61.34 150s Investment_15 1.29 4.31 150s Investment_16 -2.30 -7.50 150s Investment_17 -28.29 -84.27 150s Investment_18 5.00 13.60 150s Investment_19 60.88 173.50 150s Investment_20 -11.09 -35.08 150s Investment_21 -4.34 -12.19 150s Investment_22 -19.06 -54.86 150s PrivateWages_2 -55.26 -127.96 150s PrivateWages_3 22.02 56.38 150s PrivateWages_4 60.01 126.96 150s PrivateWages_5 -60.88 -129.29 150s PrivateWages_6 -15.06 -30.37 150s PrivateWages_7 32.14 62.92 150s PrivateWages_8 30.54 62.62 150s PrivateWages_9 50.82 108.65 150s PrivateWages_10 104.95 218.96 150s PrivateWages_11 -78.06 -157.19 150s PrivateWages_12 -12.46 -31.53 150s PrivateWages_13 -36.77 -113.33 150s PrivateWages_14 25.48 119.32 150s PrivateWages_15 -5.66 -18.96 150s PrivateWages_16 -13.14 -42.87 150s PrivateWages_17 43.19 128.65 150s PrivateWages_18 -6.24 -16.98 150s PrivateWages_19 -139.03 -396.21 150s PrivateWages_20 25.19 79.68 150s PrivateWages_21 -36.36 -102.14 150s PrivateWages_22 74.71 214.98 150s Investment_(Intercept) Investment_corpProf 150s Consumption_2 1.4757 19.56 150s Consumption_3 0.6086 10.09 150s Consumption_4 0.6425 12.39 150s Consumption_5 2.2915 48.03 150s Consumption_6 0.3879 7.67 150s Consumption_7 -1.9753 -36.03 150s Consumption_8 -2.5742 -45.24 150s Consumption_9 -1.7128 -33.47 150s Consumption_10 -0.5820 -11.86 150s Consumption_11 1.6232 27.89 150s Consumption_12 0.8484 10.78 150s Consumption_13 1.5549 13.99 150s Consumption_14 -1.8525 -16.77 150s Consumption_15 0.7646 9.69 150s Consumption_16 0.6508 9.39 150s Consumption_17 -4.1178 -60.58 150s Consumption_18 0.8965 17.75 150s Consumption_19 3.0621 58.81 150s Consumption_20 -2.2162 -38.60 150s Consumption_21 -0.7423 -15.07 150s Consumption_22 0.9663 21.89 150s Investment_2 -2.6492 -35.12 150s Investment_3 0.1787 2.96 150s Investment_4 0.5485 10.58 150s Investment_5 -2.2397 -46.94 150s Investment_6 0.0811 1.60 150s Investment_7 1.2272 22.38 150s Investment_8 1.3003 22.85 150s Investment_9 0.6853 13.39 150s Investment_10 2.7633 56.30 150s Investment_11 -1.6056 -27.58 150s Investment_12 -1.1856 -15.06 150s Investment_13 -1.5943 -14.35 150s Investment_14 2.3092 20.91 150s Investment_15 -0.1418 -1.80 150s Investment_16 0.2307 3.33 150s Investment_17 2.4940 36.69 150s Investment_18 -0.3506 -6.94 150s Investment_19 -4.3431 -83.42 150s Investment_20 0.8947 15.59 150s Investment_21 0.2820 5.73 150s Investment_22 1.1150 25.26 150s PrivateWages_2 2.6070 34.56 150s PrivateWages_3 -1.0638 -17.64 150s PrivateWages_4 -2.1276 -41.02 150s PrivateWages_5 1.9824 41.55 150s PrivateWages_6 0.4650 9.19 150s PrivateWages_7 -0.9579 -17.47 150s PrivateWages_8 -0.9336 -16.41 150s PrivateWages_9 -1.5377 -30.05 150s PrivateWages_10 -2.9800 -60.72 150s PrivateWages_11 2.1552 37.03 150s PrivateWages_12 0.4785 6.08 150s PrivateWages_13 1.9327 17.39 150s PrivateWages_14 -2.1805 -19.74 150s PrivateWages_15 0.3029 3.84 150s PrivateWages_16 0.6398 9.23 150s PrivateWages_17 -1.8483 -27.19 150s PrivateWages_18 0.2125 4.21 150s PrivateWages_19 4.8147 92.47 150s PrivateWages_20 -0.9865 -17.18 150s PrivateWages_21 1.1466 23.28 150s PrivateWages_22 -2.1213 -48.06 150s Investment_corpProfLag Investment_capitalLag 150s Consumption_2 18.74 269.8 150s Consumption_3 7.55 111.1 150s Consumption_4 10.86 118.5 150s Consumption_5 42.16 434.7 150s Consumption_6 7.53 74.8 150s Consumption_7 -39.70 -390.7 150s Consumption_8 -50.45 -523.6 150s Consumption_9 -33.91 -355.6 150s Consumption_10 -12.28 -122.6 150s Consumption_11 35.22 350.1 150s Consumption_12 13.23 183.8 150s Consumption_13 17.73 331.7 150s Consumption_14 -12.97 -383.7 150s Consumption_15 8.56 154.5 150s Consumption_16 8.01 129.5 150s Consumption_17 -57.65 -814.1 150s Consumption_18 15.78 179.1 150s Consumption_19 52.98 617.9 150s Consumption_20 -33.91 -443.0 150s Consumption_21 -14.10 -149.4 150s Consumption_22 20.39 197.6 150s Investment_2 -33.65 -484.3 150s Investment_3 2.22 32.6 150s Investment_4 9.27 101.2 150s Investment_5 -41.21 -424.9 150s Investment_6 1.57 15.6 150s Investment_7 24.67 242.7 150s Investment_8 25.49 264.5 150s Investment_9 13.57 142.3 150s Investment_10 58.30 581.9 150s Investment_11 -34.84 -346.3 150s Investment_12 -18.50 -256.9 150s Investment_13 -18.17 -340.1 150s Investment_14 16.16 478.2 150s Investment_15 -1.59 -28.6 150s Investment_16 2.84 45.9 150s Investment_17 34.92 493.1 150s Investment_18 -6.17 -70.0 150s Investment_19 -75.14 -876.4 150s Investment_20 13.69 178.9 150s Investment_21 5.36 56.7 150s Investment_22 23.53 228.0 150s PrivateWages_2 33.11 476.6 150s PrivateWages_3 -13.19 -194.3 150s PrivateWages_4 -35.96 -392.5 150s PrivateWages_5 36.48 376.1 150s PrivateWages_6 9.02 89.6 150s PrivateWages_7 -19.25 -189.5 150s PrivateWages_8 -18.30 -189.9 150s PrivateWages_9 -30.45 -319.2 150s PrivateWages_10 -62.88 -627.6 150s PrivateWages_11 46.77 464.9 150s PrivateWages_12 7.46 103.7 150s PrivateWages_13 22.03 412.2 150s PrivateWages_14 -15.26 -451.6 150s PrivateWages_15 3.39 61.2 150s PrivateWages_16 7.87 127.3 150s PrivateWages_17 -25.88 -365.4 150s PrivateWages_18 3.74 42.5 150s PrivateWages_19 83.29 971.6 150s PrivateWages_20 -15.09 -197.2 150s PrivateWages_21 21.78 230.7 150s PrivateWages_22 -44.76 -433.8 150s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 150s Consumption_2 -3.220 -153.49 -144.60 150s Consumption_3 -1.328 -65.52 -60.57 150s Consumption_4 -1.402 -79.70 -70.25 150s Consumption_5 -5.001 -303.71 -286.05 150s Consumption_6 -0.847 -51.81 -48.34 150s Consumption_7 4.311 264.22 262.96 150s Consumption_8 5.618 341.88 359.54 150s Consumption_9 3.738 233.16 240.73 150s Consumption_10 1.270 81.79 81.92 150s Consumption_11 -3.542 -228.05 -237.34 150s Consumption_12 -1.851 -101.61 -113.31 150s Consumption_13 -3.393 -159.94 -181.21 150s Consumption_14 4.043 168.34 179.10 150s Consumption_15 -1.669 -85.05 -75.26 150s Consumption_16 -1.420 -79.06 -70.59 150s Consumption_17 8.987 515.06 488.87 150s Consumption_18 -1.957 -132.41 -122.68 150s Consumption_19 -6.683 -455.83 -434.38 150s Consumption_20 4.837 323.61 294.54 150s Consumption_21 1.620 121.95 112.59 150s Consumption_22 -2.109 -182.35 -159.64 150s Investment_2 2.807 133.77 126.02 150s Investment_3 -0.189 -9.34 -8.63 150s Investment_4 -0.581 -33.02 -29.11 150s Investment_5 2.373 144.11 135.73 150s Investment_6 -0.086 -5.26 -4.91 150s Investment_7 -1.300 -79.69 -79.31 150s Investment_8 -1.378 -83.84 -88.17 150s Investment_9 -0.726 -45.28 -46.75 150s Investment_10 -2.928 -188.52 -188.82 150s Investment_11 1.701 109.51 113.97 150s Investment_12 1.256 68.94 76.87 150s Investment_13 1.689 79.61 90.20 150s Investment_14 -2.446 -101.86 -108.38 150s Investment_15 0.150 7.66 6.77 150s Investment_16 -0.244 -13.60 -12.15 150s Investment_17 -2.642 -151.44 -143.74 150s Investment_18 0.371 25.13 23.29 150s Investment_19 4.601 313.85 299.09 150s Investment_20 -0.948 -63.43 -57.73 150s Investment_21 -0.299 -22.49 -20.76 150s Investment_22 -1.181 -102.15 -89.43 150s PrivateWages_2 -8.830 -420.86 -396.47 150s PrivateWages_3 3.603 177.74 164.31 150s PrivateWages_4 7.206 409.57 361.04 150s PrivateWages_5 -6.715 -407.80 -384.07 150s PrivateWages_6 -1.575 -96.39 -89.93 150s PrivateWages_7 3.244 198.86 197.91 150s PrivateWages_8 3.162 192.44 202.38 150s PrivateWages_9 5.208 324.85 335.40 150s PrivateWages_10 10.094 649.99 651.03 150s PrivateWages_11 -7.300 -469.94 -489.08 150s PrivateWages_12 -1.621 -88.94 -99.18 150s PrivateWages_13 -6.546 -308.53 -349.56 150s PrivateWages_14 7.386 307.52 327.18 150s PrivateWages_15 -1.026 -52.30 -46.27 150s PrivateWages_16 -2.167 -120.63 -107.71 150s PrivateWages_17 6.260 358.81 340.56 150s PrivateWages_18 -0.720 -48.70 -45.12 150s PrivateWages_19 -16.308 -1112.35 -1060.00 150s PrivateWages_20 3.341 223.57 203.48 150s PrivateWages_21 -3.883 -292.34 -269.90 150s PrivateWages_22 7.185 621.32 543.91 150s PrivateWages_trend 150s Consumption_2 32.205 150s Consumption_3 11.954 150s Consumption_4 11.218 150s Consumption_5 35.006 150s Consumption_6 5.080 150s Consumption_7 -21.554 150s Consumption_8 -22.471 150s Consumption_9 -11.214 150s Consumption_10 -2.540 150s Consumption_11 3.542 150s Consumption_12 0.000 150s Consumption_13 -3.393 150s Consumption_14 8.086 150s Consumption_15 -5.006 150s Consumption_16 -5.681 150s Consumption_17 44.933 150s Consumption_18 -11.740 150s Consumption_19 -46.779 150s Consumption_20 38.692 150s Consumption_21 14.580 150s Consumption_22 -21.088 150s Investment_2 -28.067 150s Investment_3 1.704 150s Investment_4 4.648 150s Investment_5 -16.610 150s Investment_6 0.516 150s Investment_7 6.501 150s Investment_8 5.511 150s Investment_9 2.178 150s Investment_10 5.855 150s Investment_11 -1.701 150s Investment_12 0.000 150s Investment_13 1.689 150s Investment_14 -4.893 150s Investment_15 0.451 150s Investment_16 -0.978 150s Investment_17 -13.211 150s Investment_18 2.228 150s Investment_19 32.209 150s Investment_20 -7.583 150s Investment_21 -2.689 150s Investment_22 -11.813 150s PrivateWages_2 88.301 150s PrivateWages_3 -32.429 150s PrivateWages_4 -57.650 150s PrivateWages_5 47.002 150s PrivateWages_6 9.450 150s PrivateWages_7 -16.222 150s PrivateWages_8 -12.649 150s PrivateWages_9 -15.624 150s PrivateWages_10 -20.187 150s PrivateWages_11 7.300 150s PrivateWages_12 0.000 150s PrivateWages_13 -6.546 150s PrivateWages_14 14.771 150s PrivateWages_15 -3.078 150s PrivateWages_16 -8.669 150s PrivateWages_17 31.301 150s PrivateWages_18 -4.318 150s PrivateWages_19 -114.154 150s PrivateWages_20 26.730 150s PrivateWages_21 -34.951 150s PrivateWages_22 71.851 150s [1] TRUE 150s > Bread 150s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 150s [1,] 1.07e+02 -1.06982 -0.3515 150s [2,] -1.07e+00 0.73659 -0.5079 150s [3,] -3.51e-01 -0.50793 0.6355 150s [4,] -1.93e+00 -0.07361 -0.0356 150s [5,] 1.24e+02 -0.98618 3.4455 150s [6,] -2.71e+00 0.38390 -0.3719 150s [7,] 9.65e-01 -0.31139 0.3992 150s [8,] -4.61e-01 -0.00199 -0.0185 150s [9,] -3.88e+01 0.05351 1.8003 150s [10,] 6.27e-01 -0.08533 0.0556 150s [11,] -5.96e-04 0.08746 -0.0887 150s [12,] 2.14e-01 0.04029 0.0279 150s Consumption_wages Investment_(Intercept) Investment_corpProf 150s [1,] -1.934840 123.765 -2.71e+00 150s [2,] -0.073613 -0.986 3.84e-01 150s [3,] -0.035606 3.445 -3.72e-01 150s [4,] 0.090675 -3.911 5.58e-02 150s [5,] -3.910682 2907.785 -4.61e+01 150s [6,] 0.055805 -46.132 1.65e+00 150s [7,] -0.054072 38.083 -1.41e+00 150s [8,] 0.019220 -13.707 2.06e-01 150s [9,] 0.174112 17.422 -1.06e-01 150s [10,] -0.002325 2.389 2.04e-03 150s [11,] -0.000594 -2.765 -2.91e-04 150s [12,] -0.032572 -2.080 3.10e-02 150s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 150s [1,] 0.96474 -0.46130 -38.76422 150s [2,] -0.31139 -0.00199 0.05351 150s [3,] 0.39923 -0.01847 1.80032 150s [4,] -0.05407 0.01922 0.17411 150s [5,] 38.08346 -13.70662 17.42245 150s [6,] -1.40785 0.20597 -0.10564 150s [7,] 1.47348 -0.19170 -0.93153 150s [8,] -0.19170 0.06667 0.00097 150s [9,] -0.93153 0.00097 78.44334 150s [10,] 0.01112 -0.01300 -0.49810 150s [11,] 0.00455 0.01344 -0.81226 150s [12,] -0.04174 0.01117 0.88592 150s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 150s [1,] 0.62679 -0.000596 0.21374 150s [2,] -0.08533 0.087455 0.04029 150s [3,] 0.05563 -0.088660 0.02790 150s [4,] -0.00233 -0.000594 -0.03257 150s [5,] 2.38888 -2.764716 -2.07974 150s [6,] 0.00204 -0.000291 0.03105 150s [7,] 0.01112 0.004547 -0.04174 150s [8,] -0.01300 0.013443 0.01117 150s [9,] -0.49810 -0.812260 0.88592 150s [10,] 0.06376 -0.057450 -0.01781 150s [11,] -0.05745 0.073510 0.00317 150s [12,] -0.01781 0.003170 0.04916 150s > 150s > # I3SLS 150s > summary 150s 150s systemfit results 150s method: iterated 3SLS 150s 150s convergence achieved after 20 iterations 150s 150s N DF SSR detRCov OLS-R2 McElroy-R2 150s system 63 51 128 0.509 0.936 0.996 150s 150s N DF SSR MSE RMSE R2 Adj R2 150s Consumption 21 17 19.2 1.130 1.063 0.980 0.976 150s Investment 21 17 95.7 5.627 2.372 0.621 0.554 150s PrivateWages 21 17 12.7 0.748 0.865 0.984 0.981 150s 150s The covariance matrix of the residuals used for estimation 150s Consumption Investment PrivateWages 150s Consumption 0.915 0.642 -0.435 150s Investment 0.642 4.555 0.734 150s PrivateWages -0.435 0.734 0.606 150s 150s The covariance matrix of the residuals 150s Consumption Investment PrivateWages 150s Consumption 0.915 0.642 -0.435 150s Investment 0.642 4.555 0.734 150s PrivateWages -0.435 0.734 0.606 150s 150s The correlations of the residuals 150s Consumption Investment PrivateWages 150s Consumption 1.000 0.314 -0.584 150s Investment 0.314 1.000 0.442 150s PrivateWages -0.584 0.442 1.000 150s 150s 150s 3SLS estimates for 'Consumption' (equation 1) 150s Model Formula: consump ~ corpProf + corpProfLag + wages 150s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 150s gnpLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 16.5590 1.2244 13.52 1.6e-10 *** 150s corpProf 0.1645 0.0962 1.71 0.105 150s corpProfLag 0.1766 0.0901 1.96 0.067 . 150s wages 0.7658 0.0348 22.03 6.1e-14 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.063 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 19.213 MSE: 1.13 Root MSE: 1.063 150s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 150s 150s 150s 3SLS estimates for 'Investment' (equation 2) 150s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 150s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 150s gnpLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 42.8959 10.5937 4.05 0.00083 *** 150s corpProf -0.3565 0.2602 -1.37 0.18838 150s corpProfLag 1.0113 0.2488 4.07 0.00081 *** 150s capitalLag -0.2602 0.0509 -5.12 8.6e-05 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 2.372 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 95.661 MSE: 5.627 Root MSE: 2.372 150s Multiple R-Squared: 0.621 Adjusted R-Squared: 0.554 150s 150s 150s 3SLS estimates for 'PrivateWages' (equation 3) 150s Model Formula: privWage ~ gnp + gnpLag + trend 150s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 150s gnpLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 2.6247 1.1956 2.20 0.042 * 150s gnp 0.3748 0.0311 12.05 9.4e-10 *** 150s gnpLag 0.1937 0.0324 5.98 1.5e-05 *** 150s trend 0.1679 0.0289 5.80 2.1e-05 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 0.865 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 12.719 MSE: 0.748 Root MSE: 0.865 150s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.981 150s 150s > residuals 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 -0.537 -3.95419 -1.2303 150s 3 -1.187 0.00151 0.5797 150s 4 -1.705 -0.22015 1.6794 150s 5 -0.734 -2.22753 -0.0260 150s 6 -0.251 -0.10866 -0.1362 150s 7 0.600 0.83218 -0.1837 150s 8 1.142 1.46624 -0.5825 150s 9 0.921 1.62030 0.4347 150s 10 -0.745 3.40013 1.4104 150s 11 -0.197 -2.15443 -0.4679 150s 12 -0.385 -1.62274 0.0106 150s 13 -0.390 -2.62869 -0.7363 150s 14 0.749 2.80517 0.0581 150s 15 0.112 -0.27710 0.1113 150s 16 0.170 0.13598 -0.1089 150s 17 1.925 2.76200 -0.6976 150s 18 -0.341 -0.53919 0.8651 150s 19 0.219 -4.32845 -1.0116 150s 20 1.383 1.71889 -0.2087 150s 21 1.028 1.06406 -0.9656 150s 22 -1.777 2.25466 1.2061 150s > fitted 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 42.4 3.754 26.7 150s 3 46.2 1.898 28.7 150s 4 50.9 5.420 32.4 150s 5 51.3 5.228 33.9 150s 6 52.9 5.209 35.5 150s 7 54.5 4.768 37.6 150s 8 55.1 2.734 38.5 150s 9 56.4 1.380 38.8 150s 10 58.5 1.700 39.9 150s 11 55.2 3.154 38.4 150s 12 51.3 -1.777 34.5 150s 13 46.0 -3.571 29.7 150s 14 45.8 -7.905 28.4 150s 15 48.6 -2.723 30.5 150s 16 51.1 -1.436 33.3 150s 17 55.8 -0.662 37.5 150s 18 59.0 2.539 40.1 150s 19 57.3 2.428 39.2 150s 20 60.2 -0.419 41.8 150s 21 64.0 2.236 46.0 150s 22 71.5 2.645 52.1 150s > predict 150s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 150s 1 NA NA NA NA 150s 2 42.4 0.434 41.6 43.3 150s 3 46.2 0.491 45.2 47.2 150s 4 50.9 0.309 50.3 51.5 150s 5 51.3 0.351 50.6 52.0 150s 6 52.9 0.352 52.1 53.6 150s 7 54.5 0.320 53.9 55.1 150s 8 55.1 0.293 54.5 55.6 150s 9 56.4 0.324 55.7 57.0 150s 10 58.5 0.340 57.9 59.2 150s 11 55.2 0.613 54.0 56.4 150s 12 51.3 0.506 50.3 52.3 150s 13 46.0 0.649 44.7 47.3 150s 14 45.8 0.546 44.7 46.8 150s 15 48.6 0.341 47.9 49.3 150s 16 51.1 0.301 50.5 51.7 150s 17 55.8 0.357 55.1 56.5 150s 18 59.0 0.293 58.5 59.6 150s 19 57.3 0.353 56.6 58.0 150s 20 60.2 0.421 59.4 61.1 150s 21 64.0 0.409 63.2 64.8 150s 22 71.5 0.630 70.2 72.7 150s Investment.pred Investment.se.fit Investment.lwr Investment.upr 150s 1 NA NA NA NA 150s 2 3.754 1.263 1.218 6.2906 150s 3 1.898 1.022 -0.153 3.9503 150s 4 5.420 0.853 3.709 7.1317 150s 5 5.228 0.727 3.767 6.6877 150s 6 5.209 0.703 3.797 6.6200 150s 7 4.768 0.688 3.387 6.1487 150s 8 2.734 0.615 1.499 3.9683 150s 9 1.380 0.852 -0.330 3.0893 150s 10 1.700 0.938 -0.184 3.5836 150s 11 3.154 1.437 0.269 6.0398 150s 12 -1.777 1.173 -4.133 0.5780 150s 13 -3.571 1.494 -6.570 -0.5725 150s 14 -7.905 1.479 -10.875 -4.9350 150s 15 -2.723 0.778 -4.285 -1.1613 150s 16 -1.436 0.672 -2.784 -0.0875 150s 17 -0.662 0.832 -2.333 1.0088 150s 18 2.539 0.522 1.491 3.5875 150s 19 2.428 0.753 0.918 3.9392 150s 20 -0.419 0.907 -2.240 1.4019 150s 21 2.236 0.775 0.679 3.7928 150s 22 2.645 1.076 0.486 4.8047 150s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 150s 1 NA NA NA NA 150s 2 26.7 0.340 26.0 27.4 150s 3 28.7 0.339 28.0 29.4 150s 4 32.4 0.340 31.7 33.1 150s 5 33.9 0.250 33.4 34.4 150s 6 35.5 0.258 35.0 36.1 150s 7 37.6 0.256 37.1 38.1 150s 8 38.5 0.252 38.0 39.0 150s 9 38.8 0.241 38.3 39.2 150s 10 39.9 0.239 39.4 40.4 150s 11 38.4 0.314 37.7 39.0 150s 12 34.5 0.342 33.8 35.2 150s 13 29.7 0.430 28.9 30.6 150s 14 28.4 0.361 27.7 29.2 150s 15 30.5 0.336 29.8 31.2 150s 16 33.3 0.281 32.7 33.9 150s 17 37.5 0.270 37.0 38.0 150s 18 40.1 0.231 39.7 40.6 150s 19 39.2 0.343 38.5 39.9 150s 20 41.8 0.294 41.2 42.4 150s 21 46.0 0.326 45.3 46.6 150s 22 52.1 0.501 51.1 53.1 150s > model.frame 150s [1] TRUE 150s > model.matrix 150s [1] TRUE 150s > nobs 150s [1] 63 150s > linearHypothesis 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 0.59 0.45 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 52 150s 2 51 1 0.73 0.4 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 52 150s 2 51 1 0.73 0.39 150s Linear hypothesis test (Theil's F test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.72 0.49 150s Linear hypothesis test (F statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df F Pr(>F) 150s 1 53 150s 2 51 2 0.88 0.42 150s Linear hypothesis test (Chi^2 statistic of a Wald test) 150s 150s Hypothesis: 150s Consumption_corpProf + Investment_capitalLag = 0 150s Consumption_corpProfLag - PrivateWages_trend = 0 150s 150s Model 1: restricted model 150s Model 2: kleinModel 150s 150s Res.Df Df Chisq Pr(>Chisq) 150s 1 53 150s 2 51 2 1.77 0.41 150s > logLik 150s 'log Lik.' -82.3 (df=18) 150s 'log Lik.' -99.1 (df=18) 150s Estimating function 150s Consumption_(Intercept) Consumption_corpProf 150s Consumption_2 -6.979 -92.51 150s Consumption_3 -3.442 -57.06 150s Consumption_4 -3.899 -75.19 150s Consumption_5 -11.237 -235.54 150s Consumption_6 -2.642 -52.22 150s Consumption_7 8.084 147.44 150s Consumption_8 10.972 192.80 150s Consumption_9 7.028 137.33 150s Consumption_10 1.972 40.17 150s Consumption_11 -7.325 -125.85 150s Consumption_12 -3.206 -40.73 150s Consumption_13 -5.913 -53.22 150s Consumption_14 9.196 83.26 150s Consumption_15 -2.781 -35.23 150s Consumption_16 -2.363 -34.08 150s Consumption_17 18.799 276.57 150s Consumption_18 -3.872 -76.65 150s Consumption_19 -13.205 -253.63 150s Consumption_20 10.531 183.44 150s Consumption_21 3.807 77.30 150s Consumption_22 -3.522 -79.79 150s Investment_2 5.075 67.27 150s Investment_3 0.158 2.62 150s Investment_4 -0.131 -2.53 150s Investment_5 2.324 48.72 150s Investment_6 0.316 6.26 150s Investment_7 -0.482 -8.80 150s Investment_8 -0.935 -16.43 150s Investment_9 -1.481 -28.94 150s Investment_10 -4.072 -82.96 150s Investment_11 2.213 38.01 150s Investment_12 1.610 20.45 150s Investment_13 2.664 23.98 150s Investment_14 -2.837 -25.69 150s Investment_15 0.201 2.55 150s Investment_16 -0.398 -5.74 150s Investment_17 -2.409 -35.45 150s Investment_18 -0.488 -9.66 150s Investment_19 4.083 78.42 150s Investment_20 -1.607 -27.99 150s Investment_21 -1.086 -22.05 150s Investment_22 -2.718 -61.58 150s PrivateWages_2 -9.649 -127.90 150s PrivateWages_3 4.187 69.41 150s PrivateWages_4 8.749 168.69 150s PrivateWages_5 -6.685 -140.11 150s PrivateWages_6 -1.021 -20.18 150s PrivateWages_7 4.003 73.02 150s PrivateWages_8 3.592 63.12 150s PrivateWages_9 5.932 115.93 150s PrivateWages_10 11.495 234.22 150s PrivateWages_11 -7.992 -137.30 150s PrivateWages_12 -2.626 -33.36 150s PrivateWages_13 -8.660 -77.94 150s PrivateWages_14 6.531 59.13 150s PrivateWages_15 -1.757 -22.27 150s PrivateWages_16 -2.801 -40.40 150s PrivateWages_17 6.362 93.60 150s PrivateWages_18 -0.661 -13.09 150s PrivateWages_19 -18.070 -347.06 150s PrivateWages_20 3.670 63.92 150s PrivateWages_21 -3.889 -78.97 150s PrivateWages_22 9.289 210.47 150s Consumption_corpProfLag Consumption_wages 150s Consumption_2 -88.63 -205.23 150s Consumption_3 -42.68 -109.29 150s Consumption_4 -65.90 -139.41 150s Consumption_5 -206.77 -439.08 150s Consumption_6 -51.26 -103.40 150s Consumption_7 162.48 318.13 150s Consumption_8 215.04 440.87 150s Consumption_9 139.15 297.49 150s Consumption_10 41.60 86.79 150s Consumption_11 -158.95 -320.08 150s Consumption_12 -50.01 -126.56 150s Consumption_13 -67.41 -207.75 150s Consumption_14 64.37 301.49 150s Consumption_15 -31.14 -104.27 150s Consumption_16 -29.07 -94.86 150s Consumption_17 263.19 783.97 150s Consumption_18 -68.15 -185.39 150s Consumption_19 -228.45 -651.06 150s Consumption_20 161.12 509.58 150s Consumption_21 72.33 203.19 150s Consumption_22 -74.31 -213.82 150s Investment_2 64.45 149.24 150s Investment_3 1.96 5.01 150s Investment_4 -2.22 -4.70 150s Investment_5 42.77 90.82 150s Investment_6 6.14 12.39 150s Investment_7 -9.70 -18.98 150s Investment_8 -18.33 -37.57 150s Investment_9 -29.32 -62.69 150s Investment_10 -85.92 -179.25 150s Investment_11 48.02 96.69 150s Investment_12 25.11 63.55 150s Investment_13 30.37 93.60 150s Investment_14 -19.86 -93.02 150s Investment_15 2.25 7.55 150s Investment_16 -4.90 -15.98 150s Investment_17 -33.73 -100.47 150s Investment_18 -8.59 -23.36 150s Investment_19 70.63 201.29 150s Investment_20 -24.59 -77.76 150s Investment_21 -20.63 -57.96 150s Investment_22 -57.35 -165.02 150s PrivateWages_2 -122.54 -283.73 150s PrivateWages_3 51.92 132.94 150s PrivateWages_4 147.85 312.78 150s PrivateWages_5 -123.00 -261.19 150s PrivateWages_6 -19.80 -39.95 150s PrivateWages_7 80.47 157.55 150s PrivateWages_8 70.40 144.33 150s PrivateWages_9 117.46 251.13 150s PrivateWages_10 242.55 506.03 150s PrivateWages_11 -173.42 -349.22 150s PrivateWages_12 -40.96 -103.66 150s PrivateWages_13 -98.72 -304.24 150s PrivateWages_14 45.71 214.10 150s PrivateWages_15 -19.68 -65.90 150s PrivateWages_16 -34.45 -112.44 150s PrivateWages_17 89.07 265.31 150s PrivateWages_18 -11.64 -31.65 150s PrivateWages_19 -312.61 -890.90 150s PrivateWages_20 56.14 177.57 150s PrivateWages_21 -73.89 -207.57 150s PrivateWages_22 196.00 564.00 150s Investment_(Intercept) Investment_corpProf 150s Consumption_2 2.2268 29.52 150s Consumption_3 1.0983 18.21 150s Consumption_4 1.2442 23.99 150s Consumption_5 3.5856 75.15 150s Consumption_6 0.8430 16.66 150s Consumption_7 -2.5793 -47.04 150s Consumption_8 -3.5007 -61.52 150s Consumption_9 -2.2423 -43.82 150s Consumption_10 -0.6291 -12.82 150s Consumption_11 2.3372 40.15 150s Consumption_12 1.0229 13.00 150s Consumption_13 1.8868 16.98 150s Consumption_14 -2.9343 -26.57 150s Consumption_15 0.8872 11.24 150s Consumption_16 0.7541 10.87 150s Consumption_17 -5.9983 -88.25 150s Consumption_18 1.2355 24.46 150s Consumption_19 4.2135 80.93 150s Consumption_20 -3.3600 -58.53 150s Consumption_21 -1.2147 -24.67 150s Consumption_22 1.1237 25.46 150s Investment_2 -2.6152 -34.67 150s Investment_3 -0.0813 -1.35 150s Investment_4 0.0677 1.30 150s Investment_5 -1.1977 -25.10 150s Investment_6 -0.1631 -3.22 150s Investment_7 0.2486 4.53 150s Investment_8 0.4818 8.47 150s Investment_9 0.7630 14.91 150s Investment_10 2.0982 42.75 150s Investment_11 -1.1402 -19.59 150s Investment_12 -0.8295 -10.54 150s Investment_13 -1.3729 -12.36 150s Investment_14 1.4620 13.24 150s Investment_15 -0.1037 -1.31 150s Investment_16 0.2051 2.96 150s Investment_17 1.2415 18.26 150s Investment_18 0.2514 4.98 150s Investment_19 -2.1038 -40.41 150s Investment_20 0.8280 14.42 150s Investment_21 0.5596 11.36 150s Investment_22 1.4005 31.73 150s PrivateWages_2 3.7415 49.60 150s PrivateWages_3 -1.6237 -26.92 150s PrivateWages_4 -3.3924 -65.41 150s PrivateWages_5 2.5921 54.33 150s PrivateWages_6 0.3959 7.82 150s PrivateWages_7 -1.5524 -28.31 150s PrivateWages_8 -1.3929 -24.48 150s PrivateWages_9 -2.3004 -44.95 150s PrivateWages_10 -4.4576 -90.82 150s PrivateWages_11 3.0990 53.24 150s PrivateWages_12 1.0182 12.94 150s PrivateWages_13 3.3581 30.22 150s PrivateWages_14 -2.5324 -22.93 150s PrivateWages_15 0.6815 8.64 150s PrivateWages_16 1.0862 15.66 150s PrivateWages_17 -2.4670 -36.29 150s PrivateWages_18 0.2564 5.07 150s PrivateWages_19 7.0070 134.58 150s PrivateWages_20 -1.4230 -24.79 150s PrivateWages_21 1.5081 30.62 150s PrivateWages_22 -3.6021 -81.61 150s Investment_corpProfLag Investment_capitalLag 150s Consumption_2 28.28 407.1 150s Consumption_3 13.62 200.5 150s Consumption_4 21.03 229.5 150s Consumption_5 65.97 680.2 150s Consumption_6 16.35 162.4 150s Consumption_7 -51.84 -510.2 150s Consumption_8 -68.61 -712.1 150s Consumption_9 -44.40 -465.5 150s Consumption_10 -13.27 -132.5 150s Consumption_11 50.72 504.1 150s Consumption_12 15.96 221.7 150s Consumption_13 21.51 402.5 150s Consumption_14 -20.54 -607.7 150s Consumption_15 9.94 179.2 150s Consumption_16 9.27 150.1 150s Consumption_17 -83.98 -1185.9 150s Consumption_18 21.74 246.9 150s Consumption_19 72.89 850.3 150s Consumption_20 -51.41 -671.7 150s Consumption_21 -23.08 -244.4 150s Consumption_22 23.71 229.8 150s Investment_2 -33.21 -478.1 150s Investment_3 -1.01 -14.9 150s Investment_4 1.14 12.5 150s Investment_5 -22.04 -227.2 150s Investment_6 -3.16 -31.4 150s Investment_7 5.00 49.2 150s Investment_8 9.44 98.0 150s Investment_9 15.11 158.4 150s Investment_10 44.27 441.9 150s Investment_11 -24.74 -245.9 150s Investment_12 -12.94 -179.8 150s Investment_13 -15.65 -292.8 150s Investment_14 10.23 302.8 150s Investment_15 -1.16 -21.0 150s Investment_16 2.52 40.8 150s Investment_17 17.38 245.4 150s Investment_18 4.43 50.2 150s Investment_19 -36.40 -424.5 150s Investment_20 12.67 165.5 150s Investment_21 10.63 112.6 150s Investment_22 29.55 286.4 150s PrivateWages_2 47.52 683.9 150s PrivateWages_3 -20.13 -296.5 150s PrivateWages_4 -57.33 -625.9 150s PrivateWages_5 47.69 491.7 150s PrivateWages_6 7.68 76.3 150s PrivateWages_7 -31.20 -307.1 150s PrivateWages_8 -27.30 -283.3 150s PrivateWages_9 -45.55 -477.6 150s PrivateWages_10 -94.05 -938.8 150s PrivateWages_11 67.25 668.4 150s PrivateWages_12 15.88 220.6 150s PrivateWages_13 38.28 716.3 150s PrivateWages_14 -17.73 -524.5 150s PrivateWages_15 7.63 137.7 150s PrivateWages_16 13.36 216.2 150s PrivateWages_17 -34.54 -487.7 150s PrivateWages_18 4.51 51.2 150s PrivateWages_19 121.22 1414.0 150s PrivateWages_20 -21.77 -284.4 150s PrivateWages_21 28.65 303.4 150s PrivateWages_22 -76.00 -736.6 150s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 150s Consumption_2 -7.713 -367.6 -346.32 150s Consumption_3 -3.804 -187.6 -173.47 150s Consumption_4 -4.309 -244.9 -215.90 150s Consumption_5 -12.419 -754.3 -710.38 150s Consumption_6 -2.920 -178.7 -166.72 150s Consumption_7 8.934 547.6 544.97 150s Consumption_8 12.125 737.9 776.02 150s Consumption_9 7.767 484.4 500.17 150s Consumption_10 2.179 140.3 140.54 150s Consumption_11 -8.095 -521.2 -542.38 150s Consumption_12 -3.543 -194.5 -216.84 150s Consumption_13 -6.535 -308.0 -348.98 150s Consumption_14 10.163 423.2 450.24 150s Consumption_15 -3.073 -156.6 -138.60 150s Consumption_16 -2.612 -145.4 -129.81 150s Consumption_17 20.776 1190.8 1130.21 150s Consumption_18 -4.279 -289.6 -268.32 150s Consumption_19 -14.594 -995.5 -948.61 150s Consumption_20 11.638 778.7 708.75 150s Consumption_21 4.207 316.7 292.41 150s Consumption_22 -3.892 -336.6 -294.62 150s Investment_2 6.817 324.9 306.06 150s Investment_3 0.212 10.5 9.67 150s Investment_4 -0.176 -10.0 -8.84 150s Investment_5 3.122 189.6 178.58 150s Investment_6 0.425 26.0 24.27 150s Investment_7 -0.648 -39.7 -39.52 150s Investment_8 -1.256 -76.4 -80.37 150s Investment_9 -1.989 -124.1 -128.08 150s Investment_10 -5.469 -352.2 -352.75 150s Investment_11 2.972 191.3 199.12 150s Investment_12 2.162 118.7 132.32 150s Investment_13 3.579 168.7 191.09 150s Investment_14 -3.811 -158.7 -168.82 150s Investment_15 0.270 13.8 12.19 150s Investment_16 -0.535 -29.8 -26.57 150s Investment_17 -3.236 -185.5 -176.04 150s Investment_18 -0.655 -44.4 -41.09 150s Investment_19 5.484 374.0 356.44 150s Investment_20 -2.158 -144.4 -131.44 150s Investment_21 -1.459 -109.8 -101.37 150s Investment_22 -3.650 -315.7 -276.34 150s PrivateWages_2 -14.774 -704.2 -663.37 150s PrivateWages_3 6.412 316.3 292.37 150s PrivateWages_4 13.396 761.4 671.14 150s PrivateWages_5 -10.236 -621.6 -585.48 150s PrivateWages_6 -1.563 -95.7 -89.26 150s PrivateWages_7 6.130 375.7 373.95 150s PrivateWages_8 5.500 334.7 352.01 150s PrivateWages_9 9.084 566.6 585.00 150s PrivateWages_10 17.602 1133.5 1135.33 150s PrivateWages_11 -12.237 -787.8 -819.89 150s PrivateWages_12 -4.021 -220.7 -246.06 150s PrivateWages_13 -13.260 -625.0 -708.11 150s PrivateWages_14 10.000 416.4 443.00 150s PrivateWages_15 -2.691 -137.2 -121.37 150s PrivateWages_16 -4.289 -238.7 -213.18 150s PrivateWages_17 9.742 558.3 529.95 150s PrivateWages_18 -1.012 -68.5 -63.47 150s PrivateWages_19 -27.669 -1887.3 -1798.51 150s PrivateWages_20 5.619 376.0 342.19 150s PrivateWages_21 -5.955 -448.3 -413.89 150s PrivateWages_22 14.224 1230.0 1076.76 150s PrivateWages_trend 150s Consumption_2 77.130 150s Consumption_3 34.237 150s Consumption_4 34.475 150s Consumption_5 86.935 150s Consumption_6 17.519 150s Consumption_7 -44.670 150s Consumption_8 -48.501 150s Consumption_9 -23.300 150s Consumption_10 -4.358 150s Consumption_11 8.095 150s Consumption_12 0.000 150s Consumption_13 -6.535 150s Consumption_14 20.327 150s Consumption_15 -9.219 150s Consumption_16 -10.447 150s Consumption_17 103.880 150s Consumption_18 -25.676 150s Consumption_19 -102.158 150s Consumption_20 93.104 150s Consumption_21 37.866 150s Consumption_22 -38.920 150s Investment_2 -68.165 150s Investment_3 -1.908 150s Investment_4 1.411 150s Investment_5 -21.854 150s Investment_6 -2.550 150s Investment_7 3.240 150s Investment_8 5.023 150s Investment_9 5.967 150s Investment_10 10.938 150s Investment_11 -2.972 150s Investment_12 0.000 150s Investment_13 3.579 150s Investment_14 -7.622 150s Investment_15 0.811 150s Investment_16 -2.138 150s Investment_17 -16.180 150s Investment_18 -3.932 150s Investment_19 38.386 150s Investment_20 -17.267 150s Investment_21 -13.128 150s Investment_22 -36.504 150s PrivateWages_2 147.744 150s PrivateWages_3 -57.704 150s PrivateWages_4 -107.168 150s PrivateWages_5 71.650 150s PrivateWages_6 9.379 150s PrivateWages_7 -30.651 150s PrivateWages_8 -22.000 150s PrivateWages_9 -27.251 150s PrivateWages_10 -35.204 150s PrivateWages_11 12.237 150s PrivateWages_12 0.000 150s PrivateWages_13 -13.260 150s PrivateWages_14 20.000 150s PrivateWages_15 -8.073 150s PrivateWages_16 -17.157 150s PrivateWages_17 48.709 150s PrivateWages_18 -6.074 150s PrivateWages_19 -193.685 150s PrivateWages_20 44.952 150s PrivateWages_21 -53.597 150s PrivateWages_22 142.240 150s [1] TRUE 150s > Bread 150s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 150s [1,] 94.44678 -0.9198 -0.3009 150s [2,] -0.91977 0.5830 -0.4036 150s [3,] -0.30085 -0.4036 0.5114 150s [4,] -1.71741 -0.0559 -0.0303 150s [5,] 169.11432 -7.0463 6.8731 150s [6,] -3.78719 0.8222 -0.7139 150s [7,] 1.24504 -0.6799 0.7545 150s [8,] -0.61653 0.0214 -0.0358 150s [9,] -43.93927 0.0941 1.6110 150s [10,] 0.70520 -0.0665 0.0417 150s [11,] 0.00487 0.0673 -0.0710 150s [12,] 0.27782 0.0450 0.0254 150s Consumption_wages Investment_(Intercept) Investment_corpProf 150s [1,] -1.71741 169.11 -3.79e+00 150s [2,] -0.05588 -7.05 8.22e-01 150s [3,] -0.03031 6.87 -7.14e-01 150s [4,] 0.07612 -3.87 3.83e-02 150s [5,] -3.87475 7070.32 -1.04e+02 150s [6,] 0.03834 -104.41 4.26e+00 150s [7,] -0.05106 83.93 -3.59e+00 150s [8,] 0.02027 -33.26 4.55e-01 150s [9,] 0.35346 48.43 -5.08e-01 150s [10,] -0.00637 6.61 4.29e-03 150s [11,] 0.00050 -7.65 4.31e-03 150s [12,] -0.03505 -5.67 7.94e-02 150s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 150s [1,] 1.24504 -0.6165 -43.9393 150s [2,] -0.67986 0.0214 0.0941 150s [3,] 0.75452 -0.0358 1.6110 150s [4,] -0.05106 0.0203 0.3535 150s [5,] 83.92612 -33.2552 48.4291 150s [6,] -3.59218 0.4550 -0.5077 150s [7,] 3.89889 -0.4344 -3.1131 150s [8,] -0.43443 0.1630 0.0665 150s [9,] -3.11309 0.0665 90.0495 150s [10,] 0.04234 -0.0368 -0.7131 150s [11,] 0.00984 0.0370 -0.7830 150s [12,] -0.11558 0.0310 0.9385 150s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 150s [1,] 0.70520 0.00487 0.27782 150s [2,] -0.06653 0.06728 0.04499 150s [3,] 0.04169 -0.07096 0.02543 150s [4,] -0.00637 0.00050 -0.03505 150s [5,] 6.61461 -7.64810 -5.66883 150s [6,] 0.00429 0.00431 0.07939 150s [7,] 0.04234 0.00984 -0.11558 150s [8,] -0.03681 0.03698 0.03103 150s [9,] -0.71315 -0.78300 0.93852 150s [10,] 0.06094 -0.05082 -0.02122 150s [11,] -0.05082 0.06614 0.00579 150s [12,] -0.02122 0.00579 0.05272 150s > 150s > # OLS 150s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 150s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 150s > summary 150s 150s systemfit results 150s method: OLS 150s 150s N DF SSR detRCov OLS-R2 McElroy-R2 150s system 62 50 44.9 0.372 0.977 0.991 150s 150s N DF SSR MSE RMSE R2 Adj R2 150s Consumption 21 17 17.88 1.052 1.03 0.981 0.978 150s Investment 21 17 17.32 1.019 1.01 0.931 0.919 150s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 150s 150s The covariance matrix of the residuals 150s Consumption Investment PrivateWages 150s Consumption 1.0703 -0.0161 -0.463 150s Investment -0.0161 0.9435 0.199 150s PrivateWages -0.4633 0.1993 0.609 150s 150s The correlations of the residuals 150s Consumption Investment PrivateWages 150s Consumption 1.0000 -0.0201 -0.575 150s Investment -0.0201 1.0000 0.264 150s PrivateWages -0.5747 0.2639 1.000 150s 150s 150s OLS estimates for 'Consumption' (equation 1) 150s Model Formula: consump ~ corpProf + corpProfLag + wages 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 16.2366 1.3141 12.36 6.4e-10 *** 150s corpProf 0.1929 0.0920 2.10 0.051 . 150s corpProfLag 0.0899 0.0914 0.98 0.339 150s wages 0.7962 0.0403 19.76 3.6e-13 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.026 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 150s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 150s 150s 150s OLS estimates for 'Investment' (equation 2) 150s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 10.1258 5.2592 1.93 0.07108 . 150s corpProf 0.4796 0.0934 5.13 8.3e-05 *** 150s corpProfLag 0.3330 0.0971 3.43 0.00318 ** 150s capitalLag -0.1118 0.0257 -4.35 0.00044 *** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 1.009 on 17 degrees of freedom 150s Number of observations: 21 Degrees of Freedom: 17 150s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 150s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 150s 150s 150s OLS estimates for 'PrivateWages' (equation 3) 150s Model Formula: privWage ~ gnp + gnpLag + trend 150s 150s Estimate Std. Error t value Pr(>|t|) 150s (Intercept) 1.3550 1.3093 1.03 0.3161 150s gnp 0.4417 0.0331 13.33 4.4e-10 *** 150s gnpLag 0.1466 0.0381 3.85 0.0014 ** 150s trend 0.1244 0.0336 3.70 0.0020 ** 150s --- 150s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 150s 150s Residual standard error: 0.78 on 16 degrees of freedom 150s Number of observations: 20 Degrees of Freedom: 16 150s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 150s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 150s 150s compare coef with single-equation OLS 150s [1] TRUE 150s > residuals 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 -0.32389 -0.0668 -1.3389 150s 3 -1.25001 -0.0476 0.2462 150s 4 -1.56574 1.2467 1.1255 150s 5 -0.49350 -1.3512 -0.1959 150s 6 0.00761 0.4154 -0.5284 150s 7 0.86910 1.4923 NA 150s 8 1.33848 0.7889 -0.7909 150s 9 1.05498 -0.6317 0.2819 150s 10 -0.58856 1.0830 1.1384 150s 11 0.28231 0.2791 -0.1904 150s 12 -0.22965 0.0369 0.5813 150s 13 -0.32213 0.3659 0.1206 150s 14 0.32228 0.2237 0.4773 150s 15 -0.05801 -0.1728 0.3035 150s 16 -0.03466 0.0101 0.0284 150s 17 1.61650 0.9719 -0.8517 150s 18 -0.43597 0.0516 0.9908 150s 19 0.21005 -2.5656 -0.4597 150s 20 0.98920 -0.6866 -0.3819 150s 21 0.78508 -0.7807 -1.1062 150s 22 -2.17345 -0.6623 0.5501 150s > fitted 150s Consumption Investment PrivateWages 150s 1 NA NA NA 150s 2 42.2 -0.133 26.8 150s 3 46.3 1.948 29.1 150s 4 50.8 3.953 33.0 150s 5 51.1 4.351 34.1 150s 6 52.6 4.685 35.9 150s 7 54.2 4.108 NA 150s 8 54.9 3.411 38.7 150s 9 56.2 3.632 38.9 150s 10 58.4 4.017 40.2 150s 11 54.7 0.721 38.1 150s 12 51.1 -3.437 33.9 150s 13 45.9 -6.566 28.9 150s 14 46.2 -5.324 28.0 150s 15 48.8 -2.827 30.3 150s 16 51.3 -1.310 33.2 150s 17 56.1 1.128 37.7 150s 18 59.1 1.948 40.0 150s 19 57.3 0.666 38.7 150s 20 60.6 1.987 42.0 150s 21 64.2 4.081 46.1 150s 22 71.9 5.562 52.7 150s > predict 150s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 150s 1 NA NA NA NA 150s 2 42.2 0.466 40.0 44.5 150s 3 46.3 0.523 43.9 48.6 150s 4 50.8 0.344 48.6 52.9 150s 5 51.1 0.399 48.9 53.3 150s 6 52.6 0.401 50.4 54.8 150s 7 54.2 0.363 52.0 56.4 150s 8 54.9 0.330 52.7 57.0 150s 9 56.2 0.354 54.1 58.4 150s 10 58.4 0.373 56.2 60.6 150s 11 54.7 0.612 52.3 57.1 150s 12 51.1 0.489 48.8 53.4 150s 13 45.9 0.634 43.5 48.3 150s 14 46.2 0.608 43.8 48.6 150s 15 48.8 0.378 46.6 51.0 150s 16 51.3 0.336 49.2 53.5 150s 17 56.1 0.369 53.9 58.3 150s 18 59.1 0.324 57.0 61.3 150s 19 57.3 0.375 55.1 59.5 150s 20 60.6 0.437 58.4 62.9 150s 21 64.2 0.429 62.0 66.4 150s 22 71.9 0.672 69.4 74.3 150s Investment.pred Investment.se.fit Investment.lwr Investment.upr 150s 1 NA NA NA NA 150s 2 -0.133 0.584 -2.476 2.209 150s 3 1.948 0.480 -0.297 4.193 150s 4 3.953 0.432 1.748 6.159 150s 5 4.351 0.357 2.201 6.502 150s 6 4.685 0.336 2.548 6.821 150s 7 4.108 0.316 1.983 6.232 150s 8 3.411 0.281 1.306 5.516 150s 9 3.632 0.374 1.469 5.794 150s 10 4.017 0.430 1.813 6.221 150s 11 0.721 0.579 -1.616 3.058 150s 12 -3.437 0.488 -5.688 -1.185 150s 13 -6.566 0.592 -8.917 -4.215 150s 14 -5.324 0.667 -7.754 -2.893 150s 15 -2.827 0.359 -4.979 -0.675 150s 16 -1.310 0.308 -3.430 0.810 150s 17 1.128 0.334 -1.008 3.264 150s 18 1.948 0.234 -0.133 4.030 150s 19 0.666 0.300 -1.450 2.781 150s 20 1.987 0.353 -0.161 4.134 150s 21 4.081 0.319 1.954 6.207 150s 22 5.562 0.444 3.348 7.777 150s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 150s 1 NA NA NA NA 150s 2 26.8 0.366 25.1 28.6 150s 3 29.1 0.369 27.3 30.8 150s 4 33.0 0.372 31.2 34.7 150s 5 34.1 0.288 32.4 35.8 150s 6 35.9 0.287 34.3 37.6 150s 7 NA NA NA NA 150s 8 38.7 0.293 37.0 40.4 150s 9 38.9 0.279 37.3 40.6 150s 10 40.2 0.266 38.5 41.8 150s 11 38.1 0.365 36.4 39.8 150s 12 33.9 0.369 32.2 35.7 150s 13 28.9 0.438 27.1 30.7 150s 14 28.0 0.385 26.3 29.8 150s 15 30.3 0.379 28.6 32.0 150s 16 33.2 0.316 31.5 34.9 150s 17 37.7 0.310 36.0 39.3 150s 18 40.0 0.243 38.4 41.7 150s 19 38.7 0.363 36.9 40.4 150s 20 42.0 0.326 40.3 43.7 150s 21 46.1 0.341 44.4 47.8 150s 22 52.7 0.514 50.9 54.6 150s > model.frame 151s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 151s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 151s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 151s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 151s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 151s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 151s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 151s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 151s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 151s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 151s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 151s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 151s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 151s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 151s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 151s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 151s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 151s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 151s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 151s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 151s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 151s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 151s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 151s trend 151s 1 -11 151s 2 -10 151s 3 -9 151s 4 -8 151s 5 -7 151s 6 -6 151s 7 -5 151s 8 -4 151s 9 -3 151s 10 -2 151s 11 -1 151s 12 0 151s 13 1 151s 14 2 151s 15 3 151s 16 4 151s 17 5 151s 18 6 151s 19 7 151s 20 8 151s 21 9 151s 22 10 151s > model.matrix 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 1 12.4 151s Consumption_3 1 16.9 151s Consumption_4 1 18.4 151s Consumption_5 1 19.4 151s Consumption_6 1 20.1 151s Consumption_7 1 19.6 151s Consumption_8 1 19.8 151s Consumption_9 1 21.1 151s Consumption_10 1 21.7 151s Consumption_11 1 15.6 151s Consumption_12 1 11.4 151s Consumption_13 1 7.0 151s Consumption_14 1 11.2 151s Consumption_15 1 12.3 151s Consumption_16 1 14.0 151s Consumption_17 1 17.6 151s Consumption_18 1 17.3 151s Consumption_19 1 15.3 151s Consumption_20 1 19.0 151s Consumption_21 1 21.1 151s Consumption_22 1 23.5 151s Investment_2 0 0.0 151s Investment_3 0 0.0 151s Investment_4 0 0.0 151s Investment_5 0 0.0 151s Investment_6 0 0.0 151s Investment_7 0 0.0 151s Investment_8 0 0.0 151s Investment_9 0 0.0 151s Investment_10 0 0.0 151s Investment_11 0 0.0 151s Investment_12 0 0.0 151s Investment_13 0 0.0 151s Investment_14 0 0.0 151s Investment_15 0 0.0 151s Investment_16 0 0.0 151s Investment_17 0 0.0 151s Investment_18 0 0.0 151s Investment_19 0 0.0 151s Investment_20 0 0.0 151s Investment_21 0 0.0 151s Investment_22 0 0.0 151s PrivateWages_2 0 0.0 151s PrivateWages_3 0 0.0 151s PrivateWages_4 0 0.0 151s PrivateWages_5 0 0.0 151s PrivateWages_6 0 0.0 151s PrivateWages_8 0 0.0 151s PrivateWages_9 0 0.0 151s PrivateWages_10 0 0.0 151s PrivateWages_11 0 0.0 151s PrivateWages_12 0 0.0 151s PrivateWages_13 0 0.0 151s PrivateWages_14 0 0.0 151s PrivateWages_15 0 0.0 151s PrivateWages_16 0 0.0 151s PrivateWages_17 0 0.0 151s PrivateWages_18 0 0.0 151s PrivateWages_19 0 0.0 151s PrivateWages_20 0 0.0 151s PrivateWages_21 0 0.0 151s PrivateWages_22 0 0.0 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 12.7 28.2 151s Consumption_3 12.4 32.2 151s Consumption_4 16.9 37.0 151s Consumption_5 18.4 37.0 151s Consumption_6 19.4 38.6 151s Consumption_7 20.1 40.7 151s Consumption_8 19.6 41.5 151s Consumption_9 19.8 42.9 151s Consumption_10 21.1 45.3 151s Consumption_11 21.7 42.1 151s Consumption_12 15.6 39.3 151s Consumption_13 11.4 34.3 151s Consumption_14 7.0 34.1 151s Consumption_15 11.2 36.6 151s Consumption_16 12.3 39.3 151s Consumption_17 14.0 44.2 151s Consumption_18 17.6 47.7 151s Consumption_19 17.3 45.9 151s Consumption_20 15.3 49.4 151s Consumption_21 19.0 53.0 151s Consumption_22 21.1 61.8 151s Investment_2 0.0 0.0 151s Investment_3 0.0 0.0 151s Investment_4 0.0 0.0 151s Investment_5 0.0 0.0 151s Investment_6 0.0 0.0 151s Investment_7 0.0 0.0 151s Investment_8 0.0 0.0 151s Investment_9 0.0 0.0 151s Investment_10 0.0 0.0 151s Investment_11 0.0 0.0 151s Investment_12 0.0 0.0 151s Investment_13 0.0 0.0 151s Investment_14 0.0 0.0 151s Investment_15 0.0 0.0 151s Investment_16 0.0 0.0 151s Investment_17 0.0 0.0 151s Investment_18 0.0 0.0 151s Investment_19 0.0 0.0 151s Investment_20 0.0 0.0 151s Investment_21 0.0 0.0 151s Investment_22 0.0 0.0 151s PrivateWages_2 0.0 0.0 151s PrivateWages_3 0.0 0.0 151s PrivateWages_4 0.0 0.0 151s PrivateWages_5 0.0 0.0 151s PrivateWages_6 0.0 0.0 151s PrivateWages_8 0.0 0.0 151s PrivateWages_9 0.0 0.0 151s PrivateWages_10 0.0 0.0 151s PrivateWages_11 0.0 0.0 151s PrivateWages_12 0.0 0.0 151s PrivateWages_13 0.0 0.0 151s PrivateWages_14 0.0 0.0 151s PrivateWages_15 0.0 0.0 151s PrivateWages_16 0.0 0.0 151s PrivateWages_17 0.0 0.0 151s PrivateWages_18 0.0 0.0 151s PrivateWages_19 0.0 0.0 151s PrivateWages_20 0.0 0.0 151s PrivateWages_21 0.0 0.0 151s PrivateWages_22 0.0 0.0 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0 0.0 151s Consumption_3 0 0.0 151s Consumption_4 0 0.0 151s Consumption_5 0 0.0 151s Consumption_6 0 0.0 151s Consumption_7 0 0.0 151s Consumption_8 0 0.0 151s Consumption_9 0 0.0 151s Consumption_10 0 0.0 151s Consumption_11 0 0.0 151s Consumption_12 0 0.0 151s Consumption_13 0 0.0 151s Consumption_14 0 0.0 151s Consumption_15 0 0.0 151s Consumption_16 0 0.0 151s Consumption_17 0 0.0 151s Consumption_18 0 0.0 151s Consumption_19 0 0.0 151s Consumption_20 0 0.0 151s Consumption_21 0 0.0 151s Consumption_22 0 0.0 151s Investment_2 1 12.4 151s Investment_3 1 16.9 151s Investment_4 1 18.4 151s Investment_5 1 19.4 151s Investment_6 1 20.1 151s Investment_7 1 19.6 151s Investment_8 1 19.8 151s Investment_9 1 21.1 151s Investment_10 1 21.7 151s Investment_11 1 15.6 151s Investment_12 1 11.4 151s Investment_13 1 7.0 151s Investment_14 1 11.2 151s Investment_15 1 12.3 151s Investment_16 1 14.0 151s Investment_17 1 17.6 151s Investment_18 1 17.3 151s Investment_19 1 15.3 151s Investment_20 1 19.0 151s Investment_21 1 21.1 151s Investment_22 1 23.5 151s PrivateWages_2 0 0.0 151s PrivateWages_3 0 0.0 151s PrivateWages_4 0 0.0 151s PrivateWages_5 0 0.0 151s PrivateWages_6 0 0.0 151s PrivateWages_8 0 0.0 151s PrivateWages_9 0 0.0 151s PrivateWages_10 0 0.0 151s PrivateWages_11 0 0.0 151s PrivateWages_12 0 0.0 151s PrivateWages_13 0 0.0 151s PrivateWages_14 0 0.0 151s PrivateWages_15 0 0.0 151s PrivateWages_16 0 0.0 151s PrivateWages_17 0 0.0 151s PrivateWages_18 0 0.0 151s PrivateWages_19 0 0.0 151s PrivateWages_20 0 0.0 151s PrivateWages_21 0 0.0 151s PrivateWages_22 0 0.0 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.0 0 151s Consumption_3 0.0 0 151s Consumption_4 0.0 0 151s Consumption_5 0.0 0 151s Consumption_6 0.0 0 151s Consumption_7 0.0 0 151s Consumption_8 0.0 0 151s Consumption_9 0.0 0 151s Consumption_10 0.0 0 151s Consumption_11 0.0 0 151s Consumption_12 0.0 0 151s Consumption_13 0.0 0 151s Consumption_14 0.0 0 151s Consumption_15 0.0 0 151s Consumption_16 0.0 0 151s Consumption_17 0.0 0 151s Consumption_18 0.0 0 151s Consumption_19 0.0 0 151s Consumption_20 0.0 0 151s Consumption_21 0.0 0 151s Consumption_22 0.0 0 151s Investment_2 12.7 183 151s Investment_3 12.4 183 151s Investment_4 16.9 184 151s Investment_5 18.4 190 151s Investment_6 19.4 193 151s Investment_7 20.1 198 151s Investment_8 19.6 203 151s Investment_9 19.8 208 151s Investment_10 21.1 211 151s Investment_11 21.7 216 151s Investment_12 15.6 217 151s Investment_13 11.4 213 151s Investment_14 7.0 207 151s Investment_15 11.2 202 151s Investment_16 12.3 199 151s Investment_17 14.0 198 151s Investment_18 17.6 200 151s Investment_19 17.3 202 151s Investment_20 15.3 200 151s Investment_21 19.0 201 151s Investment_22 21.1 204 151s PrivateWages_2 0.0 0 151s PrivateWages_3 0.0 0 151s PrivateWages_4 0.0 0 151s PrivateWages_5 0.0 0 151s PrivateWages_6 0.0 0 151s PrivateWages_8 0.0 0 151s PrivateWages_9 0.0 0 151s PrivateWages_10 0.0 0 151s PrivateWages_11 0.0 0 151s PrivateWages_12 0.0 0 151s PrivateWages_13 0.0 0 151s PrivateWages_14 0.0 0 151s PrivateWages_15 0.0 0 151s PrivateWages_16 0.0 0 151s PrivateWages_17 0.0 0 151s PrivateWages_18 0.0 0 151s PrivateWages_19 0.0 0 151s PrivateWages_20 0.0 0 151s PrivateWages_21 0.0 0 151s PrivateWages_22 0.0 0 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 0 0.0 0.0 151s Consumption_3 0 0.0 0.0 151s Consumption_4 0 0.0 0.0 151s Consumption_5 0 0.0 0.0 151s Consumption_6 0 0.0 0.0 151s Consumption_7 0 0.0 0.0 151s Consumption_8 0 0.0 0.0 151s Consumption_9 0 0.0 0.0 151s Consumption_10 0 0.0 0.0 151s Consumption_11 0 0.0 0.0 151s Consumption_12 0 0.0 0.0 151s Consumption_13 0 0.0 0.0 151s Consumption_14 0 0.0 0.0 151s Consumption_15 0 0.0 0.0 151s Consumption_16 0 0.0 0.0 151s Consumption_17 0 0.0 0.0 151s Consumption_18 0 0.0 0.0 151s Consumption_19 0 0.0 0.0 151s Consumption_20 0 0.0 0.0 151s Consumption_21 0 0.0 0.0 151s Consumption_22 0 0.0 0.0 151s Investment_2 0 0.0 0.0 151s Investment_3 0 0.0 0.0 151s Investment_4 0 0.0 0.0 151s Investment_5 0 0.0 0.0 151s Investment_6 0 0.0 0.0 151s Investment_7 0 0.0 0.0 151s Investment_8 0 0.0 0.0 151s Investment_9 0 0.0 0.0 151s Investment_10 0 0.0 0.0 151s Investment_11 0 0.0 0.0 151s Investment_12 0 0.0 0.0 151s Investment_13 0 0.0 0.0 151s Investment_14 0 0.0 0.0 151s Investment_15 0 0.0 0.0 151s Investment_16 0 0.0 0.0 151s Investment_17 0 0.0 0.0 151s Investment_18 0 0.0 0.0 151s Investment_19 0 0.0 0.0 151s Investment_20 0 0.0 0.0 151s Investment_21 0 0.0 0.0 151s Investment_22 0 0.0 0.0 151s PrivateWages_2 1 45.6 44.9 151s PrivateWages_3 1 50.1 45.6 151s PrivateWages_4 1 57.2 50.1 151s PrivateWages_5 1 57.1 57.2 151s PrivateWages_6 1 61.0 57.1 151s PrivateWages_8 1 64.4 64.0 151s PrivateWages_9 1 64.5 64.4 151s PrivateWages_10 1 67.0 64.5 151s PrivateWages_11 1 61.2 67.0 151s PrivateWages_12 1 53.4 61.2 151s PrivateWages_13 1 44.3 53.4 151s PrivateWages_14 1 45.1 44.3 151s PrivateWages_15 1 49.7 45.1 151s PrivateWages_16 1 54.4 49.7 151s PrivateWages_17 1 62.7 54.4 151s PrivateWages_18 1 65.0 62.7 151s PrivateWages_19 1 60.9 65.0 151s PrivateWages_20 1 69.5 60.9 151s PrivateWages_21 1 75.7 69.5 151s PrivateWages_22 1 88.4 75.7 151s PrivateWages_trend 151s Consumption_2 0 151s Consumption_3 0 151s Consumption_4 0 151s Consumption_5 0 151s Consumption_6 0 151s Consumption_7 0 151s Consumption_8 0 151s Consumption_9 0 151s Consumption_10 0 151s Consumption_11 0 151s Consumption_12 0 151s Consumption_13 0 151s Consumption_14 0 151s Consumption_15 0 151s Consumption_16 0 151s Consumption_17 0 151s Consumption_18 0 151s Consumption_19 0 151s Consumption_20 0 151s Consumption_21 0 151s Consumption_22 0 151s Investment_2 0 151s Investment_3 0 151s Investment_4 0 151s Investment_5 0 151s Investment_6 0 151s Investment_7 0 151s Investment_8 0 151s Investment_9 0 151s Investment_10 0 151s Investment_11 0 151s Investment_12 0 151s Investment_13 0 151s Investment_14 0 151s Investment_15 0 151s Investment_16 0 151s Investment_17 0 151s Investment_18 0 151s Investment_19 0 151s Investment_20 0 151s Investment_21 0 151s Investment_22 0 151s PrivateWages_2 -10 151s PrivateWages_3 -9 151s PrivateWages_4 -8 151s PrivateWages_5 -7 151s PrivateWages_6 -6 151s PrivateWages_8 -4 151s PrivateWages_9 -3 151s PrivateWages_10 -2 151s PrivateWages_11 -1 151s PrivateWages_12 0 151s PrivateWages_13 1 151s PrivateWages_14 2 151s PrivateWages_15 3 151s PrivateWages_16 4 151s PrivateWages_17 5 151s PrivateWages_18 6 151s PrivateWages_19 7 151s PrivateWages_20 8 151s PrivateWages_21 9 151s PrivateWages_22 10 151s > nobs 151s [1] 62 151s > linearHypothesis 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 51 151s 2 50 1 0.8 0.37 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 51 151s 2 50 1 0.72 0.4 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 51 151s 2 50 1 0.72 0.4 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 52 151s 2 50 2 0.42 0.66 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 52 151s 2 50 2 0.37 0.69 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 52 151s 2 50 2 0.75 0.69 151s > logLik 151s 'log Lik.' -71.9 (df=13) 151s 'log Lik.' -77.1 (df=13) 151s compare log likelihood value with single-equation OLS 151s [1] "Mean relative difference: 0.000555" 151s Estimating function 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 -0.32389 -4.016 151s Consumption_3 -1.25001 -21.125 151s Consumption_4 -1.56574 -28.810 151s Consumption_5 -0.49350 -9.574 151s Consumption_6 0.00761 0.153 151s Consumption_7 0.86910 17.034 151s Consumption_8 1.33848 26.502 151s Consumption_9 1.05498 22.260 151s Consumption_10 -0.58856 -12.772 151s Consumption_11 0.28231 4.404 151s Consumption_12 -0.22965 -2.618 151s Consumption_13 -0.32213 -2.255 151s Consumption_14 0.32228 3.610 151s Consumption_15 -0.05801 -0.714 151s Consumption_16 -0.03466 -0.485 151s Consumption_17 1.61650 28.450 151s Consumption_18 -0.43597 -7.542 151s Consumption_19 0.21005 3.214 151s Consumption_20 0.98920 18.795 151s Consumption_21 0.78508 16.565 151s Consumption_22 -2.17345 -51.076 151s Investment_2 0.00000 0.000 151s Investment_3 0.00000 0.000 151s Investment_4 0.00000 0.000 151s Investment_5 0.00000 0.000 151s Investment_6 0.00000 0.000 151s Investment_7 0.00000 0.000 151s Investment_8 0.00000 0.000 151s Investment_9 0.00000 0.000 151s Investment_10 0.00000 0.000 151s Investment_11 0.00000 0.000 151s Investment_12 0.00000 0.000 151s Investment_13 0.00000 0.000 151s Investment_14 0.00000 0.000 151s Investment_15 0.00000 0.000 151s Investment_16 0.00000 0.000 151s Investment_17 0.00000 0.000 151s Investment_18 0.00000 0.000 151s Investment_19 0.00000 0.000 151s Investment_20 0.00000 0.000 151s Investment_21 0.00000 0.000 151s Investment_22 0.00000 0.000 151s PrivateWages_2 0.00000 0.000 151s PrivateWages_3 0.00000 0.000 151s PrivateWages_4 0.00000 0.000 151s PrivateWages_5 0.00000 0.000 151s PrivateWages_6 0.00000 0.000 151s PrivateWages_8 0.00000 0.000 151s PrivateWages_9 0.00000 0.000 151s PrivateWages_10 0.00000 0.000 151s PrivateWages_11 0.00000 0.000 151s PrivateWages_12 0.00000 0.000 151s PrivateWages_13 0.00000 0.000 151s PrivateWages_14 0.00000 0.000 151s PrivateWages_15 0.00000 0.000 151s PrivateWages_16 0.00000 0.000 151s PrivateWages_17 0.00000 0.000 151s PrivateWages_18 0.00000 0.000 151s PrivateWages_19 0.00000 0.000 151s PrivateWages_20 0.00000 0.000 151s PrivateWages_21 0.00000 0.000 151s PrivateWages_22 0.00000 0.000 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 -4.113 -9.134 151s Consumption_3 -15.500 -40.250 151s Consumption_4 -26.461 -57.932 151s Consumption_5 -9.080 -18.260 151s Consumption_6 0.148 0.294 151s Consumption_7 17.469 35.372 151s Consumption_8 26.234 55.547 151s Consumption_9 20.889 45.259 151s Consumption_10 -12.419 -26.662 151s Consumption_11 6.126 11.885 151s Consumption_12 -3.583 -9.025 151s Consumption_13 -3.672 -11.049 151s Consumption_14 2.256 10.990 151s Consumption_15 -0.650 -2.123 151s Consumption_16 -0.426 -1.362 151s Consumption_17 22.631 71.449 151s Consumption_18 -7.673 -20.796 151s Consumption_19 3.634 9.641 151s Consumption_20 15.135 48.867 151s Consumption_21 14.916 41.609 151s Consumption_22 -45.860 -134.319 151s Investment_2 0.000 0.000 151s Investment_3 0.000 0.000 151s Investment_4 0.000 0.000 151s Investment_5 0.000 0.000 151s Investment_6 0.000 0.000 151s Investment_7 0.000 0.000 151s Investment_8 0.000 0.000 151s Investment_9 0.000 0.000 151s Investment_10 0.000 0.000 151s Investment_11 0.000 0.000 151s Investment_12 0.000 0.000 151s Investment_13 0.000 0.000 151s Investment_14 0.000 0.000 151s Investment_15 0.000 0.000 151s Investment_16 0.000 0.000 151s Investment_17 0.000 0.000 151s Investment_18 0.000 0.000 151s Investment_19 0.000 0.000 151s Investment_20 0.000 0.000 151s Investment_21 0.000 0.000 151s Investment_22 0.000 0.000 151s PrivateWages_2 0.000 0.000 151s PrivateWages_3 0.000 0.000 151s PrivateWages_4 0.000 0.000 151s PrivateWages_5 0.000 0.000 151s PrivateWages_6 0.000 0.000 151s PrivateWages_8 0.000 0.000 151s PrivateWages_9 0.000 0.000 151s PrivateWages_10 0.000 0.000 151s PrivateWages_11 0.000 0.000 151s PrivateWages_12 0.000 0.000 151s PrivateWages_13 0.000 0.000 151s PrivateWages_14 0.000 0.000 151s PrivateWages_15 0.000 0.000 151s PrivateWages_16 0.000 0.000 151s PrivateWages_17 0.000 0.000 151s PrivateWages_18 0.000 0.000 151s PrivateWages_19 0.000 0.000 151s PrivateWages_20 0.000 0.000 151s PrivateWages_21 0.000 0.000 151s PrivateWages_22 0.000 0.000 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0.0000 0.000 151s Consumption_3 0.0000 0.000 151s Consumption_4 0.0000 0.000 151s Consumption_5 0.0000 0.000 151s Consumption_6 0.0000 0.000 151s Consumption_7 0.0000 0.000 151s Consumption_8 0.0000 0.000 151s Consumption_9 0.0000 0.000 151s Consumption_10 0.0000 0.000 151s Consumption_11 0.0000 0.000 151s Consumption_12 0.0000 0.000 151s Consumption_13 0.0000 0.000 151s Consumption_14 0.0000 0.000 151s Consumption_15 0.0000 0.000 151s Consumption_16 0.0000 0.000 151s Consumption_17 0.0000 0.000 151s Consumption_18 0.0000 0.000 151s Consumption_19 0.0000 0.000 151s Consumption_20 0.0000 0.000 151s Consumption_21 0.0000 0.000 151s Consumption_22 0.0000 0.000 151s Investment_2 -0.0668 -0.828 151s Investment_3 -0.0476 -0.804 151s Investment_4 1.2467 22.939 151s Investment_5 -1.3512 -26.213 151s Investment_6 0.4154 8.350 151s Investment_7 1.4923 29.248 151s Investment_8 0.7889 15.620 151s Investment_9 -0.6317 -13.329 151s Investment_10 1.0830 23.500 151s Investment_11 0.2791 4.353 151s Investment_12 0.0369 0.420 151s Investment_13 0.3659 2.561 151s Investment_14 0.2237 2.505 151s Investment_15 -0.1728 -2.126 151s Investment_16 0.0101 0.141 151s Investment_17 0.9719 17.105 151s Investment_18 0.0516 0.893 151s Investment_19 -2.5656 -39.254 151s Investment_20 -0.6866 -13.045 151s Investment_21 -0.7807 -16.474 151s Investment_22 -0.6623 -15.565 151s PrivateWages_2 0.0000 0.000 151s PrivateWages_3 0.0000 0.000 151s PrivateWages_4 0.0000 0.000 151s PrivateWages_5 0.0000 0.000 151s PrivateWages_6 0.0000 0.000 151s PrivateWages_8 0.0000 0.000 151s PrivateWages_9 0.0000 0.000 151s PrivateWages_10 0.0000 0.000 151s PrivateWages_11 0.0000 0.000 151s PrivateWages_12 0.0000 0.000 151s PrivateWages_13 0.0000 0.000 151s PrivateWages_14 0.0000 0.000 151s PrivateWages_15 0.0000 0.000 151s PrivateWages_16 0.0000 0.000 151s PrivateWages_17 0.0000 0.000 151s PrivateWages_18 0.0000 0.000 151s PrivateWages_19 0.0000 0.000 151s PrivateWages_20 0.0000 0.000 151s PrivateWages_21 0.0000 0.000 151s PrivateWages_22 0.0000 0.000 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.000 0.00 151s Consumption_3 0.000 0.00 151s Consumption_4 0.000 0.00 151s Consumption_5 0.000 0.00 151s Consumption_6 0.000 0.00 151s Consumption_7 0.000 0.00 151s Consumption_8 0.000 0.00 151s Consumption_9 0.000 0.00 151s Consumption_10 0.000 0.00 151s Consumption_11 0.000 0.00 151s Consumption_12 0.000 0.00 151s Consumption_13 0.000 0.00 151s Consumption_14 0.000 0.00 151s Consumption_15 0.000 0.00 151s Consumption_16 0.000 0.00 151s Consumption_17 0.000 0.00 151s Consumption_18 0.000 0.00 151s Consumption_19 0.000 0.00 151s Consumption_20 0.000 0.00 151s Consumption_21 0.000 0.00 151s Consumption_22 0.000 0.00 151s Investment_2 -0.848 -12.21 151s Investment_3 -0.590 -8.69 151s Investment_4 21.069 230.01 151s Investment_5 -24.862 -256.32 151s Investment_6 8.059 80.05 151s Investment_7 29.994 295.17 151s Investment_8 15.463 160.46 151s Investment_9 -12.507 -131.14 151s Investment_10 22.850 228.07 151s Investment_11 6.056 60.20 151s Investment_12 0.575 7.99 151s Investment_13 4.172 78.05 151s Investment_14 1.566 46.33 151s Investment_15 -1.936 -34.91 151s Investment_16 0.124 2.01 151s Investment_17 13.606 192.14 151s Investment_18 0.908 10.31 151s Investment_19 -44.385 -517.74 151s Investment_20 -10.505 -137.25 151s Investment_21 -14.834 -157.09 151s Investment_22 -13.975 -135.45 151s PrivateWages_2 0.000 0.00 151s PrivateWages_3 0.000 0.00 151s PrivateWages_4 0.000 0.00 151s PrivateWages_5 0.000 0.00 151s PrivateWages_6 0.000 0.00 151s PrivateWages_8 0.000 0.00 151s PrivateWages_9 0.000 0.00 151s PrivateWages_10 0.000 0.00 151s PrivateWages_11 0.000 0.00 151s PrivateWages_12 0.000 0.00 151s PrivateWages_13 0.000 0.00 151s PrivateWages_14 0.000 0.00 151s PrivateWages_15 0.000 0.00 151s PrivateWages_16 0.000 0.00 151s PrivateWages_17 0.000 0.00 151s PrivateWages_18 0.000 0.00 151s PrivateWages_19 0.000 0.00 151s PrivateWages_20 0.000 0.00 151s PrivateWages_21 0.000 0.00 151s PrivateWages_22 0.000 0.00 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 0.0000 0.00 0.00 151s Consumption_3 0.0000 0.00 0.00 151s Consumption_4 0.0000 0.00 0.00 151s Consumption_5 0.0000 0.00 0.00 151s Consumption_6 0.0000 0.00 0.00 151s Consumption_7 0.0000 0.00 0.00 151s Consumption_8 0.0000 0.00 0.00 151s Consumption_9 0.0000 0.00 0.00 151s Consumption_10 0.0000 0.00 0.00 151s Consumption_11 0.0000 0.00 0.00 151s Consumption_12 0.0000 0.00 0.00 151s Consumption_13 0.0000 0.00 0.00 151s Consumption_14 0.0000 0.00 0.00 151s Consumption_15 0.0000 0.00 0.00 151s Consumption_16 0.0000 0.00 0.00 151s Consumption_17 0.0000 0.00 0.00 151s Consumption_18 0.0000 0.00 0.00 151s Consumption_19 0.0000 0.00 0.00 151s Consumption_20 0.0000 0.00 0.00 151s Consumption_21 0.0000 0.00 0.00 151s Consumption_22 0.0000 0.00 0.00 151s Investment_2 0.0000 0.00 0.00 151s Investment_3 0.0000 0.00 0.00 151s Investment_4 0.0000 0.00 0.00 151s Investment_5 0.0000 0.00 0.00 151s Investment_6 0.0000 0.00 0.00 151s Investment_7 0.0000 0.00 0.00 151s Investment_8 0.0000 0.00 0.00 151s Investment_9 0.0000 0.00 0.00 151s Investment_10 0.0000 0.00 0.00 151s Investment_11 0.0000 0.00 0.00 151s Investment_12 0.0000 0.00 0.00 151s Investment_13 0.0000 0.00 0.00 151s Investment_14 0.0000 0.00 0.00 151s Investment_15 0.0000 0.00 0.00 151s Investment_16 0.0000 0.00 0.00 151s Investment_17 0.0000 0.00 0.00 151s Investment_18 0.0000 0.00 0.00 151s Investment_19 0.0000 0.00 0.00 151s Investment_20 0.0000 0.00 0.00 151s Investment_21 0.0000 0.00 0.00 151s Investment_22 0.0000 0.00 0.00 151s PrivateWages_2 -1.3389 -61.06 -60.12 151s PrivateWages_3 0.2462 12.33 11.23 151s PrivateWages_4 1.1255 64.38 56.39 151s PrivateWages_5 -0.1959 -11.18 -11.20 151s PrivateWages_6 -0.5284 -32.23 -30.17 151s PrivateWages_8 -0.7909 -50.94 -50.62 151s PrivateWages_9 0.2819 18.18 18.15 151s PrivateWages_10 1.1384 76.28 73.43 151s PrivateWages_11 -0.1904 -11.65 -12.76 151s PrivateWages_12 0.5813 31.04 35.58 151s PrivateWages_13 0.1206 5.34 6.44 151s PrivateWages_14 0.4773 21.53 21.14 151s PrivateWages_15 0.3035 15.09 13.69 151s PrivateWages_16 0.0284 1.55 1.41 151s PrivateWages_17 -0.8517 -53.40 -46.33 151s PrivateWages_18 0.9908 64.40 62.12 151s PrivateWages_19 -0.4597 -28.00 -29.88 151s PrivateWages_20 -0.3819 -26.54 -23.26 151s PrivateWages_21 -1.1062 -83.74 -76.88 151s PrivateWages_22 0.5501 48.63 41.64 151s PrivateWages_trend 151s Consumption_2 0.000 151s Consumption_3 0.000 151s Consumption_4 0.000 151s Consumption_5 0.000 151s Consumption_6 0.000 151s Consumption_7 0.000 151s Consumption_8 0.000 151s Consumption_9 0.000 151s Consumption_10 0.000 151s Consumption_11 0.000 151s Consumption_12 0.000 151s Consumption_13 0.000 151s Consumption_14 0.000 151s Consumption_15 0.000 151s Consumption_16 0.000 151s Consumption_17 0.000 151s Consumption_18 0.000 151s Consumption_19 0.000 151s Consumption_20 0.000 151s Consumption_21 0.000 151s Consumption_22 0.000 151s Investment_2 0.000 151s Investment_3 0.000 151s Investment_4 0.000 151s Investment_5 0.000 151s Investment_6 0.000 151s Investment_7 0.000 151s Investment_8 0.000 151s Investment_9 0.000 151s Investment_10 0.000 151s Investment_11 0.000 151s Investment_12 0.000 151s Investment_13 0.000 151s Investment_14 0.000 151s Investment_15 0.000 151s Investment_16 0.000 151s Investment_17 0.000 151s Investment_18 0.000 151s Investment_19 0.000 151s Investment_20 0.000 151s Investment_21 0.000 151s Investment_22 0.000 151s PrivateWages_2 13.389 151s PrivateWages_3 -2.216 151s PrivateWages_4 -9.004 151s PrivateWages_5 1.371 151s PrivateWages_6 3.170 151s PrivateWages_8 3.164 151s PrivateWages_9 -0.846 151s PrivateWages_10 -2.277 151s PrivateWages_11 0.190 151s PrivateWages_12 0.000 151s PrivateWages_13 0.121 151s PrivateWages_14 0.955 151s PrivateWages_15 0.911 151s PrivateWages_16 0.114 151s PrivateWages_17 -4.258 151s PrivateWages_18 5.945 151s PrivateWages_19 -3.218 151s PrivateWages_20 -3.055 151s PrivateWages_21 -9.956 151s PrivateWages_22 5.501 151s [1] TRUE 151s > Bread 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_(Intercept) 100.0401 0.0296 151s Consumption_corpProf 0.0296 0.4904 151s Consumption_corpProfLag -1.0438 -0.3107 151s Consumption_wages -1.9405 -0.0777 151s Investment_(Intercept) 0.0000 0.0000 151s Investment_corpProf 0.0000 0.0000 151s Investment_corpProfLag 0.0000 0.0000 151s Investment_capitalLag 0.0000 0.0000 151s PrivateWages_(Intercept) 0.0000 0.0000 151s PrivateWages_gnp 0.0000 0.0000 151s PrivateWages_gnpLag 0.0000 0.0000 151s PrivateWages_trend 0.0000 0.0000 151s Consumption_corpProfLag Consumption_wages 151s Consumption_(Intercept) -1.0438 -1.9405 151s Consumption_corpProf -0.3107 -0.0777 151s Consumption_corpProfLag 0.4844 -0.0396 151s Consumption_wages -0.0396 0.0941 151s Investment_(Intercept) 0.0000 0.0000 151s Investment_corpProf 0.0000 0.0000 151s Investment_corpProfLag 0.0000 0.0000 151s Investment_capitalLag 0.0000 0.0000 151s PrivateWages_(Intercept) 0.0000 0.0000 151s PrivateWages_gnp 0.0000 0.0000 151s PrivateWages_gnpLag 0.0000 0.0000 151s PrivateWages_trend 0.0000 0.0000 151s Investment_(Intercept) Investment_corpProf 151s Consumption_(Intercept) 0.00 0.0000 151s Consumption_corpProf 0.00 0.0000 151s Consumption_corpProfLag 0.00 0.0000 151s Consumption_wages 0.00 0.0000 151s Investment_(Intercept) 1817.57 -17.6857 151s Investment_corpProf -17.69 0.5738 151s Investment_corpProfLag 14.44 -0.4928 151s Investment_capitalLag -8.74 0.0801 151s PrivateWages_(Intercept) 0.00 0.0000 151s PrivateWages_gnp 0.00 0.0000 151s PrivateWages_gnpLag 0.00 0.0000 151s PrivateWages_trend 0.00 0.0000 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_(Intercept) 0.0000 0.0000 151s Consumption_corpProf 0.0000 0.0000 151s Consumption_corpProfLag 0.0000 0.0000 151s Consumption_wages 0.0000 0.0000 151s Investment_(Intercept) 14.4412 -8.7403 151s Investment_corpProf -0.4928 0.0801 151s Investment_corpProfLag 0.6190 -0.0811 151s Investment_capitalLag -0.0811 0.0435 151s PrivateWages_(Intercept) 0.0000 0.0000 151s PrivateWages_gnp 0.0000 0.0000 151s PrivateWages_gnpLag 0.0000 0.0000 151s PrivateWages_trend 0.0000 0.0000 151s PrivateWages_(Intercept) PrivateWages_gnp 151s Consumption_(Intercept) 0.000 0.000 151s Consumption_corpProf 0.000 0.000 151s Consumption_corpProfLag 0.000 0.000 151s Consumption_wages 0.000 0.000 151s Investment_(Intercept) 0.000 0.000 151s Investment_corpProf 0.000 0.000 151s Investment_corpProfLag 0.000 0.000 151s Investment_capitalLag 0.000 0.000 151s PrivateWages_(Intercept) 174.627 -0.658 151s PrivateWages_gnp -0.658 0.112 151s PrivateWages_gnpLag -2.295 -0.104 151s PrivateWages_trend 2.155 -0.030 151s PrivateWages_gnpLag PrivateWages_trend 151s Consumption_(Intercept) 0.00000 0.00000 151s Consumption_corpProf 0.00000 0.00000 151s Consumption_corpProfLag 0.00000 0.00000 151s Consumption_wages 0.00000 0.00000 151s Investment_(Intercept) 0.00000 0.00000 151s Investment_corpProf 0.00000 0.00000 151s Investment_corpProfLag 0.00000 0.00000 151s Investment_capitalLag 0.00000 0.00000 151s PrivateWages_(Intercept) -2.29451 2.15506 151s PrivateWages_gnp -0.10426 -0.03004 151s PrivateWages_gnpLag 0.14761 -0.00667 151s PrivateWages_trend -0.00667 0.11527 151s > 151s > # 2SLS 151s > summary 151s 151s systemfit results 151s method: 2SLS 151s 151s N DF SSR detRCov OLS-R2 McElroy-R2 151s system 60 48 53.4 0.274 0.973 0.992 151s 151s N DF SSR MSE RMSE R2 Adj R2 151s Consumption 20 16 20.67 1.292 1.14 0.978 0.974 151s Investment 20 16 23.02 1.438 1.20 0.901 0.883 151s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 151s 151s The covariance matrix of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.034 0.309 -0.383 151s Investment 0.309 1.151 0.202 151s PrivateWages -0.383 0.202 0.487 151s 151s The correlations of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.000 0.284 -0.540 151s Investment 0.284 1.000 0.269 151s PrivateWages -0.540 0.269 1.000 151s 151s 151s 2SLS estimates for 'Consumption' (equation 1) 151s Model Formula: consump ~ corpProf + corpProfLag + wages 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 16.5093 1.3121 12.58 1.0e-09 *** 151s corpProf 0.0219 0.1159 0.19 0.85 151s corpProfLag 0.1931 0.1071 1.80 0.09 . 151s wages 0.8174 0.0408 20.05 9.2e-13 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.137 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 20.671 MSE: 1.292 Root MSE: 1.137 151s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.974 151s 151s 151s 2SLS estimates for 'Investment' (equation 2) 151s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 17.843 6.850 2.60 0.01915 * 151s corpProf 0.217 0.155 1.40 0.18106 151s corpProfLag 0.542 0.148 3.65 0.00216 ** 151s capitalLag -0.145 0.033 -4.41 0.00044 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.199 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 151s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 151s 151s 151s 2SLS estimates for 'PrivateWages' (equation 3) 151s Model Formula: privWage ~ gnp + gnpLag + trend 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 1.3431 1.1772 1.14 0.27070 151s gnp 0.4438 0.0358 12.39 1.3e-09 *** 151s gnpLag 0.1447 0.0389 3.72 0.00185 ** 151s trend 0.1238 0.0306 4.05 0.00093 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 0.78 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 151s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 151s 151s > residuals 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 -0.383 -1.0104 -1.3401 151s 3 -0.593 0.2478 0.2378 151s 4 -1.219 1.0621 1.1117 151s 5 -0.130 -1.4104 -0.1954 151s 6 0.354 0.4328 -0.5355 151s 7 NA NA NA 151s 8 1.551 1.0463 -0.7908 151s 9 1.440 0.0674 0.2831 151s 10 -0.286 1.7698 1.1353 151s 11 -0.453 -0.5912 -0.1765 151s 12 -0.994 -0.6318 0.6007 151s 13 -1.300 -0.6983 0.1443 151s 14 0.521 0.9724 0.4826 151s 15 -0.157 -0.1827 0.3016 151s 16 -0.014 0.1167 0.0261 151s 17 1.974 1.6266 -0.8614 151s 18 -0.576 -0.0525 0.9927 151s 19 -0.203 -3.0656 -0.4446 151s 20 1.342 0.1393 -0.3914 151s 21 1.039 -0.1305 -1.1115 151s 22 -1.912 0.2922 0.5312 151s > fitted 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 42.3 0.810 26.8 151s 3 45.6 1.652 29.1 151s 4 50.4 4.138 33.0 151s 5 50.7 4.410 34.1 151s 6 52.2 4.667 35.9 151s 7 NA NA NA 151s 8 54.6 3.154 38.7 151s 9 55.9 2.933 38.9 151s 10 58.1 3.330 40.2 151s 11 55.5 1.591 38.1 151s 12 51.9 -2.768 33.9 151s 13 46.9 -5.502 28.9 151s 14 46.0 -6.072 28.0 151s 15 48.9 -2.817 30.3 151s 16 51.3 -1.417 33.2 151s 17 55.7 0.473 37.7 151s 18 59.3 2.053 40.0 151s 19 57.7 1.166 38.6 151s 20 60.3 1.161 42.0 151s 21 64.0 3.431 46.1 151s 22 71.6 4.608 52.8 151s > predict 151s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 151s 1 NA NA NA NA 151s 2 42.3 0.473 41.3 43.3 151s 3 45.6 0.573 44.4 46.8 151s 4 50.4 0.366 49.6 51.2 151s 5 50.7 0.423 49.8 51.6 151s 6 52.2 0.426 51.3 53.1 151s 7 NA NA NA NA 151s 8 54.6 0.347 53.9 55.4 151s 9 55.9 0.384 55.0 56.7 151s 10 58.1 0.395 57.2 58.9 151s 11 55.5 0.729 53.9 57.0 151s 12 51.9 0.594 50.6 53.2 151s 13 46.9 0.752 45.3 48.5 151s 14 46.0 0.616 44.7 47.3 151s 15 48.9 0.373 48.1 49.6 151s 16 51.3 0.331 50.6 52.0 151s 17 55.7 0.403 54.9 56.6 151s 18 59.3 0.326 58.6 60.0 151s 19 57.7 0.411 56.8 58.6 151s 20 60.3 0.472 59.3 61.3 151s 21 64.0 0.443 63.0 64.9 151s 22 71.6 0.683 70.2 73.1 151s Investment.pred Investment.se.fit Investment.lwr Investment.upr 151s 1 NA NA NA NA 151s 2 0.810 0.786 -0.8569 2.48 151s 3 1.652 0.541 0.5056 2.80 151s 4 4.138 0.511 3.0552 5.22 151s 5 4.410 0.421 3.5172 5.30 151s 6 4.667 0.395 3.8294 5.51 151s 7 NA NA NA NA 151s 8 3.154 0.327 2.4602 3.85 151s 9 2.933 0.489 1.8967 3.97 151s 10 3.330 0.537 2.1915 4.47 151s 11 1.591 0.786 -0.0748 3.26 151s 12 -2.768 0.615 -4.0716 -1.46 151s 13 -5.502 0.787 -7.1696 -3.83 151s 14 -6.072 0.842 -7.8568 -4.29 151s 15 -2.817 0.397 -3.6591 -1.98 151s 16 -1.417 0.343 -2.1436 -0.69 151s 17 0.473 0.457 -0.4954 1.44 151s 18 2.053 0.286 1.4471 2.66 151s 19 1.166 0.430 0.2549 2.08 151s 20 1.161 0.515 0.0698 2.25 151s 21 3.431 0.426 2.5282 4.33 151s 22 4.608 0.606 3.3223 5.89 151s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 151s 1 NA NA NA NA 151s 2 26.8 0.328 26.1 27.5 151s 3 29.1 0.340 28.3 29.8 151s 4 33.0 0.360 32.2 33.8 151s 5 34.1 0.258 33.5 34.6 151s 6 35.9 0.266 35.4 36.5 151s 7 NA NA NA NA 151s 8 38.7 0.262 38.1 39.2 151s 9 38.9 0.250 38.4 39.4 151s 10 40.2 0.240 39.7 40.7 151s 11 38.1 0.355 37.3 38.8 151s 12 33.9 0.382 33.1 34.7 151s 13 28.9 0.456 27.9 29.8 151s 14 28.0 0.348 27.3 28.8 151s 15 30.3 0.339 29.6 31.0 151s 16 33.2 0.284 32.6 33.8 151s 17 37.7 0.293 37.0 38.3 151s 18 40.0 0.218 39.5 40.5 151s 19 38.6 0.358 37.9 39.4 151s 20 42.0 0.307 41.3 42.6 151s 21 46.1 0.310 45.5 46.8 151s 22 52.8 0.496 51.7 53.8 151s > model.frame 151s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 151s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 151s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 151s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 151s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 151s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 151s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 151s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 151s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 151s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 151s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 151s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 151s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 151s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 151s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 151s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 151s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 151s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 151s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 151s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 151s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 151s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 151s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 151s trend 151s 1 -11 151s 2 -10 151s 3 -9 151s 4 -8 151s 5 -7 151s 6 -6 151s 7 -5 151s 8 -4 151s 9 -3 151s 10 -2 151s 11 -1 151s 12 0 151s 13 1 151s 14 2 151s 15 3 151s 16 4 151s 17 5 151s 18 6 151s 19 7 151s 20 8 151s 21 9 151s 22 10 151s > Frames of instrumental variables 151s govExp taxes govWage trend capitalLag corpProfLag gnpLag 151s 1 2.4 3.4 2.2 -11 180 NA NA 151s 2 3.9 7.7 2.7 -10 183 12.7 44.9 151s 3 3.2 3.9 2.9 -9 183 12.4 45.6 151s 4 2.8 4.7 2.9 -8 184 16.9 50.1 151s 5 3.5 3.8 3.1 -7 190 18.4 57.2 151s 6 3.3 5.5 3.2 -6 193 19.4 57.1 151s 7 3.3 7.0 3.3 -5 198 20.1 NA 151s 8 4.0 6.7 3.6 -4 203 19.6 64.0 151s 9 4.2 4.2 3.7 -3 208 19.8 64.4 151s 10 4.1 4.0 4.0 -2 211 21.1 64.5 151s 11 5.2 7.7 4.2 -1 216 21.7 67.0 151s 12 5.9 7.5 4.8 0 217 15.6 61.2 151s 13 4.9 8.3 5.3 1 213 11.4 53.4 151s 14 3.7 5.4 5.6 2 207 7.0 44.3 151s 15 4.0 6.8 6.0 3 202 11.2 45.1 151s 16 4.4 7.2 6.1 4 199 12.3 49.7 151s 17 2.9 8.3 7.4 5 198 14.0 54.4 151s 18 4.3 6.7 6.7 6 200 17.6 62.7 151s 19 5.3 7.4 7.7 7 202 17.3 65.0 151s 20 6.6 8.9 7.8 8 200 15.3 60.9 151s 21 7.4 9.6 8.0 9 201 19.0 69.5 151s 22 13.8 11.6 8.5 10 204 21.1 75.7 151s govExp taxes govWage trend capitalLag corpProfLag gnpLag 151s 1 2.4 3.4 2.2 -11 180 NA NA 151s 2 3.9 7.7 2.7 -10 183 12.7 44.9 151s 3 3.2 3.9 2.9 -9 183 12.4 45.6 151s 4 2.8 4.7 2.9 -8 184 16.9 50.1 151s 5 3.5 3.8 3.1 -7 190 18.4 57.2 151s 6 3.3 5.5 3.2 -6 193 19.4 57.1 151s 7 3.3 7.0 3.3 -5 198 20.1 NA 151s 8 4.0 6.7 3.6 -4 203 19.6 64.0 151s 9 4.2 4.2 3.7 -3 208 19.8 64.4 151s 10 4.1 4.0 4.0 -2 211 21.1 64.5 151s 11 5.2 7.7 4.2 -1 216 21.7 67.0 151s 12 5.9 7.5 4.8 0 217 15.6 61.2 151s 13 4.9 8.3 5.3 1 213 11.4 53.4 151s 14 3.7 5.4 5.6 2 207 7.0 44.3 151s 15 4.0 6.8 6.0 3 202 11.2 45.1 151s 16 4.4 7.2 6.1 4 199 12.3 49.7 151s 17 2.9 8.3 7.4 5 198 14.0 54.4 151s 18 4.3 6.7 6.7 6 200 17.6 62.7 151s 19 5.3 7.4 7.7 7 202 17.3 65.0 151s 20 6.6 8.9 7.8 8 200 15.3 60.9 151s 21 7.4 9.6 8.0 9 201 19.0 69.5 151s 22 13.8 11.6 8.5 10 204 21.1 75.7 151s govExp taxes govWage trend capitalLag corpProfLag gnpLag 151s 1 2.4 3.4 2.2 -11 180 NA NA 151s 2 3.9 7.7 2.7 -10 183 12.7 44.9 151s 3 3.2 3.9 2.9 -9 183 12.4 45.6 151s 4 2.8 4.7 2.9 -8 184 16.9 50.1 151s 5 3.5 3.8 3.1 -7 190 18.4 57.2 151s 6 3.3 5.5 3.2 -6 193 19.4 57.1 151s 7 3.3 7.0 3.3 -5 198 20.1 NA 151s 8 4.0 6.7 3.6 -4 203 19.6 64.0 151s 9 4.2 4.2 3.7 -3 208 19.8 64.4 151s 10 4.1 4.0 4.0 -2 211 21.1 64.5 151s 11 5.2 7.7 4.2 -1 216 21.7 67.0 151s 12 5.9 7.5 4.8 0 217 15.6 61.2 151s 13 4.9 8.3 5.3 1 213 11.4 53.4 151s 14 3.7 5.4 5.6 2 207 7.0 44.3 151s 15 4.0 6.8 6.0 3 202 11.2 45.1 151s 16 4.4 7.2 6.1 4 199 12.3 49.7 151s 17 2.9 8.3 7.4 5 198 14.0 54.4 151s 18 4.3 6.7 6.7 6 200 17.6 62.7 151s 19 5.3 7.4 7.7 7 202 17.3 65.0 151s 20 6.6 8.9 7.8 8 200 15.3 60.9 151s 21 7.4 9.6 8.0 9 201 19.0 69.5 151s 22 13.8 11.6 8.5 10 204 21.1 75.7 151s > model.matrix 151s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 151s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 151s [3] "Numeric: lengths (744, 720) differ" 151s > matrix of instrumental variables 151s Consumption_(Intercept) Consumption_govExp Consumption_taxes 151s Consumption_2 1 3.9 7.7 151s Consumption_3 1 3.2 3.9 151s Consumption_4 1 2.8 4.7 151s Consumption_5 1 3.5 3.8 151s Consumption_6 1 3.3 5.5 151s Consumption_8 1 4.0 6.7 151s Consumption_9 1 4.2 4.2 151s Consumption_10 1 4.1 4.0 151s Consumption_11 1 5.2 7.7 151s Consumption_12 1 5.9 7.5 151s Consumption_13 1 4.9 8.3 151s Consumption_14 1 3.7 5.4 151s Consumption_15 1 4.0 6.8 151s Consumption_16 1 4.4 7.2 151s Consumption_17 1 2.9 8.3 151s Consumption_18 1 4.3 6.7 151s Consumption_19 1 5.3 7.4 151s Consumption_20 1 6.6 8.9 151s Consumption_21 1 7.4 9.6 151s Consumption_22 1 13.8 11.6 151s Investment_2 0 0.0 0.0 151s Investment_3 0 0.0 0.0 151s Investment_4 0 0.0 0.0 151s Investment_5 0 0.0 0.0 151s Investment_6 0 0.0 0.0 151s Investment_8 0 0.0 0.0 151s Investment_9 0 0.0 0.0 151s Investment_10 0 0.0 0.0 151s Investment_11 0 0.0 0.0 151s Investment_12 0 0.0 0.0 151s Investment_13 0 0.0 0.0 151s Investment_14 0 0.0 0.0 151s Investment_15 0 0.0 0.0 151s Investment_16 0 0.0 0.0 151s Investment_17 0 0.0 0.0 151s Investment_18 0 0.0 0.0 151s Investment_19 0 0.0 0.0 151s Investment_20 0 0.0 0.0 151s Investment_21 0 0.0 0.0 151s Investment_22 0 0.0 0.0 151s PrivateWages_2 0 0.0 0.0 151s PrivateWages_3 0 0.0 0.0 151s PrivateWages_4 0 0.0 0.0 151s PrivateWages_5 0 0.0 0.0 151s PrivateWages_6 0 0.0 0.0 151s PrivateWages_8 0 0.0 0.0 151s PrivateWages_9 0 0.0 0.0 151s PrivateWages_10 0 0.0 0.0 151s PrivateWages_11 0 0.0 0.0 151s PrivateWages_12 0 0.0 0.0 151s PrivateWages_13 0 0.0 0.0 151s PrivateWages_14 0 0.0 0.0 151s PrivateWages_15 0 0.0 0.0 151s PrivateWages_16 0 0.0 0.0 151s PrivateWages_17 0 0.0 0.0 151s PrivateWages_18 0 0.0 0.0 151s PrivateWages_19 0 0.0 0.0 151s PrivateWages_20 0 0.0 0.0 151s PrivateWages_21 0 0.0 0.0 151s PrivateWages_22 0 0.0 0.0 151s Consumption_govWage Consumption_trend Consumption_capitalLag 151s Consumption_2 2.7 -10 183 151s Consumption_3 2.9 -9 183 151s Consumption_4 2.9 -8 184 151s Consumption_5 3.1 -7 190 151s Consumption_6 3.2 -6 193 151s Consumption_8 3.6 -4 203 151s Consumption_9 3.7 -3 208 151s Consumption_10 4.0 -2 211 151s Consumption_11 4.2 -1 216 151s Consumption_12 4.8 0 217 151s Consumption_13 5.3 1 213 151s Consumption_14 5.6 2 207 151s Consumption_15 6.0 3 202 151s Consumption_16 6.1 4 199 151s Consumption_17 7.4 5 198 151s Consumption_18 6.7 6 200 151s Consumption_19 7.7 7 202 151s Consumption_20 7.8 8 200 151s Consumption_21 8.0 9 201 151s Consumption_22 8.5 10 204 151s Investment_2 0.0 0 0 151s Investment_3 0.0 0 0 151s Investment_4 0.0 0 0 151s Investment_5 0.0 0 0 151s Investment_6 0.0 0 0 151s Investment_8 0.0 0 0 151s Investment_9 0.0 0 0 151s Investment_10 0.0 0 0 151s Investment_11 0.0 0 0 151s Investment_12 0.0 0 0 151s Investment_13 0.0 0 0 151s Investment_14 0.0 0 0 151s Investment_15 0.0 0 0 151s Investment_16 0.0 0 0 151s Investment_17 0.0 0 0 151s Investment_18 0.0 0 0 151s Investment_19 0.0 0 0 151s Investment_20 0.0 0 0 151s Investment_21 0.0 0 0 151s Investment_22 0.0 0 0 151s PrivateWages_2 0.0 0 0 151s PrivateWages_3 0.0 0 0 151s PrivateWages_4 0.0 0 0 151s PrivateWages_5 0.0 0 0 151s PrivateWages_6 0.0 0 0 151s PrivateWages_8 0.0 0 0 151s PrivateWages_9 0.0 0 0 151s PrivateWages_10 0.0 0 0 151s PrivateWages_11 0.0 0 0 151s PrivateWages_12 0.0 0 0 151s PrivateWages_13 0.0 0 0 151s PrivateWages_14 0.0 0 0 151s PrivateWages_15 0.0 0 0 151s PrivateWages_16 0.0 0 0 151s PrivateWages_17 0.0 0 0 151s PrivateWages_18 0.0 0 0 151s PrivateWages_19 0.0 0 0 151s PrivateWages_20 0.0 0 0 151s PrivateWages_21 0.0 0 0 151s PrivateWages_22 0.0 0 0 151s Consumption_corpProfLag Consumption_gnpLag 151s Consumption_2 12.7 44.9 151s Consumption_3 12.4 45.6 151s Consumption_4 16.9 50.1 151s Consumption_5 18.4 57.2 151s Consumption_6 19.4 57.1 151s Consumption_8 19.6 64.0 151s Consumption_9 19.8 64.4 151s Consumption_10 21.1 64.5 151s Consumption_11 21.7 67.0 151s Consumption_12 15.6 61.2 151s Consumption_13 11.4 53.4 151s Consumption_14 7.0 44.3 151s Consumption_15 11.2 45.1 151s Consumption_16 12.3 49.7 151s Consumption_17 14.0 54.4 151s Consumption_18 17.6 62.7 151s Consumption_19 17.3 65.0 151s Consumption_20 15.3 60.9 151s Consumption_21 19.0 69.5 151s Consumption_22 21.1 75.7 151s Investment_2 0.0 0.0 151s Investment_3 0.0 0.0 151s Investment_4 0.0 0.0 151s Investment_5 0.0 0.0 151s Investment_6 0.0 0.0 151s Investment_8 0.0 0.0 151s Investment_9 0.0 0.0 151s Investment_10 0.0 0.0 151s Investment_11 0.0 0.0 151s Investment_12 0.0 0.0 151s Investment_13 0.0 0.0 151s Investment_14 0.0 0.0 151s Investment_15 0.0 0.0 151s Investment_16 0.0 0.0 151s Investment_17 0.0 0.0 151s Investment_18 0.0 0.0 151s Investment_19 0.0 0.0 151s Investment_20 0.0 0.0 151s Investment_21 0.0 0.0 151s Investment_22 0.0 0.0 151s PrivateWages_2 0.0 0.0 151s PrivateWages_3 0.0 0.0 151s PrivateWages_4 0.0 0.0 151s PrivateWages_5 0.0 0.0 151s PrivateWages_6 0.0 0.0 151s PrivateWages_8 0.0 0.0 151s PrivateWages_9 0.0 0.0 151s PrivateWages_10 0.0 0.0 151s PrivateWages_11 0.0 0.0 151s PrivateWages_12 0.0 0.0 151s PrivateWages_13 0.0 0.0 151s PrivateWages_14 0.0 0.0 151s PrivateWages_15 0.0 0.0 151s PrivateWages_16 0.0 0.0 151s PrivateWages_17 0.0 0.0 151s PrivateWages_18 0.0 0.0 151s PrivateWages_19 0.0 0.0 151s PrivateWages_20 0.0 0.0 151s PrivateWages_21 0.0 0.0 151s PrivateWages_22 0.0 0.0 151s Investment_(Intercept) Investment_govExp Investment_taxes 151s Consumption_2 0 0.0 0.0 151s Consumption_3 0 0.0 0.0 151s Consumption_4 0 0.0 0.0 151s Consumption_5 0 0.0 0.0 151s Consumption_6 0 0.0 0.0 151s Consumption_8 0 0.0 0.0 151s Consumption_9 0 0.0 0.0 151s Consumption_10 0 0.0 0.0 151s Consumption_11 0 0.0 0.0 151s Consumption_12 0 0.0 0.0 151s Consumption_13 0 0.0 0.0 151s Consumption_14 0 0.0 0.0 151s Consumption_15 0 0.0 0.0 151s Consumption_16 0 0.0 0.0 151s Consumption_17 0 0.0 0.0 151s Consumption_18 0 0.0 0.0 151s Consumption_19 0 0.0 0.0 151s Consumption_20 0 0.0 0.0 151s Consumption_21 0 0.0 0.0 151s Consumption_22 0 0.0 0.0 151s Investment_2 1 3.9 7.7 151s Investment_3 1 3.2 3.9 151s Investment_4 1 2.8 4.7 151s Investment_5 1 3.5 3.8 151s Investment_6 1 3.3 5.5 151s Investment_8 1 4.0 6.7 151s Investment_9 1 4.2 4.2 151s Investment_10 1 4.1 4.0 151s Investment_11 1 5.2 7.7 151s Investment_12 1 5.9 7.5 151s Investment_13 1 4.9 8.3 151s Investment_14 1 3.7 5.4 151s Investment_15 1 4.0 6.8 151s Investment_16 1 4.4 7.2 151s Investment_17 1 2.9 8.3 151s Investment_18 1 4.3 6.7 151s Investment_19 1 5.3 7.4 151s Investment_20 1 6.6 8.9 151s Investment_21 1 7.4 9.6 151s Investment_22 1 13.8 11.6 151s PrivateWages_2 0 0.0 0.0 151s PrivateWages_3 0 0.0 0.0 151s PrivateWages_4 0 0.0 0.0 151s PrivateWages_5 0 0.0 0.0 151s PrivateWages_6 0 0.0 0.0 151s PrivateWages_8 0 0.0 0.0 151s PrivateWages_9 0 0.0 0.0 151s PrivateWages_10 0 0.0 0.0 151s PrivateWages_11 0 0.0 0.0 151s PrivateWages_12 0 0.0 0.0 151s PrivateWages_13 0 0.0 0.0 151s PrivateWages_14 0 0.0 0.0 151s PrivateWages_15 0 0.0 0.0 151s PrivateWages_16 0 0.0 0.0 151s PrivateWages_17 0 0.0 0.0 151s PrivateWages_18 0 0.0 0.0 151s PrivateWages_19 0 0.0 0.0 151s PrivateWages_20 0 0.0 0.0 151s PrivateWages_21 0 0.0 0.0 151s PrivateWages_22 0 0.0 0.0 151s Investment_govWage Investment_trend Investment_capitalLag 151s Consumption_2 0.0 0 0 151s Consumption_3 0.0 0 0 151s Consumption_4 0.0 0 0 151s Consumption_5 0.0 0 0 151s Consumption_6 0.0 0 0 151s Consumption_8 0.0 0 0 151s Consumption_9 0.0 0 0 151s Consumption_10 0.0 0 0 151s Consumption_11 0.0 0 0 151s Consumption_12 0.0 0 0 151s Consumption_13 0.0 0 0 151s Consumption_14 0.0 0 0 151s Consumption_15 0.0 0 0 151s Consumption_16 0.0 0 0 151s Consumption_17 0.0 0 0 151s Consumption_18 0.0 0 0 151s Consumption_19 0.0 0 0 151s Consumption_20 0.0 0 0 151s Consumption_21 0.0 0 0 151s Consumption_22 0.0 0 0 151s Investment_2 2.7 -10 183 151s Investment_3 2.9 -9 183 151s Investment_4 2.9 -8 184 151s Investment_5 3.1 -7 190 151s Investment_6 3.2 -6 193 151s Investment_8 3.6 -4 203 151s Investment_9 3.7 -3 208 151s Investment_10 4.0 -2 211 151s Investment_11 4.2 -1 216 151s Investment_12 4.8 0 217 151s Investment_13 5.3 1 213 151s Investment_14 5.6 2 207 151s Investment_15 6.0 3 202 151s Investment_16 6.1 4 199 151s Investment_17 7.4 5 198 151s Investment_18 6.7 6 200 151s Investment_19 7.7 7 202 151s Investment_20 7.8 8 200 151s Investment_21 8.0 9 201 151s Investment_22 8.5 10 204 151s PrivateWages_2 0.0 0 0 151s PrivateWages_3 0.0 0 0 151s PrivateWages_4 0.0 0 0 151s PrivateWages_5 0.0 0 0 151s PrivateWages_6 0.0 0 0 151s PrivateWages_8 0.0 0 0 151s PrivateWages_9 0.0 0 0 151s PrivateWages_10 0.0 0 0 151s PrivateWages_11 0.0 0 0 151s PrivateWages_12 0.0 0 0 151s PrivateWages_13 0.0 0 0 151s PrivateWages_14 0.0 0 0 151s PrivateWages_15 0.0 0 0 151s PrivateWages_16 0.0 0 0 151s PrivateWages_17 0.0 0 0 151s PrivateWages_18 0.0 0 0 151s PrivateWages_19 0.0 0 0 151s PrivateWages_20 0.0 0 0 151s PrivateWages_21 0.0 0 0 151s PrivateWages_22 0.0 0 0 151s Investment_corpProfLag Investment_gnpLag 151s Consumption_2 0.0 0.0 151s Consumption_3 0.0 0.0 151s Consumption_4 0.0 0.0 151s Consumption_5 0.0 0.0 151s Consumption_6 0.0 0.0 151s Consumption_8 0.0 0.0 151s Consumption_9 0.0 0.0 151s Consumption_10 0.0 0.0 151s Consumption_11 0.0 0.0 151s Consumption_12 0.0 0.0 151s Consumption_13 0.0 0.0 151s Consumption_14 0.0 0.0 151s Consumption_15 0.0 0.0 151s Consumption_16 0.0 0.0 151s Consumption_17 0.0 0.0 151s Consumption_18 0.0 0.0 151s Consumption_19 0.0 0.0 151s Consumption_20 0.0 0.0 151s Consumption_21 0.0 0.0 151s Consumption_22 0.0 0.0 151s Investment_2 12.7 44.9 151s Investment_3 12.4 45.6 151s Investment_4 16.9 50.1 151s Investment_5 18.4 57.2 151s Investment_6 19.4 57.1 151s Investment_8 19.6 64.0 151s Investment_9 19.8 64.4 151s Investment_10 21.1 64.5 151s Investment_11 21.7 67.0 151s Investment_12 15.6 61.2 151s Investment_13 11.4 53.4 151s Investment_14 7.0 44.3 151s Investment_15 11.2 45.1 151s Investment_16 12.3 49.7 151s Investment_17 14.0 54.4 151s Investment_18 17.6 62.7 151s Investment_19 17.3 65.0 151s Investment_20 15.3 60.9 151s Investment_21 19.0 69.5 151s Investment_22 21.1 75.7 151s PrivateWages_2 0.0 0.0 151s PrivateWages_3 0.0 0.0 151s PrivateWages_4 0.0 0.0 151s PrivateWages_5 0.0 0.0 151s PrivateWages_6 0.0 0.0 151s PrivateWages_8 0.0 0.0 151s PrivateWages_9 0.0 0.0 151s PrivateWages_10 0.0 0.0 151s PrivateWages_11 0.0 0.0 151s PrivateWages_12 0.0 0.0 151s PrivateWages_13 0.0 0.0 151s PrivateWages_14 0.0 0.0 151s PrivateWages_15 0.0 0.0 151s PrivateWages_16 0.0 0.0 151s PrivateWages_17 0.0 0.0 151s PrivateWages_18 0.0 0.0 151s PrivateWages_19 0.0 0.0 151s PrivateWages_20 0.0 0.0 151s PrivateWages_21 0.0 0.0 151s PrivateWages_22 0.0 0.0 151s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 151s Consumption_2 0 0.0 0.0 151s Consumption_3 0 0.0 0.0 151s Consumption_4 0 0.0 0.0 151s Consumption_5 0 0.0 0.0 151s Consumption_6 0 0.0 0.0 151s Consumption_8 0 0.0 0.0 151s Consumption_9 0 0.0 0.0 151s Consumption_10 0 0.0 0.0 151s Consumption_11 0 0.0 0.0 151s Consumption_12 0 0.0 0.0 151s Consumption_13 0 0.0 0.0 151s Consumption_14 0 0.0 0.0 151s Consumption_15 0 0.0 0.0 151s Consumption_16 0 0.0 0.0 151s Consumption_17 0 0.0 0.0 151s Consumption_18 0 0.0 0.0 151s Consumption_19 0 0.0 0.0 151s Consumption_20 0 0.0 0.0 151s Consumption_21 0 0.0 0.0 151s Consumption_22 0 0.0 0.0 151s Investment_2 0 0.0 0.0 151s Investment_3 0 0.0 0.0 151s Investment_4 0 0.0 0.0 151s Investment_5 0 0.0 0.0 151s Investment_6 0 0.0 0.0 151s Investment_8 0 0.0 0.0 151s Investment_9 0 0.0 0.0 151s Investment_10 0 0.0 0.0 151s Investment_11 0 0.0 0.0 151s Investment_12 0 0.0 0.0 151s Investment_13 0 0.0 0.0 151s Investment_14 0 0.0 0.0 151s Investment_15 0 0.0 0.0 151s Investment_16 0 0.0 0.0 151s Investment_17 0 0.0 0.0 151s Investment_18 0 0.0 0.0 151s Investment_19 0 0.0 0.0 151s Investment_20 0 0.0 0.0 151s Investment_21 0 0.0 0.0 151s Investment_22 0 0.0 0.0 151s PrivateWages_2 1 3.9 7.7 151s PrivateWages_3 1 3.2 3.9 151s PrivateWages_4 1 2.8 4.7 151s PrivateWages_5 1 3.5 3.8 151s PrivateWages_6 1 3.3 5.5 151s PrivateWages_8 1 4.0 6.7 151s PrivateWages_9 1 4.2 4.2 151s PrivateWages_10 1 4.1 4.0 151s PrivateWages_11 1 5.2 7.7 151s PrivateWages_12 1 5.9 7.5 151s PrivateWages_13 1 4.9 8.3 151s PrivateWages_14 1 3.7 5.4 151s PrivateWages_15 1 4.0 6.8 151s PrivateWages_16 1 4.4 7.2 151s PrivateWages_17 1 2.9 8.3 151s PrivateWages_18 1 4.3 6.7 151s PrivateWages_19 1 5.3 7.4 151s PrivateWages_20 1 6.6 8.9 151s PrivateWages_21 1 7.4 9.6 151s PrivateWages_22 1 13.8 11.6 151s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 151s Consumption_2 0.0 0 0 151s Consumption_3 0.0 0 0 151s Consumption_4 0.0 0 0 151s Consumption_5 0.0 0 0 151s Consumption_6 0.0 0 0 151s Consumption_8 0.0 0 0 151s Consumption_9 0.0 0 0 151s Consumption_10 0.0 0 0 151s Consumption_11 0.0 0 0 151s Consumption_12 0.0 0 0 151s Consumption_13 0.0 0 0 151s Consumption_14 0.0 0 0 151s Consumption_15 0.0 0 0 151s Consumption_16 0.0 0 0 151s Consumption_17 0.0 0 0 151s Consumption_18 0.0 0 0 151s Consumption_19 0.0 0 0 151s Consumption_20 0.0 0 0 151s Consumption_21 0.0 0 0 151s Consumption_22 0.0 0 0 151s Investment_2 0.0 0 0 151s Investment_3 0.0 0 0 151s Investment_4 0.0 0 0 151s Investment_5 0.0 0 0 151s Investment_6 0.0 0 0 151s Investment_8 0.0 0 0 151s Investment_9 0.0 0 0 151s Investment_10 0.0 0 0 151s Investment_11 0.0 0 0 151s Investment_12 0.0 0 0 151s Investment_13 0.0 0 0 151s Investment_14 0.0 0 0 151s Investment_15 0.0 0 0 151s Investment_16 0.0 0 0 151s Investment_17 0.0 0 0 151s Investment_18 0.0 0 0 151s Investment_19 0.0 0 0 151s Investment_20 0.0 0 0 151s Investment_21 0.0 0 0 151s Investment_22 0.0 0 0 151s PrivateWages_2 2.7 -10 183 151s PrivateWages_3 2.9 -9 183 151s PrivateWages_4 2.9 -8 184 151s PrivateWages_5 3.1 -7 190 151s PrivateWages_6 3.2 -6 193 151s PrivateWages_8 3.6 -4 203 151s PrivateWages_9 3.7 -3 208 151s PrivateWages_10 4.0 -2 211 151s PrivateWages_11 4.2 -1 216 151s PrivateWages_12 4.8 0 217 151s PrivateWages_13 5.3 1 213 151s PrivateWages_14 5.6 2 207 151s PrivateWages_15 6.0 3 202 151s PrivateWages_16 6.1 4 199 151s PrivateWages_17 7.4 5 198 151s PrivateWages_18 6.7 6 200 151s PrivateWages_19 7.7 7 202 151s PrivateWages_20 7.8 8 200 151s PrivateWages_21 8.0 9 201 151s PrivateWages_22 8.5 10 204 151s PrivateWages_corpProfLag PrivateWages_gnpLag 151s Consumption_2 0.0 0.0 151s Consumption_3 0.0 0.0 151s Consumption_4 0.0 0.0 151s Consumption_5 0.0 0.0 151s Consumption_6 0.0 0.0 151s Consumption_8 0.0 0.0 151s Consumption_9 0.0 0.0 151s Consumption_10 0.0 0.0 151s Consumption_11 0.0 0.0 151s Consumption_12 0.0 0.0 151s Consumption_13 0.0 0.0 151s Consumption_14 0.0 0.0 151s Consumption_15 0.0 0.0 151s Consumption_16 0.0 0.0 151s Consumption_17 0.0 0.0 151s Consumption_18 0.0 0.0 151s Consumption_19 0.0 0.0 151s Consumption_20 0.0 0.0 151s Consumption_21 0.0 0.0 151s Consumption_22 0.0 0.0 151s Investment_2 0.0 0.0 151s Investment_3 0.0 0.0 151s Investment_4 0.0 0.0 151s Investment_5 0.0 0.0 151s Investment_6 0.0 0.0 151s Investment_8 0.0 0.0 151s Investment_9 0.0 0.0 151s Investment_10 0.0 0.0 151s Investment_11 0.0 0.0 151s Investment_12 0.0 0.0 151s Investment_13 0.0 0.0 151s Investment_14 0.0 0.0 151s Investment_15 0.0 0.0 151s Investment_16 0.0 0.0 151s Investment_17 0.0 0.0 151s Investment_18 0.0 0.0 151s Investment_19 0.0 0.0 151s Investment_20 0.0 0.0 151s Investment_21 0.0 0.0 151s Investment_22 0.0 0.0 151s PrivateWages_2 12.7 44.9 151s PrivateWages_3 12.4 45.6 151s PrivateWages_4 16.9 50.1 151s PrivateWages_5 18.4 57.2 151s PrivateWages_6 19.4 57.1 151s PrivateWages_8 19.6 64.0 151s PrivateWages_9 19.8 64.4 151s PrivateWages_10 21.1 64.5 151s PrivateWages_11 21.7 67.0 151s PrivateWages_12 15.6 61.2 151s PrivateWages_13 11.4 53.4 151s PrivateWages_14 7.0 44.3 151s PrivateWages_15 11.2 45.1 151s PrivateWages_16 12.3 49.7 151s PrivateWages_17 14.0 54.4 151s PrivateWages_18 17.6 62.7 151s PrivateWages_19 17.3 65.0 151s PrivateWages_20 15.3 60.9 151s PrivateWages_21 19.0 69.5 151s PrivateWages_22 21.1 75.7 151s > matrix of fitted regressors 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 1 12.96 151s Consumption_3 1 16.70 151s Consumption_4 1 19.14 151s Consumption_5 1 20.94 151s Consumption_6 1 19.47 151s Consumption_8 1 17.14 151s Consumption_9 1 19.49 151s Consumption_10 1 20.46 151s Consumption_11 1 16.85 151s Consumption_12 1 12.68 151s Consumption_13 1 8.92 151s Consumption_14 1 9.30 151s Consumption_15 1 12.79 151s Consumption_16 1 14.26 151s Consumption_17 1 14.75 151s Consumption_18 1 19.54 151s Consumption_19 1 19.36 151s Consumption_20 1 17.39 151s Consumption_21 1 20.10 151s Consumption_22 1 22.86 151s Investment_2 0 0.00 151s Investment_3 0 0.00 151s Investment_4 0 0.00 151s Investment_5 0 0.00 151s Investment_6 0 0.00 151s Investment_8 0 0.00 151s Investment_9 0 0.00 151s Investment_10 0 0.00 151s Investment_11 0 0.00 151s Investment_12 0 0.00 151s Investment_13 0 0.00 151s Investment_14 0 0.00 151s Investment_15 0 0.00 151s Investment_16 0 0.00 151s Investment_17 0 0.00 151s Investment_18 0 0.00 151s Investment_19 0 0.00 151s Investment_20 0 0.00 151s Investment_21 0 0.00 151s Investment_22 0 0.00 151s PrivateWages_2 0 0.00 151s PrivateWages_3 0 0.00 151s PrivateWages_4 0 0.00 151s PrivateWages_5 0 0.00 151s PrivateWages_6 0 0.00 151s PrivateWages_8 0 0.00 151s PrivateWages_9 0 0.00 151s PrivateWages_10 0 0.00 151s PrivateWages_11 0 0.00 151s PrivateWages_12 0 0.00 151s PrivateWages_13 0 0.00 151s PrivateWages_14 0 0.00 151s PrivateWages_15 0 0.00 151s PrivateWages_16 0 0.00 151s PrivateWages_17 0 0.00 151s PrivateWages_18 0 0.00 151s PrivateWages_19 0 0.00 151s PrivateWages_20 0 0.00 151s PrivateWages_21 0 0.00 151s PrivateWages_22 0 0.00 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 12.7 29.1 151s Consumption_3 12.4 31.9 151s Consumption_4 16.9 35.6 151s Consumption_5 18.4 39.0 151s Consumption_6 19.4 38.8 151s Consumption_8 19.6 39.8 151s Consumption_9 19.8 42.3 151s Consumption_10 21.1 44.1 151s Consumption_11 21.7 43.4 151s Consumption_12 15.6 39.5 151s Consumption_13 11.4 35.1 151s Consumption_14 7.0 33.0 151s Consumption_15 11.2 37.6 151s Consumption_16 12.3 40.0 151s Consumption_17 14.0 41.7 151s Consumption_18 17.6 47.6 151s Consumption_19 17.3 49.5 151s Consumption_20 15.3 48.4 151s Consumption_21 19.0 53.2 151s Consumption_22 21.1 60.9 151s Investment_2 0.0 0.0 151s Investment_3 0.0 0.0 151s Investment_4 0.0 0.0 151s Investment_5 0.0 0.0 151s Investment_6 0.0 0.0 151s Investment_8 0.0 0.0 151s Investment_9 0.0 0.0 151s Investment_10 0.0 0.0 151s Investment_11 0.0 0.0 151s Investment_12 0.0 0.0 151s Investment_13 0.0 0.0 151s Investment_14 0.0 0.0 151s Investment_15 0.0 0.0 151s Investment_16 0.0 0.0 151s Investment_17 0.0 0.0 151s Investment_18 0.0 0.0 151s Investment_19 0.0 0.0 151s Investment_20 0.0 0.0 151s Investment_21 0.0 0.0 151s Investment_22 0.0 0.0 151s PrivateWages_2 0.0 0.0 151s PrivateWages_3 0.0 0.0 151s PrivateWages_4 0.0 0.0 151s PrivateWages_5 0.0 0.0 151s PrivateWages_6 0.0 0.0 151s PrivateWages_8 0.0 0.0 151s PrivateWages_9 0.0 0.0 151s PrivateWages_10 0.0 0.0 151s PrivateWages_11 0.0 0.0 151s PrivateWages_12 0.0 0.0 151s PrivateWages_13 0.0 0.0 151s PrivateWages_14 0.0 0.0 151s PrivateWages_15 0.0 0.0 151s PrivateWages_16 0.0 0.0 151s PrivateWages_17 0.0 0.0 151s PrivateWages_18 0.0 0.0 151s PrivateWages_19 0.0 0.0 151s PrivateWages_20 0.0 0.0 151s PrivateWages_21 0.0 0.0 151s PrivateWages_22 0.0 0.0 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0 0.00 151s Consumption_3 0 0.00 151s Consumption_4 0 0.00 151s Consumption_5 0 0.00 151s Consumption_6 0 0.00 151s Consumption_8 0 0.00 151s Consumption_9 0 0.00 151s Consumption_10 0 0.00 151s Consumption_11 0 0.00 151s Consumption_12 0 0.00 151s Consumption_13 0 0.00 151s Consumption_14 0 0.00 151s Consumption_15 0 0.00 151s Consumption_16 0 0.00 151s Consumption_17 0 0.00 151s Consumption_18 0 0.00 151s Consumption_19 0 0.00 151s Consumption_20 0 0.00 151s Consumption_21 0 0.00 151s Consumption_22 0 0.00 151s Investment_2 1 12.96 151s Investment_3 1 16.70 151s Investment_4 1 19.14 151s Investment_5 1 20.94 151s Investment_6 1 19.47 151s Investment_8 1 17.14 151s Investment_9 1 19.49 151s Investment_10 1 20.46 151s Investment_11 1 16.85 151s Investment_12 1 12.68 151s Investment_13 1 8.92 151s Investment_14 1 9.30 151s Investment_15 1 12.79 151s Investment_16 1 14.26 151s Investment_17 1 14.75 151s Investment_18 1 19.54 151s Investment_19 1 19.36 151s Investment_20 1 17.39 151s Investment_21 1 20.10 151s Investment_22 1 22.86 151s PrivateWages_2 0 0.00 151s PrivateWages_3 0 0.00 151s PrivateWages_4 0 0.00 151s PrivateWages_5 0 0.00 151s PrivateWages_6 0 0.00 151s PrivateWages_8 0 0.00 151s PrivateWages_9 0 0.00 151s PrivateWages_10 0 0.00 151s PrivateWages_11 0 0.00 151s PrivateWages_12 0 0.00 151s PrivateWages_13 0 0.00 151s PrivateWages_14 0 0.00 151s PrivateWages_15 0 0.00 151s PrivateWages_16 0 0.00 151s PrivateWages_17 0 0.00 151s PrivateWages_18 0 0.00 151s PrivateWages_19 0 0.00 151s PrivateWages_20 0 0.00 151s PrivateWages_21 0 0.00 151s PrivateWages_22 0 0.00 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.0 0 151s Consumption_3 0.0 0 151s Consumption_4 0.0 0 151s Consumption_5 0.0 0 151s Consumption_6 0.0 0 151s Consumption_8 0.0 0 151s Consumption_9 0.0 0 151s Consumption_10 0.0 0 151s Consumption_11 0.0 0 151s Consumption_12 0.0 0 151s Consumption_13 0.0 0 151s Consumption_14 0.0 0 151s Consumption_15 0.0 0 151s Consumption_16 0.0 0 151s Consumption_17 0.0 0 151s Consumption_18 0.0 0 151s Consumption_19 0.0 0 151s Consumption_20 0.0 0 151s Consumption_21 0.0 0 151s Consumption_22 0.0 0 151s Investment_2 12.7 183 151s Investment_3 12.4 183 151s Investment_4 16.9 184 151s Investment_5 18.4 190 151s Investment_6 19.4 193 151s Investment_8 19.6 203 151s Investment_9 19.8 208 151s Investment_10 21.1 211 151s Investment_11 21.7 216 151s Investment_12 15.6 217 151s Investment_13 11.4 213 151s Investment_14 7.0 207 151s Investment_15 11.2 202 151s Investment_16 12.3 199 151s Investment_17 14.0 198 151s Investment_18 17.6 200 151s Investment_19 17.3 202 151s Investment_20 15.3 200 151s Investment_21 19.0 201 151s Investment_22 21.1 204 151s PrivateWages_2 0.0 0 151s PrivateWages_3 0.0 0 151s PrivateWages_4 0.0 0 151s PrivateWages_5 0.0 0 151s PrivateWages_6 0.0 0 151s PrivateWages_8 0.0 0 151s PrivateWages_9 0.0 0 151s PrivateWages_10 0.0 0 151s PrivateWages_11 0.0 0 151s PrivateWages_12 0.0 0 151s PrivateWages_13 0.0 0 151s PrivateWages_14 0.0 0 151s PrivateWages_15 0.0 0 151s PrivateWages_16 0.0 0 151s PrivateWages_17 0.0 0 151s PrivateWages_18 0.0 0 151s PrivateWages_19 0.0 0 151s PrivateWages_20 0.0 0 151s PrivateWages_21 0.0 0 151s PrivateWages_22 0.0 0 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 0 0.0 0.0 151s Consumption_3 0 0.0 0.0 151s Consumption_4 0 0.0 0.0 151s Consumption_5 0 0.0 0.0 151s Consumption_6 0 0.0 0.0 151s Consumption_8 0 0.0 0.0 151s Consumption_9 0 0.0 0.0 151s Consumption_10 0 0.0 0.0 151s Consumption_11 0 0.0 0.0 151s Consumption_12 0 0.0 0.0 151s Consumption_13 0 0.0 0.0 151s Consumption_14 0 0.0 0.0 151s Consumption_15 0 0.0 0.0 151s Consumption_16 0 0.0 0.0 151s Consumption_17 0 0.0 0.0 151s Consumption_18 0 0.0 0.0 151s Consumption_19 0 0.0 0.0 151s Consumption_20 0 0.0 0.0 151s Consumption_21 0 0.0 0.0 151s Consumption_22 0 0.0 0.0 151s Investment_2 0 0.0 0.0 151s Investment_3 0 0.0 0.0 151s Investment_4 0 0.0 0.0 151s Investment_5 0 0.0 0.0 151s Investment_6 0 0.0 0.0 151s Investment_8 0 0.0 0.0 151s Investment_9 0 0.0 0.0 151s Investment_10 0 0.0 0.0 151s Investment_11 0 0.0 0.0 151s Investment_12 0 0.0 0.0 151s Investment_13 0 0.0 0.0 151s Investment_14 0 0.0 0.0 151s Investment_15 0 0.0 0.0 151s Investment_16 0 0.0 0.0 151s Investment_17 0 0.0 0.0 151s Investment_18 0 0.0 0.0 151s Investment_19 0 0.0 0.0 151s Investment_20 0 0.0 0.0 151s Investment_21 0 0.0 0.0 151s Investment_22 0 0.0 0.0 151s PrivateWages_2 1 47.1 44.9 151s PrivateWages_3 1 49.6 45.6 151s PrivateWages_4 1 56.5 50.1 151s PrivateWages_5 1 60.7 57.2 151s PrivateWages_6 1 60.6 57.1 151s PrivateWages_8 1 60.0 64.0 151s PrivateWages_9 1 62.3 64.4 151s PrivateWages_10 1 64.6 64.5 151s PrivateWages_11 1 63.7 67.0 151s PrivateWages_12 1 54.8 61.2 151s PrivateWages_13 1 47.0 53.4 151s PrivateWages_14 1 42.1 44.3 151s PrivateWages_15 1 51.2 45.1 151s PrivateWages_16 1 55.3 49.7 151s PrivateWages_17 1 57.4 54.4 151s PrivateWages_18 1 67.2 62.7 151s PrivateWages_19 1 68.5 65.0 151s PrivateWages_20 1 66.8 60.9 151s PrivateWages_21 1 74.9 69.5 151s PrivateWages_22 1 86.9 75.7 151s PrivateWages_trend 151s Consumption_2 0 151s Consumption_3 0 151s Consumption_4 0 151s Consumption_5 0 151s Consumption_6 0 151s Consumption_8 0 151s Consumption_9 0 151s Consumption_10 0 151s Consumption_11 0 151s Consumption_12 0 151s Consumption_13 0 151s Consumption_14 0 151s Consumption_15 0 151s Consumption_16 0 151s Consumption_17 0 151s Consumption_18 0 151s Consumption_19 0 151s Consumption_20 0 151s Consumption_21 0 151s Consumption_22 0 151s Investment_2 0 151s Investment_3 0 151s Investment_4 0 151s Investment_5 0 151s Investment_6 0 151s Investment_8 0 151s Investment_9 0 151s Investment_10 0 151s Investment_11 0 151s Investment_12 0 151s Investment_13 0 151s Investment_14 0 151s Investment_15 0 151s Investment_16 0 151s Investment_17 0 151s Investment_18 0 151s Investment_19 0 151s Investment_20 0 151s Investment_21 0 151s Investment_22 0 151s PrivateWages_2 -10 151s PrivateWages_3 -9 151s PrivateWages_4 -8 151s PrivateWages_5 -7 151s PrivateWages_6 -6 151s PrivateWages_8 -4 151s PrivateWages_9 -3 151s PrivateWages_10 -2 151s PrivateWages_11 -1 151s PrivateWages_12 0 151s PrivateWages_13 1 151s PrivateWages_14 2 151s PrivateWages_15 3 151s PrivateWages_16 4 151s PrivateWages_17 5 151s PrivateWages_18 6 151s PrivateWages_19 7 151s PrivateWages_20 8 151s PrivateWages_21 9 151s PrivateWages_22 10 151s > nobs 151s [1] 60 151s > linearHypothesis 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 49 151s 2 48 1 0.95 0.34 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 49 151s 2 48 1 1.05 0.31 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 49 151s 2 48 1 1.05 0.3 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 48 2 0.48 0.62 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 48 2 0.53 0.59 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 50 151s 2 48 2 1.06 0.59 151s > logLik 151s 'log Lik.' -72.2 (df=13) 151s 'log Lik.' -79.7 (df=13) 151s Estimating function 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 -1.1407 -14.78 151s Consumption_3 -0.3242 -5.42 151s Consumption_4 -0.0963 -1.84 151s Consumption_5 -1.8392 -38.51 151s Consumption_6 0.1702 3.31 151s Consumption_8 3.0349 52.02 151s Consumption_9 1.9822 38.63 151s Consumption_10 0.7162 14.65 151s Consumption_11 -1.5151 -25.52 151s Consumption_12 -1.1471 -14.54 151s Consumption_13 -1.9595 -17.48 151s Consumption_14 1.4394 13.39 151s Consumption_15 -1.0033 -12.84 151s Consumption_16 -0.5750 -8.20 151s Consumption_17 4.0452 59.67 151s Consumption_18 -0.5669 -11.08 151s Consumption_19 -3.1962 -61.88 151s Consumption_20 2.2286 38.75 151s Consumption_21 0.9237 18.57 151s Consumption_22 -1.1770 -26.91 151s Investment_2 0.0000 0.00 151s Investment_3 0.0000 0.00 151s Investment_4 0.0000 0.00 151s Investment_5 0.0000 0.00 151s Investment_6 0.0000 0.00 151s Investment_8 0.0000 0.00 151s Investment_9 0.0000 0.00 151s Investment_10 0.0000 0.00 151s Investment_11 0.0000 0.00 151s Investment_12 0.0000 0.00 151s Investment_13 0.0000 0.00 151s Investment_14 0.0000 0.00 151s Investment_15 0.0000 0.00 151s Investment_16 0.0000 0.00 151s Investment_17 0.0000 0.00 151s Investment_18 0.0000 0.00 151s Investment_19 0.0000 0.00 151s Investment_20 0.0000 0.00 151s Investment_21 0.0000 0.00 151s Investment_22 0.0000 0.00 151s PrivateWages_2 0.0000 0.00 151s PrivateWages_3 0.0000 0.00 151s PrivateWages_4 0.0000 0.00 151s PrivateWages_5 0.0000 0.00 151s PrivateWages_6 0.0000 0.00 151s PrivateWages_8 0.0000 0.00 151s PrivateWages_9 0.0000 0.00 151s PrivateWages_10 0.0000 0.00 151s PrivateWages_11 0.0000 0.00 151s PrivateWages_12 0.0000 0.00 151s PrivateWages_13 0.0000 0.00 151s PrivateWages_14 0.0000 0.00 151s PrivateWages_15 0.0000 0.00 151s PrivateWages_16 0.0000 0.00 151s PrivateWages_17 0.0000 0.00 151s PrivateWages_18 0.0000 0.00 151s PrivateWages_19 0.0000 0.00 151s PrivateWages_20 0.0000 0.00 151s PrivateWages_21 0.0000 0.00 151s PrivateWages_22 0.0000 0.00 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 -14.49 -33.21 151s Consumption_3 -4.02 -10.33 151s Consumption_4 -1.63 -3.43 151s Consumption_5 -33.84 -71.82 151s Consumption_6 3.30 6.61 151s Consumption_8 59.48 120.65 151s Consumption_9 39.25 83.81 151s Consumption_10 15.11 31.59 151s Consumption_11 -32.88 -65.70 151s Consumption_12 -17.89 -45.25 151s Consumption_13 -22.34 -68.69 151s Consumption_14 10.08 47.54 151s Consumption_15 -11.24 -37.74 151s Consumption_16 -7.07 -22.99 151s Consumption_17 56.63 168.85 151s Consumption_18 -9.98 -27.00 151s Consumption_19 -55.29 -158.06 151s Consumption_20 34.10 107.77 151s Consumption_21 17.55 49.11 151s Consumption_22 -24.84 -71.70 151s Investment_2 0.00 0.00 151s Investment_3 0.00 0.00 151s Investment_4 0.00 0.00 151s Investment_5 0.00 0.00 151s Investment_6 0.00 0.00 151s Investment_8 0.00 0.00 151s Investment_9 0.00 0.00 151s Investment_10 0.00 0.00 151s Investment_11 0.00 0.00 151s Investment_12 0.00 0.00 151s Investment_13 0.00 0.00 151s Investment_14 0.00 0.00 151s Investment_15 0.00 0.00 151s Investment_16 0.00 0.00 151s Investment_17 0.00 0.00 151s Investment_18 0.00 0.00 151s Investment_19 0.00 0.00 151s Investment_20 0.00 0.00 151s Investment_21 0.00 0.00 151s Investment_22 0.00 0.00 151s PrivateWages_2 0.00 0.00 151s PrivateWages_3 0.00 0.00 151s PrivateWages_4 0.00 0.00 151s PrivateWages_5 0.00 0.00 151s PrivateWages_6 0.00 0.00 151s PrivateWages_8 0.00 0.00 151s PrivateWages_9 0.00 0.00 151s PrivateWages_10 0.00 0.00 151s PrivateWages_11 0.00 0.00 151s PrivateWages_12 0.00 0.00 151s PrivateWages_13 0.00 0.00 151s PrivateWages_14 0.00 0.00 151s PrivateWages_15 0.00 0.00 151s PrivateWages_16 0.00 0.00 151s PrivateWages_17 0.00 0.00 151s PrivateWages_18 0.00 0.00 151s PrivateWages_19 0.00 0.00 151s PrivateWages_20 0.00 0.00 151s PrivateWages_21 0.00 0.00 151s PrivateWages_22 0.00 0.00 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0.0000 0.000 151s Consumption_3 0.0000 0.000 151s Consumption_4 0.0000 0.000 151s Consumption_5 0.0000 0.000 151s Consumption_6 0.0000 0.000 151s Consumption_8 0.0000 0.000 151s Consumption_9 0.0000 0.000 151s Consumption_10 0.0000 0.000 151s Consumption_11 0.0000 0.000 151s Consumption_12 0.0000 0.000 151s Consumption_13 0.0000 0.000 151s Consumption_14 0.0000 0.000 151s Consumption_15 0.0000 0.000 151s Consumption_16 0.0000 0.000 151s Consumption_17 0.0000 0.000 151s Consumption_18 0.0000 0.000 151s Consumption_19 0.0000 0.000 151s Consumption_20 0.0000 0.000 151s Consumption_21 0.0000 0.000 151s Consumption_22 0.0000 0.000 151s Investment_2 -1.1313 -14.660 151s Investment_3 0.2902 4.847 151s Investment_4 0.9027 17.274 151s Investment_5 -1.7434 -36.502 151s Investment_6 0.5695 11.088 151s Investment_8 1.6225 27.812 151s Investment_9 0.4166 8.119 151s Investment_10 2.0381 41.703 151s Investment_11 -0.8611 -14.505 151s Investment_12 -0.9091 -11.527 151s Investment_13 -1.1148 -9.946 151s Investment_14 1.3841 12.873 151s Investment_15 -0.2900 -3.710 151s Investment_16 0.0605 0.862 151s Investment_17 2.2439 33.101 151s Investment_18 -0.5390 -10.534 151s Investment_19 -3.9452 -76.375 151s Investment_20 0.4890 8.502 151s Investment_21 0.0864 1.737 151s Investment_22 0.4306 9.843 151s PrivateWages_2 0.0000 0.000 151s PrivateWages_3 0.0000 0.000 151s PrivateWages_4 0.0000 0.000 151s PrivateWages_5 0.0000 0.000 151s PrivateWages_6 0.0000 0.000 151s PrivateWages_8 0.0000 0.000 151s PrivateWages_9 0.0000 0.000 151s PrivateWages_10 0.0000 0.000 151s PrivateWages_11 0.0000 0.000 151s PrivateWages_12 0.0000 0.000 151s PrivateWages_13 0.0000 0.000 151s PrivateWages_14 0.0000 0.000 151s PrivateWages_15 0.0000 0.000 151s PrivateWages_16 0.0000 0.000 151s PrivateWages_17 0.0000 0.000 151s PrivateWages_18 0.0000 0.000 151s PrivateWages_19 0.0000 0.000 151s PrivateWages_20 0.0000 0.000 151s PrivateWages_21 0.0000 0.000 151s PrivateWages_22 0.0000 0.000 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.000 0.0 151s Consumption_3 0.000 0.0 151s Consumption_4 0.000 0.0 151s Consumption_5 0.000 0.0 151s Consumption_6 0.000 0.0 151s Consumption_8 0.000 0.0 151s Consumption_9 0.000 0.0 151s Consumption_10 0.000 0.0 151s Consumption_11 0.000 0.0 151s Consumption_12 0.000 0.0 151s Consumption_13 0.000 0.0 151s Consumption_14 0.000 0.0 151s Consumption_15 0.000 0.0 151s Consumption_16 0.000 0.0 151s Consumption_17 0.000 0.0 151s Consumption_18 0.000 0.0 151s Consumption_19 0.000 0.0 151s Consumption_20 0.000 0.0 151s Consumption_21 0.000 0.0 151s Consumption_22 0.000 0.0 151s Investment_2 -14.368 -206.8 151s Investment_3 3.598 53.0 151s Investment_4 15.256 166.5 151s Investment_5 -32.079 -330.7 151s Investment_6 11.048 109.7 151s Investment_8 31.801 330.0 151s Investment_9 8.248 86.5 151s Investment_10 43.003 429.2 151s Investment_11 -18.685 -185.7 151s Investment_12 -14.182 -197.0 151s Investment_13 -12.709 -237.8 151s Investment_14 9.689 286.6 151s Investment_15 -3.247 -58.6 151s Investment_16 0.744 12.0 151s Investment_17 31.414 443.6 151s Investment_18 -9.486 -107.7 151s Investment_19 -68.252 -796.1 151s Investment_20 7.482 97.7 151s Investment_21 1.642 17.4 151s Investment_22 9.085 88.0 151s PrivateWages_2 0.000 0.0 151s PrivateWages_3 0.000 0.0 151s PrivateWages_4 0.000 0.0 151s PrivateWages_5 0.000 0.0 151s PrivateWages_6 0.000 0.0 151s PrivateWages_8 0.000 0.0 151s PrivateWages_9 0.000 0.0 151s PrivateWages_10 0.000 0.0 151s PrivateWages_11 0.000 0.0 151s PrivateWages_12 0.000 0.0 151s PrivateWages_13 0.000 0.0 151s PrivateWages_14 0.000 0.0 151s PrivateWages_15 0.000 0.0 151s PrivateWages_16 0.000 0.0 151s PrivateWages_17 0.000 0.0 151s PrivateWages_18 0.000 0.0 151s PrivateWages_19 0.000 0.0 151s PrivateWages_20 0.000 0.0 151s PrivateWages_21 0.000 0.0 151s PrivateWages_22 0.000 0.0 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 0.0000 0.00 0.00 151s Consumption_3 0.0000 0.00 0.00 151s Consumption_4 0.0000 0.00 0.00 151s Consumption_5 0.0000 0.00 0.00 151s Consumption_6 0.0000 0.00 0.00 151s Consumption_8 0.0000 0.00 0.00 151s Consumption_9 0.0000 0.00 0.00 151s Consumption_10 0.0000 0.00 0.00 151s Consumption_11 0.0000 0.00 0.00 151s Consumption_12 0.0000 0.00 0.00 151s Consumption_13 0.0000 0.00 0.00 151s Consumption_14 0.0000 0.00 0.00 151s Consumption_15 0.0000 0.00 0.00 151s Consumption_16 0.0000 0.00 0.00 151s Consumption_17 0.0000 0.00 0.00 151s Consumption_18 0.0000 0.00 0.00 151s Consumption_19 0.0000 0.00 0.00 151s Consumption_20 0.0000 0.00 0.00 151s Consumption_21 0.0000 0.00 0.00 151s Consumption_22 0.0000 0.00 0.00 151s Investment_2 0.0000 0.00 0.00 151s Investment_3 0.0000 0.00 0.00 151s Investment_4 0.0000 0.00 0.00 151s Investment_5 0.0000 0.00 0.00 151s Investment_6 0.0000 0.00 0.00 151s Investment_8 0.0000 0.00 0.00 151s Investment_9 0.0000 0.00 0.00 151s Investment_10 0.0000 0.00 0.00 151s Investment_11 0.0000 0.00 0.00 151s Investment_12 0.0000 0.00 0.00 151s Investment_13 0.0000 0.00 0.00 151s Investment_14 0.0000 0.00 0.00 151s Investment_15 0.0000 0.00 0.00 151s Investment_16 0.0000 0.00 0.00 151s Investment_17 0.0000 0.00 0.00 151s Investment_18 0.0000 0.00 0.00 151s Investment_19 0.0000 0.00 0.00 151s Investment_20 0.0000 0.00 0.00 151s Investment_21 0.0000 0.00 0.00 151s Investment_22 0.0000 0.00 0.00 151s PrivateWages_2 -1.9924 -93.78 -89.46 151s PrivateWages_3 0.4683 23.22 21.35 151s PrivateWages_4 1.4034 79.35 70.31 151s PrivateWages_5 -1.7870 -108.45 -102.22 151s PrivateWages_6 -0.3627 -21.98 -20.71 151s PrivateWages_8 1.1629 69.77 74.43 151s PrivateWages_9 1.2735 79.30 82.01 151s PrivateWages_10 2.2141 142.96 142.81 151s PrivateWages_11 -1.2912 -82.26 -86.51 151s PrivateWages_12 -0.0350 -1.92 -2.14 151s PrivateWages_13 -1.0438 -49.04 -55.74 151s PrivateWages_14 1.8016 75.90 79.81 151s PrivateWages_15 -0.3714 -19.02 -16.75 151s PrivateWages_16 -0.3904 -21.61 -19.40 151s PrivateWages_17 1.4934 85.71 81.24 151s PrivateWages_18 0.0279 1.88 1.75 151s PrivateWages_19 -3.8229 -261.91 -248.49 151s PrivateWages_20 0.7870 52.61 47.93 151s PrivateWages_21 -0.7415 -55.52 -51.54 151s PrivateWages_22 1.2062 104.79 91.31 151s PrivateWages_trend 151s Consumption_2 0.000 151s Consumption_3 0.000 151s Consumption_4 0.000 151s Consumption_5 0.000 151s Consumption_6 0.000 151s Consumption_8 0.000 151s Consumption_9 0.000 151s Consumption_10 0.000 151s Consumption_11 0.000 151s Consumption_12 0.000 151s Consumption_13 0.000 151s Consumption_14 0.000 151s Consumption_15 0.000 151s Consumption_16 0.000 151s Consumption_17 0.000 151s Consumption_18 0.000 151s Consumption_19 0.000 151s Consumption_20 0.000 151s Consumption_21 0.000 151s Consumption_22 0.000 151s Investment_2 0.000 151s Investment_3 0.000 151s Investment_4 0.000 151s Investment_5 0.000 151s Investment_6 0.000 151s Investment_8 0.000 151s Investment_9 0.000 151s Investment_10 0.000 151s Investment_11 0.000 151s Investment_12 0.000 151s Investment_13 0.000 151s Investment_14 0.000 151s Investment_15 0.000 151s Investment_16 0.000 151s Investment_17 0.000 151s Investment_18 0.000 151s Investment_19 0.000 151s Investment_20 0.000 151s Investment_21 0.000 151s Investment_22 0.000 151s PrivateWages_2 19.924 151s PrivateWages_3 -4.214 151s PrivateWages_4 -11.227 151s PrivateWages_5 12.509 151s PrivateWages_6 2.176 151s PrivateWages_8 -4.652 151s PrivateWages_9 -3.820 151s PrivateWages_10 -4.428 151s PrivateWages_11 1.291 151s PrivateWages_12 0.000 151s PrivateWages_13 -1.044 151s PrivateWages_14 3.603 151s PrivateWages_15 -1.114 151s PrivateWages_16 -1.562 151s PrivateWages_17 7.467 151s PrivateWages_18 0.168 151s PrivateWages_19 -26.760 151s PrivateWages_20 6.296 151s PrivateWages_21 -6.674 151s PrivateWages_22 12.062 151s [1] TRUE 151s > Bread 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_(Intercept) 99.945 -0.7943 151s Consumption_corpProf -0.794 0.7797 151s Consumption_corpProfLag -0.325 -0.5285 151s Consumption_wages -1.888 -0.0894 151s Investment_(Intercept) 0.000 0.0000 151s Investment_corpProf 0.000 0.0000 151s Investment_corpProfLag 0.000 0.0000 151s Investment_capitalLag 0.000 0.0000 151s PrivateWages_(Intercept) 0.000 0.0000 151s PrivateWages_gnp 0.000 0.0000 151s PrivateWages_gnpLag 0.000 0.0000 151s PrivateWages_trend 0.000 0.0000 151s Consumption_corpProfLag Consumption_wages 151s Consumption_(Intercept) -0.3246 -1.8878 151s Consumption_corpProf -0.5285 -0.0894 151s Consumption_corpProfLag 0.6654 -0.0384 151s Consumption_wages -0.0384 0.0965 151s Investment_(Intercept) 0.0000 0.0000 151s Investment_corpProf 0.0000 0.0000 151s Investment_corpProfLag 0.0000 0.0000 151s Investment_capitalLag 0.0000 0.0000 151s PrivateWages_(Intercept) 0.0000 0.0000 151s PrivateWages_gnp 0.0000 0.0000 151s PrivateWages_gnpLag 0.0000 0.0000 151s PrivateWages_trend 0.0000 0.0000 151s Investment_(Intercept) Investment_corpProf 151s Consumption_(Intercept) 0.0 0.000 151s Consumption_corpProf 0.0 0.000 151s Consumption_corpProfLag 0.0 0.000 151s Consumption_wages 0.0 0.000 151s Investment_(Intercept) 2446.2 -38.918 151s Investment_corpProf -38.9 1.252 151s Investment_corpProfLag 33.4 -1.090 151s Investment_capitalLag -11.6 0.177 151s PrivateWages_(Intercept) 0.0 0.000 151s PrivateWages_gnp 0.0 0.000 151s PrivateWages_gnpLag 0.0 0.000 151s PrivateWages_trend 0.0 0.000 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_(Intercept) 0.000 0.0000 151s Consumption_corpProf 0.000 0.0000 151s Consumption_corpProfLag 0.000 0.0000 151s Consumption_wages 0.000 0.0000 151s Investment_(Intercept) 33.384 -11.6216 151s Investment_corpProf -1.090 0.1774 151s Investment_corpProfLag 1.148 -0.1680 151s Investment_capitalLag -0.168 0.0567 151s PrivateWages_(Intercept) 0.000 0.0000 151s PrivateWages_gnp 0.000 0.0000 151s PrivateWages_gnpLag 0.000 0.0000 151s PrivateWages_trend 0.000 0.0000 151s PrivateWages_(Intercept) PrivateWages_gnp 151s Consumption_(Intercept) 0.000 0.0000 151s Consumption_corpProf 0.000 0.0000 151s Consumption_corpProfLag 0.000 0.0000 151s Consumption_wages 0.000 0.0000 151s Investment_(Intercept) 0.000 0.0000 151s Investment_corpProf 0.000 0.0000 151s Investment_corpProfLag 0.000 0.0000 151s Investment_capitalLag 0.000 0.0000 151s PrivateWages_(Intercept) 170.714 -0.9289 151s PrivateWages_gnp -0.929 0.1580 151s PrivateWages_gnpLag -1.948 -0.1473 151s PrivateWages_trend 2.164 -0.0424 151s PrivateWages_gnpLag PrivateWages_trend 151s Consumption_(Intercept) 0.000 0.0000 151s Consumption_corpProf 0.000 0.0000 151s Consumption_corpProfLag 0.000 0.0000 151s Consumption_wages 0.000 0.0000 151s Investment_(Intercept) 0.000 0.0000 151s Investment_corpProf 0.000 0.0000 151s Investment_corpProfLag 0.000 0.0000 151s Investment_capitalLag 0.000 0.0000 151s PrivateWages_(Intercept) -1.948 2.1641 151s PrivateWages_gnp -0.147 -0.0424 151s PrivateWages_gnpLag 0.186 0.0060 151s PrivateWages_trend 0.006 0.1151 151s > 151s > # SUR 151s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 151s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 151s > summary 151s 151s systemfit results 151s method: SUR 151s 151s N DF SSR detRCov OLS-R2 McElroy-R2 151s system 62 50 46.2 0.154 0.977 0.993 151s 151s N DF SSR MSE RMSE R2 Adj R2 151s Consumption 21 17 18.1 1.062 1.031 0.981 0.977 151s Investment 21 17 17.5 1.030 1.015 0.931 0.918 151s PrivateWages 20 16 10.6 0.663 0.814 0.987 0.984 151s 151s The covariance matrix of the residuals used for estimation 151s Consumption Investment PrivateWages 151s Consumption 0.8562 -0.0129 -0.371 151s Investment -0.0129 0.7548 0.159 151s PrivateWages -0.3706 0.1594 0.487 151s 151s The covariance matrix of the residuals 151s Consumption Investment PrivateWages 151s Consumption 0.8684 0.0078 -0.442 151s Investment 0.0078 0.7702 0.237 151s PrivateWages -0.4416 0.2366 0.531 151s 151s The correlations of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.00000 0.00562 -0.651 151s Investment 0.00562 1.00000 0.372 151s PrivateWages -0.65109 0.37198 1.000 151s 151s 151s SUR estimates for 'Consumption' (equation 1) 151s Model Formula: consump ~ corpProf + corpProfLag + wages 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 16.0647 1.1729 13.70 1.3e-10 *** 151s corpProf 0.2283 0.0775 2.94 0.0091 ** 151s corpProfLag 0.0723 0.0771 0.94 0.3615 151s wages 0.7930 0.0352 22.51 4.3e-14 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.031 on 17 degrees of freedom 151s Number of observations: 21 Degrees of Freedom: 17 151s SSR: 18.06 MSE: 1.062 Root MSE: 1.031 151s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 151s 151s 151s SUR estimates for 'Investment' (equation 2) 151s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 12.3516 4.5762 2.70 0.01520 * 151s corpProf 0.4461 0.0818 5.45 4.3e-05 *** 151s corpProfLag 0.3609 0.0849 4.25 0.00054 *** 151s capitalLag -0.1224 0.0223 -5.47 4.1e-05 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.015 on 17 degrees of freedom 151s Number of observations: 21 Degrees of Freedom: 17 151s SSR: 17.514 MSE: 1.03 Root MSE: 1.015 151s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 151s 151s 151s SUR estimates for 'PrivateWages' (equation 3) 151s Model Formula: privWage ~ gnp + gnpLag + trend 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 1.5433 1.1371 1.36 0.19 151s gnp 0.4117 0.0279 14.77 9.6e-11 *** 151s gnpLag 0.1743 0.0317 5.50 4.8e-05 *** 151s trend 0.1550 0.0283 5.49 5.0e-05 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 0.814 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 10.611 MSE: 0.663 Root MSE: 0.814 151s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 151s 151s > residuals 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 -0.27628 -0.3003 -1.0910 151s 3 -1.35400 -0.1239 0.5795 151s 4 -1.62816 1.1154 1.5172 151s 5 -0.56494 -1.4358 -0.0341 151s 6 -0.06584 0.3581 -0.2772 151s 7 0.83245 1.4526 NA 151s 8 1.28855 0.8290 -0.6896 151s 9 0.96709 -0.5092 0.3445 151s 10 -0.66705 1.2210 1.2429 151s 11 0.41992 0.2497 -0.3602 151s 12 -0.05971 0.0470 0.3068 151s 13 -0.08649 0.3096 -0.2426 151s 14 0.33124 0.3652 0.3591 151s 15 -0.00604 -0.1652 0.2710 151s 16 -0.01478 0.0124 -0.0207 151s 17 1.55472 1.0339 -0.8117 151s 18 -0.41250 0.0255 0.8398 151s 19 0.29322 -2.6293 -0.8283 151s 20 0.91756 -0.5906 -0.4091 151s 21 0.71583 -0.7036 -1.2154 151s 22 -2.26223 -0.5283 0.6207 151s > fitted 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 42.2 0.100 26.6 151s 3 46.4 2.024 28.7 151s 4 50.8 4.085 32.6 151s 5 51.2 4.436 33.9 151s 6 52.7 4.742 35.7 151s 7 54.3 4.147 NA 151s 8 54.9 3.371 38.6 151s 9 56.3 3.509 38.9 151s 10 58.5 3.879 40.1 151s 11 54.6 0.750 38.3 151s 12 51.0 -3.447 34.2 151s 13 45.7 -6.510 29.2 151s 14 46.2 -5.465 28.1 151s 15 48.7 -2.835 30.3 151s 16 51.3 -1.312 33.2 151s 17 56.1 1.066 37.6 151s 18 59.1 1.974 40.2 151s 19 57.2 0.729 39.0 151s 20 60.7 1.891 42.0 151s 21 64.3 4.004 46.2 151s 22 72.0 5.428 52.7 151s > predict 151s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 151s 1 NA NA NA NA 151s 2 42.2 0.414 41.3 43.0 151s 3 46.4 0.451 45.4 47.3 151s 4 50.8 0.296 50.2 51.4 151s 5 51.2 0.342 50.5 51.9 151s 6 52.7 0.342 52.0 53.4 151s 7 54.3 0.309 53.6 54.9 151s 8 54.9 0.282 54.3 55.5 151s 9 56.3 0.303 55.7 56.9 151s 10 58.5 0.321 57.8 59.1 151s 11 54.6 0.515 53.5 55.6 151s 12 51.0 0.418 50.1 51.8 151s 13 45.7 0.548 44.6 46.8 151s 14 46.2 0.528 45.1 47.2 151s 15 48.7 0.333 48.0 49.4 151s 16 51.3 0.296 50.7 51.9 151s 17 56.1 0.321 55.5 56.8 151s 18 59.1 0.287 58.5 59.7 151s 19 57.2 0.325 56.6 57.9 151s 20 60.7 0.383 59.9 61.5 151s 21 64.3 0.382 63.5 65.1 151s 22 72.0 0.599 70.8 73.2 151s Investment.pred Investment.se.fit Investment.lwr Investment.upr 151s 1 NA NA NA NA 151s 2 0.100 0.511 -0.926 1.127 151s 3 2.024 0.425 1.170 2.878 151s 4 4.085 0.378 3.325 4.845 151s 5 4.436 0.313 3.806 5.065 151s 6 4.742 0.296 4.147 5.336 151s 7 4.147 0.279 3.586 4.709 151s 8 3.371 0.250 2.868 3.874 151s 9 3.509 0.331 2.845 4.174 151s 10 3.879 0.380 3.116 4.642 151s 11 0.750 0.512 -0.279 1.779 151s 12 -3.447 0.433 -4.316 -2.578 151s 13 -6.510 0.527 -7.568 -5.451 151s 14 -5.465 0.587 -6.645 -4.285 151s 15 -2.835 0.320 -3.477 -2.193 151s 16 -1.312 0.274 -1.863 -0.761 151s 17 1.066 0.296 0.472 1.661 151s 18 1.974 0.208 1.558 2.391 151s 19 0.729 0.265 0.197 1.262 151s 20 1.891 0.311 1.266 2.515 151s 21 4.004 0.283 3.435 4.572 151s 22 5.428 0.393 4.640 6.217 151s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 151s 1 NA NA NA NA 151s 2 26.6 0.318 26.0 27.2 151s 3 28.7 0.317 28.1 29.4 151s 4 32.6 0.315 32.0 33.2 151s 5 33.9 0.243 33.4 34.4 151s 6 35.7 0.242 35.2 36.2 151s 7 NA NA NA NA 151s 8 38.6 0.247 38.1 39.1 151s 9 38.9 0.236 38.4 39.3 151s 10 40.1 0.227 39.6 40.5 151s 11 38.3 0.306 37.6 38.9 151s 12 34.2 0.312 33.6 34.8 151s 13 29.2 0.376 28.5 30.0 151s 14 28.1 0.337 27.5 28.8 151s 15 30.3 0.328 29.7 31.0 151s 16 33.2 0.274 32.7 33.8 151s 17 37.6 0.266 37.1 38.1 151s 18 40.2 0.213 39.7 40.6 151s 19 39.0 0.310 38.4 39.7 151s 20 42.0 0.282 41.4 42.6 151s 21 46.2 0.300 45.6 46.8 151s 22 52.7 0.451 51.8 53.6 151s > model.frame 151s [1] TRUE 151s > model.matrix 151s [1] TRUE 151s > nobs 151s [1] 62 151s > linearHypothesis 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 51 151s 2 50 1 1.39 0.24 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 51 151s 2 50 1 1.7 0.2 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 51 151s 2 50 1 1.7 0.19 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 52 151s 2 50 2 0.72 0.49 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 52 151s 2 50 2 0.87 0.42 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 52 151s 2 50 2 1.75 0.42 151s > logLik 151s 'log Lik.' -69.4 (df=18) 151s 'log Lik.' -78.2 (df=18) 151s Estimating function 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 -0.49572 -6.1470 151s Consumption_3 -2.42943 -41.0573 151s Consumption_4 -2.92134 -53.7526 151s Consumption_5 -1.01365 -19.6648 151s Consumption_6 -0.11814 -2.3746 151s Consumption_7 1.49363 29.2752 151s Consumption_8 2.31199 45.7775 151s Consumption_9 1.73521 36.6129 151s Consumption_10 -1.19687 -25.9720 151s Consumption_11 0.75344 11.7537 151s Consumption_12 -0.10714 -1.2214 151s Consumption_13 -0.15519 -1.0863 151s Consumption_14 0.59434 6.6566 151s Consumption_15 -0.01083 -0.1332 151s Consumption_16 -0.02651 -0.3712 151s Consumption_17 2.78956 49.0963 151s Consumption_18 -0.74013 -12.8043 151s Consumption_19 0.52610 8.0494 151s Consumption_20 1.64635 31.2806 151s Consumption_21 1.28438 27.1004 151s Consumption_22 -4.05902 -95.3870 151s Investment_2 0.08318 1.0314 151s Investment_3 0.03433 0.5802 151s Investment_4 -0.30897 -5.6851 151s Investment_5 0.39771 7.7155 151s Investment_6 -0.09921 -1.9941 151s Investment_7 -0.40237 -7.8864 151s Investment_8 -0.22963 -4.5466 151s Investment_9 0.14106 2.9764 151s Investment_10 -0.33822 -7.3394 151s Investment_11 -0.06917 -1.0790 151s Investment_12 -0.01303 -0.1485 151s Investment_13 -0.08575 -0.6003 151s Investment_14 -0.10117 -1.1331 151s Investment_15 0.04575 0.5628 151s Investment_16 -0.00344 -0.0482 151s Investment_17 -0.28639 -5.0405 151s Investment_18 -0.00707 -0.1223 151s Investment_19 0.72832 11.1433 151s Investment_20 0.16360 3.1083 151s Investment_21 0.19490 4.1123 151s Investment_22 0.14635 3.4391 151s PrivateWages_2 -1.58896 -19.7031 151s PrivateWages_3 0.84394 14.2626 151s PrivateWages_4 2.20977 40.6598 151s PrivateWages_5 -0.04965 -0.9631 151s PrivateWages_6 -0.40373 -8.1150 151s PrivateWages_8 -1.00430 -19.8851 151s PrivateWages_9 0.50179 10.5878 151s PrivateWages_10 1.81021 39.2815 151s PrivateWages_11 -0.52455 -8.1830 151s PrivateWages_12 0.44676 5.0931 151s PrivateWages_13 -0.35330 -2.4731 151s PrivateWages_14 0.52303 5.8579 151s PrivateWages_15 0.39464 4.8541 151s PrivateWages_16 -0.03009 -0.4213 151s PrivateWages_17 -1.18225 -20.8075 151s PrivateWages_18 1.22307 21.1590 151s PrivateWages_19 -1.20633 -18.4569 151s PrivateWages_20 -0.59580 -11.3203 151s PrivateWages_21 -1.77014 -37.3499 151s PrivateWages_22 0.90407 21.2457 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 -6.2957 -13.979 151s Consumption_3 -30.1249 -78.228 151s Consumption_4 -49.3706 -108.090 151s Consumption_5 -18.6512 -37.505 151s Consumption_6 -2.2919 -4.560 151s Consumption_7 30.0220 60.791 151s Consumption_8 45.3151 95.948 151s Consumption_9 34.3571 74.440 151s Consumption_10 -25.2539 -54.218 151s Consumption_11 16.3496 31.720 151s Consumption_12 -1.6714 -4.211 151s Consumption_13 -1.7691 -5.323 151s Consumption_14 4.1604 20.267 151s Consumption_15 -0.1213 -0.396 151s Consumption_16 -0.3261 -1.042 151s Consumption_17 39.0539 123.299 151s Consumption_18 -13.0263 -35.304 151s Consumption_19 9.1016 24.148 151s Consumption_20 25.1891 81.330 151s Consumption_21 24.4032 68.072 151s Consumption_22 -85.6453 -250.847 151s Investment_2 1.0563 2.346 151s Investment_3 0.4257 1.105 151s Investment_4 -5.2216 -11.432 151s Investment_5 7.3178 14.715 151s Investment_6 -1.9246 -3.829 151s Investment_7 -8.0876 -16.376 151s Investment_8 -4.5007 -9.530 151s Investment_9 2.7930 6.052 151s Investment_10 -7.1364 -15.321 151s Investment_11 -1.5009 -2.912 151s Investment_12 -0.2033 -0.512 151s Investment_13 -0.9776 -2.941 151s Investment_14 -0.7082 -3.450 151s Investment_15 0.5124 1.675 151s Investment_16 -0.0423 -0.135 151s Investment_17 -4.0095 -12.659 151s Investment_18 -0.1244 -0.337 151s Investment_19 12.5999 33.430 151s Investment_20 2.5030 8.082 151s Investment_21 3.7031 10.330 151s Investment_22 3.0879 9.044 151s PrivateWages_2 -20.1798 -44.809 151s PrivateWages_3 10.4649 27.175 151s PrivateWages_4 37.3452 81.762 151s PrivateWages_5 -0.9135 -1.837 151s PrivateWages_6 -7.8324 -15.584 151s PrivateWages_8 -19.6842 -41.678 151s PrivateWages_9 9.9355 21.527 151s PrivateWages_10 38.1953 82.002 151s PrivateWages_11 -11.3827 -22.084 151s PrivateWages_12 6.9695 17.558 151s PrivateWages_13 -4.0277 -12.118 151s PrivateWages_14 3.6612 17.835 151s PrivateWages_15 4.4200 14.444 151s PrivateWages_16 -0.3701 -1.183 151s PrivateWages_17 -16.5515 -52.255 151s PrivateWages_18 21.5260 58.340 151s PrivateWages_19 -20.8696 -55.371 151s PrivateWages_20 -9.1158 -29.433 151s PrivateWages_21 -33.6326 -93.817 151s PrivateWages_22 19.0759 55.872 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0.07653 0.9490 151s Consumption_3 0.37506 6.3385 151s Consumption_4 0.45100 8.2984 151s Consumption_5 0.15649 3.0359 151s Consumption_6 0.01824 0.3666 151s Consumption_7 -0.23059 -4.5195 151s Consumption_8 -0.35693 -7.0672 151s Consumption_9 -0.26788 -5.6523 151s Consumption_10 0.18477 4.0096 151s Consumption_11 -0.11632 -1.8145 151s Consumption_12 0.01654 0.1886 151s Consumption_13 0.02396 0.1677 151s Consumption_14 -0.09175 -1.0277 151s Consumption_15 0.00167 0.0206 151s Consumption_16 0.00409 0.0573 151s Consumption_17 -0.43066 -7.5796 151s Consumption_18 0.11426 1.9767 151s Consumption_19 -0.08122 -1.2427 151s Consumption_20 -0.25417 -4.8291 151s Consumption_21 -0.19828 -4.1838 151s Consumption_22 0.62664 14.7260 151s Investment_2 -0.44022 -5.4587 151s Investment_3 -0.18170 -3.0707 151s Investment_4 1.63526 30.0888 151s Investment_5 -2.10489 -40.8348 151s Investment_6 0.52506 10.5537 151s Investment_7 2.12955 41.7392 151s Investment_8 1.21532 24.0633 151s Investment_9 -0.74658 -15.7528 151s Investment_10 1.79005 38.8441 151s Investment_11 0.36607 5.7107 151s Investment_12 0.06896 0.7861 151s Investment_13 0.45385 3.1769 151s Investment_14 0.53544 5.9969 151s Investment_15 -0.24215 -2.9785 151s Investment_16 0.01822 0.2551 151s Investment_17 1.51576 26.6774 151s Investment_18 0.03741 0.6472 151s Investment_19 -3.85468 -58.9766 151s Investment_20 -0.86584 -16.4509 151s Investment_21 -1.03151 -21.7649 151s Investment_22 -0.77455 -18.2019 151s PrivateWages_2 0.75366 9.3454 151s PrivateWages_3 -0.40029 -6.7649 151s PrivateWages_4 -1.04812 -19.2855 151s PrivateWages_5 0.02355 0.4568 151s PrivateWages_6 0.19149 3.8490 151s PrivateWages_8 0.47635 9.4317 151s PrivateWages_9 -0.23801 -5.0219 151s PrivateWages_10 -0.85860 -18.6317 151s PrivateWages_11 0.24880 3.8813 151s PrivateWages_12 -0.21191 -2.4157 151s PrivateWages_13 0.16758 1.1730 151s PrivateWages_14 -0.24808 -2.7785 151s PrivateWages_15 -0.18718 -2.3024 151s PrivateWages_16 0.01427 0.1998 151s PrivateWages_17 0.56075 9.8693 151s PrivateWages_18 -0.58012 -10.0360 151s PrivateWages_19 0.57218 8.7543 151s PrivateWages_20 0.28260 5.3694 151s PrivateWages_21 0.83960 17.7155 151s PrivateWages_22 -0.42881 -10.0771 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.9719 13.990 151s Consumption_3 4.6507 68.486 151s Consumption_4 7.6219 83.210 151s Consumption_5 2.8794 29.686 151s Consumption_6 0.3538 3.515 151s Consumption_7 -4.6348 -45.611 151s Consumption_8 -6.9958 -72.599 151s Consumption_9 -5.3041 -55.613 151s Consumption_10 3.8987 38.913 151s Consumption_11 -2.5241 -25.090 151s Consumption_12 0.2580 3.584 151s Consumption_13 0.2731 5.110 151s Consumption_14 -0.6423 -19.002 151s Consumption_15 0.0187 0.338 151s Consumption_16 0.0503 0.815 151s Consumption_17 -6.0292 -85.141 151s Consumption_18 2.0110 22.830 151s Consumption_19 -1.4051 -16.390 151s Consumption_20 -3.8887 -50.808 151s Consumption_21 -3.7674 -39.895 151s Consumption_22 13.2221 128.147 151s Investment_2 -5.5908 -80.472 151s Investment_3 -2.2531 -33.179 151s Investment_4 27.6359 301.706 151s Investment_5 -38.7299 -399.297 151s Investment_6 10.1862 101.179 151s Investment_7 42.8040 421.225 151s Investment_8 23.8203 247.196 151s Investment_9 -14.7822 -154.989 151s Investment_10 37.7701 376.985 151s Investment_11 7.9437 78.961 151s Investment_12 1.0757 14.943 151s Investment_13 5.1739 96.806 151s Investment_14 3.7481 110.889 151s Investment_15 -2.7121 -48.915 151s Investment_16 0.2241 3.626 151s Investment_17 21.2206 299.666 151s Investment_18 0.6585 7.475 151s Investment_19 -66.6860 -777.874 151s Investment_20 -13.2473 -173.081 151s Investment_21 -19.5987 -207.540 151s Investment_22 -16.3429 -158.395 151s PrivateWages_2 9.5715 137.769 151s PrivateWages_3 -4.9636 -73.093 151s PrivateWages_4 -17.7133 -193.379 151s PrivateWages_5 0.4333 4.467 151s PrivateWages_6 3.7150 36.901 151s PrivateWages_8 9.3365 96.890 151s PrivateWages_9 -4.7125 -49.410 151s PrivateWages_10 -18.1165 -180.822 151s PrivateWages_11 5.3990 53.666 151s PrivateWages_12 -3.3057 -45.920 151s PrivateWages_13 1.9104 35.744 151s PrivateWages_14 -1.7366 -51.377 151s PrivateWages_15 -2.0965 -37.811 151s PrivateWages_16 0.1756 2.840 151s PrivateWages_17 7.8506 110.861 151s PrivateWages_18 -10.2100 -115.907 151s PrivateWages_19 9.8987 115.466 151s PrivateWages_20 4.3237 56.491 151s PrivateWages_21 15.9524 168.927 151s PrivateWages_22 -9.0479 -87.692 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 -0.40239 -18.349 -18.067 151s Consumption_3 -1.97202 -98.798 -89.924 151s Consumption_4 -2.37131 -135.639 -118.803 151s Consumption_5 -0.82280 -46.982 -47.064 151s Consumption_6 -0.09590 -5.850 -5.476 151s Consumption_7 0.00000 0.000 0.000 151s Consumption_8 1.87670 120.859 120.108 151s Consumption_9 1.40851 90.849 90.708 151s Consumption_10 -0.97152 -65.092 -62.663 151s Consumption_11 0.61158 37.429 40.976 151s Consumption_12 -0.08697 -4.644 -5.322 151s Consumption_13 -0.12597 -5.580 -6.727 151s Consumption_14 0.48244 21.758 21.372 151s Consumption_15 -0.00879 -0.437 -0.396 151s Consumption_16 -0.02152 -1.171 -1.070 151s Consumption_17 2.26435 141.975 123.181 151s Consumption_18 -0.60078 -39.051 -37.669 151s Consumption_19 0.42705 26.007 27.758 151s Consumption_20 1.33638 92.878 81.385 151s Consumption_21 1.04256 78.922 72.458 151s Consumption_22 -3.29479 -291.260 -249.416 151s Investment_2 0.20743 9.459 9.314 151s Investment_3 0.08562 4.289 3.904 151s Investment_4 -0.77054 -44.075 -38.604 151s Investment_5 0.99183 56.634 56.733 151s Investment_6 -0.24741 -15.092 -14.127 151s Investment_7 0.00000 0.000 0.000 151s Investment_8 -0.57266 -36.880 -36.650 151s Investment_9 0.35179 22.690 22.655 151s Investment_10 -0.84348 -56.513 -54.405 151s Investment_11 -0.17249 -10.557 -11.557 151s Investment_12 -0.03249 -1.735 -1.989 151s Investment_13 -0.21385 -9.474 -11.420 151s Investment_14 -0.25230 -11.379 -11.177 151s Investment_15 0.11410 5.671 5.146 151s Investment_16 -0.00859 -0.467 -0.427 151s Investment_17 -0.71423 -44.782 -38.854 151s Investment_18 -0.01763 -1.146 -1.105 151s Investment_19 1.81634 110.615 118.062 151s Investment_20 0.40799 28.355 24.846 151s Investment_21 0.48605 36.794 33.781 151s Investment_22 0.36497 32.263 27.628 151s PrivateWages_2 -3.69675 -168.572 -165.984 151s PrivateWages_3 1.96345 98.369 89.533 151s PrivateWages_4 5.14109 294.070 257.568 151s PrivateWages_5 -0.11550 -6.595 -6.607 151s PrivateWages_6 -0.93929 -57.297 -53.633 151s PrivateWages_8 -2.33652 -150.472 -149.537 151s PrivateWages_9 1.16743 75.299 75.183 151s PrivateWages_10 4.21148 282.169 271.641 151s PrivateWages_11 -1.22037 -74.687 -81.765 151s PrivateWages_12 1.03941 55.504 63.612 151s PrivateWages_13 -0.82197 -36.413 -43.893 151s PrivateWages_14 1.21684 54.880 53.906 151s PrivateWages_15 0.91815 45.632 41.409 151s PrivateWages_16 -0.07001 -3.809 -3.480 151s PrivateWages_17 -2.75052 -172.458 -149.628 151s PrivateWages_18 2.84549 184.957 178.412 151s PrivateWages_19 -2.80656 -170.920 -182.427 151s PrivateWages_20 -1.38615 -96.338 -84.417 151s PrivateWages_21 -4.11826 -311.753 -286.219 151s PrivateWages_22 2.10334 185.935 159.223 151s PrivateWages_trend 151s Consumption_2 4.0239 151s Consumption_3 17.7482 151s Consumption_4 18.9705 151s Consumption_5 5.7596 151s Consumption_6 0.5754 151s Consumption_7 0.0000 151s Consumption_8 -7.5068 151s Consumption_9 -4.2255 151s Consumption_10 1.9430 151s Consumption_11 -0.6116 151s Consumption_12 0.0000 151s Consumption_13 -0.1260 151s Consumption_14 0.9649 151s Consumption_15 -0.0264 151s Consumption_16 -0.0861 151s Consumption_17 11.3217 151s Consumption_18 -3.6047 151s Consumption_19 2.9894 151s Consumption_20 10.6910 151s Consumption_21 9.3830 151s Consumption_22 -32.9479 151s Investment_2 -2.0743 151s Investment_3 -0.7706 151s Investment_4 6.1643 151s Investment_5 -6.9428 151s Investment_6 1.4845 151s Investment_7 0.0000 151s Investment_8 2.2907 151s Investment_9 -1.0554 151s Investment_10 1.6870 151s Investment_11 0.1725 151s Investment_12 0.0000 151s Investment_13 -0.2139 151s Investment_14 -0.5046 151s Investment_15 0.3423 151s Investment_16 -0.0343 151s Investment_17 -3.5712 151s Investment_18 -0.1058 151s Investment_19 12.7144 151s Investment_20 3.2639 151s Investment_21 4.3745 151s Investment_22 3.6497 151s PrivateWages_2 36.9675 151s PrivateWages_3 -17.6711 151s PrivateWages_4 -41.1287 151s PrivateWages_5 0.8085 151s PrivateWages_6 5.6357 151s PrivateWages_8 9.3461 151s PrivateWages_9 -3.5023 151s PrivateWages_10 -8.4230 151s PrivateWages_11 1.2204 151s PrivateWages_12 0.0000 151s PrivateWages_13 -0.8220 151s PrivateWages_14 2.4337 151s PrivateWages_15 2.7544 151s PrivateWages_16 -0.2801 151s PrivateWages_17 -13.7526 151s PrivateWages_18 17.0729 151s PrivateWages_19 -19.6459 151s PrivateWages_20 -11.0892 151s PrivateWages_21 -37.0644 151s PrivateWages_22 21.0334 151s [1] TRUE 151s > Bread 151s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 151s [1,] 85.2889 -0.01362 -0.83841 151s [2,] -0.0136 0.37283 -0.23220 151s [3,] -0.8384 -0.23220 0.36858 151s [4,] -1.6590 -0.05994 -0.03120 151s [5,] -3.1844 -0.68255 0.70355 151s [6,] 0.0595 0.01846 -0.01774 151s [7,] -0.0239 -0.01745 0.02009 151s [8,] 0.0127 0.00329 -0.00362 151s [9,] -36.0142 0.07978 1.66083 151s [10,] 0.3888 -0.06209 0.04032 151s [11,] 0.2001 0.06287 -0.07012 151s [12,] 0.1814 0.03185 0.02619 151s Consumption_wages Investment_(Intercept) Investment_corpProf 151s [1,] -1.66e+00 -3.184 0.05950 151s [2,] -5.99e-02 -0.683 0.01846 151s [3,] -3.12e-02 0.704 -0.01774 151s [4,] 7.69e-02 0.082 -0.00204 151s [5,] 8.20e-02 1298.386 -12.39923 151s [6,] -2.04e-03 -12.399 0.41486 151s [7,] -2.16e-05 9.908 -0.35328 151s [8,] -2.54e-04 -6.230 0.05576 151s [9,] 1.50e-01 24.451 -0.18195 151s [10,] 6.53e-06 0.391 0.02158 151s [11,] -2.68e-03 -0.821 -0.01913 151s [12,] -2.78e-02 -0.890 0.00590 151s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 151s [1,] -2.39e-02 0.012670 -36.0142 151s [2,] -1.75e-02 0.003286 0.0798 151s [3,] 2.01e-02 -0.003616 1.6608 151s [4,] -2.16e-05 -0.000254 0.1499 151s [5,] 9.91e+00 -6.230058 24.4513 151s [6,] -3.53e-01 0.055757 -0.1819 151s [7,] 4.47e-01 -0.056152 -0.6460 151s [8,] -5.62e-02 0.030966 -0.0512 151s [9,] -6.46e-01 -0.051180 80.1680 151s [10,] -1.22e-02 -0.002778 -0.3588 151s [11,] 2.36e-02 0.003775 -0.9890 151s [12,] -1.61e-02 0.005268 0.9201 151s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 151s [1,] 3.89e-01 0.20005 0.18143 151s [2,] -6.21e-02 0.06287 0.03185 151s [3,] 4.03e-02 -0.07012 0.02619 151s [4,] 6.53e-06 -0.00268 -0.02782 151s [5,] 3.91e-01 -0.82129 -0.89038 151s [6,] 2.16e-02 -0.01913 0.00590 151s [7,] -1.22e-02 0.02360 -0.01606 151s [8,] -2.78e-03 0.00377 0.00527 151s [9,] -3.59e-01 -0.98896 0.92007 151s [10,] 4.82e-02 -0.04360 -0.01308 151s [11,] -4.36e-02 0.06217 -0.00244 151s [12,] -1.31e-02 -0.00244 0.04948 151s > 151s > # 3SLS 151s > summary 151s 151s systemfit results 151s method: 3SLS 151s 151s N DF SSR detRCov OLS-R2 McElroy-R2 151s system 60 48 62.6 0.265 0.968 0.994 151s 151s N DF SSR MSE RMSE R2 Adj R2 151s Consumption 20 16 17.8 1.114 1.06 0.981 0.977 151s Investment 20 16 34.3 2.143 1.46 0.853 0.825 151s PrivateWages 20 16 10.5 0.656 0.81 0.987 0.984 151s 151s The covariance matrix of the residuals used for estimation 151s Consumption Investment PrivateWages 151s Consumption 1.034 0.309 -0.383 151s Investment 0.309 1.151 0.202 151s PrivateWages -0.383 0.202 0.487 151s 151s The covariance matrix of the residuals 151s Consumption Investment PrivateWages 151s Consumption 0.891 0.304 -0.391 151s Investment 0.304 1.715 0.388 151s PrivateWages -0.391 0.388 0.525 151s 151s The correlations of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.000 0.246 -0.571 151s Investment 0.246 1.000 0.409 151s PrivateWages -0.571 0.409 1.000 151s 151s 151s 3SLS estimates for 'Consumption' (equation 1) 151s Model Formula: consump ~ corpProf + corpProfLag + wages 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 16.3668 1.3024 12.57 1.1e-09 *** 151s corpProf 0.1186 0.1073 1.10 0.29 151s corpProfLag 0.1448 0.1008 1.44 0.17 151s wages 0.8006 0.0391 20.47 6.7e-13 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.056 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 17.825 MSE: 1.114 Root MSE: 1.056 151s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 151s 151s 151s 3SLS estimates for 'Investment' (equation 2) 151s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 24.8872 6.2956 3.95 0.00114 ** 151s corpProf 0.0702 0.1458 0.48 0.63648 151s corpProfLag 0.6688 0.1402 4.77 0.00021 *** 151s capitalLag -0.1786 0.0303 -5.90 2.3e-05 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.464 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 34.295 MSE: 2.143 Root MSE: 1.464 151s Multiple R-Squared: 0.853 Adjusted R-Squared: 0.825 151s 151s 151s 3SLS estimates for 'PrivateWages' (equation 3) 151s Model Formula: privWage ~ gnp + gnpLag + trend 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 1.6387 1.1457 1.43 0.17188 151s gnp 0.4062 0.0324 12.52 1.1e-09 *** 151s gnpLag 0.1784 0.0347 5.14 1.0e-04 *** 151s trend 0.1435 0.0292 4.91 0.00016 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 0.81 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 10.497 MSE: 0.656 Root MSE: 0.81 151s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 151s 151s > residuals 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 -0.3538 -1.795 -1.2388 151s 3 -0.9465 0.154 0.4649 151s 4 -1.4189 0.678 1.4344 151s 5 -0.3546 -1.666 -0.1354 151s 6 0.1366 0.251 -0.3452 151s 7 NA NA NA 151s 8 1.4213 1.150 -0.7445 151s 9 1.2173 0.476 0.3001 151s 10 -0.4636 2.200 1.2232 151s 11 -0.0650 -0.962 -0.4104 151s 12 -0.5422 -0.808 0.2495 151s 13 -0.7092 -1.098 -0.3057 151s 14 0.4898 1.542 0.3497 151s 15 -0.0502 -0.155 0.2949 151s 16 0.0272 0.154 0.0214 151s 17 1.8311 1.932 -0.7322 151s 18 -0.4567 -0.180 0.9090 151s 19 0.0650 -3.381 -0.7795 151s 20 1.2135 0.557 -0.2847 151s 21 0.9466 0.167 -1.0812 151s 22 -1.9877 0.784 0.8102 151s > fitted 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 42.3 1.595 26.7 151s 3 45.9 1.746 28.8 151s 4 50.6 4.522 32.7 151s 5 51.0 4.666 34.0 151s 6 52.5 4.849 35.7 151s 7 NA NA NA 151s 8 54.8 3.050 38.6 151s 9 56.1 2.524 38.9 151s 10 58.3 2.900 40.1 151s 11 55.1 1.962 38.3 151s 12 51.4 -2.592 34.3 151s 13 46.3 -5.102 29.3 151s 14 46.0 -6.642 28.2 151s 15 48.8 -2.845 30.3 151s 16 51.3 -1.454 33.2 151s 17 55.9 0.168 37.5 151s 18 59.2 2.180 40.1 151s 19 57.4 1.481 39.0 151s 20 60.4 0.743 41.9 151s 21 64.1 3.133 46.1 151s 22 71.7 4.116 52.5 151s > predict 151s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 151s 1 NA NA NA NA 151s 2 42.3 0.468 39.8 44.7 151s 3 45.9 0.543 43.4 48.5 151s 4 50.6 0.352 48.3 53.0 151s 5 51.0 0.407 48.6 53.4 151s 6 52.5 0.411 50.1 54.9 151s 7 NA NA NA NA 151s 8 54.8 0.340 52.4 57.1 151s 9 56.1 0.372 53.7 58.5 151s 10 58.3 0.387 55.9 60.6 151s 11 55.1 0.687 52.4 57.7 151s 12 51.4 0.558 48.9 54.0 151s 13 46.3 0.713 43.6 49.0 151s 14 46.0 0.599 43.4 48.6 151s 15 48.8 0.368 46.4 51.1 151s 16 51.3 0.326 48.9 53.6 151s 17 55.9 0.388 53.5 58.3 151s 18 59.2 0.319 56.8 61.5 151s 19 57.4 0.391 55.0 59.8 151s 20 60.4 0.457 57.9 62.8 151s 21 64.1 0.437 61.6 66.5 151s 22 71.7 0.674 69.0 74.3 151s Investment.pred Investment.se.fit Investment.lwr Investment.upr 151s 1 NA NA NA NA 151s 2 1.595 0.731 -1.8742 5.065 151s 3 1.746 0.533 -1.5566 5.050 151s 4 4.522 0.484 1.2530 7.791 151s 5 4.666 0.406 1.4458 7.887 151s 6 4.849 0.386 1.6390 8.058 151s 7 NA NA NA NA 151s 8 3.050 0.325 -0.1296 6.229 151s 9 2.524 0.467 -0.7334 5.782 151s 10 2.900 0.515 -0.3900 6.190 151s 11 1.962 0.769 -1.5438 5.467 151s 12 -2.592 0.608 -5.9519 0.769 151s 13 -5.102 0.774 -8.6129 -1.592 151s 14 -6.642 0.807 -10.1867 -3.098 151s 15 -2.845 0.395 -6.0599 0.370 151s 16 -1.454 0.341 -4.6409 1.733 151s 17 0.168 0.442 -3.0739 3.410 151s 18 2.180 0.281 -0.9807 5.340 151s 19 1.481 0.414 -1.7440 4.706 151s 20 0.743 0.492 -2.5310 4.017 151s 21 3.133 0.414 -0.0924 6.358 151s 22 4.116 0.583 0.7756 7.457 151s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 151s 1 NA NA NA NA 151s 2 26.7 0.322 24.9 28.6 151s 3 28.8 0.328 27.0 30.7 151s 4 32.7 0.340 30.8 34.5 151s 5 34.0 0.250 32.2 35.8 151s 6 35.7 0.257 33.9 37.5 151s 7 NA NA NA NA 151s 8 38.6 0.254 36.8 40.4 151s 9 38.9 0.241 37.1 40.7 151s 10 40.1 0.235 38.3 41.9 151s 11 38.3 0.325 36.5 40.2 151s 12 34.3 0.349 32.4 36.1 151s 13 29.3 0.425 27.4 31.2 151s 14 28.2 0.340 26.3 30.0 151s 15 30.3 0.326 28.5 32.2 151s 16 33.2 0.272 31.4 35.0 151s 17 37.5 0.273 35.7 39.3 151s 18 40.1 0.214 38.3 41.9 151s 19 39.0 0.336 37.1 40.8 151s 20 41.9 0.290 40.1 43.7 151s 21 46.1 0.305 44.2 47.9 151s 22 52.5 0.479 50.5 54.5 151s > model.frame 151s [1] TRUE 151s > model.matrix 151s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 151s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 151s [3] "Numeric: lengths (744, 720) differ" 151s > nobs 151s [1] 60 151s > linearHypothesis 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 49 151s 2 48 1 0.22 0.64 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 49 151s 2 48 1 0.29 0.59 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 49 151s 2 48 1 0.29 0.59 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 48 2 0.29 0.75 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 48 2 0.38 0.68 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 50 151s 2 48 2 0.77 0.68 151s > logLik 151s 'log Lik.' -71.9 (df=18) 151s 'log Lik.' -82.9 (df=18) 151s Estimating function 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 -2.1852 -28.316 151s Consumption_3 -1.2615 -21.074 151s Consumption_4 -0.7432 -14.221 151s Consumption_5 -4.1386 -86.649 151s Consumption_6 0.0344 0.669 151s Consumption_8 5.9528 102.039 151s Consumption_9 3.6199 70.548 151s Consumption_10 1.2130 24.820 151s Consumption_11 -2.3309 -39.266 151s Consumption_12 -1.5509 -19.665 151s Consumption_13 -2.9298 -26.139 151s Consumption_14 2.9907 27.815 151s Consumption_15 -1.7611 -22.533 151s Consumption_16 -1.0403 -14.834 151s Consumption_17 7.8605 115.957 151s Consumption_18 -1.2660 -24.744 151s Consumption_19 -6.1974 -119.976 151s Consumption_20 4.2546 73.971 151s Consumption_21 1.7695 35.564 151s Consumption_22 -2.2905 -52.365 151s Investment_2 1.5294 19.818 151s Investment_3 -0.1395 -2.330 151s Investment_4 -0.5222 -9.992 151s Investment_5 1.4794 30.973 151s Investment_6 -0.2466 -4.801 151s Investment_8 -1.1148 -19.108 151s Investment_9 -0.4909 -9.566 151s Investment_10 -1.9066 -39.013 151s Investment_11 0.8748 14.736 151s Investment_12 0.7489 9.496 151s Investment_13 1.0277 9.169 151s Investment_14 -1.3972 -12.995 151s Investment_15 0.1582 2.024 151s Investment_16 -0.1132 -1.614 151s Investment_17 -1.7775 -26.221 151s Investment_18 0.2812 5.496 151s Investment_19 3.0567 59.173 151s Investment_20 -0.5590 -9.719 151s Investment_21 -0.1981 -3.981 151s Investment_22 -0.6908 -15.792 151s PrivateWages_2 -3.3803 -43.802 151s PrivateWages_3 1.2445 20.789 151s PrivateWages_4 3.1328 59.947 151s PrivateWages_5 -2.9316 -61.378 151s PrivateWages_6 -0.3443 -6.703 151s PrivateWages_8 1.9219 32.944 151s PrivateWages_9 2.2216 43.296 151s PrivateWages_10 4.0703 83.288 151s PrivateWages_11 -2.6344 -44.377 151s PrivateWages_12 -0.6120 -7.760 151s PrivateWages_13 -2.5653 -22.887 151s PrivateWages_14 2.8669 26.663 151s PrivateWages_15 -0.5912 -7.565 151s PrivateWages_16 -0.6625 -9.447 151s PrivateWages_17 2.6204 38.656 151s PrivateWages_18 0.0477 0.933 151s PrivateWages_19 -7.1288 -138.006 151s PrivateWages_20 1.4620 25.419 151s PrivateWages_21 -1.3672 -27.479 151s PrivateWages_22 2.6294 60.113 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 -27.752 -63.61 151s Consumption_3 -15.643 -40.21 151s Consumption_4 -12.560 -26.46 151s Consumption_5 -76.150 -161.61 151s Consumption_6 0.667 1.34 151s Consumption_8 116.675 236.66 151s Consumption_9 71.675 153.05 151s Consumption_10 25.593 53.50 151s Consumption_11 -50.581 -101.08 151s Consumption_12 -24.194 -61.19 151s Consumption_13 -33.399 -102.70 151s Consumption_14 20.935 98.78 151s Consumption_15 -19.724 -66.25 151s Consumption_16 -12.795 -41.59 151s Consumption_17 110.047 328.11 151s Consumption_18 -22.282 -60.30 151s Consumption_19 -107.216 -306.49 151s Consumption_20 65.095 205.74 151s Consumption_21 33.620 94.08 151s Consumption_22 -48.330 -139.53 151s Investment_2 19.424 44.52 151s Investment_3 -1.729 -4.45 151s Investment_4 -8.825 -18.59 151s Investment_5 27.221 57.77 151s Investment_6 -4.784 -9.58 151s Investment_8 -21.849 -44.32 151s Investment_9 -9.719 -20.75 151s Investment_10 -40.229 -84.09 151s Investment_11 18.983 37.94 151s Investment_12 11.683 29.55 151s Investment_13 11.716 36.03 151s Investment_14 -9.780 -46.15 151s Investment_15 1.772 5.95 151s Investment_16 -1.392 -4.53 151s Investment_17 -24.885 -74.20 151s Investment_18 4.949 13.39 151s Investment_19 52.880 151.16 151s Investment_20 -8.553 -27.03 151s Investment_21 -3.764 -10.53 151s Investment_22 -14.576 -42.08 151s PrivateWages_2 -42.929 -98.41 151s PrivateWages_3 15.432 39.67 151s PrivateWages_4 52.944 111.55 151s PrivateWages_5 -53.942 -114.48 151s PrivateWages_6 -6.679 -13.37 151s PrivateWages_8 37.670 76.41 151s PrivateWages_9 43.987 93.93 151s PrivateWages_10 85.884 179.53 151s PrivateWages_11 -57.165 -114.24 151s PrivateWages_12 -9.547 -24.14 151s PrivateWages_13 -29.244 -89.93 151s PrivateWages_14 20.068 94.68 151s PrivateWages_15 -6.622 -22.24 151s PrivateWages_16 -8.149 -26.49 151s PrivateWages_17 36.686 109.38 151s PrivateWages_18 0.840 2.27 151s PrivateWages_19 -123.329 -352.55 151s PrivateWages_20 22.369 70.70 151s PrivateWages_21 -25.977 -72.69 151s PrivateWages_22 55.481 160.18 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0.9588 12.424 151s Consumption_3 0.5535 9.246 151s Consumption_4 0.3261 6.240 151s Consumption_5 1.8159 38.018 151s Consumption_6 -0.0151 -0.294 151s Consumption_8 -2.6118 -44.771 151s Consumption_9 -1.5883 -30.954 151s Consumption_10 -0.5322 -10.890 151s Consumption_11 1.0227 17.228 151s Consumption_12 0.6805 8.628 151s Consumption_13 1.2855 11.469 151s Consumption_14 -1.3122 -12.204 151s Consumption_15 0.7727 9.887 151s Consumption_16 0.4564 6.508 151s Consumption_17 -3.4489 -50.877 151s Consumption_18 0.5555 10.857 151s Consumption_19 2.7192 52.640 151s Consumption_20 -1.8667 -32.456 151s Consumption_21 -0.7764 -15.604 151s Consumption_22 1.0050 22.976 151s Investment_2 -2.3899 -30.969 151s Investment_3 0.2179 3.641 151s Investment_4 0.8160 15.614 151s Investment_5 -2.3118 -48.401 151s Investment_6 0.3854 7.502 151s Investment_8 1.7420 29.860 151s Investment_9 0.7670 14.948 151s Investment_10 2.9794 60.964 151s Investment_11 -1.3670 -23.027 151s Investment_12 -1.1702 -14.838 151s Investment_13 -1.6060 -14.328 151s Investment_14 2.1833 20.306 151s Investment_15 -0.2472 -3.163 151s Investment_16 0.1769 2.522 151s Investment_17 2.7776 40.974 151s Investment_18 -0.4394 -8.588 151s Investment_19 -4.7765 -92.468 151s Investment_20 0.8735 15.187 151s Investment_21 0.3095 6.221 151s Investment_22 1.0795 24.678 151s PrivateWages_2 2.1957 28.452 151s PrivateWages_3 -0.8084 -13.504 151s PrivateWages_4 -2.0349 -38.939 151s PrivateWages_5 1.9043 39.869 151s PrivateWages_6 0.2236 4.354 151s PrivateWages_8 -1.2484 -21.399 151s PrivateWages_9 -1.4431 -28.123 151s PrivateWages_10 -2.6439 -54.100 151s PrivateWages_11 1.7112 28.826 151s PrivateWages_12 0.3975 5.041 151s PrivateWages_13 1.6663 14.867 151s PrivateWages_14 -1.8622 -17.319 151s PrivateWages_15 0.3840 4.914 151s PrivateWages_16 0.4304 6.137 151s PrivateWages_17 -1.7021 -25.110 151s PrivateWages_18 -0.0310 -0.606 151s PrivateWages_19 4.6306 89.644 151s PrivateWages_20 -0.9497 -16.511 151s PrivateWages_21 0.8881 17.849 151s PrivateWages_22 -1.7080 -39.047 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 12.176 175.26 151s Consumption_3 6.864 101.07 151s Consumption_4 5.511 60.16 151s Consumption_5 33.412 344.47 151s Consumption_6 -0.293 -2.91 151s Consumption_8 -51.192 -531.25 151s Consumption_9 -31.448 -329.73 151s Consumption_10 -11.229 -112.08 151s Consumption_11 22.193 220.60 151s Consumption_12 10.615 147.46 151s Consumption_13 14.654 274.19 151s Consumption_14 -9.185 -271.76 151s Consumption_15 8.654 156.08 151s Consumption_16 5.614 90.83 151s Consumption_17 -48.284 -681.84 151s Consumption_18 9.776 110.98 151s Consumption_19 47.042 548.73 151s Consumption_20 -28.561 -373.16 151s Consumption_21 -14.751 -156.21 151s Consumption_22 21.205 205.52 151s Investment_2 -30.352 -436.88 151s Investment_3 2.702 39.79 151s Investment_4 13.790 150.55 151s Investment_5 -42.537 -438.54 151s Investment_6 7.476 74.26 151s Investment_8 34.143 354.32 151s Investment_9 15.187 159.24 151s Investment_10 62.865 627.45 151s Investment_11 -29.663 -294.86 151s Investment_12 -18.256 -253.59 151s Investment_13 -18.308 -342.55 151s Investment_14 15.283 452.17 151s Investment_15 -2.768 -49.93 151s Investment_16 2.176 35.20 151s Investment_17 38.886 549.13 151s Investment_18 -7.734 -87.79 151s Investment_19 -82.633 -963.90 151s Investment_20 13.365 174.61 151s Investment_21 5.881 62.28 151s Investment_22 22.777 220.75 151s PrivateWages_2 27.885 401.37 151s PrivateWages_3 -10.024 -147.61 151s PrivateWages_4 -34.390 -375.44 151s PrivateWages_5 35.039 361.24 151s PrivateWages_6 4.339 43.10 151s PrivateWages_8 -24.469 -253.93 151s PrivateWages_9 -28.572 -299.58 151s PrivateWages_10 -55.787 -556.81 151s PrivateWages_11 37.132 369.10 151s PrivateWages_12 6.201 86.14 151s PrivateWages_13 18.996 355.42 151s PrivateWages_14 -13.035 -385.66 151s PrivateWages_15 4.301 77.58 151s PrivateWages_16 5.293 85.64 151s PrivateWages_17 -23.830 -336.51 151s PrivateWages_18 -0.546 -6.19 151s PrivateWages_19 80.110 934.46 151s PrivateWages_20 -14.530 -189.84 151s PrivateWages_21 16.874 178.68 151s PrivateWages_22 -36.038 -349.28 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 -2.1174 -99.67 -95.07 151s Consumption_3 -1.2224 -60.61 -55.74 151s Consumption_4 -0.7201 -40.72 -36.08 151s Consumption_5 -4.0103 -243.37 -229.39 151s Consumption_6 0.0333 2.02 1.90 151s Consumption_8 5.7682 346.08 369.17 151s Consumption_9 3.5077 218.42 225.90 151s Consumption_10 1.1754 75.89 75.81 151s Consumption_11 -2.2587 -143.90 -151.33 151s Consumption_12 -1.5028 -82.40 -91.97 151s Consumption_13 -2.8389 -133.36 -151.60 151s Consumption_14 2.8980 122.09 128.38 151s Consumption_15 -1.7065 -87.40 -76.96 151s Consumption_16 -1.0080 -55.78 -50.10 151s Consumption_17 7.6168 437.16 414.35 151s Consumption_18 -1.2268 -82.41 -76.92 151s Consumption_19 -6.0053 -411.44 -390.34 151s Consumption_20 4.1227 275.58 251.07 151s Consumption_21 1.7146 128.37 119.16 151s Consumption_22 -2.2195 -192.83 -168.02 151s Investment_2 2.1940 103.27 98.51 151s Investment_3 -0.2001 -9.92 -9.12 151s Investment_4 -0.7491 -42.36 -37.53 151s Investment_5 2.1223 128.79 121.39 151s Investment_6 -0.3538 -21.44 -20.20 151s Investment_8 -1.5992 -95.95 -102.35 151s Investment_9 -0.7042 -43.85 -45.35 151s Investment_10 -2.7351 -176.60 -176.41 151s Investment_11 1.2549 79.95 84.08 151s Investment_12 1.0743 58.91 65.75 151s Investment_13 1.4743 69.26 78.73 151s Investment_14 -2.0044 -84.44 -88.79 151s Investment_15 0.2269 11.62 10.23 151s Investment_16 -0.1624 -8.99 -8.07 151s Investment_17 -2.5499 -146.35 -138.71 151s Investment_18 0.4034 27.10 25.29 151s Investment_19 4.3849 300.42 285.02 151s Investment_20 -0.8019 -53.60 -48.84 151s Investment_21 -0.2842 -21.27 -19.75 151s Investment_22 -0.9910 -86.09 -75.02 151s PrivateWages_2 -7.3399 -345.49 -329.56 151s PrivateWages_3 2.7024 133.99 123.23 151s PrivateWages_4 6.8025 384.63 340.81 151s PrivateWages_5 -6.3658 -386.31 -364.12 151s PrivateWages_6 -0.7476 -45.31 -42.69 151s PrivateWages_8 4.1733 250.39 267.09 151s PrivateWages_9 4.8240 300.38 310.66 151s PrivateWages_10 8.8383 570.68 570.07 151s PrivateWages_11 -5.7203 -364.45 -383.26 151s PrivateWages_12 -1.3289 -72.87 -81.33 151s PrivateWages_13 -5.5702 -261.67 -297.45 151s PrivateWages_14 6.2251 262.25 275.77 151s PrivateWages_15 -1.2838 -65.75 -57.90 151s PrivateWages_16 -1.4387 -79.61 -71.50 151s PrivateWages_17 5.6900 326.57 309.54 151s PrivateWages_18 0.1036 6.96 6.50 151s PrivateWages_19 -15.4796 -1060.55 -1006.17 151s PrivateWages_20 3.1746 212.21 193.34 151s PrivateWages_21 -2.9688 -222.26 -206.33 151s PrivateWages_22 5.7096 496.04 432.21 151s PrivateWages_trend 151s Consumption_2 21.174 151s Consumption_3 11.002 151s Consumption_4 5.761 151s Consumption_5 28.072 151s Consumption_6 -0.200 151s Consumption_8 -23.073 151s Consumption_9 -10.523 151s Consumption_10 -2.351 151s Consumption_11 2.259 151s Consumption_12 0.000 151s Consumption_13 -2.839 151s Consumption_14 5.796 151s Consumption_15 -5.119 151s Consumption_16 -4.032 151s Consumption_17 38.084 151s Consumption_18 -7.361 151s Consumption_19 -42.037 151s Consumption_20 32.981 151s Consumption_21 15.431 151s Consumption_22 -22.195 151s Investment_2 -21.940 151s Investment_3 1.801 151s Investment_4 5.993 151s Investment_5 -14.856 151s Investment_6 2.123 151s Investment_8 6.397 151s Investment_9 2.112 151s Investment_10 5.470 151s Investment_11 -1.255 151s Investment_12 0.000 151s Investment_13 1.474 151s Investment_14 -4.009 151s Investment_15 0.681 151s Investment_16 -0.650 151s Investment_17 -12.749 151s Investment_18 2.420 151s Investment_19 30.694 151s Investment_20 -6.415 151s Investment_21 -2.557 151s Investment_22 -9.910 151s PrivateWages_2 73.399 151s PrivateWages_3 -24.321 151s PrivateWages_4 -54.420 151s PrivateWages_5 44.560 151s PrivateWages_6 4.486 151s PrivateWages_8 -16.693 151s PrivateWages_9 -14.472 151s PrivateWages_10 -17.677 151s PrivateWages_11 5.720 151s PrivateWages_12 0.000 151s PrivateWages_13 -5.570 151s PrivateWages_14 12.450 151s PrivateWages_15 -3.851 151s PrivateWages_16 -5.755 151s PrivateWages_17 28.450 151s PrivateWages_18 0.622 151s PrivateWages_19 -108.357 151s PrivateWages_20 25.397 151s PrivateWages_21 -26.719 151s PrivateWages_22 57.096 151s [1] TRUE 151s > Bread 151s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 151s [1,] 101.7742 -0.858360 -0.3736 151s [2,] -0.8584 0.690973 -0.4670 151s [3,] -0.3736 -0.466994 0.6099 151s [4,] -1.8845 -0.076066 -0.0404 151s [5,] 84.1239 -0.877202 2.8173 151s [6,] -1.7843 0.267204 -0.2636 151s [7,] 0.6061 -0.218819 0.2875 151s [8,] -0.3146 -0.000285 -0.0152 151s [9,] -36.6570 0.120759 1.7724 151s [10,] 0.5673 -0.083944 0.0542 151s [11,] 0.0259 0.084615 -0.0868 151s [12,] 0.2015 0.041756 0.0283 151s Consumption_wages Investment_(Intercept) Investment_corpProf 151s [1,] -1.884465 84.124 -1.7843 151s [2,] -0.076066 -0.877 0.2672 151s [3,] -0.040367 2.817 -0.2636 151s [4,] 0.091823 -2.748 0.0379 151s [5,] -2.748307 2378.068 -36.8158 151s [6,] 0.037919 -36.816 1.2756 151s [7,] -0.038383 31.099 -1.1022 151s [8,] 0.013629 -11.271 0.1659 151s [9,] 0.115318 17.951 -0.1175 151s [10,] -0.000915 1.841 0.0121 151s [11,] -0.000905 -2.197 -0.0106 151s [12,] -0.032751 -1.985 0.0278 151s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 151s [1,] 0.60609 -3.15e-01 -3.67e+01 151s [2,] -0.21882 -2.85e-04 1.21e-01 151s [3,] 0.28746 -1.52e-02 1.77e+00 151s [4,] -0.03838 1.36e-02 1.15e-01 151s [5,] 31.09923 -1.13e+01 1.80e+01 151s [6,] -1.10217 1.66e-01 -1.17e-01 151s [7,] 1.17984 -1.58e-01 -9.59e-01 151s [8,] -0.15817 5.51e-02 7.31e-04 151s [9,] -0.95890 7.31e-04 7.88e+01 151s [10,] 0.00248 -1.04e-02 -5.11e-01 151s [11,] 0.01419 1.07e-02 -8.12e-01 151s [12,] -0.04010 1.08e-02 9.53e-01 151s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 151s [1,] 0.567318 0.025878 0.20145 151s [2,] -0.083944 0.084615 0.04176 151s [3,] 0.054179 -0.086845 0.02834 151s [4,] -0.000915 -0.000905 -0.03275 151s [5,] 1.840734 -2.196531 -1.98486 151s [6,] 0.012109 -0.010622 0.02782 151s [7,] 0.002479 0.014187 -0.04010 151s [8,] -0.010386 0.010690 0.01081 151s [9,] -0.511083 -0.811688 0.95314 151s [10,] 0.063161 -0.056453 -0.01901 151s [11,] -0.056453 0.072451 0.00297 151s [12,] -0.019011 0.002975 0.05128 151s > 151s > # I3SLS 151s > summary 151s 151s systemfit results 151s method: iterated 3SLS 151s 151s convergence achieved after 22 iterations 151s 151s N DF SSR detRCov OLS-R2 McElroy-R2 151s system 60 48 107 0.47 0.946 0.996 151s 151s N DF SSR MSE RMSE R2 Adj R2 151s Consumption 20 16 18.1 1.13 1.063 0.981 0.977 151s Investment 20 16 76.4 4.77 2.185 0.672 0.610 151s PrivateWages 20 16 12.3 0.77 0.877 0.984 0.982 151s 151s The covariance matrix of the residuals used for estimation 151s Consumption Investment PrivateWages 151s Consumption 0.905 0.509 -0.437 151s Investment 0.509 3.819 0.709 151s PrivateWages -0.437 0.709 0.616 151s 151s The covariance matrix of the residuals 151s Consumption Investment PrivateWages 151s Consumption 0.905 0.509 -0.437 151s Investment 0.509 3.819 0.709 151s PrivateWages -0.437 0.709 0.616 151s 151s The correlations of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.000 0.274 -0.585 151s Investment 0.274 1.000 0.462 151s PrivateWages -0.585 0.462 1.000 151s 151s 151s 3SLS estimates for 'Consumption' (equation 1) 151s Model Formula: consump ~ corpProf + corpProfLag + wages 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 16.4728 1.2187 13.52 3.6e-10 *** 151s corpProf 0.1642 0.0952 1.73 0.10 151s corpProfLag 0.1552 0.0903 1.72 0.11 151s wages 0.7756 0.0356 21.82 2.5e-13 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.063 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 18.095 MSE: 1.131 Root MSE: 1.063 151s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 151s 151s 151s 3SLS estimates for 'Investment' (equation 2) 151s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 38.7938 9.7249 3.99 0.00106 ** 151s corpProf -0.2501 0.2337 -1.07 0.30036 151s corpProfLag 0.9129 0.2271 4.02 0.00099 *** 151s capitalLag -0.2409 0.0469 -5.14 9.9e-05 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 2.185 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 76.371 MSE: 4.773 Root MSE: 2.185 151s Multiple R-Squared: 0.672 Adjusted R-Squared: 0.61 151s 151s 151s 3SLS estimates for 'PrivateWages' (equation 3) 151s Model Formula: privWage ~ gnp + gnpLag + trend 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 2.4620 1.2228 2.01 0.061 . 151s gnp 0.3776 0.0318 11.88 2.4e-09 *** 151s gnpLag 0.1937 0.0331 5.85 2.5e-05 *** 151s trend 0.1619 0.0300 5.40 5.9e-05 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 0.877 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 12.318 MSE: 0.77 Root MSE: 0.877 151s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.982 151s 151s > residuals 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 -0.4522 -3.4485 -1.2596 151s 3 -1.1470 0.0027 0.5437 151s 4 -1.6147 0.0274 1.6290 151s 5 -0.6117 -2.0392 -0.0707 151s 6 -0.1229 0.0457 -0.1859 151s 7 NA NA NA 151s 8 1.2461 1.4658 -0.6304 151s 9 1.0158 1.4202 0.3924 151s 10 -0.6460 3.2062 1.3671 151s 11 -0.0554 -1.7386 -0.4891 151s 12 -0.3472 -1.3793 0.0179 151s 13 -0.3947 -2.2646 -0.6968 151s 14 0.6536 2.4092 0.1021 151s 15 0.0821 -0.2787 0.1482 151s 16 0.1381 0.1196 -0.0796 151s 17 1.8826 2.5548 -0.6862 151s 18 -0.3415 -0.4009 0.8755 151s 19 0.2296 -4.0454 -0.9839 151s 20 1.3178 1.4481 -0.1989 151s 21 1.0065 0.9087 -0.9681 151s 22 -1.8388 1.9868 1.1734 151s > fitted 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 42.4 3.249 26.8 151s 3 46.1 1.897 28.8 151s 4 50.8 5.173 32.5 151s 5 51.2 5.039 34.0 151s 6 52.7 5.054 35.6 151s 7 NA NA NA 151s 8 55.0 2.734 38.5 151s 9 56.3 1.580 38.8 151s 10 58.4 1.894 39.9 151s 11 55.1 2.739 38.4 151s 12 51.2 -2.021 34.5 151s 13 46.0 -3.935 29.7 151s 14 45.8 -7.509 28.4 151s 15 48.6 -2.721 30.5 151s 16 51.2 -1.420 33.3 151s 17 55.8 -0.455 37.5 151s 18 59.0 2.401 40.1 151s 19 57.3 2.145 39.2 151s 20 60.3 -0.148 41.8 151s 21 64.0 2.391 46.0 151s 22 71.5 2.913 52.1 151s > predict 151s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 151s 1 NA NA NA NA 151s 2 42.4 0.437 41.5 43.2 151s 3 46.1 0.492 45.2 47.1 151s 4 50.8 0.321 50.2 51.5 151s 5 51.2 0.369 50.5 52.0 151s 6 52.7 0.372 52.0 53.5 151s 7 NA NA NA NA 151s 8 55.0 0.310 54.3 55.6 151s 9 56.3 0.338 55.6 57.0 151s 10 58.4 0.355 57.7 59.2 151s 11 55.1 0.618 53.8 56.3 151s 12 51.2 0.501 50.2 52.3 151s 13 46.0 0.642 44.7 47.3 151s 14 45.8 0.547 44.7 46.9 151s 15 48.6 0.340 47.9 49.3 151s 16 51.2 0.300 50.6 51.8 151s 17 55.8 0.354 55.1 56.5 151s 18 59.0 0.294 58.4 59.6 151s 19 57.3 0.354 56.6 58.0 151s 20 60.3 0.418 59.4 61.1 151s 21 64.0 0.407 63.2 64.8 151s 22 71.5 0.628 70.3 72.8 151s Investment.pred Investment.se.fit Investment.lwr Investment.upr 151s 1 NA NA NA NA 151s 2 3.249 1.160 0.91672 5.580 151s 3 1.897 0.934 0.02009 3.775 151s 4 5.173 0.803 3.55865 6.787 151s 5 5.039 0.693 3.64486 6.433 151s 6 5.054 0.674 3.69840 6.410 151s 7 NA NA NA NA 151s 8 2.734 0.584 1.56002 3.908 151s 9 1.580 0.783 0.00466 3.155 151s 10 1.894 0.868 0.14846 3.639 151s 11 2.739 1.321 0.08241 5.395 151s 12 -2.021 1.064 -4.16036 0.119 151s 13 -3.935 1.349 -6.64712 -1.224 151s 14 -7.509 1.360 -10.24349 -4.775 151s 15 -2.721 0.712 -4.15288 -1.290 151s 16 -1.420 0.614 -2.65412 -0.185 151s 17 -0.455 0.751 -1.96433 1.055 151s 18 2.401 0.498 1.39939 3.402 151s 19 2.145 0.698 0.74152 3.549 151s 20 -0.148 0.816 -1.78957 1.493 151s 21 2.391 0.713 0.95855 3.824 151s 22 2.913 0.984 0.93419 4.892 151s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 151s 1 NA NA NA NA 151s 2 26.8 0.347 26.1 27.5 151s 3 28.8 0.348 28.1 29.5 151s 4 32.5 0.354 31.8 33.2 151s 5 34.0 0.263 33.4 34.5 151s 6 35.6 0.274 35.0 36.1 151s 7 NA NA NA NA 151s 8 38.5 0.268 38.0 39.1 151s 9 38.8 0.256 38.3 39.3 151s 10 39.9 0.254 39.4 40.4 151s 11 38.4 0.323 37.7 39.0 151s 12 34.5 0.347 33.8 35.2 151s 13 29.7 0.435 28.8 30.6 151s 14 28.4 0.366 27.7 29.1 151s 15 30.5 0.341 29.8 31.1 151s 16 33.3 0.285 32.7 33.9 151s 17 37.5 0.275 36.9 38.0 151s 18 40.1 0.233 39.7 40.6 151s 19 39.2 0.346 38.5 39.9 151s 20 41.8 0.298 41.2 42.4 151s 21 46.0 0.329 45.3 46.6 151s 22 52.1 0.510 51.1 53.2 151s > model.frame 151s [1] TRUE 151s > model.matrix 151s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 151s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 151s [3] "Numeric: lengths (744, 720) differ" 151s > nobs 151s [1] 60 151s > linearHypothesis 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 49 151s 2 48 1 0.4 0.53 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 49 151s 2 48 1 0.5 0.49 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 49 151s 2 48 1 0.5 0.48 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 48 2 0.66 0.52 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 48 2 0.83 0.44 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 50 151s 2 48 2 1.66 0.44 151s > logLik 151s 'log Lik.' -77.6 (df=18) 151s 'log Lik.' -92.7 (df=18) 151s Estimating function 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 -4.9216 -63.77 151s Consumption_3 -3.3974 -56.75 151s Consumption_4 -2.5781 -49.33 151s Consumption_5 -9.6538 -202.12 151s Consumption_6 -0.8124 -15.82 151s Consumption_8 11.9408 204.68 151s Consumption_9 6.9299 135.05 151s Consumption_10 1.8984 38.85 151s Consumption_11 -4.8868 -82.32 151s Consumption_12 -2.6585 -33.71 151s Consumption_13 -5.0990 -45.49 151s Consumption_14 7.0717 65.77 151s Consumption_15 -3.1138 -39.84 151s Consumption_16 -1.6973 -24.20 151s Consumption_17 16.7458 247.03 151s Consumption_18 -2.5779 -50.39 151s Consumption_19 -12.5621 -243.19 151s Consumption_20 9.4057 163.53 151s Consumption_21 4.0953 82.31 151s Consumption_22 -4.1289 -94.39 151s Investment_2 4.3863 56.84 151s Investment_3 0.0612 1.02 151s Investment_4 -0.2801 -5.36 151s Investment_5 2.1936 45.93 151s Investment_6 0.1486 2.89 151s Investment_8 -1.0616 -18.20 151s Investment_9 -1.3484 -26.28 151s Investment_10 -3.8396 -78.57 151s Investment_11 1.8918 31.87 151s Investment_12 1.4041 17.80 151s Investment_13 2.3647 21.10 151s Investment_14 -2.5638 -23.84 151s Investment_15 0.2053 2.63 151s Investment_16 -0.2445 -3.49 151s Investment_17 -2.4423 -36.03 151s Investment_18 -0.2128 -4.16 151s Investment_19 4.0168 77.76 151s Investment_20 -1.3846 -24.07 151s Investment_21 -0.8726 -17.54 151s Investment_22 -2.4220 -55.37 151s PrivateWages_2 -7.8312 -101.48 151s PrivateWages_3 3.1927 53.33 151s PrivateWages_4 8.1013 155.02 151s PrivateWages_5 -6.1495 -128.75 151s PrivateWages_6 -0.1677 -3.26 151s PrivateWages_8 4.4536 76.34 151s PrivateWages_9 5.3302 103.88 151s PrivateWages_10 9.8611 201.78 151s PrivateWages_11 -6.2042 -104.51 151s PrivateWages_12 -2.2572 -28.62 151s PrivateWages_13 -7.3701 -65.76 151s PrivateWages_14 5.2841 49.14 151s PrivateWages_15 -1.8316 -23.44 151s PrivateWages_16 -1.8732 -26.71 151s PrivateWages_17 5.6855 83.87 151s PrivateWages_18 0.2354 4.60 151s PrivateWages_19 -16.6516 -322.36 151s PrivateWages_20 3.4690 60.31 151s PrivateWages_21 -2.8192 -56.66 151s PrivateWages_22 7.5425 172.43 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 -62.504 -143.28 151s Consumption_3 -42.128 -108.30 151s Consumption_4 -43.571 -91.80 151s Consumption_5 -177.629 -376.98 151s Consumption_6 -15.760 -31.55 151s Consumption_8 234.039 474.72 151s Consumption_9 137.212 292.99 151s Consumption_10 40.056 83.73 151s Consumption_11 -106.045 -211.93 151s Consumption_12 -41.472 -104.88 151s Consumption_13 -58.128 -178.75 151s Consumption_14 49.502 233.56 151s Consumption_15 -34.874 -117.14 151s Consumption_16 -20.877 -67.86 151s Consumption_17 234.441 699.00 151s Consumption_18 -45.372 -122.79 151s Consumption_19 -217.325 -621.24 151s Consumption_20 143.908 454.84 151s Consumption_21 77.811 217.74 151s Consumption_22 -87.120 -251.52 151s Investment_2 55.705 127.69 151s Investment_3 0.759 1.95 151s Investment_4 -4.734 -9.97 151s Investment_5 40.363 85.66 151s Investment_6 2.882 5.77 151s Investment_8 -20.807 -42.21 151s Investment_9 -26.697 -57.01 151s Investment_10 -81.017 -169.36 151s Investment_11 41.052 82.04 151s Investment_12 21.904 55.40 151s Investment_13 26.957 82.89 151s Investment_14 -17.946 -84.67 151s Investment_15 2.299 7.72 151s Investment_16 -3.007 -9.77 151s Investment_17 -34.192 -101.95 151s Investment_18 -3.746 -10.14 151s Investment_19 69.491 198.65 151s Investment_20 -21.185 -66.96 151s Investment_21 -16.580 -46.40 151s Investment_22 -51.104 -147.54 151s PrivateWages_2 -99.457 -227.98 151s PrivateWages_3 39.589 101.77 151s PrivateWages_4 136.911 288.46 151s PrivateWages_5 -113.151 -240.14 151s PrivateWages_6 -3.252 -6.51 151s PrivateWages_8 87.291 177.06 151s PrivateWages_9 105.538 225.36 151s PrivateWages_10 208.070 434.95 151s PrivateWages_11 -134.631 -269.05 151s PrivateWages_12 -35.213 -89.05 151s PrivateWages_13 -84.019 -258.36 151s PrivateWages_14 36.989 174.52 151s PrivateWages_15 -20.514 -68.91 151s PrivateWages_16 -23.040 -74.89 151s PrivateWages_17 79.598 237.33 151s PrivateWages_18 4.143 11.21 151s PrivateWages_19 -288.073 -823.48 151s PrivateWages_20 53.076 167.75 151s PrivateWages_21 -53.565 -149.89 151s PrivateWages_22 159.147 459.47 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 1.6584 21.489 151s Consumption_3 1.1448 19.123 151s Consumption_4 0.8687 16.623 151s Consumption_5 3.2529 68.104 151s Consumption_6 0.2737 5.329 151s Consumption_8 -4.0235 -68.968 151s Consumption_9 -2.3351 -45.507 151s Consumption_10 -0.6397 -13.089 151s Consumption_11 1.6466 27.739 151s Consumption_12 0.8958 11.358 151s Consumption_13 1.7181 15.329 151s Consumption_14 -2.3828 -22.161 151s Consumption_15 1.0492 13.424 151s Consumption_16 0.5719 8.155 151s Consumption_17 -5.6426 -83.238 151s Consumption_18 0.8686 16.978 151s Consumption_19 4.2329 81.944 151s Consumption_20 -3.1693 -55.102 151s Consumption_21 -1.3799 -27.735 151s Consumption_22 1.3913 31.806 151s Investment_2 -2.5801 -33.433 151s Investment_3 -0.0360 -0.601 151s Investment_4 0.1648 3.153 151s Investment_5 -1.2904 -27.016 151s Investment_6 -0.0874 -1.701 151s Investment_8 0.6245 10.704 151s Investment_9 0.7931 15.457 151s Investment_10 2.2586 46.215 151s Investment_11 -1.1128 -18.746 151s Investment_12 -0.8259 -10.473 151s Investment_13 -1.3910 -12.410 151s Investment_14 1.5081 14.026 151s Investment_15 -0.1208 -1.545 151s Investment_16 0.1438 2.050 151s Investment_17 1.4366 21.193 151s Investment_18 0.1252 2.447 151s Investment_19 -2.3628 -45.741 151s Investment_20 0.8145 14.161 151s Investment_21 0.5133 10.317 151s Investment_22 1.4247 32.570 151s PrivateWages_2 3.3346 43.210 151s PrivateWages_3 -1.3594 -22.709 151s PrivateWages_4 -3.4495 -66.008 151s PrivateWages_5 2.6185 54.822 151s PrivateWages_6 0.0714 1.390 151s PrivateWages_8 -1.8964 -32.506 151s PrivateWages_9 -2.2696 -44.232 151s PrivateWages_10 -4.1989 -85.919 151s PrivateWages_11 2.6418 44.502 151s PrivateWages_12 0.9611 12.187 151s PrivateWages_13 3.1382 27.999 151s PrivateWages_14 -2.2500 -20.926 151s PrivateWages_15 0.7799 9.979 151s PrivateWages_16 0.7976 11.373 151s PrivateWages_17 -2.4209 -35.713 151s PrivateWages_18 -0.1002 -1.959 151s PrivateWages_19 7.0903 137.261 151s PrivateWages_20 -1.4771 -25.682 151s PrivateWages_21 1.2004 24.127 151s PrivateWages_22 -3.2116 -73.422 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 21.061 303.15 151s Consumption_3 14.195 209.04 151s Consumption_4 14.681 160.28 151s Consumption_5 59.853 617.07 151s Consumption_6 5.310 52.75 151s Consumption_8 -78.860 -818.38 151s Consumption_9 -46.234 -484.76 151s Consumption_10 -13.497 -134.72 151s Consumption_11 35.732 355.18 151s Consumption_12 13.974 194.12 151s Consumption_13 19.587 366.47 151s Consumption_14 -16.680 -493.49 151s Consumption_15 11.751 211.94 151s Consumption_16 7.034 113.81 151s Consumption_17 -78.996 -1115.54 151s Consumption_18 15.288 173.56 151s Consumption_19 73.229 854.19 151s Consumption_20 -48.490 -633.54 151s Consumption_21 -26.219 -277.64 151s Consumption_22 29.355 284.51 151s Investment_2 -32.767 -471.64 151s Investment_3 -0.446 -6.57 151s Investment_4 2.785 30.40 151s Investment_5 -23.742 -244.78 151s Investment_6 -1.695 -16.84 151s Investment_8 12.239 127.02 151s Investment_9 15.704 164.66 151s Investment_10 47.656 475.66 151s Investment_11 -24.148 -240.03 151s Investment_12 -12.884 -178.98 151s Investment_13 -15.857 -296.69 151s Investment_14 10.556 312.32 151s Investment_15 -1.352 -24.39 151s Investment_16 1.769 28.62 151s Investment_17 20.113 284.02 151s Investment_18 2.203 25.01 151s Investment_19 -40.876 -476.81 151s Investment_20 12.461 162.81 151s Investment_21 9.753 103.28 151s Investment_22 30.061 291.35 151s PrivateWages_2 42.349 609.56 151s PrivateWages_3 -16.857 -248.23 151s PrivateWages_4 -58.297 -636.44 151s PrivateWages_5 48.180 496.72 151s PrivateWages_6 1.385 13.76 151s PrivateWages_8 -37.169 -385.72 151s PrivateWages_9 -44.939 -471.17 151s PrivateWages_10 -88.597 -884.29 151s PrivateWages_11 57.326 569.83 151s PrivateWages_12 14.994 208.28 151s PrivateWages_13 35.776 669.38 151s PrivateWages_14 -15.750 -465.97 151s PrivateWages_15 8.735 157.54 151s PrivateWages_16 9.810 158.72 151s PrivateWages_17 -33.893 -478.62 151s PrivateWages_18 -1.764 -20.03 151s PrivateWages_19 122.662 1430.82 151s PrivateWages_20 -22.600 -295.28 151s PrivateWages_21 22.808 241.53 151s PrivateWages_22 -67.765 -656.78 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 -5.3990 -254.13 -242.42 151s Consumption_3 -3.7270 -184.79 -169.95 151s Consumption_4 -2.8282 -159.92 -141.69 151s Consumption_5 -10.5903 -642.68 -605.76 151s Consumption_6 -0.8912 -54.02 -50.89 151s Consumption_8 13.0991 785.91 838.34 151s Consumption_9 7.6022 473.37 489.58 151s Consumption_10 2.0826 134.47 134.33 151s Consumption_11 -5.3609 -341.55 -359.18 151s Consumption_12 -2.9163 -159.91 -178.48 151s Consumption_13 -5.5936 -262.77 -298.70 151s Consumption_14 7.7577 326.81 343.67 151s Consumption_15 -3.4158 -174.95 -154.05 151s Consumption_16 -1.8619 -103.04 -92.54 151s Consumption_17 18.3702 1054.34 999.34 151s Consumption_18 -2.8280 -189.97 -177.32 151s Consumption_19 -13.7808 -944.16 -895.75 151s Consumption_20 10.3182 689.71 628.38 151s Consumption_21 4.4926 336.34 312.24 151s Consumption_22 -4.5294 -393.51 -342.88 151s Investment_2 6.0805 286.21 273.02 151s Investment_3 0.0848 4.21 3.87 151s Investment_4 -0.3883 -21.96 -19.45 151s Investment_5 3.0410 184.55 173.94 151s Investment_6 0.2060 12.48 11.76 151s Investment_8 -1.4717 -88.30 -94.19 151s Investment_9 -1.8692 -116.39 -120.38 151s Investment_10 -5.3228 -343.69 -343.32 151s Investment_11 2.6225 167.09 175.71 151s Investment_12 1.9465 106.73 119.12 151s Investment_13 3.2781 154.00 175.05 151s Investment_14 -3.5541 -149.72 -157.44 151s Investment_15 0.2846 14.58 12.84 151s Investment_16 -0.3389 -18.75 -16.84 151s Investment_17 -3.3857 -194.32 -184.18 151s Investment_18 -0.2951 -19.82 -18.50 151s Investment_19 5.5684 381.50 361.95 151s Investment_20 -1.9195 -128.31 -116.90 151s Investment_21 -1.2097 -90.57 -84.07 151s Investment_22 -3.3575 -291.70 -254.16 151s PrivateWages_2 -12.3381 -580.75 -553.98 151s PrivateWages_3 5.0300 249.39 229.37 151s PrivateWages_4 12.7635 721.68 639.45 151s PrivateWages_5 -9.6885 -587.96 -554.18 151s PrivateWages_6 -0.2641 -16.01 -15.08 151s PrivateWages_8 7.0167 420.99 449.07 151s PrivateWages_9 8.3978 522.92 540.82 151s PrivateWages_10 15.5362 1003.16 1002.09 151s PrivateWages_11 -9.7747 -622.76 -654.90 151s PrivateWages_12 -3.5562 -195.00 -217.64 151s PrivateWages_13 -11.6116 -545.48 -620.06 151s PrivateWages_14 8.3251 350.72 368.80 151s PrivateWages_15 -2.8858 -147.80 -130.15 151s PrivateWages_16 -2.9512 -163.31 -146.67 151s PrivateWages_17 8.9576 514.11 487.29 151s PrivateWages_18 0.3709 24.92 23.26 151s PrivateWages_19 -26.2346 -1797.40 -1705.25 151s PrivateWages_20 5.4654 365.33 332.84 151s PrivateWages_21 -4.4417 -332.53 -308.70 151s PrivateWages_22 11.8832 1032.40 899.56 151s PrivateWages_trend 151s Consumption_2 53.990 151s Consumption_3 33.543 151s Consumption_4 22.626 151s Consumption_5 74.132 151s Consumption_6 5.347 151s Consumption_8 -52.396 151s Consumption_9 -22.806 151s Consumption_10 -4.165 151s Consumption_11 5.361 151s Consumption_12 0.000 151s Consumption_13 -5.594 151s Consumption_14 15.515 151s Consumption_15 -10.247 151s Consumption_16 -7.448 151s Consumption_17 91.851 151s Consumption_18 -16.968 151s Consumption_19 -96.465 151s Consumption_20 82.545 151s Consumption_21 40.433 151s Consumption_22 -45.294 151s Investment_2 -60.805 151s Investment_3 -0.763 151s Investment_4 3.106 151s Investment_5 -21.287 151s Investment_6 -1.236 151s Investment_8 5.887 151s Investment_9 5.608 151s Investment_10 10.646 151s Investment_11 -2.623 151s Investment_12 0.000 151s Investment_13 3.278 151s Investment_14 -7.108 151s Investment_15 0.854 151s Investment_16 -1.356 151s Investment_17 -16.928 151s Investment_18 -1.770 151s Investment_19 38.979 151s Investment_20 -15.356 151s Investment_21 -10.887 151s Investment_22 -33.575 151s PrivateWages_2 123.381 151s PrivateWages_3 -45.270 151s PrivateWages_4 -102.108 151s PrivateWages_5 67.820 151s PrivateWages_6 1.585 151s PrivateWages_8 -28.067 151s PrivateWages_9 -25.193 151s PrivateWages_10 -31.072 151s PrivateWages_11 9.775 151s PrivateWages_12 0.000 151s PrivateWages_13 -11.612 151s PrivateWages_14 16.650 151s PrivateWages_15 -8.657 151s PrivateWages_16 -11.805 151s PrivateWages_17 44.788 151s PrivateWages_18 2.225 151s PrivateWages_19 -183.642 151s PrivateWages_20 43.723 151s PrivateWages_21 -39.975 151s PrivateWages_22 118.832 151s [1] TRUE 151s > Bread 151s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 151s [1,] 89.117 -0.7628 -0.3161 151s [2,] -0.763 0.5437 -0.3702 151s [3,] -0.316 -0.3702 0.4897 151s [4,] -1.650 -0.0567 -0.0339 151s [5,] 127.149 -5.8142 6.0484 151s [6,] -2.757 0.6390 -0.5640 151s [7,] 0.822 -0.5332 0.6080 151s [8,] -0.462 0.0186 -0.0321 151s [9,] -41.723 0.1554 1.5996 151s [10,] 0.652 -0.0670 0.0422 151s [11,] 0.023 0.0665 -0.0715 151s [12,] 0.266 0.0460 0.0263 151s Consumption_wages Investment_(Intercept) Investment_corpProf 151s [1,] -1.649949 127.15 -2.7567 151s [2,] -0.056675 -5.81 0.6390 151s [3,] -0.033922 6.05 -0.5640 151s [4,] 0.075837 -3.04 0.0284 151s [5,] -3.037786 5674.46 -81.6232 151s [6,] 0.028439 -81.62 3.2764 151s [7,] -0.041721 66.55 -2.7837 151s [8,] 0.016133 -26.78 0.3579 151s [9,] 0.286845 49.74 -0.5482 151s [10,] -0.005120 5.39 0.0206 151s [11,] 0.000492 -6.38 -0.0122 151s [12,] -0.035219 -5.00 0.0650 151s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 151s [1,] 0.8223 -0.4623 -41.7225 151s [2,] -0.5332 0.0186 0.1554 151s [3,] 0.6080 -0.0321 1.5996 151s [4,] -0.0417 0.0161 0.2868 151s [5,] 66.5535 -26.7802 49.7422 151s [6,] -2.7837 0.3579 -0.5482 151s [7,] 3.0944 -0.3490 -2.9105 151s [8,] -0.3490 0.1318 0.0433 151s [9,] -2.9105 0.0433 89.7087 151s [10,] 0.0256 -0.0306 -0.7102 151s [11,] 0.0243 0.0308 -0.7883 151s [12,] -0.1021 0.0277 0.9946 151s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 151s [1,] 0.65175 0.023034 0.26557 151s [2,] -0.06703 0.066494 0.04602 151s [3,] 0.04225 -0.071498 0.02630 151s [4,] -0.00512 0.000492 -0.03522 151s [5,] 5.38683 -6.377135 -4.99571 151s [6,] 0.02064 -0.012164 0.06501 151s [7,] 0.02556 0.024313 -0.10213 151s [8,] -0.03064 0.030839 0.02771 151s [9,] -0.71025 -0.788347 0.99462 151s [10,] 0.06062 -0.050369 -0.02195 151s [11,] -0.05037 0.065741 0.00529 151s [12,] -0.02195 0.005286 0.05391 151s > 151s > # OLS 151s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 151s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 151s > summary 151s 151s systemfit results 151s method: OLS 151s 151s N DF SSR detRCov OLS-R2 McElroy-R2 151s system 61 49 44.5 0.382 0.977 0.99 151s 151s N DF SSR MSE RMSE R2 Adj R2 151s Consumption 20 16 17.48 1.093 1.04 0.981 0.978 151s Investment 21 17 17.32 1.019 1.01 0.931 0.919 151s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 151s 151s The covariance matrix of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.124 0.034 -0.442 151s Investment 0.034 0.928 0.130 151s PrivateWages -0.442 0.130 0.563 151s 151s The correlations of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.0000 0.0266 -0.563 151s Investment 0.0266 1.0000 0.169 151s PrivateWages -0.5630 0.1689 1.000 151s 151s 151s OLS estimates for 'Consumption' (equation 1) 151s Model Formula: consump ~ corpProf + corpProfLag + wages 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 16.1357 1.3571 11.89 2.4e-09 *** 151s corpProf 0.1994 0.0949 2.10 0.052 . 151s corpProfLag 0.0969 0.0944 1.03 0.320 151s wages 0.7940 0.0415 19.16 1.9e-12 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.045 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 17.481 MSE: 1.093 Root MSE: 1.045 151s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 151s 151s 151s OLS estimates for 'Investment' (equation 2) 151s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 10.1258 5.2164 1.94 0.06901 . 151s corpProf 0.4796 0.0927 5.17 7.6e-05 *** 151s corpProfLag 0.3330 0.0963 3.46 0.00299 ** 151s capitalLag -0.1118 0.0255 -4.38 0.00041 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.009 on 17 degrees of freedom 151s Number of observations: 21 Degrees of Freedom: 17 151s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 151s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 151s 151s 151s OLS estimates for 'PrivateWages' (equation 3) 151s Model Formula: privWage ~ gnp + gnpLag + trend 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 1.3550 1.2591 1.08 0.2978 151s gnp 0.4417 0.0319 13.86 2.5e-10 *** 151s gnpLag 0.1466 0.0366 4.01 0.0010 ** 151s trend 0.1244 0.0323 3.85 0.0014 ** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 0.78 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 151s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 151s 151s compare coef with single-equation OLS 151s [1] TRUE 151s > residuals 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 -0.3304 -0.0668 -1.3389 151s 3 -1.2748 -0.0476 0.2462 151s 4 -1.6213 1.2467 1.1255 151s 5 -0.5661 -1.3512 -0.1959 151s 6 -0.0730 0.4154 -0.5284 151s 7 0.7915 1.4923 NA 151s 8 1.2648 0.7889 -0.7909 151s 9 0.9746 -0.6317 0.2819 151s 10 NA 1.0830 1.1384 151s 11 0.2225 0.2791 -0.1904 151s 12 -0.2256 0.0369 0.5813 151s 13 -0.2711 0.3659 0.1206 151s 14 0.3765 0.2237 0.4773 151s 15 -0.0349 -0.1728 0.3035 151s 16 -0.0243 0.0101 0.0284 151s 17 1.6023 0.9719 -0.8517 151s 18 -0.4658 0.0516 0.9908 151s 19 0.1914 -2.5656 -0.4597 151s 20 0.9683 -0.6866 -0.3819 151s 21 0.7325 -0.7807 -1.1062 151s 22 -2.2370 -0.6623 0.5501 151s > fitted 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 42.2 -0.133 26.8 151s 3 46.3 1.948 29.1 151s 4 50.8 3.953 33.0 151s 5 51.2 4.351 34.1 151s 6 52.7 4.685 35.9 151s 7 54.3 4.108 NA 151s 8 54.9 3.411 38.7 151s 9 56.3 3.632 38.9 151s 10 NA 4.017 40.2 151s 11 54.8 0.721 38.1 151s 12 51.1 -3.437 33.9 151s 13 45.9 -6.566 28.9 151s 14 46.1 -5.324 28.0 151s 15 48.7 -2.827 30.3 151s 16 51.3 -1.310 33.2 151s 17 56.1 1.128 37.7 151s 18 59.2 1.948 40.0 151s 19 57.3 0.666 38.7 151s 20 60.6 1.987 42.0 151s 21 64.3 4.081 46.1 151s 22 71.9 5.562 52.7 151s > predict 151s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 151s 1 NA NA NA NA 151s 2 42.2 0.478 39.9 44.5 151s 3 46.3 0.537 43.9 48.6 151s 4 50.8 0.364 48.6 53.0 151s 5 51.2 0.427 48.9 53.4 151s 6 52.7 0.433 50.4 54.9 151s 7 54.3 0.394 52.1 56.6 151s 8 54.9 0.360 52.7 57.2 151s 9 56.3 0.387 54.1 58.6 151s 10 NA NA NA NA 151s 11 54.8 0.635 52.3 57.2 151s 12 51.1 0.501 48.8 53.5 151s 13 45.9 0.656 43.4 48.4 151s 14 46.1 0.629 43.7 48.6 151s 15 48.7 0.389 46.5 51.0 151s 16 51.3 0.345 49.1 53.5 151s 17 56.1 0.379 53.9 58.3 151s 18 59.2 0.336 57.0 61.4 151s 19 57.3 0.385 55.1 59.5 151s 20 60.6 0.450 58.3 62.9 151s 21 64.3 0.448 62.0 66.6 151s 22 71.9 0.697 69.4 74.5 151s Investment.pred Investment.se.fit Investment.lwr Investment.upr 151s 1 NA NA NA NA 151s 2 -0.133 0.579 -2.472 2.206 151s 3 1.948 0.476 -0.295 4.190 151s 4 3.953 0.428 1.750 6.157 151s 5 4.351 0.354 2.202 6.501 151s 6 4.685 0.333 2.548 6.821 151s 7 4.108 0.314 1.983 6.232 151s 8 3.411 0.279 1.306 5.516 151s 9 3.632 0.371 1.470 5.793 151s 10 4.017 0.426 1.815 6.219 151s 11 0.721 0.574 -1.613 3.054 151s 12 -3.437 0.484 -5.686 -1.188 151s 13 -6.566 0.588 -8.913 -4.219 151s 14 -5.324 0.662 -7.750 -2.898 151s 15 -2.827 0.356 -4.978 -0.676 151s 16 -1.310 0.305 -3.429 0.809 151s 17 1.128 0.332 -1.007 3.263 151s 18 1.948 0.232 -0.133 4.030 151s 19 0.666 0.298 -1.449 2.781 151s 20 1.987 0.350 -0.160 4.133 151s 21 4.081 0.317 1.955 6.207 151s 22 5.562 0.440 3.349 7.775 151s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 151s 1 NA NA NA NA 151s 2 26.8 0.352 25.1 28.6 151s 3 29.1 0.355 27.3 30.8 151s 4 33.0 0.358 31.2 34.7 151s 5 34.1 0.277 32.4 35.8 151s 6 35.9 0.276 34.3 37.6 151s 7 NA NA NA NA 151s 8 38.7 0.282 37.0 40.4 151s 9 38.9 0.268 37.3 40.6 151s 10 40.2 0.255 38.5 41.8 151s 11 38.1 0.351 36.4 39.8 151s 12 33.9 0.355 32.2 35.6 151s 13 28.9 0.421 27.1 30.7 151s 14 28.0 0.370 26.3 29.8 151s 15 30.3 0.364 28.6 32.0 151s 16 33.2 0.304 31.5 34.9 151s 17 37.7 0.298 36.0 39.3 151s 18 40.0 0.233 38.4 41.6 151s 19 38.7 0.349 36.9 40.4 151s 20 42.0 0.314 40.3 43.7 151s 21 46.1 0.328 44.4 47.8 151s 22 52.7 0.494 50.9 54.6 151s > model.frame 151s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 151s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 151s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 151s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 151s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 151s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 151s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 151s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 151s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 151s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 151s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 151s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 151s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 151s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 151s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 151s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 151s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 151s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 151s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 151s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 151s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 151s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 151s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 151s trend 151s 1 -11 151s 2 -10 151s 3 -9 151s 4 -8 151s 5 -7 151s 6 -6 151s 7 -5 151s 8 -4 151s 9 -3 151s 10 -2 151s 11 -1 151s 12 0 151s 13 1 151s 14 2 151s 15 3 151s 16 4 151s 17 5 151s 18 6 151s 19 7 151s 20 8 151s 21 9 151s 22 10 151s > model.matrix 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 1 12.4 151s Consumption_3 1 16.9 151s Consumption_4 1 18.4 151s Consumption_5 1 19.4 151s Consumption_6 1 20.1 151s Consumption_7 1 19.6 151s Consumption_8 1 19.8 151s Consumption_9 1 21.1 151s Consumption_11 1 15.6 151s Consumption_12 1 11.4 151s Consumption_13 1 7.0 151s Consumption_14 1 11.2 151s Consumption_15 1 12.3 151s Consumption_16 1 14.0 151s Consumption_17 1 17.6 151s Consumption_18 1 17.3 151s Consumption_19 1 15.3 151s Consumption_20 1 19.0 151s Consumption_21 1 21.1 151s Consumption_22 1 23.5 151s Investment_2 0 0.0 151s Investment_3 0 0.0 151s Investment_4 0 0.0 151s Investment_5 0 0.0 151s Investment_6 0 0.0 151s Investment_7 0 0.0 151s Investment_8 0 0.0 151s Investment_9 0 0.0 151s Investment_10 0 0.0 151s Investment_11 0 0.0 151s Investment_12 0 0.0 151s Investment_13 0 0.0 151s Investment_14 0 0.0 151s Investment_15 0 0.0 151s Investment_16 0 0.0 151s Investment_17 0 0.0 151s Investment_18 0 0.0 151s Investment_19 0 0.0 151s Investment_20 0 0.0 151s Investment_21 0 0.0 151s Investment_22 0 0.0 151s PrivateWages_2 0 0.0 151s PrivateWages_3 0 0.0 151s PrivateWages_4 0 0.0 151s PrivateWages_5 0 0.0 151s PrivateWages_6 0 0.0 151s PrivateWages_8 0 0.0 151s PrivateWages_9 0 0.0 151s PrivateWages_10 0 0.0 151s PrivateWages_11 0 0.0 151s PrivateWages_12 0 0.0 151s PrivateWages_13 0 0.0 151s PrivateWages_14 0 0.0 151s PrivateWages_15 0 0.0 151s PrivateWages_16 0 0.0 151s PrivateWages_17 0 0.0 151s PrivateWages_18 0 0.0 151s PrivateWages_19 0 0.0 151s PrivateWages_20 0 0.0 151s PrivateWages_21 0 0.0 151s PrivateWages_22 0 0.0 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 12.7 28.2 151s Consumption_3 12.4 32.2 151s Consumption_4 16.9 37.0 151s Consumption_5 18.4 37.0 151s Consumption_6 19.4 38.6 151s Consumption_7 20.1 40.7 151s Consumption_8 19.6 41.5 151s Consumption_9 19.8 42.9 151s Consumption_11 21.7 42.1 151s Consumption_12 15.6 39.3 151s Consumption_13 11.4 34.3 151s Consumption_14 7.0 34.1 151s Consumption_15 11.2 36.6 151s Consumption_16 12.3 39.3 151s Consumption_17 14.0 44.2 151s Consumption_18 17.6 47.7 151s Consumption_19 17.3 45.9 151s Consumption_20 15.3 49.4 151s Consumption_21 19.0 53.0 151s Consumption_22 21.1 61.8 151s Investment_2 0.0 0.0 151s Investment_3 0.0 0.0 151s Investment_4 0.0 0.0 151s Investment_5 0.0 0.0 151s Investment_6 0.0 0.0 151s Investment_7 0.0 0.0 151s Investment_8 0.0 0.0 151s Investment_9 0.0 0.0 151s Investment_10 0.0 0.0 151s Investment_11 0.0 0.0 151s Investment_12 0.0 0.0 151s Investment_13 0.0 0.0 151s Investment_14 0.0 0.0 151s Investment_15 0.0 0.0 151s Investment_16 0.0 0.0 151s Investment_17 0.0 0.0 151s Investment_18 0.0 0.0 151s Investment_19 0.0 0.0 151s Investment_20 0.0 0.0 151s Investment_21 0.0 0.0 151s Investment_22 0.0 0.0 151s PrivateWages_2 0.0 0.0 151s PrivateWages_3 0.0 0.0 151s PrivateWages_4 0.0 0.0 151s PrivateWages_5 0.0 0.0 151s PrivateWages_6 0.0 0.0 151s PrivateWages_8 0.0 0.0 151s PrivateWages_9 0.0 0.0 151s PrivateWages_10 0.0 0.0 151s PrivateWages_11 0.0 0.0 151s PrivateWages_12 0.0 0.0 151s PrivateWages_13 0.0 0.0 151s PrivateWages_14 0.0 0.0 151s PrivateWages_15 0.0 0.0 151s PrivateWages_16 0.0 0.0 151s PrivateWages_17 0.0 0.0 151s PrivateWages_18 0.0 0.0 151s PrivateWages_19 0.0 0.0 151s PrivateWages_20 0.0 0.0 151s PrivateWages_21 0.0 0.0 151s PrivateWages_22 0.0 0.0 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0 0.0 151s Consumption_3 0 0.0 151s Consumption_4 0 0.0 151s Consumption_5 0 0.0 151s Consumption_6 0 0.0 151s Consumption_7 0 0.0 151s Consumption_8 0 0.0 151s Consumption_9 0 0.0 151s Consumption_11 0 0.0 151s Consumption_12 0 0.0 151s Consumption_13 0 0.0 151s Consumption_14 0 0.0 151s Consumption_15 0 0.0 151s Consumption_16 0 0.0 151s Consumption_17 0 0.0 151s Consumption_18 0 0.0 151s Consumption_19 0 0.0 151s Consumption_20 0 0.0 151s Consumption_21 0 0.0 151s Consumption_22 0 0.0 151s Investment_2 1 12.4 151s Investment_3 1 16.9 151s Investment_4 1 18.4 151s Investment_5 1 19.4 151s Investment_6 1 20.1 151s Investment_7 1 19.6 151s Investment_8 1 19.8 151s Investment_9 1 21.1 151s Investment_10 1 21.7 151s Investment_11 1 15.6 151s Investment_12 1 11.4 151s Investment_13 1 7.0 151s Investment_14 1 11.2 151s Investment_15 1 12.3 151s Investment_16 1 14.0 151s Investment_17 1 17.6 151s Investment_18 1 17.3 151s Investment_19 1 15.3 151s Investment_20 1 19.0 151s Investment_21 1 21.1 151s Investment_22 1 23.5 151s PrivateWages_2 0 0.0 151s PrivateWages_3 0 0.0 151s PrivateWages_4 0 0.0 151s PrivateWages_5 0 0.0 151s PrivateWages_6 0 0.0 151s PrivateWages_8 0 0.0 151s PrivateWages_9 0 0.0 151s PrivateWages_10 0 0.0 151s PrivateWages_11 0 0.0 151s PrivateWages_12 0 0.0 151s PrivateWages_13 0 0.0 151s PrivateWages_14 0 0.0 151s PrivateWages_15 0 0.0 151s PrivateWages_16 0 0.0 151s PrivateWages_17 0 0.0 151s PrivateWages_18 0 0.0 151s PrivateWages_19 0 0.0 151s PrivateWages_20 0 0.0 151s PrivateWages_21 0 0.0 151s PrivateWages_22 0 0.0 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.0 0 151s Consumption_3 0.0 0 151s Consumption_4 0.0 0 151s Consumption_5 0.0 0 151s Consumption_6 0.0 0 151s Consumption_7 0.0 0 151s Consumption_8 0.0 0 151s Consumption_9 0.0 0 151s Consumption_11 0.0 0 151s Consumption_12 0.0 0 151s Consumption_13 0.0 0 151s Consumption_14 0.0 0 151s Consumption_15 0.0 0 151s Consumption_16 0.0 0 151s Consumption_17 0.0 0 151s Consumption_18 0.0 0 151s Consumption_19 0.0 0 151s Consumption_20 0.0 0 151s Consumption_21 0.0 0 151s Consumption_22 0.0 0 151s Investment_2 12.7 183 151s Investment_3 12.4 183 151s Investment_4 16.9 184 151s Investment_5 18.4 190 151s Investment_6 19.4 193 151s Investment_7 20.1 198 151s Investment_8 19.6 203 151s Investment_9 19.8 208 151s Investment_10 21.1 211 151s Investment_11 21.7 216 151s Investment_12 15.6 217 151s Investment_13 11.4 213 151s Investment_14 7.0 207 151s Investment_15 11.2 202 151s Investment_16 12.3 199 151s Investment_17 14.0 198 151s Investment_18 17.6 200 151s Investment_19 17.3 202 151s Investment_20 15.3 200 151s Investment_21 19.0 201 151s Investment_22 21.1 204 151s PrivateWages_2 0.0 0 151s PrivateWages_3 0.0 0 151s PrivateWages_4 0.0 0 151s PrivateWages_5 0.0 0 151s PrivateWages_6 0.0 0 151s PrivateWages_8 0.0 0 151s PrivateWages_9 0.0 0 151s PrivateWages_10 0.0 0 151s PrivateWages_11 0.0 0 151s PrivateWages_12 0.0 0 151s PrivateWages_13 0.0 0 151s PrivateWages_14 0.0 0 151s PrivateWages_15 0.0 0 151s PrivateWages_16 0.0 0 151s PrivateWages_17 0.0 0 151s PrivateWages_18 0.0 0 151s PrivateWages_19 0.0 0 151s PrivateWages_20 0.0 0 151s PrivateWages_21 0.0 0 151s PrivateWages_22 0.0 0 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 0 0.0 0.0 151s Consumption_3 0 0.0 0.0 151s Consumption_4 0 0.0 0.0 151s Consumption_5 0 0.0 0.0 151s Consumption_6 0 0.0 0.0 151s Consumption_7 0 0.0 0.0 151s Consumption_8 0 0.0 0.0 151s Consumption_9 0 0.0 0.0 151s Consumption_11 0 0.0 0.0 151s Consumption_12 0 0.0 0.0 151s Consumption_13 0 0.0 0.0 151s Consumption_14 0 0.0 0.0 151s Consumption_15 0 0.0 0.0 151s Consumption_16 0 0.0 0.0 151s Consumption_17 0 0.0 0.0 151s Consumption_18 0 0.0 0.0 151s Consumption_19 0 0.0 0.0 151s Consumption_20 0 0.0 0.0 151s Consumption_21 0 0.0 0.0 151s Consumption_22 0 0.0 0.0 151s Investment_2 0 0.0 0.0 151s Investment_3 0 0.0 0.0 151s Investment_4 0 0.0 0.0 151s Investment_5 0 0.0 0.0 151s Investment_6 0 0.0 0.0 151s Investment_7 0 0.0 0.0 151s Investment_8 0 0.0 0.0 151s Investment_9 0 0.0 0.0 151s Investment_10 0 0.0 0.0 151s Investment_11 0 0.0 0.0 151s Investment_12 0 0.0 0.0 151s Investment_13 0 0.0 0.0 151s Investment_14 0 0.0 0.0 151s Investment_15 0 0.0 0.0 151s Investment_16 0 0.0 0.0 151s Investment_17 0 0.0 0.0 151s Investment_18 0 0.0 0.0 151s Investment_19 0 0.0 0.0 151s Investment_20 0 0.0 0.0 151s Investment_21 0 0.0 0.0 151s Investment_22 0 0.0 0.0 151s PrivateWages_2 1 45.6 44.9 151s PrivateWages_3 1 50.1 45.6 151s PrivateWages_4 1 57.2 50.1 151s PrivateWages_5 1 57.1 57.2 151s PrivateWages_6 1 61.0 57.1 151s PrivateWages_8 1 64.4 64.0 151s PrivateWages_9 1 64.5 64.4 151s PrivateWages_10 1 67.0 64.5 151s PrivateWages_11 1 61.2 67.0 151s PrivateWages_12 1 53.4 61.2 151s PrivateWages_13 1 44.3 53.4 151s PrivateWages_14 1 45.1 44.3 151s PrivateWages_15 1 49.7 45.1 151s PrivateWages_16 1 54.4 49.7 151s PrivateWages_17 1 62.7 54.4 151s PrivateWages_18 1 65.0 62.7 151s PrivateWages_19 1 60.9 65.0 151s PrivateWages_20 1 69.5 60.9 151s PrivateWages_21 1 75.7 69.5 151s PrivateWages_22 1 88.4 75.7 151s PrivateWages_trend 151s Consumption_2 0 151s Consumption_3 0 151s Consumption_4 0 151s Consumption_5 0 151s Consumption_6 0 151s Consumption_7 0 151s Consumption_8 0 151s Consumption_9 0 151s Consumption_11 0 151s Consumption_12 0 151s Consumption_13 0 151s Consumption_14 0 151s Consumption_15 0 151s Consumption_16 0 151s Consumption_17 0 151s Consumption_18 0 151s Consumption_19 0 151s Consumption_20 0 151s Consumption_21 0 151s Consumption_22 0 151s Investment_2 0 151s Investment_3 0 151s Investment_4 0 151s Investment_5 0 151s Investment_6 0 151s Investment_7 0 151s Investment_8 0 151s Investment_9 0 151s Investment_10 0 151s Investment_11 0 151s Investment_12 0 151s Investment_13 0 151s Investment_14 0 151s Investment_15 0 151s Investment_16 0 151s Investment_17 0 151s Investment_18 0 151s Investment_19 0 151s Investment_20 0 151s Investment_21 0 151s Investment_22 0 151s PrivateWages_2 -10 151s PrivateWages_3 -9 151s PrivateWages_4 -8 151s PrivateWages_5 -7 151s PrivateWages_6 -6 151s PrivateWages_8 -4 151s PrivateWages_9 -3 151s PrivateWages_10 -2 151s PrivateWages_11 -1 151s PrivateWages_12 0 151s PrivateWages_13 1 151s PrivateWages_14 2 151s PrivateWages_15 3 151s PrivateWages_16 4 151s PrivateWages_17 5 151s PrivateWages_18 6 151s PrivateWages_19 7 151s PrivateWages_20 8 151s PrivateWages_21 9 151s PrivateWages_22 10 151s > nobs 151s [1] 61 151s > linearHypothesis 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 49 1 0.87 0.35 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 49 1 0.8 0.38 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 50 151s 2 49 1 0.8 0.37 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 51 151s 2 49 2 0.48 0.62 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 51 151s 2 49 2 0.43 0.65 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 51 151s 2 49 2 0.87 0.65 151s > logLik 151s 'log Lik.' -71.7 (df=13) 151s 'log Lik.' -76.1 (df=13) 151s compare log likelihood value with single-equation OLS 151s [1] "Mean relative difference: 0.00159" 151s Estimating function 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 -0.3304 -4.097 151s Consumption_3 -1.2748 -21.544 151s Consumption_4 -1.6213 -29.832 151s Consumption_5 -0.5661 -10.982 151s Consumption_6 -0.0730 -1.467 151s Consumption_7 0.7915 15.513 151s Consumption_8 1.2648 25.043 151s Consumption_9 0.9746 20.563 151s Consumption_11 0.2225 3.470 151s Consumption_12 -0.2256 -2.572 151s Consumption_13 -0.2711 -1.898 151s Consumption_14 0.3765 4.217 151s Consumption_15 -0.0349 -0.429 151s Consumption_16 -0.0243 -0.341 151s Consumption_17 1.6023 28.201 151s Consumption_18 -0.4658 -8.058 151s Consumption_19 0.1914 2.928 151s Consumption_20 0.9683 18.397 151s Consumption_21 0.7325 15.456 151s Consumption_22 -2.2370 -52.569 151s Investment_2 0.0000 0.000 151s Investment_3 0.0000 0.000 151s Investment_4 0.0000 0.000 151s Investment_5 0.0000 0.000 151s Investment_6 0.0000 0.000 151s Investment_7 0.0000 0.000 151s Investment_8 0.0000 0.000 151s Investment_9 0.0000 0.000 151s Investment_10 0.0000 0.000 151s Investment_11 0.0000 0.000 151s Investment_12 0.0000 0.000 151s Investment_13 0.0000 0.000 151s Investment_14 0.0000 0.000 151s Investment_15 0.0000 0.000 151s Investment_16 0.0000 0.000 151s Investment_17 0.0000 0.000 151s Investment_18 0.0000 0.000 151s Investment_19 0.0000 0.000 151s Investment_20 0.0000 0.000 151s Investment_21 0.0000 0.000 151s Investment_22 0.0000 0.000 151s PrivateWages_2 0.0000 0.000 151s PrivateWages_3 0.0000 0.000 151s PrivateWages_4 0.0000 0.000 151s PrivateWages_5 0.0000 0.000 151s PrivateWages_6 0.0000 0.000 151s PrivateWages_8 0.0000 0.000 151s PrivateWages_9 0.0000 0.000 151s PrivateWages_10 0.0000 0.000 151s PrivateWages_11 0.0000 0.000 151s PrivateWages_12 0.0000 0.000 151s PrivateWages_13 0.0000 0.000 151s PrivateWages_14 0.0000 0.000 151s PrivateWages_15 0.0000 0.000 151s PrivateWages_16 0.0000 0.000 151s PrivateWages_17 0.0000 0.000 151s PrivateWages_18 0.0000 0.000 151s PrivateWages_19 0.0000 0.000 151s PrivateWages_20 0.0000 0.000 151s PrivateWages_21 0.0000 0.000 151s PrivateWages_22 0.0000 0.000 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 -4.196 -9.318 151s Consumption_3 -15.808 -41.049 151s Consumption_4 -27.400 -59.988 151s Consumption_5 -10.416 -20.944 151s Consumption_6 -1.416 -2.817 151s Consumption_7 15.908 32.212 151s Consumption_8 24.790 52.490 151s Consumption_9 19.296 41.809 151s Consumption_11 4.827 9.366 151s Consumption_12 -3.520 -8.867 151s Consumption_13 -3.091 -9.299 151s Consumption_14 2.636 12.839 151s Consumption_15 -0.391 -1.277 151s Consumption_16 -0.299 -0.957 151s Consumption_17 22.433 70.823 151s Consumption_18 -8.197 -22.217 151s Consumption_19 3.311 8.785 151s Consumption_20 14.815 47.833 151s Consumption_21 13.917 38.822 151s Consumption_22 -47.200 -138.245 151s Investment_2 0.000 0.000 151s Investment_3 0.000 0.000 151s Investment_4 0.000 0.000 151s Investment_5 0.000 0.000 151s Investment_6 0.000 0.000 151s Investment_7 0.000 0.000 151s Investment_8 0.000 0.000 151s Investment_9 0.000 0.000 151s Investment_10 0.000 0.000 151s Investment_11 0.000 0.000 151s Investment_12 0.000 0.000 151s Investment_13 0.000 0.000 151s Investment_14 0.000 0.000 151s Investment_15 0.000 0.000 151s Investment_16 0.000 0.000 151s Investment_17 0.000 0.000 151s Investment_18 0.000 0.000 151s Investment_19 0.000 0.000 151s Investment_20 0.000 0.000 151s Investment_21 0.000 0.000 151s Investment_22 0.000 0.000 151s PrivateWages_2 0.000 0.000 151s PrivateWages_3 0.000 0.000 151s PrivateWages_4 0.000 0.000 151s PrivateWages_5 0.000 0.000 151s PrivateWages_6 0.000 0.000 151s PrivateWages_8 0.000 0.000 151s PrivateWages_9 0.000 0.000 151s PrivateWages_10 0.000 0.000 151s PrivateWages_11 0.000 0.000 151s PrivateWages_12 0.000 0.000 151s PrivateWages_13 0.000 0.000 151s PrivateWages_14 0.000 0.000 151s PrivateWages_15 0.000 0.000 151s PrivateWages_16 0.000 0.000 151s PrivateWages_17 0.000 0.000 151s PrivateWages_18 0.000 0.000 151s PrivateWages_19 0.000 0.000 151s PrivateWages_20 0.000 0.000 151s PrivateWages_21 0.000 0.000 151s PrivateWages_22 0.000 0.000 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0.0000 0.000 151s Consumption_3 0.0000 0.000 151s Consumption_4 0.0000 0.000 151s Consumption_5 0.0000 0.000 151s Consumption_6 0.0000 0.000 151s Consumption_7 0.0000 0.000 151s Consumption_8 0.0000 0.000 151s Consumption_9 0.0000 0.000 151s Consumption_11 0.0000 0.000 151s Consumption_12 0.0000 0.000 151s Consumption_13 0.0000 0.000 151s Consumption_14 0.0000 0.000 151s Consumption_15 0.0000 0.000 151s Consumption_16 0.0000 0.000 151s Consumption_17 0.0000 0.000 151s Consumption_18 0.0000 0.000 151s Consumption_19 0.0000 0.000 151s Consumption_20 0.0000 0.000 151s Consumption_21 0.0000 0.000 151s Consumption_22 0.0000 0.000 151s Investment_2 -0.0668 -0.828 151s Investment_3 -0.0476 -0.804 151s Investment_4 1.2467 22.939 151s Investment_5 -1.3512 -26.213 151s Investment_6 0.4154 8.350 151s Investment_7 1.4923 29.248 151s Investment_8 0.7889 15.620 151s Investment_9 -0.6317 -13.329 151s Investment_10 1.0830 23.500 151s Investment_11 0.2791 4.353 151s Investment_12 0.0369 0.420 151s Investment_13 0.3659 2.561 151s Investment_14 0.2237 2.505 151s Investment_15 -0.1728 -2.126 151s Investment_16 0.0101 0.141 151s Investment_17 0.9719 17.105 151s Investment_18 0.0516 0.893 151s Investment_19 -2.5656 -39.254 151s Investment_20 -0.6866 -13.045 151s Investment_21 -0.7807 -16.474 151s Investment_22 -0.6623 -15.565 151s PrivateWages_2 0.0000 0.000 151s PrivateWages_3 0.0000 0.000 151s PrivateWages_4 0.0000 0.000 151s PrivateWages_5 0.0000 0.000 151s PrivateWages_6 0.0000 0.000 151s PrivateWages_8 0.0000 0.000 151s PrivateWages_9 0.0000 0.000 151s PrivateWages_10 0.0000 0.000 151s PrivateWages_11 0.0000 0.000 151s PrivateWages_12 0.0000 0.000 151s PrivateWages_13 0.0000 0.000 151s PrivateWages_14 0.0000 0.000 151s PrivateWages_15 0.0000 0.000 151s PrivateWages_16 0.0000 0.000 151s PrivateWages_17 0.0000 0.000 151s PrivateWages_18 0.0000 0.000 151s PrivateWages_19 0.0000 0.000 151s PrivateWages_20 0.0000 0.000 151s PrivateWages_21 0.0000 0.000 151s PrivateWages_22 0.0000 0.000 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.000 0.00 151s Consumption_3 0.000 0.00 151s Consumption_4 0.000 0.00 151s Consumption_5 0.000 0.00 151s Consumption_6 0.000 0.00 151s Consumption_7 0.000 0.00 151s Consumption_8 0.000 0.00 151s Consumption_9 0.000 0.00 151s Consumption_11 0.000 0.00 151s Consumption_12 0.000 0.00 151s Consumption_13 0.000 0.00 151s Consumption_14 0.000 0.00 151s Consumption_15 0.000 0.00 151s Consumption_16 0.000 0.00 151s Consumption_17 0.000 0.00 151s Consumption_18 0.000 0.00 151s Consumption_19 0.000 0.00 151s Consumption_20 0.000 0.00 151s Consumption_21 0.000 0.00 151s Consumption_22 0.000 0.00 151s Investment_2 -0.848 -12.21 151s Investment_3 -0.590 -8.69 151s Investment_4 21.069 230.01 151s Investment_5 -24.862 -256.32 151s Investment_6 8.059 80.05 151s Investment_7 29.994 295.17 151s Investment_8 15.463 160.46 151s Investment_9 -12.507 -131.14 151s Investment_10 22.850 228.07 151s Investment_11 6.056 60.20 151s Investment_12 0.575 7.99 151s Investment_13 4.172 78.05 151s Investment_14 1.566 46.33 151s Investment_15 -1.936 -34.91 151s Investment_16 0.124 2.01 151s Investment_17 13.606 192.14 151s Investment_18 0.908 10.31 151s Investment_19 -44.385 -517.74 151s Investment_20 -10.505 -137.25 151s Investment_21 -14.834 -157.09 151s Investment_22 -13.975 -135.45 151s PrivateWages_2 0.000 0.00 151s PrivateWages_3 0.000 0.00 151s PrivateWages_4 0.000 0.00 151s PrivateWages_5 0.000 0.00 151s PrivateWages_6 0.000 0.00 151s PrivateWages_8 0.000 0.00 151s PrivateWages_9 0.000 0.00 151s PrivateWages_10 0.000 0.00 151s PrivateWages_11 0.000 0.00 151s PrivateWages_12 0.000 0.00 151s PrivateWages_13 0.000 0.00 151s PrivateWages_14 0.000 0.00 151s PrivateWages_15 0.000 0.00 151s PrivateWages_16 0.000 0.00 151s PrivateWages_17 0.000 0.00 151s PrivateWages_18 0.000 0.00 151s PrivateWages_19 0.000 0.00 151s PrivateWages_20 0.000 0.00 151s PrivateWages_21 0.000 0.00 151s PrivateWages_22 0.000 0.00 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 0.0000 0.00 0.00 151s Consumption_3 0.0000 0.00 0.00 151s Consumption_4 0.0000 0.00 0.00 151s Consumption_5 0.0000 0.00 0.00 151s Consumption_6 0.0000 0.00 0.00 151s Consumption_7 0.0000 0.00 0.00 151s Consumption_8 0.0000 0.00 0.00 151s Consumption_9 0.0000 0.00 0.00 151s Consumption_11 0.0000 0.00 0.00 151s Consumption_12 0.0000 0.00 0.00 151s Consumption_13 0.0000 0.00 0.00 151s Consumption_14 0.0000 0.00 0.00 151s Consumption_15 0.0000 0.00 0.00 151s Consumption_16 0.0000 0.00 0.00 151s Consumption_17 0.0000 0.00 0.00 151s Consumption_18 0.0000 0.00 0.00 151s Consumption_19 0.0000 0.00 0.00 151s Consumption_20 0.0000 0.00 0.00 151s Consumption_21 0.0000 0.00 0.00 151s Consumption_22 0.0000 0.00 0.00 151s Investment_2 0.0000 0.00 0.00 151s Investment_3 0.0000 0.00 0.00 151s Investment_4 0.0000 0.00 0.00 151s Investment_5 0.0000 0.00 0.00 151s Investment_6 0.0000 0.00 0.00 151s Investment_7 0.0000 0.00 0.00 151s Investment_8 0.0000 0.00 0.00 151s Investment_9 0.0000 0.00 0.00 151s Investment_10 0.0000 0.00 0.00 151s Investment_11 0.0000 0.00 0.00 151s Investment_12 0.0000 0.00 0.00 151s Investment_13 0.0000 0.00 0.00 151s Investment_14 0.0000 0.00 0.00 151s Investment_15 0.0000 0.00 0.00 151s Investment_16 0.0000 0.00 0.00 151s Investment_17 0.0000 0.00 0.00 151s Investment_18 0.0000 0.00 0.00 151s Investment_19 0.0000 0.00 0.00 151s Investment_20 0.0000 0.00 0.00 151s Investment_21 0.0000 0.00 0.00 151s Investment_22 0.0000 0.00 0.00 151s PrivateWages_2 -1.3389 -61.06 -60.12 151s PrivateWages_3 0.2462 12.33 11.23 151s PrivateWages_4 1.1255 64.38 56.39 151s PrivateWages_5 -0.1959 -11.18 -11.20 151s PrivateWages_6 -0.5284 -32.23 -30.17 151s PrivateWages_8 -0.7909 -50.94 -50.62 151s PrivateWages_9 0.2819 18.18 18.15 151s PrivateWages_10 1.1384 76.28 73.43 151s PrivateWages_11 -0.1904 -11.65 -12.76 151s PrivateWages_12 0.5813 31.04 35.58 151s PrivateWages_13 0.1206 5.34 6.44 151s PrivateWages_14 0.4773 21.53 21.14 151s PrivateWages_15 0.3035 15.09 13.69 151s PrivateWages_16 0.0284 1.55 1.41 151s PrivateWages_17 -0.8517 -53.40 -46.33 151s PrivateWages_18 0.9908 64.40 62.12 151s PrivateWages_19 -0.4597 -28.00 -29.88 151s PrivateWages_20 -0.3819 -26.54 -23.26 151s PrivateWages_21 -1.1062 -83.74 -76.88 151s PrivateWages_22 0.5501 48.63 41.64 151s PrivateWages_trend 151s Consumption_2 0.000 151s Consumption_3 0.000 151s Consumption_4 0.000 151s Consumption_5 0.000 151s Consumption_6 0.000 151s Consumption_7 0.000 151s Consumption_8 0.000 151s Consumption_9 0.000 151s Consumption_11 0.000 151s Consumption_12 0.000 151s Consumption_13 0.000 151s Consumption_14 0.000 151s Consumption_15 0.000 151s Consumption_16 0.000 151s Consumption_17 0.000 151s Consumption_18 0.000 151s Consumption_19 0.000 151s Consumption_20 0.000 151s Consumption_21 0.000 151s Consumption_22 0.000 151s Investment_2 0.000 151s Investment_3 0.000 151s Investment_4 0.000 151s Investment_5 0.000 151s Investment_6 0.000 151s Investment_7 0.000 151s Investment_8 0.000 151s Investment_9 0.000 151s Investment_10 0.000 151s Investment_11 0.000 151s Investment_12 0.000 151s Investment_13 0.000 151s Investment_14 0.000 151s Investment_15 0.000 151s Investment_16 0.000 151s Investment_17 0.000 151s Investment_18 0.000 151s Investment_19 0.000 151s Investment_20 0.000 151s Investment_21 0.000 151s Investment_22 0.000 151s PrivateWages_2 13.389 151s PrivateWages_3 -2.216 151s PrivateWages_4 -9.004 151s PrivateWages_5 1.371 151s PrivateWages_6 3.170 151s PrivateWages_8 3.164 151s PrivateWages_9 -0.846 151s PrivateWages_10 -2.277 151s PrivateWages_11 0.190 151s PrivateWages_12 0.000 151s PrivateWages_13 0.121 151s PrivateWages_14 0.955 151s PrivateWages_15 0.911 151s PrivateWages_16 0.114 151s PrivateWages_17 -4.258 151s PrivateWages_18 5.945 151s PrivateWages_19 -3.218 151s PrivateWages_20 -3.055 151s PrivateWages_21 -9.956 151s PrivateWages_22 5.501 151s [1] TRUE 151s > Bread 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_(Intercept) 99.9867 -0.0712 151s Consumption_corpProf -0.0712 0.4890 151s Consumption_corpProfLag -1.1355 -0.2987 151s Consumption_wages -1.8752 -0.0787 151s Investment_(Intercept) 0.0000 0.0000 151s Investment_corpProf 0.0000 0.0000 151s Investment_corpProfLag 0.0000 0.0000 151s Investment_capitalLag 0.0000 0.0000 151s PrivateWages_(Intercept) 0.0000 0.0000 151s PrivateWages_gnp 0.0000 0.0000 151s PrivateWages_gnpLag 0.0000 0.0000 151s PrivateWages_trend 0.0000 0.0000 151s Consumption_corpProfLag Consumption_wages 151s Consumption_(Intercept) -1.1355 -1.8752 151s Consumption_corpProf -0.2987 -0.0787 151s Consumption_corpProfLag 0.4841 -0.0413 151s Consumption_wages -0.0413 0.0933 151s Investment_(Intercept) 0.0000 0.0000 151s Investment_corpProf 0.0000 0.0000 151s Investment_corpProfLag 0.0000 0.0000 151s Investment_capitalLag 0.0000 0.0000 151s PrivateWages_(Intercept) 0.0000 0.0000 151s PrivateWages_gnp 0.0000 0.0000 151s PrivateWages_gnpLag 0.0000 0.0000 151s PrivateWages_trend 0.0000 0.0000 151s Investment_(Intercept) Investment_corpProf 151s Consumption_(Intercept) 0.0 0.0000 151s Consumption_corpProf 0.0 0.0000 151s Consumption_corpProfLag 0.0 0.0000 151s Consumption_wages 0.0 0.0000 151s Investment_(Intercept) 1788.3 -17.4004 151s Investment_corpProf -17.4 0.5646 151s Investment_corpProfLag 14.2 -0.4849 151s Investment_capitalLag -8.6 0.0788 151s PrivateWages_(Intercept) 0.0 0.0000 151s PrivateWages_gnp 0.0 0.0000 151s PrivateWages_gnpLag 0.0 0.0000 151s PrivateWages_trend 0.0 0.0000 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_(Intercept) 0.0000 0.0000 151s Consumption_corpProf 0.0000 0.0000 151s Consumption_corpProfLag 0.0000 0.0000 151s Consumption_wages 0.0000 0.0000 151s Investment_(Intercept) 14.2083 -8.5994 151s Investment_corpProf -0.4849 0.0788 151s Investment_corpProfLag 0.6090 -0.0798 151s Investment_capitalLag -0.0798 0.0428 151s PrivateWages_(Intercept) 0.0000 0.0000 151s PrivateWages_gnp 0.0000 0.0000 151s PrivateWages_gnpLag 0.0000 0.0000 151s PrivateWages_trend 0.0000 0.0000 151s PrivateWages_(Intercept) PrivateWages_gnp 151s Consumption_(Intercept) 0.000 0.0000 151s Consumption_corpProf 0.000 0.0000 151s Consumption_corpProfLag 0.000 0.0000 151s Consumption_wages 0.000 0.0000 151s Investment_(Intercept) 0.000 0.0000 151s Investment_corpProf 0.000 0.0000 151s Investment_corpProfLag 0.000 0.0000 151s Investment_capitalLag 0.000 0.0000 151s PrivateWages_(Intercept) 171.811 -0.6470 151s PrivateWages_gnp -0.647 0.1100 151s PrivateWages_gnpLag -2.257 -0.1026 151s PrivateWages_trend 2.120 -0.0296 151s PrivateWages_gnpLag PrivateWages_trend 151s Consumption_(Intercept) 0.00000 0.00000 151s Consumption_corpProf 0.00000 0.00000 151s Consumption_corpProfLag 0.00000 0.00000 151s Consumption_wages 0.00000 0.00000 151s Investment_(Intercept) 0.00000 0.00000 151s Investment_corpProf 0.00000 0.00000 151s Investment_corpProfLag 0.00000 0.00000 151s Investment_capitalLag 0.00000 0.00000 151s PrivateWages_(Intercept) -2.25750 2.12030 151s PrivateWages_gnp -0.10258 -0.02955 151s PrivateWages_gnpLag 0.14523 -0.00656 151s PrivateWages_trend -0.00656 0.11341 151s > 151s > # 2SLS 151s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 151s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 151s > summary 151s 151s systemfit results 151s method: 2SLS 151s 151s N DF SSR detRCov OLS-R2 McElroy-R2 151s system 59 47 53.2 0.251 0.973 0.991 151s 151s N DF SSR MSE RMSE R2 Adj R2 151s Consumption 19 15 20.49 1.366 1.17 0.978 0.973 151s Investment 20 16 23.02 1.438 1.20 0.901 0.883 151s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 151s 151s The covariance matrix of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.079 0.354 -0.383 151s Investment 0.354 1.047 0.107 151s PrivateWages -0.383 0.107 0.445 151s 151s The correlations of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.000 0.335 -0.556 151s Investment 0.335 1.000 0.149 151s PrivateWages -0.556 0.149 1.000 151s 151s 151s 2SLS estimates for 'Consumption' (equation 1) 151s Model Formula: consump ~ corpProf + corpProfLag + wages 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 16.4657 1.3505 12.19 3.5e-09 *** 151s corpProf 0.0243 0.1180 0.21 0.839 151s corpProfLag 0.1981 0.1087 1.82 0.088 . 151s wages 0.8159 0.0420 19.45 4.7e-12 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.169 on 15 degrees of freedom 151s Number of observations: 19 Degrees of Freedom: 15 151s SSR: 20.493 MSE: 1.366 Root MSE: 1.169 151s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.973 151s 151s 151s 2SLS estimates for 'Investment' (equation 2) 151s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 17.8425 6.5319 2.73 0.01478 * 151s corpProf 0.2167 0.1478 1.47 0.16189 151s corpProfLag 0.5416 0.1415 3.83 0.00149 ** 151s capitalLag -0.1455 0.0314 -4.63 0.00028 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.199 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 151s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 151s 151s 151s 2SLS estimates for 'PrivateWages' (equation 3) 151s Model Formula: privWage ~ gnp + gnpLag + trend 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 1.3431 1.1250 1.19 0.24995 151s gnp 0.4438 0.0342 12.97 6.6e-10 *** 151s gnpLag 0.1447 0.0371 3.90 0.00128 ** 151s trend 0.1238 0.0292 4.24 0.00063 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 0.78 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 151s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 151s 151s > residuals 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 -0.39161 -1.0104 -1.3401 151s 3 -0.60524 0.2478 0.2378 151s 4 -1.24952 1.0621 1.1117 151s 5 -0.17101 -1.4104 -0.1954 151s 6 0.30841 0.4328 -0.5355 151s 7 NA NA NA 151s 8 1.50999 1.0463 -0.7908 151s 9 1.39649 0.0674 0.2831 151s 10 NA 1.7698 1.1353 151s 11 -0.49339 -0.5912 -0.1765 151s 12 -0.99824 -0.6318 0.6007 151s 13 -1.27965 -0.6983 0.1443 151s 14 0.55302 0.9724 0.4826 151s 15 -0.14553 -0.1827 0.3016 151s 16 -0.00773 0.1167 0.0261 151s 17 1.97001 1.6266 -0.8614 151s 18 -0.59152 -0.0525 0.9927 151s 19 -0.21481 -3.0656 -0.4446 151s 20 1.33575 0.1393 -0.3914 151s 21 1.01443 -0.1305 -1.1115 151s 22 -1.93986 0.2922 0.5312 151s > fitted 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 42.3 0.810 26.8 151s 3 45.6 1.652 29.1 151s 4 50.4 4.138 33.0 151s 5 50.8 4.410 34.1 151s 6 52.3 4.667 35.9 151s 7 NA NA NA 151s 8 54.7 3.154 38.7 151s 9 55.9 2.933 38.9 151s 10 NA 3.330 40.2 151s 11 55.5 1.591 38.1 151s 12 51.9 -2.768 33.9 151s 13 46.9 -5.502 28.9 151s 14 45.9 -6.072 28.0 151s 15 48.8 -2.817 30.3 151s 16 51.3 -1.417 33.2 151s 17 55.7 0.473 37.7 151s 18 59.3 2.053 40.0 151s 19 57.7 1.166 38.6 151s 20 60.3 1.161 42.0 151s 21 64.0 3.431 46.1 151s 22 71.6 4.608 52.8 151s > predict 151s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 151s 1 NA NA NA NA 151s 2 42.3 0.483 41.3 43.3 151s 3 45.6 0.586 44.4 46.9 151s 4 50.4 0.390 49.6 51.3 151s 5 50.8 0.456 49.8 51.7 151s 6 52.3 0.463 51.3 53.3 151s 7 NA NA NA NA 151s 8 54.7 0.382 53.9 55.5 151s 9 55.9 0.422 55.0 56.8 151s 10 NA NA NA NA 151s 11 55.5 0.742 53.9 57.1 151s 12 51.9 0.600 50.6 53.2 151s 13 46.9 0.770 45.2 48.5 151s 14 45.9 0.635 44.6 47.3 151s 15 48.8 0.383 48.0 49.7 151s 16 51.3 0.339 50.6 52.0 151s 17 55.7 0.410 54.9 56.6 151s 18 59.3 0.336 58.6 60.0 151s 19 57.7 0.418 56.8 58.6 151s 20 60.3 0.481 59.2 61.3 151s 21 64.0 0.462 63.0 65.0 151s 22 71.6 0.706 70.1 73.1 151s Investment.pred Investment.se.fit Investment.lwr Investment.upr 151s 1 NA NA NA NA 151s 2 0.810 0.750 -0.77956 2.400 151s 3 1.652 0.516 0.55883 2.746 151s 4 4.138 0.487 3.10541 5.170 151s 5 4.410 0.402 3.55860 5.262 151s 6 4.667 0.377 3.86830 5.466 151s 7 NA NA NA NA 151s 8 3.154 0.312 2.49238 3.815 151s 9 2.933 0.466 1.94478 3.920 151s 10 3.330 0.512 2.24435 4.416 151s 11 1.591 0.749 0.00249 3.180 151s 12 -2.768 0.586 -4.01111 -1.525 151s 13 -5.502 0.750 -7.09222 -3.911 151s 14 -6.072 0.803 -7.77404 -4.371 151s 15 -2.817 0.379 -3.62002 -2.015 151s 16 -1.417 0.327 -2.10985 -0.723 151s 17 0.473 0.436 -0.45046 1.397 151s 18 2.053 0.272 1.47523 2.630 151s 19 1.166 0.410 0.29710 2.034 151s 20 1.161 0.491 0.12044 2.201 151s 21 3.431 0.406 2.57004 4.291 151s 22 4.608 0.578 3.38197 5.834 151s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 151s 1 NA NA NA NA 151s 2 26.8 0.313 26.2 27.5 151s 3 29.1 0.325 28.4 29.8 151s 4 33.0 0.344 32.3 33.7 151s 5 34.1 0.246 33.6 34.6 151s 6 35.9 0.254 35.4 36.5 151s 7 NA NA NA NA 151s 8 38.7 0.251 38.2 39.2 151s 9 38.9 0.239 38.4 39.4 151s 10 40.2 0.229 39.7 40.7 151s 11 38.1 0.339 37.4 38.8 151s 12 33.9 0.365 33.1 34.7 151s 13 28.9 0.436 27.9 29.8 151s 14 28.0 0.333 27.3 28.7 151s 15 30.3 0.324 29.6 31.0 151s 16 33.2 0.271 32.6 33.7 151s 17 37.7 0.280 37.1 38.3 151s 18 40.0 0.208 39.6 40.4 151s 19 38.6 0.342 37.9 39.4 151s 20 42.0 0.293 41.4 42.6 151s 21 46.1 0.296 45.5 46.7 151s 22 52.8 0.474 51.8 53.8 151s > model.frame 151s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 151s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 151s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 151s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 151s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 151s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 151s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 151s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 151s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 151s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 151s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 151s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 151s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 151s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 151s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 151s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 151s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 151s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 151s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 151s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 151s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 151s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 151s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 151s trend 151s 1 -11 151s 2 -10 151s 3 -9 151s 4 -8 151s 5 -7 151s 6 -6 151s 7 -5 151s 8 -4 151s 9 -3 151s 10 -2 151s 11 -1 151s 12 0 151s 13 1 151s 14 2 151s 15 3 151s 16 4 151s 17 5 151s 18 6 151s 19 7 151s 20 8 151s 21 9 151s 22 10 151s > Frames of instrumental variables 151s govExp taxes govWage trend capitalLag corpProfLag gnpLag 151s 1 2.4 3.4 2.2 -11 180 NA NA 151s 2 3.9 7.7 2.7 -10 183 12.7 44.9 151s 3 3.2 3.9 2.9 -9 183 12.4 45.6 151s 4 2.8 4.7 2.9 -8 184 16.9 50.1 151s 5 3.5 3.8 3.1 -7 190 18.4 57.2 151s 6 3.3 5.5 3.2 -6 193 19.4 57.1 151s 7 3.3 7.0 3.3 -5 198 20.1 NA 151s 8 4.0 6.7 3.6 -4 203 19.6 64.0 151s 9 4.2 4.2 3.7 -3 208 19.8 64.4 151s 10 4.1 4.0 4.0 -2 211 21.1 64.5 151s 11 5.2 7.7 4.2 -1 216 21.7 67.0 151s 12 5.9 7.5 4.8 0 217 15.6 61.2 151s 13 4.9 8.3 5.3 1 213 11.4 53.4 151s 14 3.7 5.4 5.6 2 207 7.0 44.3 151s 15 4.0 6.8 6.0 3 202 11.2 45.1 151s 16 4.4 7.2 6.1 4 199 12.3 49.7 151s 17 2.9 8.3 7.4 5 198 14.0 54.4 151s 18 4.3 6.7 6.7 6 200 17.6 62.7 151s 19 5.3 7.4 7.7 7 202 17.3 65.0 151s 20 6.6 8.9 7.8 8 200 15.3 60.9 151s 21 7.4 9.6 8.0 9 201 19.0 69.5 151s 22 13.8 11.6 8.5 10 204 21.1 75.7 151s govExp taxes govWage trend capitalLag corpProfLag gnpLag 151s 1 2.4 3.4 2.2 -11 180 NA NA 151s 2 3.9 7.7 2.7 -10 183 12.7 44.9 151s 3 3.2 3.9 2.9 -9 183 12.4 45.6 151s 4 2.8 4.7 2.9 -8 184 16.9 50.1 151s 5 3.5 3.8 3.1 -7 190 18.4 57.2 151s 6 3.3 5.5 3.2 -6 193 19.4 57.1 151s 7 3.3 7.0 3.3 -5 198 20.1 NA 151s 8 4.0 6.7 3.6 -4 203 19.6 64.0 151s 9 4.2 4.2 3.7 -3 208 19.8 64.4 151s 10 4.1 4.0 4.0 -2 211 21.1 64.5 151s 11 5.2 7.7 4.2 -1 216 21.7 67.0 151s 12 5.9 7.5 4.8 0 217 15.6 61.2 151s 13 4.9 8.3 5.3 1 213 11.4 53.4 151s 14 3.7 5.4 5.6 2 207 7.0 44.3 151s 15 4.0 6.8 6.0 3 202 11.2 45.1 151s 16 4.4 7.2 6.1 4 199 12.3 49.7 151s 17 2.9 8.3 7.4 5 198 14.0 54.4 151s 18 4.3 6.7 6.7 6 200 17.6 62.7 151s 19 5.3 7.4 7.7 7 202 17.3 65.0 151s 20 6.6 8.9 7.8 8 200 15.3 60.9 151s 21 7.4 9.6 8.0 9 201 19.0 69.5 151s 22 13.8 11.6 8.5 10 204 21.1 75.7 151s govExp taxes govWage trend capitalLag corpProfLag gnpLag 151s 1 2.4 3.4 2.2 -11 180 NA NA 151s 2 3.9 7.7 2.7 -10 183 12.7 44.9 151s 3 3.2 3.9 2.9 -9 183 12.4 45.6 151s 4 2.8 4.7 2.9 -8 184 16.9 50.1 151s 5 3.5 3.8 3.1 -7 190 18.4 57.2 151s 6 3.3 5.5 3.2 -6 193 19.4 57.1 151s 7 3.3 7.0 3.3 -5 198 20.1 NA 151s 8 4.0 6.7 3.6 -4 203 19.6 64.0 151s 9 4.2 4.2 3.7 -3 208 19.8 64.4 151s 10 4.1 4.0 4.0 -2 211 21.1 64.5 151s 11 5.2 7.7 4.2 -1 216 21.7 67.0 151s 12 5.9 7.5 4.8 0 217 15.6 61.2 151s 13 4.9 8.3 5.3 1 213 11.4 53.4 151s 14 3.7 5.4 5.6 2 207 7.0 44.3 151s 15 4.0 6.8 6.0 3 202 11.2 45.1 151s 16 4.4 7.2 6.1 4 199 12.3 49.7 151s 17 2.9 8.3 7.4 5 198 14.0 54.4 151s 18 4.3 6.7 6.7 6 200 17.6 62.7 151s 19 5.3 7.4 7.7 7 202 17.3 65.0 151s 20 6.6 8.9 7.8 8 200 15.3 60.9 151s 21 7.4 9.6 8.0 9 201 19.0 69.5 151s 22 13.8 11.6 8.5 10 204 21.1 75.7 151s > model.matrix 151s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 151s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 151s [3] "Numeric: lengths (732, 708) differ" 151s > matrix of instrumental variables 151s Consumption_(Intercept) Consumption_govExp Consumption_taxes 151s Consumption_2 1 3.9 7.7 151s Consumption_3 1 3.2 3.9 151s Consumption_4 1 2.8 4.7 151s Consumption_5 1 3.5 3.8 151s Consumption_6 1 3.3 5.5 151s Consumption_8 1 4.0 6.7 151s Consumption_9 1 4.2 4.2 151s Consumption_11 1 5.2 7.7 151s Consumption_12 1 5.9 7.5 151s Consumption_13 1 4.9 8.3 151s Consumption_14 1 3.7 5.4 151s Consumption_15 1 4.0 6.8 151s Consumption_16 1 4.4 7.2 151s Consumption_17 1 2.9 8.3 151s Consumption_18 1 4.3 6.7 151s Consumption_19 1 5.3 7.4 151s Consumption_20 1 6.6 8.9 151s Consumption_21 1 7.4 9.6 151s Consumption_22 1 13.8 11.6 151s Investment_2 0 0.0 0.0 151s Investment_3 0 0.0 0.0 151s Investment_4 0 0.0 0.0 151s Investment_5 0 0.0 0.0 151s Investment_6 0 0.0 0.0 151s Investment_8 0 0.0 0.0 151s Investment_9 0 0.0 0.0 151s Investment_10 0 0.0 0.0 151s Investment_11 0 0.0 0.0 151s Investment_12 0 0.0 0.0 151s Investment_13 0 0.0 0.0 151s Investment_14 0 0.0 0.0 151s Investment_15 0 0.0 0.0 151s Investment_16 0 0.0 0.0 151s Investment_17 0 0.0 0.0 151s Investment_18 0 0.0 0.0 151s Investment_19 0 0.0 0.0 151s Investment_20 0 0.0 0.0 151s Investment_21 0 0.0 0.0 151s Investment_22 0 0.0 0.0 151s PrivateWages_2 0 0.0 0.0 151s PrivateWages_3 0 0.0 0.0 151s PrivateWages_4 0 0.0 0.0 151s PrivateWages_5 0 0.0 0.0 151s PrivateWages_6 0 0.0 0.0 151s PrivateWages_8 0 0.0 0.0 151s PrivateWages_9 0 0.0 0.0 151s PrivateWages_10 0 0.0 0.0 151s PrivateWages_11 0 0.0 0.0 151s PrivateWages_12 0 0.0 0.0 151s PrivateWages_13 0 0.0 0.0 151s PrivateWages_14 0 0.0 0.0 151s PrivateWages_15 0 0.0 0.0 151s PrivateWages_16 0 0.0 0.0 151s PrivateWages_17 0 0.0 0.0 151s PrivateWages_18 0 0.0 0.0 151s PrivateWages_19 0 0.0 0.0 151s PrivateWages_20 0 0.0 0.0 151s PrivateWages_21 0 0.0 0.0 151s PrivateWages_22 0 0.0 0.0 151s Consumption_govWage Consumption_trend Consumption_capitalLag 151s Consumption_2 2.7 -10 183 151s Consumption_3 2.9 -9 183 151s Consumption_4 2.9 -8 184 151s Consumption_5 3.1 -7 190 151s Consumption_6 3.2 -6 193 151s Consumption_8 3.6 -4 203 151s Consumption_9 3.7 -3 208 151s Consumption_11 4.2 -1 216 151s Consumption_12 4.8 0 217 151s Consumption_13 5.3 1 213 151s Consumption_14 5.6 2 207 151s Consumption_15 6.0 3 202 151s Consumption_16 6.1 4 199 151s Consumption_17 7.4 5 198 151s Consumption_18 6.7 6 200 151s Consumption_19 7.7 7 202 151s Consumption_20 7.8 8 200 151s Consumption_21 8.0 9 201 151s Consumption_22 8.5 10 204 151s Investment_2 0.0 0 0 151s Investment_3 0.0 0 0 151s Investment_4 0.0 0 0 151s Investment_5 0.0 0 0 151s Investment_6 0.0 0 0 151s Investment_8 0.0 0 0 151s Investment_9 0.0 0 0 151s Investment_10 0.0 0 0 151s Investment_11 0.0 0 0 151s Investment_12 0.0 0 0 151s Investment_13 0.0 0 0 151s Investment_14 0.0 0 0 151s Investment_15 0.0 0 0 151s Investment_16 0.0 0 0 151s Investment_17 0.0 0 0 151s Investment_18 0.0 0 0 151s Investment_19 0.0 0 0 151s Investment_20 0.0 0 0 151s Investment_21 0.0 0 0 151s Investment_22 0.0 0 0 151s PrivateWages_2 0.0 0 0 151s PrivateWages_3 0.0 0 0 151s PrivateWages_4 0.0 0 0 151s PrivateWages_5 0.0 0 0 151s PrivateWages_6 0.0 0 0 151s PrivateWages_8 0.0 0 0 151s PrivateWages_9 0.0 0 0 151s PrivateWages_10 0.0 0 0 151s PrivateWages_11 0.0 0 0 151s PrivateWages_12 0.0 0 0 151s PrivateWages_13 0.0 0 0 151s PrivateWages_14 0.0 0 0 151s PrivateWages_15 0.0 0 0 151s PrivateWages_16 0.0 0 0 151s PrivateWages_17 0.0 0 0 151s PrivateWages_18 0.0 0 0 151s PrivateWages_19 0.0 0 0 151s PrivateWages_20 0.0 0 0 151s PrivateWages_21 0.0 0 0 151s PrivateWages_22 0.0 0 0 151s Consumption_corpProfLag Consumption_gnpLag 151s Consumption_2 12.7 44.9 151s Consumption_3 12.4 45.6 151s Consumption_4 16.9 50.1 151s Consumption_5 18.4 57.2 151s Consumption_6 19.4 57.1 151s Consumption_8 19.6 64.0 151s Consumption_9 19.8 64.4 151s Consumption_11 21.7 67.0 151s Consumption_12 15.6 61.2 151s Consumption_13 11.4 53.4 151s Consumption_14 7.0 44.3 151s Consumption_15 11.2 45.1 151s Consumption_16 12.3 49.7 151s Consumption_17 14.0 54.4 151s Consumption_18 17.6 62.7 151s Consumption_19 17.3 65.0 151s Consumption_20 15.3 60.9 151s Consumption_21 19.0 69.5 151s Consumption_22 21.1 75.7 151s Investment_2 0.0 0.0 151s Investment_3 0.0 0.0 151s Investment_4 0.0 0.0 151s Investment_5 0.0 0.0 151s Investment_6 0.0 0.0 151s Investment_8 0.0 0.0 151s Investment_9 0.0 0.0 151s Investment_10 0.0 0.0 151s Investment_11 0.0 0.0 151s Investment_12 0.0 0.0 151s Investment_13 0.0 0.0 151s Investment_14 0.0 0.0 151s Investment_15 0.0 0.0 151s Investment_16 0.0 0.0 151s Investment_17 0.0 0.0 151s Investment_18 0.0 0.0 151s Investment_19 0.0 0.0 151s Investment_20 0.0 0.0 151s Investment_21 0.0 0.0 151s Investment_22 0.0 0.0 151s PrivateWages_2 0.0 0.0 151s PrivateWages_3 0.0 0.0 151s PrivateWages_4 0.0 0.0 151s PrivateWages_5 0.0 0.0 151s PrivateWages_6 0.0 0.0 151s PrivateWages_8 0.0 0.0 151s PrivateWages_9 0.0 0.0 151s PrivateWages_10 0.0 0.0 151s PrivateWages_11 0.0 0.0 151s PrivateWages_12 0.0 0.0 151s PrivateWages_13 0.0 0.0 151s PrivateWages_14 0.0 0.0 151s PrivateWages_15 0.0 0.0 151s PrivateWages_16 0.0 0.0 151s PrivateWages_17 0.0 0.0 151s PrivateWages_18 0.0 0.0 151s PrivateWages_19 0.0 0.0 151s PrivateWages_20 0.0 0.0 151s PrivateWages_21 0.0 0.0 151s PrivateWages_22 0.0 0.0 151s Investment_(Intercept) Investment_govExp Investment_taxes 151s Consumption_2 0 0.0 0.0 151s Consumption_3 0 0.0 0.0 151s Consumption_4 0 0.0 0.0 151s Consumption_5 0 0.0 0.0 151s Consumption_6 0 0.0 0.0 151s Consumption_8 0 0.0 0.0 151s Consumption_9 0 0.0 0.0 151s Consumption_11 0 0.0 0.0 151s Consumption_12 0 0.0 0.0 151s Consumption_13 0 0.0 0.0 151s Consumption_14 0 0.0 0.0 151s Consumption_15 0 0.0 0.0 151s Consumption_16 0 0.0 0.0 151s Consumption_17 0 0.0 0.0 151s Consumption_18 0 0.0 0.0 151s Consumption_19 0 0.0 0.0 151s Consumption_20 0 0.0 0.0 151s Consumption_21 0 0.0 0.0 151s Consumption_22 0 0.0 0.0 151s Investment_2 1 3.9 7.7 151s Investment_3 1 3.2 3.9 151s Investment_4 1 2.8 4.7 151s Investment_5 1 3.5 3.8 151s Investment_6 1 3.3 5.5 151s Investment_8 1 4.0 6.7 151s Investment_9 1 4.2 4.2 151s Investment_10 1 4.1 4.0 151s Investment_11 1 5.2 7.7 151s Investment_12 1 5.9 7.5 151s Investment_13 1 4.9 8.3 151s Investment_14 1 3.7 5.4 151s Investment_15 1 4.0 6.8 151s Investment_16 1 4.4 7.2 151s Investment_17 1 2.9 8.3 151s Investment_18 1 4.3 6.7 151s Investment_19 1 5.3 7.4 151s Investment_20 1 6.6 8.9 151s Investment_21 1 7.4 9.6 151s Investment_22 1 13.8 11.6 151s PrivateWages_2 0 0.0 0.0 151s PrivateWages_3 0 0.0 0.0 151s PrivateWages_4 0 0.0 0.0 151s PrivateWages_5 0 0.0 0.0 151s PrivateWages_6 0 0.0 0.0 151s PrivateWages_8 0 0.0 0.0 151s PrivateWages_9 0 0.0 0.0 151s PrivateWages_10 0 0.0 0.0 151s PrivateWages_11 0 0.0 0.0 151s PrivateWages_12 0 0.0 0.0 151s PrivateWages_13 0 0.0 0.0 151s PrivateWages_14 0 0.0 0.0 151s PrivateWages_15 0 0.0 0.0 151s PrivateWages_16 0 0.0 0.0 151s PrivateWages_17 0 0.0 0.0 151s PrivateWages_18 0 0.0 0.0 151s PrivateWages_19 0 0.0 0.0 151s PrivateWages_20 0 0.0 0.0 151s PrivateWages_21 0 0.0 0.0 151s PrivateWages_22 0 0.0 0.0 151s Investment_govWage Investment_trend Investment_capitalLag 151s Consumption_2 0.0 0 0 151s Consumption_3 0.0 0 0 151s Consumption_4 0.0 0 0 151s Consumption_5 0.0 0 0 151s Consumption_6 0.0 0 0 151s Consumption_8 0.0 0 0 151s Consumption_9 0.0 0 0 151s Consumption_11 0.0 0 0 151s Consumption_12 0.0 0 0 151s Consumption_13 0.0 0 0 151s Consumption_14 0.0 0 0 151s Consumption_15 0.0 0 0 151s Consumption_16 0.0 0 0 151s Consumption_17 0.0 0 0 151s Consumption_18 0.0 0 0 151s Consumption_19 0.0 0 0 151s Consumption_20 0.0 0 0 151s Consumption_21 0.0 0 0 151s Consumption_22 0.0 0 0 151s Investment_2 2.7 -10 183 151s Investment_3 2.9 -9 183 151s Investment_4 2.9 -8 184 151s Investment_5 3.1 -7 190 151s Investment_6 3.2 -6 193 151s Investment_8 3.6 -4 203 151s Investment_9 3.7 -3 208 151s Investment_10 4.0 -2 211 151s Investment_11 4.2 -1 216 151s Investment_12 4.8 0 217 151s Investment_13 5.3 1 213 151s Investment_14 5.6 2 207 151s Investment_15 6.0 3 202 151s Investment_16 6.1 4 199 151s Investment_17 7.4 5 198 151s Investment_18 6.7 6 200 151s Investment_19 7.7 7 202 151s Investment_20 7.8 8 200 151s Investment_21 8.0 9 201 151s Investment_22 8.5 10 204 151s PrivateWages_2 0.0 0 0 151s PrivateWages_3 0.0 0 0 151s PrivateWages_4 0.0 0 0 151s PrivateWages_5 0.0 0 0 151s PrivateWages_6 0.0 0 0 151s PrivateWages_8 0.0 0 0 151s PrivateWages_9 0.0 0 0 151s PrivateWages_10 0.0 0 0 151s PrivateWages_11 0.0 0 0 151s PrivateWages_12 0.0 0 0 151s PrivateWages_13 0.0 0 0 151s PrivateWages_14 0.0 0 0 151s PrivateWages_15 0.0 0 0 151s PrivateWages_16 0.0 0 0 151s PrivateWages_17 0.0 0 0 151s PrivateWages_18 0.0 0 0 151s PrivateWages_19 0.0 0 0 151s PrivateWages_20 0.0 0 0 151s PrivateWages_21 0.0 0 0 151s PrivateWages_22 0.0 0 0 151s Investment_corpProfLag Investment_gnpLag 151s Consumption_2 0.0 0.0 151s Consumption_3 0.0 0.0 151s Consumption_4 0.0 0.0 151s Consumption_5 0.0 0.0 151s Consumption_6 0.0 0.0 151s Consumption_8 0.0 0.0 151s Consumption_9 0.0 0.0 151s Consumption_11 0.0 0.0 151s Consumption_12 0.0 0.0 151s Consumption_13 0.0 0.0 151s Consumption_14 0.0 0.0 151s Consumption_15 0.0 0.0 151s Consumption_16 0.0 0.0 151s Consumption_17 0.0 0.0 151s Consumption_18 0.0 0.0 151s Consumption_19 0.0 0.0 151s Consumption_20 0.0 0.0 151s Consumption_21 0.0 0.0 151s Consumption_22 0.0 0.0 151s Investment_2 12.7 44.9 151s Investment_3 12.4 45.6 151s Investment_4 16.9 50.1 151s Investment_5 18.4 57.2 151s Investment_6 19.4 57.1 151s Investment_8 19.6 64.0 151s Investment_9 19.8 64.4 151s Investment_10 21.1 64.5 151s Investment_11 21.7 67.0 151s Investment_12 15.6 61.2 151s Investment_13 11.4 53.4 151s Investment_14 7.0 44.3 151s Investment_15 11.2 45.1 151s Investment_16 12.3 49.7 151s Investment_17 14.0 54.4 151s Investment_18 17.6 62.7 151s Investment_19 17.3 65.0 151s Investment_20 15.3 60.9 151s Investment_21 19.0 69.5 151s Investment_22 21.1 75.7 151s PrivateWages_2 0.0 0.0 151s PrivateWages_3 0.0 0.0 151s PrivateWages_4 0.0 0.0 151s PrivateWages_5 0.0 0.0 151s PrivateWages_6 0.0 0.0 151s PrivateWages_8 0.0 0.0 151s PrivateWages_9 0.0 0.0 151s PrivateWages_10 0.0 0.0 151s PrivateWages_11 0.0 0.0 151s PrivateWages_12 0.0 0.0 151s PrivateWages_13 0.0 0.0 151s PrivateWages_14 0.0 0.0 151s PrivateWages_15 0.0 0.0 151s PrivateWages_16 0.0 0.0 151s PrivateWages_17 0.0 0.0 151s PrivateWages_18 0.0 0.0 151s PrivateWages_19 0.0 0.0 151s PrivateWages_20 0.0 0.0 151s PrivateWages_21 0.0 0.0 151s PrivateWages_22 0.0 0.0 151s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 151s Consumption_2 0 0.0 0.0 151s Consumption_3 0 0.0 0.0 151s Consumption_4 0 0.0 0.0 151s Consumption_5 0 0.0 0.0 151s Consumption_6 0 0.0 0.0 151s Consumption_8 0 0.0 0.0 151s Consumption_9 0 0.0 0.0 151s Consumption_11 0 0.0 0.0 151s Consumption_12 0 0.0 0.0 151s Consumption_13 0 0.0 0.0 151s Consumption_14 0 0.0 0.0 151s Consumption_15 0 0.0 0.0 151s Consumption_16 0 0.0 0.0 151s Consumption_17 0 0.0 0.0 151s Consumption_18 0 0.0 0.0 151s Consumption_19 0 0.0 0.0 151s Consumption_20 0 0.0 0.0 151s Consumption_21 0 0.0 0.0 151s Consumption_22 0 0.0 0.0 151s Investment_2 0 0.0 0.0 151s Investment_3 0 0.0 0.0 151s Investment_4 0 0.0 0.0 151s Investment_5 0 0.0 0.0 151s Investment_6 0 0.0 0.0 151s Investment_8 0 0.0 0.0 151s Investment_9 0 0.0 0.0 151s Investment_10 0 0.0 0.0 151s Investment_11 0 0.0 0.0 151s Investment_12 0 0.0 0.0 151s Investment_13 0 0.0 0.0 151s Investment_14 0 0.0 0.0 151s Investment_15 0 0.0 0.0 151s Investment_16 0 0.0 0.0 151s Investment_17 0 0.0 0.0 151s Investment_18 0 0.0 0.0 151s Investment_19 0 0.0 0.0 151s Investment_20 0 0.0 0.0 151s Investment_21 0 0.0 0.0 151s Investment_22 0 0.0 0.0 151s PrivateWages_2 1 3.9 7.7 151s PrivateWages_3 1 3.2 3.9 151s PrivateWages_4 1 2.8 4.7 151s PrivateWages_5 1 3.5 3.8 151s PrivateWages_6 1 3.3 5.5 151s PrivateWages_8 1 4.0 6.7 151s PrivateWages_9 1 4.2 4.2 151s PrivateWages_10 1 4.1 4.0 151s PrivateWages_11 1 5.2 7.7 151s PrivateWages_12 1 5.9 7.5 151s PrivateWages_13 1 4.9 8.3 151s PrivateWages_14 1 3.7 5.4 151s PrivateWages_15 1 4.0 6.8 151s PrivateWages_16 1 4.4 7.2 151s PrivateWages_17 1 2.9 8.3 151s PrivateWages_18 1 4.3 6.7 151s PrivateWages_19 1 5.3 7.4 151s PrivateWages_20 1 6.6 8.9 151s PrivateWages_21 1 7.4 9.6 151s PrivateWages_22 1 13.8 11.6 151s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 151s Consumption_2 0.0 0 0 151s Consumption_3 0.0 0 0 151s Consumption_4 0.0 0 0 151s Consumption_5 0.0 0 0 151s Consumption_6 0.0 0 0 151s Consumption_8 0.0 0 0 151s Consumption_9 0.0 0 0 151s Consumption_11 0.0 0 0 151s Consumption_12 0.0 0 0 151s Consumption_13 0.0 0 0 151s Consumption_14 0.0 0 0 151s Consumption_15 0.0 0 0 151s Consumption_16 0.0 0 0 151s Consumption_17 0.0 0 0 151s Consumption_18 0.0 0 0 151s Consumption_19 0.0 0 0 151s Consumption_20 0.0 0 0 151s Consumption_21 0.0 0 0 151s Consumption_22 0.0 0 0 151s Investment_2 0.0 0 0 151s Investment_3 0.0 0 0 151s Investment_4 0.0 0 0 151s Investment_5 0.0 0 0 151s Investment_6 0.0 0 0 151s Investment_8 0.0 0 0 151s Investment_9 0.0 0 0 151s Investment_10 0.0 0 0 151s Investment_11 0.0 0 0 151s Investment_12 0.0 0 0 151s Investment_13 0.0 0 0 151s Investment_14 0.0 0 0 151s Investment_15 0.0 0 0 151s Investment_16 0.0 0 0 151s Investment_17 0.0 0 0 151s Investment_18 0.0 0 0 151s Investment_19 0.0 0 0 151s Investment_20 0.0 0 0 151s Investment_21 0.0 0 0 151s Investment_22 0.0 0 0 151s PrivateWages_2 2.7 -10 183 151s PrivateWages_3 2.9 -9 183 151s PrivateWages_4 2.9 -8 184 151s PrivateWages_5 3.1 -7 190 151s PrivateWages_6 3.2 -6 193 151s PrivateWages_8 3.6 -4 203 151s PrivateWages_9 3.7 -3 208 151s PrivateWages_10 4.0 -2 211 151s PrivateWages_11 4.2 -1 216 151s PrivateWages_12 4.8 0 217 151s PrivateWages_13 5.3 1 213 151s PrivateWages_14 5.6 2 207 151s PrivateWages_15 6.0 3 202 151s PrivateWages_16 6.1 4 199 151s PrivateWages_17 7.4 5 198 151s PrivateWages_18 6.7 6 200 151s PrivateWages_19 7.7 7 202 151s PrivateWages_20 7.8 8 200 151s PrivateWages_21 8.0 9 201 151s PrivateWages_22 8.5 10 204 151s PrivateWages_corpProfLag PrivateWages_gnpLag 151s Consumption_2 0.0 0.0 151s Consumption_3 0.0 0.0 151s Consumption_4 0.0 0.0 151s Consumption_5 0.0 0.0 151s Consumption_6 0.0 0.0 151s Consumption_8 0.0 0.0 151s Consumption_9 0.0 0.0 151s Consumption_11 0.0 0.0 151s Consumption_12 0.0 0.0 151s Consumption_13 0.0 0.0 151s Consumption_14 0.0 0.0 151s Consumption_15 0.0 0.0 151s Consumption_16 0.0 0.0 151s Consumption_17 0.0 0.0 151s Consumption_18 0.0 0.0 151s Consumption_19 0.0 0.0 151s Consumption_20 0.0 0.0 151s Consumption_21 0.0 0.0 151s Consumption_22 0.0 0.0 151s Investment_2 0.0 0.0 151s Investment_3 0.0 0.0 151s Investment_4 0.0 0.0 151s Investment_5 0.0 0.0 151s Investment_6 0.0 0.0 151s Investment_8 0.0 0.0 151s Investment_9 0.0 0.0 151s Investment_10 0.0 0.0 151s Investment_11 0.0 0.0 151s Investment_12 0.0 0.0 151s Investment_13 0.0 0.0 151s Investment_14 0.0 0.0 151s Investment_15 0.0 0.0 151s Investment_16 0.0 0.0 151s Investment_17 0.0 0.0 151s Investment_18 0.0 0.0 151s Investment_19 0.0 0.0 151s Investment_20 0.0 0.0 151s Investment_21 0.0 0.0 151s Investment_22 0.0 0.0 151s PrivateWages_2 12.7 44.9 151s PrivateWages_3 12.4 45.6 151s PrivateWages_4 16.9 50.1 151s PrivateWages_5 18.4 57.2 151s PrivateWages_6 19.4 57.1 151s PrivateWages_8 19.6 64.0 151s PrivateWages_9 19.8 64.4 151s PrivateWages_10 21.1 64.5 151s PrivateWages_11 21.7 67.0 151s PrivateWages_12 15.6 61.2 151s PrivateWages_13 11.4 53.4 151s PrivateWages_14 7.0 44.3 151s PrivateWages_15 11.2 45.1 151s PrivateWages_16 12.3 49.7 151s PrivateWages_17 14.0 54.4 151s PrivateWages_18 17.6 62.7 151s PrivateWages_19 17.3 65.0 151s PrivateWages_20 15.3 60.9 151s PrivateWages_21 19.0 69.5 151s PrivateWages_22 21.1 75.7 151s > matrix of fitted regressors 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 1 13.44 151s Consumption_3 1 16.68 151s Consumption_4 1 18.95 151s Consumption_5 1 20.63 151s Consumption_6 1 19.28 151s Consumption_8 1 17.21 151s Consumption_9 1 18.99 151s Consumption_11 1 16.43 151s Consumption_12 1 12.49 151s Consumption_13 1 9.06 151s Consumption_14 1 9.28 151s Consumption_15 1 12.49 151s Consumption_16 1 14.39 151s Consumption_17 1 14.69 151s Consumption_18 1 19.60 151s Consumption_19 1 19.15 151s Consumption_20 1 17.54 151s Consumption_21 1 20.33 151s Consumption_22 1 22.78 151s Investment_2 0 0.00 151s Investment_3 0 0.00 151s Investment_4 0 0.00 151s Investment_5 0 0.00 151s Investment_6 0 0.00 151s Investment_8 0 0.00 151s Investment_9 0 0.00 151s Investment_10 0 0.00 151s Investment_11 0 0.00 151s Investment_12 0 0.00 151s Investment_13 0 0.00 151s Investment_14 0 0.00 151s Investment_15 0 0.00 151s Investment_16 0 0.00 151s Investment_17 0 0.00 151s Investment_18 0 0.00 151s Investment_19 0 0.00 151s Investment_20 0 0.00 151s Investment_21 0 0.00 151s Investment_22 0 0.00 151s PrivateWages_2 0 0.00 151s PrivateWages_3 0 0.00 151s PrivateWages_4 0 0.00 151s PrivateWages_5 0 0.00 151s PrivateWages_6 0 0.00 151s PrivateWages_8 0 0.00 151s PrivateWages_9 0 0.00 151s PrivateWages_10 0 0.00 151s PrivateWages_11 0 0.00 151s PrivateWages_12 0 0.00 151s PrivateWages_13 0 0.00 151s PrivateWages_14 0 0.00 151s PrivateWages_15 0 0.00 151s PrivateWages_16 0 0.00 151s PrivateWages_17 0 0.00 151s PrivateWages_18 0 0.00 151s PrivateWages_19 0 0.00 151s PrivateWages_20 0 0.00 151s PrivateWages_21 0 0.00 151s PrivateWages_22 0 0.00 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 12.7 29.6 151s Consumption_3 12.4 31.9 151s Consumption_4 16.9 35.4 151s Consumption_5 18.4 38.8 151s Consumption_6 19.4 38.7 151s Consumption_8 19.6 39.8 151s Consumption_9 19.8 41.8 151s Consumption_11 21.7 43.0 151s Consumption_12 15.6 39.3 151s Consumption_13 11.4 35.2 151s Consumption_14 7.0 33.0 151s Consumption_15 11.2 37.3 151s Consumption_16 12.3 40.1 151s Consumption_17 14.0 41.7 151s Consumption_18 17.6 47.7 151s Consumption_19 17.3 49.2 151s Consumption_20 15.3 48.5 151s Consumption_21 19.0 53.4 151s Consumption_22 21.1 60.8 151s Investment_2 0.0 0.0 151s Investment_3 0.0 0.0 151s Investment_4 0.0 0.0 151s Investment_5 0.0 0.0 151s Investment_6 0.0 0.0 151s Investment_8 0.0 0.0 151s Investment_9 0.0 0.0 151s Investment_10 0.0 0.0 151s Investment_11 0.0 0.0 151s Investment_12 0.0 0.0 151s Investment_13 0.0 0.0 151s Investment_14 0.0 0.0 151s Investment_15 0.0 0.0 151s Investment_16 0.0 0.0 151s Investment_17 0.0 0.0 151s Investment_18 0.0 0.0 151s Investment_19 0.0 0.0 151s Investment_20 0.0 0.0 151s Investment_21 0.0 0.0 151s Investment_22 0.0 0.0 151s PrivateWages_2 0.0 0.0 151s PrivateWages_3 0.0 0.0 151s PrivateWages_4 0.0 0.0 151s PrivateWages_5 0.0 0.0 151s PrivateWages_6 0.0 0.0 151s PrivateWages_8 0.0 0.0 151s PrivateWages_9 0.0 0.0 151s PrivateWages_10 0.0 0.0 151s PrivateWages_11 0.0 0.0 151s PrivateWages_12 0.0 0.0 151s PrivateWages_13 0.0 0.0 151s PrivateWages_14 0.0 0.0 151s PrivateWages_15 0.0 0.0 151s PrivateWages_16 0.0 0.0 151s PrivateWages_17 0.0 0.0 151s PrivateWages_18 0.0 0.0 151s PrivateWages_19 0.0 0.0 151s PrivateWages_20 0.0 0.0 151s PrivateWages_21 0.0 0.0 151s PrivateWages_22 0.0 0.0 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0 0.00 151s Consumption_3 0 0.00 151s Consumption_4 0 0.00 151s Consumption_5 0 0.00 151s Consumption_6 0 0.00 151s Consumption_8 0 0.00 151s Consumption_9 0 0.00 151s Consumption_11 0 0.00 151s Consumption_12 0 0.00 151s Consumption_13 0 0.00 151s Consumption_14 0 0.00 151s Consumption_15 0 0.00 151s Consumption_16 0 0.00 151s Consumption_17 0 0.00 151s Consumption_18 0 0.00 151s Consumption_19 0 0.00 151s Consumption_20 0 0.00 151s Consumption_21 0 0.00 151s Consumption_22 0 0.00 151s Investment_2 1 12.96 151s Investment_3 1 16.70 151s Investment_4 1 19.14 151s Investment_5 1 20.94 151s Investment_6 1 19.47 151s Investment_8 1 17.14 151s Investment_9 1 19.49 151s Investment_10 1 20.46 151s Investment_11 1 16.85 151s Investment_12 1 12.68 151s Investment_13 1 8.92 151s Investment_14 1 9.30 151s Investment_15 1 12.79 151s Investment_16 1 14.26 151s Investment_17 1 14.75 151s Investment_18 1 19.54 151s Investment_19 1 19.36 151s Investment_20 1 17.39 151s Investment_21 1 20.10 151s Investment_22 1 22.86 151s PrivateWages_2 0 0.00 151s PrivateWages_3 0 0.00 151s PrivateWages_4 0 0.00 151s PrivateWages_5 0 0.00 151s PrivateWages_6 0 0.00 151s PrivateWages_8 0 0.00 151s PrivateWages_9 0 0.00 151s PrivateWages_10 0 0.00 151s PrivateWages_11 0 0.00 151s PrivateWages_12 0 0.00 151s PrivateWages_13 0 0.00 151s PrivateWages_14 0 0.00 151s PrivateWages_15 0 0.00 151s PrivateWages_16 0 0.00 151s PrivateWages_17 0 0.00 151s PrivateWages_18 0 0.00 151s PrivateWages_19 0 0.00 151s PrivateWages_20 0 0.00 151s PrivateWages_21 0 0.00 151s PrivateWages_22 0 0.00 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.0 0 151s Consumption_3 0.0 0 151s Consumption_4 0.0 0 151s Consumption_5 0.0 0 151s Consumption_6 0.0 0 151s Consumption_8 0.0 0 151s Consumption_9 0.0 0 151s Consumption_11 0.0 0 151s Consumption_12 0.0 0 151s Consumption_13 0.0 0 151s Consumption_14 0.0 0 151s Consumption_15 0.0 0 151s Consumption_16 0.0 0 151s Consumption_17 0.0 0 151s Consumption_18 0.0 0 151s Consumption_19 0.0 0 151s Consumption_20 0.0 0 151s Consumption_21 0.0 0 151s Consumption_22 0.0 0 151s Investment_2 12.7 183 151s Investment_3 12.4 183 151s Investment_4 16.9 184 151s Investment_5 18.4 190 151s Investment_6 19.4 193 151s Investment_8 19.6 203 151s Investment_9 19.8 208 151s Investment_10 21.1 211 151s Investment_11 21.7 216 151s Investment_12 15.6 217 151s Investment_13 11.4 213 151s Investment_14 7.0 207 151s Investment_15 11.2 202 151s Investment_16 12.3 199 151s Investment_17 14.0 198 151s Investment_18 17.6 200 151s Investment_19 17.3 202 151s Investment_20 15.3 200 151s Investment_21 19.0 201 151s Investment_22 21.1 204 151s PrivateWages_2 0.0 0 151s PrivateWages_3 0.0 0 151s PrivateWages_4 0.0 0 151s PrivateWages_5 0.0 0 151s PrivateWages_6 0.0 0 151s PrivateWages_8 0.0 0 151s PrivateWages_9 0.0 0 151s PrivateWages_10 0.0 0 151s PrivateWages_11 0.0 0 151s PrivateWages_12 0.0 0 151s PrivateWages_13 0.0 0 151s PrivateWages_14 0.0 0 151s PrivateWages_15 0.0 0 151s PrivateWages_16 0.0 0 151s PrivateWages_17 0.0 0 151s PrivateWages_18 0.0 0 151s PrivateWages_19 0.0 0 151s PrivateWages_20 0.0 0 151s PrivateWages_21 0.0 0 151s PrivateWages_22 0.0 0 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 0 0.0 0.0 151s Consumption_3 0 0.0 0.0 151s Consumption_4 0 0.0 0.0 151s Consumption_5 0 0.0 0.0 151s Consumption_6 0 0.0 0.0 151s Consumption_8 0 0.0 0.0 151s Consumption_9 0 0.0 0.0 151s Consumption_11 0 0.0 0.0 151s Consumption_12 0 0.0 0.0 151s Consumption_13 0 0.0 0.0 151s Consumption_14 0 0.0 0.0 151s Consumption_15 0 0.0 0.0 151s Consumption_16 0 0.0 0.0 151s Consumption_17 0 0.0 0.0 151s Consumption_18 0 0.0 0.0 151s Consumption_19 0 0.0 0.0 151s Consumption_20 0 0.0 0.0 151s Consumption_21 0 0.0 0.0 151s Consumption_22 0 0.0 0.0 151s Investment_2 0 0.0 0.0 151s Investment_3 0 0.0 0.0 151s Investment_4 0 0.0 0.0 151s Investment_5 0 0.0 0.0 151s Investment_6 0 0.0 0.0 151s Investment_8 0 0.0 0.0 151s Investment_9 0 0.0 0.0 151s Investment_10 0 0.0 0.0 151s Investment_11 0 0.0 0.0 151s Investment_12 0 0.0 0.0 151s Investment_13 0 0.0 0.0 151s Investment_14 0 0.0 0.0 151s Investment_15 0 0.0 0.0 151s Investment_16 0 0.0 0.0 151s Investment_17 0 0.0 0.0 151s Investment_18 0 0.0 0.0 151s Investment_19 0 0.0 0.0 151s Investment_20 0 0.0 0.0 151s Investment_21 0 0.0 0.0 151s Investment_22 0 0.0 0.0 151s PrivateWages_2 1 47.1 44.9 151s PrivateWages_3 1 49.6 45.6 151s PrivateWages_4 1 56.5 50.1 151s PrivateWages_5 1 60.7 57.2 151s PrivateWages_6 1 60.6 57.1 151s PrivateWages_8 1 60.0 64.0 151s PrivateWages_9 1 62.3 64.4 151s PrivateWages_10 1 64.6 64.5 151s PrivateWages_11 1 63.7 67.0 151s PrivateWages_12 1 54.8 61.2 151s PrivateWages_13 1 47.0 53.4 151s PrivateWages_14 1 42.1 44.3 151s PrivateWages_15 1 51.2 45.1 151s PrivateWages_16 1 55.3 49.7 151s PrivateWages_17 1 57.4 54.4 151s PrivateWages_18 1 67.2 62.7 151s PrivateWages_19 1 68.5 65.0 151s PrivateWages_20 1 66.8 60.9 151s PrivateWages_21 1 74.9 69.5 151s PrivateWages_22 1 86.9 75.7 151s PrivateWages_trend 151s Consumption_2 0 151s Consumption_3 0 151s Consumption_4 0 151s Consumption_5 0 151s Consumption_6 0 151s Consumption_8 0 151s Consumption_9 0 151s Consumption_11 0 151s Consumption_12 0 151s Consumption_13 0 151s Consumption_14 0 151s Consumption_15 0 151s Consumption_16 0 151s Consumption_17 0 151s Consumption_18 0 151s Consumption_19 0 151s Consumption_20 0 151s Consumption_21 0 151s Consumption_22 0 151s Investment_2 0 151s Investment_3 0 151s Investment_4 0 151s Investment_5 0 151s Investment_6 0 151s Investment_8 0 151s Investment_9 0 151s Investment_10 0 151s Investment_11 0 151s Investment_12 0 151s Investment_13 0 151s Investment_14 0 151s Investment_15 0 151s Investment_16 0 151s Investment_17 0 151s Investment_18 0 151s Investment_19 0 151s Investment_20 0 151s Investment_21 0 151s Investment_22 0 151s PrivateWages_2 -10 151s PrivateWages_3 -9 151s PrivateWages_4 -8 151s PrivateWages_5 -7 151s PrivateWages_6 -6 151s PrivateWages_8 -4 151s PrivateWages_9 -3 151s PrivateWages_10 -2 151s PrivateWages_11 -1 151s PrivateWages_12 0 151s PrivateWages_13 1 151s PrivateWages_14 2 151s PrivateWages_15 3 151s PrivateWages_16 4 151s PrivateWages_17 5 151s PrivateWages_18 6 151s PrivateWages_19 7 151s PrivateWages_20 8 151s PrivateWages_21 9 151s PrivateWages_22 10 151s > nobs 151s [1] 59 151s > linearHypothesis 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 48 151s 2 47 1 0.87 0.36 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 48 151s 2 47 1 0.98 0.33 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 48 151s 2 47 1 0.98 0.32 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 49 151s 2 47 2 0.43 0.65 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 49 151s 2 47 2 0.49 0.61 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 49 151s 2 47 2 0.98 0.61 151s > logLik 151s 'log Lik.' -71.5 (df=13) 151s 'log Lik.' -78.7 (df=13) 151s Estimating function 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 -1.5371 -20.65 151s Consumption_3 -0.3191 -5.32 151s Consumption_4 0.0169 0.32 151s Consumption_5 -1.6346 -33.73 151s Consumption_6 0.2820 5.44 151s Consumption_8 2.9429 50.64 151s Consumption_9 2.3495 44.61 151s Consumption_11 -1.2221 -20.08 151s Consumption_12 -1.0034 -12.54 151s Consumption_13 -2.0551 -18.62 151s Consumption_14 1.4937 13.86 151s Consumption_15 -0.7418 -9.26 151s Consumption_16 -0.6703 -9.64 151s Consumption_17 4.0943 60.15 151s Consumption_18 -0.6347 -12.44 151s Consumption_19 -3.0409 -58.22 151s Consumption_20 2.1019 36.86 151s Consumption_21 0.7142 14.52 151s Consumption_22 -1.1363 -25.88 151s Investment_2 0.0000 0.00 151s Investment_3 0.0000 0.00 151s Investment_4 0.0000 0.00 151s Investment_5 0.0000 0.00 151s Investment_6 0.0000 0.00 151s Investment_8 0.0000 0.00 151s Investment_9 0.0000 0.00 151s Investment_10 0.0000 0.00 151s Investment_11 0.0000 0.00 151s Investment_12 0.0000 0.00 151s Investment_13 0.0000 0.00 151s Investment_14 0.0000 0.00 151s Investment_15 0.0000 0.00 151s Investment_16 0.0000 0.00 151s Investment_17 0.0000 0.00 151s Investment_18 0.0000 0.00 151s Investment_19 0.0000 0.00 151s Investment_20 0.0000 0.00 151s Investment_21 0.0000 0.00 151s Investment_22 0.0000 0.00 151s PrivateWages_2 0.0000 0.00 151s PrivateWages_3 0.0000 0.00 151s PrivateWages_4 0.0000 0.00 151s PrivateWages_5 0.0000 0.00 151s PrivateWages_6 0.0000 0.00 151s PrivateWages_8 0.0000 0.00 151s PrivateWages_9 0.0000 0.00 151s PrivateWages_10 0.0000 0.00 151s PrivateWages_11 0.0000 0.00 151s PrivateWages_12 0.0000 0.00 151s PrivateWages_13 0.0000 0.00 151s PrivateWages_14 0.0000 0.00 151s PrivateWages_15 0.0000 0.00 151s PrivateWages_16 0.0000 0.00 151s PrivateWages_17 0.0000 0.00 151s PrivateWages_18 0.0000 0.00 151s PrivateWages_19 0.0000 0.00 151s PrivateWages_20 0.0000 0.00 151s PrivateWages_21 0.0000 0.00 151s PrivateWages_22 0.0000 0.00 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 -19.521 -45.456 151s Consumption_3 -3.957 -10.167 151s Consumption_4 0.286 0.599 151s Consumption_5 -30.078 -63.354 151s Consumption_6 5.471 10.901 151s Consumption_8 57.681 117.190 151s Consumption_9 46.520 98.197 151s Consumption_11 -26.520 -52.512 151s Consumption_12 -15.653 -39.407 151s Consumption_13 -23.428 -72.317 151s Consumption_14 10.456 49.297 151s Consumption_15 -8.308 -27.687 151s Consumption_16 -8.244 -26.878 151s Consumption_17 57.321 170.665 151s Consumption_18 -11.170 -30.264 151s Consumption_19 -52.608 -149.761 151s Consumption_20 32.159 101.952 151s Consumption_21 13.570 38.131 151s Consumption_22 -23.976 -69.128 151s Investment_2 0.000 0.000 151s Investment_3 0.000 0.000 151s Investment_4 0.000 0.000 151s Investment_5 0.000 0.000 151s Investment_6 0.000 0.000 151s Investment_8 0.000 0.000 151s Investment_9 0.000 0.000 151s Investment_10 0.000 0.000 151s Investment_11 0.000 0.000 151s Investment_12 0.000 0.000 151s Investment_13 0.000 0.000 151s Investment_14 0.000 0.000 151s Investment_15 0.000 0.000 151s Investment_16 0.000 0.000 151s Investment_17 0.000 0.000 151s Investment_18 0.000 0.000 151s Investment_19 0.000 0.000 151s Investment_20 0.000 0.000 151s Investment_21 0.000 0.000 151s Investment_22 0.000 0.000 151s PrivateWages_2 0.000 0.000 151s PrivateWages_3 0.000 0.000 151s PrivateWages_4 0.000 0.000 151s PrivateWages_5 0.000 0.000 151s PrivateWages_6 0.000 0.000 151s PrivateWages_8 0.000 0.000 151s PrivateWages_9 0.000 0.000 151s PrivateWages_10 0.000 0.000 151s PrivateWages_11 0.000 0.000 151s PrivateWages_12 0.000 0.000 151s PrivateWages_13 0.000 0.000 151s PrivateWages_14 0.000 0.000 151s PrivateWages_15 0.000 0.000 151s PrivateWages_16 0.000 0.000 151s PrivateWages_17 0.000 0.000 151s PrivateWages_18 0.000 0.000 151s PrivateWages_19 0.000 0.000 151s PrivateWages_20 0.000 0.000 151s PrivateWages_21 0.000 0.000 151s PrivateWages_22 0.000 0.000 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0.0000 0.000 151s Consumption_3 0.0000 0.000 151s Consumption_4 0.0000 0.000 151s Consumption_5 0.0000 0.000 151s Consumption_6 0.0000 0.000 151s Consumption_8 0.0000 0.000 151s Consumption_9 0.0000 0.000 151s Consumption_11 0.0000 0.000 151s Consumption_12 0.0000 0.000 151s Consumption_13 0.0000 0.000 151s Consumption_14 0.0000 0.000 151s Consumption_15 0.0000 0.000 151s Consumption_16 0.0000 0.000 151s Consumption_17 0.0000 0.000 151s Consumption_18 0.0000 0.000 151s Consumption_19 0.0000 0.000 151s Consumption_20 0.0000 0.000 151s Consumption_21 0.0000 0.000 151s Consumption_22 0.0000 0.000 151s Investment_2 -1.1313 -14.660 151s Investment_3 0.2902 4.847 151s Investment_4 0.9027 17.274 151s Investment_5 -1.7434 -36.502 151s Investment_6 0.5695 11.088 151s Investment_8 1.6225 27.812 151s Investment_9 0.4166 8.119 151s Investment_10 2.0381 41.703 151s Investment_11 -0.8611 -14.505 151s Investment_12 -0.9091 -11.527 151s Investment_13 -1.1148 -9.946 151s Investment_14 1.3841 12.873 151s Investment_15 -0.2900 -3.710 151s Investment_16 0.0605 0.862 151s Investment_17 2.2439 33.101 151s Investment_18 -0.5390 -10.534 151s Investment_19 -3.9452 -76.375 151s Investment_20 0.4890 8.502 151s Investment_21 0.0864 1.737 151s Investment_22 0.4306 9.843 151s PrivateWages_2 0.0000 0.000 151s PrivateWages_3 0.0000 0.000 151s PrivateWages_4 0.0000 0.000 151s PrivateWages_5 0.0000 0.000 151s PrivateWages_6 0.0000 0.000 151s PrivateWages_8 0.0000 0.000 151s PrivateWages_9 0.0000 0.000 151s PrivateWages_10 0.0000 0.000 151s PrivateWages_11 0.0000 0.000 151s PrivateWages_12 0.0000 0.000 151s PrivateWages_13 0.0000 0.000 151s PrivateWages_14 0.0000 0.000 151s PrivateWages_15 0.0000 0.000 151s PrivateWages_16 0.0000 0.000 151s PrivateWages_17 0.0000 0.000 151s PrivateWages_18 0.0000 0.000 151s PrivateWages_19 0.0000 0.000 151s PrivateWages_20 0.0000 0.000 151s PrivateWages_21 0.0000 0.000 151s PrivateWages_22 0.0000 0.000 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.000 0.0 151s Consumption_3 0.000 0.0 151s Consumption_4 0.000 0.0 151s Consumption_5 0.000 0.0 151s Consumption_6 0.000 0.0 151s Consumption_8 0.000 0.0 151s Consumption_9 0.000 0.0 151s Consumption_11 0.000 0.0 151s Consumption_12 0.000 0.0 151s Consumption_13 0.000 0.0 151s Consumption_14 0.000 0.0 151s Consumption_15 0.000 0.0 151s Consumption_16 0.000 0.0 151s Consumption_17 0.000 0.0 151s Consumption_18 0.000 0.0 151s Consumption_19 0.000 0.0 151s Consumption_20 0.000 0.0 151s Consumption_21 0.000 0.0 151s Consumption_22 0.000 0.0 151s Investment_2 -14.368 -206.8 151s Investment_3 3.598 53.0 151s Investment_4 15.256 166.5 151s Investment_5 -32.079 -330.7 151s Investment_6 11.048 109.7 151s Investment_8 31.801 330.0 151s Investment_9 8.248 86.5 151s Investment_10 43.003 429.2 151s Investment_11 -18.685 -185.7 151s Investment_12 -14.182 -197.0 151s Investment_13 -12.709 -237.8 151s Investment_14 9.689 286.6 151s Investment_15 -3.247 -58.6 151s Investment_16 0.744 12.0 151s Investment_17 31.414 443.6 151s Investment_18 -9.486 -107.7 151s Investment_19 -68.252 -796.1 151s Investment_20 7.482 97.7 151s Investment_21 1.642 17.4 151s Investment_22 9.085 88.0 151s PrivateWages_2 0.000 0.0 151s PrivateWages_3 0.000 0.0 151s PrivateWages_4 0.000 0.0 151s PrivateWages_5 0.000 0.0 151s PrivateWages_6 0.000 0.0 151s PrivateWages_8 0.000 0.0 151s PrivateWages_9 0.000 0.0 151s PrivateWages_10 0.000 0.0 151s PrivateWages_11 0.000 0.0 151s PrivateWages_12 0.000 0.0 151s PrivateWages_13 0.000 0.0 151s PrivateWages_14 0.000 0.0 151s PrivateWages_15 0.000 0.0 151s PrivateWages_16 0.000 0.0 151s PrivateWages_17 0.000 0.0 151s PrivateWages_18 0.000 0.0 151s PrivateWages_19 0.000 0.0 151s PrivateWages_20 0.000 0.0 151s PrivateWages_21 0.000 0.0 151s PrivateWages_22 0.000 0.0 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 0.0000 0.00 0.00 151s Consumption_3 0.0000 0.00 0.00 151s Consumption_4 0.0000 0.00 0.00 151s Consumption_5 0.0000 0.00 0.00 151s Consumption_6 0.0000 0.00 0.00 151s Consumption_8 0.0000 0.00 0.00 151s Consumption_9 0.0000 0.00 0.00 151s Consumption_11 0.0000 0.00 0.00 151s Consumption_12 0.0000 0.00 0.00 151s Consumption_13 0.0000 0.00 0.00 151s Consumption_14 0.0000 0.00 0.00 151s Consumption_15 0.0000 0.00 0.00 151s Consumption_16 0.0000 0.00 0.00 151s Consumption_17 0.0000 0.00 0.00 151s Consumption_18 0.0000 0.00 0.00 151s Consumption_19 0.0000 0.00 0.00 151s Consumption_20 0.0000 0.00 0.00 151s Consumption_21 0.0000 0.00 0.00 151s Consumption_22 0.0000 0.00 0.00 151s Investment_2 0.0000 0.00 0.00 151s Investment_3 0.0000 0.00 0.00 151s Investment_4 0.0000 0.00 0.00 151s Investment_5 0.0000 0.00 0.00 151s Investment_6 0.0000 0.00 0.00 151s Investment_8 0.0000 0.00 0.00 151s Investment_9 0.0000 0.00 0.00 151s Investment_10 0.0000 0.00 0.00 151s Investment_11 0.0000 0.00 0.00 151s Investment_12 0.0000 0.00 0.00 151s Investment_13 0.0000 0.00 0.00 151s Investment_14 0.0000 0.00 0.00 151s Investment_15 0.0000 0.00 0.00 151s Investment_16 0.0000 0.00 0.00 151s Investment_17 0.0000 0.00 0.00 151s Investment_18 0.0000 0.00 0.00 151s Investment_19 0.0000 0.00 0.00 151s Investment_20 0.0000 0.00 0.00 151s Investment_21 0.0000 0.00 0.00 151s Investment_22 0.0000 0.00 0.00 151s PrivateWages_2 -1.9924 -93.78 -89.46 151s PrivateWages_3 0.4683 23.22 21.35 151s PrivateWages_4 1.4034 79.35 70.31 151s PrivateWages_5 -1.7870 -108.45 -102.22 151s PrivateWages_6 -0.3627 -21.98 -20.71 151s PrivateWages_8 1.1629 69.77 74.43 151s PrivateWages_9 1.2735 79.30 82.01 151s PrivateWages_10 2.2141 142.96 142.81 151s PrivateWages_11 -1.2912 -82.26 -86.51 151s PrivateWages_12 -0.0350 -1.92 -2.14 151s PrivateWages_13 -1.0438 -49.04 -55.74 151s PrivateWages_14 1.8016 75.90 79.81 151s PrivateWages_15 -0.3714 -19.02 -16.75 151s PrivateWages_16 -0.3904 -21.61 -19.40 151s PrivateWages_17 1.4934 85.71 81.24 151s PrivateWages_18 0.0279 1.88 1.75 151s PrivateWages_19 -3.8229 -261.91 -248.49 151s PrivateWages_20 0.7870 52.61 47.93 151s PrivateWages_21 -0.7415 -55.52 -51.54 151s PrivateWages_22 1.2062 104.79 91.31 151s PrivateWages_trend 151s Consumption_2 0.000 151s Consumption_3 0.000 151s Consumption_4 0.000 151s Consumption_5 0.000 151s Consumption_6 0.000 151s Consumption_8 0.000 151s Consumption_9 0.000 151s Consumption_11 0.000 151s Consumption_12 0.000 151s Consumption_13 0.000 151s Consumption_14 0.000 151s Consumption_15 0.000 151s Consumption_16 0.000 151s Consumption_17 0.000 151s Consumption_18 0.000 151s Consumption_19 0.000 151s Consumption_20 0.000 151s Consumption_21 0.000 151s Consumption_22 0.000 151s Investment_2 0.000 151s Investment_3 0.000 151s Investment_4 0.000 151s Investment_5 0.000 151s Investment_6 0.000 151s Investment_8 0.000 151s Investment_9 0.000 151s Investment_10 0.000 151s Investment_11 0.000 151s Investment_12 0.000 151s Investment_13 0.000 151s Investment_14 0.000 151s Investment_15 0.000 151s Investment_16 0.000 151s Investment_17 0.000 151s Investment_18 0.000 151s Investment_19 0.000 151s Investment_20 0.000 151s Investment_21 0.000 151s Investment_22 0.000 151s PrivateWages_2 19.924 151s PrivateWages_3 -4.214 151s PrivateWages_4 -11.227 151s PrivateWages_5 12.509 151s PrivateWages_6 2.176 151s PrivateWages_8 -4.652 151s PrivateWages_9 -3.820 151s PrivateWages_10 -4.428 151s PrivateWages_11 1.291 151s PrivateWages_12 0.000 151s PrivateWages_13 -1.044 151s PrivateWages_14 3.603 151s PrivateWages_15 -1.114 151s PrivateWages_16 -1.562 151s PrivateWages_17 7.467 151s PrivateWages_18 0.168 151s PrivateWages_19 -26.760 151s PrivateWages_20 6.296 151s PrivateWages_21 -6.674 151s PrivateWages_22 12.062 151s [1] TRUE 151s > Bread 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_(Intercept) 99.763 -0.8715 151s Consumption_corpProf -0.872 0.7621 151s Consumption_corpProfLag -0.479 -0.4940 151s Consumption_wages -1.807 -0.0927 151s Investment_(Intercept) 0.000 0.0000 151s Investment_corpProf 0.000 0.0000 151s Investment_corpProfLag 0.000 0.0000 151s Investment_capitalLag 0.000 0.0000 151s PrivateWages_(Intercept) 0.000 0.0000 151s PrivateWages_gnp 0.000 0.0000 151s PrivateWages_gnpLag 0.000 0.0000 151s PrivateWages_trend 0.000 0.0000 151s Consumption_corpProfLag Consumption_wages 151s Consumption_(Intercept) -0.4786 -1.8068 151s Consumption_corpProf -0.4940 -0.0927 151s Consumption_corpProfLag 0.6462 -0.0403 151s Consumption_wages -0.0403 0.0963 151s Investment_(Intercept) 0.0000 0.0000 151s Investment_corpProf 0.0000 0.0000 151s Investment_corpProfLag 0.0000 0.0000 151s Investment_capitalLag 0.0000 0.0000 151s PrivateWages_(Intercept) 0.0000 0.0000 151s PrivateWages_gnp 0.0000 0.0000 151s PrivateWages_gnpLag 0.0000 0.0000 151s PrivateWages_trend 0.0000 0.0000 151s Investment_(Intercept) Investment_corpProf 151s Consumption_(Intercept) 0.0 0.000 151s Consumption_corpProf 0.0 0.000 151s Consumption_corpProfLag 0.0 0.000 151s Consumption_wages 0.0 0.000 151s Investment_(Intercept) 2405.5 -38.269 151s Investment_corpProf -38.3 1.231 151s Investment_corpProfLag 32.8 -1.072 151s Investment_capitalLag -11.4 0.174 151s PrivateWages_(Intercept) 0.0 0.000 151s PrivateWages_gnp 0.0 0.000 151s PrivateWages_gnpLag 0.0 0.000 151s PrivateWages_trend 0.0 0.000 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_(Intercept) 0.000 0.0000 151s Consumption_corpProf 0.000 0.0000 151s Consumption_corpProfLag 0.000 0.0000 151s Consumption_wages 0.000 0.0000 151s Investment_(Intercept) 32.828 -11.4279 151s Investment_corpProf -1.072 0.1744 151s Investment_corpProfLag 1.129 -0.1652 151s Investment_capitalLag -0.165 0.0557 151s PrivateWages_(Intercept) 0.000 0.0000 151s PrivateWages_gnp 0.000 0.0000 151s PrivateWages_gnpLag 0.000 0.0000 151s PrivateWages_trend 0.000 0.0000 151s PrivateWages_(Intercept) PrivateWages_gnp 151s Consumption_(Intercept) 0.000 0.0000 151s Consumption_corpProf 0.000 0.0000 151s Consumption_corpProfLag 0.000 0.0000 151s Consumption_wages 0.000 0.0000 151s Investment_(Intercept) 0.000 0.0000 151s Investment_corpProf 0.000 0.0000 151s Investment_corpProfLag 0.000 0.0000 151s Investment_capitalLag 0.000 0.0000 151s PrivateWages_(Intercept) 167.869 -0.9135 151s PrivateWages_gnp -0.913 0.1554 151s PrivateWages_gnpLag -1.915 -0.1448 151s PrivateWages_trend 2.128 -0.0417 151s PrivateWages_gnpLag PrivateWages_trend 151s Consumption_(Intercept) 0.0000 0.0000 151s Consumption_corpProf 0.0000 0.0000 151s Consumption_corpProfLag 0.0000 0.0000 151s Consumption_wages 0.0000 0.0000 151s Investment_(Intercept) 0.0000 0.0000 151s Investment_corpProf 0.0000 0.0000 151s Investment_corpProfLag 0.0000 0.0000 151s Investment_capitalLag 0.0000 0.0000 151s PrivateWages_(Intercept) -1.9153 2.1280 151s PrivateWages_gnp -0.1448 -0.0417 151s PrivateWages_gnpLag 0.1830 0.0059 151s PrivateWages_trend 0.0059 0.1132 151s > 151s > # SUR 151s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 151s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 151s > summary 151s 151s systemfit results 151s method: SUR 151s 151s N DF SSR detRCov OLS-R2 McElroy-R2 151s system 61 49 45.4 0.151 0.977 0.992 151s 151s N DF SSR MSE RMSE R2 Adj R2 151s Consumption 20 16 17.6 1.102 1.050 0.981 0.977 151s Investment 21 17 17.5 1.029 1.015 0.931 0.918 151s PrivateWages 20 16 10.3 0.643 0.802 0.987 0.985 151s 151s The covariance matrix of the residuals used for estimation 151s Consumption Investment PrivateWages 151s Consumption 0.8871 0.0268 -0.349 151s Investment 0.0268 0.7328 0.103 151s PrivateWages -0.3492 0.1029 0.444 151s 151s The covariance matrix of the residuals 151s Consumption Investment PrivateWages 151s Consumption 0.8852 0.0508 -0.406 151s Investment 0.0508 0.7313 0.161 151s PrivateWages -0.4063 0.1609 0.467 151s 151s The correlations of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.000 0.065 -0.635 151s Investment 0.065 1.000 0.262 151s PrivateWages -0.635 0.262 1.000 151s 151s 151s SUR estimates for 'Consumption' (equation 1) 151s Model Formula: consump ~ corpProf + corpProfLag + wages 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 16.0876 1.2010 13.39 4.1e-10 *** 151s corpProf 0.2173 0.0799 2.72 0.015 * 151s corpProfLag 0.0694 0.0793 0.88 0.394 151s wages 0.7975 0.0360 22.15 2.0e-13 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.05 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 17.63 MSE: 1.102 Root MSE: 1.05 151s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 151s 151s 151s SUR estimates for 'Investment' (equation 2) 151s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 12.3518 4.5615 2.71 0.01493 * 151s corpProf 0.4511 0.0814 5.54 3.6e-05 *** 151s corpProfLag 0.3570 0.0846 4.22 0.00058 *** 151s capitalLag -0.1225 0.0223 -5.49 4.0e-05 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.015 on 17 degrees of freedom 151s Number of observations: 21 Degrees of Freedom: 17 151s SSR: 17.5 MSE: 1.029 Root MSE: 1.015 151s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 151s 151s 151s SUR estimates for 'PrivateWages' (equation 3) 151s Model Formula: privWage ~ gnp + gnpLag + trend 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 1.3964 1.0825 1.29 0.22 151s gnp 0.4177 0.0269 15.55 4.4e-11 *** 151s gnpLag 0.1709 0.0306 5.59 4.0e-05 *** 151s trend 0.1467 0.0272 5.40 5.9e-05 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 0.802 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 10.284 MSE: 0.643 Root MSE: 0.802 151s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 151s 151s > residuals 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 -0.2529 -0.2920 -1.15193 151s 3 -1.2998 -0.1392 0.50193 151s 4 -1.5662 1.1106 1.42026 151s 5 -0.4876 -1.4391 -0.09801 151s 6 0.0149 0.3556 -0.35678 151s 7 0.9002 1.4558 NA 151s 8 1.3535 0.8299 -0.74964 151s 9 1.0406 -0.5136 0.29355 151s 10 NA 1.2191 1.18544 151s 11 0.4417 0.2810 -0.36558 151s 12 -0.0892 0.0754 0.33733 151s 13 -0.1541 0.3429 -0.17490 151s 14 0.2984 0.3597 0.39941 151s 15 -0.0260 -0.1602 0.29441 151s 16 -0.0250 0.0130 -0.00177 151s 17 1.5671 1.0231 -0.81891 151s 18 -0.4089 0.0306 0.85516 151s 19 0.2819 -2.6153 -0.77184 151s 20 0.9257 -0.6030 -0.41040 151s 21 0.7415 -0.7118 -1.21679 151s 22 -2.2437 -0.5398 0.57166 151s > fitted 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 42.2 0.092 26.7 151s 3 46.3 2.039 28.8 151s 4 50.8 4.089 32.7 151s 5 51.1 4.439 34.0 151s 6 52.6 4.744 35.8 151s 7 54.2 4.144 NA 151s 8 54.8 3.370 38.6 151s 9 56.3 3.514 38.9 151s 10 NA 3.881 40.1 151s 11 54.6 0.719 38.3 151s 12 51.0 -3.475 34.2 151s 13 45.8 -6.543 29.2 151s 14 46.2 -5.460 28.1 151s 15 48.7 -2.840 30.3 151s 16 51.3 -1.313 33.2 151s 17 56.1 1.077 37.6 151s 18 59.1 1.969 40.1 151s 19 57.2 0.715 39.0 151s 20 60.7 1.903 42.0 151s 21 64.3 4.012 46.2 151s 22 71.9 5.440 52.7 151s > predict 151s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 151s 1 NA NA NA NA 151s 2 42.2 0.422 41.3 43.0 151s 3 46.3 0.462 45.4 47.2 151s 4 50.8 0.309 50.1 51.4 151s 5 51.1 0.359 50.4 51.8 151s 6 52.6 0.362 51.9 53.3 151s 7 54.2 0.328 53.5 54.9 151s 8 54.8 0.300 54.2 55.4 151s 9 56.3 0.323 55.6 56.9 151s 10 NA NA NA NA 151s 11 54.6 0.531 53.5 55.6 151s 12 51.0 0.427 50.1 51.8 151s 13 45.8 0.564 44.6 46.9 151s 14 46.2 0.543 45.1 47.3 151s 15 48.7 0.341 48.0 49.4 151s 16 51.3 0.302 50.7 51.9 151s 17 56.1 0.328 55.5 56.8 151s 18 59.1 0.294 58.5 59.7 151s 19 57.2 0.332 56.6 57.9 151s 20 60.7 0.392 59.9 61.5 151s 21 64.3 0.394 63.5 65.0 151s 22 71.9 0.615 70.7 73.2 151s Investment.pred Investment.se.fit Investment.lwr Investment.upr 151s 1 NA NA NA NA 151s 2 0.092 0.508 -0.929 1.113 151s 3 2.039 0.421 1.193 2.885 151s 4 4.089 0.376 3.333 4.846 151s 5 4.439 0.311 3.813 5.065 151s 6 4.744 0.294 4.154 5.335 151s 7 4.144 0.277 3.587 4.701 151s 8 3.370 0.247 2.873 3.867 151s 9 3.514 0.328 2.855 4.172 151s 10 3.881 0.376 3.126 4.636 151s 11 0.719 0.508 -0.301 1.739 151s 12 -3.475 0.428 -4.336 -2.615 151s 13 -6.543 0.521 -7.590 -5.496 151s 14 -5.460 0.583 -6.632 -4.288 151s 15 -2.840 0.316 -3.474 -2.205 151s 16 -1.313 0.271 -1.857 -0.769 151s 17 1.077 0.293 0.488 1.666 151s 18 1.969 0.205 1.557 2.382 151s 19 0.715 0.263 0.187 1.244 151s 20 1.903 0.309 1.283 2.523 151s 21 4.012 0.280 3.449 4.574 151s 22 5.440 0.389 4.659 6.221 151s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 151s 1 NA NA NA NA 151s 2 26.7 0.306 26.0 27.3 151s 3 28.8 0.305 28.2 29.4 151s 4 32.7 0.302 32.1 33.3 151s 5 34.0 0.231 33.5 34.5 151s 6 35.8 0.230 35.3 36.2 151s 7 NA NA NA NA 151s 8 38.6 0.233 38.2 39.1 151s 9 38.9 0.222 38.5 39.4 151s 10 40.1 0.213 39.7 40.5 151s 11 38.3 0.292 37.7 38.9 151s 12 34.2 0.300 33.6 34.8 151s 13 29.2 0.361 28.4 29.9 151s 14 28.1 0.322 27.5 28.7 151s 15 30.3 0.314 29.7 30.9 151s 16 33.2 0.263 32.7 33.7 151s 17 37.6 0.256 37.1 38.1 151s 18 40.1 0.204 39.7 40.6 151s 19 39.0 0.298 38.4 39.6 151s 20 42.0 0.272 41.5 42.6 151s 21 46.2 0.288 45.6 46.8 151s 22 52.7 0.431 51.9 53.6 151s > model.frame 151s [1] TRUE 151s > model.matrix 151s [1] TRUE 151s > nobs 151s [1] 61 151s > linearHypothesis 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 49 1 1.01 0.32 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 50 151s 2 49 1 1.3 0.26 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 50 151s 2 49 1 1.3 0.25 151s Linear hypothesis test (Theil's F test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 51 151s 2 49 2 0.53 0.59 151s Linear hypothesis test (F statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df F Pr(>F) 151s 1 51 151s 2 49 2 0.69 0.51 151s Linear hypothesis test (Chi^2 statistic of a Wald test) 151s 151s Hypothesis: 151s Consumption_corpProf + Investment_capitalLag = 0 151s Consumption_corpProfLag - PrivateWages_trend = 0 151s 151s Model 1: restricted model 151s Model 2: kleinModel 151s 151s Res.Df Df Chisq Pr(>Chisq) 151s 1 51 151s 2 49 2 1.38 0.5 151s > logLik 151s 'log Lik.' -69.6 (df=18) 151s 'log Lik.' -76.9 (df=18) 151s Estimating function 151s Consumption_(Intercept) Consumption_corpProf 151s Consumption_2 -0.42417 -5.2597 151s Consumption_3 -2.17982 -36.8390 151s Consumption_4 -2.62648 -48.3271 151s Consumption_5 -0.81768 -15.8630 151s Consumption_6 0.02500 0.5025 151s Consumption_7 1.50966 29.5894 151s Consumption_8 2.26980 44.9421 151s Consumption_9 1.74517 36.8231 151s Consumption_11 0.74077 11.5559 151s Consumption_12 -0.14959 -1.7053 151s Consumption_13 -0.25842 -1.8090 151s Consumption_14 0.50036 5.6040 151s Consumption_15 -0.04361 -0.5363 151s Consumption_16 -0.04189 -0.5865 151s Consumption_17 2.62802 46.2532 151s Consumption_18 -0.68580 -11.8643 151s Consumption_19 0.47280 7.2339 151s Consumption_20 1.55235 29.4946 151s Consumption_21 1.24350 26.2379 151s Consumption_22 -3.76279 -88.4255 151s Investment_2 0.07441 0.9227 151s Investment_3 0.03547 0.5995 151s Investment_4 -0.28298 -5.2069 151s Investment_5 0.36669 7.1139 151s Investment_6 -0.09061 -1.8212 151s Investment_7 -0.37095 -7.2706 151s Investment_8 -0.21146 -4.1868 151s Investment_9 0.13086 2.7611 151s Investment_10 0.00000 0.0000 151s Investment_11 -0.07161 -1.1172 151s Investment_12 -0.01921 -0.2190 151s Investment_13 -0.08737 -0.6116 151s Investment_14 -0.09166 -1.0266 151s Investment_15 0.04082 0.5021 151s Investment_16 -0.00330 -0.0462 151s Investment_17 -0.26069 -4.5882 151s Investment_18 -0.00779 -0.1348 151s Investment_19 0.66639 10.1958 151s Investment_20 0.15365 2.9194 151s Investment_21 0.18136 3.8268 151s Investment_22 0.13754 3.2323 151s PrivateWages_2 -1.58616 -19.6684 151s PrivateWages_3 0.69114 11.6803 151s PrivateWages_4 1.95564 35.9837 151s PrivateWages_5 -0.13496 -2.6181 151s PrivateWages_6 -0.49127 -9.8746 151s PrivateWages_8 -1.03222 -20.4380 151s PrivateWages_9 0.40421 8.5288 151s PrivateWages_10 0.00000 0.0000 151s PrivateWages_11 -0.50339 -7.8529 151s PrivateWages_12 0.46449 5.2952 151s PrivateWages_13 -0.24083 -1.6858 151s PrivateWages_14 0.54997 6.1596 151s PrivateWages_15 0.40539 4.9863 151s PrivateWages_16 -0.00244 -0.0342 151s PrivateWages_17 -1.12761 -19.8459 151s PrivateWages_18 1.17751 20.3710 151s PrivateWages_19 -1.06279 -16.2607 151s PrivateWages_20 -0.56511 -10.7371 151s PrivateWages_21 -1.67547 -35.3524 151s PrivateWages_22 0.78715 18.4981 151s Consumption_corpProfLag Consumption_wages 151s Consumption_2 -5.3870 -11.962 151s Consumption_3 -27.0298 -70.190 151s Consumption_4 -44.3874 -97.180 151s Consumption_5 -15.0453 -30.254 151s Consumption_6 0.4850 0.965 151s Consumption_7 30.3442 61.443 151s Consumption_8 44.4881 94.197 151s Consumption_9 34.5544 74.868 151s Consumption_11 16.0746 31.186 151s Consumption_12 -2.3336 -5.879 151s Consumption_13 -2.9460 -8.864 151s Consumption_14 3.5025 17.062 151s Consumption_15 -0.4884 -1.596 151s Consumption_16 -0.5153 -1.646 151s Consumption_17 36.7923 116.159 151s Consumption_18 -12.0701 -32.713 151s Consumption_19 8.1795 21.702 151s Consumption_20 23.7509 76.686 151s Consumption_21 23.6265 65.906 151s Consumption_22 -79.3948 -232.540 151s Investment_2 0.9450 2.098 151s Investment_3 0.4399 1.142 151s Investment_4 -4.7824 -10.470 151s Investment_5 6.7472 13.568 151s Investment_6 -1.7577 -3.497 151s Investment_7 -7.4561 -15.098 151s Investment_8 -4.1445 -8.775 151s Investment_9 2.5910 5.614 151s Investment_10 0.0000 0.000 151s Investment_11 -1.5540 -3.015 151s Investment_12 -0.2997 -0.755 151s Investment_13 -0.9961 -2.997 151s Investment_14 -0.6416 -3.126 151s Investment_15 0.4572 1.494 151s Investment_16 -0.0406 -0.130 151s Investment_17 -3.6497 -11.523 151s Investment_18 -0.1371 -0.372 151s Investment_19 11.5286 30.587 151s Investment_20 2.3509 7.590 151s Investment_21 3.4459 9.612 151s Investment_22 2.9022 8.500 151s PrivateWages_2 -20.1442 -44.730 151s PrivateWages_3 8.5702 22.255 151s PrivateWages_4 33.0503 72.359 151s PrivateWages_5 -2.4832 -4.993 151s PrivateWages_6 -9.5307 -18.963 151s PrivateWages_8 -20.2315 -42.837 151s PrivateWages_9 8.0034 17.341 151s PrivateWages_10 0.0000 0.000 151s PrivateWages_11 -10.9235 -21.193 151s PrivateWages_12 7.2461 18.254 151s PrivateWages_13 -2.7454 -8.260 151s PrivateWages_14 3.8498 18.754 151s PrivateWages_15 4.5404 14.837 151s PrivateWages_16 -0.0300 -0.096 151s PrivateWages_17 -15.7865 -49.840 151s PrivateWages_18 20.7242 56.167 151s PrivateWages_19 -18.3863 -48.782 151s PrivateWages_20 -8.6462 -27.916 151s PrivateWages_21 -31.8339 -88.800 151s PrivateWages_22 16.6089 48.646 151s Investment_(Intercept) Investment_corpProf 151s Consumption_2 0.064449 0.7992 151s Consumption_3 0.331201 5.5973 151s Consumption_4 0.399066 7.3428 151s Consumption_5 0.124238 2.4102 151s Consumption_6 -0.003798 -0.0763 151s Consumption_7 -0.229378 -4.4958 151s Consumption_8 -0.344873 -6.8285 151s Consumption_9 -0.265161 -5.5949 151s Consumption_11 -0.112552 -1.7558 151s Consumption_12 0.022729 0.2591 151s Consumption_13 0.039265 0.2749 151s Consumption_14 -0.076024 -0.8515 151s Consumption_15 0.006625 0.0815 151s Consumption_16 0.006365 0.0891 151s Consumption_17 -0.399301 -7.0277 151s Consumption_18 0.104200 1.8027 151s Consumption_19 -0.071838 -1.0991 151s Consumption_20 -0.235863 -4.4814 151s Consumption_21 -0.188937 -3.9866 151s Consumption_22 0.571717 13.4353 151s Investment_2 -0.423201 -5.2477 151s Investment_3 -0.201766 -3.4098 151s Investment_4 1.609495 29.6147 151s Investment_5 -2.085613 -40.4609 151s Investment_6 0.515327 10.3581 151s Investment_7 2.109824 41.3526 151s Investment_8 1.202679 23.8131 151s Investment_9 -0.744277 -15.7042 151s Investment_10 1.766841 38.3405 151s Investment_11 0.407303 6.3539 151s Investment_12 0.109258 1.2455 151s Investment_13 0.496948 3.4786 151s Investment_14 0.521347 5.8391 151s Investment_15 -0.232156 -2.8555 151s Investment_16 0.018782 0.2630 151s Investment_17 1.482721 26.0959 151s Investment_18 0.044303 0.7664 151s Investment_19 -3.790179 -57.9897 151s Investment_20 -0.873905 -16.6042 151s Investment_21 -1.031520 -21.7651 151s Investment_22 -0.782292 -18.3839 151s PrivateWages_2 0.617327 7.6549 151s PrivateWages_3 -0.268990 -4.5459 151s PrivateWages_4 -0.761128 -14.0048 151s PrivateWages_5 0.052525 1.0190 151s PrivateWages_6 0.191202 3.8432 151s PrivateWages_8 0.401737 7.9544 151s PrivateWages_9 -0.157317 -3.3194 151s PrivateWages_10 -0.635285 -13.7857 151s PrivateWages_11 0.195917 3.0563 151s PrivateWages_12 -0.180778 -2.0609 151s PrivateWages_13 0.093729 0.6561 151s PrivateWages_14 -0.214045 -2.3973 151s PrivateWages_15 -0.157776 -1.9406 151s PrivateWages_16 0.000951 0.0133 151s PrivateWages_17 0.438862 7.7240 151s PrivateWages_18 -0.458284 -7.9283 151s PrivateWages_19 0.413636 6.3286 151s PrivateWages_20 0.219939 4.1788 151s PrivateWages_21 0.652086 13.7590 151s PrivateWages_22 -0.306358 -7.1994 151s Investment_corpProfLag Investment_capitalLag 151s Consumption_2 0.8185 11.781 151s Consumption_3 4.1069 60.477 151s Consumption_4 6.7442 73.628 151s Consumption_5 2.2860 23.568 151s Consumption_6 -0.0737 -0.732 151s Consumption_7 -4.6105 -45.371 151s Consumption_8 -6.7595 -70.147 151s Consumption_9 -5.2502 -55.047 151s Consumption_11 -2.4424 -24.277 151s Consumption_12 0.3546 4.925 151s Consumption_13 0.4476 8.375 151s Consumption_14 -0.5322 -15.745 151s Consumption_15 0.0742 1.338 151s Consumption_16 0.0783 1.267 151s Consumption_17 -5.5902 -78.942 151s Consumption_18 1.8339 20.819 151s Consumption_19 -1.2428 -14.497 151s Consumption_20 -3.6087 -47.149 151s Consumption_21 -3.5898 -38.014 151s Consumption_22 12.0632 116.916 151s Investment_2 -5.3746 -77.361 151s Investment_3 -2.5019 -36.842 151s Investment_4 27.2005 296.952 151s Investment_5 -38.3753 -395.641 151s Investment_6 9.9974 99.304 151s Investment_7 42.4075 417.323 151s Investment_8 23.5725 244.625 151s Investment_9 -14.7367 -154.512 151s Investment_10 37.2803 372.097 151s Investment_11 8.8385 87.855 151s Investment_12 1.7044 23.676 151s Investment_13 5.6652 105.999 151s Investment_14 3.6494 107.971 151s Investment_15 -2.6002 -46.896 151s Investment_16 0.2310 3.738 151s Investment_17 20.7581 293.134 151s Investment_18 0.7797 8.852 151s Investment_19 -65.5701 -764.858 151s Investment_20 -13.3707 -174.694 151s Investment_21 -19.5989 -207.542 151s Investment_22 -16.5064 -159.979 151s PrivateWages_2 7.8401 112.847 151s PrivateWages_3 -3.3355 -49.118 151s PrivateWages_4 -12.8631 -140.428 151s PrivateWages_5 0.9665 9.964 151s PrivateWages_6 3.7093 36.845 151s PrivateWages_8 7.8740 81.713 151s PrivateWages_9 -3.1149 -32.659 151s PrivateWages_10 -13.4045 -133.791 151s PrivateWages_11 4.2514 42.259 151s PrivateWages_12 -2.8201 -39.175 151s PrivateWages_13 1.0685 19.992 151s PrivateWages_14 -1.4983 -44.329 151s PrivateWages_15 -1.7671 -31.871 151s PrivateWages_16 0.0117 0.189 151s PrivateWages_17 6.1441 86.763 151s PrivateWages_18 -8.0658 -91.565 151s PrivateWages_19 7.1559 83.472 151s PrivateWages_20 3.3651 43.966 151s PrivateWages_21 12.3896 131.200 151s PrivateWages_22 -6.4641 -62.650 151s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 151s Consumption_2 -0.34828 -15.881 -15.638 151s Consumption_3 -1.78978 -89.668 -81.614 151s Consumption_4 -2.15652 -123.353 -108.042 151s Consumption_5 -0.67137 -38.335 -38.402 151s Consumption_6 0.02052 1.252 1.172 151s Consumption_7 0.00000 0.000 0.000 151s Consumption_8 1.86367 120.020 119.275 151s Consumption_9 1.43291 92.422 92.279 151s Consumption_11 0.60822 37.223 40.751 151s Consumption_12 -0.12282 -6.559 -7.517 151s Consumption_13 -0.21218 -9.400 -11.331 151s Consumption_14 0.41083 18.528 18.200 151s Consumption_15 -0.03580 -1.779 -1.615 151s Consumption_16 -0.03440 -1.871 -1.710 151s Consumption_17 2.15779 135.293 117.384 151s Consumption_18 -0.56309 -36.601 -35.306 151s Consumption_19 0.38821 23.642 25.233 151s Consumption_20 1.27458 88.584 77.622 151s Consumption_21 1.02100 77.290 70.960 151s Consumption_22 -3.08951 -273.113 -233.876 151s Investment_2 0.15649 7.136 7.027 151s Investment_3 0.07461 3.738 3.402 151s Investment_4 -0.59517 -34.043 -29.818 151s Investment_5 0.77123 44.037 44.114 151s Investment_6 -0.19056 -11.624 -10.881 151s Investment_7 0.00000 0.000 0.000 151s Investment_8 -0.44473 -28.641 -28.463 151s Investment_9 0.27522 17.752 17.724 151s Investment_10 -0.65335 -43.774 -42.141 151s Investment_11 -0.15061 -9.218 -10.091 151s Investment_12 -0.04040 -2.157 -2.473 151s Investment_13 -0.18376 -8.141 -9.813 151s Investment_14 -0.19279 -8.695 -8.540 151s Investment_15 0.08585 4.267 3.872 151s Investment_16 -0.00695 -0.378 -0.345 151s Investment_17 -0.54829 -34.378 -29.827 151s Investment_18 -0.01638 -1.065 -1.027 151s Investment_19 1.40155 85.354 91.101 151s Investment_20 0.32316 22.459 19.680 151s Investment_21 0.38144 28.875 26.510 151s Investment_22 0.28928 25.572 21.898 151s PrivateWages_2 -3.98191 -181.575 -178.788 151s PrivateWages_3 1.73505 86.926 79.118 151s PrivateWages_4 4.90946 280.821 245.964 151s PrivateWages_5 -0.33880 -19.345 -19.379 151s PrivateWages_6 -1.23330 -75.231 -70.421 151s PrivateWages_8 -2.59130 -166.880 -165.843 151s PrivateWages_9 1.01473 65.450 65.349 151s PrivateWages_10 4.09774 274.549 264.304 151s PrivateWages_11 -1.26371 -77.339 -84.669 151s PrivateWages_12 1.16606 62.268 71.363 151s PrivateWages_13 -0.60457 -26.783 -32.284 151s PrivateWages_14 1.38064 62.267 61.163 151s PrivateWages_15 1.01769 50.579 45.898 151s PrivateWages_16 -0.00613 -0.334 -0.305 151s PrivateWages_17 -2.83076 -177.489 -153.993 151s PrivateWages_18 2.95604 192.143 185.344 151s PrivateWages_19 -2.66805 -162.484 -173.423 151s PrivateWages_20 -1.41866 -98.597 -86.396 151s PrivateWages_21 -4.20611 -318.403 -292.325 151s PrivateWages_22 1.97608 174.686 149.589 151s PrivateWages_trend 151s Consumption_2 3.4828 151s Consumption_3 16.1081 151s Consumption_4 17.2522 151s Consumption_5 4.6996 151s Consumption_6 -0.1231 151s Consumption_7 0.0000 151s Consumption_8 -7.4547 151s Consumption_9 -4.2987 151s Consumption_11 -0.6082 151s Consumption_12 0.0000 151s Consumption_13 -0.2122 151s Consumption_14 0.8217 151s Consumption_15 -0.1074 151s Consumption_16 -0.1376 151s Consumption_17 10.7889 151s Consumption_18 -3.3785 151s Consumption_19 2.7174 151s Consumption_20 10.1967 151s Consumption_21 9.1890 151s Consumption_22 -30.8951 151s Investment_2 -1.5649 151s Investment_3 -0.6715 151s Investment_4 4.7613 151s Investment_5 -5.3986 151s Investment_6 1.1434 151s Investment_7 0.0000 151s Investment_8 1.7789 151s Investment_9 -0.8257 151s Investment_10 1.3067 151s Investment_11 0.1506 151s Investment_12 0.0000 151s Investment_13 -0.1838 151s Investment_14 -0.3856 151s Investment_15 0.2575 151s Investment_16 -0.0278 151s Investment_17 -2.7414 151s Investment_18 -0.0983 151s Investment_19 9.8108 151s Investment_20 2.5853 151s Investment_21 3.4330 151s Investment_22 2.8928 151s PrivateWages_2 39.8191 151s PrivateWages_3 -15.6154 151s PrivateWages_4 -39.2757 151s PrivateWages_5 2.3716 151s PrivateWages_6 7.3998 151s PrivateWages_8 10.3652 151s PrivateWages_9 -3.0442 151s PrivateWages_10 -8.1955 151s PrivateWages_11 1.2637 151s PrivateWages_12 0.0000 151s PrivateWages_13 -0.6046 151s PrivateWages_14 2.7613 151s PrivateWages_15 3.0531 151s PrivateWages_16 -0.0245 151s PrivateWages_17 -14.1538 151s PrivateWages_18 17.7363 151s PrivateWages_19 -18.6764 151s PrivateWages_20 -11.3493 151s PrivateWages_21 -37.8550 151s PrivateWages_22 19.7608 151s [1] TRUE 151s > Bread 151s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 151s [1,] 87.9904 -0.088084 -0.91416 151s [2,] -0.0881 0.389639 -0.23612 151s [3,] -0.9142 -0.236125 0.38341 151s [4,] -1.6692 -0.062952 -0.03326 151s [5,] 2.6851 -0.188961 0.72342 151s [6,] -0.0355 0.023370 -0.02643 151s [7,] -0.0563 -0.020038 0.03196 151s [8,] -0.0054 0.000618 -0.00397 151s [9,] -33.1687 0.063156 1.54217 151s [10,] 0.3665 -0.059172 0.03813 151s [11,] 0.1741 0.060188 -0.06574 151s [12,] 0.1831 0.029476 0.02425 151s Consumption_wages Investment_(Intercept) Investment_corpProf 151s [1,] -1.669236 2.685 -0.03549 151s [2,] -0.062952 -0.189 0.02337 151s [3,] -0.033257 0.723 -0.02643 151s [4,] 0.079061 -0.248 0.00151 151s [5,] -0.248317 1269.247 -12.23080 151s [6,] 0.001506 -12.231 0.40462 151s [7,] -0.002778 9.884 -0.34614 151s [8,] 0.001327 -6.097 0.05519 151s [9,] 0.134743 17.903 -0.13872 151s [10,] 0.000196 0.262 0.01397 151s [11,] -0.002616 -0.581 -0.01197 151s [12,] -0.026193 -0.551 0.00355 151s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 151s [1,] -0.05628 -0.005396 -33.1687 151s [2,] -0.02004 0.000618 0.0632 151s [3,] 0.03196 -0.003967 1.5422 151s [4,] -0.00278 0.001327 0.1347 151s [5,] 9.88435 -6.096982 17.9032 151s [6,] -0.34614 0.055190 -0.1387 151s [7,] 0.43632 -0.055785 -0.4000 151s [8,] -0.05578 0.030317 -0.0433 151s [9,] -0.40000 -0.043343 71.4840 151s [10,] -0.00786 -0.001844 -0.3085 151s [11,] 0.01493 0.002686 -0.8909 151s [12,] -0.01033 0.003295 0.8146 151s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 151s [1,] 0.366465 0.17405 0.18311 151s [2,] -0.059172 0.06019 0.02948 151s [3,] 0.038129 -0.06574 0.02425 151s [4,] 0.000196 -0.00262 -0.02619 151s [5,] 0.262390 -0.58123 -0.55064 151s [6,] 0.013966 -0.01197 0.00355 151s [7,] -0.007857 0.01493 -0.01033 151s [8,] -0.001844 0.00269 0.00330 151s [9,] -0.308484 -0.89087 0.81461 151s [10,] 0.044017 -0.04022 -0.01158 151s [11,] -0.040216 0.05696 -0.00212 151s [12,] -0.011575 -0.00212 0.04506 151s > 151s > # 3SLS 151s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 151s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 151s > summary 151s 151s systemfit results 151s method: 3SLS 151s 151s N DF SSR detRCov OLS-R2 McElroy-R2 151s system 59 47 59.5 0.241 0.97 0.994 151s 151s N DF SSR MSE RMSE R2 Adj R2 151s Consumption 19 15 18.1 1.203 1.097 0.980 0.977 151s Investment 20 16 31.1 1.945 1.395 0.866 0.841 151s PrivateWages 20 16 10.3 0.645 0.803 0.987 0.985 151s 151s The covariance matrix of the residuals used for estimation 151s Consumption Investment PrivateWages 151s Consumption 1.079 0.354 -0.383 151s Investment 0.354 1.047 0.107 151s PrivateWages -0.383 0.107 0.445 151s 151s The covariance matrix of the residuals 151s Consumption Investment PrivateWages 151s Consumption 0.950 0.324 -0.395 151s Investment 0.324 1.385 0.242 151s PrivateWages -0.395 0.242 0.475 151s 151s The correlations of the residuals 151s Consumption Investment PrivateWages 151s Consumption 1.000 0.293 -0.582 151s Investment 0.293 1.000 0.292 151s PrivateWages -0.582 0.292 1.000 151s 151s 151s 3SLS estimates for 'Consumption' (equation 1) 151s Model Formula: consump ~ corpProf + corpProfLag + wages 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 16.5606 1.3295 12.46 2.6e-09 *** 151s corpProf 0.1100 0.1098 1.00 0.33 151s corpProfLag 0.1155 0.1007 1.15 0.27 151s wages 0.8086 0.0401 20.18 2.8e-12 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.097 on 15 degrees of freedom 151s Number of observations: 19 Degrees of Freedom: 15 151s SSR: 18.051 MSE: 1.203 Root MSE: 1.097 151s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 151s 151s 151s 3SLS estimates for 'Investment' (equation 2) 151s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 23.6871 6.1159 3.87 0.00135 ** 151s corpProf 0.1072 0.1414 0.76 0.45918 151s corpProfLag 0.6278 0.1361 4.61 0.00029 *** 151s capitalLag -0.1726 0.0295 -5.85 2.5e-05 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 1.395 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 31.126 MSE: 1.945 Root MSE: 1.395 151s Multiple R-Squared: 0.866 Adjusted R-Squared: 0.841 151s 151s 151s 3SLS estimates for 'PrivateWages' (equation 3) 151s Model Formula: privWage ~ gnp + gnpLag + trend 151s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 151s gnpLag 151s 151s Estimate Std. Error t value Pr(>|t|) 151s (Intercept) 1.3603 1.0927 1.24 0.23109 151s gnp 0.4117 0.0315 13.06 6.0e-10 *** 151s gnpLag 0.1782 0.0336 5.31 7.1e-05 *** 151s trend 0.1370 0.0280 4.89 0.00016 *** 151s --- 151s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 151s 151s Residual standard error: 0.803 on 16 degrees of freedom 151s Number of observations: 20 Degrees of Freedom: 16 151s SSR: 10.318 MSE: 0.645 Root MSE: 0.803 151s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 151s 151s > residuals 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 -0.29542 -1.636 -1.2658 151s 3 -0.89033 0.135 0.4198 151s 4 -1.25669 0.777 1.3578 151s 5 -0.14000 -1.574 -0.2036 151s 6 0.37365 0.341 -0.4283 151s 7 NA NA NA 151s 8 1.63850 1.194 -0.8319 151s 9 1.44030 0.454 0.2186 151s 10 NA 2.192 1.1346 151s 11 0.17274 -0.750 -0.4603 151s 12 -0.49629 -0.698 0.2476 151s 13 -0.78384 -0.976 -0.2528 151s 14 0.32420 1.365 0.4028 151s 15 -0.10364 -0.170 0.3295 151s 16 -0.00105 0.140 0.0377 151s 17 1.84421 1.862 -0.7540 151s 18 -0.36893 -0.103 0.8827 151s 19 0.14129 -3.255 -0.7764 151s 20 1.23511 0.475 -0.3230 151s 21 1.06553 0.152 -1.1453 151s 22 -1.85709 0.746 0.6843 151s > fitted 151s Consumption Investment PrivateWages 151s 1 NA NA NA 151s 2 42.2 1.436 26.8 151s 3 45.9 1.765 28.9 151s 4 50.5 4.423 32.7 151s 5 50.7 4.574 34.1 151s 6 52.2 4.759 35.8 151s 7 NA NA NA 151s 8 54.6 3.006 38.7 151s 9 55.9 2.546 39.0 151s 10 NA 2.908 40.2 151s 11 54.8 1.750 38.4 151s 12 51.4 -2.702 34.3 151s 13 46.4 -5.224 29.3 151s 14 46.2 -6.465 28.1 151s 15 48.8 -2.830 30.3 151s 16 51.3 -1.440 33.2 151s 17 55.9 0.238 37.6 151s 18 59.1 2.103 40.1 151s 19 57.4 1.355 39.0 151s 20 60.4 0.825 41.9 151s 21 63.9 3.148 46.1 151s 22 71.6 4.154 52.6 151s > predict 152s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 152s 1 NA NA NA NA 152s 2 42.2 0.475 39.6 44.7 152s 3 45.9 0.557 43.3 48.5 152s 4 50.5 0.372 48.0 52.9 152s 5 50.7 0.433 48.2 53.3 152s 6 52.2 0.438 49.7 54.7 152s 7 NA NA NA NA 152s 8 54.6 0.362 52.1 57.0 152s 9 55.9 0.401 53.4 58.3 152s 10 NA NA NA NA 152s 11 54.8 0.684 52.1 57.6 152s 12 51.4 0.563 48.8 54.0 152s 13 46.4 0.733 43.6 49.2 152s 14 46.2 0.612 43.5 48.9 152s 15 48.8 0.379 46.3 51.3 152s 16 51.3 0.334 48.9 53.7 152s 17 55.9 0.394 53.4 58.3 152s 18 59.1 0.322 56.6 61.5 152s 19 57.4 0.392 54.9 59.8 152s 20 60.4 0.462 57.8 62.9 152s 21 63.9 0.448 61.4 66.5 152s 22 71.6 0.686 68.8 74.3 152s Investment.pred Investment.se.fit Investment.lwr Investment.upr 152s 1 NA NA NA NA 152s 2 1.436 0.709 -1.8811 4.754 152s 3 1.765 0.512 -1.3848 4.915 152s 4 4.423 0.470 1.3027 7.543 152s 5 4.574 0.392 1.5029 7.645 152s 6 4.759 0.370 1.7000 7.818 152s 7 NA NA NA NA 152s 8 3.006 0.306 -0.0214 6.033 152s 9 2.546 0.444 -0.5575 5.649 152s 10 2.908 0.488 -0.2245 6.041 152s 11 1.750 0.738 -1.5953 5.096 152s 12 -2.702 0.583 -5.9068 0.503 152s 13 -5.224 0.743 -8.5738 -1.874 152s 14 -6.465 0.780 -9.8530 -3.077 152s 15 -2.830 0.378 -5.8936 0.233 152s 16 -1.440 0.326 -4.4762 1.597 152s 17 0.238 0.426 -2.8533 3.329 152s 18 2.103 0.268 -0.9077 5.114 152s 19 1.355 0.399 -1.7201 4.431 152s 20 0.825 0.474 -2.2981 3.947 152s 21 3.148 0.393 0.0761 6.220 152s 22 4.154 0.555 0.9719 7.336 152s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 152s 1 NA NA NA NA 152s 2 26.8 0.309 24.9 28.6 152s 3 28.9 0.315 27.1 30.7 152s 4 32.7 0.326 30.9 34.6 152s 5 34.1 0.236 32.3 35.9 152s 6 35.8 0.244 34.0 37.6 152s 7 NA NA NA NA 152s 8 38.7 0.237 37.0 40.5 152s 9 39.0 0.225 37.2 40.7 152s 10 40.2 0.219 38.4 41.9 152s 11 38.4 0.309 36.5 40.2 152s 12 34.3 0.336 32.4 36.1 152s 13 29.3 0.411 27.3 31.2 152s 14 28.1 0.326 26.3 29.9 152s 15 30.3 0.313 28.4 32.1 152s 16 33.2 0.262 31.4 35.0 152s 17 37.6 0.265 35.8 39.3 152s 18 40.1 0.205 38.4 41.9 152s 19 39.0 0.323 37.1 40.8 152s 20 41.9 0.282 40.1 43.7 152s 21 46.1 0.293 44.3 48.0 152s 22 52.6 0.463 50.7 54.6 152s > model.frame 152s [1] TRUE 152s > model.matrix 152s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 152s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 152s [3] "Numeric: lengths (732, 708) differ" 152s > nobs 152s [1] 59 152s > linearHypothesis 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 47 1 0.23 0.64 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 47 1 0.31 0.58 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 48 152s 2 47 1 0.31 0.58 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 49 152s 2 47 2 0.5 0.61 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 49 152s 2 47 2 0.68 0.51 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 49 152s 2 47 2 1.37 0.5 152s > logLik 152s 'log Lik.' -71 (df=18) 152s 'log Lik.' -81.1 (df=18) 152s Estimating function 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 -2.7455 -36.891 152s Consumption_3 -1.0626 -17.729 152s Consumption_4 -0.0885 -1.678 152s Consumption_5 -3.0649 -63.238 152s Consumption_6 0.7553 14.561 152s Consumption_8 5.9278 102.010 152s Consumption_9 4.6365 88.027 152s Consumption_11 -1.1219 -18.435 152s Consumption_12 -1.0756 -13.439 152s Consumption_13 -3.1243 -28.309 152s Consumption_14 2.5683 23.826 152s Consumption_15 -1.2839 -16.033 152s Consumption_16 -1.2479 -17.951 152s Consumption_17 7.5868 111.454 152s Consumption_18 -1.1010 -21.581 152s Consumption_19 -5.4018 -103.426 152s Consumption_20 3.8300 67.171 152s Consumption_21 1.5068 30.633 152s Consumption_22 -1.8041 -41.092 152s Investment_2 1.3384 17.984 152s Investment_3 -0.1231 -2.053 152s Investment_4 -0.5511 -10.444 152s Investment_5 1.3722 28.313 152s Investment_6 -0.3224 -6.215 152s Investment_8 -1.1676 -20.092 152s Investment_9 -0.4950 -9.397 152s Investment_10 0.0000 0.000 152s Investment_11 0.6975 11.462 152s Investment_12 0.6591 8.235 152s Investment_13 0.9331 8.455 152s Investment_14 -1.2380 -11.485 152s Investment_15 0.1758 2.195 152s Investment_16 -0.0882 -1.269 152s Investment_17 -1.7103 -25.126 152s Investment_18 0.2715 5.322 152s Investment_19 2.9123 55.761 152s Investment_20 -0.5118 -8.975 152s Investment_21 -0.2046 -4.160 152s Investment_22 -0.6426 -14.637 152s PrivateWages_2 -3.2663 -43.888 152s PrivateWages_3 1.1062 18.456 152s PrivateWages_4 2.8429 53.880 152s PrivateWages_5 -2.9330 -60.515 152s PrivateWages_6 -0.4678 -9.018 152s PrivateWages_8 1.7117 29.456 152s PrivateWages_9 1.9856 37.698 152s PrivateWages_10 0.0000 0.000 152s PrivateWages_11 -2.6089 -42.870 152s PrivateWages_12 -0.5972 -7.462 152s PrivateWages_13 -2.3655 -21.434 152s PrivateWages_14 2.8394 26.341 152s PrivateWages_15 -0.5146 -6.427 152s PrivateWages_16 -0.6088 -8.757 152s PrivateWages_17 2.4972 36.686 152s PrivateWages_18 -0.0214 -0.419 152s PrivateWages_19 -6.8265 -130.705 152s PrivateWages_20 1.3447 23.584 152s PrivateWages_21 -1.4002 -28.468 152s PrivateWages_22 2.2878 52.110 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 -34.868 -81.19 152s Consumption_3 -13.177 -33.85 152s Consumption_4 -1.496 -3.14 152s Consumption_5 -56.394 -118.79 152s Consumption_6 14.654 29.20 152s Consumption_8 116.186 236.05 152s Consumption_9 91.802 193.78 152s Consumption_11 -24.345 -48.21 152s Consumption_12 -16.779 -42.24 152s Consumption_13 -35.617 -109.94 152s Consumption_14 17.978 84.77 152s Consumption_15 -14.380 -47.92 152s Consumption_16 -15.349 -50.04 152s Consumption_17 106.215 316.24 152s Consumption_18 -19.377 -52.50 152s Consumption_19 -93.451 -266.03 152s Consumption_20 58.598 185.77 152s Consumption_21 28.629 80.45 152s Consumption_22 -38.066 -109.75 152s Investment_2 16.998 39.58 152s Investment_3 -1.526 -3.92 152s Investment_4 -9.313 -19.52 152s Investment_5 25.249 53.18 152s Investment_6 -6.254 -12.46 152s Investment_8 -22.884 -46.49 152s Investment_9 -9.800 -20.69 152s Investment_10 0.000 0.00 152s Investment_11 15.136 29.97 152s Investment_12 10.282 25.88 152s Investment_13 10.638 32.84 152s Investment_14 -8.666 -40.86 152s Investment_15 1.969 6.56 152s Investment_16 -1.085 -3.54 152s Investment_17 -23.945 -71.29 152s Investment_18 4.779 12.95 152s Investment_19 50.383 143.43 152s Investment_20 -7.830 -24.82 152s Investment_21 -3.888 -10.92 152s Investment_22 -13.559 -39.09 152s PrivateWages_2 -41.482 -96.59 152s PrivateWages_3 13.717 35.24 152s PrivateWages_4 48.044 100.73 152s PrivateWages_5 -53.966 -113.67 152s PrivateWages_6 -9.075 -18.08 152s PrivateWages_8 33.550 68.16 152s PrivateWages_9 39.314 82.99 152s PrivateWages_10 0.000 0.00 152s PrivateWages_11 -56.613 -112.10 152s PrivateWages_12 -9.317 -23.46 152s PrivateWages_13 -26.967 -83.24 152s PrivateWages_14 19.876 93.71 152s PrivateWages_15 -5.764 -19.21 152s PrivateWages_16 -7.488 -24.41 152s PrivateWages_17 34.961 104.09 152s PrivateWages_18 -0.376 -1.02 152s PrivateWages_19 -118.099 -336.20 152s PrivateWages_20 20.574 65.22 152s PrivateWages_21 -26.605 -74.76 152s PrivateWages_22 48.272 139.18 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 1.1993 15.540 152s Consumption_3 0.4642 7.754 152s Consumption_4 0.0387 0.740 152s Consumption_5 1.3388 28.029 152s Consumption_6 -0.3299 -6.424 152s Consumption_8 -2.5893 -44.384 152s Consumption_9 -2.0252 -39.469 152s Consumption_11 0.4900 8.255 152s Consumption_12 0.4698 5.957 152s Consumption_13 1.3647 12.176 152s Consumption_14 -1.1219 -10.434 152s Consumption_15 0.5608 7.176 152s Consumption_16 0.5451 7.773 152s Consumption_17 -3.3140 -48.887 152s Consumption_18 0.4809 9.399 152s Consumption_19 2.3595 45.678 152s Consumption_20 -1.6729 -29.086 152s Consumption_21 -0.6582 -13.228 152s Consumption_22 0.7880 18.015 152s Investment_2 -2.2459 -29.102 152s Investment_3 0.2065 3.450 152s Investment_4 0.9247 17.694 152s Investment_5 -2.3026 -48.209 152s Investment_6 0.5410 10.532 152s Investment_8 1.9592 33.583 152s Investment_9 0.8306 16.187 152s Investment_10 3.0781 62.986 152s Investment_11 -1.1704 -19.716 152s Investment_12 -1.1059 -14.023 152s Investment_13 -1.5658 -13.970 152s Investment_14 2.0775 19.321 152s Investment_15 -0.2950 -3.775 152s Investment_16 0.1480 2.111 152s Investment_17 2.8700 42.338 152s Investment_18 -0.4556 -8.905 152s Investment_19 -4.8870 -94.607 152s Investment_20 0.8587 14.930 152s Investment_21 0.3434 6.901 152s Investment_22 1.0783 24.652 152s PrivateWages_2 1.8660 24.179 152s PrivateWages_3 -0.6320 -10.557 152s PrivateWages_4 -1.6241 -31.077 152s PrivateWages_5 1.6755 35.080 152s PrivateWages_6 0.2672 5.203 152s PrivateWages_8 -0.9779 -16.762 152s PrivateWages_9 -1.1343 -22.106 152s PrivateWages_10 -2.1296 -43.576 152s PrivateWages_11 1.4904 25.106 152s PrivateWages_12 0.3412 4.326 152s PrivateWages_13 1.3514 12.057 152s PrivateWages_14 -1.6221 -15.086 152s PrivateWages_15 0.2940 3.762 152s PrivateWages_16 0.3478 4.959 152s PrivateWages_17 -1.4266 -21.045 152s PrivateWages_18 0.0122 0.239 152s PrivateWages_19 3.8998 75.496 152s PrivateWages_20 -0.7682 -13.356 152s PrivateWages_21 0.7999 16.078 152s PrivateWages_22 -1.3070 -29.879 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 15.231 219.22 152s Consumption_3 5.756 84.76 152s Consumption_4 0.654 7.13 152s Consumption_5 24.633 253.96 152s Consumption_6 -6.401 -63.58 152s Consumption_8 -50.751 -526.67 152s Consumption_9 -40.100 -420.44 152s Consumption_11 10.634 105.70 152s Consumption_12 7.329 101.81 152s Consumption_13 15.558 291.09 152s Consumption_14 -7.853 -232.34 152s Consumption_15 6.281 113.29 152s Consumption_16 6.705 108.47 152s Consumption_17 -46.395 -655.17 152s Consumption_18 8.464 96.09 152s Consumption_19 40.820 476.15 152s Consumption_20 -25.596 -334.42 152s Consumption_21 -12.505 -132.42 152s Consumption_22 16.627 161.15 152s Investment_2 -28.522 -410.54 152s Investment_3 2.561 37.71 152s Investment_4 15.627 170.61 152s Investment_5 -42.368 -436.81 152s Investment_6 10.495 104.25 152s Investment_8 38.400 398.50 152s Investment_9 16.445 172.43 152s Investment_10 64.949 648.26 152s Investment_11 -25.398 -252.46 152s Investment_12 -17.253 -239.66 152s Investment_13 -17.850 -333.99 152s Investment_14 14.542 430.24 152s Investment_15 -3.304 -59.59 152s Investment_16 1.821 29.46 152s Investment_17 40.180 567.40 152s Investment_18 -8.019 -91.03 152s Investment_19 -84.545 -986.19 152s Investment_20 13.139 171.66 152s Investment_21 6.524 69.08 152s Investment_22 22.753 220.52 152s PrivateWages_2 23.698 341.10 152s PrivateWages_3 -7.836 -115.39 152s PrivateWages_4 -27.446 -299.64 152s PrivateWages_5 30.830 317.85 152s PrivateWages_6 5.185 51.50 152s PrivateWages_8 -19.166 -198.90 152s PrivateWages_9 -22.459 -235.48 152s PrivateWages_10 -44.934 -448.49 152s PrivateWages_11 32.341 321.48 152s PrivateWages_12 5.323 73.94 152s PrivateWages_13 15.406 288.25 152s PrivateWages_14 -11.355 -335.93 152s PrivateWages_15 3.293 59.39 152s PrivateWages_16 4.278 69.21 152s PrivateWages_17 -19.973 -282.04 152s PrivateWages_18 0.215 2.44 152s PrivateWages_19 67.467 786.98 152s PrivateWages_20 -11.753 -153.56 152s PrivateWages_21 15.199 160.94 152s PrivateWages_22 -27.577 -267.27 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 -2.6531 -124.88 -119.13 152s Consumption_3 -1.0269 -50.91 -46.83 152s Consumption_4 -0.0856 -4.84 -4.29 152s Consumption_5 -2.9618 -179.74 -169.41 152s Consumption_6 0.7299 44.24 41.68 152s Consumption_8 5.7284 343.69 366.62 152s Consumption_9 4.4804 278.99 288.54 152s Consumption_11 -1.0841 -69.07 -72.64 152s Consumption_12 -1.0394 -56.99 -63.61 152s Consumption_13 -3.0192 -141.83 -161.22 152s Consumption_14 2.4819 104.56 109.95 152s Consumption_15 -1.2407 -63.55 -55.96 152s Consumption_16 -1.2059 -66.73 -59.93 152s Consumption_17 7.3315 420.78 398.83 152s Consumption_18 -1.0639 -71.47 -66.71 152s Consumption_19 -5.2200 -357.64 -339.30 152s Consumption_20 3.7011 247.40 225.40 152s Consumption_21 1.4561 109.01 101.20 152s Consumption_22 -1.7434 -151.46 -131.97 152s Investment_2 1.6915 79.62 75.95 152s Investment_3 -0.1555 -7.71 -7.09 152s Investment_4 -0.6965 -39.38 -34.89 152s Investment_5 1.7343 105.25 99.20 152s Investment_6 -0.4074 -24.70 -23.26 152s Investment_8 -1.4756 -88.53 -94.44 152s Investment_9 -0.6256 -38.95 -40.29 152s Investment_10 -2.3184 -149.69 -149.53 152s Investment_11 0.8815 56.16 59.06 152s Investment_12 0.8330 45.67 50.98 152s Investment_13 1.1793 55.40 62.98 152s Investment_14 -1.5647 -65.92 -69.32 152s Investment_15 0.2222 11.38 10.02 152s Investment_16 -0.1115 -6.17 -5.54 152s Investment_17 -2.1616 -124.06 -117.59 152s Investment_18 0.3432 23.05 21.52 152s Investment_19 3.6807 252.18 239.25 152s Investment_20 -0.6468 -43.23 -39.39 152s Investment_21 -0.2586 -19.36 -17.97 152s Investment_22 -0.8122 -70.56 -61.48 152s PrivateWages_2 -7.4676 -351.50 -335.29 152s PrivateWages_3 2.5291 125.39 115.33 152s PrivateWages_4 6.4995 367.50 325.62 152s PrivateWages_5 -6.7054 -406.93 -383.55 152s PrivateWages_6 -1.0695 -64.82 -61.07 152s PrivateWages_8 3.9134 234.79 250.46 152s PrivateWages_9 4.5395 282.67 292.34 152s PrivateWages_10 8.5226 550.30 549.71 152s PrivateWages_11 -5.9646 -380.01 -399.63 152s PrivateWages_12 -1.3654 -74.87 -83.57 152s PrivateWages_13 -5.4082 -254.06 -288.80 152s PrivateWages_14 6.4916 273.48 287.58 152s PrivateWages_15 -1.1766 -60.26 -53.06 152s PrivateWages_16 -1.3918 -77.02 -69.17 152s PrivateWages_17 5.7093 327.68 310.59 152s PrivateWages_18 -0.0489 -3.28 -3.07 152s PrivateWages_19 -15.6071 -1069.28 -1014.46 152s PrivateWages_20 3.0743 205.50 187.22 152s PrivateWages_21 -3.2013 -239.67 -222.49 152s PrivateWages_22 5.2304 454.42 395.94 152s PrivateWages_trend 152s Consumption_2 26.531 152s Consumption_3 9.242 152s Consumption_4 0.684 152s Consumption_5 20.732 152s Consumption_6 -4.380 152s Consumption_8 -22.913 152s Consumption_9 -13.441 152s Consumption_11 1.084 152s Consumption_12 0.000 152s Consumption_13 -3.019 152s Consumption_14 4.964 152s Consumption_15 -3.722 152s Consumption_16 -4.824 152s Consumption_17 36.658 152s Consumption_18 -6.384 152s Consumption_19 -36.540 152s Consumption_20 29.609 152s Consumption_21 13.105 152s Consumption_22 -17.434 152s Investment_2 -16.915 152s Investment_3 1.400 152s Investment_4 5.572 152s Investment_5 -12.140 152s Investment_6 2.445 152s Investment_8 5.902 152s Investment_9 1.877 152s Investment_10 4.637 152s Investment_11 -0.882 152s Investment_12 0.000 152s Investment_13 1.179 152s Investment_14 -3.129 152s Investment_15 0.667 152s Investment_16 -0.446 152s Investment_17 -10.808 152s Investment_18 2.059 152s Investment_19 25.765 152s Investment_20 -5.174 152s Investment_21 -2.327 152s Investment_22 -8.122 152s PrivateWages_2 74.676 152s PrivateWages_3 -22.762 152s PrivateWages_4 -51.996 152s PrivateWages_5 46.938 152s PrivateWages_6 6.417 152s PrivateWages_8 -15.654 152s PrivateWages_9 -13.618 152s PrivateWages_10 -17.045 152s PrivateWages_11 5.965 152s PrivateWages_12 0.000 152s PrivateWages_13 -5.408 152s PrivateWages_14 12.983 152s PrivateWages_15 -3.530 152s PrivateWages_16 -5.567 152s PrivateWages_17 28.547 152s PrivateWages_18 -0.293 152s PrivateWages_19 -109.250 152s PrivateWages_20 24.594 152s PrivateWages_21 -28.812 152s PrivateWages_22 52.304 152s [1] TRUE 152s > Bread 152s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 152s [1,] 104.28657 -1.0082 -0.4696 152s [2,] -1.00824 0.7107 -0.4494 152s [3,] -0.46959 -0.4494 0.5979 152s [4,] -1.85053 -0.0857 -0.0409 152s [5,] 80.53000 1.3241 3.0428 152s [6,] -1.81359 0.2334 -0.2583 152s [7,] 0.54047 -0.1847 0.2826 152s [8,] -0.28778 -0.0112 -0.0165 152s [9,] -35.77159 0.2050 1.7044 152s [10,] 0.58031 -0.0870 0.0510 152s [11,] -0.00461 0.0862 -0.0821 152s [12,] 0.19369 0.0416 0.0268 152s Consumption_wages Investment_(Intercept) Investment_corpProf 152s [1,] -1.850529 80.530 -1.81359 152s [2,] -0.085701 1.324 0.23344 152s [3,] -0.040883 3.043 -0.25828 152s [4,] 0.094773 -3.542 0.04931 152s [5,] -3.542001 2206.842 -34.41529 152s [6,] 0.049311 -34.415 1.17951 152s [7,] -0.048133 29.517 -1.02562 152s [8,] 0.017421 -10.487 0.15573 152s [9,] 0.083728 18.025 -0.14810 152s [10,] 0.000958 1.156 0.00386 152s [11,] -0.002304 -1.519 -0.00126 152s [12,] -0.031989 -0.955 0.01443 152s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 152s [1,] 0.54047 -0.28778 -35.7716 152s [2,] -0.18475 -0.01117 0.2050 152s [3,] 0.28258 -0.01647 1.7044 152s [4,] -0.04813 0.01742 0.0837 152s [5,] 29.51706 -10.48672 18.0248 152s [6,] -1.02562 0.15573 -0.1481 152s [7,] 1.09362 -0.14971 -0.4803 152s [8,] -0.14971 0.05132 -0.0381 152s [9,] -0.48030 -0.03806 70.4425 152s [10,] 0.00353 -0.00637 -0.4681 152s [11,] 0.00471 0.00732 -0.7110 152s [12,] -0.02247 0.00534 0.8424 152s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 152s [1,] 0.580315 -0.00461 0.19369 152s [2,] -0.086985 0.08623 0.04160 152s [3,] 0.051027 -0.08213 0.02678 152s [4,] 0.000958 -0.00230 -0.03199 152s [5,] 1.156385 -1.51874 -0.95497 152s [6,] 0.003856 -0.00126 0.01443 152s [7,] 0.003528 0.00471 -0.02247 152s [8,] -0.006374 0.00732 0.00534 152s [9,] -0.468096 -0.71104 0.84245 152s [10,] 0.058634 -0.05251 -0.01709 152s [11,] -0.052508 0.06655 0.00301 152s [12,] -0.017087 0.00301 0.04635 152s > 152s > # I3SLS 152s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 152s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 152s > summary 152s 152s systemfit results 152s method: iterated 3SLS 152s 152s convergence achieved after 15 iterations 152s 152s N DF SSR detRCov OLS-R2 McElroy-R2 152s system 59 47 81.3 0.349 0.958 0.995 152s 152s N DF SSR MSE RMSE R2 Adj R2 152s Consumption 19 15 18.1 1.209 1.100 0.980 0.976 152s Investment 20 16 52.0 3.250 1.803 0.776 0.735 152s PrivateWages 20 16 11.2 0.699 0.836 0.986 0.983 152s 152s The covariance matrix of the residuals used for estimation 152s Consumption Investment PrivateWages 152s Consumption 0.955 0.456 -0.421 152s Investment 0.456 2.294 0.375 152s PrivateWages -0.421 0.375 0.522 152s 152s The covariance matrix of the residuals 152s Consumption Investment PrivateWages 152s Consumption 0.955 0.456 -0.421 152s Investment 0.456 2.294 0.375 152s PrivateWages -0.421 0.375 0.522 152s 152s The correlations of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.000 0.322 -0.582 152s Investment 0.322 1.000 0.341 152s PrivateWages -0.582 0.341 1.000 152s 152s 152s 3SLS estimates for 'Consumption' (equation 1) 152s Model Formula: consump ~ corpProf + corpProfLag + wages 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 16.8311 1.2489 13.48 8.7e-10 *** 152s corpProf 0.1468 0.0991 1.48 0.16 152s corpProfLag 0.0924 0.0906 1.02 0.32 152s wages 0.7945 0.0371 21.43 1.2e-12 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.1 on 15 degrees of freedom 152s Number of observations: 19 Degrees of Freedom: 15 152s SSR: 18.14 MSE: 1.209 Root MSE: 1.1 152s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 152s 152s 152s 3SLS estimates for 'Investment' (equation 2) 152s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 32.4128 8.2695 3.92 0.00122 ** 152s corpProf -0.0799 0.1934 -0.41 0.68498 152s corpProfLag 0.7607 0.1878 4.05 0.00093 *** 152s capitalLag -0.2114 0.0400 -5.29 7.4e-05 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.803 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 51.999 MSE: 3.25 Root MSE: 1.803 152s Multiple R-Squared: 0.776 Adjusted R-Squared: 0.735 152s 152s 152s 3SLS estimates for 'PrivateWages' (equation 3) 152s Model Formula: privWage ~ gnp + gnpLag + trend 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 1.5421 1.1496 1.34 0.19852 152s gnp 0.3936 0.0313 12.57 1.0e-09 *** 152s gnpLag 0.1945 0.0328 5.93 2.1e-05 *** 152s trend 0.1416 0.0286 4.95 0.00014 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 0.836 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 11.181 MSE: 0.699 Root MSE: 0.836 152s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.983 152s 152s > residuals 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 -0.3309 -2.6308 -1.3061 152s 3 -1.0419 0.0146 0.4450 152s 4 -1.2918 0.4128 1.4338 152s 5 -0.1772 -1.7488 -0.2494 152s 6 0.3563 0.2807 -0.4066 152s 7 NA NA NA 152s 8 1.6778 1.4671 -0.8700 152s 9 1.4561 1.1068 0.1712 152s 10 NA 2.9002 1.1262 152s 11 0.4237 -1.0652 -0.6189 152s 12 -0.2711 -0.9488 0.0375 152s 13 -0.5643 -1.6241 -0.5055 152s 14 0.2845 1.8477 0.3080 152s 15 -0.0514 -0.2379 0.3003 152s 16 0.0521 0.1268 0.0141 152s 17 1.8733 2.2462 -0.7083 152s 18 -0.1962 -0.1724 0.8305 152s 19 0.3553 -3.5810 -0.9448 152s 20 1.3161 1.0343 -0.2738 152s 21 1.2055 0.6622 -1.1283 152s 22 -1.6327 1.5541 0.8257 152s > fitted 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 42.2 2.431 26.8 152s 3 46.0 1.885 28.9 152s 4 50.5 4.787 32.7 152s 5 50.8 4.749 34.1 152s 6 52.2 4.819 35.8 152s 7 NA NA NA 152s 8 54.5 2.733 38.8 152s 9 55.8 1.893 39.0 152s 10 NA 2.200 40.2 152s 11 54.6 2.065 38.5 152s 12 51.2 -2.451 34.5 152s 13 46.2 -4.576 29.5 152s 14 46.2 -6.948 28.2 152s 15 48.8 -2.762 30.3 152s 16 51.2 -1.427 33.2 152s 17 55.8 -0.146 37.5 152s 18 58.9 2.172 40.2 152s 19 57.1 1.681 39.1 152s 20 60.3 0.266 41.9 152s 21 63.8 2.638 46.1 152s 22 71.3 3.346 52.5 152s > predict 152s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 152s 1 NA NA NA NA 152s 2 42.2 0.446 41.3 43.1 152s 3 46.0 0.511 45.0 47.1 152s 4 50.5 0.340 49.8 51.2 152s 5 50.8 0.393 50.0 51.6 152s 6 52.2 0.396 51.4 53.0 152s 7 NA NA NA NA 152s 8 54.5 0.326 53.9 55.2 152s 9 55.8 0.362 55.1 56.6 152s 10 NA NA NA NA 152s 11 54.6 0.612 53.3 55.8 152s 12 51.2 0.511 50.1 52.2 152s 13 46.2 0.671 44.8 47.5 152s 14 46.2 0.563 45.1 47.3 152s 15 48.8 0.354 48.0 49.5 152s 16 51.2 0.311 50.6 51.9 152s 17 55.8 0.362 55.1 56.6 152s 18 58.9 0.297 58.3 59.5 152s 19 57.1 0.357 56.4 57.9 152s 20 60.3 0.427 59.4 61.1 152s 21 63.8 0.416 63.0 64.6 152s 22 71.3 0.640 70.0 72.6 152s Investment.pred Investment.se.fit Investment.lwr Investment.upr 152s 1 NA NA NA NA 152s 2 2.431 0.970 0.4798 4.382 152s 3 1.885 0.745 0.3859 3.385 152s 4 4.787 0.664 3.4506 6.124 152s 5 4.749 0.562 3.6174 5.880 152s 6 4.819 0.537 3.7391 5.900 152s 7 NA NA NA NA 152s 8 2.733 0.446 1.8351 3.631 152s 9 1.893 0.620 0.6455 3.141 152s 10 2.200 0.684 0.8232 3.576 152s 11 2.065 1.055 -0.0569 4.187 152s 12 -2.451 0.845 -4.1517 -0.751 152s 13 -4.576 1.070 -6.7293 -2.423 152s 14 -6.948 1.103 -9.1676 -4.728 152s 15 -2.762 0.556 -3.8806 -1.644 152s 16 -1.427 0.480 -2.3919 -0.462 152s 17 -0.146 0.603 -1.3588 1.066 152s 18 2.172 0.390 1.3869 2.958 152s 19 1.681 0.563 0.5476 2.815 152s 20 0.266 0.661 -1.0634 1.595 152s 21 2.638 0.558 1.5144 3.761 152s 22 3.346 0.778 1.7808 4.911 152s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 152s 1 NA NA NA NA 152s 2 26.8 0.326 26.2 27.5 152s 3 28.9 0.328 28.2 29.5 152s 4 32.7 0.334 32.0 33.3 152s 5 34.1 0.242 33.7 34.6 152s 6 35.8 0.252 35.3 36.3 152s 7 NA NA NA NA 152s 8 38.8 0.244 38.3 39.3 152s 9 39.0 0.232 38.6 39.5 152s 10 40.2 0.230 39.7 40.6 152s 11 38.5 0.308 37.9 39.1 152s 12 34.5 0.336 33.8 35.1 152s 13 29.5 0.420 28.7 30.4 152s 14 28.2 0.345 27.5 28.9 152s 15 30.3 0.325 29.6 31.0 152s 16 33.2 0.271 32.6 33.7 152s 17 37.5 0.267 37.0 38.0 152s 18 40.2 0.218 39.7 40.6 152s 19 39.1 0.331 38.5 39.8 152s 20 41.9 0.289 41.3 42.5 152s 21 46.1 0.311 45.5 46.8 152s 22 52.5 0.485 51.5 53.5 152s > model.frame 152s [1] TRUE 152s > model.matrix 152s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 152s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 152s [3] "Numeric: lengths (732, 708) differ" 152s > nobs 152s [1] 59 152s > linearHypothesis 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 47 1 0.28 0.6 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 47 1 0.37 0.55 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 48 152s 2 47 1 0.37 0.54 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 49 152s 2 47 2 1.25 0.3 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 49 152s 2 47 2 1.64 0.21 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 49 152s 2 47 2 3.28 0.19 152s > logLik 152s 'log Lik.' -74.5 (df=18) 152s 'log Lik.' -87.1 (df=18) 152s Estimating function 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 -4.75944 -63.951 152s Consumption_3 -2.22772 -37.167 152s Consumption_4 -0.38275 -7.254 152s Consumption_5 -5.30482 -109.454 152s Consumption_6 1.30597 25.176 152s Consumption_8 10.25777 176.523 152s Consumption_9 7.99665 151.823 152s Consumption_11 -1.17443 -19.299 152s Consumption_12 -1.24242 -15.523 152s Consumption_13 -4.75716 -43.103 152s Consumption_14 4.34635 40.320 152s Consumption_15 -1.98107 -24.739 152s Consumption_16 -1.93670 -27.859 152s Consumption_17 13.00314 191.023 152s Consumption_18 -1.57749 -30.922 152s Consumption_19 -8.67959 -166.185 152s Consumption_20 6.77999 118.909 152s Consumption_21 3.04771 61.962 152s Consumption_22 -2.30170 -52.427 152s Investment_2 2.92832 39.347 152s Investment_3 0.00114 0.019 152s Investment_4 -0.53396 -10.120 152s Investment_5 1.84118 37.989 152s Investment_6 -0.26074 -5.026 152s Investment_8 -1.42063 -24.447 152s Investment_9 -1.10750 -21.027 152s Investment_10 0.00000 0.000 152s Investment_11 1.09344 17.968 152s Investment_12 0.95848 11.975 152s Investment_13 1.66503 15.086 152s Investment_14 -1.92032 -17.814 152s Investment_15 0.22458 2.804 152s Investment_16 -0.16698 -2.402 152s Investment_17 -2.28568 -33.578 152s Investment_18 -0.00785 -0.154 152s Investment_19 3.68757 70.604 152s Investment_20 -1.02511 -17.979 152s Investment_21 -0.65919 -13.402 152s Investment_22 -1.70192 -38.765 152s PrivateWages_2 -6.13297 -82.407 152s PrivateWages_3 2.11354 35.262 152s PrivateWages_4 5.50774 104.386 152s PrivateWages_5 -5.40526 -111.526 152s PrivateWages_6 -0.82424 -15.889 152s PrivateWages_8 2.80754 48.314 152s PrivateWages_9 3.41557 64.847 152s PrivateWages_10 0.00000 0.000 152s PrivateWages_11 -5.23135 -85.964 152s PrivateWages_12 -1.71264 -21.398 152s PrivateWages_13 -5.07393 -45.974 152s PrivateWages_14 4.80915 44.613 152s PrivateWages_15 -0.96519 -12.053 152s PrivateWages_16 -1.15621 -16.632 152s PrivateWages_17 4.49108 65.976 152s PrivateWages_18 -0.08188 -1.605 152s PrivateWages_19 -12.82495 -245.555 152s PrivateWages_20 2.51036 44.027 152s PrivateWages_21 -2.60385 -52.938 152s PrivateWages_22 4.63537 105.582 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 -60.4449 -140.7509 152s Consumption_3 -27.6237 -70.9657 152s Consumption_4 -6.4685 -13.5614 152s Consumption_5 -97.6087 -205.5997 152s Consumption_6 25.3358 50.4846 152s Consumption_8 201.0522 408.4748 152s Consumption_9 158.3336 334.2197 152s Consumption_11 -25.4852 -50.4634 152s Consumption_12 -19.3817 -48.7944 152s Consumption_13 -54.2317 -167.3998 152s Consumption_14 30.4244 143.4489 152s Consumption_15 -22.1880 -73.9440 152s Consumption_16 -23.8214 -77.6627 152s Consumption_17 182.0440 542.0110 152s Consumption_18 -27.7639 -75.2217 152s Consumption_19 -150.1568 -427.4616 152s Consumption_20 103.7339 328.8605 152s Consumption_21 57.9064 162.7199 152s Consumption_22 -48.5659 -140.0278 152s Investment_2 37.1896 86.5991 152s Investment_3 0.0141 0.0362 152s Investment_4 -9.0240 -18.9190 152s Investment_5 33.8777 71.3589 152s Investment_6 -5.0583 -10.0793 152s Investment_8 -27.8443 -56.5709 152s Investment_9 -21.9285 -46.2880 152s Investment_10 0.0000 0.0000 152s Investment_11 23.7276 46.9832 152s Investment_12 14.9524 37.6432 152s Investment_13 18.9813 58.5907 152s Investment_14 -13.4423 -63.3793 152s Investment_15 2.5153 8.3824 152s Investment_16 -2.0538 -6.6959 152s Investment_17 -31.9996 -95.2743 152s Investment_18 -0.1382 -0.3745 152s Investment_19 63.7949 181.6093 152s Investment_20 -15.6841 -49.7224 152s Investment_21 -12.5246 -35.1949 152s Investment_22 -35.9105 -103.5390 152s PrivateWages_2 -77.8887 -181.3703 152s PrivateWages_3 26.2079 67.3285 152s PrivateWages_4 93.0807 195.1464 152s PrivateWages_5 -99.4568 -209.4924 152s PrivateWages_6 -15.9902 -31.8624 152s PrivateWages_8 55.0278 111.7991 152s PrivateWages_9 67.6282 142.7536 152s PrivateWages_10 0.0000 0.0000 152s PrivateWages_11 -113.5202 -224.7822 152s PrivateWages_12 -26.7172 -67.2617 152s PrivateWages_13 -57.8428 -178.5466 152s PrivateWages_14 33.6641 158.7235 152s PrivateWages_15 -10.8101 -36.0260 152s PrivateWages_16 -14.2214 -46.3646 152s PrivateWages_17 62.8751 187.2021 152s PrivateWages_18 -1.4410 -3.9043 152s PrivateWages_19 -221.8716 -631.6170 152s PrivateWages_20 38.4085 121.7638 152s PrivateWages_21 -49.4732 -139.0222 152s PrivateWages_22 97.8064 282.0006 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 1.782157 23.0934 152s Consumption_3 0.834162 13.9344 152s Consumption_4 0.143320 2.7425 152s Consumption_5 1.986375 41.5880 152s Consumption_6 -0.489016 -9.5207 152s Consumption_8 -3.840991 -65.8399 152s Consumption_9 -2.994321 -58.3554 152s Consumption_11 0.439763 7.4080 152s Consumption_12 0.465220 5.8989 152s Consumption_13 1.781306 15.8927 152s Consumption_14 -1.627477 -15.1363 152s Consumption_15 0.741807 9.4914 152s Consumption_16 0.725191 10.3407 152s Consumption_17 -4.868989 -71.8262 152s Consumption_18 0.590688 11.5449 152s Consumption_19 3.250046 62.9174 152s Consumption_20 -2.538748 -44.1394 152s Consumption_21 -1.141204 -22.9368 152s Consumption_22 0.861865 19.7035 152s Investment_2 -2.373514 -30.7562 152s Investment_3 -0.000921 -0.0154 152s Investment_4 0.432798 8.2817 152s Investment_5 -1.492349 -31.2447 152s Investment_6 0.211337 4.1146 152s Investment_8 1.151475 19.7379 152s Investment_9 0.897673 17.4945 152s Investment_10 2.570865 52.6054 152s Investment_11 -0.886274 -14.9297 152s Investment_12 -0.776889 -9.8508 152s Investment_13 -1.349570 -12.0408 152s Investment_14 1.556498 14.4761 152s Investment_15 -0.182029 -2.3291 152s Investment_16 0.135342 1.9299 152s Investment_17 1.852635 27.3297 152s Investment_18 0.006366 0.1244 152s Investment_19 -2.988917 -57.8622 152s Investment_20 0.830890 14.4461 152s Investment_21 0.534301 10.7388 152s Investment_22 1.379471 31.5367 152s PrivateWages_2 2.964495 38.4142 152s PrivateWages_3 -1.021623 -17.0659 152s PrivateWages_4 -2.662277 -50.9436 152s PrivateWages_5 2.612743 54.7020 152s PrivateWages_6 0.398411 7.7567 152s PrivateWages_8 -1.357082 -23.2623 152s PrivateWages_9 -1.650985 -32.1755 152s PrivateWages_10 -3.276467 -67.0436 152s PrivateWages_11 2.528678 42.5968 152s PrivateWages_12 0.827840 10.4968 152s PrivateWages_13 2.452590 21.8819 152s PrivateWages_14 -2.324602 -21.6199 152s PrivateWages_15 0.466545 5.9694 152s PrivateWages_16 0.558877 7.9692 152s PrivateWages_17 -2.170857 -32.0240 152s PrivateWages_18 0.039577 0.7735 152s PrivateWages_19 6.199203 120.0098 152s PrivateWages_20 -1.213433 -21.0971 152s PrivateWages_21 1.258626 25.2969 152s PrivateWages_22 -2.240603 -51.2233 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 22.6334 325.778 152s Consumption_3 10.3436 152.318 152s Consumption_4 2.4221 26.443 152s Consumption_5 36.5493 376.815 152s Consumption_6 -9.4869 -94.233 152s Consumption_8 -75.2834 -781.258 152s Consumption_9 -59.2876 -621.621 152s Consumption_11 9.5429 94.857 152s Consumption_12 7.2574 100.813 152s Consumption_13 20.3069 379.952 152s Consumption_14 -11.3923 -337.050 152s Consumption_15 8.3082 149.845 152s Consumption_16 8.9199 144.313 152s Consumption_17 -68.1658 -962.599 152s Consumption_18 10.3961 118.019 152s Consumption_19 56.2258 655.859 152s Consumption_20 -38.8428 -507.496 152s Consumption_21 -21.6829 -229.610 152s Consumption_22 18.1854 176.251 152s Investment_2 -30.1436 -433.878 152s Investment_3 -0.0114 -0.168 152s Investment_4 7.3143 79.851 152s Investment_5 -27.4592 -283.099 152s Investment_6 4.0999 40.725 152s Investment_8 22.5689 234.210 152s Investment_9 17.7739 186.357 152s Investment_10 54.2453 541.424 152s Investment_11 -19.2321 -191.169 152s Investment_12 -12.1195 -168.352 152s Investment_13 -15.3851 -287.863 152s Investment_14 10.8955 322.351 152s Investment_15 -2.0387 -36.770 152s Investment_16 1.6647 26.933 152s Investment_17 25.9369 366.266 152s Investment_18 0.1120 1.272 152s Investment_19 -51.7083 -603.163 152s Investment_20 12.7126 166.095 152s Investment_21 10.1517 107.501 152s Investment_22 29.1068 282.102 152s PrivateWages_2 37.6491 541.910 152s PrivateWages_3 -12.6681 -186.548 152s PrivateWages_4 -44.9925 -491.190 152s PrivateWages_5 48.0745 495.637 152s PrivateWages_6 7.7292 76.774 152s PrivateWages_8 -26.5988 -276.031 152s PrivateWages_9 -32.6895 -342.744 152s PrivateWages_10 -69.1335 -690.024 152s PrivateWages_11 54.8723 545.436 152s PrivateWages_12 12.9143 179.393 152s PrivateWages_13 27.9595 523.137 152s PrivateWages_14 -16.2722 -481.425 152s PrivateWages_15 5.2253 94.242 152s PrivateWages_16 6.8742 111.217 152s PrivateWages_17 -30.3920 -429.178 152s PrivateWages_18 0.6966 7.908 152s PrivateWages_19 107.2462 1250.999 152s PrivateWages_20 -18.5655 -242.565 152s PrivateWages_21 23.9139 253.236 152s PrivateWages_22 -47.2767 -458.203 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 -5.12212 -2.41e+02 -229.983 152s Consumption_3 -2.39748 -1.19e+02 -109.325 152s Consumption_4 -0.41192 -2.33e+01 -20.637 152s Consumption_5 -5.70906 -3.46e+02 -326.558 152s Consumption_6 1.40549 8.52e+01 80.253 152s Consumption_8 11.03944 6.62e+02 706.524 152s Consumption_9 8.60601 5.36e+02 554.227 152s Consumption_11 -1.26393 -8.05e+01 -84.683 152s Consumption_12 -1.33709 -7.33e+01 -81.830 152s Consumption_13 -5.11967 -2.41e+02 -273.390 152s Consumption_14 4.67755 1.97e+02 207.216 152s Consumption_15 -2.13204 -1.09e+02 -96.155 152s Consumption_16 -2.08428 -1.15e+02 -103.589 152s Consumption_17 13.99402 8.03e+02 761.275 152s Consumption_18 -1.69770 -1.14e+02 -106.446 152s Consumption_19 -9.34099 -6.40e+02 -607.165 152s Consumption_20 7.29665 4.88e+02 444.366 152s Consumption_21 3.27995 2.46e+02 227.957 152s Consumption_22 -2.47710 -2.15e+02 -187.516 152s Investment_2 4.06820 1.91e+02 182.662 152s Investment_3 0.00158 7.83e-02 0.072 152s Investment_4 -0.74181 -4.19e+01 -37.165 152s Investment_5 2.55788 1.55e+02 146.311 152s Investment_6 -0.36223 -2.20e+01 -20.683 152s Investment_8 -1.97362 -1.18e+02 -126.312 152s Investment_9 -1.53861 -9.58e+01 -99.086 152s Investment_10 -4.40645 -2.85e+02 -284.216 152s Investment_11 1.51907 9.68e+01 101.778 152s Investment_12 1.33159 7.30e+01 81.493 152s Investment_13 2.31316 1.09e+02 123.523 152s Investment_14 -2.66783 -1.12e+02 -118.185 152s Investment_15 0.31200 1.60e+01 14.071 152s Investment_16 -0.23198 -1.28e+01 -11.529 152s Investment_17 -3.17541 -1.82e+02 -172.742 152s Investment_18 -0.01091 -7.33e-01 -0.684 152s Investment_19 5.12299 3.51e+02 332.995 152s Investment_20 -1.42414 -9.52e+01 -86.730 152s Investment_21 -0.91579 -6.86e+01 -63.647 152s Investment_22 -2.36441 -2.05e+02 -178.986 152s PrivateWages_2 -10.69229 -5.03e+02 -480.084 152s PrivateWages_3 3.68477 1.83e+02 168.026 152s PrivateWages_4 9.60226 5.43e+02 481.073 152s PrivateWages_5 -9.42360 -5.72e+02 -539.030 152s PrivateWages_6 -1.43698 -8.71e+01 -82.052 152s PrivateWages_8 4.89470 2.94e+02 313.261 152s PrivateWages_9 5.95474 3.71e+02 383.486 152s PrivateWages_10 11.81751 7.63e+02 762.229 152s PrivateWages_11 -9.12040 -5.81e+02 -611.067 152s PrivateWages_12 -2.98584 -1.64e+02 -182.733 152s PrivateWages_13 -8.84596 -4.16e+02 -472.374 152s PrivateWages_14 8.38434 3.53e+02 371.426 152s PrivateWages_15 -1.68273 -8.62e+01 -75.891 152s PrivateWages_16 -2.01575 -1.12e+02 -100.183 152s PrivateWages_17 7.82981 4.49e+02 425.942 152s PrivateWages_18 -0.14275 -9.59e+00 -8.950 152s PrivateWages_19 -22.35918 -1.53e+03 -1453.347 152s PrivateWages_20 4.37659 2.93e+02 266.534 152s PrivateWages_21 -4.53959 -3.40e+02 -315.502 152s PrivateWages_22 8.08137 7.02e+02 611.760 152s PrivateWages_trend 152s Consumption_2 51.2212 152s Consumption_3 21.5773 152s Consumption_4 3.2953 152s Consumption_5 39.9635 152s Consumption_6 -8.4329 152s Consumption_8 -44.1578 152s Consumption_9 -25.8180 152s Consumption_11 1.2639 152s Consumption_12 0.0000 152s Consumption_13 -5.1197 152s Consumption_14 9.3551 152s Consumption_15 -6.3961 152s Consumption_16 -8.3371 152s Consumption_17 69.9701 152s Consumption_18 -10.1862 152s Consumption_19 -65.3870 152s Consumption_20 58.3732 152s Consumption_21 29.5195 152s Consumption_22 -24.7710 152s Investment_2 -40.6819 152s Investment_3 -0.0142 152s Investment_4 5.9345 152s Investment_5 -17.9052 152s Investment_6 2.1734 152s Investment_8 7.8945 152s Investment_9 4.6158 152s Investment_10 8.8129 152s Investment_11 -1.5191 152s Investment_12 0.0000 152s Investment_13 2.3132 152s Investment_14 -5.3357 152s Investment_15 0.9360 152s Investment_16 -0.9279 152s Investment_17 -15.8771 152s Investment_18 -0.0655 152s Investment_19 35.8610 152s Investment_20 -11.3931 152s Investment_21 -8.2421 152s Investment_22 -23.6441 152s PrivateWages_2 106.9229 152s PrivateWages_3 -33.1629 152s PrivateWages_4 -76.8181 152s PrivateWages_5 65.9652 152s PrivateWages_6 8.6219 152s PrivateWages_8 -19.5788 152s PrivateWages_9 -17.8642 152s PrivateWages_10 -23.6350 152s PrivateWages_11 9.1204 152s PrivateWages_12 0.0000 152s PrivateWages_13 -8.8460 152s PrivateWages_14 16.7687 152s PrivateWages_15 -5.0482 152s PrivateWages_16 -8.0630 152s PrivateWages_17 39.1491 152s PrivateWages_18 -0.8565 152s PrivateWages_19 -156.5143 152s PrivateWages_20 35.0127 152s PrivateWages_21 -40.8563 152s PrivateWages_22 80.8137 152s [1] TRUE 152s > Bread 152s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 152s [1,] 92.02523 -0.8883 -0.3567 152s [2,] -0.88834 0.5799 -0.3635 152s [3,] -0.35667 -0.3635 0.4840 152s [4,] -1.65059 -0.0695 -0.0345 152s [5,] 87.30345 -0.4940 5.6093 152s [6,] -2.09669 0.4100 -0.4129 152s [7,] 0.52353 -0.3352 0.4397 152s [8,] -0.29441 -0.0047 -0.0291 152s [9,] -39.25694 0.2930 1.5879 152s [10,] 0.63395 -0.0766 0.0444 152s [11,] -0.00377 0.0739 -0.0730 152s [12,] 0.26412 0.0450 0.0239 152s Consumption_wages Investment_(Intercept) Investment_corpProf 152s [1,] -1.650593 87.303 -2.09669 152s [2,] -0.069509 -0.494 0.41001 152s [3,] -0.034488 5.609 -0.41285 152s [4,] 0.081060 -3.868 0.04419 152s [5,] -3.867758 4034.682 -59.45928 152s [6,] 0.044186 -59.459 2.20583 152s [7,] -0.048017 50.679 -1.90719 152s [8,] 0.019469 -19.184 0.26586 152s [9,] 0.172081 52.203 -0.49762 152s [10,] -0.001839 2.943 0.01728 152s [11,] -0.000946 -3.971 -0.00883 152s [12,] -0.034168 -2.641 0.03741 152s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 152s [1,] 0.52353 -0.2944 -39.2569 152s [2,] -0.33517 -0.0047 0.2930 152s [3,] 0.43972 -0.0291 1.5879 152s [4,] -0.04802 0.0195 0.1721 152s [5,] 50.67914 -19.1839 52.2027 152s [6,] -1.90719 0.2659 -0.4976 152s [7,] 2.08136 -0.2612 -1.5286 152s [8,] -0.26125 0.0944 -0.0914 152s [9,] -1.52864 -0.0914 77.9751 152s [10,] 0.00872 -0.0168 -0.5909 152s [11,] 0.01756 0.0191 -0.7086 152s [12,] -0.06267 0.0150 0.8675 152s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 152s [1,] 0.63395 -0.003771 0.26412 152s [2,] -0.07661 0.073937 0.04500 152s [3,] 0.04435 -0.072979 0.02395 152s [4,] -0.00184 -0.000946 -0.03417 152s [5,] 2.94321 -3.971150 -2.64074 152s [6,] 0.01728 -0.008829 0.03741 152s [7,] 0.00872 0.017559 -0.06267 152s [8,] -0.01682 0.019146 0.01504 152s [9,] -0.59094 -0.708614 0.86750 152s [10,] 0.05781 -0.049542 -0.01891 152s [11,] -0.04954 0.063408 0.00453 152s [12,] -0.01891 0.004534 0.04825 152s > 152s > # OLS 152s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 152s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 152s > summary 152s 152s systemfit results 152s method: OLS 152s 152s N DF SSR detRCov OLS-R2 McElroy-R2 152s system 59 47 44.2 0.453 0.976 0.99 152s 152s N DF SSR MSE RMSE R2 Adj R2 152s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 152s Investment 20 16 17.11 1.069 1.03 0.912 0.895 152s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 152s 152s The covariance matrix of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.1939 0.0559 -0.474 152s Investment 0.0559 0.9839 0.140 152s PrivateWages -0.4745 0.1403 0.602 152s 152s The correlations of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.0000 0.0447 -0.568 152s Investment 0.0447 1.0000 0.169 152s PrivateWages -0.5680 0.1689 1.000 152s 152s 152s OLS estimates for 'Consumption' (equation 1) 152s Model Formula: consump ~ corpProf + corpProfLag + wages 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 16.2957 1.4879 10.95 1.5e-08 *** 152s corpProf 0.1796 0.1162 1.55 0.14 152s corpProfLag 0.1032 0.0994 1.04 0.32 152s wages 0.7962 0.0433 18.39 1.1e-11 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.076 on 15 degrees of freedom 152s Number of observations: 19 Degrees of Freedom: 15 152s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 152s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 152s 152s 152s OLS estimates for 'Investment' (equation 2) 152s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 10.1813 5.3720 1.90 0.07627 . 152s corpProf 0.5003 0.1052 4.75 0.00022 *** 152s corpProfLag 0.3259 0.1003 3.25 0.00502 ** 152s capitalLag -0.1134 0.0265 -4.28 0.00057 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.034 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 17.109 MSE: 1.069 Root MSE: 1.034 152s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.895 152s 152s 152s OLS estimates for 'PrivateWages' (equation 3) 152s Model Formula: privWage ~ gnp + gnpLag + trend 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 1.3550 1.3021 1.04 0.3135 152s gnp 0.4417 0.0330 13.40 4.1e-10 *** 152s gnpLag 0.1466 0.0379 3.87 0.0013 ** 152s trend 0.1244 0.0335 3.72 0.0019 ** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 0.78 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 152s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 152s 152s compare coef with single-equation OLS 152s [1] TRUE 152s > residuals 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 -0.3863 -0.000301 -1.3389 152s 3 -1.2484 -0.076489 0.2462 152s 4 -1.6040 1.221792 1.1255 152s 5 -0.5384 -1.377872 -0.1959 152s 6 -0.0413 0.386104 -0.5284 152s 7 0.8043 1.486279 NA 152s 8 1.2830 0.784055 -0.7909 152s 9 1.0142 -0.655354 0.2819 152s 10 NA 1.060871 1.1384 152s 11 0.1429 0.395249 -0.1904 152s 12 -0.3439 0.198005 0.5813 152s 13 NA NA 0.1206 152s 14 0.3199 0.312725 0.4773 152s 15 -0.1016 -0.084685 0.3035 152s 16 -0.0702 0.066194 0.0284 152s 17 1.6064 0.963697 -0.8517 152s 18 -0.4980 0.078506 0.9908 152s 19 0.1253 -2.496401 -0.4597 152s 20 0.9805 -0.711004 -0.3819 152s 21 0.7551 -0.820172 -1.1062 152s 22 -2.1992 -0.731199 0.5501 152s > fitted 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 42.3 -0.200 26.8 152s 3 46.2 1.976 29.1 152s 4 50.8 3.978 33.0 152s 5 51.1 4.378 34.1 152s 6 52.6 4.714 35.9 152s 7 54.3 4.114 NA 152s 8 54.9 3.416 38.7 152s 9 56.3 3.655 38.9 152s 10 NA 4.039 40.2 152s 11 54.9 0.605 38.1 152s 12 51.2 -3.598 33.9 152s 13 NA NA 28.9 152s 14 46.2 -5.413 28.0 152s 15 48.8 -2.915 30.3 152s 16 51.4 -1.366 33.2 152s 17 56.1 1.136 37.7 152s 18 59.2 1.921 40.0 152s 19 57.4 0.596 38.7 152s 20 60.6 2.011 42.0 152s 21 64.2 4.120 46.1 152s 22 71.9 5.631 52.7 152s > predict 152s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 152s 1 NA NA NA NA 152s 2 42.3 0.523 39.9 44.7 152s 3 46.2 0.560 43.8 48.7 152s 4 50.8 0.379 48.5 53.1 152s 5 51.1 0.448 48.8 53.5 152s 6 52.6 0.457 50.3 55.0 152s 7 54.3 0.408 52.0 56.6 152s 8 54.9 0.375 52.6 57.2 152s 9 56.3 0.418 54.0 58.6 152s 10 NA NA NA NA 152s 11 54.9 0.701 52.3 57.4 152s 12 51.2 0.638 48.7 53.8 152s 13 NA NA NA NA 152s 14 46.2 0.673 43.6 48.7 152s 15 48.8 0.453 46.5 51.2 152s 16 51.4 0.384 49.1 53.7 152s 17 56.1 0.391 53.8 58.4 152s 18 59.2 0.361 56.9 61.5 152s 19 57.4 0.449 55.0 59.7 152s 20 60.6 0.465 58.3 63.0 152s 21 64.2 0.468 61.9 66.6 152s 22 71.9 0.728 69.3 74.5 152s Investment.pred Investment.se.fit Investment.lwr Investment.upr 152s 1 NA NA NA NA 152s 2 -0.200 0.613 -2.618 2.219 152s 3 1.976 0.494 -0.329 4.282 152s 4 3.978 0.444 1.714 6.242 152s 5 4.378 0.369 2.169 6.587 152s 6 4.714 0.349 2.519 6.909 152s 7 4.114 0.323 1.934 6.293 152s 8 3.416 0.287 1.257 5.575 152s 9 3.655 0.386 1.435 5.876 152s 10 4.039 0.441 1.777 6.301 152s 11 0.605 0.641 -1.843 3.053 152s 12 -3.598 0.606 -6.010 -1.186 152s 13 NA NA NA NA 152s 14 -5.413 0.708 -7.934 -2.892 152s 15 -2.915 0.412 -5.155 -0.676 152s 16 -1.366 0.336 -3.554 0.821 152s 17 1.136 0.342 -1.055 3.327 152s 18 1.921 0.246 -0.217 4.060 152s 19 0.596 0.341 -1.594 2.787 152s 20 2.011 0.364 -0.194 4.216 152s 21 4.120 0.337 1.932 6.308 152s 22 5.631 0.477 3.341 7.922 152s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 152s 1 NA NA NA NA 152s 2 26.8 0.364 25.1 28.6 152s 3 29.1 0.367 27.3 30.8 152s 4 33.0 0.370 31.2 34.7 152s 5 34.1 0.286 32.4 35.8 152s 6 35.9 0.285 34.3 37.6 152s 7 NA NA NA NA 152s 8 38.7 0.292 37.0 40.4 152s 9 38.9 0.277 37.3 40.6 152s 10 40.2 0.264 38.5 41.8 152s 11 38.1 0.363 36.4 39.8 152s 12 33.9 0.367 32.2 35.7 152s 13 28.9 0.435 27.1 30.7 152s 14 28.0 0.383 26.3 29.8 152s 15 30.3 0.377 28.6 32.0 152s 16 33.2 0.315 31.5 34.9 152s 17 37.7 0.308 36.0 39.3 152s 18 40.0 0.241 38.4 41.7 152s 19 38.7 0.361 36.9 40.4 152s 20 42.0 0.324 40.3 43.7 152s 21 46.1 0.339 44.4 47.8 152s 22 52.7 0.511 50.9 54.6 152s > model.frame 152s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 152s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 152s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 152s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 152s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 152s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 152s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 152s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 152s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 152s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 152s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 152s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 152s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 152s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 152s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 152s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 152s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 152s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 152s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 152s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 152s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 152s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 152s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 152s trend 152s 1 -11 152s 2 -10 152s 3 -9 152s 4 -8 152s 5 -7 152s 6 -6 152s 7 -5 152s 8 -4 152s 9 -3 152s 10 -2 152s 11 -1 152s 12 0 152s 13 1 152s 14 2 152s 15 3 152s 16 4 152s 17 5 152s 18 6 152s 19 7 152s 20 8 152s 21 9 152s 22 10 152s > model.matrix 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 1 12.4 152s Consumption_3 1 16.9 152s Consumption_4 1 18.4 152s Consumption_5 1 19.4 152s Consumption_6 1 20.1 152s Consumption_7 1 19.6 152s Consumption_8 1 19.8 152s Consumption_9 1 21.1 152s Consumption_11 1 15.6 152s Consumption_12 1 11.4 152s Consumption_14 1 11.2 152s Consumption_15 1 12.3 152s Consumption_16 1 14.0 152s Consumption_17 1 17.6 152s Consumption_18 1 17.3 152s Consumption_19 1 15.3 152s Consumption_20 1 19.0 152s Consumption_21 1 21.1 152s Consumption_22 1 23.5 152s Investment_2 0 0.0 152s Investment_3 0 0.0 152s Investment_4 0 0.0 152s Investment_5 0 0.0 152s Investment_6 0 0.0 152s Investment_7 0 0.0 152s Investment_8 0 0.0 152s Investment_9 0 0.0 152s Investment_10 0 0.0 152s Investment_11 0 0.0 152s Investment_12 0 0.0 152s Investment_14 0 0.0 152s Investment_15 0 0.0 152s Investment_16 0 0.0 152s Investment_17 0 0.0 152s Investment_18 0 0.0 152s Investment_19 0 0.0 152s Investment_20 0 0.0 152s Investment_21 0 0.0 152s Investment_22 0 0.0 152s PrivateWages_2 0 0.0 152s PrivateWages_3 0 0.0 152s PrivateWages_4 0 0.0 152s PrivateWages_5 0 0.0 152s PrivateWages_6 0 0.0 152s PrivateWages_8 0 0.0 152s PrivateWages_9 0 0.0 152s PrivateWages_10 0 0.0 152s PrivateWages_11 0 0.0 152s PrivateWages_12 0 0.0 152s PrivateWages_13 0 0.0 152s PrivateWages_14 0 0.0 152s PrivateWages_15 0 0.0 152s PrivateWages_16 0 0.0 152s PrivateWages_17 0 0.0 152s PrivateWages_18 0 0.0 152s PrivateWages_19 0 0.0 152s PrivateWages_20 0 0.0 152s PrivateWages_21 0 0.0 152s PrivateWages_22 0 0.0 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 12.7 28.2 152s Consumption_3 12.4 32.2 152s Consumption_4 16.9 37.0 152s Consumption_5 18.4 37.0 152s Consumption_6 19.4 38.6 152s Consumption_7 20.1 40.7 152s Consumption_8 19.6 41.5 152s Consumption_9 19.8 42.9 152s Consumption_11 21.7 42.1 152s Consumption_12 15.6 39.3 152s Consumption_14 7.0 34.1 152s Consumption_15 11.2 36.6 152s Consumption_16 12.3 39.3 152s Consumption_17 14.0 44.2 152s Consumption_18 17.6 47.7 152s Consumption_19 17.3 45.9 152s Consumption_20 15.3 49.4 152s Consumption_21 19.0 53.0 152s Consumption_22 21.1 61.8 152s Investment_2 0.0 0.0 152s Investment_3 0.0 0.0 152s Investment_4 0.0 0.0 152s Investment_5 0.0 0.0 152s Investment_6 0.0 0.0 152s Investment_7 0.0 0.0 152s Investment_8 0.0 0.0 152s Investment_9 0.0 0.0 152s Investment_10 0.0 0.0 152s Investment_11 0.0 0.0 152s Investment_12 0.0 0.0 152s Investment_14 0.0 0.0 152s Investment_15 0.0 0.0 152s Investment_16 0.0 0.0 152s Investment_17 0.0 0.0 152s Investment_18 0.0 0.0 152s Investment_19 0.0 0.0 152s Investment_20 0.0 0.0 152s Investment_21 0.0 0.0 152s Investment_22 0.0 0.0 152s PrivateWages_2 0.0 0.0 152s PrivateWages_3 0.0 0.0 152s PrivateWages_4 0.0 0.0 152s PrivateWages_5 0.0 0.0 152s PrivateWages_6 0.0 0.0 152s PrivateWages_8 0.0 0.0 152s PrivateWages_9 0.0 0.0 152s PrivateWages_10 0.0 0.0 152s PrivateWages_11 0.0 0.0 152s PrivateWages_12 0.0 0.0 152s PrivateWages_13 0.0 0.0 152s PrivateWages_14 0.0 0.0 152s PrivateWages_15 0.0 0.0 152s PrivateWages_16 0.0 0.0 152s PrivateWages_17 0.0 0.0 152s PrivateWages_18 0.0 0.0 152s PrivateWages_19 0.0 0.0 152s PrivateWages_20 0.0 0.0 152s PrivateWages_21 0.0 0.0 152s PrivateWages_22 0.0 0.0 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 0 0.0 152s Consumption_3 0 0.0 152s Consumption_4 0 0.0 152s Consumption_5 0 0.0 152s Consumption_6 0 0.0 152s Consumption_7 0 0.0 152s Consumption_8 0 0.0 152s Consumption_9 0 0.0 152s Consumption_11 0 0.0 152s Consumption_12 0 0.0 152s Consumption_14 0 0.0 152s Consumption_15 0 0.0 152s Consumption_16 0 0.0 152s Consumption_17 0 0.0 152s Consumption_18 0 0.0 152s Consumption_19 0 0.0 152s Consumption_20 0 0.0 152s Consumption_21 0 0.0 152s Consumption_22 0 0.0 152s Investment_2 1 12.4 152s Investment_3 1 16.9 152s Investment_4 1 18.4 152s Investment_5 1 19.4 152s Investment_6 1 20.1 152s Investment_7 1 19.6 152s Investment_8 1 19.8 152s Investment_9 1 21.1 152s Investment_10 1 21.7 152s Investment_11 1 15.6 152s Investment_12 1 11.4 152s Investment_14 1 11.2 152s Investment_15 1 12.3 152s Investment_16 1 14.0 152s Investment_17 1 17.6 152s Investment_18 1 17.3 152s Investment_19 1 15.3 152s Investment_20 1 19.0 152s Investment_21 1 21.1 152s Investment_22 1 23.5 152s PrivateWages_2 0 0.0 152s PrivateWages_3 0 0.0 152s PrivateWages_4 0 0.0 152s PrivateWages_5 0 0.0 152s PrivateWages_6 0 0.0 152s PrivateWages_8 0 0.0 152s PrivateWages_9 0 0.0 152s PrivateWages_10 0 0.0 152s PrivateWages_11 0 0.0 152s PrivateWages_12 0 0.0 152s PrivateWages_13 0 0.0 152s PrivateWages_14 0 0.0 152s PrivateWages_15 0 0.0 152s PrivateWages_16 0 0.0 152s PrivateWages_17 0 0.0 152s PrivateWages_18 0 0.0 152s PrivateWages_19 0 0.0 152s PrivateWages_20 0 0.0 152s PrivateWages_21 0 0.0 152s PrivateWages_22 0 0.0 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 0.0 0 152s Consumption_3 0.0 0 152s Consumption_4 0.0 0 152s Consumption_5 0.0 0 152s Consumption_6 0.0 0 152s Consumption_7 0.0 0 152s Consumption_8 0.0 0 152s Consumption_9 0.0 0 152s Consumption_11 0.0 0 152s Consumption_12 0.0 0 152s Consumption_14 0.0 0 152s Consumption_15 0.0 0 152s Consumption_16 0.0 0 152s Consumption_17 0.0 0 152s Consumption_18 0.0 0 152s Consumption_19 0.0 0 152s Consumption_20 0.0 0 152s Consumption_21 0.0 0 152s Consumption_22 0.0 0 152s Investment_2 12.7 183 152s Investment_3 12.4 183 152s Investment_4 16.9 184 152s Investment_5 18.4 190 152s Investment_6 19.4 193 152s Investment_7 20.1 198 152s Investment_8 19.6 203 152s Investment_9 19.8 208 152s Investment_10 21.1 211 152s Investment_11 21.7 216 152s Investment_12 15.6 217 152s Investment_14 7.0 207 152s Investment_15 11.2 202 152s Investment_16 12.3 199 152s Investment_17 14.0 198 152s Investment_18 17.6 200 152s Investment_19 17.3 202 152s Investment_20 15.3 200 152s Investment_21 19.0 201 152s Investment_22 21.1 204 152s PrivateWages_2 0.0 0 152s PrivateWages_3 0.0 0 152s PrivateWages_4 0.0 0 152s PrivateWages_5 0.0 0 152s PrivateWages_6 0.0 0 152s PrivateWages_8 0.0 0 152s PrivateWages_9 0.0 0 152s PrivateWages_10 0.0 0 152s PrivateWages_11 0.0 0 152s PrivateWages_12 0.0 0 152s PrivateWages_13 0.0 0 152s PrivateWages_14 0.0 0 152s PrivateWages_15 0.0 0 152s PrivateWages_16 0.0 0 152s PrivateWages_17 0.0 0 152s PrivateWages_18 0.0 0 152s PrivateWages_19 0.0 0 152s PrivateWages_20 0.0 0 152s PrivateWages_21 0.0 0 152s PrivateWages_22 0.0 0 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 0 0.0 0.0 152s Consumption_3 0 0.0 0.0 152s Consumption_4 0 0.0 0.0 152s Consumption_5 0 0.0 0.0 152s Consumption_6 0 0.0 0.0 152s Consumption_7 0 0.0 0.0 152s Consumption_8 0 0.0 0.0 152s Consumption_9 0 0.0 0.0 152s Consumption_11 0 0.0 0.0 152s Consumption_12 0 0.0 0.0 152s Consumption_14 0 0.0 0.0 152s Consumption_15 0 0.0 0.0 152s Consumption_16 0 0.0 0.0 152s Consumption_17 0 0.0 0.0 152s Consumption_18 0 0.0 0.0 152s Consumption_19 0 0.0 0.0 152s Consumption_20 0 0.0 0.0 152s Consumption_21 0 0.0 0.0 152s Consumption_22 0 0.0 0.0 152s Investment_2 0 0.0 0.0 152s Investment_3 0 0.0 0.0 152s Investment_4 0 0.0 0.0 152s Investment_5 0 0.0 0.0 152s Investment_6 0 0.0 0.0 152s Investment_7 0 0.0 0.0 152s Investment_8 0 0.0 0.0 152s Investment_9 0 0.0 0.0 152s Investment_10 0 0.0 0.0 152s Investment_11 0 0.0 0.0 152s Investment_12 0 0.0 0.0 152s Investment_14 0 0.0 0.0 152s Investment_15 0 0.0 0.0 152s Investment_16 0 0.0 0.0 152s Investment_17 0 0.0 0.0 152s Investment_18 0 0.0 0.0 152s Investment_19 0 0.0 0.0 152s Investment_20 0 0.0 0.0 152s Investment_21 0 0.0 0.0 152s Investment_22 0 0.0 0.0 152s PrivateWages_2 1 45.6 44.9 152s PrivateWages_3 1 50.1 45.6 152s PrivateWages_4 1 57.2 50.1 152s PrivateWages_5 1 57.1 57.2 152s PrivateWages_6 1 61.0 57.1 152s PrivateWages_8 1 64.4 64.0 152s PrivateWages_9 1 64.5 64.4 152s PrivateWages_10 1 67.0 64.5 152s PrivateWages_11 1 61.2 67.0 152s PrivateWages_12 1 53.4 61.2 152s PrivateWages_13 1 44.3 53.4 152s PrivateWages_14 1 45.1 44.3 152s PrivateWages_15 1 49.7 45.1 152s PrivateWages_16 1 54.4 49.7 152s PrivateWages_17 1 62.7 54.4 152s PrivateWages_18 1 65.0 62.7 152s PrivateWages_19 1 60.9 65.0 152s PrivateWages_20 1 69.5 60.9 152s PrivateWages_21 1 75.7 69.5 152s PrivateWages_22 1 88.4 75.7 152s PrivateWages_trend 152s Consumption_2 0 152s Consumption_3 0 152s Consumption_4 0 152s Consumption_5 0 152s Consumption_6 0 152s Consumption_7 0 152s Consumption_8 0 152s Consumption_9 0 152s Consumption_11 0 152s Consumption_12 0 152s Consumption_14 0 152s Consumption_15 0 152s Consumption_16 0 152s Consumption_17 0 152s Consumption_18 0 152s Consumption_19 0 152s Consumption_20 0 152s Consumption_21 0 152s Consumption_22 0 152s Investment_2 0 152s Investment_3 0 152s Investment_4 0 152s Investment_5 0 152s Investment_6 0 152s Investment_7 0 152s Investment_8 0 152s Investment_9 0 152s Investment_10 0 152s Investment_11 0 152s Investment_12 0 152s Investment_14 0 152s Investment_15 0 152s Investment_16 0 152s Investment_17 0 152s Investment_18 0 152s Investment_19 0 152s Investment_20 0 152s Investment_21 0 152s Investment_22 0 152s PrivateWages_2 -10 152s PrivateWages_3 -9 152s PrivateWages_4 -8 152s PrivateWages_5 -7 152s PrivateWages_6 -6 152s PrivateWages_8 -4 152s PrivateWages_9 -3 152s PrivateWages_10 -2 152s PrivateWages_11 -1 152s PrivateWages_12 0 152s PrivateWages_13 1 152s PrivateWages_14 2 152s PrivateWages_15 3 152s PrivateWages_16 4 152s PrivateWages_17 5 152s PrivateWages_18 6 152s PrivateWages_19 7 152s PrivateWages_20 8 152s PrivateWages_21 9 152s PrivateWages_22 10 152s > nobs 152s [1] 59 152s > linearHypothesis 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 47 1 0.33 0.57 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 47 1 0.31 0.58 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 48 152s 2 47 1 0.31 0.58 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 49 152s 2 47 2 0.17 0.84 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 49 152s 2 47 2 0.16 0.85 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 49 152s 2 47 2 0.33 0.85 152s > logLik 152s 'log Lik.' -69.6 (df=13) 152s 'log Lik.' -74.2 (df=13) 152s compare log likelihood value with single-equation OLS 152s [1] "Mean relative difference: 0.00099" 152s Estimating function 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 -0.3863 -4.791 152s Consumption_3 -1.2484 -21.098 152s Consumption_4 -1.6040 -29.514 152s Consumption_5 -0.5384 -10.446 152s Consumption_6 -0.0413 -0.830 152s Consumption_7 0.8043 15.763 152s Consumption_8 1.2830 25.403 152s Consumption_9 1.0142 21.399 152s Consumption_11 0.1429 2.229 152s Consumption_12 -0.3439 -3.920 152s Consumption_14 0.3199 3.583 152s Consumption_15 -0.1016 -1.250 152s Consumption_16 -0.0702 -0.983 152s Consumption_17 1.6064 28.272 152s Consumption_18 -0.4980 -8.616 152s Consumption_19 0.1253 1.917 152s Consumption_20 0.9805 18.629 152s Consumption_21 0.7551 15.933 152s Consumption_22 -2.1992 -51.681 152s Investment_2 0.0000 0.000 152s Investment_3 0.0000 0.000 152s Investment_4 0.0000 0.000 152s Investment_5 0.0000 0.000 152s Investment_6 0.0000 0.000 152s Investment_7 0.0000 0.000 152s Investment_8 0.0000 0.000 152s Investment_9 0.0000 0.000 152s Investment_10 0.0000 0.000 152s Investment_11 0.0000 0.000 152s Investment_12 0.0000 0.000 152s Investment_14 0.0000 0.000 152s Investment_15 0.0000 0.000 152s Investment_16 0.0000 0.000 152s Investment_17 0.0000 0.000 152s Investment_18 0.0000 0.000 152s Investment_19 0.0000 0.000 152s Investment_20 0.0000 0.000 152s Investment_21 0.0000 0.000 152s Investment_22 0.0000 0.000 152s PrivateWages_2 0.0000 0.000 152s PrivateWages_3 0.0000 0.000 152s PrivateWages_4 0.0000 0.000 152s PrivateWages_5 0.0000 0.000 152s PrivateWages_6 0.0000 0.000 152s PrivateWages_8 0.0000 0.000 152s PrivateWages_9 0.0000 0.000 152s PrivateWages_10 0.0000 0.000 152s PrivateWages_11 0.0000 0.000 152s PrivateWages_12 0.0000 0.000 152s PrivateWages_13 0.0000 0.000 152s PrivateWages_14 0.0000 0.000 152s PrivateWages_15 0.0000 0.000 152s PrivateWages_16 0.0000 0.000 152s PrivateWages_17 0.0000 0.000 152s PrivateWages_18 0.0000 0.000 152s PrivateWages_19 0.0000 0.000 152s PrivateWages_20 0.0000 0.000 152s PrivateWages_21 0.0000 0.000 152s PrivateWages_22 0.0000 0.000 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 -4.907 -10.90 152s Consumption_3 -15.480 -40.20 152s Consumption_4 -27.108 -59.35 152s Consumption_5 -9.907 -19.92 152s Consumption_6 -0.801 -1.59 152s Consumption_7 16.166 32.73 152s Consumption_8 25.146 53.24 152s Consumption_9 20.081 43.51 152s Consumption_11 3.100 6.01 152s Consumption_12 -5.364 -13.51 152s Consumption_14 2.239 10.91 152s Consumption_15 -1.138 -3.72 152s Consumption_16 -0.864 -2.76 152s Consumption_17 22.489 71.00 152s Consumption_18 -8.765 -23.76 152s Consumption_19 2.168 5.75 152s Consumption_20 15.002 48.44 152s Consumption_21 14.348 40.02 152s Consumption_22 -46.403 -135.91 152s Investment_2 0.000 0.00 152s Investment_3 0.000 0.00 152s Investment_4 0.000 0.00 152s Investment_5 0.000 0.00 152s Investment_6 0.000 0.00 152s Investment_7 0.000 0.00 152s Investment_8 0.000 0.00 152s Investment_9 0.000 0.00 152s Investment_10 0.000 0.00 152s Investment_11 0.000 0.00 152s Investment_12 0.000 0.00 152s Investment_14 0.000 0.00 152s Investment_15 0.000 0.00 152s Investment_16 0.000 0.00 152s Investment_17 0.000 0.00 152s Investment_18 0.000 0.00 152s Investment_19 0.000 0.00 152s Investment_20 0.000 0.00 152s Investment_21 0.000 0.00 152s Investment_22 0.000 0.00 152s PrivateWages_2 0.000 0.00 152s PrivateWages_3 0.000 0.00 152s PrivateWages_4 0.000 0.00 152s PrivateWages_5 0.000 0.00 152s PrivateWages_6 0.000 0.00 152s PrivateWages_8 0.000 0.00 152s PrivateWages_9 0.000 0.00 152s PrivateWages_10 0.000 0.00 152s PrivateWages_11 0.000 0.00 152s PrivateWages_12 0.000 0.00 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 0.000 0.00 152s PrivateWages_15 0.000 0.00 152s PrivateWages_16 0.000 0.00 152s PrivateWages_17 0.000 0.00 152s PrivateWages_18 0.000 0.00 152s PrivateWages_19 0.000 0.00 152s PrivateWages_20 0.000 0.00 152s PrivateWages_21 0.000 0.00 152s PrivateWages_22 0.000 0.00 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 0.000000 0.00000 152s Consumption_3 0.000000 0.00000 152s Consumption_4 0.000000 0.00000 152s Consumption_5 0.000000 0.00000 152s Consumption_6 0.000000 0.00000 152s Consumption_7 0.000000 0.00000 152s Consumption_8 0.000000 0.00000 152s Consumption_9 0.000000 0.00000 152s Consumption_11 0.000000 0.00000 152s Consumption_12 0.000000 0.00000 152s Consumption_14 0.000000 0.00000 152s Consumption_15 0.000000 0.00000 152s Consumption_16 0.000000 0.00000 152s Consumption_17 0.000000 0.00000 152s Consumption_18 0.000000 0.00000 152s Consumption_19 0.000000 0.00000 152s Consumption_20 0.000000 0.00000 152s Consumption_21 0.000000 0.00000 152s Consumption_22 0.000000 0.00000 152s Investment_2 -0.000301 -0.00373 152s Investment_3 -0.076489 -1.29266 152s Investment_4 1.221792 22.48097 152s Investment_5 -1.377872 -26.73071 152s Investment_6 0.386104 7.76068 152s Investment_7 1.486279 29.13107 152s Investment_8 0.784055 15.52429 152s Investment_9 -0.655354 -13.82796 152s Investment_10 1.060871 23.02091 152s Investment_11 0.395249 6.16588 152s Investment_12 0.198005 2.25726 152s Investment_14 0.312725 3.50252 152s Investment_15 -0.084685 -1.04163 152s Investment_16 0.066194 0.92672 152s Investment_17 0.963697 16.96106 152s Investment_18 0.078506 1.35816 152s Investment_19 -2.496401 -38.19494 152s Investment_20 -0.711004 -13.50907 152s Investment_21 -0.820172 -17.30564 152s Investment_22 -0.731199 -17.18317 152s PrivateWages_2 0.000000 0.00000 152s PrivateWages_3 0.000000 0.00000 152s PrivateWages_4 0.000000 0.00000 152s PrivateWages_5 0.000000 0.00000 152s PrivateWages_6 0.000000 0.00000 152s PrivateWages_8 0.000000 0.00000 152s PrivateWages_9 0.000000 0.00000 152s PrivateWages_10 0.000000 0.00000 152s PrivateWages_11 0.000000 0.00000 152s PrivateWages_12 0.000000 0.00000 152s PrivateWages_13 0.000000 0.00000 152s PrivateWages_14 0.000000 0.00000 152s PrivateWages_15 0.000000 0.00000 152s PrivateWages_16 0.000000 0.00000 152s PrivateWages_17 0.000000 0.00000 152s PrivateWages_18 0.000000 0.00000 152s PrivateWages_19 0.000000 0.00000 152s PrivateWages_20 0.000000 0.00000 152s PrivateWages_21 0.000000 0.00000 152s PrivateWages_22 0.000000 0.00000 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 0.00000 0.000 152s Consumption_3 0.00000 0.000 152s Consumption_4 0.00000 0.000 152s Consumption_5 0.00000 0.000 152s Consumption_6 0.00000 0.000 152s Consumption_7 0.00000 0.000 152s Consumption_8 0.00000 0.000 152s Consumption_9 0.00000 0.000 152s Consumption_11 0.00000 0.000 152s Consumption_12 0.00000 0.000 152s Consumption_14 0.00000 0.000 152s Consumption_15 0.00000 0.000 152s Consumption_16 0.00000 0.000 152s Consumption_17 0.00000 0.000 152s Consumption_18 0.00000 0.000 152s Consumption_19 0.00000 0.000 152s Consumption_20 0.00000 0.000 152s Consumption_21 0.00000 0.000 152s Consumption_22 0.00000 0.000 152s Investment_2 -0.00382 -0.055 152s Investment_3 -0.94846 -13.967 152s Investment_4 20.64828 225.421 152s Investment_5 -25.35284 -261.382 152s Investment_6 7.49041 74.402 152s Investment_7 29.87421 293.986 152s Investment_8 15.36748 159.477 152s Investment_9 -12.97600 -136.051 152s Investment_10 22.38438 223.419 152s Investment_11 8.57690 85.255 152s Investment_12 3.08888 42.908 152s Investment_14 2.18907 64.765 152s Investment_15 -0.94848 -17.106 152s Investment_16 0.81419 13.173 152s Investment_17 13.49175 190.523 152s Investment_18 1.38171 15.686 152s Investment_19 -43.18774 -503.774 152s Investment_20 -10.87836 -142.130 152s Investment_21 -15.58327 -165.019 152s Investment_22 -15.42829 -149.530 152s PrivateWages_2 0.00000 0.000 152s PrivateWages_3 0.00000 0.000 152s PrivateWages_4 0.00000 0.000 152s PrivateWages_5 0.00000 0.000 152s PrivateWages_6 0.00000 0.000 152s PrivateWages_8 0.00000 0.000 152s PrivateWages_9 0.00000 0.000 152s PrivateWages_10 0.00000 0.000 152s PrivateWages_11 0.00000 0.000 152s PrivateWages_12 0.00000 0.000 152s PrivateWages_13 0.00000 0.000 152s PrivateWages_14 0.00000 0.000 152s PrivateWages_15 0.00000 0.000 152s PrivateWages_16 0.00000 0.000 152s PrivateWages_17 0.00000 0.000 152s PrivateWages_18 0.00000 0.000 152s PrivateWages_19 0.00000 0.000 152s PrivateWages_20 0.00000 0.000 152s PrivateWages_21 0.00000 0.000 152s PrivateWages_22 0.00000 0.000 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 0.0000 0.00 0.00 152s Consumption_3 0.0000 0.00 0.00 152s Consumption_4 0.0000 0.00 0.00 152s Consumption_5 0.0000 0.00 0.00 152s Consumption_6 0.0000 0.00 0.00 152s Consumption_7 0.0000 0.00 0.00 152s Consumption_8 0.0000 0.00 0.00 152s Consumption_9 0.0000 0.00 0.00 152s Consumption_11 0.0000 0.00 0.00 152s Consumption_12 0.0000 0.00 0.00 152s Consumption_14 0.0000 0.00 0.00 152s Consumption_15 0.0000 0.00 0.00 152s Consumption_16 0.0000 0.00 0.00 152s Consumption_17 0.0000 0.00 0.00 152s Consumption_18 0.0000 0.00 0.00 152s Consumption_19 0.0000 0.00 0.00 152s Consumption_20 0.0000 0.00 0.00 152s Consumption_21 0.0000 0.00 0.00 152s Consumption_22 0.0000 0.00 0.00 152s Investment_2 0.0000 0.00 0.00 152s Investment_3 0.0000 0.00 0.00 152s Investment_4 0.0000 0.00 0.00 152s Investment_5 0.0000 0.00 0.00 152s Investment_6 0.0000 0.00 0.00 152s Investment_7 0.0000 0.00 0.00 152s Investment_8 0.0000 0.00 0.00 152s Investment_9 0.0000 0.00 0.00 152s Investment_10 0.0000 0.00 0.00 152s Investment_11 0.0000 0.00 0.00 152s Investment_12 0.0000 0.00 0.00 152s Investment_14 0.0000 0.00 0.00 152s Investment_15 0.0000 0.00 0.00 152s Investment_16 0.0000 0.00 0.00 152s Investment_17 0.0000 0.00 0.00 152s Investment_18 0.0000 0.00 0.00 152s Investment_19 0.0000 0.00 0.00 152s Investment_20 0.0000 0.00 0.00 152s Investment_21 0.0000 0.00 0.00 152s Investment_22 0.0000 0.00 0.00 152s PrivateWages_2 -1.3389 -61.06 -60.12 152s PrivateWages_3 0.2462 12.33 11.23 152s PrivateWages_4 1.1255 64.38 56.39 152s PrivateWages_5 -0.1959 -11.18 -11.20 152s PrivateWages_6 -0.5284 -32.23 -30.17 152s PrivateWages_8 -0.7909 -50.94 -50.62 152s PrivateWages_9 0.2819 18.18 18.15 152s PrivateWages_10 1.1384 76.28 73.43 152s PrivateWages_11 -0.1904 -11.65 -12.76 152s PrivateWages_12 0.5813 31.04 35.58 152s PrivateWages_13 0.1206 5.34 6.44 152s PrivateWages_14 0.4773 21.53 21.14 152s PrivateWages_15 0.3035 15.09 13.69 152s PrivateWages_16 0.0284 1.55 1.41 152s PrivateWages_17 -0.8517 -53.40 -46.33 152s PrivateWages_18 0.9908 64.40 62.12 152s PrivateWages_19 -0.4597 -28.00 -29.88 152s PrivateWages_20 -0.3819 -26.54 -23.26 152s PrivateWages_21 -1.1062 -83.74 -76.88 152s PrivateWages_22 0.5501 48.63 41.64 152s PrivateWages_trend 152s Consumption_2 0.000 152s Consumption_3 0.000 152s Consumption_4 0.000 152s Consumption_5 0.000 152s Consumption_6 0.000 152s Consumption_7 0.000 152s Consumption_8 0.000 152s Consumption_9 0.000 152s Consumption_11 0.000 152s Consumption_12 0.000 152s Consumption_14 0.000 152s Consumption_15 0.000 152s Consumption_16 0.000 152s Consumption_17 0.000 152s Consumption_18 0.000 152s Consumption_19 0.000 152s Consumption_20 0.000 152s Consumption_21 0.000 152s Consumption_22 0.000 152s Investment_2 0.000 152s Investment_3 0.000 152s Investment_4 0.000 152s Investment_5 0.000 152s Investment_6 0.000 152s Investment_7 0.000 152s Investment_8 0.000 152s Investment_9 0.000 152s Investment_10 0.000 152s Investment_11 0.000 152s Investment_12 0.000 152s Investment_14 0.000 152s Investment_15 0.000 152s Investment_16 0.000 152s Investment_17 0.000 152s Investment_18 0.000 152s Investment_19 0.000 152s Investment_20 0.000 152s Investment_21 0.000 152s Investment_22 0.000 152s PrivateWages_2 13.389 152s PrivateWages_3 -2.216 152s PrivateWages_4 -9.004 152s PrivateWages_5 1.371 152s PrivateWages_6 3.170 152s PrivateWages_8 3.164 152s PrivateWages_9 -0.846 152s PrivateWages_10 -2.277 152s PrivateWages_11 0.190 152s PrivateWages_12 0.000 152s PrivateWages_13 0.121 152s PrivateWages_14 0.955 152s PrivateWages_15 0.911 152s PrivateWages_16 0.114 152s PrivateWages_17 -4.258 152s PrivateWages_18 5.945 152s PrivateWages_19 -3.218 152s PrivateWages_20 -3.055 152s PrivateWages_21 -9.956 152s PrivateWages_22 5.501 152s [1] TRUE 152s > Bread 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_(Intercept) 109.396 -1.6401 152s Consumption_corpProf -1.640 0.6675 152s Consumption_corpProfLag -0.598 -0.3509 152s Consumption_wages -1.641 -0.0975 152s Investment_(Intercept) 0.000 0.0000 152s Investment_corpProf 0.000 0.0000 152s Investment_corpProfLag 0.000 0.0000 152s Investment_capitalLag 0.000 0.0000 152s PrivateWages_(Intercept) 0.000 0.0000 152s PrivateWages_gnp 0.000 0.0000 152s PrivateWages_gnpLag 0.000 0.0000 152s PrivateWages_trend 0.000 0.0000 152s Consumption_corpProfLag Consumption_wages 152s Consumption_(Intercept) -0.5979 -1.6408 152s Consumption_corpProf -0.3509 -0.0975 152s Consumption_corpProfLag 0.4880 -0.0331 152s Consumption_wages -0.0331 0.0926 152s Investment_(Intercept) 0.0000 0.0000 152s Investment_corpProf 0.0000 0.0000 152s Investment_corpProfLag 0.0000 0.0000 152s Investment_capitalLag 0.0000 0.0000 152s PrivateWages_(Intercept) 0.0000 0.0000 152s PrivateWages_gnp 0.0000 0.0000 152s PrivateWages_gnpLag 0.0000 0.0000 152s PrivateWages_trend 0.0000 0.0000 152s Investment_(Intercept) Investment_corpProf 152s Consumption_(Intercept) 0.00 0.0000 152s Consumption_corpProf 0.00 0.0000 152s Consumption_corpProfLag 0.00 0.0000 152s Consumption_wages 0.00 0.0000 152s Investment_(Intercept) 1730.48 -16.5126 152s Investment_corpProf -16.51 0.6641 152s Investment_corpProfLag 13.63 -0.5096 152s Investment_capitalLag -8.34 0.0672 152s PrivateWages_(Intercept) 0.00 0.0000 152s PrivateWages_gnp 0.00 0.0000 152s PrivateWages_gnpLag 0.00 0.0000 152s PrivateWages_trend 0.00 0.0000 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_(Intercept) 0.000 0.0000 152s Consumption_corpProf 0.000 0.0000 152s Consumption_corpProfLag 0.000 0.0000 152s Consumption_wages 0.000 0.0000 152s Investment_(Intercept) 13.633 -8.3416 152s Investment_corpProf -0.510 0.0672 152s Investment_corpProfLag 0.603 -0.0740 152s Investment_capitalLag -0.074 0.0420 152s PrivateWages_(Intercept) 0.000 0.0000 152s PrivateWages_gnp 0.000 0.0000 152s PrivateWages_gnpLag 0.000 0.0000 152s PrivateWages_trend 0.000 0.0000 152s PrivateWages_(Intercept) PrivateWages_gnp 152s Consumption_(Intercept) 0.000 0.0000 152s Consumption_corpProf 0.000 0.0000 152s Consumption_corpProfLag 0.000 0.0000 152s Consumption_wages 0.000 0.0000 152s Investment_(Intercept) 0.000 0.0000 152s Investment_corpProf 0.000 0.0000 152s Investment_corpProfLag 0.000 0.0000 152s Investment_capitalLag 0.000 0.0000 152s PrivateWages_(Intercept) 166.178 -0.6258 152s PrivateWages_gnp -0.626 0.1064 152s PrivateWages_gnpLag -2.183 -0.0992 152s PrivateWages_trend 2.051 -0.0286 152s PrivateWages_gnpLag PrivateWages_trend 152s Consumption_(Intercept) 0.00000 0.00000 152s Consumption_corpProf 0.00000 0.00000 152s Consumption_corpProfLag 0.00000 0.00000 152s Consumption_wages 0.00000 0.00000 152s Investment_(Intercept) 0.00000 0.00000 152s Investment_corpProf 0.00000 0.00000 152s Investment_corpProfLag 0.00000 0.00000 152s Investment_capitalLag 0.00000 0.00000 152s PrivateWages_(Intercept) -2.18348 2.05079 152s PrivateWages_gnp -0.09921 -0.02859 152s PrivateWages_gnpLag 0.14047 -0.00635 152s PrivateWages_trend -0.00635 0.10969 152s > 152s > # 2SLS 152s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 152s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 152s > summary 152s 152s systemfit results 152s method: 2SLS 152s 152s N DF SSR detRCov OLS-R2 McElroy-R2 152s system 57 45 58.2 0.333 0.968 0.991 152s 152s N DF SSR MSE RMSE R2 Adj R2 152s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 152s Investment 19 15 26.21 1.748 1.32 0.852 0.823 152s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 152s 152s The covariance matrix of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.237 0.518 -0.408 152s Investment 0.518 1.263 0.113 152s PrivateWages -0.408 0.113 0.468 152s 152s The correlations of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.000 0.416 -0.538 152s Investment 0.416 1.000 0.139 152s PrivateWages -0.538 0.139 1.000 152s 152s 152s 2SLS estimates for 'Consumption' (equation 1) 152s Model Formula: consump ~ corpProf + corpProfLag + wages 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 17.2849 1.6018 10.79 3.6e-08 *** 152s corpProf -0.0770 0.1637 -0.47 0.645 152s corpProfLag 0.2327 0.1242 1.87 0.082 . 152s wages 0.8259 0.0459 17.98 4.5e-11 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.261 on 14 degrees of freedom 152s Number of observations: 18 Degrees of Freedom: 14 152s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 152s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 152s 152s 152s 2SLS estimates for 'Investment' (equation 2) 152s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 18.4005 7.1627 2.57 0.02138 * 152s corpProf 0.1507 0.1905 0.79 0.44118 152s corpProfLag 0.5757 0.1634 3.52 0.00307 ** 152s capitalLag -0.1452 0.0339 -4.28 0.00065 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.322 on 15 degrees of freedom 152s Number of observations: 19 Degrees of Freedom: 15 152s SSR: 26.213 MSE: 1.748 Root MSE: 1.322 152s Multiple R-Squared: 0.852 Adjusted R-Squared: 0.823 152s 152s 152s 2SLS estimates for 'PrivateWages' (equation 3) 152s Model Formula: privWage ~ gnp + gnpLag + trend 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 1.3431 1.1544 1.16 0.26172 152s gnp 0.4438 0.0351 12.64 9.7e-10 *** 152s gnpLag 0.1447 0.0381 3.80 0.00158 ** 152s trend 0.1238 0.0300 4.13 0.00078 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 0.78 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 152s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 152s 152s > residuals 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 -0.6754 -1.23599 -1.3401 152s 3 -0.4627 0.32957 0.2378 152s 4 -1.1585 1.08894 1.1117 152s 5 -0.0305 -1.37017 -0.1954 152s 6 0.4693 0.48431 -0.5355 152s 7 NA NA NA 152s 8 1.6045 1.06811 -0.7908 152s 9 1.6018 0.16695 0.2831 152s 10 NA 1.86380 1.1353 152s 11 -0.9031 -0.92183 -0.1765 152s 12 -1.5948 -1.03217 0.6007 152s 13 NA NA 0.1443 152s 14 0.2854 0.85468 0.4826 152s 15 -0.4718 -0.36943 0.3016 152s 16 -0.2268 0.00554 0.0261 152s 17 2.0079 1.69566 -0.8614 152s 18 -0.7434 -0.12659 0.9927 152s 19 -0.5410 -3.26209 -0.4446 152s 20 1.4186 0.25579 -0.3914 152s 21 1.1462 -0.00185 -1.1115 152s 22 -1.7256 0.50679 0.5312 152s > fitted 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 42.6 1.036 26.8 152s 3 45.5 1.570 29.1 152s 4 50.4 4.111 33.0 152s 5 50.6 4.370 34.1 152s 6 52.1 4.616 35.9 152s 7 NA NA NA 152s 8 54.6 3.132 38.7 152s 9 55.7 2.833 38.9 152s 10 NA 3.236 40.2 152s 11 55.9 1.922 38.1 152s 12 52.5 -2.368 33.9 152s 13 NA NA 28.9 152s 14 46.2 -5.955 28.0 152s 15 49.2 -2.631 30.3 152s 16 51.5 -1.306 33.2 152s 17 55.7 0.404 37.7 152s 18 59.4 2.127 40.0 152s 19 58.0 1.362 38.6 152s 20 60.2 1.044 42.0 152s 21 63.9 3.302 46.1 152s 22 71.4 4.393 52.8 152s > predict 152s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 152s 1 NA NA NA NA 152s 2 42.6 0.571 41.4 43.8 152s 3 45.5 0.656 44.1 46.9 152s 4 50.4 0.431 49.4 51.3 152s 5 50.6 0.510 49.5 51.7 152s 6 52.1 0.521 51.0 53.2 152s 7 NA NA NA NA 152s 8 54.6 0.419 53.7 55.5 152s 9 55.7 0.496 54.6 56.8 152s 10 NA NA NA NA 152s 11 55.9 0.910 54.0 57.9 152s 12 52.5 0.869 50.6 54.4 152s 13 NA NA NA NA 152s 14 46.2 0.694 44.7 47.7 152s 15 49.2 0.487 48.1 50.2 152s 16 51.5 0.396 50.7 52.4 152s 17 55.7 0.445 54.7 56.6 152s 18 59.4 0.386 58.6 60.3 152s 19 58.0 0.548 56.9 59.2 152s 20 60.2 0.528 59.0 61.3 152s 21 63.9 0.515 62.8 65.0 152s 22 71.4 0.786 69.7 73.1 152s Investment.pred Investment.se.fit Investment.lwr Investment.upr 152s 1 NA NA NA NA 152s 2 1.036 0.892 -0.865 2.937 152s 3 1.570 0.579 0.335 2.805 152s 4 4.111 0.531 2.979 5.243 152s 5 4.370 0.440 3.432 5.308 152s 6 4.616 0.416 3.729 5.502 152s 7 NA NA NA NA 152s 8 3.132 0.344 2.398 3.866 152s 9 2.833 0.533 1.696 3.970 152s 10 3.236 0.580 2.000 4.473 152s 11 1.922 0.959 -0.122 3.966 152s 12 -2.368 0.860 -4.201 -0.534 152s 13 NA NA NA NA 152s 14 -5.955 0.865 -7.799 -4.110 152s 15 -2.631 0.479 -3.652 -1.610 152s 16 -1.306 0.382 -2.120 -0.491 152s 17 0.404 0.487 -0.635 1.443 152s 18 2.127 0.319 1.447 2.806 152s 19 1.362 0.537 0.218 2.506 152s 20 1.044 0.566 -0.162 2.250 152s 21 3.302 0.486 2.265 4.339 152s 22 4.393 0.713 2.874 5.912 152s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 152s 1 NA NA NA NA 152s 2 26.8 0.321 26.2 27.5 152s 3 29.1 0.334 28.4 29.8 152s 4 33.0 0.353 32.2 33.7 152s 5 34.1 0.253 33.6 34.6 152s 6 35.9 0.261 35.4 36.5 152s 7 NA NA NA NA 152s 8 38.7 0.257 38.1 39.2 152s 9 38.9 0.245 38.4 39.4 152s 10 40.2 0.235 39.7 40.7 152s 11 38.1 0.348 37.3 38.8 152s 12 33.9 0.374 33.1 34.7 152s 13 28.9 0.447 27.9 29.8 152s 14 28.0 0.341 27.3 28.7 152s 15 30.3 0.333 29.6 31.0 152s 16 33.2 0.278 32.6 33.8 152s 17 37.7 0.288 37.1 38.3 152s 18 40.0 0.214 39.6 40.5 152s 19 38.6 0.351 37.9 39.4 152s 20 42.0 0.301 41.4 42.6 152s 21 46.1 0.304 45.5 46.8 152s 22 52.8 0.486 51.7 53.8 152s > model.frame 152s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 152s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 152s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 152s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 152s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 152s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 152s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 152s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 152s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 152s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 152s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 152s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 152s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 152s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 152s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 152s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 152s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 152s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 152s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 152s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 152s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 152s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 152s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 152s trend 152s 1 -11 152s 2 -10 152s 3 -9 152s 4 -8 152s 5 -7 152s 6 -6 152s 7 -5 152s 8 -4 152s 9 -3 152s 10 -2 152s 11 -1 152s 12 0 152s 13 1 152s 14 2 152s 15 3 152s 16 4 152s 17 5 152s 18 6 152s 19 7 152s 20 8 152s 21 9 152s 22 10 152s > Frames of instrumental variables 152s govExp taxes govWage trend capitalLag corpProfLag gnpLag 152s 1 2.4 3.4 2.2 -11 180 NA NA 152s 2 3.9 7.7 2.7 -10 183 12.7 44.9 152s 3 3.2 3.9 2.9 -9 183 12.4 45.6 152s 4 2.8 4.7 2.9 -8 184 16.9 50.1 152s 5 3.5 3.8 3.1 -7 190 18.4 57.2 152s 6 3.3 5.5 3.2 -6 193 19.4 57.1 152s 7 3.3 7.0 3.3 -5 198 20.1 NA 152s 8 4.0 6.7 3.6 -4 203 19.6 64.0 152s 9 4.2 4.2 3.7 -3 208 19.8 64.4 152s 10 4.1 4.0 4.0 -2 211 21.1 64.5 152s 11 5.2 7.7 4.2 -1 216 21.7 67.0 152s 12 5.9 7.5 4.8 0 217 15.6 61.2 152s 13 4.9 8.3 5.3 1 213 11.4 53.4 152s 14 3.7 5.4 5.6 2 207 7.0 44.3 152s 15 4.0 6.8 6.0 3 202 11.2 45.1 152s 16 4.4 7.2 6.1 4 199 12.3 49.7 152s 17 2.9 8.3 7.4 5 198 14.0 54.4 152s 18 4.3 6.7 6.7 6 200 17.6 62.7 152s 19 5.3 7.4 7.7 7 202 17.3 65.0 152s 20 6.6 8.9 7.8 8 200 15.3 60.9 152s 21 7.4 9.6 8.0 9 201 19.0 69.5 152s 22 13.8 11.6 8.5 10 204 21.1 75.7 152s govExp taxes govWage trend capitalLag corpProfLag gnpLag 152s 1 2.4 3.4 2.2 -11 180 NA NA 152s 2 3.9 7.7 2.7 -10 183 12.7 44.9 152s 3 3.2 3.9 2.9 -9 183 12.4 45.6 152s 4 2.8 4.7 2.9 -8 184 16.9 50.1 152s 5 3.5 3.8 3.1 -7 190 18.4 57.2 152s 6 3.3 5.5 3.2 -6 193 19.4 57.1 152s 7 3.3 7.0 3.3 -5 198 20.1 NA 152s 8 4.0 6.7 3.6 -4 203 19.6 64.0 152s 9 4.2 4.2 3.7 -3 208 19.8 64.4 152s 10 4.1 4.0 4.0 -2 211 21.1 64.5 152s 11 5.2 7.7 4.2 -1 216 21.7 67.0 152s 12 5.9 7.5 4.8 0 217 15.6 61.2 152s 13 4.9 8.3 5.3 1 213 11.4 53.4 152s 14 3.7 5.4 5.6 2 207 7.0 44.3 152s 15 4.0 6.8 6.0 3 202 11.2 45.1 152s 16 4.4 7.2 6.1 4 199 12.3 49.7 152s 17 2.9 8.3 7.4 5 198 14.0 54.4 152s 18 4.3 6.7 6.7 6 200 17.6 62.7 152s 19 5.3 7.4 7.7 7 202 17.3 65.0 152s 20 6.6 8.9 7.8 8 200 15.3 60.9 152s 21 7.4 9.6 8.0 9 201 19.0 69.5 152s 22 13.8 11.6 8.5 10 204 21.1 75.7 152s govExp taxes govWage trend capitalLag corpProfLag gnpLag 152s 1 2.4 3.4 2.2 -11 180 NA NA 152s 2 3.9 7.7 2.7 -10 183 12.7 44.9 152s 3 3.2 3.9 2.9 -9 183 12.4 45.6 152s 4 2.8 4.7 2.9 -8 184 16.9 50.1 152s 5 3.5 3.8 3.1 -7 190 18.4 57.2 152s 6 3.3 5.5 3.2 -6 193 19.4 57.1 152s 7 3.3 7.0 3.3 -5 198 20.1 NA 152s 8 4.0 6.7 3.6 -4 203 19.6 64.0 152s 9 4.2 4.2 3.7 -3 208 19.8 64.4 152s 10 4.1 4.0 4.0 -2 211 21.1 64.5 152s 11 5.2 7.7 4.2 -1 216 21.7 67.0 152s 12 5.9 7.5 4.8 0 217 15.6 61.2 152s 13 4.9 8.3 5.3 1 213 11.4 53.4 152s 14 3.7 5.4 5.6 2 207 7.0 44.3 152s 15 4.0 6.8 6.0 3 202 11.2 45.1 152s 16 4.4 7.2 6.1 4 199 12.3 49.7 152s 17 2.9 8.3 7.4 5 198 14.0 54.4 152s 18 4.3 6.7 6.7 6 200 17.6 62.7 152s 19 5.3 7.4 7.7 7 202 17.3 65.0 152s 20 6.6 8.9 7.8 8 200 15.3 60.9 152s 21 7.4 9.6 8.0 9 201 19.0 69.5 152s 22 13.8 11.6 8.5 10 204 21.1 75.7 152s > model.matrix 152s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 152s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 152s [3] "Numeric: lengths (708, 684) differ" 152s > matrix of instrumental variables 152s Consumption_(Intercept) Consumption_govExp Consumption_taxes 152s Consumption_2 1 3.9 7.7 152s Consumption_3 1 3.2 3.9 152s Consumption_4 1 2.8 4.7 152s Consumption_5 1 3.5 3.8 152s Consumption_6 1 3.3 5.5 152s Consumption_8 1 4.0 6.7 152s Consumption_9 1 4.2 4.2 152s Consumption_11 1 5.2 7.7 152s Consumption_12 1 5.9 7.5 152s Consumption_14 1 3.7 5.4 152s Consumption_15 1 4.0 6.8 152s Consumption_16 1 4.4 7.2 152s Consumption_17 1 2.9 8.3 152s Consumption_18 1 4.3 6.7 152s Consumption_19 1 5.3 7.4 152s Consumption_20 1 6.6 8.9 152s Consumption_21 1 7.4 9.6 152s Consumption_22 1 13.8 11.6 152s Investment_2 0 0.0 0.0 152s Investment_3 0 0.0 0.0 152s Investment_4 0 0.0 0.0 152s Investment_5 0 0.0 0.0 152s Investment_6 0 0.0 0.0 152s Investment_8 0 0.0 0.0 152s Investment_9 0 0.0 0.0 152s Investment_10 0 0.0 0.0 152s Investment_11 0 0.0 0.0 152s Investment_12 0 0.0 0.0 152s Investment_14 0 0.0 0.0 152s Investment_15 0 0.0 0.0 152s Investment_16 0 0.0 0.0 152s Investment_17 0 0.0 0.0 152s Investment_18 0 0.0 0.0 152s Investment_19 0 0.0 0.0 152s Investment_20 0 0.0 0.0 152s Investment_21 0 0.0 0.0 152s Investment_22 0 0.0 0.0 152s PrivateWages_2 0 0.0 0.0 152s PrivateWages_3 0 0.0 0.0 152s PrivateWages_4 0 0.0 0.0 152s PrivateWages_5 0 0.0 0.0 152s PrivateWages_6 0 0.0 0.0 152s PrivateWages_8 0 0.0 0.0 152s PrivateWages_9 0 0.0 0.0 152s PrivateWages_10 0 0.0 0.0 152s PrivateWages_11 0 0.0 0.0 152s PrivateWages_12 0 0.0 0.0 152s PrivateWages_13 0 0.0 0.0 152s PrivateWages_14 0 0.0 0.0 152s PrivateWages_15 0 0.0 0.0 152s PrivateWages_16 0 0.0 0.0 152s PrivateWages_17 0 0.0 0.0 152s PrivateWages_18 0 0.0 0.0 152s PrivateWages_19 0 0.0 0.0 152s PrivateWages_20 0 0.0 0.0 152s PrivateWages_21 0 0.0 0.0 152s PrivateWages_22 0 0.0 0.0 152s Consumption_govWage Consumption_trend Consumption_capitalLag 152s Consumption_2 2.7 -10 183 152s Consumption_3 2.9 -9 183 152s Consumption_4 2.9 -8 184 152s Consumption_5 3.1 -7 190 152s Consumption_6 3.2 -6 193 152s Consumption_8 3.6 -4 203 152s Consumption_9 3.7 -3 208 152s Consumption_11 4.2 -1 216 152s Consumption_12 4.8 0 217 152s Consumption_14 5.6 2 207 152s Consumption_15 6.0 3 202 152s Consumption_16 6.1 4 199 152s Consumption_17 7.4 5 198 152s Consumption_18 6.7 6 200 152s Consumption_19 7.7 7 202 152s Consumption_20 7.8 8 200 152s Consumption_21 8.0 9 201 152s Consumption_22 8.5 10 204 152s Investment_2 0.0 0 0 152s Investment_3 0.0 0 0 152s Investment_4 0.0 0 0 152s Investment_5 0.0 0 0 152s Investment_6 0.0 0 0 152s Investment_8 0.0 0 0 152s Investment_9 0.0 0 0 152s Investment_10 0.0 0 0 152s Investment_11 0.0 0 0 152s Investment_12 0.0 0 0 152s Investment_14 0.0 0 0 152s Investment_15 0.0 0 0 152s Investment_16 0.0 0 0 152s Investment_17 0.0 0 0 152s Investment_18 0.0 0 0 152s Investment_19 0.0 0 0 152s Investment_20 0.0 0 0 152s Investment_21 0.0 0 0 152s Investment_22 0.0 0 0 152s PrivateWages_2 0.0 0 0 152s PrivateWages_3 0.0 0 0 152s PrivateWages_4 0.0 0 0 152s PrivateWages_5 0.0 0 0 152s PrivateWages_6 0.0 0 0 152s PrivateWages_8 0.0 0 0 152s PrivateWages_9 0.0 0 0 152s PrivateWages_10 0.0 0 0 152s PrivateWages_11 0.0 0 0 152s PrivateWages_12 0.0 0 0 152s PrivateWages_13 0.0 0 0 152s PrivateWages_14 0.0 0 0 152s PrivateWages_15 0.0 0 0 152s PrivateWages_16 0.0 0 0 152s PrivateWages_17 0.0 0 0 152s PrivateWages_18 0.0 0 0 152s PrivateWages_19 0.0 0 0 152s PrivateWages_20 0.0 0 0 152s PrivateWages_21 0.0 0 0 152s PrivateWages_22 0.0 0 0 152s Consumption_corpProfLag Consumption_gnpLag 152s Consumption_2 12.7 44.9 152s Consumption_3 12.4 45.6 152s Consumption_4 16.9 50.1 152s Consumption_5 18.4 57.2 152s Consumption_6 19.4 57.1 152s Consumption_8 19.6 64.0 152s Consumption_9 19.8 64.4 152s Consumption_11 21.7 67.0 152s Consumption_12 15.6 61.2 152s Consumption_14 7.0 44.3 152s Consumption_15 11.2 45.1 152s Consumption_16 12.3 49.7 152s Consumption_17 14.0 54.4 152s Consumption_18 17.6 62.7 152s Consumption_19 17.3 65.0 152s Consumption_20 15.3 60.9 152s Consumption_21 19.0 69.5 152s Consumption_22 21.1 75.7 152s Investment_2 0.0 0.0 152s Investment_3 0.0 0.0 152s Investment_4 0.0 0.0 152s Investment_5 0.0 0.0 152s Investment_6 0.0 0.0 152s Investment_8 0.0 0.0 152s Investment_9 0.0 0.0 152s Investment_10 0.0 0.0 152s Investment_11 0.0 0.0 152s Investment_12 0.0 0.0 152s Investment_14 0.0 0.0 152s Investment_15 0.0 0.0 152s Investment_16 0.0 0.0 152s Investment_17 0.0 0.0 152s Investment_18 0.0 0.0 152s Investment_19 0.0 0.0 152s Investment_20 0.0 0.0 152s Investment_21 0.0 0.0 152s Investment_22 0.0 0.0 152s PrivateWages_2 0.0 0.0 152s PrivateWages_3 0.0 0.0 152s PrivateWages_4 0.0 0.0 152s PrivateWages_5 0.0 0.0 152s PrivateWages_6 0.0 0.0 152s PrivateWages_8 0.0 0.0 152s PrivateWages_9 0.0 0.0 152s PrivateWages_10 0.0 0.0 152s PrivateWages_11 0.0 0.0 152s PrivateWages_12 0.0 0.0 152s PrivateWages_13 0.0 0.0 152s PrivateWages_14 0.0 0.0 152s PrivateWages_15 0.0 0.0 152s PrivateWages_16 0.0 0.0 152s PrivateWages_17 0.0 0.0 152s PrivateWages_18 0.0 0.0 152s PrivateWages_19 0.0 0.0 152s PrivateWages_20 0.0 0.0 152s PrivateWages_21 0.0 0.0 152s PrivateWages_22 0.0 0.0 152s Investment_(Intercept) Investment_govExp Investment_taxes 152s Consumption_2 0 0.0 0.0 152s Consumption_3 0 0.0 0.0 152s Consumption_4 0 0.0 0.0 152s Consumption_5 0 0.0 0.0 152s Consumption_6 0 0.0 0.0 152s Consumption_8 0 0.0 0.0 152s Consumption_9 0 0.0 0.0 152s Consumption_11 0 0.0 0.0 152s Consumption_12 0 0.0 0.0 152s Consumption_14 0 0.0 0.0 152s Consumption_15 0 0.0 0.0 152s Consumption_16 0 0.0 0.0 152s Consumption_17 0 0.0 0.0 152s Consumption_18 0 0.0 0.0 152s Consumption_19 0 0.0 0.0 152s Consumption_20 0 0.0 0.0 152s Consumption_21 0 0.0 0.0 152s Consumption_22 0 0.0 0.0 152s Investment_2 1 3.9 7.7 152s Investment_3 1 3.2 3.9 152s Investment_4 1 2.8 4.7 152s Investment_5 1 3.5 3.8 152s Investment_6 1 3.3 5.5 152s Investment_8 1 4.0 6.7 152s Investment_9 1 4.2 4.2 152s Investment_10 1 4.1 4.0 152s Investment_11 1 5.2 7.7 152s Investment_12 1 5.9 7.5 152s Investment_14 1 3.7 5.4 152s Investment_15 1 4.0 6.8 152s Investment_16 1 4.4 7.2 152s Investment_17 1 2.9 8.3 152s Investment_18 1 4.3 6.7 152s Investment_19 1 5.3 7.4 152s Investment_20 1 6.6 8.9 152s Investment_21 1 7.4 9.6 152s Investment_22 1 13.8 11.6 152s PrivateWages_2 0 0.0 0.0 152s PrivateWages_3 0 0.0 0.0 152s PrivateWages_4 0 0.0 0.0 152s PrivateWages_5 0 0.0 0.0 152s PrivateWages_6 0 0.0 0.0 152s PrivateWages_8 0 0.0 0.0 152s PrivateWages_9 0 0.0 0.0 152s PrivateWages_10 0 0.0 0.0 152s PrivateWages_11 0 0.0 0.0 152s PrivateWages_12 0 0.0 0.0 152s PrivateWages_13 0 0.0 0.0 152s PrivateWages_14 0 0.0 0.0 152s PrivateWages_15 0 0.0 0.0 152s PrivateWages_16 0 0.0 0.0 152s PrivateWages_17 0 0.0 0.0 152s PrivateWages_18 0 0.0 0.0 152s PrivateWages_19 0 0.0 0.0 152s PrivateWages_20 0 0.0 0.0 152s PrivateWages_21 0 0.0 0.0 152s PrivateWages_22 0 0.0 0.0 152s Investment_govWage Investment_trend Investment_capitalLag 152s Consumption_2 0.0 0 0 152s Consumption_3 0.0 0 0 152s Consumption_4 0.0 0 0 152s Consumption_5 0.0 0 0 152s Consumption_6 0.0 0 0 152s Consumption_8 0.0 0 0 152s Consumption_9 0.0 0 0 152s Consumption_11 0.0 0 0 152s Consumption_12 0.0 0 0 152s Consumption_14 0.0 0 0 152s Consumption_15 0.0 0 0 152s Consumption_16 0.0 0 0 152s Consumption_17 0.0 0 0 152s Consumption_18 0.0 0 0 152s Consumption_19 0.0 0 0 152s Consumption_20 0.0 0 0 152s Consumption_21 0.0 0 0 152s Consumption_22 0.0 0 0 152s Investment_2 2.7 -10 183 152s Investment_3 2.9 -9 183 152s Investment_4 2.9 -8 184 152s Investment_5 3.1 -7 190 152s Investment_6 3.2 -6 193 152s Investment_8 3.6 -4 203 152s Investment_9 3.7 -3 208 152s Investment_10 4.0 -2 211 152s Investment_11 4.2 -1 216 152s Investment_12 4.8 0 217 152s Investment_14 5.6 2 207 152s Investment_15 6.0 3 202 152s Investment_16 6.1 4 199 152s Investment_17 7.4 5 198 152s Investment_18 6.7 6 200 152s Investment_19 7.7 7 202 152s Investment_20 7.8 8 200 152s Investment_21 8.0 9 201 152s Investment_22 8.5 10 204 152s PrivateWages_2 0.0 0 0 152s PrivateWages_3 0.0 0 0 152s PrivateWages_4 0.0 0 0 152s PrivateWages_5 0.0 0 0 152s PrivateWages_6 0.0 0 0 152s PrivateWages_8 0.0 0 0 152s PrivateWages_9 0.0 0 0 152s PrivateWages_10 0.0 0 0 152s PrivateWages_11 0.0 0 0 152s PrivateWages_12 0.0 0 0 152s PrivateWages_13 0.0 0 0 152s PrivateWages_14 0.0 0 0 152s PrivateWages_15 0.0 0 0 152s PrivateWages_16 0.0 0 0 152s PrivateWages_17 0.0 0 0 152s PrivateWages_18 0.0 0 0 152s PrivateWages_19 0.0 0 0 152s PrivateWages_20 0.0 0 0 152s PrivateWages_21 0.0 0 0 152s PrivateWages_22 0.0 0 0 152s Investment_corpProfLag Investment_gnpLag 152s Consumption_2 0.0 0.0 152s Consumption_3 0.0 0.0 152s Consumption_4 0.0 0.0 152s Consumption_5 0.0 0.0 152s Consumption_6 0.0 0.0 152s Consumption_8 0.0 0.0 152s Consumption_9 0.0 0.0 152s Consumption_11 0.0 0.0 152s Consumption_12 0.0 0.0 152s Consumption_14 0.0 0.0 152s Consumption_15 0.0 0.0 152s Consumption_16 0.0 0.0 152s Consumption_17 0.0 0.0 152s Consumption_18 0.0 0.0 152s Consumption_19 0.0 0.0 152s Consumption_20 0.0 0.0 152s Consumption_21 0.0 0.0 152s Consumption_22 0.0 0.0 152s Investment_2 12.7 44.9 152s Investment_3 12.4 45.6 152s Investment_4 16.9 50.1 152s Investment_5 18.4 57.2 152s Investment_6 19.4 57.1 152s Investment_8 19.6 64.0 152s Investment_9 19.8 64.4 152s Investment_10 21.1 64.5 152s Investment_11 21.7 67.0 152s Investment_12 15.6 61.2 152s Investment_14 7.0 44.3 152s Investment_15 11.2 45.1 152s Investment_16 12.3 49.7 152s Investment_17 14.0 54.4 152s Investment_18 17.6 62.7 152s Investment_19 17.3 65.0 152s Investment_20 15.3 60.9 152s Investment_21 19.0 69.5 152s Investment_22 21.1 75.7 152s PrivateWages_2 0.0 0.0 152s PrivateWages_3 0.0 0.0 152s PrivateWages_4 0.0 0.0 152s PrivateWages_5 0.0 0.0 152s PrivateWages_6 0.0 0.0 152s PrivateWages_8 0.0 0.0 152s PrivateWages_9 0.0 0.0 152s PrivateWages_10 0.0 0.0 152s PrivateWages_11 0.0 0.0 152s PrivateWages_12 0.0 0.0 152s PrivateWages_13 0.0 0.0 152s PrivateWages_14 0.0 0.0 152s PrivateWages_15 0.0 0.0 152s PrivateWages_16 0.0 0.0 152s PrivateWages_17 0.0 0.0 152s PrivateWages_18 0.0 0.0 152s PrivateWages_19 0.0 0.0 152s PrivateWages_20 0.0 0.0 152s PrivateWages_21 0.0 0.0 152s PrivateWages_22 0.0 0.0 152s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 152s Consumption_2 0 0.0 0.0 152s Consumption_3 0 0.0 0.0 152s Consumption_4 0 0.0 0.0 152s Consumption_5 0 0.0 0.0 152s Consumption_6 0 0.0 0.0 152s Consumption_8 0 0.0 0.0 152s Consumption_9 0 0.0 0.0 152s Consumption_11 0 0.0 0.0 152s Consumption_12 0 0.0 0.0 152s Consumption_14 0 0.0 0.0 152s Consumption_15 0 0.0 0.0 152s Consumption_16 0 0.0 0.0 152s Consumption_17 0 0.0 0.0 152s Consumption_18 0 0.0 0.0 152s Consumption_19 0 0.0 0.0 152s Consumption_20 0 0.0 0.0 152s Consumption_21 0 0.0 0.0 152s Consumption_22 0 0.0 0.0 152s Investment_2 0 0.0 0.0 152s Investment_3 0 0.0 0.0 152s Investment_4 0 0.0 0.0 152s Investment_5 0 0.0 0.0 152s Investment_6 0 0.0 0.0 152s Investment_8 0 0.0 0.0 152s Investment_9 0 0.0 0.0 152s Investment_10 0 0.0 0.0 152s Investment_11 0 0.0 0.0 152s Investment_12 0 0.0 0.0 152s Investment_14 0 0.0 0.0 152s Investment_15 0 0.0 0.0 152s Investment_16 0 0.0 0.0 152s Investment_17 0 0.0 0.0 152s Investment_18 0 0.0 0.0 152s Investment_19 0 0.0 0.0 152s Investment_20 0 0.0 0.0 152s Investment_21 0 0.0 0.0 152s Investment_22 0 0.0 0.0 152s PrivateWages_2 1 3.9 7.7 152s PrivateWages_3 1 3.2 3.9 152s PrivateWages_4 1 2.8 4.7 152s PrivateWages_5 1 3.5 3.8 152s PrivateWages_6 1 3.3 5.5 152s PrivateWages_8 1 4.0 6.7 152s PrivateWages_9 1 4.2 4.2 152s PrivateWages_10 1 4.1 4.0 152s PrivateWages_11 1 5.2 7.7 152s PrivateWages_12 1 5.9 7.5 152s PrivateWages_13 1 4.9 8.3 152s PrivateWages_14 1 3.7 5.4 152s PrivateWages_15 1 4.0 6.8 152s PrivateWages_16 1 4.4 7.2 152s PrivateWages_17 1 2.9 8.3 152s PrivateWages_18 1 4.3 6.7 152s PrivateWages_19 1 5.3 7.4 152s PrivateWages_20 1 6.6 8.9 152s PrivateWages_21 1 7.4 9.6 152s PrivateWages_22 1 13.8 11.6 152s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 152s Consumption_2 0.0 0 0 152s Consumption_3 0.0 0 0 152s Consumption_4 0.0 0 0 152s Consumption_5 0.0 0 0 152s Consumption_6 0.0 0 0 152s Consumption_8 0.0 0 0 152s Consumption_9 0.0 0 0 152s Consumption_11 0.0 0 0 152s Consumption_12 0.0 0 0 152s Consumption_14 0.0 0 0 152s Consumption_15 0.0 0 0 152s Consumption_16 0.0 0 0 152s Consumption_17 0.0 0 0 152s Consumption_18 0.0 0 0 152s Consumption_19 0.0 0 0 152s Consumption_20 0.0 0 0 152s Consumption_21 0.0 0 0 152s Consumption_22 0.0 0 0 152s Investment_2 0.0 0 0 152s Investment_3 0.0 0 0 152s Investment_4 0.0 0 0 152s Investment_5 0.0 0 0 152s Investment_6 0.0 0 0 152s Investment_8 0.0 0 0 152s Investment_9 0.0 0 0 152s Investment_10 0.0 0 0 152s Investment_11 0.0 0 0 152s Investment_12 0.0 0 0 152s Investment_14 0.0 0 0 152s Investment_15 0.0 0 0 152s Investment_16 0.0 0 0 152s Investment_17 0.0 0 0 152s Investment_18 0.0 0 0 152s Investment_19 0.0 0 0 152s Investment_20 0.0 0 0 152s Investment_21 0.0 0 0 152s Investment_22 0.0 0 0 152s PrivateWages_2 2.7 -10 183 152s PrivateWages_3 2.9 -9 183 152s PrivateWages_4 2.9 -8 184 152s PrivateWages_5 3.1 -7 190 152s PrivateWages_6 3.2 -6 193 152s PrivateWages_8 3.6 -4 203 152s PrivateWages_9 3.7 -3 208 152s PrivateWages_10 4.0 -2 211 152s PrivateWages_11 4.2 -1 216 152s PrivateWages_12 4.8 0 217 152s PrivateWages_13 5.3 1 213 152s PrivateWages_14 5.6 2 207 152s PrivateWages_15 6.0 3 202 152s PrivateWages_16 6.1 4 199 152s PrivateWages_17 7.4 5 198 152s PrivateWages_18 6.7 6 200 152s PrivateWages_19 7.7 7 202 152s PrivateWages_20 7.8 8 200 152s PrivateWages_21 8.0 9 201 152s PrivateWages_22 8.5 10 204 152s PrivateWages_corpProfLag PrivateWages_gnpLag 152s Consumption_2 0.0 0.0 152s Consumption_3 0.0 0.0 152s Consumption_4 0.0 0.0 152s Consumption_5 0.0 0.0 152s Consumption_6 0.0 0.0 152s Consumption_8 0.0 0.0 152s Consumption_9 0.0 0.0 152s Consumption_11 0.0 0.0 152s Consumption_12 0.0 0.0 152s Consumption_14 0.0 0.0 152s Consumption_15 0.0 0.0 152s Consumption_16 0.0 0.0 152s Consumption_17 0.0 0.0 152s Consumption_18 0.0 0.0 152s Consumption_19 0.0 0.0 152s Consumption_20 0.0 0.0 152s Consumption_21 0.0 0.0 152s Consumption_22 0.0 0.0 152s Investment_2 0.0 0.0 152s Investment_3 0.0 0.0 152s Investment_4 0.0 0.0 152s Investment_5 0.0 0.0 152s Investment_6 0.0 0.0 152s Investment_8 0.0 0.0 152s Investment_9 0.0 0.0 152s Investment_10 0.0 0.0 152s Investment_11 0.0 0.0 152s Investment_12 0.0 0.0 152s Investment_14 0.0 0.0 152s Investment_15 0.0 0.0 152s Investment_16 0.0 0.0 152s Investment_17 0.0 0.0 152s Investment_18 0.0 0.0 152s Investment_19 0.0 0.0 152s Investment_20 0.0 0.0 152s Investment_21 0.0 0.0 152s Investment_22 0.0 0.0 152s PrivateWages_2 12.7 44.9 152s PrivateWages_3 12.4 45.6 152s PrivateWages_4 16.9 50.1 152s PrivateWages_5 18.4 57.2 152s PrivateWages_6 19.4 57.1 152s PrivateWages_8 19.6 64.0 152s PrivateWages_9 19.8 64.4 152s PrivateWages_10 21.1 64.5 152s PrivateWages_11 21.7 67.0 152s PrivateWages_12 15.6 61.2 152s PrivateWages_13 11.4 53.4 152s PrivateWages_14 7.0 44.3 152s PrivateWages_15 11.2 45.1 152s PrivateWages_16 12.3 49.7 152s PrivateWages_17 14.0 54.4 152s PrivateWages_18 17.6 62.7 152s PrivateWages_19 17.3 65.0 152s PrivateWages_20 15.3 60.9 152s PrivateWages_21 19.0 69.5 152s PrivateWages_22 21.1 75.7 152s > matrix of fitted regressors 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 1 14.0 152s Consumption_3 1 16.7 152s Consumption_4 1 18.5 152s Consumption_5 1 20.3 152s Consumption_6 1 19.0 152s Consumption_8 1 17.6 152s Consumption_9 1 18.9 152s Consumption_11 1 16.7 152s Consumption_12 1 13.4 152s Consumption_14 1 10.0 152s Consumption_15 1 12.5 152s Consumption_16 1 14.5 152s Consumption_17 1 14.9 152s Consumption_18 1 19.4 152s Consumption_19 1 19.1 152s Consumption_20 1 17.7 152s Consumption_21 1 20.4 152s Consumption_22 1 22.7 152s Investment_2 0 0.0 152s Investment_3 0 0.0 152s Investment_4 0 0.0 152s Investment_5 0 0.0 152s Investment_6 0 0.0 152s Investment_8 0 0.0 152s Investment_9 0 0.0 152s Investment_10 0 0.0 152s Investment_11 0 0.0 152s Investment_12 0 0.0 152s Investment_14 0 0.0 152s Investment_15 0 0.0 152s Investment_16 0 0.0 152s Investment_17 0 0.0 152s Investment_18 0 0.0 152s Investment_19 0 0.0 152s Investment_20 0 0.0 152s Investment_21 0 0.0 152s Investment_22 0 0.0 152s PrivateWages_2 0 0.0 152s PrivateWages_3 0 0.0 152s PrivateWages_4 0 0.0 152s PrivateWages_5 0 0.0 152s PrivateWages_6 0 0.0 152s PrivateWages_8 0 0.0 152s PrivateWages_9 0 0.0 152s PrivateWages_10 0 0.0 152s PrivateWages_11 0 0.0 152s PrivateWages_12 0 0.0 152s PrivateWages_13 0 0.0 152s PrivateWages_14 0 0.0 152s PrivateWages_15 0 0.0 152s PrivateWages_16 0 0.0 152s PrivateWages_17 0 0.0 152s PrivateWages_18 0 0.0 152s PrivateWages_19 0 0.0 152s PrivateWages_20 0 0.0 152s PrivateWages_21 0 0.0 152s PrivateWages_22 0 0.0 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 12.7 29.8 152s Consumption_3 12.4 31.8 152s Consumption_4 16.9 35.3 152s Consumption_5 18.4 38.6 152s Consumption_6 19.4 38.5 152s Consumption_8 19.6 40.0 152s Consumption_9 19.8 41.8 152s Consumption_11 21.7 43.1 152s Consumption_12 15.6 39.7 152s Consumption_14 7.0 33.3 152s Consumption_15 11.2 37.3 152s Consumption_16 12.3 40.1 152s Consumption_17 14.0 41.8 152s Consumption_18 17.6 47.6 152s Consumption_19 17.3 49.2 152s Consumption_20 15.3 48.6 152s Consumption_21 19.0 53.4 152s Consumption_22 21.1 60.8 152s Investment_2 0.0 0.0 152s Investment_3 0.0 0.0 152s Investment_4 0.0 0.0 152s Investment_5 0.0 0.0 152s Investment_6 0.0 0.0 152s Investment_8 0.0 0.0 152s Investment_9 0.0 0.0 152s Investment_10 0.0 0.0 152s Investment_11 0.0 0.0 152s Investment_12 0.0 0.0 152s Investment_14 0.0 0.0 152s Investment_15 0.0 0.0 152s Investment_16 0.0 0.0 152s Investment_17 0.0 0.0 152s Investment_18 0.0 0.0 152s Investment_19 0.0 0.0 152s Investment_20 0.0 0.0 152s Investment_21 0.0 0.0 152s Investment_22 0.0 0.0 152s PrivateWages_2 0.0 0.0 152s PrivateWages_3 0.0 0.0 152s PrivateWages_4 0.0 0.0 152s PrivateWages_5 0.0 0.0 152s PrivateWages_6 0.0 0.0 152s PrivateWages_8 0.0 0.0 152s PrivateWages_9 0.0 0.0 152s PrivateWages_10 0.0 0.0 152s PrivateWages_11 0.0 0.0 152s PrivateWages_12 0.0 0.0 152s PrivateWages_13 0.0 0.0 152s PrivateWages_14 0.0 0.0 152s PrivateWages_15 0.0 0.0 152s PrivateWages_16 0.0 0.0 152s PrivateWages_17 0.0 0.0 152s PrivateWages_18 0.0 0.0 152s PrivateWages_19 0.0 0.0 152s PrivateWages_20 0.0 0.0 152s PrivateWages_21 0.0 0.0 152s PrivateWages_22 0.0 0.0 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 0 0.00 152s Consumption_3 0 0.00 152s Consumption_4 0 0.00 152s Consumption_5 0 0.00 152s Consumption_6 0 0.00 152s Consumption_8 0 0.00 152s Consumption_9 0 0.00 152s Consumption_11 0 0.00 152s Consumption_12 0 0.00 152s Consumption_14 0 0.00 152s Consumption_15 0 0.00 152s Consumption_16 0 0.00 152s Consumption_17 0 0.00 152s Consumption_18 0 0.00 152s Consumption_19 0 0.00 152s Consumption_20 0 0.00 152s Consumption_21 0 0.00 152s Consumption_22 0 0.00 152s Investment_2 1 13.41 152s Investment_3 1 16.69 152s Investment_4 1 18.79 152s Investment_5 1 20.65 152s Investment_6 1 19.26 152s Investment_8 1 17.53 152s Investment_9 1 19.53 152s Investment_10 1 20.27 152s Investment_11 1 17.19 152s Investment_12 1 13.52 152s Investment_14 1 9.99 152s Investment_15 1 12.86 152s Investment_16 1 14.33 152s Investment_17 1 14.97 152s Investment_18 1 19.37 152s Investment_19 1 19.36 152s Investment_20 1 17.47 152s Investment_21 1 20.12 152s Investment_22 1 22.78 152s PrivateWages_2 0 0.00 152s PrivateWages_3 0 0.00 152s PrivateWages_4 0 0.00 152s PrivateWages_5 0 0.00 152s PrivateWages_6 0 0.00 152s PrivateWages_8 0 0.00 152s PrivateWages_9 0 0.00 152s PrivateWages_10 0 0.00 152s PrivateWages_11 0 0.00 152s PrivateWages_12 0 0.00 152s PrivateWages_13 0 0.00 152s PrivateWages_14 0 0.00 152s PrivateWages_15 0 0.00 152s PrivateWages_16 0 0.00 152s PrivateWages_17 0 0.00 152s PrivateWages_18 0 0.00 152s PrivateWages_19 0 0.00 152s PrivateWages_20 0 0.00 152s PrivateWages_21 0 0.00 152s PrivateWages_22 0 0.00 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 0.0 0 152s Consumption_3 0.0 0 152s Consumption_4 0.0 0 152s Consumption_5 0.0 0 152s Consumption_6 0.0 0 152s Consumption_8 0.0 0 152s Consumption_9 0.0 0 152s Consumption_11 0.0 0 152s Consumption_12 0.0 0 152s Consumption_14 0.0 0 152s Consumption_15 0.0 0 152s Consumption_16 0.0 0 152s Consumption_17 0.0 0 152s Consumption_18 0.0 0 152s Consumption_19 0.0 0 152s Consumption_20 0.0 0 152s Consumption_21 0.0 0 152s Consumption_22 0.0 0 152s Investment_2 12.7 183 152s Investment_3 12.4 183 152s Investment_4 16.9 184 152s Investment_5 18.4 190 152s Investment_6 19.4 193 152s Investment_8 19.6 203 152s Investment_9 19.8 208 152s Investment_10 21.1 211 152s Investment_11 21.7 216 152s Investment_12 15.6 217 152s Investment_14 7.0 207 152s Investment_15 11.2 202 152s Investment_16 12.3 199 152s Investment_17 14.0 198 152s Investment_18 17.6 200 152s Investment_19 17.3 202 152s Investment_20 15.3 200 152s Investment_21 19.0 201 152s Investment_22 21.1 204 152s PrivateWages_2 0.0 0 152s PrivateWages_3 0.0 0 152s PrivateWages_4 0.0 0 152s PrivateWages_5 0.0 0 152s PrivateWages_6 0.0 0 152s PrivateWages_8 0.0 0 152s PrivateWages_9 0.0 0 152s PrivateWages_10 0.0 0 152s PrivateWages_11 0.0 0 152s PrivateWages_12 0.0 0 152s PrivateWages_13 0.0 0 152s PrivateWages_14 0.0 0 152s PrivateWages_15 0.0 0 152s PrivateWages_16 0.0 0 152s PrivateWages_17 0.0 0 152s PrivateWages_18 0.0 0 152s PrivateWages_19 0.0 0 152s PrivateWages_20 0.0 0 152s PrivateWages_21 0.0 0 152s PrivateWages_22 0.0 0 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 0 0.0 0.0 152s Consumption_3 0 0.0 0.0 152s Consumption_4 0 0.0 0.0 152s Consumption_5 0 0.0 0.0 152s Consumption_6 0 0.0 0.0 152s Consumption_8 0 0.0 0.0 152s Consumption_9 0 0.0 0.0 152s Consumption_11 0 0.0 0.0 152s Consumption_12 0 0.0 0.0 152s Consumption_14 0 0.0 0.0 152s Consumption_15 0 0.0 0.0 152s Consumption_16 0 0.0 0.0 152s Consumption_17 0 0.0 0.0 152s Consumption_18 0 0.0 0.0 152s Consumption_19 0 0.0 0.0 152s Consumption_20 0 0.0 0.0 152s Consumption_21 0 0.0 0.0 152s Consumption_22 0 0.0 0.0 152s Investment_2 0 0.0 0.0 152s Investment_3 0 0.0 0.0 152s Investment_4 0 0.0 0.0 152s Investment_5 0 0.0 0.0 152s Investment_6 0 0.0 0.0 152s Investment_8 0 0.0 0.0 152s Investment_9 0 0.0 0.0 152s Investment_10 0 0.0 0.0 152s Investment_11 0 0.0 0.0 152s Investment_12 0 0.0 0.0 152s Investment_14 0 0.0 0.0 152s Investment_15 0 0.0 0.0 152s Investment_16 0 0.0 0.0 152s Investment_17 0 0.0 0.0 152s Investment_18 0 0.0 0.0 152s Investment_19 0 0.0 0.0 152s Investment_20 0 0.0 0.0 152s Investment_21 0 0.0 0.0 152s Investment_22 0 0.0 0.0 152s PrivateWages_2 1 47.1 44.9 152s PrivateWages_3 1 49.6 45.6 152s PrivateWages_4 1 56.5 50.1 152s PrivateWages_5 1 60.7 57.2 152s PrivateWages_6 1 60.6 57.1 152s PrivateWages_8 1 60.0 64.0 152s PrivateWages_9 1 62.3 64.4 152s PrivateWages_10 1 64.6 64.5 152s PrivateWages_11 1 63.7 67.0 152s PrivateWages_12 1 54.8 61.2 152s PrivateWages_13 1 47.0 53.4 152s PrivateWages_14 1 42.1 44.3 152s PrivateWages_15 1 51.2 45.1 152s PrivateWages_16 1 55.3 49.7 152s PrivateWages_17 1 57.4 54.4 152s PrivateWages_18 1 67.2 62.7 152s PrivateWages_19 1 68.5 65.0 152s PrivateWages_20 1 66.8 60.9 152s PrivateWages_21 1 74.9 69.5 152s PrivateWages_22 1 86.9 75.7 152s PrivateWages_trend 152s Consumption_2 0 152s Consumption_3 0 152s Consumption_4 0 152s Consumption_5 0 152s Consumption_6 0 152s Consumption_8 0 152s Consumption_9 0 152s Consumption_11 0 152s Consumption_12 0 152s Consumption_14 0 152s Consumption_15 0 152s Consumption_16 0 152s Consumption_17 0 152s Consumption_18 0 152s Consumption_19 0 152s Consumption_20 0 152s Consumption_21 0 152s Consumption_22 0 152s Investment_2 0 152s Investment_3 0 152s Investment_4 0 152s Investment_5 0 152s Investment_6 0 152s Investment_8 0 152s Investment_9 0 152s Investment_10 0 152s Investment_11 0 152s Investment_12 0 152s Investment_14 0 152s Investment_15 0 152s Investment_16 0 152s Investment_17 0 152s Investment_18 0 152s Investment_19 0 152s Investment_20 0 152s Investment_21 0 152s Investment_22 0 152s PrivateWages_2 -10 152s PrivateWages_3 -9 152s PrivateWages_4 -8 152s PrivateWages_5 -7 152s PrivateWages_6 -6 152s PrivateWages_8 -4 152s PrivateWages_9 -3 152s PrivateWages_10 -2 152s PrivateWages_11 -1 152s PrivateWages_12 0 152s PrivateWages_13 1 152s PrivateWages_14 2 152s PrivateWages_15 3 152s PrivateWages_16 4 152s PrivateWages_17 5 152s PrivateWages_18 6 152s PrivateWages_19 7 152s PrivateWages_20 8 152s PrivateWages_21 9 152s PrivateWages_22 10 152s > nobs 152s [1] 57 152s > linearHypothesis 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 46 152s 2 45 1 1.37 0.25 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 46 152s 2 45 1 1.77 0.19 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 46 152s 2 45 1 1.77 0.18 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 47 152s 2 45 2 0.69 0.51 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 47 152s 2 45 2 0.89 0.42 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 47 152s 2 45 2 1.78 0.41 152s > logLik 152s 'log Lik.' -70.6 (df=13) 152s 'log Lik.' -78.7 (df=13) 152s Estimating function 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 -1.891 -26.49 152s Consumption_3 -0.190 -3.16 152s Consumption_4 0.294 5.45 152s Consumption_5 -1.285 -26.05 152s Consumption_6 0.431 8.19 152s Consumption_8 2.670 47.11 152s Consumption_9 2.363 44.77 152s Consumption_11 -1.642 -27.49 152s Consumption_12 -1.735 -23.21 152s Consumption_14 0.834 8.35 152s Consumption_15 -1.061 -13.27 152s Consumption_16 -0.885 -12.82 152s Consumption_17 3.801 56.68 152s Consumption_18 -0.502 -9.76 152s Consumption_19 -3.000 -57.33 152s Consumption_20 2.012 35.52 152s Consumption_21 0.746 15.21 152s Consumption_22 -0.957 -21.70 152s Investment_2 0.000 0.00 152s Investment_3 0.000 0.00 152s Investment_4 0.000 0.00 152s Investment_5 0.000 0.00 152s Investment_6 0.000 0.00 152s Investment_8 0.000 0.00 152s Investment_9 0.000 0.00 152s Investment_10 0.000 0.00 152s Investment_11 0.000 0.00 152s Investment_12 0.000 0.00 152s Investment_14 0.000 0.00 152s Investment_15 0.000 0.00 152s Investment_16 0.000 0.00 152s Investment_17 0.000 0.00 152s Investment_18 0.000 0.00 152s Investment_19 0.000 0.00 152s Investment_20 0.000 0.00 152s Investment_21 0.000 0.00 152s Investment_22 0.000 0.00 152s PrivateWages_2 0.000 0.00 152s PrivateWages_3 0.000 0.00 152s PrivateWages_4 0.000 0.00 152s PrivateWages_5 0.000 0.00 152s PrivateWages_6 0.000 0.00 152s PrivateWages_8 0.000 0.00 152s PrivateWages_9 0.000 0.00 152s PrivateWages_10 0.000 0.00 152s PrivateWages_11 0.000 0.00 152s PrivateWages_12 0.000 0.00 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 0.000 0.00 152s PrivateWages_15 0.000 0.00 152s PrivateWages_16 0.000 0.00 152s PrivateWages_17 0.000 0.00 152s PrivateWages_18 0.000 0.00 152s PrivateWages_19 0.000 0.00 152s PrivateWages_20 0.000 0.00 152s PrivateWages_21 0.000 0.00 152s PrivateWages_22 0.000 0.00 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 -24.01 -56.38 152s Consumption_3 -2.35 -6.04 152s Consumption_4 4.96 10.35 152s Consumption_5 -23.65 -49.61 152s Consumption_6 8.35 16.60 152s Consumption_8 52.33 106.81 152s Consumption_9 46.80 98.74 152s Consumption_11 -35.64 -70.78 152s Consumption_12 -27.07 -68.81 152s Consumption_14 5.83 27.78 152s Consumption_15 -11.88 -39.61 152s Consumption_16 -10.89 -35.54 152s Consumption_17 53.21 158.79 152s Consumption_18 -8.84 -23.92 152s Consumption_19 -51.90 -147.70 152s Consumption_20 30.78 97.67 152s Consumption_21 14.17 39.83 152s Consumption_22 -20.20 -58.19 152s Investment_2 0.00 0.00 152s Investment_3 0.00 0.00 152s Investment_4 0.00 0.00 152s Investment_5 0.00 0.00 152s Investment_6 0.00 0.00 152s Investment_8 0.00 0.00 152s Investment_9 0.00 0.00 152s Investment_10 0.00 0.00 152s Investment_11 0.00 0.00 152s Investment_12 0.00 0.00 152s Investment_14 0.00 0.00 152s Investment_15 0.00 0.00 152s Investment_16 0.00 0.00 152s Investment_17 0.00 0.00 152s Investment_18 0.00 0.00 152s Investment_19 0.00 0.00 152s Investment_20 0.00 0.00 152s Investment_21 0.00 0.00 152s Investment_22 0.00 0.00 152s PrivateWages_2 0.00 0.00 152s PrivateWages_3 0.00 0.00 152s PrivateWages_4 0.00 0.00 152s PrivateWages_5 0.00 0.00 152s PrivateWages_6 0.00 0.00 152s PrivateWages_8 0.00 0.00 152s PrivateWages_9 0.00 0.00 152s PrivateWages_10 0.00 0.00 152s PrivateWages_11 0.00 0.00 152s PrivateWages_12 0.00 0.00 152s PrivateWages_13 0.00 0.00 152s PrivateWages_14 0.00 0.00 152s PrivateWages_15 0.00 0.00 152s PrivateWages_16 0.00 0.00 152s PrivateWages_17 0.00 0.00 152s PrivateWages_18 0.00 0.00 152s PrivateWages_19 0.00 0.00 152s PrivateWages_20 0.00 0.00 152s PrivateWages_21 0.00 0.00 152s PrivateWages_22 0.00 0.00 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 0.000 0.000 152s Consumption_3 0.000 0.000 152s Consumption_4 0.000 0.000 152s Consumption_5 0.000 0.000 152s Consumption_6 0.000 0.000 152s Consumption_8 0.000 0.000 152s Consumption_9 0.000 0.000 152s Consumption_11 0.000 0.000 152s Consumption_12 0.000 0.000 152s Consumption_14 0.000 0.000 152s Consumption_15 0.000 0.000 152s Consumption_16 0.000 0.000 152s Consumption_17 0.000 0.000 152s Consumption_18 0.000 0.000 152s Consumption_19 0.000 0.000 152s Consumption_20 0.000 0.000 152s Consumption_21 0.000 0.000 152s Consumption_22 0.000 0.000 152s Investment_2 -1.389 -18.632 152s Investment_3 0.361 6.028 152s Investment_4 1.031 19.362 152s Investment_5 -1.558 -32.177 152s Investment_6 0.610 11.759 152s Investment_8 1.410 24.716 152s Investment_9 0.404 7.885 152s Investment_10 2.080 42.149 152s Investment_11 -1.162 -19.982 152s Investment_12 -1.352 -18.282 152s Investment_14 1.037 10.359 152s Investment_15 -0.454 -5.832 152s Investment_16 -0.044 -0.631 152s Investment_17 2.093 31.318 152s Investment_18 -0.438 -8.488 152s Investment_19 -3.873 -74.977 152s Investment_20 0.486 8.486 152s Investment_21 0.145 2.925 152s Investment_22 0.615 14.015 152s PrivateWages_2 0.000 0.000 152s PrivateWages_3 0.000 0.000 152s PrivateWages_4 0.000 0.000 152s PrivateWages_5 0.000 0.000 152s PrivateWages_6 0.000 0.000 152s PrivateWages_8 0.000 0.000 152s PrivateWages_9 0.000 0.000 152s PrivateWages_10 0.000 0.000 152s PrivateWages_11 0.000 0.000 152s PrivateWages_12 0.000 0.000 152s PrivateWages_13 0.000 0.000 152s PrivateWages_14 0.000 0.000 152s PrivateWages_15 0.000 0.000 152s PrivateWages_16 0.000 0.000 152s PrivateWages_17 0.000 0.000 152s PrivateWages_18 0.000 0.000 152s PrivateWages_19 0.000 0.000 152s PrivateWages_20 0.000 0.000 152s PrivateWages_21 0.000 0.000 152s PrivateWages_22 0.000 0.000 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 0.000 0.00 152s Consumption_3 0.000 0.00 152s Consumption_4 0.000 0.00 152s Consumption_5 0.000 0.00 152s Consumption_6 0.000 0.00 152s Consumption_8 0.000 0.00 152s Consumption_9 0.000 0.00 152s Consumption_11 0.000 0.00 152s Consumption_12 0.000 0.00 152s Consumption_14 0.000 0.00 152s Consumption_15 0.000 0.00 152s Consumption_16 0.000 0.00 152s Consumption_17 0.000 0.00 152s Consumption_18 0.000 0.00 152s Consumption_19 0.000 0.00 152s Consumption_20 0.000 0.00 152s Consumption_21 0.000 0.00 152s Consumption_22 0.000 0.00 152s Investment_2 -17.639 -253.89 152s Investment_3 4.479 65.95 152s Investment_4 17.417 190.14 152s Investment_5 -28.673 -295.61 152s Investment_6 11.843 117.63 152s Investment_8 27.629 286.73 152s Investment_9 7.995 83.82 152s Investment_10 43.878 437.95 152s Investment_11 -25.218 -250.67 152s Investment_12 -21.091 -292.97 152s Investment_14 7.256 214.68 152s Investment_15 -5.080 -91.62 152s Investment_16 -0.541 -8.76 152s Investment_17 29.296 413.70 152s Investment_18 -7.713 -87.56 152s Investment_19 -67.010 -781.66 152s Investment_20 7.430 97.07 152s Investment_21 2.762 29.24 152s Investment_22 12.981 125.81 152s PrivateWages_2 0.000 0.00 152s PrivateWages_3 0.000 0.00 152s PrivateWages_4 0.000 0.00 152s PrivateWages_5 0.000 0.00 152s PrivateWages_6 0.000 0.00 152s PrivateWages_8 0.000 0.00 152s PrivateWages_9 0.000 0.00 152s PrivateWages_10 0.000 0.00 152s PrivateWages_11 0.000 0.00 152s PrivateWages_12 0.000 0.00 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 0.000 0.00 152s PrivateWages_15 0.000 0.00 152s PrivateWages_16 0.000 0.00 152s PrivateWages_17 0.000 0.00 152s PrivateWages_18 0.000 0.00 152s PrivateWages_19 0.000 0.00 152s PrivateWages_20 0.000 0.00 152s PrivateWages_21 0.000 0.00 152s PrivateWages_22 0.000 0.00 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 0.0000 0.00 0.00 152s Consumption_3 0.0000 0.00 0.00 152s Consumption_4 0.0000 0.00 0.00 152s Consumption_5 0.0000 0.00 0.00 152s Consumption_6 0.0000 0.00 0.00 152s Consumption_8 0.0000 0.00 0.00 152s Consumption_9 0.0000 0.00 0.00 152s Consumption_11 0.0000 0.00 0.00 152s Consumption_12 0.0000 0.00 0.00 152s Consumption_14 0.0000 0.00 0.00 152s Consumption_15 0.0000 0.00 0.00 152s Consumption_16 0.0000 0.00 0.00 152s Consumption_17 0.0000 0.00 0.00 152s Consumption_18 0.0000 0.00 0.00 152s Consumption_19 0.0000 0.00 0.00 152s Consumption_20 0.0000 0.00 0.00 152s Consumption_21 0.0000 0.00 0.00 152s Consumption_22 0.0000 0.00 0.00 152s Investment_2 0.0000 0.00 0.00 152s Investment_3 0.0000 0.00 0.00 152s Investment_4 0.0000 0.00 0.00 152s Investment_5 0.0000 0.00 0.00 152s Investment_6 0.0000 0.00 0.00 152s Investment_8 0.0000 0.00 0.00 152s Investment_9 0.0000 0.00 0.00 152s Investment_10 0.0000 0.00 0.00 152s Investment_11 0.0000 0.00 0.00 152s Investment_12 0.0000 0.00 0.00 152s Investment_14 0.0000 0.00 0.00 152s Investment_15 0.0000 0.00 0.00 152s Investment_16 0.0000 0.00 0.00 152s Investment_17 0.0000 0.00 0.00 152s Investment_18 0.0000 0.00 0.00 152s Investment_19 0.0000 0.00 0.00 152s Investment_20 0.0000 0.00 0.00 152s Investment_21 0.0000 0.00 0.00 152s Investment_22 0.0000 0.00 0.00 152s PrivateWages_2 -1.9924 -93.78 -89.46 152s PrivateWages_3 0.4683 23.22 21.35 152s PrivateWages_4 1.4034 79.35 70.31 152s PrivateWages_5 -1.7870 -108.45 -102.22 152s PrivateWages_6 -0.3627 -21.98 -20.71 152s PrivateWages_8 1.1629 69.77 74.43 152s PrivateWages_9 1.2735 79.30 82.01 152s PrivateWages_10 2.2141 142.96 142.81 152s PrivateWages_11 -1.2912 -82.26 -86.51 152s PrivateWages_12 -0.0350 -1.92 -2.14 152s PrivateWages_13 -1.0438 -49.04 -55.74 152s PrivateWages_14 1.8016 75.90 79.81 152s PrivateWages_15 -0.3714 -19.02 -16.75 152s PrivateWages_16 -0.3904 -21.61 -19.40 152s PrivateWages_17 1.4934 85.71 81.24 152s PrivateWages_18 0.0279 1.88 1.75 152s PrivateWages_19 -3.8229 -261.91 -248.49 152s PrivateWages_20 0.7870 52.61 47.93 152s PrivateWages_21 -0.7415 -55.52 -51.54 152s PrivateWages_22 1.2062 104.79 91.31 152s PrivateWages_trend 152s Consumption_2 0.000 152s Consumption_3 0.000 152s Consumption_4 0.000 152s Consumption_5 0.000 152s Consumption_6 0.000 152s Consumption_8 0.000 152s Consumption_9 0.000 152s Consumption_11 0.000 152s Consumption_12 0.000 152s Consumption_14 0.000 152s Consumption_15 0.000 152s Consumption_16 0.000 152s Consumption_17 0.000 152s Consumption_18 0.000 152s Consumption_19 0.000 152s Consumption_20 0.000 152s Consumption_21 0.000 152s Consumption_22 0.000 152s Investment_2 0.000 152s Investment_3 0.000 152s Investment_4 0.000 152s Investment_5 0.000 152s Investment_6 0.000 152s Investment_8 0.000 152s Investment_9 0.000 152s Investment_10 0.000 152s Investment_11 0.000 152s Investment_12 0.000 152s Investment_14 0.000 152s Investment_15 0.000 152s Investment_16 0.000 152s Investment_17 0.000 152s Investment_18 0.000 152s Investment_19 0.000 152s Investment_20 0.000 152s Investment_21 0.000 152s Investment_22 0.000 152s PrivateWages_2 19.924 152s PrivateWages_3 -4.214 152s PrivateWages_4 -11.227 152s PrivateWages_5 12.509 152s PrivateWages_6 2.176 152s PrivateWages_8 -4.652 152s PrivateWages_9 -3.820 152s PrivateWages_10 -4.428 152s PrivateWages_11 1.291 152s PrivateWages_12 0.000 152s PrivateWages_13 -1.044 152s PrivateWages_14 3.603 152s PrivateWages_15 -1.114 152s PrivateWages_16 -1.562 152s PrivateWages_17 7.467 152s PrivateWages_18 0.168 152s PrivateWages_19 -26.760 152s PrivateWages_20 6.296 152s PrivateWages_21 -6.674 152s PrivateWages_22 12.062 152s [1] TRUE 152s > Bread 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_(Intercept) 118.21 -4.213 152s Consumption_corpProf -4.21 1.235 152s Consumption_corpProfLag 1.03 -0.689 152s Consumption_wages -1.44 -0.136 152s Investment_(Intercept) 0.00 0.000 152s Investment_corpProf 0.00 0.000 152s Investment_corpProfLag 0.00 0.000 152s Investment_capitalLag 0.00 0.000 152s PrivateWages_(Intercept) 0.00 0.000 152s PrivateWages_gnp 0.00 0.000 152s PrivateWages_gnpLag 0.00 0.000 152s PrivateWages_trend 0.00 0.000 152s Consumption_corpProfLag Consumption_wages 152s Consumption_(Intercept) 1.0298 -1.4384 152s Consumption_corpProf -0.6891 -0.1356 152s Consumption_corpProfLag 0.7104 -0.0191 152s Consumption_wages -0.0191 0.0972 152s Investment_(Intercept) 0.0000 0.0000 152s Investment_corpProf 0.0000 0.0000 152s Investment_corpProfLag 0.0000 0.0000 152s Investment_capitalLag 0.0000 0.0000 152s PrivateWages_(Intercept) 0.0000 0.0000 152s PrivateWages_gnp 0.0000 0.0000 152s PrivateWages_gnpLag 0.0000 0.0000 152s PrivateWages_trend 0.0000 0.0000 152s Investment_(Intercept) Investment_corpProf 152s Consumption_(Intercept) 0.0 0.000 152s Consumption_corpProf 0.0 0.000 152s Consumption_corpProfLag 0.0 0.000 152s Consumption_wages 0.0 0.000 152s Investment_(Intercept) 2314.8 -41.107 152s Investment_corpProf -41.1 1.637 152s Investment_corpProfLag 33.2 -1.272 152s Investment_capitalLag -10.7 0.169 152s PrivateWages_(Intercept) 0.0 0.000 152s PrivateWages_gnp 0.0 0.000 152s PrivateWages_gnpLag 0.0 0.000 152s PrivateWages_trend 0.0 0.000 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_(Intercept) 0.000 0.0000 152s Consumption_corpProf 0.000 0.0000 152s Consumption_corpProfLag 0.000 0.0000 152s Consumption_wages 0.000 0.0000 152s Investment_(Intercept) 33.159 -10.7377 152s Investment_corpProf -1.272 0.1688 152s Investment_corpProfLag 1.204 -0.1550 152s Investment_capitalLag -0.155 0.0519 152s PrivateWages_(Intercept) 0.000 0.0000 152s PrivateWages_gnp 0.000 0.0000 152s PrivateWages_gnpLag 0.000 0.0000 152s PrivateWages_trend 0.000 0.0000 152s PrivateWages_(Intercept) PrivateWages_gnp 152s Consumption_(Intercept) 0.000 0.0000 152s Consumption_corpProf 0.000 0.0000 152s Consumption_corpProfLag 0.000 0.0000 152s Consumption_wages 0.000 0.0000 152s Investment_(Intercept) 0.000 0.0000 152s Investment_corpProf 0.000 0.0000 152s Investment_corpProfLag 0.000 0.0000 152s Investment_capitalLag 0.000 0.0000 152s PrivateWages_(Intercept) 162.179 -0.8825 152s PrivateWages_gnp -0.882 0.1501 152s PrivateWages_gnpLag -1.850 -0.1399 152s PrivateWages_trend 2.056 -0.0403 152s PrivateWages_gnpLag PrivateWages_trend 152s Consumption_(Intercept) 0.0000 0.0000 152s Consumption_corpProf 0.0000 0.0000 152s Consumption_corpProfLag 0.0000 0.0000 152s Consumption_wages 0.0000 0.0000 152s Investment_(Intercept) 0.0000 0.0000 152s Investment_corpProf 0.0000 0.0000 152s Investment_corpProfLag 0.0000 0.0000 152s Investment_capitalLag 0.0000 0.0000 152s PrivateWages_(Intercept) -1.8504 2.0559 152s PrivateWages_gnp -0.1399 -0.0403 152s PrivateWages_gnpLag 0.1768 0.0057 152s PrivateWages_trend 0.0057 0.1094 152s > 152s > # SUR 152s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 152s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 152s > summary 152s 152s systemfit results 152s method: SUR 152s 152s N DF SSR detRCov OLS-R2 McElroy-R2 152s system 59 47 45.1 0.168 0.976 0.992 152s 152s N DF SSR MSE RMSE R2 Adj R2 152s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 152s Investment 20 16 17.3 1.083 1.041 0.911 0.894 152s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 152s 152s The covariance matrix of the residuals used for estimation 152s Consumption Investment PrivateWages 152s Consumption 0.9286 0.0435 -0.369 152s Investment 0.0435 0.7653 0.109 152s PrivateWages -0.3690 0.1091 0.468 152s 152s The covariance matrix of the residuals 152s Consumption Investment PrivateWages 152s Consumption 0.9251 0.0748 -0.427 152s Investment 0.0748 0.7653 0.171 152s PrivateWages -0.4268 0.1706 0.492 152s 152s The correlations of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.0000 0.0888 -0.636 152s Investment 0.0888 1.0000 0.268 152s PrivateWages -0.6364 0.2678 1.000 152s 152s 152s SUR estimates for 'Consumption' (equation 1) 152s Model Formula: consump ~ corpProf + corpProfLag + wages 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 16.2684 1.2781 12.73 1.9e-09 *** 152s corpProf 0.1942 0.0927 2.10 0.054 . 152s corpProfLag 0.0746 0.0819 0.91 0.377 152s wages 0.8011 0.0372 21.53 1.1e-12 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.08 on 15 degrees of freedom 152s Number of observations: 19 Degrees of Freedom: 15 152s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 152s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 152s 152s 152s SUR estimates for 'Investment' (equation 2) 152s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 12.6462 4.6500 2.72 0.01515 * 152s corpProf 0.4707 0.0916 5.14 9.9e-05 *** 152s corpProfLag 0.3519 0.0874 4.03 0.00097 *** 152s capitalLag -0.1253 0.0229 -5.47 5.1e-05 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.041 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 17.325 MSE: 1.083 Root MSE: 1.041 152s Multiple R-Squared: 0.911 Adjusted R-Squared: 0.894 152s 152s 152s SUR estimates for 'PrivateWages' (equation 3) 152s Model Formula: privWage ~ gnp + gnpLag + trend 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 1.3245 1.0946 1.21 0.24 152s gnp 0.4184 0.0260 16.08 2.7e-11 *** 152s gnpLag 0.1714 0.0307 5.59 4.1e-05 *** 152s trend 0.1455 0.0276 5.27 7.6e-05 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 0.801 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 10.265 MSE: 0.642 Root MSE: 0.801 152s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 152s 152s > residuals 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 -0.3146 -0.2419 -1.1439 152s 3 -1.2707 -0.1795 0.5080 152s 4 -1.5428 1.0691 1.4208 152s 5 -0.4489 -1.4778 -0.1000 152s 6 0.0588 0.3168 -0.3599 152s 7 0.9215 1.4450 NA 152s 8 1.3791 0.8287 -0.7561 152s 9 1.0901 -0.5272 0.2880 152s 10 NA 1.2089 1.1795 152s 11 0.3577 0.4081 -0.3681 152s 12 -0.2286 0.2569 0.3439 152s 13 NA NA -0.1574 152s 14 0.2172 0.4743 0.4225 152s 15 -0.1124 -0.0607 0.3154 152s 16 -0.0876 0.0761 0.0151 152s 17 1.5611 1.0205 -0.8084 152s 18 -0.4529 0.0580 0.8611 152s 19 0.1999 -2.5444 -0.7635 152s 20 0.9266 -0.6202 -0.4039 152s 21 0.7589 -0.7478 -1.2175 152s 22 -2.2135 -0.6029 0.5611 152s > fitted 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 42.2 0.0419 26.6 152s 3 46.3 2.0795 28.8 152s 4 50.7 4.1309 32.7 152s 5 51.0 4.4778 34.0 152s 6 52.5 4.7832 35.8 152s 7 54.2 4.1550 NA 152s 8 54.8 3.3713 38.7 152s 9 56.2 3.5272 38.9 152s 10 NA 3.8911 40.1 152s 11 54.6 0.5919 38.3 152s 12 51.1 -3.6569 34.2 152s 13 NA NA 29.2 152s 14 46.3 -5.5743 28.1 152s 15 48.8 -2.9393 30.3 152s 16 51.4 -1.3761 33.2 152s 17 56.1 1.0795 37.6 152s 18 59.2 1.9420 40.1 152s 19 57.3 0.6444 39.0 152s 20 60.7 1.9202 42.0 152s 21 64.2 4.0478 46.2 152s 22 71.9 5.5029 52.7 152s > predict 152s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 152s 1 NA NA NA NA 152s 2 42.2 0.448 41.3 43.1 152s 3 46.3 0.476 45.3 47.2 152s 4 50.7 0.318 50.1 51.4 152s 5 51.0 0.373 50.3 51.8 152s 6 52.5 0.378 51.8 53.3 152s 7 54.2 0.337 53.5 54.9 152s 8 54.8 0.310 54.2 55.4 152s 9 56.2 0.343 55.5 56.9 152s 10 NA NA NA NA 152s 11 54.6 0.567 53.5 55.8 152s 12 51.1 0.509 50.1 52.2 152s 13 NA NA NA NA 152s 14 46.3 0.573 45.1 47.4 152s 15 48.8 0.382 48.0 49.6 152s 16 51.4 0.328 50.7 52.0 152s 17 56.1 0.336 55.5 56.8 152s 18 59.2 0.309 58.5 59.8 152s 19 57.3 0.370 56.6 58.0 152s 20 60.7 0.401 59.9 61.5 152s 21 64.2 0.405 63.4 65.1 152s 22 71.9 0.633 70.6 73.2 152s Investment.pred Investment.se.fit Investment.lwr Investment.upr 152s 1 NA NA NA NA 152s 2 0.0419 0.533 -1.0309 1.115 152s 3 2.0795 0.433 1.2082 2.951 152s 4 4.1309 0.387 3.3532 4.909 152s 5 4.4778 0.322 3.8307 5.125 152s 6 4.7832 0.305 4.1700 5.396 152s 7 4.1550 0.283 3.5852 4.725 152s 8 3.3713 0.253 2.8630 3.880 152s 9 3.5272 0.337 2.8488 4.206 152s 10 3.8911 0.386 3.1149 4.667 152s 11 0.5919 0.561 -0.5376 1.722 152s 12 -3.6569 0.530 -4.7223 -2.591 152s 13 NA NA NA NA 152s 14 -5.5743 0.618 -6.8176 -4.331 152s 15 -2.9393 0.362 -3.6671 -2.212 152s 16 -1.3761 0.296 -1.9710 -0.781 152s 17 1.0795 0.300 0.4763 1.683 152s 18 1.9420 0.216 1.5081 2.376 152s 19 0.6444 0.298 0.0451 1.244 152s 20 1.9202 0.318 1.2798 2.561 152s 21 4.0478 0.295 3.4537 4.642 152s 22 5.5029 0.417 4.6638 6.342 152s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 152s 1 NA NA NA NA 152s 2 26.6 0.312 26.0 27.3 152s 3 28.8 0.312 28.2 29.4 152s 4 32.7 0.307 32.1 33.3 152s 5 34.0 0.237 33.5 34.5 152s 6 35.8 0.235 35.3 36.2 152s 7 NA NA NA NA 152s 8 38.7 0.239 38.2 39.1 152s 9 38.9 0.228 38.5 39.4 152s 10 40.1 0.218 39.7 40.6 152s 11 38.3 0.293 37.7 38.9 152s 12 34.2 0.290 33.6 34.7 152s 13 29.2 0.343 28.5 29.8 152s 14 28.1 0.321 27.4 28.7 152s 15 30.3 0.320 29.6 30.9 152s 16 33.2 0.268 32.6 33.7 152s 17 37.6 0.263 37.1 38.1 152s 18 40.1 0.207 39.7 40.6 152s 19 39.0 0.293 38.4 39.6 152s 20 42.0 0.279 41.4 42.6 152s 21 46.2 0.295 45.6 46.8 152s 22 52.7 0.435 51.9 53.6 152s > model.frame 152s [1] TRUE 152s > model.matrix 152s [1] TRUE 152s > nobs 152s [1] 59 152s > linearHypothesis 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 47 1 0.41 0.52 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 47 1 0.52 0.47 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 48 152s 2 47 1 0.52 0.47 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 49 152s 2 47 2 0.31 0.73 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 49 152s 2 47 2 0.4 0.67 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 49 152s 2 47 2 0.79 0.67 152s > logLik 152s 'log Lik.' -67.3 (df=18) 152s 'log Lik.' -74.9 (df=18) 152s Estimating function 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 -0.5115 -6.342 152s Consumption_3 -2.0659 -34.913 152s Consumption_4 -2.5083 -46.152 152s Consumption_5 -0.7298 -14.158 152s Consumption_6 0.0957 1.923 152s Consumption_7 1.4982 29.364 152s Consumption_8 2.2421 44.394 152s Consumption_9 1.7723 37.396 152s Consumption_11 0.5815 9.072 152s Consumption_12 -0.3716 -4.237 152s Consumption_14 0.3531 3.954 152s Consumption_15 -0.1827 -2.248 152s Consumption_16 -0.1424 -1.993 152s Consumption_17 2.5380 44.669 152s Consumption_18 -0.7363 -12.738 152s Consumption_19 0.3251 4.973 152s Consumption_20 1.5064 28.622 152s Consumption_21 1.2337 26.032 152s Consumption_22 -3.5987 -84.568 152s Investment_2 0.0688 0.854 152s Investment_3 0.0511 0.863 152s Investment_4 -0.3043 -5.599 152s Investment_5 0.4206 8.160 152s Investment_6 -0.0902 -1.813 152s Investment_7 -0.4113 -8.061 152s Investment_8 -0.2359 -4.670 152s Investment_9 0.1501 3.166 152s Investment_10 0.0000 0.000 152s Investment_11 -0.1161 -1.812 152s Investment_12 -0.0731 -0.834 152s Investment_14 -0.1350 -1.512 152s Investment_15 0.0173 0.212 152s Investment_16 -0.0217 -0.303 152s Investment_17 -0.2904 -5.112 152s Investment_18 -0.0165 -0.286 152s Investment_19 0.7242 11.080 152s Investment_20 0.1765 3.354 152s Investment_21 0.2128 4.491 152s Investment_22 0.1716 4.032 152s PrivateWages_2 -1.5418 -19.118 152s PrivateWages_3 0.6847 11.571 152s PrivateWages_4 1.9149 35.234 152s PrivateWages_5 -0.1348 -2.615 152s PrivateWages_6 -0.4851 -9.750 152s PrivateWages_8 -1.0191 -20.178 152s PrivateWages_9 0.3882 8.190 152s PrivateWages_10 0.0000 0.000 152s PrivateWages_11 -0.4961 -7.739 152s PrivateWages_12 0.4635 5.284 152s PrivateWages_13 0.0000 0.000 152s PrivateWages_14 0.5694 6.377 152s PrivateWages_15 0.4251 5.229 152s PrivateWages_16 0.0204 0.286 152s PrivateWages_17 -1.0895 -19.175 152s PrivateWages_18 1.1605 20.077 152s PrivateWages_19 -1.0290 -15.743 152s PrivateWages_20 -0.5443 -10.343 152s PrivateWages_21 -1.6408 -34.622 152s PrivateWages_22 0.7563 17.772 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 -6.496 -14.423 152s Consumption_3 -25.617 -66.521 152s Consumption_4 -42.390 -92.806 152s Consumption_5 -13.428 -27.003 152s Consumption_6 1.856 3.693 152s Consumption_7 30.114 60.976 152s Consumption_8 43.945 93.047 152s Consumption_9 35.092 76.033 152s Consumption_11 12.619 24.482 152s Consumption_12 -5.798 -14.606 152s Consumption_14 2.471 12.039 152s Consumption_15 -2.047 -6.688 152s Consumption_16 -1.751 -5.595 152s Consumption_17 35.532 112.180 152s Consumption_18 -12.959 -35.121 152s Consumption_19 5.624 14.920 152s Consumption_20 23.048 74.417 152s Consumption_21 23.441 65.389 152s Consumption_22 -75.932 -222.397 152s Investment_2 0.874 1.941 152s Investment_3 0.633 1.645 152s Investment_4 -5.142 -11.258 152s Investment_5 7.739 15.562 152s Investment_6 -1.749 -3.481 152s Investment_7 -8.267 -16.739 152s Investment_8 -4.623 -9.788 152s Investment_9 2.971 6.437 152s Investment_10 0.000 0.000 152s Investment_11 -2.520 -4.889 152s Investment_12 -1.141 -2.873 152s Investment_14 -0.945 -4.603 152s Investment_15 0.193 0.632 152s Investment_16 -0.266 -0.851 152s Investment_17 -4.066 -12.838 152s Investment_18 -0.291 -0.787 152s Investment_19 12.528 33.240 152s Investment_20 2.701 8.720 152s Investment_21 4.044 11.280 152s Investment_22 3.620 10.604 152s PrivateWages_2 -19.580 -43.478 152s PrivateWages_3 8.490 22.046 152s PrivateWages_4 32.362 70.851 152s PrivateWages_5 -2.480 -4.987 152s PrivateWages_6 -9.410 -18.724 152s PrivateWages_8 -19.974 -42.291 152s PrivateWages_9 7.686 16.652 152s PrivateWages_10 0.000 0.000 152s PrivateWages_11 -10.765 -20.886 152s PrivateWages_12 7.230 18.215 152s PrivateWages_13 0.000 0.000 152s PrivateWages_14 3.986 19.417 152s PrivateWages_15 4.762 15.560 152s PrivateWages_16 0.251 0.802 152s PrivateWages_17 -15.253 -48.156 152s PrivateWages_18 20.425 55.356 152s PrivateWages_19 -17.801 -47.230 152s PrivateWages_20 -8.329 -26.891 152s PrivateWages_21 -31.176 -86.965 152s PrivateWages_22 15.957 46.737 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 0.08954 1.110 152s Consumption_3 0.36165 6.112 152s Consumption_4 0.43910 8.079 152s Consumption_5 0.12776 2.479 152s Consumption_6 -0.01675 -0.337 152s Consumption_7 -0.26227 -5.141 152s Consumption_8 -0.39250 -7.772 152s Consumption_9 -0.31026 -6.547 152s Consumption_11 -0.10180 -1.588 152s Consumption_12 0.06506 0.742 152s Consumption_14 -0.06181 -0.692 152s Consumption_15 0.03199 0.393 152s Consumption_16 0.02492 0.349 152s Consumption_17 -0.44431 -7.820 152s Consumption_18 0.12890 2.230 152s Consumption_19 -0.05691 -0.871 152s Consumption_20 -0.26372 -5.011 152s Consumption_21 -0.21598 -4.557 152s Consumption_22 0.62998 14.805 152s Investment_2 -0.33900 -4.204 152s Investment_3 -0.25149 -4.250 152s Investment_4 1.49825 27.568 152s Investment_5 -2.07104 -40.178 152s Investment_6 0.44402 8.925 152s Investment_7 2.02512 39.692 152s Investment_8 1.16134 22.995 152s Investment_9 -0.73888 -15.590 152s Investment_10 1.69419 36.764 152s Investment_11 0.57188 8.921 152s Investment_12 0.36002 4.104 152s Investment_14 0.66469 7.445 152s Investment_15 -0.08500 -1.046 152s Investment_16 0.10666 1.493 152s Investment_17 1.43016 25.171 152s Investment_18 0.08129 1.406 152s Investment_19 -3.56588 -54.558 152s Investment_20 -0.86923 -16.515 152s Investment_21 -1.04801 -22.113 152s Investment_22 -0.84488 -19.855 152s PrivateWages_2 0.63026 7.815 152s PrivateWages_3 -0.27988 -4.730 152s PrivateWages_4 -0.78278 -14.403 152s PrivateWages_5 0.05510 1.069 152s PrivateWages_6 0.19829 3.986 152s PrivateWages_8 0.41658 8.248 152s PrivateWages_9 -0.15868 -3.348 152s PrivateWages_10 -0.64985 -14.102 152s PrivateWages_11 0.20280 3.164 152s PrivateWages_12 -0.18947 -2.160 152s PrivateWages_13 0.00000 0.000 152s PrivateWages_14 -0.23276 -2.607 152s PrivateWages_15 -0.17379 -2.138 152s PrivateWages_16 -0.00834 -0.117 152s PrivateWages_17 0.44538 7.839 152s PrivateWages_18 -0.47440 -8.207 152s PrivateWages_19 0.42063 6.436 152s PrivateWages_20 0.22252 4.228 152s PrivateWages_21 0.67076 14.153 152s PrivateWages_22 -0.30915 -7.265 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 1.137 16.37 152s Consumption_3 4.484 66.04 152s Consumption_4 7.421 81.01 152s Consumption_5 2.351 24.24 152s Consumption_6 -0.325 -3.23 152s Consumption_7 -5.272 -51.88 152s Consumption_8 -7.693 -79.84 152s Consumption_9 -6.143 -64.41 152s Consumption_11 -2.209 -21.96 152s Consumption_12 1.015 14.10 152s Consumption_14 -0.433 -12.80 152s Consumption_15 0.358 6.46 152s Consumption_16 0.307 4.96 152s Consumption_17 -6.220 -87.84 152s Consumption_18 2.269 25.75 152s Consumption_19 -0.984 -11.48 152s Consumption_20 -4.035 -52.72 152s Consumption_21 -4.104 -43.46 152s Consumption_22 13.293 128.83 152s Investment_2 -4.305 -61.97 152s Investment_3 -3.118 -45.92 152s Investment_4 25.320 276.43 152s Investment_5 -38.107 -392.88 152s Investment_6 8.614 85.56 152s Investment_7 40.705 400.57 152s Investment_8 22.762 236.22 152s Investment_9 -14.630 -153.39 152s Investment_10 35.747 356.80 152s Investment_11 12.410 123.35 152s Investment_12 5.616 78.02 152s Investment_14 4.653 137.66 152s Investment_15 -0.952 -17.17 152s Investment_16 1.312 21.22 152s Investment_17 20.022 282.74 152s Investment_18 1.431 16.24 152s Investment_19 -61.690 -719.59 152s Investment_20 -13.299 -173.76 152s Investment_21 -19.912 -210.86 152s Investment_22 -17.827 -172.78 152s PrivateWages_2 8.004 115.21 152s PrivateWages_3 -3.471 -51.11 152s PrivateWages_4 -13.229 -144.42 152s PrivateWages_5 1.014 10.45 152s PrivateWages_6 3.847 38.21 152s PrivateWages_8 8.165 84.73 152s PrivateWages_9 -3.142 -32.94 152s PrivateWages_10 -13.712 -136.86 152s PrivateWages_11 4.401 43.74 152s PrivateWages_12 -2.956 -41.06 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 -1.629 -48.21 152s PrivateWages_15 -1.946 -35.11 152s PrivateWages_16 -0.103 -1.66 152s PrivateWages_17 6.235 88.05 152s PrivateWages_18 -8.349 -94.78 152s PrivateWages_19 7.277 84.88 152s PrivateWages_20 3.405 44.48 152s PrivateWages_21 12.744 134.96 152s PrivateWages_22 -6.523 -63.22 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 -0.4240 -19.33 -19.04 152s Consumption_3 -1.7126 -85.80 -78.09 152s Consumption_4 -2.0793 -118.94 -104.17 152s Consumption_5 -0.6050 -34.54 -34.61 152s Consumption_6 0.0793 4.84 4.53 152s Consumption_7 0.0000 0.00 0.00 152s Consumption_8 1.8587 119.70 118.95 152s Consumption_9 1.4692 94.76 94.62 152s Consumption_11 0.4821 29.50 32.30 152s Consumption_12 -0.3081 -16.45 -18.85 152s Consumption_14 0.2927 13.20 12.97 152s Consumption_15 -0.1515 -7.53 -6.83 152s Consumption_16 -0.1180 -6.42 -5.87 152s Consumption_17 2.1040 131.92 114.46 152s Consumption_18 -0.6104 -39.67 -38.27 152s Consumption_19 0.2695 16.41 17.52 152s Consumption_20 1.2488 86.79 76.05 152s Consumption_21 1.0228 77.42 71.08 152s Consumption_22 -2.9832 -263.72 -225.83 152s Investment_2 0.1333 6.08 5.98 152s Investment_3 0.0989 4.95 4.51 152s Investment_4 -0.5890 -33.69 -29.51 152s Investment_5 0.8142 46.49 46.57 152s Investment_6 -0.1746 -10.65 -9.97 152s Investment_7 0.0000 0.00 0.00 152s Investment_8 -0.4566 -29.40 -29.22 152s Investment_9 0.2905 18.74 18.71 152s Investment_10 -0.6660 -44.62 -42.96 152s Investment_11 -0.2248 -13.76 -15.06 152s Investment_12 -0.1415 -7.56 -8.66 152s Investment_14 -0.2613 -11.79 -11.58 152s Investment_15 0.0334 1.66 1.51 152s Investment_16 -0.0419 -2.28 -2.08 152s Investment_17 -0.5622 -35.25 -30.59 152s Investment_18 -0.0320 -2.08 -2.00 152s Investment_19 1.4018 85.37 91.12 152s Investment_20 0.3417 23.75 20.81 152s Investment_21 0.4120 31.19 28.63 152s Investment_22 0.3321 29.36 25.14 152s PrivateWages_2 -3.8052 -173.52 -170.85 152s PrivateWages_3 1.6898 84.66 77.06 152s PrivateWages_4 4.7261 270.33 236.78 152s PrivateWages_5 -0.3327 -19.00 -19.03 152s PrivateWages_6 -1.1972 -73.03 -68.36 152s PrivateWages_8 -2.5152 -161.98 -160.97 152s PrivateWages_9 0.9580 61.79 61.70 152s PrivateWages_10 3.9235 262.88 253.07 152s PrivateWages_11 -1.2244 -74.93 -82.04 152s PrivateWages_12 1.1439 61.09 70.01 152s PrivateWages_13 -0.5236 -23.19 -27.96 152s PrivateWages_14 1.4053 63.38 62.26 152s PrivateWages_15 1.0493 52.15 47.32 152s PrivateWages_16 0.0503 2.74 2.50 152s PrivateWages_17 -2.6890 -168.60 -146.28 152s PrivateWages_18 2.8642 186.17 179.59 152s PrivateWages_19 -2.5396 -154.66 -165.07 152s PrivateWages_20 -1.3435 -93.37 -81.82 152s PrivateWages_21 -4.0497 -306.57 -281.46 152s PrivateWages_22 1.8665 165.00 141.30 152s PrivateWages_trend 152s Consumption_2 4.240 152s Consumption_3 15.413 152s Consumption_4 16.634 152s Consumption_5 4.235 152s Consumption_6 -0.476 152s Consumption_7 0.000 152s Consumption_8 -7.435 152s Consumption_9 -4.408 152s Consumption_11 -0.482 152s Consumption_12 0.000 152s Consumption_14 0.585 152s Consumption_15 -0.454 152s Consumption_16 -0.472 152s Consumption_17 10.520 152s Consumption_18 -3.662 152s Consumption_19 1.886 152s Consumption_20 9.990 152s Consumption_21 9.205 152s Consumption_22 -29.832 152s Investment_2 -1.333 152s Investment_3 -0.890 152s Investment_4 4.712 152s Investment_5 -5.699 152s Investment_6 1.047 152s Investment_7 0.000 152s Investment_8 1.826 152s Investment_9 -0.871 152s Investment_10 1.332 152s Investment_11 0.225 152s Investment_12 0.000 152s Investment_14 -0.523 152s Investment_15 0.100 152s Investment_16 -0.168 152s Investment_17 -2.811 152s Investment_18 -0.192 152s Investment_19 9.813 152s Investment_20 2.734 152s Investment_21 3.708 152s Investment_22 3.321 152s PrivateWages_2 38.052 152s PrivateWages_3 -15.208 152s PrivateWages_4 -37.809 152s PrivateWages_5 2.329 152s PrivateWages_6 7.183 152s PrivateWages_8 10.061 152s PrivateWages_9 -2.874 152s PrivateWages_10 -7.847 152s PrivateWages_11 1.224 152s PrivateWages_12 0.000 152s PrivateWages_13 -0.524 152s PrivateWages_14 2.811 152s PrivateWages_15 3.148 152s PrivateWages_16 0.201 152s PrivateWages_17 -13.445 152s PrivateWages_18 17.185 152s PrivateWages_19 -17.777 152s PrivateWages_20 -10.748 152s PrivateWages_21 -36.448 152s PrivateWages_22 18.665 152s [1] TRUE 152s > Bread 152s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 152s [1,] 9.64e+01 -1.01207 -0.67760 152s [2,] -1.01e+00 0.50717 -0.26912 152s [3,] -6.78e-01 -0.26912 0.39547 152s [4,] -1.57e+00 -0.07816 -0.02960 152s [5,] 4.72e+00 -0.06998 0.78589 152s [6,] -2.60e-01 0.05062 -0.04147 152s [7,] 5.84e-03 -0.03341 0.04369 152s [8,] -2.63e-04 -0.00132 -0.00391 152s [9,] -3.35e+01 0.06371 1.58512 152s [10,] 2.97e-01 -0.05279 0.03618 152s [11,] 2.54e-01 0.05334 -0.06435 152s [12,] 1.92e-01 0.03084 0.02478 152s Consumption_wages Investment_(Intercept) Investment_corpProf 152s [1,] -1.566759 4.725 -0.25994 152s [2,] -0.078160 -0.070 0.05062 152s [3,] -0.029602 0.786 -0.04147 152s [4,] 0.081697 -0.368 0.00116 152s [5,] -0.368191 1275.706 -12.07893 152s [6,] 0.001158 -12.079 0.49514 152s [7,] -0.003210 9.845 -0.37888 152s [8,] 0.001998 -6.140 0.04890 152s [9,] 0.126305 19.264 -0.14904 152s [10,] -0.000206 0.266 0.01283 152s [11,] -0.002055 -0.608 -0.01053 152s [12,] -0.027162 -0.549 0.00394 152s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 152s [1,] 0.00584 -0.000263 -33.5037 152s [2,] -0.03341 -0.001318 0.0637 152s [3,] 0.04369 -0.003914 1.5851 152s [4,] -0.00321 0.001998 0.1263 152s [5,] 9.84516 -6.139910 19.2637 152s [6,] -0.37888 0.048897 -0.1490 152s [7,] 0.45026 -0.053769 -0.4040 152s [8,] -0.05377 0.030940 -0.0490 152s [9,] -0.40395 -0.049007 70.6849 152s [10,] -0.00755 -0.001777 -0.2111 152s [11,] 0.01465 0.002709 -0.9817 152s [12,] -0.01065 0.003278 0.7839 152s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 152s [1,] 0.297134 0.25379 0.19157 152s [2,] -0.052789 0.05334 0.03084 152s [3,] 0.036177 -0.06435 0.02478 152s [4,] -0.000206 -0.00206 -0.02716 152s [5,] 0.265808 -0.60808 -0.54935 152s [6,] 0.012829 -0.01053 0.00394 152s [7,] -0.007548 0.01465 -0.01065 152s [8,] -0.001777 0.00271 0.00328 152s [9,] -0.211061 -0.98166 0.78387 152s [10,] 0.039911 -0.03744 -0.00955 152s [11,] -0.037441 0.05550 -0.00377 152s [12,] -0.009553 -0.00377 0.04488 152s > 152s > # 3SLS 152s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 152s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 152s > summary 152s 152s systemfit results 152s method: 3SLS 152s 152s N DF SSR detRCov OLS-R2 McElroy-R2 152s system 57 45 66.8 0.361 0.963 0.993 152s 152s N DF SSR MSE RMSE R2 Adj R2 152s Consumption 18 14 22.6 1.616 1.271 0.974 0.968 152s Investment 19 15 34.1 2.277 1.509 0.807 0.769 152s PrivateWages 20 16 10.1 0.628 0.793 0.987 0.985 152s 152s The covariance matrix of the residuals used for estimation 152s Consumption Investment PrivateWages 152s Consumption 1.237 0.518 -0.408 152s Investment 0.518 1.263 0.113 152s PrivateWages -0.408 0.113 0.468 152s 152s The covariance matrix of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.257 0.601 -0.421 152s Investment 0.601 1.601 0.214 152s PrivateWages -0.421 0.214 0.491 152s 152s The correlations of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.000 0.425 -0.537 152s Investment 0.425 1.000 0.239 152s PrivateWages -0.537 0.239 1.000 152s 152s 152s 3SLS estimates for 'Consumption' (equation 1) 152s Model Formula: consump ~ corpProf + corpProfLag + wages 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 18.2100 1.5273 11.92 1e-08 *** 152s corpProf -0.0639 0.1461 -0.44 0.67 152s corpProfLag 0.1687 0.1125 1.50 0.16 152s wages 0.8230 0.0431 19.07 2e-11 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.271 on 14 degrees of freedom 152s Number of observations: 18 Degrees of Freedom: 14 152s SSR: 22.626 MSE: 1.616 Root MSE: 1.271 152s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 152s 152s 152s 3SLS estimates for 'Investment' (equation 2) 152s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 24.7534 6.5548 3.78 0.00183 ** 152s corpProf 0.0524 0.1807 0.29 0.77600 152s corpProfLag 0.6584 0.1551 4.24 0.00071 *** 152s capitalLag -0.1756 0.0311 -5.64 4.7e-05 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.509 on 15 degrees of freedom 152s Number of observations: 19 Degrees of Freedom: 15 152s SSR: 34.149 MSE: 2.277 Root MSE: 1.509 152s Multiple R-Squared: 0.807 Adjusted R-Squared: 0.769 152s 152s 152s 3SLS estimates for 'PrivateWages' (equation 3) 152s Model Formula: privWage ~ gnp + gnpLag + trend 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 0.8154 1.0961 0.74 0.46772 152s gnp 0.4250 0.0299 14.19 1.7e-10 *** 152s gnpLag 0.1731 0.0331 5.23 8.3e-05 *** 152s trend 0.1255 0.0283 4.43 0.00042 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 0.793 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 10.054 MSE: 0.628 Root MSE: 0.793 152s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 152s 152s > residuals 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 -0.8680 -1.857 -1.21010 152s 3 -0.7217 0.170 0.43075 152s 4 -1.1353 0.762 1.30899 152s 5 0.0755 -1.565 -0.20270 152s 6 0.6348 0.367 -0.46842 152s 7 NA NA NA 152s 8 1.7953 1.230 -0.85853 152s 9 1.7924 0.568 0.20422 152s 10 NA 2.308 1.09889 152s 11 -0.5211 -0.972 -0.39427 152s 12 -1.5560 -0.960 0.39889 152s 13 NA NA -0.00934 152s 14 -0.2384 1.327 0.59990 152s 15 -0.7342 -0.292 0.48094 152s 16 -0.4331 0.068 0.16188 152s 17 1.8775 1.932 -0.70448 152s 18 -0.6294 -0.154 0.95616 152s 19 -0.4252 -3.400 -0.62489 152s 20 1.3682 0.589 -0.29589 152s 21 1.3155 0.271 -1.14466 152s 22 -1.4276 0.942 0.55941 152s > fitted 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 42.8 1.657 26.7 152s 3 45.7 1.730 28.9 152s 4 50.3 4.438 32.8 152s 5 50.5 4.565 34.1 152s 6 52.0 4.733 35.9 152s 7 NA NA NA 152s 8 54.4 2.970 38.8 152s 9 55.5 2.432 39.0 152s 10 NA 2.792 40.2 152s 11 55.5 1.972 38.3 152s 12 52.5 -2.440 34.1 152s 13 NA NA 29.0 152s 14 46.7 -6.427 27.9 152s 15 49.4 -2.708 30.1 152s 16 51.7 -1.368 33.0 152s 17 55.8 0.168 37.5 152s 18 59.3 2.154 40.0 152s 19 57.9 1.500 38.8 152s 20 60.2 0.711 41.9 152s 21 63.7 3.029 46.1 152s 22 71.1 3.958 52.7 152s > predict 152s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 152s 1 NA NA NA NA 152s 2 42.8 0.542 39.8 45.7 152s 3 45.7 0.612 42.7 48.7 152s 4 50.3 0.407 47.5 53.2 152s 5 50.5 0.478 47.6 53.4 152s 6 52.0 0.488 49.0 54.9 152s 7 NA NA NA NA 152s 8 54.4 0.394 51.5 57.3 152s 9 55.5 0.464 52.6 58.4 152s 10 NA NA NA NA 152s 11 55.5 0.811 52.3 58.8 152s 12 52.5 0.773 49.3 55.6 152s 13 NA NA NA NA 152s 14 46.7 0.666 43.7 49.8 152s 15 49.4 0.463 46.5 52.3 152s 16 51.7 0.381 48.9 54.6 152s 17 55.8 0.424 52.9 58.7 152s 18 59.3 0.359 56.5 62.2 152s 19 57.9 0.492 55.0 60.8 152s 20 60.2 0.501 57.3 63.2 152s 21 63.7 0.491 60.8 66.6 152s 22 71.1 0.749 68.0 74.3 152s Investment.pred Investment.se.fit Investment.lwr Investment.upr 152s 1 NA NA NA NA 152s 2 1.657 0.831 -2.015 5.329 152s 3 1.730 0.574 -1.711 5.171 152s 4 4.438 0.507 1.045 7.831 152s 5 4.565 0.426 1.223 7.907 152s 6 4.733 0.406 1.402 8.064 152s 7 NA NA NA NA 152s 8 2.970 0.334 -0.324 6.263 152s 9 2.432 0.501 -0.957 5.820 152s 10 2.792 0.544 -0.627 6.211 152s 11 1.972 0.937 -1.814 5.757 152s 12 -2.440 0.849 -6.131 1.250 152s 13 NA NA NA NA 152s 14 -6.427 0.836 -10.104 -2.750 152s 15 -2.708 0.477 -6.081 0.665 152s 16 -1.368 0.381 -4.685 1.949 152s 17 0.168 0.473 -3.202 3.538 152s 18 2.154 0.311 -1.130 5.438 152s 19 1.500 0.518 -1.900 4.900 152s 20 0.711 0.541 -2.705 4.127 152s 21 3.029 0.467 -0.338 6.395 152s 22 3.958 0.677 0.432 7.483 152s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 152s 1 NA NA NA NA 152s 2 26.7 0.315 24.9 28.5 152s 3 28.9 0.322 27.1 30.7 152s 4 32.8 0.330 31.0 34.6 152s 5 34.1 0.241 32.3 35.9 152s 6 35.9 0.249 34.1 37.6 152s 7 NA NA NA NA 152s 8 38.8 0.243 37.0 40.5 152s 9 39.0 0.231 37.2 40.7 152s 10 40.2 0.225 38.5 41.9 152s 11 38.3 0.305 36.5 40.1 152s 12 34.1 0.317 32.3 35.9 152s 13 29.0 0.382 27.1 30.9 152s 14 27.9 0.321 26.1 29.7 152s 15 30.1 0.316 28.3 31.9 152s 16 33.0 0.265 31.3 34.8 152s 17 37.5 0.270 35.7 39.3 152s 18 40.0 0.207 38.3 41.8 152s 19 38.8 0.311 37.0 40.6 152s 20 41.9 0.287 40.1 43.7 152s 21 46.1 0.300 44.3 47.9 152s 22 52.7 0.463 50.8 54.7 152s > model.frame 152s [1] TRUE 152s > model.matrix 152s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 152s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 152s [3] "Numeric: lengths (708, 684) differ" 152s > nobs 152s [1] 57 152s > linearHypothesis 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 46 152s 2 45 1 1.95 0.17 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 46 152s 2 45 1 2.71 0.11 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 46 152s 2 45 1 2.71 0.1 . 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 47 152s 2 45 2 1.78 0.18 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 47 152s 2 45 2 2.48 0.095 . 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 47 152s 2 45 2 4.95 0.084 . 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s > logLik 152s 'log Lik.' -71.2 (df=18) 152s 'log Lik.' -81.7 (df=18) 152s Estimating function 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 -3.6474 -51.112 152s Consumption_3 -0.7759 -12.930 152s Consumption_4 0.5383 9.982 152s Consumption_5 -2.0601 -41.756 152s Consumption_6 1.0597 20.157 152s Consumption_8 5.0108 88.416 152s Consumption_9 4.4804 84.874 152s Consumption_11 -2.2103 -37.003 152s Consumption_12 -2.9903 -39.999 152s Consumption_14 0.5609 5.622 152s Consumption_15 -2.2997 -28.756 152s Consumption_16 -1.9032 -27.562 152s Consumption_17 6.4249 95.811 152s Consumption_18 -0.7235 -14.050 152s Consumption_19 -5.0805 -97.079 152s Consumption_20 3.4333 60.632 152s Consumption_21 1.6077 32.791 152s Consumption_22 -1.1313 -25.654 152s Investment_2 1.6537 23.174 152s Investment_3 -0.1564 -2.607 152s Investment_4 -0.6420 -11.906 152s Investment_5 1.4113 28.605 152s Investment_6 -0.3557 -6.767 152s Investment_8 -1.1680 -20.610 152s Investment_9 -0.5634 -10.672 152s Investment_10 0.0000 0.000 152s Investment_11 0.9137 15.295 152s Investment_12 0.9272 12.402 152s Investment_14 -1.2036 -12.064 152s Investment_15 0.2779 3.475 152s Investment_16 -0.0439 -0.636 152s Investment_17 -1.7918 -26.720 152s Investment_18 0.2271 4.411 152s Investment_19 3.1278 59.767 152s Investment_20 -0.5790 -10.225 152s Investment_21 -0.2789 -5.690 152s Investment_22 -0.8484 -19.238 152s PrivateWages_2 -3.1568 -44.237 152s PrivateWages_3 1.1209 18.679 152s PrivateWages_4 2.7328 50.677 152s PrivateWages_5 -2.9712 -60.223 152s PrivateWages_6 -0.5212 -9.913 152s PrivateWages_8 1.7420 30.738 152s PrivateWages_9 1.9832 37.569 152s PrivateWages_10 0.0000 0.000 152s PrivateWages_11 -2.5151 -42.105 152s PrivateWages_12 -0.3611 -4.830 152s PrivateWages_13 0.0000 0.000 152s PrivateWages_14 3.2055 32.130 152s PrivateWages_15 -0.2814 -3.519 152s PrivateWages_16 -0.4078 -5.906 152s PrivateWages_17 2.6678 39.784 152s PrivateWages_18 0.0554 1.076 152s PrivateWages_19 -6.6416 -126.909 152s PrivateWages_20 1.4327 25.301 152s PrivateWages_21 -1.3598 -27.735 152s PrivateWages_22 2.0747 47.044 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 -46.322 -108.77 152s Consumption_3 -9.621 -24.71 152s Consumption_4 9.097 18.98 152s Consumption_5 -37.905 -79.52 152s Consumption_6 20.558 40.85 152s Consumption_8 98.211 200.48 152s Consumption_9 88.711 187.18 152s Consumption_11 -47.964 -95.27 152s Consumption_12 -46.648 -118.58 152s Consumption_14 3.926 18.69 152s Consumption_15 -25.757 -85.85 152s Consumption_16 -23.410 -76.40 152s Consumption_17 89.949 268.43 152s Consumption_18 -12.733 -34.44 152s Consumption_19 -87.892 -250.13 152s Consumption_20 52.529 166.71 152s Consumption_21 30.546 85.88 152s Consumption_22 -23.871 -68.78 152s Investment_2 21.002 49.32 152s Investment_3 -1.940 -4.98 152s Investment_4 -10.851 -22.64 152s Investment_5 25.967 54.47 152s Investment_6 -6.901 -13.71 152s Investment_8 -22.893 -46.73 152s Investment_9 -11.154 -23.53 152s Investment_10 0.000 0.00 152s Investment_11 19.827 39.38 152s Investment_12 14.464 36.77 152s Investment_14 -8.425 -40.11 152s Investment_15 3.113 10.38 152s Investment_16 -0.540 -1.76 152s Investment_17 -25.085 -74.86 152s Investment_18 3.997 10.81 152s Investment_19 54.111 153.99 152s Investment_20 -8.858 -28.11 152s Investment_21 -5.300 -14.90 152s Investment_22 -17.901 -51.58 152s PrivateWages_2 -40.091 -94.14 152s PrivateWages_3 13.899 35.70 152s PrivateWages_4 46.184 96.34 152s PrivateWages_5 -54.670 -114.69 152s PrivateWages_6 -10.110 -20.09 152s PrivateWages_8 34.144 69.70 152s PrivateWages_9 39.267 82.85 152s PrivateWages_10 0.000 0.00 152s PrivateWages_11 -54.578 -108.40 152s PrivateWages_12 -5.633 -14.32 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 22.438 106.83 152s PrivateWages_15 -3.152 -10.51 152s PrivateWages_16 -5.016 -16.37 152s PrivateWages_17 37.350 111.46 152s PrivateWages_18 0.975 2.64 152s PrivateWages_19 -114.899 -326.98 152s PrivateWages_20 21.920 69.57 152s PrivateWages_21 -25.836 -72.64 152s PrivateWages_22 43.775 126.12 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 1.8176 24.384 152s Consumption_3 0.3867 6.453 152s Consumption_4 -0.2682 -5.040 152s Consumption_5 1.0266 21.198 152s Consumption_6 -0.5281 -10.172 152s Consumption_8 -2.4970 -43.782 152s Consumption_9 -2.2327 -43.602 152s Consumption_11 1.1015 18.940 152s Consumption_12 1.4902 20.151 152s Consumption_14 -0.2795 -2.793 152s Consumption_15 1.1460 14.736 152s Consumption_16 0.9485 13.590 152s Consumption_17 -3.2018 -47.918 152s Consumption_18 0.3605 6.983 152s Consumption_19 2.5318 49.008 152s Consumption_20 -1.7109 -29.898 152s Consumption_21 -0.8012 -16.122 152s Consumption_22 0.5638 12.844 152s Investment_2 -2.3696 -31.787 152s Investment_3 0.2241 3.741 152s Investment_4 0.9200 17.284 152s Investment_5 -2.0221 -41.754 152s Investment_6 0.5097 9.819 152s Investment_8 1.6736 29.344 152s Investment_9 0.8072 15.764 152s Investment_10 2.9560 59.913 152s Investment_11 -1.3092 -22.510 152s Investment_12 -1.3285 -17.964 152s Investment_14 1.7246 17.233 152s Investment_15 -0.3982 -5.120 152s Investment_16 0.0630 0.902 152s Investment_17 2.5674 38.424 152s Investment_18 -0.3254 -6.303 152s Investment_19 -4.4817 -86.752 152s Investment_20 0.8296 14.497 152s Investment_21 0.3997 8.043 152s Investment_22 1.2156 27.693 152s PrivateWages_2 1.9315 25.910 152s PrivateWages_3 -0.6858 -11.446 152s PrivateWages_4 -1.6720 -31.413 152s PrivateWages_5 1.8179 37.537 152s PrivateWages_6 0.3189 6.142 152s PrivateWages_8 -1.0659 -18.688 152s PrivateWages_9 -1.2134 -23.696 152s PrivateWages_10 -2.2443 -45.488 152s PrivateWages_11 1.5389 26.460 152s PrivateWages_12 0.2209 2.988 152s PrivateWages_13 0.0000 0.000 152s PrivateWages_14 -1.9613 -19.598 152s PrivateWages_15 0.1722 2.214 152s PrivateWages_16 0.2495 3.576 152s PrivateWages_17 -1.6323 -24.429 152s PrivateWages_18 -0.0339 -0.657 152s PrivateWages_19 4.0636 78.659 152s PrivateWages_20 -0.8766 -15.318 152s PrivateWages_21 0.8320 16.742 152s PrivateWages_22 -1.2694 -28.917 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 23.084 332.27 152s Consumption_3 4.795 70.60 152s Consumption_4 -4.533 -49.49 152s Consumption_5 18.890 194.75 152s Consumption_6 -10.245 -101.76 152s Consumption_8 -48.942 -507.90 152s Consumption_9 -44.208 -463.52 152s Consumption_11 23.902 237.59 152s Consumption_12 23.247 322.92 152s Consumption_14 -1.957 -57.89 152s Consumption_15 12.836 231.50 152s Consumption_16 11.666 188.74 152s Consumption_17 -44.825 -632.99 152s Consumption_18 6.345 72.04 152s Consumption_19 43.800 510.92 152s Consumption_20 -26.177 -342.01 152s Consumption_21 -15.222 -161.20 152s Consumption_22 11.896 115.30 152s Investment_2 -30.093 -433.16 152s Investment_3 2.779 40.93 152s Investment_4 15.547 169.73 152s Investment_5 -37.208 -383.60 152s Investment_6 9.888 98.22 152s Investment_8 32.803 340.41 152s Investment_9 15.983 167.58 152s Investment_10 62.371 622.53 152s Investment_11 -28.409 -282.39 152s Investment_12 -20.724 -287.88 152s Investment_14 12.072 357.16 152s Investment_15 -4.460 -80.44 152s Investment_16 0.774 12.53 152s Investment_17 35.944 507.58 152s Investment_18 -5.727 -65.02 152s Investment_19 -77.534 -904.41 152s Investment_20 12.693 165.84 152s Investment_21 7.594 80.42 152s Investment_22 25.650 248.60 152s PrivateWages_2 24.530 353.07 152s PrivateWages_3 -8.504 -125.23 152s PrivateWages_4 -28.257 -308.49 152s PrivateWages_5 33.450 344.86 152s PrivateWages_6 6.186 61.45 152s PrivateWages_8 -20.891 -216.79 152s PrivateWages_9 -24.025 -251.90 152s PrivateWages_10 -47.355 -472.65 152s PrivateWages_11 33.393 331.93 152s PrivateWages_12 3.447 47.88 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 -13.729 -406.18 152s PrivateWages_15 1.929 34.78 152s PrivateWages_16 3.069 49.66 152s PrivateWages_17 -22.852 -322.71 152s PrivateWages_18 -0.597 -6.77 152s PrivateWages_19 70.300 820.04 152s PrivateWages_20 -13.412 -175.23 152s PrivateWages_21 15.807 167.39 152s PrivateWages_22 -26.784 -259.59 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 -3.6123 -170.03 -162.19 152s Consumption_3 -0.7684 -38.10 -35.04 152s Consumption_4 0.5331 30.14 26.71 152s Consumption_5 -2.0403 -123.82 -116.70 152s Consumption_6 1.0495 63.61 59.93 152s Consumption_8 4.9625 297.74 317.60 152s Consumption_9 4.4373 276.30 285.76 152s Consumption_11 -2.1891 -139.47 -146.67 152s Consumption_12 -2.9615 -162.39 -181.24 152s Consumption_14 0.5555 23.40 24.61 152s Consumption_15 -2.2776 -116.65 -102.72 152s Consumption_16 -1.8849 -104.31 -93.68 152s Consumption_17 6.3631 365.20 346.15 152s Consumption_18 -0.7165 -48.13 -44.93 152s Consumption_19 -5.0316 -344.73 -327.05 152s Consumption_20 3.4002 227.29 207.07 152s Consumption_21 1.5922 119.20 110.66 152s Consumption_22 -1.1205 -97.34 -84.82 152s Investment_2 2.0108 94.65 90.29 152s Investment_3 -0.1902 -9.43 -8.67 152s Investment_4 -0.7807 -44.14 -39.11 152s Investment_5 1.7160 104.14 98.16 152s Investment_6 -0.4326 -26.22 -24.70 152s Investment_8 -1.4203 -85.21 -90.90 152s Investment_9 -0.6850 -42.65 -44.11 152s Investment_10 -2.5085 -161.97 -161.80 152s Investment_11 1.1110 70.78 74.44 152s Investment_12 1.1274 61.82 69.00 152s Investment_14 -1.4635 -61.65 -64.83 152s Investment_15 0.3379 17.31 15.24 152s Investment_16 -0.0534 -2.96 -2.66 152s Investment_17 -2.1788 -125.05 -118.52 152s Investment_18 0.2762 18.55 17.32 152s Investment_19 3.8033 260.57 247.21 152s Investment_20 -0.7040 -47.06 -42.87 152s Investment_21 -0.3392 -25.39 -23.57 152s Investment_22 -1.0316 -89.62 -78.09 152s PrivateWages_2 -7.1301 -335.61 -320.14 152s PrivateWages_3 2.5317 125.52 115.44 152s PrivateWages_4 6.1723 349.00 309.23 152s PrivateWages_5 -6.7109 -407.26 -383.86 152s PrivateWages_6 -1.1771 -71.34 -67.21 152s PrivateWages_8 3.9346 236.07 251.82 152s PrivateWages_9 4.4793 278.92 288.47 152s PrivateWages_10 8.2849 534.95 534.38 152s PrivateWages_11 -5.6807 -361.93 -380.61 152s PrivateWages_12 -0.8156 -44.72 -49.92 152s PrivateWages_13 -4.4579 -209.42 -238.05 152s PrivateWages_14 7.2401 305.01 320.74 152s PrivateWages_15 -0.6357 -32.56 -28.67 152s PrivateWages_16 -0.9212 -50.98 -45.78 152s PrivateWages_17 6.0257 345.84 327.80 152s PrivateWages_18 0.1252 8.41 7.85 152s PrivateWages_19 -15.0009 -1027.75 -975.06 152s PrivateWages_20 3.2360 216.31 197.07 152s PrivateWages_21 -3.0713 -229.93 -213.45 152s PrivateWages_22 4.6859 407.11 354.72 152s PrivateWages_trend 152s Consumption_2 36.123 152s Consumption_3 6.916 152s Consumption_4 -4.265 152s Consumption_5 14.282 152s Consumption_6 -6.297 152s Consumption_8 -19.850 152s Consumption_9 -13.312 152s Consumption_11 2.189 152s Consumption_12 0.000 152s Consumption_14 1.111 152s Consumption_15 -6.833 152s Consumption_16 -7.540 152s Consumption_17 31.815 152s Consumption_18 -4.299 152s Consumption_19 -35.221 152s Consumption_20 27.202 152s Consumption_21 14.330 152s Consumption_22 -11.205 152s Investment_2 -20.108 152s Investment_3 1.712 152s Investment_4 6.246 152s Investment_5 -12.012 152s Investment_6 2.595 152s Investment_8 5.681 152s Investment_9 2.055 152s Investment_10 5.017 152s Investment_11 -1.111 152s Investment_12 0.000 152s Investment_14 -2.927 152s Investment_15 1.014 152s Investment_16 -0.214 152s Investment_17 -10.894 152s Investment_18 1.657 152s Investment_19 26.623 152s Investment_20 -5.632 152s Investment_21 -3.053 152s Investment_22 -10.316 152s PrivateWages_2 71.301 152s PrivateWages_3 -22.785 152s PrivateWages_4 -49.379 152s PrivateWages_5 46.976 152s PrivateWages_6 7.063 152s PrivateWages_8 -15.738 152s PrivateWages_9 -13.438 152s PrivateWages_10 -16.570 152s PrivateWages_11 5.681 152s PrivateWages_12 0.000 152s PrivateWages_13 -4.458 152s PrivateWages_14 14.480 152s PrivateWages_15 -1.907 152s PrivateWages_16 -3.685 152s PrivateWages_17 30.129 152s PrivateWages_18 0.751 152s PrivateWages_19 -105.007 152s PrivateWages_20 25.888 152s PrivateWages_21 -27.641 152s PrivateWages_22 46.859 152s [1] TRUE 152s > Bread 152s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 152s [1,] 132.9647 -4.1876 0.7762 152s [2,] -4.1876 1.2160 -0.6687 152s [3,] 0.7762 -0.6687 0.7219 152s [4,] -1.6897 -0.1344 -0.0278 152s [5,] 101.6483 3.2473 3.4997 152s [6,] -4.3150 0.5140 -0.4474 152s [7,] 1.5566 -0.3374 0.4240 152s [8,] -0.2539 -0.0329 -0.0138 152s [9,] -35.7522 0.3296 1.6708 152s [10,] 0.5355 -0.0797 0.0478 152s [11,] 0.0459 0.0759 -0.0780 152s [12,] 0.1973 0.0481 0.0250 152s Consumption_wages Investment_(Intercept) Investment_corpProf 152s [1,] -1.689687 101.65 -4.32e+00 152s [2,] -0.134421 3.25 5.14e-01 152s [3,] -0.027837 3.50 -4.47e-01 152s [4,] 0.106098 -5.00 6.63e-02 152s [5,] -4.996393 2449.02 -4.26e+01 152s [6,] 0.066338 -42.57 1.86e+00 152s [7,] -0.064579 34.21 -1.44e+00 152s [8,] 0.024569 -11.36 1.70e-01 152s [9,] 0.047220 27.91 -2.66e-01 152s [10,] 0.000172 1.31 3.12e-04 152s [11,] -0.000827 -1.84 4.41e-03 152s [12,] -0.034079 -0.80 1.58e-02 152s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 152s [1,] 1.55659 -0.25392 -35.7522 152s [2,] -0.33742 -0.03292 0.3296 152s [3,] 0.42396 -0.01383 1.6708 152s [4,] -0.06458 0.02457 0.0472 152s [5,] 34.20897 -11.35519 27.9136 152s [6,] -1.43523 0.17002 -0.2656 152s [7,] 1.37137 -0.15991 -0.3976 152s [8,] -0.15991 0.05521 -0.0847 152s [9,] -0.39759 -0.08475 68.4821 152s [10,] 0.00601 -0.00701 -0.3279 152s [11,] 0.00088 0.00875 -0.8283 152s [12,] -0.02279 0.00445 0.7887 152s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 152s [1,] 0.535460 0.045866 0.197271 152s [2,] -0.079666 0.075947 0.048142 152s [3,] 0.047829 -0.078006 0.025001 152s [4,] 0.000172 -0.000827 -0.034079 152s [5,] 1.306914 -1.841775 -0.800037 152s [6,] 0.000312 0.004408 0.015824 152s [7,] 0.006007 0.000880 -0.022790 152s [8,] -0.007006 0.008751 0.004448 152s [9,] -0.327909 -0.828330 0.788744 152s [10,] 0.051096 -0.046839 -0.013933 152s [11,] -0.046839 0.062505 0.000532 152s [12,] -0.013933 0.000532 0.045663 152s > 152s > # I3SLS 152s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 152s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 152s > summary 152s 152s systemfit results 152s method: iterated 3SLS 152s 152s convergence achieved after 9 iterations 152s 152s N DF SSR detRCov OLS-R2 McElroy-R2 152s system 57 45 75 0.422 0.959 0.993 152s 152s N DF SSR MSE RMSE R2 Adj R2 152s Consumption 18 14 22.7 1.622 1.273 0.973 0.968 152s Investment 19 15 42.1 2.809 1.676 0.762 0.715 152s PrivateWages 20 16 10.2 0.638 0.799 0.987 0.985 152s 152s The covariance matrix of the residuals used for estimation 152s Consumption Investment PrivateWages 152s Consumption 1.261 0.675 -0.439 152s Investment 0.675 1.949 0.237 152s PrivateWages -0.439 0.237 0.503 152s 152s The covariance matrix of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.261 0.675 -0.439 152s Investment 0.675 1.949 0.237 152s PrivateWages -0.439 0.237 0.503 152s 152s The correlations of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.000 0.431 -0.550 152s Investment 0.431 1.000 0.239 152s PrivateWages -0.550 0.239 1.000 152s 152s 152s 3SLS estimates for 'Consumption' (equation 1) 152s Model Formula: consump ~ corpProf + corpProfLag + wages 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 18.5887 1.5250 12.19 7.6e-09 *** 152s corpProf -0.0438 0.1441 -0.30 0.77 152s corpProfLag 0.1456 0.1109 1.31 0.21 152s wages 0.8141 0.0428 19.01 2.1e-11 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.273 on 14 degrees of freedom 152s Number of observations: 18 Degrees of Freedom: 14 152s SSR: 22.704 MSE: 1.622 Root MSE: 1.273 152s Multiple R-Squared: 0.973 Adjusted R-Squared: 0.968 152s 152s 152s 3SLS estimates for 'Investment' (equation 2) 152s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 29.4725 7.6857 3.83 0.0016 ** 152s corpProf -0.0183 0.2154 -0.09 0.9333 152s corpProfLag 0.7195 0.1850 3.89 0.0015 ** 152s capitalLag -0.1985 0.0366 -5.43 6.9e-05 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.676 on 15 degrees of freedom 152s Number of observations: 19 Degrees of Freedom: 15 152s SSR: 42.136 MSE: 2.809 Root MSE: 1.676 152s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.715 152s 152s 152s 3SLS estimates for 'PrivateWages' (equation 3) 152s Model Formula: privWage ~ gnp + gnpLag + trend 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 0.5385 1.1055 0.49 0.63277 152s gnp 0.4251 0.0287 14.80 9.3e-11 *** 152s gnpLag 0.1776 0.0322 5.51 4.7e-05 *** 152s trend 0.1211 0.0283 4.28 0.00057 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 0.799 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 10.204 MSE: 0.638 Root MSE: 0.799 152s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 152s 152s > residuals 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 -0.9524 -2.2888 -1.1837 152s 3 -0.8681 0.0698 0.4581 152s 4 -1.1653 0.5368 1.3199 152s 5 0.0601 -1.6917 -0.2194 152s 6 0.6426 0.2972 -0.4805 152s 7 NA NA NA 152s 8 1.8394 1.3723 -0.8931 152s 9 1.8275 0.8861 0.1723 152s 10 NA 2.6574 1.0707 152s 11 -0.3387 -0.9736 -0.4288 152s 12 -1.4550 -0.8630 0.3956 152s 13 NA NA 0.0277 152s 14 -0.3782 1.7151 0.6823 152s 15 -0.7768 -0.1993 0.5638 152s 16 -0.4606 0.1448 0.2281 152s 17 1.8605 2.1295 -0.6557 152s 18 -0.5262 -0.1493 0.9718 152s 19 -0.3047 -3.4730 -0.6148 152s 20 1.3992 0.8566 -0.2636 152s 21 1.4216 0.4910 -1.1472 152s 22 -1.2431 1.2792 0.5323 152s > fitted 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 42.9 2.0888 26.7 152s 3 45.9 1.8302 28.8 152s 4 50.4 4.6632 32.8 152s 5 50.5 4.6917 34.1 152s 6 52.0 4.8028 35.9 152s 7 NA NA NA 152s 8 54.4 2.8277 38.8 152s 9 55.5 2.1139 39.0 152s 10 NA 2.4426 40.2 152s 11 55.3 1.9736 38.3 152s 12 52.4 -2.5370 34.1 152s 13 NA NA 29.0 152s 14 46.9 -6.8151 27.8 152s 15 49.5 -2.8007 30.0 152s 16 51.8 -1.4448 33.0 152s 17 55.8 -0.0295 37.5 152s 18 59.2 2.1493 40.0 152s 19 57.8 1.5730 38.8 152s 20 60.2 0.4434 41.9 152s 21 63.6 2.8090 46.1 152s 22 70.9 3.6208 52.8 152s > predict 152s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 152s 1 NA NA NA NA 152s 2 42.9 0.541 41.8 43.9 152s 3 45.9 0.608 44.6 47.1 152s 4 50.4 0.403 49.6 51.2 152s 5 50.5 0.472 49.6 51.5 152s 6 52.0 0.481 51.0 52.9 152s 7 NA NA NA NA 152s 8 54.4 0.388 53.6 55.1 152s 9 55.5 0.458 54.6 56.4 152s 10 NA NA NA NA 152s 11 55.3 0.795 53.7 56.9 152s 12 52.4 0.762 50.8 53.9 152s 13 NA NA NA NA 152s 14 46.9 0.663 45.5 48.2 152s 15 49.5 0.462 48.5 50.4 152s 16 51.8 0.381 51.0 52.5 152s 17 55.8 0.423 55.0 56.7 152s 18 59.2 0.355 58.5 59.9 152s 19 57.8 0.484 56.8 58.8 152s 20 60.2 0.500 59.2 61.2 152s 21 63.6 0.490 62.6 64.6 152s 22 70.9 0.747 69.4 72.4 152s Investment.pred Investment.se.fit Investment.lwr Investment.upr 152s 1 NA NA NA NA 152s 2 2.0888 0.985 0.105 4.072 152s 3 1.8302 0.708 0.404 3.257 152s 4 4.6632 0.612 3.430 5.897 152s 5 4.6917 0.519 3.645 5.738 152s 6 4.8028 0.498 3.800 5.806 152s 7 NA NA NA NA 152s 8 2.8277 0.410 2.003 3.653 152s 9 2.1139 0.599 0.908 3.320 152s 10 2.4426 0.651 1.131 3.754 152s 11 1.9736 1.138 -0.320 4.267 152s 12 -2.5370 1.038 -4.627 -0.447 152s 13 NA NA NA NA 152s 14 -6.8151 1.011 -8.851 -4.779 152s 15 -2.8007 0.587 -3.984 -1.617 152s 16 -1.4448 0.470 -2.392 -0.498 152s 17 -0.0295 0.573 -1.183 1.124 152s 18 2.1493 0.380 1.384 2.915 152s 19 1.5730 0.624 0.315 2.831 152s 20 0.4434 0.649 -0.864 1.751 152s 21 2.8090 0.565 1.671 3.947 152s 22 3.6208 0.814 1.982 5.260 152s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 152s 1 NA NA NA NA 152s 2 26.7 0.322 26.0 27.3 152s 3 28.8 0.328 28.2 29.5 152s 4 32.8 0.332 32.1 33.4 152s 5 34.1 0.244 33.6 34.6 152s 6 35.9 0.252 35.4 36.4 152s 7 NA NA NA NA 152s 8 38.8 0.246 38.3 39.3 152s 9 39.0 0.234 38.6 39.5 152s 10 40.2 0.230 39.8 40.7 152s 11 38.3 0.299 37.7 38.9 152s 12 34.1 0.304 33.5 34.7 152s 13 29.0 0.366 28.2 29.7 152s 14 27.8 0.321 27.2 28.5 152s 15 30.0 0.317 29.4 30.7 152s 16 33.0 0.266 32.4 33.5 152s 17 37.5 0.270 36.9 38.0 152s 18 40.0 0.211 39.6 40.5 152s 19 38.8 0.305 38.2 39.4 152s 20 41.9 0.290 41.3 42.4 152s 21 46.1 0.309 45.5 46.8 152s 22 52.8 0.468 51.8 53.7 152s > model.frame 152s [1] TRUE 152s > model.matrix 152s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 152s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 152s [3] "Numeric: lengths (708, 684) differ" 152s > nobs 152s [1] 57 152s > linearHypothesis 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 46 152s 2 45 1 2.17 0.15 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 46 152s 2 45 1 2.84 0.099 . 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 46 152s 2 45 1 2.84 0.092 . 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 47 152s 2 45 2 2.45 0.098 . 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 47 152s 2 45 2 3.2 0.05 . 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 47 152s 2 45 2 6.4 0.041 * 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s > logLik 152s 'log Lik.' -72.7 (df=18) 152s 'log Lik.' -83.9 (df=18) 152s Estimating function 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 -4.8293 -67.67 152s Consumption_3 -1.2969 -21.61 152s Consumption_4 0.5735 10.64 152s Consumption_5 -2.6416 -53.54 152s Consumption_6 1.4014 26.66 152s Consumption_8 6.4885 114.49 152s Consumption_9 5.8062 109.99 152s Consumption_11 -2.4210 -40.53 152s Consumption_12 -3.6335 -48.60 152s Consumption_14 0.4385 4.39 152s Consumption_15 -2.9914 -37.40 152s Consumption_16 -2.4677 -35.74 152s Consumption_17 8.1448 121.46 152s Consumption_18 -0.7823 -15.19 152s Consumption_19 -6.2524 -119.47 152s Consumption_20 4.4447 78.49 152s Consumption_21 2.3016 46.94 152s Consumption_22 -1.0069 -22.83 152s Investment_2 2.3888 33.48 152s Investment_3 -0.0694 -1.16 152s Investment_4 -0.5723 -10.61 152s Investment_5 1.7561 35.59 152s Investment_6 -0.2966 -5.64 152s Investment_8 -1.4003 -24.71 152s Investment_9 -0.9021 -17.09 152s Investment_10 0.0000 0.00 152s Investment_11 0.9937 16.63 152s Investment_12 0.8671 11.60 152s Investment_14 -1.7814 -17.86 152s Investment_15 0.1989 2.49 152s Investment_16 -0.1587 -2.30 152s Investment_17 -2.1900 -32.66 152s Investment_18 0.1172 2.28 152s Investment_19 3.5762 68.34 152s Investment_20 -0.8719 -15.40 152s Investment_21 -0.4978 -10.15 152s Investment_22 -1.3322 -30.21 152s PrivateWages_2 -4.3522 -60.99 152s PrivateWages_3 1.6337 27.22 152s PrivateWages_4 3.8487 71.37 152s PrivateWages_5 -4.1966 -85.06 152s PrivateWages_6 -0.7579 -14.42 152s PrivateWages_8 2.3542 41.54 152s PrivateWages_9 2.6975 51.10 152s PrivateWages_10 0.0000 0.00 152s PrivateWages_11 -3.6015 -60.29 152s PrivateWages_12 -0.5133 -6.87 152s PrivateWages_13 0.0000 0.00 152s PrivateWages_14 4.6825 46.94 152s PrivateWages_15 -0.1944 -2.43 152s PrivateWages_16 -0.4112 -5.96 152s PrivateWages_17 3.8500 57.41 152s PrivateWages_18 0.1148 2.23 152s PrivateWages_19 -9.2669 -177.08 152s PrivateWages_20 2.0821 36.77 152s PrivateWages_21 -1.9079 -38.91 152s PrivateWages_22 2.8370 64.33 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 -61.332 -144.02 152s Consumption_3 -16.082 -41.30 152s Consumption_4 9.693 20.22 152s Consumption_5 -48.605 -101.97 152s Consumption_6 27.187 54.02 152s Consumption_8 127.174 259.60 152s Consumption_9 114.963 242.56 152s Consumption_11 -52.537 -104.35 152s Consumption_12 -56.683 -144.08 152s Consumption_14 3.069 14.61 152s Consumption_15 -33.504 -111.68 152s Consumption_16 -30.352 -99.06 152s Consumption_17 114.027 340.28 152s Consumption_18 -13.768 -37.24 152s Consumption_19 -108.167 -307.82 152s Consumption_20 68.004 215.82 152s Consumption_21 43.729 122.95 152s Consumption_22 -21.245 -61.21 152s Investment_2 30.338 71.24 152s Investment_3 -0.861 -2.21 152s Investment_4 -9.672 -20.18 152s Investment_5 32.311 67.78 152s Investment_6 -5.754 -11.43 152s Investment_8 -27.445 -56.02 152s Investment_9 -17.861 -37.69 152s Investment_10 0.000 0.00 152s Investment_11 21.563 42.83 152s Investment_12 13.527 34.39 152s Investment_14 -12.470 -59.37 152s Investment_15 2.228 7.43 152s Investment_16 -1.952 -6.37 152s Investment_17 -30.659 -91.49 152s Investment_18 2.063 5.58 152s Investment_19 61.869 176.07 152s Investment_20 -13.340 -42.34 152s Investment_21 -9.458 -26.59 152s Investment_22 -28.109 -80.99 152s PrivateWages_2 -55.273 -129.79 152s PrivateWages_3 20.257 52.03 152s PrivateWages_4 65.044 135.69 152s PrivateWages_5 -77.218 -161.99 152s PrivateWages_6 -14.704 -29.21 152s PrivateWages_8 46.143 94.19 152s PrivateWages_9 53.410 112.69 152s PrivateWages_10 0.000 0.00 152s PrivateWages_11 -78.152 -155.23 152s PrivateWages_12 -8.008 -20.36 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 32.778 156.05 152s PrivateWages_15 -2.178 -7.26 152s PrivateWages_16 -5.058 -16.51 152s PrivateWages_17 53.901 160.85 152s PrivateWages_18 2.020 5.46 152s PrivateWages_19 -160.318 -456.23 152s PrivateWages_20 31.857 101.10 152s PrivateWages_21 -36.250 -101.92 152s PrivateWages_22 59.861 172.47 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 2.3171 31.08 152s Consumption_3 0.6223 10.39 152s Consumption_4 -0.2752 -5.17 152s Consumption_5 1.2675 26.17 152s Consumption_6 -0.6724 -12.95 152s Consumption_8 -3.1132 -54.59 152s Consumption_9 -2.7858 -54.40 152s Consumption_11 1.1616 19.97 152s Consumption_12 1.7434 23.57 152s Consumption_14 -0.2104 -2.10 152s Consumption_15 1.4353 18.46 152s Consumption_16 1.1840 16.97 152s Consumption_17 -3.9079 -58.49 152s Consumption_18 0.3753 7.27 152s Consumption_19 2.9999 58.07 152s Consumption_20 -2.1326 -37.27 152s Consumption_21 -1.1043 -22.22 152s Consumption_22 0.4831 11.01 152s Investment_2 -2.3817 -31.95 152s Investment_3 0.0692 1.16 152s Investment_4 0.5706 10.72 152s Investment_5 -1.7509 -36.15 152s Investment_6 0.2957 5.70 152s Investment_8 1.3961 24.48 152s Investment_9 0.8994 17.56 152s Investment_10 2.7604 55.95 152s Investment_11 -0.9907 -17.04 152s Investment_12 -0.8646 -11.69 152s Investment_14 1.7761 17.75 152s Investment_15 -0.1983 -2.55 152s Investment_16 0.1582 2.27 152s Investment_17 2.1835 32.68 152s Investment_18 -0.1169 -2.26 152s Investment_19 -3.5657 -69.02 152s Investment_20 0.8693 15.19 152s Investment_21 0.4963 9.99 152s Investment_22 1.3282 30.26 152s PrivateWages_2 2.5510 34.22 152s PrivateWages_3 -0.9575 -15.98 152s PrivateWages_4 -2.2559 -42.38 152s PrivateWages_5 2.4598 50.79 152s PrivateWages_6 0.4442 8.56 152s PrivateWages_8 -1.3799 -24.19 152s PrivateWages_9 -1.5811 -30.88 152s PrivateWages_10 -2.9678 -60.15 152s PrivateWages_11 2.1109 36.30 152s PrivateWages_12 0.3009 4.07 152s PrivateWages_13 0.0000 0.00 152s PrivateWages_14 -2.7446 -27.43 152s PrivateWages_15 0.1140 1.47 152s PrivateWages_16 0.2410 3.45 152s PrivateWages_17 -2.2567 -33.77 152s PrivateWages_18 -0.0673 -1.30 152s PrivateWages_19 5.4317 105.14 152s PrivateWages_20 -1.2204 -21.33 152s PrivateWages_21 1.1183 22.50 152s PrivateWages_22 -1.6629 -37.88 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 29.428 423.6 152s Consumption_3 7.716 113.6 152s Consumption_4 -4.651 -50.8 152s Consumption_5 23.321 240.4 152s Consumption_6 -13.045 -129.6 152s Consumption_8 -61.019 -633.2 152s Consumption_9 -55.160 -578.3 152s Consumption_11 25.207 250.6 152s Consumption_12 27.197 377.8 152s Consumption_14 -1.473 -43.6 152s Consumption_15 16.075 289.9 152s Consumption_16 14.563 235.6 152s Consumption_17 -54.711 -772.6 152s Consumption_18 6.606 75.0 152s Consumption_19 51.899 605.4 152s Consumption_20 -32.629 -426.3 152s Consumption_21 -20.982 -222.2 152s Consumption_22 10.194 98.8 152s Investment_2 -30.248 -435.4 152s Investment_3 0.858 12.6 152s Investment_4 9.643 105.3 152s Investment_5 -32.216 -332.1 152s Investment_6 5.737 57.0 152s Investment_8 27.364 284.0 152s Investment_9 17.808 186.7 152s Investment_10 58.244 581.3 152s Investment_11 -21.499 -213.7 152s Investment_12 -13.487 -187.4 152s Investment_14 12.433 367.8 152s Investment_15 -2.221 -40.1 152s Investment_16 1.946 31.5 152s Investment_17 30.569 431.7 152s Investment_18 -2.057 -23.4 152s Investment_19 -61.686 -719.5 152s Investment_20 13.301 173.8 152s Investment_21 9.430 99.9 152s Investment_22 28.026 271.6 152s PrivateWages_2 32.397 466.3 152s PrivateWages_3 -11.874 -174.8 152s PrivateWages_4 -38.124 -416.2 152s PrivateWages_5 45.260 466.6 152s PrivateWages_6 8.618 85.6 152s PrivateWages_8 -27.046 -280.7 152s PrivateWages_9 -31.306 -328.2 152s PrivateWages_10 -62.621 -625.0 152s PrivateWages_11 45.808 455.3 152s PrivateWages_12 4.694 65.2 152s PrivateWages_13 0.000 0.0 152s PrivateWages_14 -19.212 -568.4 152s PrivateWages_15 1.276 23.0 152s PrivateWages_16 2.965 48.0 152s PrivateWages_17 -31.593 -446.1 152s PrivateWages_18 -1.184 -13.4 152s PrivateWages_19 93.968 1096.1 152s PrivateWages_20 -18.672 -244.0 152s PrivateWages_21 21.247 225.0 152s PrivateWages_22 -35.087 -340.1 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 -5.2993 -249.44 -237.94 152s Consumption_3 -1.4232 -70.56 -64.90 152s Consumption_4 0.6293 35.58 31.53 152s Consumption_5 -2.8987 -175.91 -165.80 152s Consumption_6 1.5378 93.21 87.81 152s Consumption_8 7.1199 427.18 455.67 152s Consumption_9 6.3712 396.73 410.31 152s Consumption_11 -2.6567 -169.26 -178.00 152s Consumption_12 -3.9871 -218.62 -244.01 152s Consumption_14 0.4811 20.27 21.31 152s Consumption_15 -3.2826 -168.12 -148.04 152s Consumption_16 -2.7078 -149.85 -134.58 152s Consumption_17 8.9374 512.95 486.20 152s Consumption_18 -0.8584 -57.66 -53.82 152s Consumption_19 -6.8609 -470.06 -445.96 152s Consumption_20 4.8772 326.02 297.02 152s Consumption_21 2.5255 189.08 175.52 152s Consumption_22 -1.1049 -95.99 -83.64 152s Investment_2 3.2022 150.73 143.78 152s Investment_3 -0.0931 -4.61 -4.24 152s Investment_4 -0.7671 -43.38 -38.43 152s Investment_5 2.3540 142.85 134.65 152s Investment_6 -0.3976 -24.10 -22.70 152s Investment_8 -1.8770 -112.62 -120.13 152s Investment_9 -1.2092 -75.30 -77.87 152s Investment_10 -3.7113 -239.64 -239.38 152s Investment_11 1.3320 84.87 89.25 152s Investment_12 1.1624 63.74 71.14 152s Investment_14 -2.3880 -100.60 -105.79 152s Investment_15 0.2667 13.66 12.03 152s Investment_16 -0.2127 -11.77 -10.57 152s Investment_17 -2.9356 -168.49 -159.70 152s Investment_18 0.1571 10.56 9.85 152s Investment_19 4.7939 328.45 311.61 152s Investment_20 -1.1688 -78.13 -71.18 152s Investment_21 -0.6673 -49.96 -46.38 152s Investment_22 -1.7858 -155.15 -135.18 152s PrivateWages_2 -8.5877 -404.22 -385.59 152s PrivateWages_3 3.2235 159.82 146.99 152s PrivateWages_4 7.5943 429.40 380.48 152s PrivateWages_5 -8.2808 -502.53 -473.66 152s PrivateWages_6 -1.4955 -90.64 -85.39 152s PrivateWages_8 4.6454 278.71 297.31 152s PrivateWages_9 5.3226 331.43 342.78 152s PrivateWages_10 9.9910 645.11 644.42 152s PrivateWages_11 -7.1064 -452.76 -476.13 152s PrivateWages_12 -1.0129 -55.54 -61.99 152s PrivateWages_13 -5.2725 -247.69 -281.55 152s PrivateWages_14 9.2395 389.24 409.31 152s PrivateWages_15 -0.3837 -19.65 -17.30 152s PrivateWages_16 -0.8115 -44.91 -40.33 152s PrivateWages_17 7.5969 436.02 413.27 152s PrivateWages_18 0.2264 15.21 14.20 152s PrivateWages_19 -18.2855 -1252.79 -1188.56 152s PrivateWages_20 4.1085 274.63 250.21 152s PrivateWages_21 -3.7647 -281.85 -261.64 152s PrivateWages_22 5.5980 486.35 423.77 152s PrivateWages_trend 152s Consumption_2 52.993 152s Consumption_3 12.808 152s Consumption_4 -5.035 152s Consumption_5 20.291 152s Consumption_6 -9.227 152s Consumption_8 -28.480 152s Consumption_9 -19.114 152s Consumption_11 2.657 152s Consumption_12 0.000 152s Consumption_14 0.962 152s Consumption_15 -9.848 152s Consumption_16 -10.831 152s Consumption_17 44.687 152s Consumption_18 -5.151 152s Consumption_19 -48.026 152s Consumption_20 39.018 152s Consumption_21 22.730 152s Consumption_22 -11.049 152s Investment_2 -32.022 152s Investment_3 0.838 152s Investment_4 6.137 152s Investment_5 -16.478 152s Investment_6 2.386 152s Investment_8 7.508 152s Investment_9 3.628 152s Investment_10 7.423 152s Investment_11 -1.332 152s Investment_12 0.000 152s Investment_14 -4.776 152s Investment_15 0.800 152s Investment_16 -0.851 152s Investment_17 -14.678 152s Investment_18 0.943 152s Investment_19 33.558 152s Investment_20 -9.351 152s Investment_21 -6.006 152s Investment_22 -17.858 152s PrivateWages_2 85.877 152s PrivateWages_3 -29.012 152s PrivateWages_4 -60.755 152s PrivateWages_5 57.966 152s PrivateWages_6 8.973 152s PrivateWages_8 -18.582 152s PrivateWages_9 -15.968 152s PrivateWages_10 -19.982 152s PrivateWages_11 7.106 152s PrivateWages_12 0.000 152s PrivateWages_13 -5.272 152s PrivateWages_14 18.479 152s PrivateWages_15 -1.151 152s PrivateWages_16 -3.246 152s PrivateWages_17 37.985 152s PrivateWages_18 1.359 152s PrivateWages_19 -127.998 152s PrivateWages_20 32.868 152s PrivateWages_21 -33.882 152s PrivateWages_22 55.980 152s [1] TRUE 152s > Bread 152s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 152s [1,] 132.5589 -4.1405 0.7711 152s [2,] -4.1405 1.1839 -0.6491 152s [3,] 0.7711 -0.6491 0.7009 152s [4,] -1.6944 -0.1297 -0.0283 152s [5,] 114.8656 3.1837 5.1587 152s [6,] -5.5704 0.7491 -0.6223 152s [7,] 1.9218 -0.4973 0.5817 152s [8,] -0.2370 -0.0398 -0.0201 152s [9,] -36.8131 0.3292 1.6643 152s [10,] 0.5110 -0.0698 0.0440 152s [11,] 0.0898 0.0655 -0.0737 152s [12,] 0.2835 0.0505 0.0244 152s Consumption_wages Investment_(Intercept) Investment_corpProf 152s [1,] -1.694379 114.87 -5.57043 152s [2,] -0.129702 3.18 0.74914 152s [3,] -0.028262 5.16 -0.62232 152s [4,] 0.104489 -5.87 0.06772 152s [5,] -5.874854 3366.95 -56.98587 152s [6,] 0.067720 -56.99 2.64551 152s [7,] -0.069795 45.44 -2.02544 152s [8,] 0.029271 -15.60 0.22292 152s [9,] 0.075832 53.51 -0.48750 152s [10,] -0.001892 2.12 0.00442 152s [11,] 0.000817 -3.12 0.00410 152s [12,] -0.036920 -1.40 0.02820 152s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 152s [1,] 1.92185 -0.23700 -36.8131 152s [2,] -0.49725 -0.03983 0.3292 152s [3,] 0.58170 -0.02007 1.6643 152s [4,] -0.06979 0.02927 0.0758 152s [5,] 45.44092 -15.60143 53.5110 152s [6,] -2.02544 0.22292 -0.4875 152s [7,] 1.95029 -0.21271 -0.7904 152s [8,] -0.21271 0.07616 -0.1618 152s [9,] -0.79038 -0.16180 69.6580 152s [10,] 0.00806 -0.01150 -0.3039 152s [11,] 0.00580 0.01472 -0.8753 152s [12,] -0.04133 0.00782 0.7539 152s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 152s [1,] 0.51104 0.089786 0.283482 152s [2,] -0.06979 0.065456 0.050508 152s [3,] 0.04399 -0.073692 0.024378 152s [4,] -0.00189 0.000817 -0.036920 152s [5,] 2.11576 -3.117775 -1.396100 152s [6,] 0.00442 0.004099 0.028202 152s [7,] 0.00806 0.005798 -0.041335 152s [8,] -0.01150 0.014719 0.007824 152s [9,] -0.30387 -0.875279 0.753905 152s [10,] 0.04699 -0.042862 -0.013049 152s [11,] -0.04286 0.059096 0.000172 152s [12,] -0.01305 0.000172 0.045631 152s > 152s > # OLS 152s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 152s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 152s > summary 152s 152s systemfit results 152s method: OLS 152s 152s N DF SSR detRCov OLS-R2 McElroy-R2 152s system 58 46 44.2 0.565 0.976 0.991 152s 152s N DF SSR MSE RMSE R2 Adj R2 152s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 152s Investment 19 15 17.11 1.140 1.07 0.907 0.889 152s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 152s 152s The covariance matrix of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.285 0.061 -0.511 152s Investment 0.061 1.059 0.151 152s PrivateWages -0.511 0.151 0.648 152s 152s The correlations of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.0000 0.0457 -0.568 152s Investment 0.0457 1.0000 0.168 152s PrivateWages -0.5681 0.1676 1.000 152s 152s 152s OLS estimates for 'Consumption' (equation 1) 152s Model Formula: consump ~ corpProf + corpProfLag + wages 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 16.2957 1.5438 10.56 2.4e-08 *** 152s corpProf 0.1796 0.1206 1.49 0.16 152s corpProfLag 0.1032 0.1031 1.00 0.33 152s wages 0.7962 0.0449 17.73 1.8e-11 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.076 on 15 degrees of freedom 152s Number of observations: 19 Degrees of Freedom: 15 152s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 152s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 152s 152s 152s OLS estimates for 'Investment' (equation 2) 152s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 10.1724 5.5758 1.82 0.08808 . 152s corpProf 0.5004 0.1092 4.58 0.00036 *** 152s corpProfLag 0.3270 0.1052 3.11 0.00718 ** 152s capitalLag -0.1134 0.0275 -4.13 0.00090 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.068 on 15 degrees of freedom 152s Number of observations: 19 Degrees of Freedom: 15 152s SSR: 17.105 MSE: 1.14 Root MSE: 1.068 152s Multiple R-Squared: 0.907 Adjusted R-Squared: 0.889 152s 152s 152s OLS estimates for 'PrivateWages' (equation 3) 152s Model Formula: privWage ~ gnp + gnpLag + trend 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 1.3550 1.3512 1.00 0.3309 152s gnp 0.4417 0.0342 12.92 7e-10 *** 152s gnpLag 0.1466 0.0393 3.73 0.0018 ** 152s trend 0.1244 0.0347 3.58 0.0025 ** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 0.78 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 152s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 152s 152s compare coef with single-equation OLS 152s [1] TRUE 152s > residuals 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 -0.3863 0.00693 -1.3389 152s 3 -1.2484 -0.06954 0.2462 152s 4 -1.6040 1.22401 1.1255 152s 5 -0.5384 -1.37697 -0.1959 152s 6 -0.0413 0.38610 -0.5284 152s 7 0.8043 1.48598 NA 152s 8 1.2830 0.78465 -0.7909 152s 9 1.0142 -0.65483 0.2819 152s 10 NA 1.06018 1.1384 152s 11 0.1429 0.39508 -0.1904 152s 12 -0.3439 0.20479 0.5813 152s 13 NA NA 0.1206 152s 14 0.3199 0.32778 0.4773 152s 15 -0.1016 -0.07450 0.3035 152s 16 -0.0702 NA 0.0284 152s 17 1.6064 0.96998 -0.8517 152s 18 -0.4980 0.08124 0.9908 152s 19 0.1253 -2.49295 -0.4597 152s 20 0.9805 -0.70609 -0.3819 152s 21 0.7551 -0.81928 -1.1062 152s 22 -2.1992 -0.73256 0.5501 152s > fitted 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 42.3 -0.207 26.8 152s 3 46.2 1.970 29.1 152s 4 50.8 3.976 33.0 152s 5 51.1 4.377 34.1 152s 6 52.6 4.714 35.9 152s 7 54.3 4.114 NA 152s 8 54.9 3.415 38.7 152s 9 56.3 3.655 38.9 152s 10 NA 4.040 40.2 152s 11 54.9 0.605 38.1 152s 12 51.2 -3.605 33.9 152s 13 NA NA 28.9 152s 14 46.2 -5.428 28.0 152s 15 48.8 -2.926 30.3 152s 16 51.4 NA 33.2 152s 17 56.1 1.130 37.7 152s 18 59.2 1.919 40.0 152s 19 57.4 0.593 38.7 152s 20 60.6 2.006 42.0 152s 21 64.2 4.119 46.1 152s 22 71.9 5.633 52.7 152s > predict 152s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 152s 1 NA NA NA NA 152s 2 42.3 0.543 39.9 44.7 152s 3 46.2 0.581 43.8 48.7 152s 4 50.8 0.394 48.5 53.1 152s 5 51.1 0.465 48.8 53.5 152s 6 52.6 0.474 50.3 55.0 152s 7 54.3 0.423 52.0 56.6 152s 8 54.9 0.389 52.6 57.2 152s 9 56.3 0.434 54.0 58.6 152s 10 NA NA NA NA 152s 11 54.9 0.727 52.2 57.5 152s 12 51.2 0.662 48.7 53.8 152s 13 NA NA NA NA 152s 14 46.2 0.698 43.6 48.8 152s 15 48.8 0.470 46.4 51.2 152s 16 51.4 0.398 49.1 53.7 152s 17 56.1 0.405 53.8 58.4 152s 18 59.2 0.375 56.9 61.5 152s 19 57.4 0.466 55.0 59.7 152s 20 60.6 0.482 58.2 63.0 152s 21 64.2 0.485 61.9 66.6 152s 22 71.9 0.755 69.3 74.5 152s Investment.pred Investment.se.fit Investment.lwr Investment.upr 152s 1 NA NA NA NA 152s 2 -0.207 0.645 -2.718 2.30 152s 3 1.970 0.523 -0.423 4.36 152s 4 3.976 0.462 1.634 6.32 152s 5 4.377 0.383 2.094 6.66 152s 6 4.714 0.362 2.444 6.98 152s 7 4.114 0.336 1.861 6.37 152s 8 3.415 0.298 1.184 5.65 152s 9 3.655 0.400 1.359 5.95 152s 10 4.040 0.458 1.701 6.38 152s 11 0.605 0.666 -1.928 3.14 152s 12 -3.605 0.637 -6.108 -1.10 152s 13 NA NA NA NA 152s 14 -5.428 0.767 -8.074 -2.78 152s 15 -2.926 0.453 -5.261 -0.59 152s 16 NA NA NA NA 152s 17 1.130 0.366 -1.142 3.40 152s 18 1.919 0.258 -0.293 4.13 152s 19 0.593 0.357 -1.674 2.86 152s 20 2.006 0.384 -0.278 4.29 152s 21 4.119 0.350 1.858 6.38 152s 22 5.633 0.495 3.263 8.00 152s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 152s 1 NA NA NA NA 152s 2 26.8 0.378 25.1 28.6 152s 3 29.1 0.381 27.3 30.8 152s 4 33.0 0.384 31.2 34.7 152s 5 34.1 0.297 32.4 35.8 152s 6 35.9 0.296 34.2 37.6 152s 7 NA NA NA NA 152s 8 38.7 0.303 37.0 40.4 152s 9 38.9 0.288 37.2 40.6 152s 10 40.2 0.274 38.5 41.8 152s 11 38.1 0.377 36.3 39.8 152s 12 33.9 0.381 32.2 35.7 152s 13 28.9 0.452 27.1 30.7 152s 14 28.0 0.397 26.3 29.8 152s 15 30.3 0.391 28.5 32.1 152s 16 33.2 0.327 31.5 34.9 152s 17 37.7 0.320 36.0 39.3 152s 18 40.0 0.250 38.4 41.7 152s 19 38.7 0.375 36.9 40.4 152s 20 42.0 0.337 40.3 43.7 152s 21 46.1 0.352 44.4 47.8 152s 22 52.7 0.530 50.9 54.6 152s > model.frame 152s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 152s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 152s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 152s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 152s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 152s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 152s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 152s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 152s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 152s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 152s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 152s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 152s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 152s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 152s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 152s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 152s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 152s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 152s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 152s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 152s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 152s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 152s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 152s trend 152s 1 -11 152s 2 -10 152s 3 -9 152s 4 -8 152s 5 -7 152s 6 -6 152s 7 -5 152s 8 -4 152s 9 -3 152s 10 -2 152s 11 -1 152s 12 0 152s 13 1 152s 14 2 152s 15 3 152s 16 4 152s 17 5 152s 18 6 152s 19 7 152s 20 8 152s 21 9 152s 22 10 152s > model.matrix 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 1 12.4 152s Consumption_3 1 16.9 152s Consumption_4 1 18.4 152s Consumption_5 1 19.4 152s Consumption_6 1 20.1 152s Consumption_7 1 19.6 152s Consumption_8 1 19.8 152s Consumption_9 1 21.1 152s Consumption_11 1 15.6 152s Consumption_12 1 11.4 152s Consumption_14 1 11.2 152s Consumption_15 1 12.3 152s Consumption_16 1 14.0 152s Consumption_17 1 17.6 152s Consumption_18 1 17.3 152s Consumption_19 1 15.3 152s Consumption_20 1 19.0 152s Consumption_21 1 21.1 152s Consumption_22 1 23.5 152s Investment_2 0 0.0 152s Investment_3 0 0.0 152s Investment_4 0 0.0 152s Investment_5 0 0.0 152s Investment_6 0 0.0 152s Investment_7 0 0.0 152s Investment_8 0 0.0 152s Investment_9 0 0.0 152s Investment_10 0 0.0 152s Investment_11 0 0.0 152s Investment_12 0 0.0 152s Investment_14 0 0.0 152s Investment_15 0 0.0 152s Investment_17 0 0.0 152s Investment_18 0 0.0 152s Investment_19 0 0.0 152s Investment_20 0 0.0 152s Investment_21 0 0.0 152s Investment_22 0 0.0 152s PrivateWages_2 0 0.0 152s PrivateWages_3 0 0.0 152s PrivateWages_4 0 0.0 152s PrivateWages_5 0 0.0 152s PrivateWages_6 0 0.0 152s PrivateWages_8 0 0.0 152s PrivateWages_9 0 0.0 152s PrivateWages_10 0 0.0 152s PrivateWages_11 0 0.0 152s PrivateWages_12 0 0.0 152s PrivateWages_13 0 0.0 152s PrivateWages_14 0 0.0 152s PrivateWages_15 0 0.0 152s PrivateWages_16 0 0.0 152s PrivateWages_17 0 0.0 152s PrivateWages_18 0 0.0 152s PrivateWages_19 0 0.0 152s PrivateWages_20 0 0.0 152s PrivateWages_21 0 0.0 152s PrivateWages_22 0 0.0 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 12.7 28.2 152s Consumption_3 12.4 32.2 152s Consumption_4 16.9 37.0 152s Consumption_5 18.4 37.0 152s Consumption_6 19.4 38.6 152s Consumption_7 20.1 40.7 152s Consumption_8 19.6 41.5 152s Consumption_9 19.8 42.9 152s Consumption_11 21.7 42.1 152s Consumption_12 15.6 39.3 152s Consumption_14 7.0 34.1 152s Consumption_15 11.2 36.6 152s Consumption_16 12.3 39.3 152s Consumption_17 14.0 44.2 152s Consumption_18 17.6 47.7 152s Consumption_19 17.3 45.9 152s Consumption_20 15.3 49.4 152s Consumption_21 19.0 53.0 152s Consumption_22 21.1 61.8 152s Investment_2 0.0 0.0 152s Investment_3 0.0 0.0 152s Investment_4 0.0 0.0 152s Investment_5 0.0 0.0 152s Investment_6 0.0 0.0 152s Investment_7 0.0 0.0 152s Investment_8 0.0 0.0 152s Investment_9 0.0 0.0 152s Investment_10 0.0 0.0 152s Investment_11 0.0 0.0 152s Investment_12 0.0 0.0 152s Investment_14 0.0 0.0 152s Investment_15 0.0 0.0 152s Investment_17 0.0 0.0 152s Investment_18 0.0 0.0 152s Investment_19 0.0 0.0 152s Investment_20 0.0 0.0 152s Investment_21 0.0 0.0 152s Investment_22 0.0 0.0 152s PrivateWages_2 0.0 0.0 152s PrivateWages_3 0.0 0.0 152s PrivateWages_4 0.0 0.0 152s PrivateWages_5 0.0 0.0 152s PrivateWages_6 0.0 0.0 152s PrivateWages_8 0.0 0.0 152s PrivateWages_9 0.0 0.0 152s PrivateWages_10 0.0 0.0 152s PrivateWages_11 0.0 0.0 152s PrivateWages_12 0.0 0.0 152s PrivateWages_13 0.0 0.0 152s PrivateWages_14 0.0 0.0 152s PrivateWages_15 0.0 0.0 152s PrivateWages_16 0.0 0.0 152s PrivateWages_17 0.0 0.0 152s PrivateWages_18 0.0 0.0 152s PrivateWages_19 0.0 0.0 152s PrivateWages_20 0.0 0.0 152s PrivateWages_21 0.0 0.0 152s PrivateWages_22 0.0 0.0 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 0 0.0 152s Consumption_3 0 0.0 152s Consumption_4 0 0.0 152s Consumption_5 0 0.0 152s Consumption_6 0 0.0 152s Consumption_7 0 0.0 152s Consumption_8 0 0.0 152s Consumption_9 0 0.0 152s Consumption_11 0 0.0 152s Consumption_12 0 0.0 152s Consumption_14 0 0.0 152s Consumption_15 0 0.0 152s Consumption_16 0 0.0 152s Consumption_17 0 0.0 152s Consumption_18 0 0.0 152s Consumption_19 0 0.0 152s Consumption_20 0 0.0 152s Consumption_21 0 0.0 152s Consumption_22 0 0.0 152s Investment_2 1 12.4 152s Investment_3 1 16.9 152s Investment_4 1 18.4 152s Investment_5 1 19.4 152s Investment_6 1 20.1 152s Investment_7 1 19.6 152s Investment_8 1 19.8 152s Investment_9 1 21.1 152s Investment_10 1 21.7 152s Investment_11 1 15.6 152s Investment_12 1 11.4 152s Investment_14 1 11.2 152s Investment_15 1 12.3 152s Investment_17 1 17.6 152s Investment_18 1 17.3 152s Investment_19 1 15.3 152s Investment_20 1 19.0 152s Investment_21 1 21.1 152s Investment_22 1 23.5 152s PrivateWages_2 0 0.0 152s PrivateWages_3 0 0.0 152s PrivateWages_4 0 0.0 152s PrivateWages_5 0 0.0 152s PrivateWages_6 0 0.0 152s PrivateWages_8 0 0.0 152s PrivateWages_9 0 0.0 152s PrivateWages_10 0 0.0 152s PrivateWages_11 0 0.0 152s PrivateWages_12 0 0.0 152s PrivateWages_13 0 0.0 152s PrivateWages_14 0 0.0 152s PrivateWages_15 0 0.0 152s PrivateWages_16 0 0.0 152s PrivateWages_17 0 0.0 152s PrivateWages_18 0 0.0 152s PrivateWages_19 0 0.0 152s PrivateWages_20 0 0.0 152s PrivateWages_21 0 0.0 152s PrivateWages_22 0 0.0 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 0.0 0 152s Consumption_3 0.0 0 152s Consumption_4 0.0 0 152s Consumption_5 0.0 0 152s Consumption_6 0.0 0 152s Consumption_7 0.0 0 152s Consumption_8 0.0 0 152s Consumption_9 0.0 0 152s Consumption_11 0.0 0 152s Consumption_12 0.0 0 152s Consumption_14 0.0 0 152s Consumption_15 0.0 0 152s Consumption_16 0.0 0 152s Consumption_17 0.0 0 152s Consumption_18 0.0 0 152s Consumption_19 0.0 0 152s Consumption_20 0.0 0 152s Consumption_21 0.0 0 152s Consumption_22 0.0 0 152s Investment_2 12.7 183 152s Investment_3 12.4 183 152s Investment_4 16.9 184 152s Investment_5 18.4 190 152s Investment_6 19.4 193 152s Investment_7 20.1 198 152s Investment_8 19.6 203 152s Investment_9 19.8 208 152s Investment_10 21.1 211 152s Investment_11 21.7 216 152s Investment_12 15.6 217 152s Investment_14 7.0 207 152s Investment_15 11.2 202 152s Investment_17 14.0 198 152s Investment_18 17.6 200 152s Investment_19 17.3 202 152s Investment_20 15.3 200 152s Investment_21 19.0 201 152s Investment_22 21.1 204 152s PrivateWages_2 0.0 0 152s PrivateWages_3 0.0 0 152s PrivateWages_4 0.0 0 152s PrivateWages_5 0.0 0 152s PrivateWages_6 0.0 0 152s PrivateWages_8 0.0 0 152s PrivateWages_9 0.0 0 152s PrivateWages_10 0.0 0 152s PrivateWages_11 0.0 0 152s PrivateWages_12 0.0 0 152s PrivateWages_13 0.0 0 152s PrivateWages_14 0.0 0 152s PrivateWages_15 0.0 0 152s PrivateWages_16 0.0 0 152s PrivateWages_17 0.0 0 152s PrivateWages_18 0.0 0 152s PrivateWages_19 0.0 0 152s PrivateWages_20 0.0 0 152s PrivateWages_21 0.0 0 152s PrivateWages_22 0.0 0 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 0 0.0 0.0 152s Consumption_3 0 0.0 0.0 152s Consumption_4 0 0.0 0.0 152s Consumption_5 0 0.0 0.0 152s Consumption_6 0 0.0 0.0 152s Consumption_7 0 0.0 0.0 152s Consumption_8 0 0.0 0.0 152s Consumption_9 0 0.0 0.0 152s Consumption_11 0 0.0 0.0 152s Consumption_12 0 0.0 0.0 152s Consumption_14 0 0.0 0.0 152s Consumption_15 0 0.0 0.0 152s Consumption_16 0 0.0 0.0 152s Consumption_17 0 0.0 0.0 152s Consumption_18 0 0.0 0.0 152s Consumption_19 0 0.0 0.0 152s Consumption_20 0 0.0 0.0 152s Consumption_21 0 0.0 0.0 152s Consumption_22 0 0.0 0.0 152s Investment_2 0 0.0 0.0 152s Investment_3 0 0.0 0.0 152s Investment_4 0 0.0 0.0 152s Investment_5 0 0.0 0.0 152s Investment_6 0 0.0 0.0 152s Investment_7 0 0.0 0.0 152s Investment_8 0 0.0 0.0 152s Investment_9 0 0.0 0.0 152s Investment_10 0 0.0 0.0 152s Investment_11 0 0.0 0.0 152s Investment_12 0 0.0 0.0 152s Investment_14 0 0.0 0.0 152s Investment_15 0 0.0 0.0 152s Investment_17 0 0.0 0.0 152s Investment_18 0 0.0 0.0 152s Investment_19 0 0.0 0.0 152s Investment_20 0 0.0 0.0 152s Investment_21 0 0.0 0.0 152s Investment_22 0 0.0 0.0 152s PrivateWages_2 1 45.6 44.9 152s PrivateWages_3 1 50.1 45.6 152s PrivateWages_4 1 57.2 50.1 152s PrivateWages_5 1 57.1 57.2 152s PrivateWages_6 1 61.0 57.1 152s PrivateWages_8 1 64.4 64.0 152s PrivateWages_9 1 64.5 64.4 152s PrivateWages_10 1 67.0 64.5 152s PrivateWages_11 1 61.2 67.0 152s PrivateWages_12 1 53.4 61.2 152s PrivateWages_13 1 44.3 53.4 152s PrivateWages_14 1 45.1 44.3 152s PrivateWages_15 1 49.7 45.1 152s PrivateWages_16 1 54.4 49.7 152s PrivateWages_17 1 62.7 54.4 152s PrivateWages_18 1 65.0 62.7 152s PrivateWages_19 1 60.9 65.0 152s PrivateWages_20 1 69.5 60.9 152s PrivateWages_21 1 75.7 69.5 152s PrivateWages_22 1 88.4 75.7 152s PrivateWages_trend 152s Consumption_2 0 152s Consumption_3 0 152s Consumption_4 0 152s Consumption_5 0 152s Consumption_6 0 152s Consumption_7 0 152s Consumption_8 0 152s Consumption_9 0 152s Consumption_11 0 152s Consumption_12 0 152s Consumption_14 0 152s Consumption_15 0 152s Consumption_16 0 152s Consumption_17 0 152s Consumption_18 0 152s Consumption_19 0 152s Consumption_20 0 152s Consumption_21 0 152s Consumption_22 0 152s Investment_2 0 152s Investment_3 0 152s Investment_4 0 152s Investment_5 0 152s Investment_6 0 152s Investment_7 0 152s Investment_8 0 152s Investment_9 0 152s Investment_10 0 152s Investment_11 0 152s Investment_12 0 152s Investment_14 0 152s Investment_15 0 152s Investment_17 0 152s Investment_18 0 152s Investment_19 0 152s Investment_20 0 152s Investment_21 0 152s Investment_22 0 152s PrivateWages_2 -10 152s PrivateWages_3 -9 152s PrivateWages_4 -8 152s PrivateWages_5 -7 152s PrivateWages_6 -6 152s PrivateWages_8 -4 152s PrivateWages_9 -3 152s PrivateWages_10 -2 152s PrivateWages_11 -1 152s PrivateWages_12 0 152s PrivateWages_13 1 152s PrivateWages_14 2 152s PrivateWages_15 3 152s PrivateWages_16 4 152s PrivateWages_17 5 152s PrivateWages_18 6 152s PrivateWages_19 7 152s PrivateWages_20 8 152s PrivateWages_21 9 152s PrivateWages_22 10 152s > nobs 152s [1] 58 152s > linearHypothesis 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 47 152s 2 46 1 0.3 0.59 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 47 152s 2 46 1 0.29 0.6 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 47 152s 2 46 1 0.29 0.59 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 46 2 0.16 0.85 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 48 152s 2 46 2 0.15 0.86 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 48 152s 2 46 2 0.3 0.86 152s > logLik 152s 'log Lik.' -68.8 (df=13) 152s 'log Lik.' -73.3 (df=13) 152s compare log likelihood value with single-equation OLS 152s [1] "Mean relative difference: 0.0011" 152s Estimating function 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 -0.3863 -4.791 152s Consumption_3 -1.2484 -21.098 152s Consumption_4 -1.6040 -29.514 152s Consumption_5 -0.5384 -10.446 152s Consumption_6 -0.0413 -0.830 152s Consumption_7 0.8043 15.763 152s Consumption_8 1.2830 25.403 152s Consumption_9 1.0142 21.399 152s Consumption_11 0.1429 2.229 152s Consumption_12 -0.3439 -3.920 152s Consumption_14 0.3199 3.583 152s Consumption_15 -0.1016 -1.250 152s Consumption_16 -0.0702 -0.983 152s Consumption_17 1.6064 28.272 152s Consumption_18 -0.4980 -8.616 152s Consumption_19 0.1253 1.917 152s Consumption_20 0.9805 18.629 152s Consumption_21 0.7551 15.933 152s Consumption_22 -2.1992 -51.681 152s Investment_2 0.0000 0.000 152s Investment_3 0.0000 0.000 152s Investment_4 0.0000 0.000 152s Investment_5 0.0000 0.000 152s Investment_6 0.0000 0.000 152s Investment_7 0.0000 0.000 152s Investment_8 0.0000 0.000 152s Investment_9 0.0000 0.000 152s Investment_10 0.0000 0.000 152s Investment_11 0.0000 0.000 152s Investment_12 0.0000 0.000 152s Investment_14 0.0000 0.000 152s Investment_15 0.0000 0.000 152s Investment_17 0.0000 0.000 152s Investment_18 0.0000 0.000 152s Investment_19 0.0000 0.000 152s Investment_20 0.0000 0.000 152s Investment_21 0.0000 0.000 152s Investment_22 0.0000 0.000 152s PrivateWages_2 0.0000 0.000 152s PrivateWages_3 0.0000 0.000 152s PrivateWages_4 0.0000 0.000 152s PrivateWages_5 0.0000 0.000 152s PrivateWages_6 0.0000 0.000 152s PrivateWages_8 0.0000 0.000 152s PrivateWages_9 0.0000 0.000 152s PrivateWages_10 0.0000 0.000 152s PrivateWages_11 0.0000 0.000 152s PrivateWages_12 0.0000 0.000 152s PrivateWages_13 0.0000 0.000 152s PrivateWages_14 0.0000 0.000 152s PrivateWages_15 0.0000 0.000 152s PrivateWages_16 0.0000 0.000 152s PrivateWages_17 0.0000 0.000 152s PrivateWages_18 0.0000 0.000 152s PrivateWages_19 0.0000 0.000 152s PrivateWages_20 0.0000 0.000 152s PrivateWages_21 0.0000 0.000 152s PrivateWages_22 0.0000 0.000 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 -4.907 -10.90 152s Consumption_3 -15.480 -40.20 152s Consumption_4 -27.108 -59.35 152s Consumption_5 -9.907 -19.92 152s Consumption_6 -0.801 -1.59 152s Consumption_7 16.166 32.73 152s Consumption_8 25.146 53.24 152s Consumption_9 20.081 43.51 152s Consumption_11 3.100 6.01 152s Consumption_12 -5.364 -13.51 152s Consumption_14 2.239 10.91 152s Consumption_15 -1.138 -3.72 152s Consumption_16 -0.864 -2.76 152s Consumption_17 22.489 71.00 152s Consumption_18 -8.765 -23.76 152s Consumption_19 2.168 5.75 152s Consumption_20 15.002 48.44 152s Consumption_21 14.348 40.02 152s Consumption_22 -46.403 -135.91 152s Investment_2 0.000 0.00 152s Investment_3 0.000 0.00 152s Investment_4 0.000 0.00 152s Investment_5 0.000 0.00 152s Investment_6 0.000 0.00 152s Investment_7 0.000 0.00 152s Investment_8 0.000 0.00 152s Investment_9 0.000 0.00 152s Investment_10 0.000 0.00 152s Investment_11 0.000 0.00 152s Investment_12 0.000 0.00 152s Investment_14 0.000 0.00 152s Investment_15 0.000 0.00 152s Investment_17 0.000 0.00 152s Investment_18 0.000 0.00 152s Investment_19 0.000 0.00 152s Investment_20 0.000 0.00 152s Investment_21 0.000 0.00 152s Investment_22 0.000 0.00 152s PrivateWages_2 0.000 0.00 152s PrivateWages_3 0.000 0.00 152s PrivateWages_4 0.000 0.00 152s PrivateWages_5 0.000 0.00 152s PrivateWages_6 0.000 0.00 152s PrivateWages_8 0.000 0.00 152s PrivateWages_9 0.000 0.00 152s PrivateWages_10 0.000 0.00 152s PrivateWages_11 0.000 0.00 152s PrivateWages_12 0.000 0.00 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 0.000 0.00 152s PrivateWages_15 0.000 0.00 152s PrivateWages_16 0.000 0.00 152s PrivateWages_17 0.000 0.00 152s PrivateWages_18 0.000 0.00 152s PrivateWages_19 0.000 0.00 152s PrivateWages_20 0.000 0.00 152s PrivateWages_21 0.000 0.00 152s PrivateWages_22 0.000 0.00 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 0.00000 0.000 152s Consumption_3 0.00000 0.000 152s Consumption_4 0.00000 0.000 152s Consumption_5 0.00000 0.000 152s Consumption_6 0.00000 0.000 152s Consumption_7 0.00000 0.000 152s Consumption_8 0.00000 0.000 152s Consumption_9 0.00000 0.000 152s Consumption_11 0.00000 0.000 152s Consumption_12 0.00000 0.000 152s Consumption_14 0.00000 0.000 152s Consumption_15 0.00000 0.000 152s Consumption_16 0.00000 0.000 152s Consumption_17 0.00000 0.000 152s Consumption_18 0.00000 0.000 152s Consumption_19 0.00000 0.000 152s Consumption_20 0.00000 0.000 152s Consumption_21 0.00000 0.000 152s Consumption_22 0.00000 0.000 152s Investment_2 0.00693 0.086 152s Investment_3 -0.06954 -1.175 152s Investment_4 1.22401 22.522 152s Investment_5 -1.37696 -26.713 152s Investment_6 0.38610 7.761 152s Investment_7 1.48598 29.125 152s Investment_8 0.78465 15.536 152s Investment_9 -0.65483 -13.817 152s Investment_10 1.06018 23.006 152s Investment_11 0.39508 6.163 152s Investment_12 0.20479 2.335 152s Investment_14 0.32778 3.671 152s Investment_15 -0.07450 -0.916 152s Investment_17 0.96998 17.072 152s Investment_18 0.08124 1.405 152s Investment_19 -2.49295 -38.142 152s Investment_20 -0.70609 -13.416 152s Investment_21 -0.81928 -17.287 152s Investment_22 -0.73256 -17.215 152s PrivateWages_2 0.00000 0.000 152s PrivateWages_3 0.00000 0.000 152s PrivateWages_4 0.00000 0.000 152s PrivateWages_5 0.00000 0.000 152s PrivateWages_6 0.00000 0.000 152s PrivateWages_8 0.00000 0.000 152s PrivateWages_9 0.00000 0.000 152s PrivateWages_10 0.00000 0.000 152s PrivateWages_11 0.00000 0.000 152s PrivateWages_12 0.00000 0.000 152s PrivateWages_13 0.00000 0.000 152s PrivateWages_14 0.00000 0.000 152s PrivateWages_15 0.00000 0.000 152s PrivateWages_16 0.00000 0.000 152s PrivateWages_17 0.00000 0.000 152s PrivateWages_18 0.00000 0.000 152s PrivateWages_19 0.00000 0.000 152s PrivateWages_20 0.00000 0.000 152s PrivateWages_21 0.00000 0.000 152s PrivateWages_22 0.00000 0.000 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 0.0000 0.00 152s Consumption_3 0.0000 0.00 152s Consumption_4 0.0000 0.00 152s Consumption_5 0.0000 0.00 152s Consumption_6 0.0000 0.00 152s Consumption_7 0.0000 0.00 152s Consumption_8 0.0000 0.00 152s Consumption_9 0.0000 0.00 152s Consumption_11 0.0000 0.00 152s Consumption_12 0.0000 0.00 152s Consumption_14 0.0000 0.00 152s Consumption_15 0.0000 0.00 152s Consumption_16 0.0000 0.00 152s Consumption_17 0.0000 0.00 152s Consumption_18 0.0000 0.00 152s Consumption_19 0.0000 0.00 152s Consumption_20 0.0000 0.00 152s Consumption_21 0.0000 0.00 152s Consumption_22 0.0000 0.00 152s Investment_2 0.0881 1.27 152s Investment_3 -0.8622 -12.70 152s Investment_4 20.6858 225.83 152s Investment_5 -25.3362 -261.21 152s Investment_6 7.4903 74.40 152s Investment_7 29.8681 293.93 152s Investment_8 15.3791 159.60 152s Investment_9 -12.9657 -135.94 152s Investment_10 22.3698 223.27 152s Investment_11 8.5733 85.22 152s Investment_12 3.1947 44.38 152s Investment_14 2.2945 67.88 152s Investment_15 -0.8344 -15.05 152s Investment_17 13.5797 191.77 152s Investment_18 1.4298 16.23 152s Investment_19 -43.1281 -503.08 152s Investment_20 -10.8032 -141.15 152s Investment_21 -15.5663 -164.84 152s Investment_22 -15.4570 -149.81 152s PrivateWages_2 0.0000 0.00 152s PrivateWages_3 0.0000 0.00 152s PrivateWages_4 0.0000 0.00 152s PrivateWages_5 0.0000 0.00 152s PrivateWages_6 0.0000 0.00 152s PrivateWages_8 0.0000 0.00 152s PrivateWages_9 0.0000 0.00 152s PrivateWages_10 0.0000 0.00 152s PrivateWages_11 0.0000 0.00 152s PrivateWages_12 0.0000 0.00 152s PrivateWages_13 0.0000 0.00 152s PrivateWages_14 0.0000 0.00 152s PrivateWages_15 0.0000 0.00 152s PrivateWages_16 0.0000 0.00 152s PrivateWages_17 0.0000 0.00 152s PrivateWages_18 0.0000 0.00 152s PrivateWages_19 0.0000 0.00 152s PrivateWages_20 0.0000 0.00 152s PrivateWages_21 0.0000 0.00 152s PrivateWages_22 0.0000 0.00 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 0.0000 0.00 0.00 152s Consumption_3 0.0000 0.00 0.00 152s Consumption_4 0.0000 0.00 0.00 152s Consumption_5 0.0000 0.00 0.00 152s Consumption_6 0.0000 0.00 0.00 152s Consumption_7 0.0000 0.00 0.00 152s Consumption_8 0.0000 0.00 0.00 152s Consumption_9 0.0000 0.00 0.00 152s Consumption_11 0.0000 0.00 0.00 152s Consumption_12 0.0000 0.00 0.00 152s Consumption_14 0.0000 0.00 0.00 152s Consumption_15 0.0000 0.00 0.00 152s Consumption_16 0.0000 0.00 0.00 152s Consumption_17 0.0000 0.00 0.00 152s Consumption_18 0.0000 0.00 0.00 152s Consumption_19 0.0000 0.00 0.00 152s Consumption_20 0.0000 0.00 0.00 152s Consumption_21 0.0000 0.00 0.00 152s Consumption_22 0.0000 0.00 0.00 152s Investment_2 0.0000 0.00 0.00 152s Investment_3 0.0000 0.00 0.00 152s Investment_4 0.0000 0.00 0.00 152s Investment_5 0.0000 0.00 0.00 152s Investment_6 0.0000 0.00 0.00 152s Investment_7 0.0000 0.00 0.00 152s Investment_8 0.0000 0.00 0.00 152s Investment_9 0.0000 0.00 0.00 152s Investment_10 0.0000 0.00 0.00 152s Investment_11 0.0000 0.00 0.00 152s Investment_12 0.0000 0.00 0.00 152s Investment_14 0.0000 0.00 0.00 152s Investment_15 0.0000 0.00 0.00 152s Investment_17 0.0000 0.00 0.00 152s Investment_18 0.0000 0.00 0.00 152s Investment_19 0.0000 0.00 0.00 152s Investment_20 0.0000 0.00 0.00 152s Investment_21 0.0000 0.00 0.00 152s Investment_22 0.0000 0.00 0.00 152s PrivateWages_2 -1.3389 -61.06 -60.12 152s PrivateWages_3 0.2462 12.33 11.23 152s PrivateWages_4 1.1255 64.38 56.39 152s PrivateWages_5 -0.1959 -11.18 -11.20 152s PrivateWages_6 -0.5284 -32.23 -30.17 152s PrivateWages_8 -0.7909 -50.94 -50.62 152s PrivateWages_9 0.2819 18.18 18.15 152s PrivateWages_10 1.1384 76.28 73.43 152s PrivateWages_11 -0.1904 -11.65 -12.76 152s PrivateWages_12 0.5813 31.04 35.58 152s PrivateWages_13 0.1206 5.34 6.44 152s PrivateWages_14 0.4773 21.53 21.14 152s PrivateWages_15 0.3035 15.09 13.69 152s PrivateWages_16 0.0284 1.55 1.41 152s PrivateWages_17 -0.8517 -53.40 -46.33 152s PrivateWages_18 0.9908 64.40 62.12 152s PrivateWages_19 -0.4597 -28.00 -29.88 152s PrivateWages_20 -0.3819 -26.54 -23.26 152s PrivateWages_21 -1.1062 -83.74 -76.88 152s PrivateWages_22 0.5501 48.63 41.64 152s PrivateWages_trend 152s Consumption_2 0.000 152s Consumption_3 0.000 152s Consumption_4 0.000 152s Consumption_5 0.000 152s Consumption_6 0.000 152s Consumption_7 0.000 152s Consumption_8 0.000 152s Consumption_9 0.000 152s Consumption_11 0.000 152s Consumption_12 0.000 152s Consumption_14 0.000 152s Consumption_15 0.000 152s Consumption_16 0.000 152s Consumption_17 0.000 152s Consumption_18 0.000 152s Consumption_19 0.000 152s Consumption_20 0.000 152s Consumption_21 0.000 152s Consumption_22 0.000 152s Investment_2 0.000 152s Investment_3 0.000 152s Investment_4 0.000 152s Investment_5 0.000 152s Investment_6 0.000 152s Investment_7 0.000 152s Investment_8 0.000 152s Investment_9 0.000 152s Investment_10 0.000 152s Investment_11 0.000 152s Investment_12 0.000 152s Investment_14 0.000 152s Investment_15 0.000 152s Investment_17 0.000 152s Investment_18 0.000 152s Investment_19 0.000 152s Investment_20 0.000 152s Investment_21 0.000 152s Investment_22 0.000 152s PrivateWages_2 13.389 152s PrivateWages_3 -2.216 152s PrivateWages_4 -9.004 152s PrivateWages_5 1.371 152s PrivateWages_6 3.170 152s PrivateWages_8 3.164 152s PrivateWages_9 -0.846 152s PrivateWages_10 -2.277 152s PrivateWages_11 0.190 152s PrivateWages_12 0.000 152s PrivateWages_13 0.121 152s PrivateWages_14 0.955 152s PrivateWages_15 0.911 152s PrivateWages_16 0.114 152s PrivateWages_17 -4.258 152s PrivateWages_18 5.945 152s PrivateWages_19 -3.218 152s PrivateWages_20 -3.055 152s PrivateWages_21 -9.956 152s PrivateWages_22 5.501 152s [1] TRUE 152s > Bread 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_(Intercept) 107.542 -1.6123 152s Consumption_corpProf -1.612 0.6562 152s Consumption_corpProfLag -0.588 -0.3449 152s Consumption_wages -1.613 -0.0959 152s Investment_(Intercept) 0.000 0.0000 152s Investment_corpProf 0.000 0.0000 152s Investment_corpProfLag 0.000 0.0000 152s Investment_capitalLag 0.000 0.0000 152s PrivateWages_(Intercept) 0.000 0.0000 152s PrivateWages_gnp 0.000 0.0000 152s PrivateWages_gnpLag 0.000 0.0000 152s PrivateWages_trend 0.000 0.0000 152s Consumption_corpProfLag Consumption_wages 152s Consumption_(Intercept) -0.5878 -1.6130 152s Consumption_corpProf -0.3449 -0.0959 152s Consumption_corpProfLag 0.4797 -0.0326 152s Consumption_wages -0.0326 0.0910 152s Investment_(Intercept) 0.0000 0.0000 152s Investment_corpProf 0.0000 0.0000 152s Investment_corpProfLag 0.0000 0.0000 152s Investment_capitalLag 0.0000 0.0000 152s PrivateWages_(Intercept) 0.0000 0.0000 152s PrivateWages_gnp 0.0000 0.0000 152s PrivateWages_gnpLag 0.0000 0.0000 152s PrivateWages_trend 0.0000 0.0000 152s Investment_(Intercept) Investment_corpProf 152s Consumption_(Intercept) 0.00 0.000 152s Consumption_corpProf 0.00 0.000 152s Consumption_corpProfLag 0.00 0.000 152s Consumption_wages 0.00 0.000 152s Investment_(Intercept) 1702.08 -16.246 152s Investment_corpProf -16.25 0.653 152s Investment_corpProfLag 13.29 -0.499 152s Investment_capitalLag -8.19 0.066 152s PrivateWages_(Intercept) 0.00 0.000 152s PrivateWages_gnp 0.00 0.000 152s PrivateWages_gnpLag 0.00 0.000 152s PrivateWages_trend 0.00 0.000 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_(Intercept) 0.0000 0.0000 152s Consumption_corpProf 0.0000 0.0000 152s Consumption_corpProfLag 0.0000 0.0000 152s Consumption_wages 0.0000 0.0000 152s Investment_(Intercept) 13.2940 -8.1927 152s Investment_corpProf -0.4994 0.0660 152s Investment_corpProfLag 0.6054 -0.0737 152s Investment_capitalLag -0.0737 0.0414 152s PrivateWages_(Intercept) 0.0000 0.0000 152s PrivateWages_gnp 0.0000 0.0000 152s PrivateWages_gnpLag 0.0000 0.0000 152s PrivateWages_trend 0.0000 0.0000 152s PrivateWages_(Intercept) PrivateWages_gnp 152s Consumption_(Intercept) 0.000 0.0000 152s Consumption_corpProf 0.000 0.0000 152s Consumption_corpProfLag 0.000 0.0000 152s Consumption_wages 0.000 0.0000 152s Investment_(Intercept) 0.000 0.0000 152s Investment_corpProf 0.000 0.0000 152s Investment_corpProfLag 0.000 0.0000 152s Investment_capitalLag 0.000 0.0000 152s PrivateWages_(Intercept) 163.361 -0.6152 152s PrivateWages_gnp -0.615 0.1046 152s PrivateWages_gnpLag -2.146 -0.0975 152s PrivateWages_trend 2.016 -0.0281 152s PrivateWages_gnpLag PrivateWages_trend 152s Consumption_(Intercept) 0.00000 0.00000 152s Consumption_corpProf 0.00000 0.00000 152s Consumption_corpProfLag 0.00000 0.00000 152s Consumption_wages 0.00000 0.00000 152s Investment_(Intercept) 0.00000 0.00000 152s Investment_corpProf 0.00000 0.00000 152s Investment_corpProfLag 0.00000 0.00000 152s Investment_capitalLag 0.00000 0.00000 152s PrivateWages_(Intercept) -2.14647 2.01603 152s PrivateWages_gnp -0.09753 -0.02810 152s PrivateWages_gnpLag 0.13809 -0.00624 152s PrivateWages_trend -0.00624 0.10783 152s > 152s > # 2SLS 152s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 152s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 152s > summary 152s 152s systemfit results 152s method: 2SLS 152s 152s N DF SSR detRCov OLS-R2 McElroy-R2 152s system 56 44 57.9 0.391 0.968 0.992 152s 152s N DF SSR MSE RMSE R2 Adj R2 152s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 152s Investment 18 14 25.85 1.847 1.36 0.847 0.815 152s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 152s 152s The covariance matrix of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.307 0.540 -0.431 152s Investment 0.540 1.319 0.119 152s PrivateWages -0.431 0.119 0.496 152s 152s The correlations of the residuals 152s Consumption Investment PrivateWages 152s Consumption 1.000 0.414 -0.538 152s Investment 0.414 1.000 0.139 152s PrivateWages -0.538 0.139 1.000 152s 152s 152s 2SLS estimates for 'Consumption' (equation 1) 152s Model Formula: consump ~ corpProf + corpProfLag + wages 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 17.2849 1.6463 10.50 5.1e-08 *** 152s corpProf -0.0770 0.1683 -0.46 0.65 152s corpProfLag 0.2327 0.1276 1.82 0.09 . 152s wages 0.8259 0.0472 17.49 6.6e-11 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.261 on 14 degrees of freedom 152s Number of observations: 18 Degrees of Freedom: 14 152s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 152s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 152s 152s 152s 2SLS estimates for 'Investment' (equation 2) 152s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 18.2571 7.3132 2.50 0.02564 * 152s corpProf 0.1564 0.1942 0.81 0.43408 152s corpProfLag 0.5714 0.1672 3.42 0.00417 ** 152s capitalLag -0.1446 0.0346 -4.18 0.00093 *** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 1.359 on 14 degrees of freedom 152s Number of observations: 18 Degrees of Freedom: 14 152s SSR: 25.852 MSE: 1.847 Root MSE: 1.359 152s Multiple R-Squared: 0.847 Adjusted R-Squared: 0.815 152s 152s 152s 2SLS estimates for 'PrivateWages' (equation 3) 152s Model Formula: privWage ~ gnp + gnpLag + trend 152s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 152s gnpLag 152s 152s Estimate Std. Error t value Pr(>|t|) 152s (Intercept) 1.3431 1.1879 1.13 0.275 152s gnp 0.4438 0.0361 12.28 1.5e-09 *** 152s gnpLag 0.1447 0.0392 3.69 0.002 ** 152s trend 0.1238 0.0308 4.01 0.001 ** 152s --- 152s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 152s 152s Residual standard error: 0.78 on 16 degrees of freedom 152s Number of observations: 20 Degrees of Freedom: 16 152s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 152s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 152s 152s > residuals 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 -0.6754 -1.214 -1.3401 152s 3 -0.4627 0.325 0.2378 152s 4 -1.1585 1.094 1.1117 152s 5 -0.0305 -1.368 -0.1954 152s 6 0.4693 0.486 -0.5355 152s 7 NA NA NA 152s 8 1.6045 1.066 -0.7908 152s 9 1.6018 0.156 0.2831 152s 10 NA 1.853 1.1353 152s 11 -0.9031 -0.898 -0.1765 152s 12 -1.5948 -1.012 0.6007 152s 13 NA NA 0.1443 152s 14 0.2854 0.845 0.4826 152s 15 -0.4718 -0.365 0.3016 152s 16 -0.2268 NA 0.0261 152s 17 2.0079 1.685 -0.8614 152s 18 -0.7434 -0.121 0.9927 152s 19 -0.5410 -3.248 -0.4446 152s 20 1.4186 0.241 -0.3914 152s 21 1.1462 -0.013 -1.1115 152s 22 -1.7256 0.489 0.5312 152s > fitted 152s Consumption Investment PrivateWages 152s 1 NA NA NA 152s 2 42.6 1.014 26.8 152s 3 45.5 1.575 29.1 152s 4 50.4 4.106 33.0 152s 5 50.6 4.368 34.1 152s 6 52.1 4.614 35.9 152s 7 NA NA NA 152s 8 54.6 3.134 38.7 152s 9 55.7 2.844 38.9 152s 10 NA 3.247 40.2 152s 11 55.9 1.898 38.1 152s 12 52.5 -2.388 33.9 152s 13 NA NA 28.9 152s 14 46.2 -5.945 28.0 152s 15 49.2 -2.635 30.3 152s 16 51.5 NA 33.2 152s 17 55.7 0.415 37.7 152s 18 59.4 2.121 40.0 152s 19 58.0 1.348 38.6 152s 20 60.2 1.059 42.0 152s 21 63.9 3.313 46.1 152s 22 71.4 4.411 52.8 152s > predict 152s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 152s 1 NA NA NA NA 152s 2 42.6 0.586 41.3 43.8 152s 3 45.5 0.674 44.0 46.9 152s 4 50.4 0.443 49.4 51.3 152s 5 50.6 0.524 49.5 51.8 152s 6 52.1 0.535 51.0 53.3 152s 7 NA NA NA NA 152s 8 54.6 0.431 53.7 55.5 152s 9 55.7 0.510 54.6 56.8 152s 10 NA NA NA NA 152s 11 55.9 0.936 53.9 57.9 152s 12 52.5 0.893 50.6 54.4 152s 13 NA NA NA NA 152s 14 46.2 0.713 44.7 47.7 152s 15 49.2 0.501 48.1 50.2 152s 16 51.5 0.407 50.7 52.4 152s 17 55.7 0.457 54.7 56.7 152s 18 59.4 0.397 58.6 60.3 152s 19 58.0 0.564 56.8 59.2 152s 20 60.2 0.543 59.0 61.3 152s 21 63.9 0.529 62.7 65.0 152s 22 71.4 0.808 69.7 73.2 152s Investment.pred Investment.se.fit Investment.lwr Investment.upr 152s 1 NA NA NA NA 152s 2 1.014 0.919 -0.957 2.985 152s 3 1.575 0.602 0.284 2.867 152s 4 4.106 0.544 2.940 5.272 152s 5 4.368 0.450 3.402 5.333 152s 6 4.614 0.425 3.703 5.526 152s 7 NA NA NA NA 152s 8 3.134 0.352 2.380 3.889 152s 9 2.844 0.544 1.677 4.012 152s 10 3.247 0.592 1.976 4.518 152s 11 1.898 0.978 -0.200 3.996 152s 12 -2.388 0.886 -4.289 -0.488 152s 13 NA NA NA NA 152s 14 -5.945 0.916 -7.909 -3.980 152s 15 -2.635 0.518 -3.745 -1.525 152s 16 NA NA NA NA 152s 17 0.415 0.507 -0.671 1.501 152s 18 2.121 0.329 1.416 2.826 152s 19 1.348 0.551 0.166 2.529 152s 20 1.059 0.582 -0.189 2.306 152s 21 3.313 0.496 2.248 4.377 152s 22 4.411 0.728 2.850 5.971 152s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 152s 1 NA NA NA NA 152s 2 26.8 0.330 26.1 27.5 152s 3 29.1 0.344 28.3 29.8 152s 4 33.0 0.363 32.2 33.8 152s 5 34.1 0.260 33.5 34.6 152s 6 35.9 0.268 35.4 36.5 152s 7 NA NA NA NA 152s 8 38.7 0.265 38.1 39.3 152s 9 38.9 0.252 38.4 39.5 152s 10 40.2 0.242 39.7 40.7 152s 11 38.1 0.358 37.3 38.8 152s 12 33.9 0.385 33.1 34.7 152s 13 28.9 0.460 27.9 29.8 152s 14 28.0 0.351 27.3 28.8 152s 15 30.3 0.343 29.6 31.0 152s 16 33.2 0.287 32.6 33.8 152s 17 37.7 0.296 37.0 38.3 152s 18 40.0 0.220 39.5 40.5 152s 19 38.6 0.361 37.9 39.4 152s 20 42.0 0.309 41.3 42.6 152s 21 46.1 0.312 45.4 46.8 152s 22 52.8 0.501 51.7 53.8 152s > model.frame 152s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 152s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 152s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 152s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 152s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 152s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 152s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 152s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 152s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 152s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 152s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 152s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 152s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 152s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 152s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 152s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 152s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 152s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 152s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 152s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 152s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 152s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 152s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 152s trend 152s 1 -11 152s 2 -10 152s 3 -9 152s 4 -8 152s 5 -7 152s 6 -6 152s 7 -5 152s 8 -4 152s 9 -3 152s 10 -2 152s 11 -1 152s 12 0 152s 13 1 152s 14 2 152s 15 3 152s 16 4 152s 17 5 152s 18 6 152s 19 7 152s 20 8 152s 21 9 152s 22 10 152s > Frames of instrumental variables 152s govExp taxes govWage trend capitalLag corpProfLag gnpLag 152s 1 2.4 3.4 2.2 -11 180 NA NA 152s 2 3.9 7.7 2.7 -10 183 12.7 44.9 152s 3 3.2 3.9 2.9 -9 183 12.4 45.6 152s 4 2.8 4.7 2.9 -8 184 16.9 50.1 152s 5 3.5 3.8 3.1 -7 190 18.4 57.2 152s 6 3.3 5.5 3.2 -6 193 19.4 57.1 152s 7 3.3 7.0 3.3 -5 198 20.1 NA 152s 8 4.0 6.7 3.6 -4 203 19.6 64.0 152s 9 4.2 4.2 3.7 -3 208 19.8 64.4 152s 10 4.1 4.0 4.0 -2 211 21.1 64.5 152s 11 5.2 7.7 4.2 -1 216 21.7 67.0 152s 12 5.9 7.5 4.8 0 217 15.6 61.2 152s 13 4.9 8.3 5.3 1 213 11.4 53.4 152s 14 3.7 5.4 5.6 2 207 7.0 44.3 152s 15 4.0 6.8 6.0 3 202 11.2 45.1 152s 16 4.4 7.2 6.1 4 199 12.3 49.7 152s 17 2.9 8.3 7.4 5 198 14.0 54.4 152s 18 4.3 6.7 6.7 6 200 17.6 62.7 152s 19 5.3 7.4 7.7 7 202 17.3 65.0 152s 20 6.6 8.9 7.8 8 200 15.3 60.9 152s 21 7.4 9.6 8.0 9 201 19.0 69.5 152s 22 13.8 11.6 8.5 10 204 21.1 75.7 152s govExp taxes govWage trend capitalLag corpProfLag gnpLag 152s 1 2.4 3.4 2.2 -11 180 NA NA 152s 2 3.9 7.7 2.7 -10 183 12.7 44.9 152s 3 3.2 3.9 2.9 -9 183 12.4 45.6 152s 4 2.8 4.7 2.9 -8 184 16.9 50.1 152s 5 3.5 3.8 3.1 -7 190 18.4 57.2 152s 6 3.3 5.5 3.2 -6 193 19.4 57.1 152s 7 3.3 7.0 3.3 -5 198 20.1 NA 152s 8 4.0 6.7 3.6 -4 203 19.6 64.0 152s 9 4.2 4.2 3.7 -3 208 19.8 64.4 152s 10 4.1 4.0 4.0 -2 211 21.1 64.5 152s 11 5.2 7.7 4.2 -1 216 21.7 67.0 152s 12 5.9 7.5 4.8 0 217 15.6 61.2 152s 13 4.9 8.3 5.3 1 213 11.4 53.4 152s 14 3.7 5.4 5.6 2 207 7.0 44.3 152s 15 4.0 6.8 6.0 3 202 11.2 45.1 152s 16 4.4 7.2 6.1 4 199 12.3 49.7 152s 17 2.9 8.3 7.4 5 198 14.0 54.4 152s 18 4.3 6.7 6.7 6 200 17.6 62.7 152s 19 5.3 7.4 7.7 7 202 17.3 65.0 152s 20 6.6 8.9 7.8 8 200 15.3 60.9 152s 21 7.4 9.6 8.0 9 201 19.0 69.5 152s 22 13.8 11.6 8.5 10 204 21.1 75.7 152s govExp taxes govWage trend capitalLag corpProfLag gnpLag 152s 1 2.4 3.4 2.2 -11 180 NA NA 152s 2 3.9 7.7 2.7 -10 183 12.7 44.9 152s 3 3.2 3.9 2.9 -9 183 12.4 45.6 152s 4 2.8 4.7 2.9 -8 184 16.9 50.1 152s 5 3.5 3.8 3.1 -7 190 18.4 57.2 152s 6 3.3 5.5 3.2 -6 193 19.4 57.1 152s 7 3.3 7.0 3.3 -5 198 20.1 NA 152s 8 4.0 6.7 3.6 -4 203 19.6 64.0 152s 9 4.2 4.2 3.7 -3 208 19.8 64.4 152s 10 4.1 4.0 4.0 -2 211 21.1 64.5 152s 11 5.2 7.7 4.2 -1 216 21.7 67.0 152s 12 5.9 7.5 4.8 0 217 15.6 61.2 152s 13 4.9 8.3 5.3 1 213 11.4 53.4 152s 14 3.7 5.4 5.6 2 207 7.0 44.3 152s 15 4.0 6.8 6.0 3 202 11.2 45.1 152s 16 4.4 7.2 6.1 4 199 12.3 49.7 152s 17 2.9 8.3 7.4 5 198 14.0 54.4 152s 18 4.3 6.7 6.7 6 200 17.6 62.7 152s 19 5.3 7.4 7.7 7 202 17.3 65.0 152s 20 6.6 8.9 7.8 8 200 15.3 60.9 152s 21 7.4 9.6 8.0 9 201 19.0 69.5 152s 22 13.8 11.6 8.5 10 204 21.1 75.7 152s > model.matrix 152s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 152s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 152s [3] "Numeric: lengths (696, 672) differ" 152s > matrix of instrumental variables 152s Consumption_(Intercept) Consumption_govExp Consumption_taxes 152s Consumption_2 1 3.9 7.7 152s Consumption_3 1 3.2 3.9 152s Consumption_4 1 2.8 4.7 152s Consumption_5 1 3.5 3.8 152s Consumption_6 1 3.3 5.5 152s Consumption_8 1 4.0 6.7 152s Consumption_9 1 4.2 4.2 152s Consumption_11 1 5.2 7.7 152s Consumption_12 1 5.9 7.5 152s Consumption_14 1 3.7 5.4 152s Consumption_15 1 4.0 6.8 152s Consumption_16 1 4.4 7.2 152s Consumption_17 1 2.9 8.3 152s Consumption_18 1 4.3 6.7 152s Consumption_19 1 5.3 7.4 152s Consumption_20 1 6.6 8.9 152s Consumption_21 1 7.4 9.6 152s Consumption_22 1 13.8 11.6 152s Investment_2 0 0.0 0.0 152s Investment_3 0 0.0 0.0 152s Investment_4 0 0.0 0.0 152s Investment_5 0 0.0 0.0 152s Investment_6 0 0.0 0.0 152s Investment_8 0 0.0 0.0 152s Investment_9 0 0.0 0.0 152s Investment_10 0 0.0 0.0 152s Investment_11 0 0.0 0.0 152s Investment_12 0 0.0 0.0 152s Investment_14 0 0.0 0.0 152s Investment_15 0 0.0 0.0 152s Investment_17 0 0.0 0.0 152s Investment_18 0 0.0 0.0 152s Investment_19 0 0.0 0.0 152s Investment_20 0 0.0 0.0 152s Investment_21 0 0.0 0.0 152s Investment_22 0 0.0 0.0 152s PrivateWages_2 0 0.0 0.0 152s PrivateWages_3 0 0.0 0.0 152s PrivateWages_4 0 0.0 0.0 152s PrivateWages_5 0 0.0 0.0 152s PrivateWages_6 0 0.0 0.0 152s PrivateWages_8 0 0.0 0.0 152s PrivateWages_9 0 0.0 0.0 152s PrivateWages_10 0 0.0 0.0 152s PrivateWages_11 0 0.0 0.0 152s PrivateWages_12 0 0.0 0.0 152s PrivateWages_13 0 0.0 0.0 152s PrivateWages_14 0 0.0 0.0 152s PrivateWages_15 0 0.0 0.0 152s PrivateWages_16 0 0.0 0.0 152s PrivateWages_17 0 0.0 0.0 152s PrivateWages_18 0 0.0 0.0 152s PrivateWages_19 0 0.0 0.0 152s PrivateWages_20 0 0.0 0.0 152s PrivateWages_21 0 0.0 0.0 152s PrivateWages_22 0 0.0 0.0 152s Consumption_govWage Consumption_trend Consumption_capitalLag 152s Consumption_2 2.7 -10 183 152s Consumption_3 2.9 -9 183 152s Consumption_4 2.9 -8 184 152s Consumption_5 3.1 -7 190 152s Consumption_6 3.2 -6 193 152s Consumption_8 3.6 -4 203 152s Consumption_9 3.7 -3 208 152s Consumption_11 4.2 -1 216 152s Consumption_12 4.8 0 217 152s Consumption_14 5.6 2 207 152s Consumption_15 6.0 3 202 152s Consumption_16 6.1 4 199 152s Consumption_17 7.4 5 198 152s Consumption_18 6.7 6 200 152s Consumption_19 7.7 7 202 152s Consumption_20 7.8 8 200 152s Consumption_21 8.0 9 201 152s Consumption_22 8.5 10 204 152s Investment_2 0.0 0 0 152s Investment_3 0.0 0 0 152s Investment_4 0.0 0 0 152s Investment_5 0.0 0 0 152s Investment_6 0.0 0 0 152s Investment_8 0.0 0 0 152s Investment_9 0.0 0 0 152s Investment_10 0.0 0 0 152s Investment_11 0.0 0 0 152s Investment_12 0.0 0 0 152s Investment_14 0.0 0 0 152s Investment_15 0.0 0 0 152s Investment_17 0.0 0 0 152s Investment_18 0.0 0 0 152s Investment_19 0.0 0 0 152s Investment_20 0.0 0 0 152s Investment_21 0.0 0 0 152s Investment_22 0.0 0 0 152s PrivateWages_2 0.0 0 0 152s PrivateWages_3 0.0 0 0 152s PrivateWages_4 0.0 0 0 152s PrivateWages_5 0.0 0 0 152s PrivateWages_6 0.0 0 0 152s PrivateWages_8 0.0 0 0 152s PrivateWages_9 0.0 0 0 152s PrivateWages_10 0.0 0 0 152s PrivateWages_11 0.0 0 0 152s PrivateWages_12 0.0 0 0 152s PrivateWages_13 0.0 0 0 152s PrivateWages_14 0.0 0 0 152s PrivateWages_15 0.0 0 0 152s PrivateWages_16 0.0 0 0 152s PrivateWages_17 0.0 0 0 152s PrivateWages_18 0.0 0 0 152s PrivateWages_19 0.0 0 0 152s PrivateWages_20 0.0 0 0 152s PrivateWages_21 0.0 0 0 152s PrivateWages_22 0.0 0 0 152s Consumption_corpProfLag Consumption_gnpLag 152s Consumption_2 12.7 44.9 152s Consumption_3 12.4 45.6 152s Consumption_4 16.9 50.1 152s Consumption_5 18.4 57.2 152s Consumption_6 19.4 57.1 152s Consumption_8 19.6 64.0 152s Consumption_9 19.8 64.4 152s Consumption_11 21.7 67.0 152s Consumption_12 15.6 61.2 152s Consumption_14 7.0 44.3 152s Consumption_15 11.2 45.1 152s Consumption_16 12.3 49.7 152s Consumption_17 14.0 54.4 152s Consumption_18 17.6 62.7 152s Consumption_19 17.3 65.0 152s Consumption_20 15.3 60.9 152s Consumption_21 19.0 69.5 152s Consumption_22 21.1 75.7 152s Investment_2 0.0 0.0 152s Investment_3 0.0 0.0 152s Investment_4 0.0 0.0 152s Investment_5 0.0 0.0 152s Investment_6 0.0 0.0 152s Investment_8 0.0 0.0 152s Investment_9 0.0 0.0 152s Investment_10 0.0 0.0 152s Investment_11 0.0 0.0 152s Investment_12 0.0 0.0 152s Investment_14 0.0 0.0 152s Investment_15 0.0 0.0 152s Investment_17 0.0 0.0 152s Investment_18 0.0 0.0 152s Investment_19 0.0 0.0 152s Investment_20 0.0 0.0 152s Investment_21 0.0 0.0 152s Investment_22 0.0 0.0 152s PrivateWages_2 0.0 0.0 152s PrivateWages_3 0.0 0.0 152s PrivateWages_4 0.0 0.0 152s PrivateWages_5 0.0 0.0 152s PrivateWages_6 0.0 0.0 152s PrivateWages_8 0.0 0.0 152s PrivateWages_9 0.0 0.0 152s PrivateWages_10 0.0 0.0 152s PrivateWages_11 0.0 0.0 152s PrivateWages_12 0.0 0.0 152s PrivateWages_13 0.0 0.0 152s PrivateWages_14 0.0 0.0 152s PrivateWages_15 0.0 0.0 152s PrivateWages_16 0.0 0.0 152s PrivateWages_17 0.0 0.0 152s PrivateWages_18 0.0 0.0 152s PrivateWages_19 0.0 0.0 152s PrivateWages_20 0.0 0.0 152s PrivateWages_21 0.0 0.0 152s PrivateWages_22 0.0 0.0 152s Investment_(Intercept) Investment_govExp Investment_taxes 152s Consumption_2 0 0.0 0.0 152s Consumption_3 0 0.0 0.0 152s Consumption_4 0 0.0 0.0 152s Consumption_5 0 0.0 0.0 152s Consumption_6 0 0.0 0.0 152s Consumption_8 0 0.0 0.0 152s Consumption_9 0 0.0 0.0 152s Consumption_11 0 0.0 0.0 152s Consumption_12 0 0.0 0.0 152s Consumption_14 0 0.0 0.0 152s Consumption_15 0 0.0 0.0 152s Consumption_16 0 0.0 0.0 152s Consumption_17 0 0.0 0.0 152s Consumption_18 0 0.0 0.0 152s Consumption_19 0 0.0 0.0 152s Consumption_20 0 0.0 0.0 152s Consumption_21 0 0.0 0.0 152s Consumption_22 0 0.0 0.0 152s Investment_2 1 3.9 7.7 152s Investment_3 1 3.2 3.9 152s Investment_4 1 2.8 4.7 152s Investment_5 1 3.5 3.8 152s Investment_6 1 3.3 5.5 152s Investment_8 1 4.0 6.7 152s Investment_9 1 4.2 4.2 152s Investment_10 1 4.1 4.0 152s Investment_11 1 5.2 7.7 152s Investment_12 1 5.9 7.5 152s Investment_14 1 3.7 5.4 152s Investment_15 1 4.0 6.8 152s Investment_17 1 2.9 8.3 152s Investment_18 1 4.3 6.7 152s Investment_19 1 5.3 7.4 152s Investment_20 1 6.6 8.9 152s Investment_21 1 7.4 9.6 152s Investment_22 1 13.8 11.6 152s PrivateWages_2 0 0.0 0.0 152s PrivateWages_3 0 0.0 0.0 152s PrivateWages_4 0 0.0 0.0 152s PrivateWages_5 0 0.0 0.0 152s PrivateWages_6 0 0.0 0.0 152s PrivateWages_8 0 0.0 0.0 152s PrivateWages_9 0 0.0 0.0 152s PrivateWages_10 0 0.0 0.0 152s PrivateWages_11 0 0.0 0.0 152s PrivateWages_12 0 0.0 0.0 152s PrivateWages_13 0 0.0 0.0 152s PrivateWages_14 0 0.0 0.0 152s PrivateWages_15 0 0.0 0.0 152s PrivateWages_16 0 0.0 0.0 152s PrivateWages_17 0 0.0 0.0 152s PrivateWages_18 0 0.0 0.0 152s PrivateWages_19 0 0.0 0.0 152s PrivateWages_20 0 0.0 0.0 152s PrivateWages_21 0 0.0 0.0 152s PrivateWages_22 0 0.0 0.0 152s Investment_govWage Investment_trend Investment_capitalLag 152s Consumption_2 0.0 0 0 152s Consumption_3 0.0 0 0 152s Consumption_4 0.0 0 0 152s Consumption_5 0.0 0 0 152s Consumption_6 0.0 0 0 152s Consumption_8 0.0 0 0 152s Consumption_9 0.0 0 0 152s Consumption_11 0.0 0 0 152s Consumption_12 0.0 0 0 152s Consumption_14 0.0 0 0 152s Consumption_15 0.0 0 0 152s Consumption_16 0.0 0 0 152s Consumption_17 0.0 0 0 152s Consumption_18 0.0 0 0 152s Consumption_19 0.0 0 0 152s Consumption_20 0.0 0 0 152s Consumption_21 0.0 0 0 152s Consumption_22 0.0 0 0 152s Investment_2 2.7 -10 183 152s Investment_3 2.9 -9 183 152s Investment_4 2.9 -8 184 152s Investment_5 3.1 -7 190 152s Investment_6 3.2 -6 193 152s Investment_8 3.6 -4 203 152s Investment_9 3.7 -3 208 152s Investment_10 4.0 -2 211 152s Investment_11 4.2 -1 216 152s Investment_12 4.8 0 217 152s Investment_14 5.6 2 207 152s Investment_15 6.0 3 202 152s Investment_17 7.4 5 198 152s Investment_18 6.7 6 200 152s Investment_19 7.7 7 202 152s Investment_20 7.8 8 200 152s Investment_21 8.0 9 201 152s Investment_22 8.5 10 204 152s PrivateWages_2 0.0 0 0 152s PrivateWages_3 0.0 0 0 152s PrivateWages_4 0.0 0 0 152s PrivateWages_5 0.0 0 0 152s PrivateWages_6 0.0 0 0 152s PrivateWages_8 0.0 0 0 152s PrivateWages_9 0.0 0 0 152s PrivateWages_10 0.0 0 0 152s PrivateWages_11 0.0 0 0 152s PrivateWages_12 0.0 0 0 152s PrivateWages_13 0.0 0 0 152s PrivateWages_14 0.0 0 0 152s PrivateWages_15 0.0 0 0 152s PrivateWages_16 0.0 0 0 152s PrivateWages_17 0.0 0 0 152s PrivateWages_18 0.0 0 0 152s PrivateWages_19 0.0 0 0 152s PrivateWages_20 0.0 0 0 152s PrivateWages_21 0.0 0 0 152s PrivateWages_22 0.0 0 0 152s Investment_corpProfLag Investment_gnpLag 152s Consumption_2 0.0 0.0 152s Consumption_3 0.0 0.0 152s Consumption_4 0.0 0.0 152s Consumption_5 0.0 0.0 152s Consumption_6 0.0 0.0 152s Consumption_8 0.0 0.0 152s Consumption_9 0.0 0.0 152s Consumption_11 0.0 0.0 152s Consumption_12 0.0 0.0 152s Consumption_14 0.0 0.0 152s Consumption_15 0.0 0.0 152s Consumption_16 0.0 0.0 152s Consumption_17 0.0 0.0 152s Consumption_18 0.0 0.0 152s Consumption_19 0.0 0.0 152s Consumption_20 0.0 0.0 152s Consumption_21 0.0 0.0 152s Consumption_22 0.0 0.0 152s Investment_2 12.7 44.9 152s Investment_3 12.4 45.6 152s Investment_4 16.9 50.1 152s Investment_5 18.4 57.2 152s Investment_6 19.4 57.1 152s Investment_8 19.6 64.0 152s Investment_9 19.8 64.4 152s Investment_10 21.1 64.5 152s Investment_11 21.7 67.0 152s Investment_12 15.6 61.2 152s Investment_14 7.0 44.3 152s Investment_15 11.2 45.1 152s Investment_17 14.0 54.4 152s Investment_18 17.6 62.7 152s Investment_19 17.3 65.0 152s Investment_20 15.3 60.9 152s Investment_21 19.0 69.5 152s Investment_22 21.1 75.7 152s PrivateWages_2 0.0 0.0 152s PrivateWages_3 0.0 0.0 152s PrivateWages_4 0.0 0.0 152s PrivateWages_5 0.0 0.0 152s PrivateWages_6 0.0 0.0 152s PrivateWages_8 0.0 0.0 152s PrivateWages_9 0.0 0.0 152s PrivateWages_10 0.0 0.0 152s PrivateWages_11 0.0 0.0 152s PrivateWages_12 0.0 0.0 152s PrivateWages_13 0.0 0.0 152s PrivateWages_14 0.0 0.0 152s PrivateWages_15 0.0 0.0 152s PrivateWages_16 0.0 0.0 152s PrivateWages_17 0.0 0.0 152s PrivateWages_18 0.0 0.0 152s PrivateWages_19 0.0 0.0 152s PrivateWages_20 0.0 0.0 152s PrivateWages_21 0.0 0.0 152s PrivateWages_22 0.0 0.0 152s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 152s Consumption_2 0 0.0 0.0 152s Consumption_3 0 0.0 0.0 152s Consumption_4 0 0.0 0.0 152s Consumption_5 0 0.0 0.0 152s Consumption_6 0 0.0 0.0 152s Consumption_8 0 0.0 0.0 152s Consumption_9 0 0.0 0.0 152s Consumption_11 0 0.0 0.0 152s Consumption_12 0 0.0 0.0 152s Consumption_14 0 0.0 0.0 152s Consumption_15 0 0.0 0.0 152s Consumption_16 0 0.0 0.0 152s Consumption_17 0 0.0 0.0 152s Consumption_18 0 0.0 0.0 152s Consumption_19 0 0.0 0.0 152s Consumption_20 0 0.0 0.0 152s Consumption_21 0 0.0 0.0 152s Consumption_22 0 0.0 0.0 152s Investment_2 0 0.0 0.0 152s Investment_3 0 0.0 0.0 152s Investment_4 0 0.0 0.0 152s Investment_5 0 0.0 0.0 152s Investment_6 0 0.0 0.0 152s Investment_8 0 0.0 0.0 152s Investment_9 0 0.0 0.0 152s Investment_10 0 0.0 0.0 152s Investment_11 0 0.0 0.0 152s Investment_12 0 0.0 0.0 152s Investment_14 0 0.0 0.0 152s Investment_15 0 0.0 0.0 152s Investment_17 0 0.0 0.0 152s Investment_18 0 0.0 0.0 152s Investment_19 0 0.0 0.0 152s Investment_20 0 0.0 0.0 152s Investment_21 0 0.0 0.0 152s Investment_22 0 0.0 0.0 152s PrivateWages_2 1 3.9 7.7 152s PrivateWages_3 1 3.2 3.9 152s PrivateWages_4 1 2.8 4.7 152s PrivateWages_5 1 3.5 3.8 152s PrivateWages_6 1 3.3 5.5 152s PrivateWages_8 1 4.0 6.7 152s PrivateWages_9 1 4.2 4.2 152s PrivateWages_10 1 4.1 4.0 152s PrivateWages_11 1 5.2 7.7 152s PrivateWages_12 1 5.9 7.5 152s PrivateWages_13 1 4.9 8.3 152s PrivateWages_14 1 3.7 5.4 152s PrivateWages_15 1 4.0 6.8 152s PrivateWages_16 1 4.4 7.2 152s PrivateWages_17 1 2.9 8.3 152s PrivateWages_18 1 4.3 6.7 152s PrivateWages_19 1 5.3 7.4 152s PrivateWages_20 1 6.6 8.9 152s PrivateWages_21 1 7.4 9.6 152s PrivateWages_22 1 13.8 11.6 152s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 152s Consumption_2 0.0 0 0 152s Consumption_3 0.0 0 0 152s Consumption_4 0.0 0 0 152s Consumption_5 0.0 0 0 152s Consumption_6 0.0 0 0 152s Consumption_8 0.0 0 0 152s Consumption_9 0.0 0 0 152s Consumption_11 0.0 0 0 152s Consumption_12 0.0 0 0 152s Consumption_14 0.0 0 0 152s Consumption_15 0.0 0 0 152s Consumption_16 0.0 0 0 152s Consumption_17 0.0 0 0 152s Consumption_18 0.0 0 0 152s Consumption_19 0.0 0 0 152s Consumption_20 0.0 0 0 152s Consumption_21 0.0 0 0 152s Consumption_22 0.0 0 0 152s Investment_2 0.0 0 0 152s Investment_3 0.0 0 0 152s Investment_4 0.0 0 0 152s Investment_5 0.0 0 0 152s Investment_6 0.0 0 0 152s Investment_8 0.0 0 0 152s Investment_9 0.0 0 0 152s Investment_10 0.0 0 0 152s Investment_11 0.0 0 0 152s Investment_12 0.0 0 0 152s Investment_14 0.0 0 0 152s Investment_15 0.0 0 0 152s Investment_17 0.0 0 0 152s Investment_18 0.0 0 0 152s Investment_19 0.0 0 0 152s Investment_20 0.0 0 0 152s Investment_21 0.0 0 0 152s Investment_22 0.0 0 0 152s PrivateWages_2 2.7 -10 183 152s PrivateWages_3 2.9 -9 183 152s PrivateWages_4 2.9 -8 184 152s PrivateWages_5 3.1 -7 190 152s PrivateWages_6 3.2 -6 193 152s PrivateWages_8 3.6 -4 203 152s PrivateWages_9 3.7 -3 208 152s PrivateWages_10 4.0 -2 211 152s PrivateWages_11 4.2 -1 216 152s PrivateWages_12 4.8 0 217 152s PrivateWages_13 5.3 1 213 152s PrivateWages_14 5.6 2 207 152s PrivateWages_15 6.0 3 202 152s PrivateWages_16 6.1 4 199 152s PrivateWages_17 7.4 5 198 152s PrivateWages_18 6.7 6 200 152s PrivateWages_19 7.7 7 202 152s PrivateWages_20 7.8 8 200 152s PrivateWages_21 8.0 9 201 152s PrivateWages_22 8.5 10 204 152s PrivateWages_corpProfLag PrivateWages_gnpLag 152s Consumption_2 0.0 0.0 152s Consumption_3 0.0 0.0 152s Consumption_4 0.0 0.0 152s Consumption_5 0.0 0.0 152s Consumption_6 0.0 0.0 152s Consumption_8 0.0 0.0 152s Consumption_9 0.0 0.0 152s Consumption_11 0.0 0.0 152s Consumption_12 0.0 0.0 152s Consumption_14 0.0 0.0 152s Consumption_15 0.0 0.0 152s Consumption_16 0.0 0.0 152s Consumption_17 0.0 0.0 152s Consumption_18 0.0 0.0 152s Consumption_19 0.0 0.0 152s Consumption_20 0.0 0.0 152s Consumption_21 0.0 0.0 152s Consumption_22 0.0 0.0 152s Investment_2 0.0 0.0 152s Investment_3 0.0 0.0 152s Investment_4 0.0 0.0 152s Investment_5 0.0 0.0 152s Investment_6 0.0 0.0 152s Investment_8 0.0 0.0 152s Investment_9 0.0 0.0 152s Investment_10 0.0 0.0 152s Investment_11 0.0 0.0 152s Investment_12 0.0 0.0 152s Investment_14 0.0 0.0 152s Investment_15 0.0 0.0 152s Investment_17 0.0 0.0 152s Investment_18 0.0 0.0 152s Investment_19 0.0 0.0 152s Investment_20 0.0 0.0 152s Investment_21 0.0 0.0 152s Investment_22 0.0 0.0 152s PrivateWages_2 12.7 44.9 152s PrivateWages_3 12.4 45.6 152s PrivateWages_4 16.9 50.1 152s PrivateWages_5 18.4 57.2 152s PrivateWages_6 19.4 57.1 152s PrivateWages_8 19.6 64.0 152s PrivateWages_9 19.8 64.4 152s PrivateWages_10 21.1 64.5 152s PrivateWages_11 21.7 67.0 152s PrivateWages_12 15.6 61.2 152s PrivateWages_13 11.4 53.4 152s PrivateWages_14 7.0 44.3 152s PrivateWages_15 11.2 45.1 152s PrivateWages_16 12.3 49.7 152s PrivateWages_17 14.0 54.4 152s PrivateWages_18 17.6 62.7 152s PrivateWages_19 17.3 65.0 152s PrivateWages_20 15.3 60.9 152s PrivateWages_21 19.0 69.5 152s PrivateWages_22 21.1 75.7 152s > matrix of fitted regressors 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 1 14.0 152s Consumption_3 1 16.7 152s Consumption_4 1 18.5 152s Consumption_5 1 20.3 152s Consumption_6 1 19.0 152s Consumption_8 1 17.6 152s Consumption_9 1 18.9 152s Consumption_11 1 16.7 152s Consumption_12 1 13.4 152s Consumption_14 1 10.0 152s Consumption_15 1 12.5 152s Consumption_16 1 14.5 152s Consumption_17 1 14.9 152s Consumption_18 1 19.4 152s Consumption_19 1 19.1 152s Consumption_20 1 17.7 152s Consumption_21 1 20.4 152s Consumption_22 1 22.7 152s Investment_2 0 0.0 152s Investment_3 0 0.0 152s Investment_4 0 0.0 152s Investment_5 0 0.0 152s Investment_6 0 0.0 152s Investment_8 0 0.0 152s Investment_9 0 0.0 152s Investment_10 0 0.0 152s Investment_11 0 0.0 152s Investment_12 0 0.0 152s Investment_14 0 0.0 152s Investment_15 0 0.0 152s Investment_17 0 0.0 152s Investment_18 0 0.0 152s Investment_19 0 0.0 152s Investment_20 0 0.0 152s Investment_21 0 0.0 152s Investment_22 0 0.0 152s PrivateWages_2 0 0.0 152s PrivateWages_3 0 0.0 152s PrivateWages_4 0 0.0 152s PrivateWages_5 0 0.0 152s PrivateWages_6 0 0.0 152s PrivateWages_8 0 0.0 152s PrivateWages_9 0 0.0 152s PrivateWages_10 0 0.0 152s PrivateWages_11 0 0.0 152s PrivateWages_12 0 0.0 152s PrivateWages_13 0 0.0 152s PrivateWages_14 0 0.0 152s PrivateWages_15 0 0.0 152s PrivateWages_16 0 0.0 152s PrivateWages_17 0 0.0 152s PrivateWages_18 0 0.0 152s PrivateWages_19 0 0.0 152s PrivateWages_20 0 0.0 152s PrivateWages_21 0 0.0 152s PrivateWages_22 0 0.0 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 12.7 29.8 152s Consumption_3 12.4 31.8 152s Consumption_4 16.9 35.3 152s Consumption_5 18.4 38.6 152s Consumption_6 19.4 38.5 152s Consumption_8 19.6 40.0 152s Consumption_9 19.8 41.8 152s Consumption_11 21.7 43.1 152s Consumption_12 15.6 39.7 152s Consumption_14 7.0 33.3 152s Consumption_15 11.2 37.3 152s Consumption_16 12.3 40.1 152s Consumption_17 14.0 41.8 152s Consumption_18 17.6 47.6 152s Consumption_19 17.3 49.2 152s Consumption_20 15.3 48.6 152s Consumption_21 19.0 53.4 152s Consumption_22 21.1 60.8 152s Investment_2 0.0 0.0 152s Investment_3 0.0 0.0 152s Investment_4 0.0 0.0 152s Investment_5 0.0 0.0 152s Investment_6 0.0 0.0 152s Investment_8 0.0 0.0 152s Investment_9 0.0 0.0 152s Investment_10 0.0 0.0 152s Investment_11 0.0 0.0 152s Investment_12 0.0 0.0 152s Investment_14 0.0 0.0 152s Investment_15 0.0 0.0 152s Investment_17 0.0 0.0 152s Investment_18 0.0 0.0 152s Investment_19 0.0 0.0 152s Investment_20 0.0 0.0 152s Investment_21 0.0 0.0 152s Investment_22 0.0 0.0 152s PrivateWages_2 0.0 0.0 152s PrivateWages_3 0.0 0.0 152s PrivateWages_4 0.0 0.0 152s PrivateWages_5 0.0 0.0 152s PrivateWages_6 0.0 0.0 152s PrivateWages_8 0.0 0.0 152s PrivateWages_9 0.0 0.0 152s PrivateWages_10 0.0 0.0 152s PrivateWages_11 0.0 0.0 152s PrivateWages_12 0.0 0.0 152s PrivateWages_13 0.0 0.0 152s PrivateWages_14 0.0 0.0 152s PrivateWages_15 0.0 0.0 152s PrivateWages_16 0.0 0.0 152s PrivateWages_17 0.0 0.0 152s PrivateWages_18 0.0 0.0 152s PrivateWages_19 0.0 0.0 152s PrivateWages_20 0.0 0.0 152s PrivateWages_21 0.0 0.0 152s PrivateWages_22 0.0 0.0 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 0 0.0 152s Consumption_3 0 0.0 152s Consumption_4 0 0.0 152s Consumption_5 0 0.0 152s Consumption_6 0 0.0 152s Consumption_8 0 0.0 152s Consumption_9 0 0.0 152s Consumption_11 0 0.0 152s Consumption_12 0 0.0 152s Consumption_14 0 0.0 152s Consumption_15 0 0.0 152s Consumption_16 0 0.0 152s Consumption_17 0 0.0 152s Consumption_18 0 0.0 152s Consumption_19 0 0.0 152s Consumption_20 0 0.0 152s Consumption_21 0 0.0 152s Consumption_22 0 0.0 152s Investment_2 1 13.4 152s Investment_3 1 16.7 152s Investment_4 1 18.8 152s Investment_5 1 20.6 152s Investment_6 1 19.3 152s Investment_8 1 17.5 152s Investment_9 1 19.5 152s Investment_10 1 20.2 152s Investment_11 1 17.2 152s Investment_12 1 13.5 152s Investment_14 1 10.1 152s Investment_15 1 13.0 152s Investment_17 1 14.9 152s Investment_18 1 19.5 152s Investment_19 1 19.3 152s Investment_20 1 17.5 152s Investment_21 1 20.2 152s Investment_22 1 22.8 152s PrivateWages_2 0 0.0 152s PrivateWages_3 0 0.0 152s PrivateWages_4 0 0.0 152s PrivateWages_5 0 0.0 152s PrivateWages_6 0 0.0 152s PrivateWages_8 0 0.0 152s PrivateWages_9 0 0.0 152s PrivateWages_10 0 0.0 152s PrivateWages_11 0 0.0 152s PrivateWages_12 0 0.0 152s PrivateWages_13 0 0.0 152s PrivateWages_14 0 0.0 152s PrivateWages_15 0 0.0 152s PrivateWages_16 0 0.0 152s PrivateWages_17 0 0.0 152s PrivateWages_18 0 0.0 152s PrivateWages_19 0 0.0 152s PrivateWages_20 0 0.0 152s PrivateWages_21 0 0.0 152s PrivateWages_22 0 0.0 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 0.0 0 152s Consumption_3 0.0 0 152s Consumption_4 0.0 0 152s Consumption_5 0.0 0 152s Consumption_6 0.0 0 152s Consumption_8 0.0 0 152s Consumption_9 0.0 0 152s Consumption_11 0.0 0 152s Consumption_12 0.0 0 152s Consumption_14 0.0 0 152s Consumption_15 0.0 0 152s Consumption_16 0.0 0 152s Consumption_17 0.0 0 152s Consumption_18 0.0 0 152s Consumption_19 0.0 0 152s Consumption_20 0.0 0 152s Consumption_21 0.0 0 152s Consumption_22 0.0 0 152s Investment_2 12.7 183 152s Investment_3 12.4 183 152s Investment_4 16.9 184 152s Investment_5 18.4 190 152s Investment_6 19.4 193 152s Investment_8 19.6 203 152s Investment_9 19.8 208 152s Investment_10 21.1 211 152s Investment_11 21.7 216 152s Investment_12 15.6 217 152s Investment_14 7.0 207 152s Investment_15 11.2 202 152s Investment_17 14.0 198 152s Investment_18 17.6 200 152s Investment_19 17.3 202 152s Investment_20 15.3 200 152s Investment_21 19.0 201 152s Investment_22 21.1 204 152s PrivateWages_2 0.0 0 152s PrivateWages_3 0.0 0 152s PrivateWages_4 0.0 0 152s PrivateWages_5 0.0 0 152s PrivateWages_6 0.0 0 152s PrivateWages_8 0.0 0 152s PrivateWages_9 0.0 0 152s PrivateWages_10 0.0 0 152s PrivateWages_11 0.0 0 152s PrivateWages_12 0.0 0 152s PrivateWages_13 0.0 0 152s PrivateWages_14 0.0 0 152s PrivateWages_15 0.0 0 152s PrivateWages_16 0.0 0 152s PrivateWages_17 0.0 0 152s PrivateWages_18 0.0 0 152s PrivateWages_19 0.0 0 152s PrivateWages_20 0.0 0 152s PrivateWages_21 0.0 0 152s PrivateWages_22 0.0 0 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 0 0.0 0.0 152s Consumption_3 0 0.0 0.0 152s Consumption_4 0 0.0 0.0 152s Consumption_5 0 0.0 0.0 152s Consumption_6 0 0.0 0.0 152s Consumption_8 0 0.0 0.0 152s Consumption_9 0 0.0 0.0 152s Consumption_11 0 0.0 0.0 152s Consumption_12 0 0.0 0.0 152s Consumption_14 0 0.0 0.0 152s Consumption_15 0 0.0 0.0 152s Consumption_16 0 0.0 0.0 152s Consumption_17 0 0.0 0.0 152s Consumption_18 0 0.0 0.0 152s Consumption_19 0 0.0 0.0 152s Consumption_20 0 0.0 0.0 152s Consumption_21 0 0.0 0.0 152s Consumption_22 0 0.0 0.0 152s Investment_2 0 0.0 0.0 152s Investment_3 0 0.0 0.0 152s Investment_4 0 0.0 0.0 152s Investment_5 0 0.0 0.0 152s Investment_6 0 0.0 0.0 152s Investment_8 0 0.0 0.0 152s Investment_9 0 0.0 0.0 152s Investment_10 0 0.0 0.0 152s Investment_11 0 0.0 0.0 152s Investment_12 0 0.0 0.0 152s Investment_14 0 0.0 0.0 152s Investment_15 0 0.0 0.0 152s Investment_17 0 0.0 0.0 152s Investment_18 0 0.0 0.0 152s Investment_19 0 0.0 0.0 152s Investment_20 0 0.0 0.0 152s Investment_21 0 0.0 0.0 152s Investment_22 0 0.0 0.0 152s PrivateWages_2 1 47.1 44.9 152s PrivateWages_3 1 49.6 45.6 152s PrivateWages_4 1 56.5 50.1 152s PrivateWages_5 1 60.7 57.2 152s PrivateWages_6 1 60.6 57.1 152s PrivateWages_8 1 60.0 64.0 152s PrivateWages_9 1 62.3 64.4 152s PrivateWages_10 1 64.6 64.5 152s PrivateWages_11 1 63.7 67.0 152s PrivateWages_12 1 54.8 61.2 152s PrivateWages_13 1 47.0 53.4 152s PrivateWages_14 1 42.1 44.3 152s PrivateWages_15 1 51.2 45.1 152s PrivateWages_16 1 55.3 49.7 152s PrivateWages_17 1 57.4 54.4 152s PrivateWages_18 1 67.2 62.7 152s PrivateWages_19 1 68.5 65.0 152s PrivateWages_20 1 66.8 60.9 152s PrivateWages_21 1 74.9 69.5 152s PrivateWages_22 1 86.9 75.7 152s PrivateWages_trend 152s Consumption_2 0 152s Consumption_3 0 152s Consumption_4 0 152s Consumption_5 0 152s Consumption_6 0 152s Consumption_8 0 152s Consumption_9 0 152s Consumption_11 0 152s Consumption_12 0 152s Consumption_14 0 152s Consumption_15 0 152s Consumption_16 0 152s Consumption_17 0 152s Consumption_18 0 152s Consumption_19 0 152s Consumption_20 0 152s Consumption_21 0 152s Consumption_22 0 152s Investment_2 0 152s Investment_3 0 152s Investment_4 0 152s Investment_5 0 152s Investment_6 0 152s Investment_8 0 152s Investment_9 0 152s Investment_10 0 152s Investment_11 0 152s Investment_12 0 152s Investment_14 0 152s Investment_15 0 152s Investment_17 0 152s Investment_18 0 152s Investment_19 0 152s Investment_20 0 152s Investment_21 0 152s Investment_22 0 152s PrivateWages_2 -10 152s PrivateWages_3 -9 152s PrivateWages_4 -8 152s PrivateWages_5 -7 152s PrivateWages_6 -6 152s PrivateWages_8 -4 152s PrivateWages_9 -3 152s PrivateWages_10 -2 152s PrivateWages_11 -1 152s PrivateWages_12 0 152s PrivateWages_13 1 152s PrivateWages_14 2 152s PrivateWages_15 3 152s PrivateWages_16 4 152s PrivateWages_17 5 152s PrivateWages_18 6 152s PrivateWages_19 7 152s PrivateWages_20 8 152s PrivateWages_21 9 152s PrivateWages_22 10 152s > nobs 152s [1] 56 152s > linearHypothesis 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 45 152s 2 44 1 1.27 0.27 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 45 152s 2 44 1 1.66 0.2 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 45 152s 2 44 1 1.66 0.2 152s Linear hypothesis test (Theil's F test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 46 152s 2 44 2 0.64 0.53 152s Linear hypothesis test (F statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df F Pr(>F) 152s 1 46 152s 2 44 2 0.84 0.44 152s Linear hypothesis test (Chi^2 statistic of a Wald test) 152s 152s Hypothesis: 152s Consumption_corpProf + Investment_capitalLag = 0 152s Consumption_corpProfLag - PrivateWages_trend = 0 152s 152s Model 1: restricted model 152s Model 2: kleinModel 152s 152s Res.Df Df Chisq Pr(>Chisq) 152s 1 46 152s 2 44 2 1.68 0.43 152s > logLik 152s 'log Lik.' -69.5 (df=13) 152s 'log Lik.' -77.5 (df=13) 152s Estimating function 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_2 -1.891 -26.49 152s Consumption_3 -0.190 -3.16 152s Consumption_4 0.294 5.45 152s Consumption_5 -1.285 -26.05 152s Consumption_6 0.431 8.19 152s Consumption_8 2.670 47.11 152s Consumption_9 2.363 44.77 152s Consumption_11 -1.642 -27.49 152s Consumption_12 -1.735 -23.21 152s Consumption_14 0.834 8.35 152s Consumption_15 -1.061 -13.27 152s Consumption_16 -0.885 -12.82 152s Consumption_17 3.801 56.68 152s Consumption_18 -0.502 -9.76 152s Consumption_19 -3.000 -57.33 152s Consumption_20 2.012 35.52 152s Consumption_21 0.746 15.21 152s Consumption_22 -0.957 -21.70 152s Investment_2 0.000 0.00 152s Investment_3 0.000 0.00 152s Investment_4 0.000 0.00 152s Investment_5 0.000 0.00 152s Investment_6 0.000 0.00 152s Investment_8 0.000 0.00 152s Investment_9 0.000 0.00 152s Investment_10 0.000 0.00 152s Investment_11 0.000 0.00 152s Investment_12 0.000 0.00 152s Investment_14 0.000 0.00 152s Investment_15 0.000 0.00 152s Investment_17 0.000 0.00 152s Investment_18 0.000 0.00 152s Investment_19 0.000 0.00 152s Investment_20 0.000 0.00 152s Investment_21 0.000 0.00 152s Investment_22 0.000 0.00 152s PrivateWages_2 0.000 0.00 152s PrivateWages_3 0.000 0.00 152s PrivateWages_4 0.000 0.00 152s PrivateWages_5 0.000 0.00 152s PrivateWages_6 0.000 0.00 152s PrivateWages_8 0.000 0.00 152s PrivateWages_9 0.000 0.00 152s PrivateWages_10 0.000 0.00 152s PrivateWages_11 0.000 0.00 152s PrivateWages_12 0.000 0.00 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 0.000 0.00 152s PrivateWages_15 0.000 0.00 152s PrivateWages_16 0.000 0.00 152s PrivateWages_17 0.000 0.00 152s PrivateWages_18 0.000 0.00 152s PrivateWages_19 0.000 0.00 152s PrivateWages_20 0.000 0.00 152s PrivateWages_21 0.000 0.00 152s PrivateWages_22 0.000 0.00 152s Consumption_corpProfLag Consumption_wages 152s Consumption_2 -24.01 -56.38 152s Consumption_3 -2.35 -6.04 152s Consumption_4 4.96 10.35 152s Consumption_5 -23.65 -49.61 152s Consumption_6 8.35 16.60 152s Consumption_8 52.33 106.81 152s Consumption_9 46.80 98.74 152s Consumption_11 -35.64 -70.78 152s Consumption_12 -27.07 -68.81 152s Consumption_14 5.83 27.78 152s Consumption_15 -11.88 -39.61 152s Consumption_16 -10.89 -35.54 152s Consumption_17 53.21 158.79 152s Consumption_18 -8.84 -23.92 152s Consumption_19 -51.90 -147.70 152s Consumption_20 30.78 97.67 152s Consumption_21 14.17 39.83 152s Consumption_22 -20.20 -58.19 152s Investment_2 0.00 0.00 152s Investment_3 0.00 0.00 152s Investment_4 0.00 0.00 152s Investment_5 0.00 0.00 152s Investment_6 0.00 0.00 152s Investment_8 0.00 0.00 152s Investment_9 0.00 0.00 152s Investment_10 0.00 0.00 152s Investment_11 0.00 0.00 152s Investment_12 0.00 0.00 152s Investment_14 0.00 0.00 152s Investment_15 0.00 0.00 152s Investment_17 0.00 0.00 152s Investment_18 0.00 0.00 152s Investment_19 0.00 0.00 152s Investment_20 0.00 0.00 152s Investment_21 0.00 0.00 152s Investment_22 0.00 0.00 152s PrivateWages_2 0.00 0.00 152s PrivateWages_3 0.00 0.00 152s PrivateWages_4 0.00 0.00 152s PrivateWages_5 0.00 0.00 152s PrivateWages_6 0.00 0.00 152s PrivateWages_8 0.00 0.00 152s PrivateWages_9 0.00 0.00 152s PrivateWages_10 0.00 0.00 152s PrivateWages_11 0.00 0.00 152s PrivateWages_12 0.00 0.00 152s PrivateWages_13 0.00 0.00 152s PrivateWages_14 0.00 0.00 152s PrivateWages_15 0.00 0.00 152s PrivateWages_16 0.00 0.00 152s PrivateWages_17 0.00 0.00 152s PrivateWages_18 0.00 0.00 152s PrivateWages_19 0.00 0.00 152s PrivateWages_20 0.00 0.00 152s PrivateWages_21 0.00 0.00 152s PrivateWages_22 0.00 0.00 152s Investment_(Intercept) Investment_corpProf 152s Consumption_2 0.000 0.00 152s Consumption_3 0.000 0.00 152s Consumption_4 0.000 0.00 152s Consumption_5 0.000 0.00 152s Consumption_6 0.000 0.00 152s Consumption_8 0.000 0.00 152s Consumption_9 0.000 0.00 152s Consumption_11 0.000 0.00 152s Consumption_12 0.000 0.00 152s Consumption_14 0.000 0.00 152s Consumption_15 0.000 0.00 152s Consumption_16 0.000 0.00 152s Consumption_17 0.000 0.00 152s Consumption_18 0.000 0.00 152s Consumption_19 0.000 0.00 152s Consumption_20 0.000 0.00 152s Consumption_21 0.000 0.00 152s Consumption_22 0.000 0.00 152s Investment_2 -1.375 -18.47 152s Investment_3 0.361 6.02 152s Investment_4 1.027 19.33 152s Investment_5 -1.558 -32.12 152s Investment_6 0.610 11.77 152s Investment_8 1.420 24.90 152s Investment_9 0.404 7.88 152s Investment_10 2.082 42.13 152s Investment_11 -1.150 -19.79 152s Investment_12 -1.339 -18.06 152s Investment_14 1.019 10.28 152s Investment_15 -0.475 -6.17 152s Investment_17 2.105 31.39 152s Investment_18 -0.465 -9.06 152s Investment_19 -3.871 -74.65 152s Investment_20 0.469 8.23 152s Investment_21 0.132 2.65 152s Investment_22 0.603 13.74 152s PrivateWages_2 0.000 0.00 152s PrivateWages_3 0.000 0.00 152s PrivateWages_4 0.000 0.00 152s PrivateWages_5 0.000 0.00 152s PrivateWages_6 0.000 0.00 152s PrivateWages_8 0.000 0.00 152s PrivateWages_9 0.000 0.00 152s PrivateWages_10 0.000 0.00 152s PrivateWages_11 0.000 0.00 152s PrivateWages_12 0.000 0.00 152s PrivateWages_13 0.000 0.00 152s PrivateWages_14 0.000 0.00 152s PrivateWages_15 0.000 0.00 152s PrivateWages_16 0.000 0.00 152s PrivateWages_17 0.000 0.00 152s PrivateWages_18 0.000 0.00 152s PrivateWages_19 0.000 0.00 152s PrivateWages_20 0.000 0.00 152s PrivateWages_21 0.000 0.00 152s PrivateWages_22 0.000 0.00 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_2 0.00 0.0 152s Consumption_3 0.00 0.0 152s Consumption_4 0.00 0.0 152s Consumption_5 0.00 0.0 152s Consumption_6 0.00 0.0 152s Consumption_8 0.00 0.0 152s Consumption_9 0.00 0.0 152s Consumption_11 0.00 0.0 152s Consumption_12 0.00 0.0 152s Consumption_14 0.00 0.0 152s Consumption_15 0.00 0.0 152s Consumption_16 0.00 0.0 152s Consumption_17 0.00 0.0 152s Consumption_18 0.00 0.0 152s Consumption_19 0.00 0.0 152s Consumption_20 0.00 0.0 152s Consumption_21 0.00 0.0 152s Consumption_22 0.00 0.0 152s Investment_2 -17.46 -251.4 152s Investment_3 4.48 65.9 152s Investment_4 17.35 189.4 152s Investment_5 -28.67 -295.5 152s Investment_6 11.83 117.5 152s Investment_8 27.83 288.8 152s Investment_9 8.00 83.9 152s Investment_10 43.93 438.5 152s Investment_11 -24.96 -248.1 152s Investment_12 -20.88 -290.1 152s Investment_14 7.14 211.1 152s Investment_15 -5.32 -95.9 152s Investment_17 29.48 416.3 152s Investment_18 -8.18 -92.9 152s Investment_19 -66.97 -781.2 152s Investment_20 7.18 93.8 152s Investment_21 2.50 26.5 152s Investment_22 12.73 123.4 152s PrivateWages_2 0.00 0.0 152s PrivateWages_3 0.00 0.0 152s PrivateWages_4 0.00 0.0 152s PrivateWages_5 0.00 0.0 152s PrivateWages_6 0.00 0.0 152s PrivateWages_8 0.00 0.0 152s PrivateWages_9 0.00 0.0 152s PrivateWages_10 0.00 0.0 152s PrivateWages_11 0.00 0.0 152s PrivateWages_12 0.00 0.0 152s PrivateWages_13 0.00 0.0 152s PrivateWages_14 0.00 0.0 152s PrivateWages_15 0.00 0.0 152s PrivateWages_16 0.00 0.0 152s PrivateWages_17 0.00 0.0 152s PrivateWages_18 0.00 0.0 152s PrivateWages_19 0.00 0.0 152s PrivateWages_20 0.00 0.0 152s PrivateWages_21 0.00 0.0 152s PrivateWages_22 0.00 0.0 152s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 152s Consumption_2 0.0000 0.00 0.00 152s Consumption_3 0.0000 0.00 0.00 152s Consumption_4 0.0000 0.00 0.00 152s Consumption_5 0.0000 0.00 0.00 152s Consumption_6 0.0000 0.00 0.00 152s Consumption_8 0.0000 0.00 0.00 152s Consumption_9 0.0000 0.00 0.00 152s Consumption_11 0.0000 0.00 0.00 152s Consumption_12 0.0000 0.00 0.00 152s Consumption_14 0.0000 0.00 0.00 152s Consumption_15 0.0000 0.00 0.00 152s Consumption_16 0.0000 0.00 0.00 152s Consumption_17 0.0000 0.00 0.00 152s Consumption_18 0.0000 0.00 0.00 152s Consumption_19 0.0000 0.00 0.00 152s Consumption_20 0.0000 0.00 0.00 152s Consumption_21 0.0000 0.00 0.00 152s Consumption_22 0.0000 0.00 0.00 152s Investment_2 0.0000 0.00 0.00 152s Investment_3 0.0000 0.00 0.00 152s Investment_4 0.0000 0.00 0.00 152s Investment_5 0.0000 0.00 0.00 152s Investment_6 0.0000 0.00 0.00 152s Investment_8 0.0000 0.00 0.00 152s Investment_9 0.0000 0.00 0.00 152s Investment_10 0.0000 0.00 0.00 152s Investment_11 0.0000 0.00 0.00 152s Investment_12 0.0000 0.00 0.00 152s Investment_14 0.0000 0.00 0.00 152s Investment_15 0.0000 0.00 0.00 152s Investment_17 0.0000 0.00 0.00 152s Investment_18 0.0000 0.00 0.00 152s Investment_19 0.0000 0.00 0.00 152s Investment_20 0.0000 0.00 0.00 152s Investment_21 0.0000 0.00 0.00 152s Investment_22 0.0000 0.00 0.00 152s PrivateWages_2 -1.9924 -93.78 -89.46 152s PrivateWages_3 0.4683 23.22 21.35 152s PrivateWages_4 1.4034 79.35 70.31 152s PrivateWages_5 -1.7870 -108.45 -102.22 152s PrivateWages_6 -0.3627 -21.98 -20.71 152s PrivateWages_8 1.1629 69.77 74.43 152s PrivateWages_9 1.2735 79.30 82.01 152s PrivateWages_10 2.2141 142.96 142.81 152s PrivateWages_11 -1.2912 -82.26 -86.51 152s PrivateWages_12 -0.0350 -1.92 -2.14 152s PrivateWages_13 -1.0438 -49.04 -55.74 152s PrivateWages_14 1.8016 75.90 79.81 152s PrivateWages_15 -0.3714 -19.02 -16.75 152s PrivateWages_16 -0.3904 -21.61 -19.40 152s PrivateWages_17 1.4934 85.71 81.24 152s PrivateWages_18 0.0279 1.88 1.75 152s PrivateWages_19 -3.8229 -261.91 -248.49 152s PrivateWages_20 0.7870 52.61 47.93 152s PrivateWages_21 -0.7415 -55.52 -51.54 152s PrivateWages_22 1.2062 104.79 91.31 152s PrivateWages_trend 152s Consumption_2 0.000 152s Consumption_3 0.000 152s Consumption_4 0.000 152s Consumption_5 0.000 152s Consumption_6 0.000 152s Consumption_8 0.000 152s Consumption_9 0.000 152s Consumption_11 0.000 152s Consumption_12 0.000 152s Consumption_14 0.000 152s Consumption_15 0.000 152s Consumption_16 0.000 152s Consumption_17 0.000 152s Consumption_18 0.000 152s Consumption_19 0.000 152s Consumption_20 0.000 152s Consumption_21 0.000 152s Consumption_22 0.000 152s Investment_2 0.000 152s Investment_3 0.000 152s Investment_4 0.000 152s Investment_5 0.000 152s Investment_6 0.000 152s Investment_8 0.000 152s Investment_9 0.000 152s Investment_10 0.000 152s Investment_11 0.000 152s Investment_12 0.000 152s Investment_14 0.000 152s Investment_15 0.000 152s Investment_17 0.000 152s Investment_18 0.000 152s Investment_19 0.000 152s Investment_20 0.000 152s Investment_21 0.000 152s Investment_22 0.000 152s PrivateWages_2 19.924 152s PrivateWages_3 -4.214 152s PrivateWages_4 -11.227 152s PrivateWages_5 12.509 152s PrivateWages_6 2.176 152s PrivateWages_8 -4.652 152s PrivateWages_9 -3.820 152s PrivateWages_10 -4.428 152s PrivateWages_11 1.291 152s PrivateWages_12 0.000 152s PrivateWages_13 -1.044 152s PrivateWages_14 3.603 152s PrivateWages_15 -1.114 152s PrivateWages_16 -1.562 152s PrivateWages_17 7.467 152s PrivateWages_18 0.168 152s PrivateWages_19 -26.760 152s PrivateWages_20 6.296 152s PrivateWages_21 -6.674 152s PrivateWages_22 12.062 152s [1] TRUE 152s > Bread 152s Consumption_(Intercept) Consumption_corpProf 152s Consumption_(Intercept) 116.13 -4.139 152s Consumption_corpProf -4.14 1.213 152s Consumption_corpProfLag 1.01 -0.677 152s Consumption_wages -1.41 -0.133 152s Investment_(Intercept) 0.00 0.000 152s Investment_corpProf 0.00 0.000 152s Investment_corpProfLag 0.00 0.000 152s Investment_capitalLag 0.00 0.000 152s PrivateWages_(Intercept) 0.00 0.000 152s PrivateWages_gnp 0.00 0.000 152s PrivateWages_gnpLag 0.00 0.000 152s PrivateWages_trend 0.00 0.000 152s Consumption_corpProfLag Consumption_wages 152s Consumption_(Intercept) 1.0117 -1.4132 152s Consumption_corpProf -0.6770 -0.1333 152s Consumption_corpProfLag 0.6979 -0.0188 152s Consumption_wages -0.0188 0.0955 152s Investment_(Intercept) 0.0000 0.0000 152s Investment_corpProf 0.0000 0.0000 152s Investment_corpProfLag 0.0000 0.0000 152s Investment_capitalLag 0.0000 0.0000 152s PrivateWages_(Intercept) 0.0000 0.0000 152s PrivateWages_gnp 0.0000 0.0000 152s PrivateWages_gnpLag 0.0000 0.0000 152s PrivateWages_trend 0.0000 0.0000 152s Investment_(Intercept) Investment_corpProf 152s Consumption_(Intercept) 0.0 0.000 152s Consumption_corpProf 0.0 0.000 152s Consumption_corpProfLag 0.0 0.000 152s Consumption_wages 0.0 0.000 152s Investment_(Intercept) 2271.1 -40.229 152s Investment_corpProf -40.2 1.601 152s Investment_corpProfLag 32.3 -1.240 152s Investment_capitalLag -10.5 0.165 152s PrivateWages_(Intercept) 0.0 0.000 152s PrivateWages_gnp 0.0 0.000 152s PrivateWages_gnpLag 0.0 0.000 152s PrivateWages_trend 0.0 0.000 152s Investment_corpProfLag Investment_capitalLag 152s Consumption_(Intercept) 0.000 0.0000 152s Consumption_corpProf 0.000 0.0000 152s Consumption_corpProfLag 0.000 0.0000 152s Consumption_wages 0.000 0.0000 152s Investment_(Intercept) 32.280 -10.5200 152s Investment_corpProf -1.240 0.1648 152s Investment_corpProfLag 1.187 -0.1522 152s Investment_capitalLag -0.152 0.0509 152s PrivateWages_(Intercept) 0.000 0.0000 152s PrivateWages_gnp 0.000 0.0000 152s PrivateWages_gnpLag 0.000 0.0000 152s PrivateWages_trend 0.000 0.0000 152s PrivateWages_(Intercept) PrivateWages_gnp 152s Consumption_(Intercept) 0.000 0.0000 152s Consumption_corpProf 0.000 0.0000 152s Consumption_corpProfLag 0.000 0.0000 152s Consumption_wages 0.000 0.0000 152s Investment_(Intercept) 0.000 0.0000 152s Investment_corpProf 0.000 0.0000 152s Investment_corpProfLag 0.000 0.0000 152s Investment_capitalLag 0.000 0.0000 152s PrivateWages_(Intercept) 159.333 -0.8670 152s PrivateWages_gnp -0.867 0.1475 152s PrivateWages_gnpLag -1.818 -0.1375 152s PrivateWages_trend 2.020 -0.0396 152s PrivateWages_gnpLag PrivateWages_trend 152s Consumption_(Intercept) 0.0000 0.0000 152s Consumption_corpProf 0.0000 0.0000 152s Consumption_corpProfLag 0.0000 0.0000 152s Consumption_wages 0.0000 0.0000 152s Investment_(Intercept) 0.0000 0.0000 152s Investment_corpProf 0.0000 0.0000 152s Investment_corpProfLag 0.0000 0.0000 152s Investment_capitalLag 0.0000 0.0000 152s PrivateWages_(Intercept) -1.8179 2.0198 152s PrivateWages_gnp -0.1375 -0.0396 152s PrivateWages_gnpLag 0.1737 0.0056 152s PrivateWages_trend 0.0056 0.1075 152s > 152s > # SUR 152s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 152s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 152s > summary 153s 153s systemfit results 153s method: SUR 153s 153s N DF SSR detRCov OLS-R2 McElroy-R2 153s system 58 46 45.1 0.199 0.975 0.993 153s 153s N DF SSR MSE RMSE R2 Adj R2 153s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 153s Investment 19 15 17.3 1.155 1.075 0.906 0.887 153s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 153s 153s The covariance matrix of the residuals used for estimation 153s Consumption Investment PrivateWages 153s Consumption 0.9830 0.0466 -0.391 153s Investment 0.0466 0.8101 0.115 153s PrivateWages -0.3906 0.1155 0.496 153s 153s The covariance matrix of the residuals 153s Consumption Investment PrivateWages 153s Consumption 0.979 0.080 -0.452 153s Investment 0.080 0.810 0.181 153s PrivateWages -0.452 0.181 0.521 153s 153s The correlations of the residuals 153s Consumption Investment PrivateWages 153s Consumption 1.0000 0.0907 -0.636 153s Investment 0.0907 1.0000 0.267 153s PrivateWages -0.6362 0.2671 1.000 153s 153s 153s SUR estimates for 'Consumption' (equation 1) 153s Model Formula: consump ~ corpProf + corpProfLag + wages 153s 153s Estimate Std. Error t value Pr(>|t|) 153s (Intercept) 16.2670 1.3148 12.37 2.8e-09 *** 153s corpProf 0.1942 0.0954 2.04 0.06 . 153s corpProfLag 0.0747 0.0842 0.89 0.39 153s wages 0.8011 0.0383 20.93 1.6e-12 *** 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s 153s Residual standard error: 1.08 on 15 degrees of freedom 153s Number of observations: 19 Degrees of Freedom: 15 153s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 153s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 153s 153s 153s SUR estimates for 'Investment' (equation 2) 153s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 153s 153s Estimate Std. Error t value Pr(>|t|) 153s (Intercept) 12.6390 4.7856 2.64 0.01852 * 153s corpProf 0.4708 0.0943 4.99 0.00016 *** 153s corpProfLag 0.3533 0.0907 3.89 0.00144 ** 153s capitalLag -0.1254 0.0236 -5.32 8.6e-05 *** 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s 153s Residual standard error: 1.075 on 15 degrees of freedom 153s Number of observations: 19 Degrees of Freedom: 15 153s SSR: 17.321 MSE: 1.155 Root MSE: 1.075 153s Multiple R-Squared: 0.906 Adjusted R-Squared: 0.887 153s 153s 153s SUR estimates for 'PrivateWages' (equation 3) 153s Model Formula: privWage ~ gnp + gnpLag + trend 153s 153s Estimate Std. Error t value Pr(>|t|) 153s (Intercept) 1.3264 1.1240 1.18 0.2552 153s gnp 0.4184 0.0268 15.63 4.1e-11 *** 153s gnpLag 0.1714 0.0315 5.43 5.5e-05 *** 153s trend 0.1456 0.0284 5.13 0.0001 *** 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s 153s Residual standard error: 0.801 on 16 degrees of freedom 153s Number of observations: 20 Degrees of Freedom: 16 153s SSR: 10.266 MSE: 0.642 Root MSE: 0.801 153s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 153s 153s > residuals 153s Consumption Investment PrivateWages 153s 1 NA NA NA 153s 2 -0.3143 -0.2326 -1.1434 153s 3 -1.2700 -0.1705 0.5084 153s 4 -1.5426 1.0718 1.4211 153s 5 -0.4489 -1.4767 -0.0992 153s 6 0.0588 0.3167 -0.3594 153s 7 0.9213 1.4446 NA 153s 8 1.3789 0.8296 -0.7554 153s 9 1.0900 -0.5263 0.2887 153s 10 NA 1.2083 1.1800 153s 11 0.3569 0.4082 -0.3673 153s 12 -0.2288 0.2663 0.3445 153s 13 NA NA -0.1571 153s 14 0.2181 0.4946 0.4220 153s 15 -0.1120 -0.0470 0.3147 153s 16 -0.0872 NA 0.0145 153s 17 1.5615 1.0289 -0.8091 153s 18 -0.4530 0.0617 0.8608 153s 19 0.1997 -2.5397 -0.7635 153s 20 0.9268 -0.6136 -0.4046 153s 21 0.7588 -0.7465 -1.2179 153s 22 -2.2137 -0.6044 0.5606 153s > fitted 153s Consumption Investment PrivateWages 153s 1 NA NA NA 153s 2 42.2 0.0326 26.6 153s 3 46.3 2.0705 28.8 153s 4 50.7 4.1282 32.7 153s 5 51.0 4.4767 34.0 153s 6 52.5 4.7833 35.8 153s 7 54.2 4.1554 NA 153s 8 54.8 3.3704 38.7 153s 9 56.2 3.5263 38.9 153s 10 NA 3.8917 40.1 153s 11 54.6 0.5918 38.3 153s 12 51.1 -3.6663 34.2 153s 13 NA NA 29.2 153s 14 46.3 -5.5946 28.1 153s 15 48.8 -2.9530 30.3 153s 16 51.4 NA 33.2 153s 17 56.1 1.0711 37.6 153s 18 59.2 1.9383 40.1 153s 19 57.3 0.6397 39.0 153s 20 60.7 1.9136 42.0 153s 21 64.2 4.0465 46.2 153s 22 71.9 5.5044 52.7 153s > predict 153s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 153s 1 NA NA NA NA 153s 2 42.2 0.460 41.3 43.1 153s 3 46.3 0.489 45.3 47.3 153s 4 50.7 0.328 50.1 51.4 153s 5 51.0 0.384 50.3 51.8 153s 6 52.5 0.389 51.8 53.3 153s 7 54.2 0.347 53.5 54.9 153s 8 54.8 0.319 54.2 55.5 153s 9 56.2 0.353 55.5 56.9 153s 10 NA NA NA NA 153s 11 54.6 0.583 53.5 55.8 153s 12 51.1 0.524 50.1 52.2 153s 13 NA NA NA NA 153s 14 46.3 0.589 45.1 47.5 153s 15 48.8 0.393 48.0 49.6 153s 16 51.4 0.337 50.7 52.1 153s 17 56.1 0.345 55.4 56.8 153s 18 59.2 0.318 58.5 59.8 153s 19 57.3 0.381 56.5 58.1 153s 20 60.7 0.413 59.8 61.5 153s 21 64.2 0.417 63.4 65.1 153s 22 71.9 0.651 70.6 73.2 153s Investment.pred Investment.se.fit Investment.lwr Investment.upr 153s 1 NA NA NA NA 153s 2 0.0326 0.556 -1.0866 1.15 153s 3 2.0705 0.454 1.1575 2.98 153s 4 4.1282 0.399 3.3256 4.93 153s 5 4.4767 0.331 3.8101 5.14 153s 6 4.7833 0.314 4.1520 5.41 153s 7 4.1554 0.291 3.5687 4.74 153s 8 3.3704 0.260 2.8469 3.89 153s 9 3.5263 0.347 2.8278 4.22 153s 10 3.8917 0.397 3.0924 4.69 153s 11 0.5918 0.578 -0.5711 1.75 153s 12 -3.6663 0.551 -4.7762 -2.56 153s 13 NA NA NA NA 153s 14 -5.5946 0.661 -6.9261 -4.26 153s 15 -2.9530 0.392 -3.7430 -2.16 153s 16 NA NA NA NA 153s 17 1.0711 0.318 0.4315 1.71 153s 18 1.9383 0.225 1.4863 2.39 153s 19 0.6397 0.310 0.0165 1.26 153s 20 1.9136 0.333 1.2436 2.58 153s 21 4.0465 0.304 3.4345 4.66 153s 22 5.5044 0.429 4.6400 6.37 153s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 153s 1 NA NA NA NA 153s 2 26.6 0.321 26.0 27.3 153s 3 28.8 0.321 28.1 29.4 153s 4 32.7 0.316 32.0 33.3 153s 5 34.0 0.244 33.5 34.5 153s 6 35.8 0.242 35.3 36.2 153s 7 NA NA NA NA 153s 8 38.7 0.246 38.2 39.2 153s 9 38.9 0.234 38.4 39.4 153s 10 40.1 0.225 39.7 40.6 153s 11 38.3 0.301 37.7 38.9 153s 12 34.2 0.298 33.6 34.8 153s 13 29.2 0.353 28.4 29.9 153s 14 28.1 0.330 27.4 28.7 153s 15 30.3 0.328 29.6 30.9 153s 16 33.2 0.275 32.6 33.7 153s 17 37.6 0.270 37.1 38.2 153s 18 40.1 0.213 39.7 40.6 153s 19 39.0 0.301 38.4 39.6 153s 20 42.0 0.287 41.4 42.6 153s 21 46.2 0.304 45.6 46.8 153s 22 52.7 0.448 51.8 53.6 153s > model.frame 153s [1] TRUE 153s > model.matrix 153s [1] TRUE 153s > nobs 153s [1] 58 153s > linearHypothesis 153s Linear hypothesis test (Theil's F test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 47 153s 2 46 1 0.4 0.53 153s Linear hypothesis test (F statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 47 153s 2 46 1 0.49 0.49 153s Linear hypothesis test (Chi^2 statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df Chisq Pr(>Chisq) 153s 1 47 153s 2 46 1 0.49 0.48 153s Linear hypothesis test (Theil's F test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s Consumption_corpProfLag - PrivateWages_trend = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 48 153s 2 46 2 0.31 0.74 153s Linear hypothesis test (F statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s Consumption_corpProfLag - PrivateWages_trend = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 48 153s 2 46 2 0.37 0.69 153s Linear hypothesis test (Chi^2 statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s Consumption_corpProfLag - PrivateWages_trend = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df Chisq Pr(>Chisq) 153s 1 48 153s 2 46 2 0.75 0.69 153s > logLik 153s 'log Lik.' -66.4 (df=18) 153s 'log Lik.' -74.1 (df=18) 153s Estimating function 153s Consumption_(Intercept) Consumption_corpProf 153s Consumption_2 -0.4828 -5.986 153s Consumption_3 -1.9510 -32.972 153s Consumption_4 -2.3698 -43.605 153s Consumption_5 -0.6896 -13.377 153s Consumption_6 0.0903 1.814 153s Consumption_7 1.4152 27.739 153s Consumption_8 2.1183 41.942 153s Consumption_9 1.6745 35.332 153s Consumption_11 0.5483 8.553 153s Consumption_12 -0.3515 -4.008 153s Consumption_14 0.3350 3.752 153s Consumption_15 -0.1720 -2.116 153s Consumption_16 -0.1339 -1.875 153s Consumption_17 2.3987 42.218 153s Consumption_18 -0.6959 -12.040 153s Consumption_19 0.3068 4.694 153s Consumption_20 1.4238 27.052 153s Consumption_21 1.1656 24.594 153s Consumption_22 -3.4008 -79.918 153s Investment_2 0.0628 0.779 153s Investment_3 0.0460 0.778 153s Investment_4 -0.2893 -5.322 153s Investment_5 0.3986 7.732 153s Investment_6 -0.0855 -1.718 153s Investment_7 -0.3899 -7.642 153s Investment_8 -0.2239 -4.433 153s Investment_9 0.1420 2.997 153s Investment_10 0.0000 0.000 153s Investment_11 -0.1102 -1.719 153s Investment_12 -0.0719 -0.819 153s Investment_14 -0.1335 -1.495 153s Investment_15 0.0127 0.156 153s Investment_17 -0.2777 -4.887 153s Investment_18 -0.0167 -0.288 153s Investment_19 0.6855 10.488 153s Investment_20 0.1656 3.146 153s Investment_21 0.2015 4.251 153s Investment_22 0.1631 3.834 153s PrivateWages_2 -1.4560 -18.055 153s PrivateWages_3 0.6473 10.940 153s PrivateWages_4 1.8097 33.298 153s PrivateWages_5 -0.1264 -2.452 153s PrivateWages_6 -0.4576 -9.199 153s PrivateWages_8 -0.9619 -19.046 153s PrivateWages_9 0.3676 7.757 153s PrivateWages_10 0.0000 0.000 153s PrivateWages_11 -0.4677 -7.296 153s PrivateWages_12 0.4387 5.001 153s PrivateWages_13 0.0000 0.000 153s PrivateWages_14 0.5373 6.018 153s PrivateWages_15 0.4008 4.929 153s PrivateWages_16 0.0184 0.258 153s PrivateWages_17 -1.0303 -18.134 153s PrivateWages_18 1.0961 18.963 153s PrivateWages_19 -0.9722 -14.875 153s PrivateWages_20 -0.5153 -9.790 153s PrivateWages_21 -1.5509 -32.724 153s PrivateWages_22 0.7139 16.776 153s Consumption_corpProfLag Consumption_wages 153s Consumption_2 -6.131 -13.614 153s Consumption_3 -24.192 -62.822 153s Consumption_4 -40.050 -87.684 153s Consumption_5 -12.688 -25.514 153s Consumption_6 1.751 3.484 153s Consumption_7 28.447 57.601 153s Consumption_8 41.518 87.909 153s Consumption_9 33.155 71.835 153s Consumption_11 11.898 23.083 153s Consumption_12 -5.484 -13.816 153s Consumption_14 2.345 11.425 153s Consumption_15 -1.926 -6.295 153s Consumption_16 -1.647 -5.263 153s Consumption_17 33.582 106.024 153s Consumption_18 -12.249 -33.196 153s Consumption_19 5.307 14.081 153s Consumption_20 21.784 70.336 153s Consumption_21 22.146 61.777 153s Consumption_22 -71.756 -210.167 153s Investment_2 0.797 1.770 153s Investment_3 0.571 1.482 153s Investment_4 -4.889 -10.703 153s Investment_5 7.333 14.747 153s Investment_6 -1.658 -3.300 153s Investment_7 -7.837 -15.869 153s Investment_8 -4.389 -9.292 153s Investment_9 2.812 6.093 153s Investment_10 0.000 0.000 153s Investment_11 -2.391 -4.638 153s Investment_12 -1.121 -2.825 153s Investment_14 -0.934 -4.552 153s Investment_15 0.142 0.464 153s Investment_17 -3.888 -12.274 153s Investment_18 -0.293 -0.794 153s Investment_19 11.859 31.463 153s Investment_20 2.534 8.181 153s Investment_21 3.828 10.678 153s Investment_22 3.442 10.082 153s PrivateWages_2 -18.491 -41.059 153s PrivateWages_3 8.027 20.845 153s PrivateWages_4 30.584 66.958 153s PrivateWages_5 -2.325 -4.676 153s PrivateWages_6 -8.878 -17.665 153s PrivateWages_8 -18.854 -39.920 153s PrivateWages_9 7.279 15.770 153s PrivateWages_10 0.000 0.000 153s PrivateWages_11 -10.149 -19.690 153s PrivateWages_12 6.843 17.240 153s PrivateWages_13 0.000 0.000 153s PrivateWages_14 3.761 18.323 153s PrivateWages_15 4.489 14.668 153s PrivateWages_16 0.227 0.725 153s PrivateWages_17 -14.424 -45.540 153s PrivateWages_18 19.292 52.286 153s PrivateWages_19 -16.820 -44.626 153s PrivateWages_20 -7.884 -25.455 153s PrivateWages_21 -29.467 -82.197 153s PrivateWages_22 15.062 44.116 153s Investment_(Intercept) Investment_corpProf 153s Consumption_2 0.0848 1.052 153s Consumption_3 0.3428 5.793 153s Consumption_4 0.4164 7.661 153s Consumption_5 0.1211 2.350 153s Consumption_6 -0.0159 -0.319 153s Consumption_7 -0.2486 -4.873 153s Consumption_8 -0.3722 -7.369 153s Consumption_9 -0.2942 -6.207 153s Consumption_11 -0.0963 -1.503 153s Consumption_12 0.0618 0.704 153s Consumption_14 -0.0589 -0.659 153s Consumption_15 0.0302 0.372 153s Consumption_16 0.0000 0.000 153s Consumption_17 -0.4214 -7.417 153s Consumption_18 0.1223 2.115 153s Consumption_19 -0.0539 -0.825 153s Consumption_20 -0.2501 -4.753 153s Consumption_21 -0.2048 -4.321 153s Consumption_22 0.5975 14.041 153s Investment_2 -0.3080 -3.820 153s Investment_3 -0.2258 -3.815 153s Investment_4 1.4192 26.112 153s Investment_5 -1.9554 -37.935 153s Investment_6 0.4194 8.430 153s Investment_7 1.9129 37.493 153s Investment_8 1.0985 21.751 153s Investment_9 -0.6968 -14.703 153s Investment_10 1.6000 34.719 153s Investment_11 0.5405 8.432 153s Investment_12 0.3526 4.020 153s Investment_14 0.6549 7.335 153s Investment_15 -0.0622 -0.766 153s Investment_17 1.3624 23.978 153s Investment_18 0.0817 1.413 153s Investment_19 -3.3630 -51.454 153s Investment_20 -0.8125 -15.437 153s Investment_21 -0.9884 -20.856 153s Investment_22 -0.8004 -18.809 153s PrivateWages_2 0.5958 7.388 153s PrivateWages_3 -0.2649 -4.477 153s PrivateWages_4 -0.7405 -13.626 153s PrivateWages_5 0.0517 1.003 153s PrivateWages_6 0.1873 3.764 153s PrivateWages_8 0.3936 7.794 153s PrivateWages_9 -0.1504 -3.174 153s PrivateWages_10 -0.6149 -13.343 153s PrivateWages_11 0.1914 2.986 153s PrivateWages_12 -0.1795 -2.046 153s PrivateWages_13 0.0000 0.000 153s PrivateWages_14 -0.2199 -2.463 153s PrivateWages_15 -0.1640 -2.017 153s PrivateWages_16 0.0000 0.000 153s PrivateWages_17 0.4216 7.420 153s PrivateWages_18 -0.4485 -7.760 153s PrivateWages_19 0.3978 6.087 153s PrivateWages_20 0.2109 4.006 153s PrivateWages_21 0.6346 13.391 153s PrivateWages_22 -0.2921 -6.865 153s Investment_corpProfLag Investment_capitalLag 153s Consumption_2 1.077 15.50 153s Consumption_3 4.250 62.59 153s Consumption_4 7.036 76.82 153s Consumption_5 2.229 22.98 153s Consumption_6 -0.308 -3.06 153s Consumption_7 -4.998 -49.18 153s Consumption_8 -7.294 -75.70 153s Consumption_9 -5.825 -61.07 153s Consumption_11 -2.090 -20.78 153s Consumption_12 0.963 13.38 153s Consumption_14 -0.412 -12.19 153s Consumption_15 0.338 6.10 153s Consumption_16 0.000 0.00 153s Consumption_17 -5.900 -83.32 153s Consumption_18 2.152 24.43 153s Consumption_19 -0.932 -10.88 153s Consumption_20 -3.827 -50.00 153s Consumption_21 -3.891 -41.20 153s Consumption_22 12.607 122.18 153s Investment_2 -3.912 -56.31 153s Investment_3 -2.799 -41.22 153s Investment_4 23.984 261.83 153s Investment_5 -35.979 -370.94 153s Investment_6 8.137 80.82 153s Investment_7 38.449 378.37 153s Investment_8 21.531 223.44 153s Investment_9 -13.797 -144.66 153s Investment_10 33.759 336.95 153s Investment_11 11.729 116.59 153s Investment_12 5.501 76.41 153s Investment_14 4.584 135.62 153s Investment_15 -0.697 -12.57 153s Investment_17 19.074 269.35 153s Investment_18 1.438 16.32 153s Investment_19 -58.180 -678.65 153s Investment_20 -12.431 -162.42 153s Investment_21 -18.780 -198.88 153s Investment_22 -16.888 -163.68 153s PrivateWages_2 7.567 108.91 153s PrivateWages_3 -3.285 -48.37 153s PrivateWages_4 -12.515 -136.63 153s PrivateWages_5 0.951 9.81 153s PrivateWages_6 3.633 36.09 153s PrivateWages_8 7.715 80.06 153s PrivateWages_9 -2.978 -31.23 153s PrivateWages_10 -12.974 -129.50 153s PrivateWages_11 4.153 41.28 153s PrivateWages_12 -2.800 -38.90 153s PrivateWages_13 0.000 0.00 153s PrivateWages_14 -1.539 -45.54 153s PrivateWages_15 -1.837 -33.13 153s PrivateWages_16 0.000 0.00 153s PrivateWages_17 5.903 83.35 153s PrivateWages_18 -7.894 -89.62 153s PrivateWages_19 6.883 80.29 153s PrivateWages_20 3.226 42.15 153s PrivateWages_21 12.058 127.69 153s PrivateWages_22 -6.164 -59.74 153s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 153s Consumption_2 -0.4002 -18.25 -17.97 153s Consumption_3 -1.6172 -81.02 -73.75 153s Consumption_4 -1.9644 -112.37 -98.42 153s Consumption_5 -0.5716 -32.64 -32.70 153s Consumption_6 0.0748 4.56 4.27 153s Consumption_7 0.0000 0.00 0.00 153s Consumption_8 1.7559 113.08 112.38 153s Consumption_9 1.3880 89.53 89.39 153s Consumption_11 0.4545 27.81 30.45 153s Consumption_12 -0.2914 -15.56 -17.83 153s Consumption_14 0.2777 12.53 12.30 153s Consumption_15 -0.1426 -7.09 -6.43 153s Consumption_16 -0.1110 -6.04 -5.52 153s Consumption_17 1.9884 124.67 108.17 153s Consumption_18 -0.5769 -37.50 -36.17 153s Consumption_19 0.2543 15.49 16.53 153s Consumption_20 1.1803 82.03 71.88 153s Consumption_21 0.9662 73.14 67.15 153s Consumption_22 -2.8190 -249.20 -213.40 153s Investment_2 0.1212 5.53 5.44 153s Investment_3 0.0888 4.45 4.05 153s Investment_4 -0.5585 -31.95 -27.98 153s Investment_5 0.7695 43.94 44.02 153s Investment_6 -0.1651 -10.07 -9.42 153s Investment_7 0.0000 0.00 0.00 153s Investment_8 -0.4323 -27.84 -27.67 153s Investment_9 0.2742 17.69 17.66 153s Investment_10 -0.6296 -42.19 -40.61 153s Investment_11 -0.2127 -13.02 -14.25 153s Investment_12 -0.1388 -7.41 -8.49 153s Investment_14 -0.2577 -11.62 -11.42 153s Investment_15 0.0245 1.22 1.10 153s Investment_17 -0.5361 -33.62 -29.17 153s Investment_18 -0.0322 -2.09 -2.02 153s Investment_19 1.3234 80.60 86.02 153s Investment_20 0.3197 22.22 19.47 153s Investment_21 0.3890 29.45 27.03 153s Investment_22 0.3150 27.84 23.84 153s PrivateWages_2 -3.5926 -163.82 -161.31 153s PrivateWages_3 1.5973 80.02 72.84 153s PrivateWages_4 4.4653 255.42 223.71 153s PrivateWages_5 -0.3118 -17.80 -17.84 153s PrivateWages_6 -1.1292 -68.88 -64.48 153s PrivateWages_8 -2.3735 -152.85 -151.90 153s PrivateWages_9 0.9071 58.50 58.41 153s PrivateWages_10 3.7077 248.42 239.15 153s PrivateWages_11 -1.1540 -70.63 -77.32 153s PrivateWages_12 1.0824 57.80 66.24 153s PrivateWages_13 -0.4937 -21.87 -26.36 153s PrivateWages_14 1.3258 59.79 58.73 153s PrivateWages_15 0.9889 49.15 44.60 153s PrivateWages_16 0.0455 2.48 2.26 153s PrivateWages_17 -2.5423 -159.40 -138.30 153s PrivateWages_18 2.7047 175.80 169.58 153s PrivateWages_19 -2.3990 -146.10 -155.93 153s PrivateWages_20 -1.2714 -88.36 -77.43 153s PrivateWages_21 -3.8267 -289.68 -265.96 153s PrivateWages_22 1.7614 155.71 133.34 153s PrivateWages_trend 153s Consumption_2 4.0019 153s Consumption_3 14.5552 153s Consumption_4 15.7155 153s Consumption_5 4.0012 153s Consumption_6 -0.4490 153s Consumption_7 0.0000 153s Consumption_8 -7.0237 153s Consumption_9 -4.1641 153s Consumption_11 -0.4545 153s Consumption_12 0.0000 153s Consumption_14 0.5555 153s Consumption_15 -0.4277 153s Consumption_16 -0.4440 153s Consumption_17 9.9420 153s Consumption_18 -3.4614 153s Consumption_19 1.7801 153s Consumption_20 9.4420 153s Consumption_21 8.6959 153s Consumption_22 -28.1902 153s Investment_2 -1.2122 153s Investment_3 -0.7996 153s Investment_4 4.4678 153s Investment_5 -5.3865 153s Investment_6 0.9903 153s Investment_7 0.0000 153s Investment_8 1.7292 153s Investment_9 -0.8227 153s Investment_10 1.2593 153s Investment_11 0.2127 153s Investment_12 0.0000 153s Investment_14 -0.5154 153s Investment_15 0.0735 153s Investment_17 -2.6807 153s Investment_18 -0.1929 153s Investment_19 9.2640 153s Investment_20 2.5579 153s Investment_21 3.5008 153s Investment_22 3.1497 153s PrivateWages_2 35.9264 153s PrivateWages_3 -14.3757 153s PrivateWages_4 -35.7225 153s PrivateWages_5 2.1827 153s PrivateWages_6 6.7753 153s PrivateWages_8 9.4940 153s PrivateWages_9 -2.7212 153s PrivateWages_10 -7.4154 153s PrivateWages_11 1.1540 153s PrivateWages_12 0.0000 153s PrivateWages_13 -0.4937 153s PrivateWages_14 2.6517 153s PrivateWages_15 2.9666 153s PrivateWages_16 0.1820 153s PrivateWages_17 -12.7113 153s PrivateWages_18 16.2281 153s PrivateWages_19 -16.7928 153s PrivateWages_20 -10.1714 153s PrivateWages_21 -34.4407 153s PrivateWages_22 17.6141 153s [1] TRUE 153s > Bread 153s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 153s [1,] 1.00e+02 -1.05144 -0.70595 153s [2,] -1.05e+00 0.52767 -0.28007 153s [3,] -7.06e-01 -0.28007 0.41162 153s [4,] -1.63e+00 -0.08132 -0.03081 153s [5,] 5.03e+00 -0.06375 0.80965 153s [6,] -2.73e-01 0.05286 -0.04323 153s [7,] 4.77e-03 -0.03564 0.04677 153s [8,] -4.66e-04 -0.00135 -0.00415 153s [9,] -3.50e+01 0.07154 1.64913 153s [10,] 3.09e-01 -0.05491 0.03767 153s [11,] 2.66e-01 0.05541 -0.06699 153s [12,] 1.98e-01 0.03217 0.02582 153s Consumption_wages Investment_(Intercept) Investment_corpProf 153s [1,] -1.63020 5.0343 -0.27333 153s [2,] -0.08132 -0.0638 0.05286 153s [3,] -0.03081 0.8097 -0.04323 153s [4,] 0.08501 -0.3863 0.00122 153s [5,] -0.38629 1328.3034 -12.58281 153s [6,] 0.00122 -12.5828 0.51550 153s [7,] -0.00347 10.1576 -0.39286 153s [8,] 0.00211 -6.3831 0.05078 153s [9,] 0.13121 19.8408 -0.15336 153s [10,] -0.00022 0.2731 0.01339 153s [11,] -0.00213 -0.6257 -0.01103 153s [12,] -0.02827 -0.5788 0.00418 153s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 153s [1,] 0.00477 -0.000466 -34.9530 153s [2,] -0.03564 -0.001347 0.0715 153s [3,] 0.04677 -0.004153 1.6491 153s [4,] -0.00347 0.002105 0.1312 153s [5,] 10.15755 -6.383136 19.8408 153s [6,] -0.39286 0.050784 -0.1534 153s [7,] 0.47726 -0.056526 -0.3957 153s [8,] -0.05653 0.032233 -0.0526 153s [9,] -0.39566 -0.052599 73.2779 153s [10,] -0.00743 -0.001878 -0.2209 153s [11,] 0.01439 0.002876 -1.0159 153s [12,] -0.01026 0.003357 0.8108 153s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 153s [1,] 0.30855 0.26619 0.19754 153s [2,] -0.05491 0.05541 0.03217 153s [3,] 0.03767 -0.06699 0.02582 153s [4,] -0.00022 -0.00213 -0.02827 153s [5,] 0.27312 -0.62569 -0.57877 153s [6,] 0.01339 -0.01103 0.00418 153s [7,] -0.00743 0.01439 -0.01026 153s [8,] -0.00188 0.00288 0.00336 153s [9,] -0.22091 -1.01587 0.81082 153s [10,] 0.04154 -0.03895 -0.00995 153s [11,] -0.03895 0.05766 -0.00383 153s [12,] -0.00995 -0.00383 0.04664 153s > 153s > # 3SLS 153s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 153s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 153s > summary 153s 153s systemfit results 153s method: 3SLS 153s 153s N DF SSR detRCov OLS-R2 McElroy-R2 153s system 56 44 67.5 0.436 0.963 0.993 153s 153s N DF SSR MSE RMSE R2 Adj R2 153s Consumption 18 14 22.4 1.598 1.264 0.974 0.968 153s Investment 18 14 35.0 2.503 1.582 0.793 0.749 153s PrivateWages 20 16 10.1 0.629 0.793 0.987 0.985 153s 153s The covariance matrix of the residuals used for estimation 153s Consumption Investment PrivateWages 153s Consumption 1.307 0.540 -0.431 153s Investment 0.540 1.319 0.119 153s PrivateWages -0.431 0.119 0.496 153s 153s The covariance matrix of the residuals 153s Consumption Investment PrivateWages 153s Consumption 1.309 0.638 -0.440 153s Investment 0.638 1.749 0.233 153s PrivateWages -0.440 0.233 0.519 153s 153s The correlations of the residuals 153s Consumption Investment PrivateWages 153s Consumption 1.000 0.422 -0.532 153s Investment 0.422 1.000 0.247 153s PrivateWages -0.532 0.247 1.000 153s 153s 153s 3SLS estimates for 'Consumption' (equation 1) 153s Model Formula: consump ~ corpProf + corpProfLag + wages 153s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 153s gnpLag 153s 153s Estimate Std. Error t value Pr(>|t|) 153s (Intercept) 18.0338 1.5648 11.52 1.6e-08 *** 153s corpProf -0.0632 0.1500 -0.42 0.68 153s corpProfLag 0.1784 0.1154 1.55 0.14 153s wages 0.8224 0.0444 18.54 3.0e-11 *** 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s 153s Residual standard error: 1.264 on 14 degrees of freedom 153s Number of observations: 18 Degrees of Freedom: 14 153s SSR: 22.377 MSE: 1.598 Root MSE: 1.264 153s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 153s 153s 153s 3SLS estimates for 'Investment' (equation 2) 153s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 153s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 153s gnpLag 153s 153s Estimate Std. Error t value Pr(>|t|) 153s (Intercept) 24.6766 6.7008 3.68 0.00246 ** 153s corpProf 0.0472 0.1843 0.26 0.80149 153s corpProfLag 0.6874 0.1577 4.36 0.00065 *** 153s capitalLag -0.1776 0.0318 -5.59 6.7e-05 *** 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s 153s Residual standard error: 1.582 on 14 degrees of freedom 153s Number of observations: 18 Degrees of Freedom: 14 153s SSR: 35.037 MSE: 2.503 Root MSE: 1.582 153s Multiple R-Squared: 0.793 Adjusted R-Squared: 0.749 153s 153s 153s 3SLS estimates for 'PrivateWages' (equation 3) 153s Model Formula: privWage ~ gnp + gnpLag + trend 153s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 153s gnpLag 153s 153s Estimate Std. Error t value Pr(>|t|) 153s (Intercept) 0.7823 1.1254 0.70 0.49695 153s gnp 0.4257 0.0308 13.80 2.6e-10 *** 153s gnpLag 0.1728 0.0341 5.07 0.00011 *** 153s trend 0.1252 0.0291 4.30 0.00055 *** 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s 153s Residual standard error: 0.793 on 16 degrees of freedom 153s Number of observations: 20 Degrees of Freedom: 16 153s SSR: 10.057 MSE: 0.629 Root MSE: 0.793 153s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 153s 153s > residuals 153s Consumption Investment PrivateWages 153s 1 NA NA NA 153s 2 -0.8058 -1.721 -1.20135 153s 3 -0.6573 0.337 0.43696 153s 4 -1.1124 0.810 1.31177 153s 5 0.0833 -1.544 -0.19794 153s 6 0.6334 0.368 -0.46596 153s 7 NA NA NA 153s 8 1.7939 1.245 -0.85614 153s 9 1.7891 0.593 0.20698 153s 10 NA 2.303 1.10034 153s 11 -0.5397 -1.015 -0.38801 153s 12 -1.5147 -0.846 0.40949 153s 13 NA NA 0.00602 153s 14 -0.1171 1.670 0.61306 153s 15 -0.6526 -0.075 0.49152 153s 16 -0.3617 NA 0.17066 153s 17 1.9331 2.086 -0.69991 153s 18 -0.6063 -0.101 0.96136 153s 19 -0.3990 -3.345 -0.61606 153s 20 1.4134 0.717 -0.29343 153s 21 1.3257 0.306 -1.14412 153s 22 -1.4340 0.935 0.55310 153s > fitted 153s Consumption Investment PrivateWages 153s 1 NA NA NA 153s 2 42.7 1.5213 26.7 153s 3 45.7 1.5632 28.9 153s 4 50.3 4.3898 32.8 153s 5 50.5 4.5444 34.1 153s 6 52.0 4.7320 35.9 153s 7 NA NA NA 153s 8 54.4 2.9547 38.8 153s 9 55.5 2.4075 39.0 153s 10 NA 2.7965 40.2 153s 11 55.5 2.0150 38.3 153s 12 52.4 -2.5541 34.1 153s 13 NA NA 29.0 153s 14 46.6 -6.7699 27.9 153s 15 49.4 -2.9250 30.1 153s 16 51.7 NA 33.0 153s 17 55.8 0.0139 37.5 153s 18 59.3 2.1013 40.0 153s 19 57.9 1.4453 38.8 153s 20 60.2 0.5828 41.9 153s 21 63.7 2.9944 46.1 153s 22 71.1 3.9651 52.7 153s > predict 153s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 153s 1 NA NA NA NA 153s 2 42.7 0.555 39.7 45.7 153s 3 45.7 0.628 42.6 48.7 153s 4 50.3 0.418 47.5 53.2 153s 5 50.5 0.492 47.6 53.4 153s 6 52.0 0.501 49.0 54.9 153s 7 NA NA NA NA 153s 8 54.4 0.405 51.6 57.3 153s 9 55.5 0.477 52.6 58.4 153s 10 NA NA NA NA 153s 11 55.5 0.832 52.3 58.8 153s 12 52.4 0.792 49.2 55.6 153s 13 NA NA NA NA 153s 14 46.6 0.676 43.5 49.7 153s 15 49.4 0.470 46.5 52.2 153s 16 51.7 0.386 48.8 54.5 153s 17 55.8 0.433 52.9 58.6 153s 18 59.3 0.368 56.5 62.1 153s 19 57.9 0.504 55.0 60.8 153s 20 60.2 0.513 57.3 63.1 153s 21 63.7 0.505 60.8 66.6 153s 22 71.1 0.771 68.0 74.3 153s Investment.pred Investment.se.fit Investment.lwr Investment.upr 153s 1 NA NA NA NA 153s 2 1.5213 0.857 -2.337 5.380 153s 3 1.5632 0.589 -2.058 5.184 153s 4 4.3898 0.519 0.819 7.961 153s 5 4.5444 0.436 1.025 8.064 153s 6 4.7320 0.415 1.224 8.240 153s 7 NA NA NA NA 153s 8 2.9547 0.342 -0.517 6.426 153s 9 2.4075 0.511 -1.158 5.973 153s 10 2.7965 0.556 -0.800 6.393 153s 11 2.0150 0.955 -1.948 5.978 153s 12 -2.5541 0.874 -6.431 1.323 153s 13 NA NA NA NA 153s 14 -6.7699 0.865 -10.637 -2.903 153s 15 -2.9250 0.503 -6.485 0.635 153s 16 NA NA NA NA 153s 17 0.0139 0.483 -3.534 3.561 153s 18 2.1013 0.320 -1.361 5.563 153s 19 1.4453 0.532 -2.134 5.025 153s 20 0.5828 0.550 -3.010 4.175 153s 21 2.9944 0.476 -0.549 6.538 153s 22 3.9651 0.692 0.261 7.669 153s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 153s 1 NA NA NA NA 153s 2 26.7 0.324 24.9 28.5 153s 3 28.9 0.331 27.0 30.7 153s 4 32.8 0.339 31.0 34.6 153s 5 34.1 0.248 32.3 35.9 153s 6 35.9 0.256 34.1 37.6 153s 7 NA NA NA NA 153s 8 38.8 0.251 37.0 40.5 153s 9 39.0 0.238 37.2 40.7 153s 10 40.2 0.232 38.4 42.0 153s 11 38.3 0.314 36.5 40.1 153s 12 34.1 0.327 32.3 35.9 153s 13 29.0 0.393 27.1 30.9 153s 14 27.9 0.329 26.1 29.7 153s 15 30.1 0.324 28.3 31.9 153s 16 33.0 0.271 31.3 34.8 153s 17 37.5 0.277 35.7 39.3 153s 18 40.0 0.213 38.3 41.8 153s 19 38.8 0.320 37.0 40.6 153s 20 41.9 0.295 40.1 43.7 153s 21 46.1 0.309 44.3 47.9 153s 22 52.7 0.476 50.8 54.7 153s > model.frame 153s [1] TRUE 153s > model.matrix 153s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 153s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 153s [3] "Numeric: lengths (696, 672) differ" 153s > nobs 153s [1] 56 153s > linearHypothesis 153s Linear hypothesis test (Theil's F test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 45 153s 2 44 1 1.91 0.17 153s Linear hypothesis test (F statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 45 153s 2 44 1 2.6 0.11 153s Linear hypothesis test (Chi^2 statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df Chisq Pr(>Chisq) 153s 1 45 153s 2 44 1 2.6 0.11 153s Linear hypothesis test (Theil's F test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s Consumption_corpProfLag - PrivateWages_trend = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 46 153s 2 44 2 1.62 0.21 153s Linear hypothesis test (F statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s Consumption_corpProfLag - PrivateWages_trend = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 46 153s 2 44 2 2.2 0.12 153s Linear hypothesis test (Chi^2 statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s Consumption_corpProfLag - PrivateWages_trend = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df Chisq Pr(>Chisq) 153s 1 46 153s 2 44 2 4.41 0.11 153s > logLik 153s 'log Lik.' -70.1 (df=18) 153s 'log Lik.' -80.6 (df=18) 153s Estimating function 153s Consumption_(Intercept) Consumption_corpProf 153s Consumption_2 -3.3369 -46.76 153s Consumption_3 -0.6260 -10.43 153s Consumption_4 0.5431 10.07 153s Consumption_5 -1.9287 -39.09 153s Consumption_6 0.9979 18.98 153s Consumption_8 4.7224 83.33 153s Consumption_9 4.2195 79.93 153s Consumption_11 -2.1144 -35.40 153s Consumption_12 -2.7531 -36.83 153s Consumption_14 0.7280 7.30 153s Consumption_15 -2.0340 -25.43 153s Consumption_16 -1.6770 -24.29 153s Consumption_17 6.1486 91.69 153s Consumption_18 -0.6466 -12.56 153s Consumption_19 -4.7474 -90.72 153s Consumption_20 3.3112 58.48 153s Consumption_21 1.5335 31.28 153s Consumption_22 -1.0772 -24.43 153s Investment_2 1.4470 20.28 153s Investment_3 -0.2844 -4.74 153s Investment_4 -0.6458 -11.98 153s Investment_5 1.3096 26.54 153s Investment_6 -0.3315 -6.31 153s Investment_8 -1.1056 -19.51 153s Investment_9 -0.5457 -10.34 153s Investment_10 0.0000 0.00 153s Investment_11 0.8919 14.93 153s Investment_12 0.7723 10.33 153s Investment_14 -1.4083 -14.12 153s Investment_15 0.0885 1.11 153s Investment_17 -1.8093 -26.98 153s Investment_18 0.1676 3.25 153s Investment_19 2.8888 55.20 153s Investment_20 -0.6425 -11.35 153s Investment_21 -0.2855 -5.82 153s Investment_22 -0.7925 -17.97 153s PrivateWages_2 -2.9611 -41.49 153s PrivateWages_3 1.0665 17.77 153s PrivateWages_4 2.5794 47.83 153s PrivateWages_5 -2.7951 -56.65 153s PrivateWages_6 -0.4865 -9.25 153s PrivateWages_8 1.6497 29.11 153s PrivateWages_9 1.8751 35.52 153s PrivateWages_10 0.0000 0.00 153s PrivateWages_11 -2.3618 -39.54 153s PrivateWages_12 -0.3246 -4.34 153s PrivateWages_13 0.0000 0.00 153s PrivateWages_14 3.0441 30.51 153s PrivateWages_15 -0.2496 -3.12 153s PrivateWages_16 -0.3710 -5.37 153s PrivateWages_17 2.5263 37.67 153s PrivateWages_18 0.0583 1.13 153s PrivateWages_19 -6.2503 -119.43 153s PrivateWages_20 1.3565 23.96 153s PrivateWages_21 -1.2791 -26.09 153s PrivateWages_22 1.9457 44.12 153s Consumption_corpProfLag Consumption_wages 153s Consumption_2 -42.379 -99.51 153s Consumption_3 -7.762 -19.94 153s Consumption_4 9.179 19.15 153s Consumption_5 -35.489 -74.45 153s Consumption_6 19.359 38.46 153s Consumption_8 92.559 188.94 153s Consumption_9 83.547 176.28 153s Consumption_11 -45.883 -91.13 153s Consumption_12 -42.949 -109.17 153s Consumption_14 5.096 24.26 153s Consumption_15 -22.780 -75.93 153s Consumption_16 -20.627 -67.32 153s Consumption_17 86.080 256.88 153s Consumption_18 -11.379 -30.78 153s Consumption_19 -82.131 -233.73 153s Consumption_20 50.662 160.78 153s Consumption_21 29.137 81.92 153s Consumption_22 -22.729 -65.49 153s Investment_2 18.377 43.15 153s Investment_3 -3.526 -9.06 153s Investment_4 -10.914 -22.77 153s Investment_5 24.097 50.55 153s Investment_6 -6.431 -12.78 153s Investment_8 -21.669 -44.23 153s Investment_9 -10.805 -22.80 153s Investment_10 0.000 0.00 153s Investment_11 19.355 38.44 153s Investment_12 12.047 30.62 153s Investment_14 -9.858 -46.93 153s Investment_15 0.992 3.31 153s Investment_17 -25.331 -75.59 153s Investment_18 2.950 7.98 153s Investment_19 49.976 142.22 153s Investment_20 -9.831 -31.20 153s Investment_21 -5.425 -15.25 153s Investment_22 -16.723 -48.18 153s PrivateWages_2 -37.606 -88.31 153s PrivateWages_3 13.225 33.97 153s PrivateWages_4 43.593 90.94 153s PrivateWages_5 -51.429 -107.89 153s PrivateWages_6 -9.438 -18.75 153s PrivateWages_8 32.333 66.00 153s PrivateWages_9 37.126 78.33 153s PrivateWages_10 0.000 0.00 153s PrivateWages_11 -51.251 -101.80 153s PrivateWages_12 -5.063 -12.87 153s PrivateWages_13 0.000 0.00 153s PrivateWages_14 21.309 101.45 153s PrivateWages_15 -2.796 -9.32 153s PrivateWages_16 -4.563 -14.89 153s PrivateWages_17 35.368 105.55 153s PrivateWages_18 1.025 2.77 153s PrivateWages_19 -108.130 -307.72 153s PrivateWages_20 20.754 65.87 153s PrivateWages_21 -24.303 -68.33 153s PrivateWages_22 41.055 118.29 153s Investment_(Intercept) Investment_corpProf 153s Consumption_2 1.6657 22.369 153s Consumption_3 0.3125 5.208 153s Consumption_4 -0.2711 -5.105 153s Consumption_5 0.9628 19.850 153s Consumption_6 -0.4981 -9.617 153s Consumption_8 -2.3573 -41.335 153s Consumption_9 -2.1063 -41.098 153s Consumption_11 1.0555 18.165 153s Consumption_12 1.3743 18.540 153s Consumption_14 -0.3634 -3.664 153s Consumption_15 1.0153 13.204 153s Consumption_16 0.0000 0.000 153s Consumption_17 -3.0693 -45.765 153s Consumption_18 0.3228 6.293 153s Consumption_19 2.3698 45.702 153s Consumption_20 -1.6529 -29.000 153s Consumption_21 -0.7655 -15.445 153s Consumption_22 0.5377 12.243 153s Investment_2 -2.0943 -28.124 153s Investment_3 0.4116 6.860 153s Investment_4 0.9347 17.600 153s Investment_5 -1.8955 -39.080 153s Investment_6 0.4798 9.263 153s Investment_8 1.6002 28.058 153s Investment_9 0.7899 15.412 153s Investment_10 2.8075 56.810 153s Investment_11 -1.2910 -22.218 153s Investment_12 -1.1178 -15.079 153s Investment_14 2.0383 20.552 153s Investment_15 -0.1282 -1.667 153s Investment_17 2.6188 39.047 153s Investment_18 -0.2426 -4.730 153s Investment_19 -4.1811 -80.631 153s Investment_20 0.9300 16.316 153s Investment_21 0.4133 8.338 153s Investment_22 1.1471 26.118 153s PrivateWages_2 1.8190 24.427 153s PrivateWages_3 -0.6551 -10.919 153s PrivateWages_4 -1.5845 -29.835 153s PrivateWages_5 1.7170 35.400 153s PrivateWages_6 0.2989 5.770 153s PrivateWages_8 -1.0134 -17.769 153s PrivateWages_9 -1.1518 -22.474 153s PrivateWages_10 -2.1257 -43.013 153s PrivateWages_11 1.4508 24.969 153s PrivateWages_12 0.1994 2.690 153s PrivateWages_13 0.0000 0.000 153s PrivateWages_14 -1.8700 -18.855 153s PrivateWages_15 0.1533 1.994 153s PrivateWages_16 0.0000 0.000 153s PrivateWages_17 -1.5519 -23.140 153s PrivateWages_18 -0.0358 -0.698 153s PrivateWages_19 3.8395 74.045 153s PrivateWages_20 -0.8333 -14.620 153s PrivateWages_21 0.7858 15.853 153s PrivateWages_22 -1.1953 -27.215 153s Investment_corpProfLag Investment_capitalLag 153s Consumption_2 21.15 304.50 153s Consumption_3 3.87 57.06 153s Consumption_4 -4.58 -50.02 153s Consumption_5 17.72 182.64 153s Consumption_6 -9.66 -95.99 153s Consumption_8 -46.20 -479.48 153s Consumption_9 -41.70 -437.27 153s Consumption_11 22.90 227.67 153s Consumption_12 21.44 297.81 153s Consumption_14 -2.54 -75.26 153s Consumption_15 11.37 205.09 153s Consumption_16 0.00 0.00 153s Consumption_17 -42.97 -606.79 153s Consumption_18 5.68 64.49 153s Consumption_19 41.00 478.23 153s Consumption_20 -25.29 -330.42 153s Consumption_21 -14.54 -154.02 153s Consumption_22 11.35 109.96 153s Investment_2 -26.60 -382.84 153s Investment_3 5.10 75.16 153s Investment_4 15.80 172.46 153s Investment_5 -34.88 -359.58 153s Investment_6 9.31 92.46 153s Investment_8 31.36 325.47 153s Investment_9 15.64 163.98 153s Investment_10 59.24 591.25 153s Investment_11 -28.01 -278.46 153s Investment_12 -17.44 -242.22 153s Investment_14 14.27 422.14 153s Investment_15 -1.44 -25.89 153s Investment_17 36.66 517.73 153s Investment_18 -4.27 -48.47 153s Investment_19 -72.33 -843.75 153s Investment_20 14.23 185.90 153s Investment_21 7.85 83.15 153s Investment_22 24.20 234.58 153s PrivateWages_2 23.10 332.51 153s PrivateWages_3 -8.12 -119.63 153s PrivateWages_4 -26.78 -292.35 153s PrivateWages_5 31.59 325.71 153s PrivateWages_6 5.80 57.59 153s PrivateWages_8 -19.86 -206.12 153s PrivateWages_9 -22.81 -239.12 153s PrivateWages_10 -44.85 -447.66 153s PrivateWages_11 31.48 312.95 153s PrivateWages_12 3.11 43.21 153s PrivateWages_13 0.00 0.00 153s PrivateWages_14 -13.09 -387.28 153s PrivateWages_15 1.72 30.97 153s PrivateWages_16 0.00 0.00 153s PrivateWages_17 -21.73 -306.81 153s PrivateWages_18 -0.63 -7.15 153s PrivateWages_19 66.42 774.82 153s PrivateWages_20 -12.75 -166.57 153s PrivateWages_21 14.93 158.09 153s PrivateWages_22 -25.22 -244.43 153s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 153s Consumption_2 -3.302 -155.43 -148.27 153s Consumption_3 -0.619 -30.71 -28.25 153s Consumption_4 0.537 30.39 26.93 153s Consumption_5 -1.909 -115.83 -109.18 153s Consumption_6 0.987 59.85 56.39 153s Consumption_8 4.673 280.38 299.09 153s Consumption_9 4.176 260.01 268.91 153s Consumption_11 -2.092 -133.31 -140.19 153s Consumption_12 -2.724 -149.39 -166.74 153s Consumption_14 0.720 30.35 31.91 153s Consumption_15 -2.013 -103.09 -90.78 153s Consumption_16 -1.660 -91.84 -82.48 153s Consumption_17 6.085 349.22 331.00 153s Consumption_18 -0.640 -42.98 -40.12 153s Consumption_19 -4.698 -321.88 -305.37 153s Consumption_20 3.277 219.03 199.56 153s Consumption_21 1.518 113.62 105.47 153s Consumption_22 -1.066 -92.61 -80.70 153s Investment_2 1.762 82.94 79.12 153s Investment_3 -0.346 -17.17 -15.79 153s Investment_4 -0.786 -44.47 -39.40 153s Investment_5 1.595 96.79 91.23 153s Investment_6 -0.404 -24.47 -23.05 153s Investment_8 -1.346 -80.78 -86.17 153s Investment_9 -0.665 -41.38 -42.80 153s Investment_10 -2.362 -152.52 -152.36 153s Investment_11 1.086 69.20 72.78 153s Investment_12 0.940 51.57 57.56 153s Investment_14 -1.715 -72.25 -75.98 153s Investment_15 0.108 5.52 4.86 153s Investment_17 -2.203 -126.46 -119.87 153s Investment_18 0.204 13.71 12.80 153s Investment_19 3.518 241.02 228.67 153s Investment_20 -0.782 -52.30 -47.65 153s Investment_21 -0.348 -26.03 -24.17 153s Investment_22 -0.965 -83.85 -73.06 153s PrivateWages_2 -6.697 -315.21 -300.67 153s PrivateWages_3 2.412 119.58 109.98 153s PrivateWages_4 5.833 329.84 292.25 153s PrivateWages_5 -6.321 -383.60 -361.56 153s PrivateWages_6 -1.100 -66.69 -62.82 153s PrivateWages_8 3.731 223.83 238.77 153s PrivateWages_9 4.240 264.05 273.09 153s PrivateWages_10 7.826 505.29 504.75 153s PrivateWages_11 -5.341 -340.30 -357.86 153s PrivateWages_12 -0.734 -40.25 -44.92 153s PrivateWages_13 -4.155 -195.19 -221.87 153s PrivateWages_14 6.884 290.02 304.97 153s PrivateWages_15 -0.565 -28.91 -25.46 153s PrivateWages_16 -0.839 -46.43 -41.70 153s PrivateWages_17 5.713 327.90 310.80 153s PrivateWages_18 0.132 8.85 8.26 153s PrivateWages_19 -14.135 -968.43 -918.78 153s PrivateWages_20 3.068 205.06 186.82 153s PrivateWages_21 -2.893 -216.57 -201.04 153s PrivateWages_22 4.400 382.29 333.10 153s PrivateWages_trend 153s Consumption_2 33.022 153s Consumption_3 5.575 153s Consumption_4 -4.300 153s Consumption_5 13.361 153s Consumption_6 -5.925 153s Consumption_8 -18.693 153s Consumption_9 -12.527 153s Consumption_11 2.092 153s Consumption_12 0.000 153s Consumption_14 1.441 153s Consumption_15 -6.038 153s Consumption_16 -6.638 153s Consumption_17 30.423 153s Consumption_18 -3.839 153s Consumption_19 -32.886 153s Consumption_20 26.214 153s Consumption_21 13.658 153s Consumption_22 -10.660 153s Investment_2 -17.621 153s Investment_3 3.117 153s Investment_4 6.292 153s Investment_5 -11.164 153s Investment_6 2.422 153s Investment_8 5.385 153s Investment_9 1.994 153s Investment_10 4.724 153s Investment_11 -1.086 153s Investment_12 0.000 153s Investment_14 -3.430 153s Investment_15 0.323 153s Investment_17 -11.017 153s Investment_18 1.225 153s Investment_19 24.626 153s Investment_20 -6.260 153s Investment_21 -3.129 153s Investment_22 -9.652 153s PrivateWages_2 66.965 153s PrivateWages_3 -21.707 153s PrivateWages_4 -46.667 153s PrivateWages_5 44.247 153s PrivateWages_6 6.602 153s PrivateWages_8 -14.923 153s PrivateWages_9 -12.721 153s PrivateWages_10 -15.651 153s PrivateWages_11 5.341 153s PrivateWages_12 0.000 153s PrivateWages_13 -4.155 153s PrivateWages_14 13.769 153s PrivateWages_15 -1.694 153s PrivateWages_16 -3.356 153s PrivateWages_17 28.566 153s PrivateWages_18 0.791 153s PrivateWages_19 -98.946 153s PrivateWages_20 24.542 153s PrivateWages_21 -26.035 153s PrivateWages_22 44.003 153s [1] TRUE 153s > Bread 153s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 153s [1,] 137.1267 -4.2997 0.8463 153s [2,] -4.2997 1.2597 -0.6942 153s [3,] 0.8463 -0.6942 0.7454 153s [4,] -1.7733 -0.1394 -0.0281 153s [5,] 105.0265 3.4241 3.4807 153s [6,] -4.4721 0.5244 -0.4530 153s [7,] 1.6442 -0.3454 0.4268 153s [8,] -0.2644 -0.0340 -0.0134 153s [9,] -38.0151 0.3680 1.7655 153s [10,] 0.5379 -0.0825 0.0502 153s [11,] 0.0809 0.0782 -0.0821 153s [12,] 0.1895 0.0505 0.0265 153s Consumption_wages Investment_(Intercept) Investment_corpProf 153s [1,] -1.773256 105.03 -4.47211 153s [2,] -0.139424 3.42 0.52437 153s [3,] -0.028067 3.48 -0.45300 153s [4,] 0.110155 -5.14 0.06784 153s [5,] -5.138461 2514.46 -43.59967 153s [6,] 0.067843 -43.60 1.90216 153s [7,] -0.064178 34.75 -1.45456 153s [8,] 0.025084 -11.63 0.17310 153s [9,] 0.044238 27.92 -0.25822 153s [10,] 0.000203 1.31 0.00136 153s [11,] -0.000811 -1.85 0.00316 153s [12,] -0.035488 -0.85 0.01679 153s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 153s [1,] 1.64420 -0.26436 -38.0151 153s [2,] -0.34536 -0.03402 0.3680 153s [3,] 0.42680 -0.01343 1.7655 153s [4,] -0.06418 0.02508 0.0442 153s [5,] 34.75055 -11.63252 27.9186 153s [6,] -1.45456 0.17310 -0.2582 153s [7,] 1.39257 -0.16270 -0.3518 153s [8,] -0.16270 0.05655 -0.0905 153s [9,] -0.35175 -0.09046 70.9283 153s [10,] 0.00769 -0.00730 -0.3444 153s [11,] -0.00156 0.00915 -0.8533 153s [12,] -0.02239 0.00456 0.8163 153s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 153s [1,] 0.537909 0.080946 0.189459 153s [2,] -0.082456 0.078164 0.050460 153s [3,] 0.050248 -0.082092 0.026511 153s [4,] 0.000203 -0.000811 -0.035488 153s [5,] 1.312267 -1.847095 -0.850461 153s [6,] 0.001362 0.003160 0.016792 153s [7,] 0.007689 -0.001565 -0.022388 153s [8,] -0.007301 0.009148 0.004555 153s [9,] -0.344428 -0.853347 0.816265 153s [10,] 0.053258 -0.048785 -0.014522 153s [11,] -0.048785 0.064956 0.000648 153s [12,] -0.014522 0.000648 0.047452 153s > 153s > # I3SLS 153s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 153s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 153s > summary 153s 153s systemfit results 153s method: iterated 3SLS 153s 153s convergence achieved after 10 iterations 153s 153s N DF SSR detRCov OLS-R2 McElroy-R2 153s system 56 44 79.4 0.55 0.956 0.994 153s 153s N DF SSR MSE RMSE R2 Adj R2 153s Consumption 18 14 22.3 1.595 1.263 0.974 0.968 153s Investment 18 14 46.8 3.346 1.829 0.724 0.664 153s PrivateWages 20 16 10.2 0.639 0.799 0.987 0.985 153s 153s The covariance matrix of the residuals used for estimation 153s Consumption Investment PrivateWages 153s Consumption 1.307 0.750 -0.452 153s Investment 0.750 2.318 0.272 153s PrivateWages -0.452 0.272 0.530 153s 153s The covariance matrix of the residuals 153s Consumption Investment PrivateWages 153s Consumption 1.307 0.750 -0.452 153s Investment 0.750 2.318 0.272 153s PrivateWages -0.452 0.272 0.530 153s 153s The correlations of the residuals 153s Consumption Investment PrivateWages 153s Consumption 1.000 0.424 -0.542 153s Investment 0.424 1.000 0.254 153s PrivateWages -0.542 0.254 1.000 153s 153s 153s 3SLS estimates for 'Consumption' (equation 1) 153s Model Formula: consump ~ corpProf + corpProfLag + wages 153s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 153s gnpLag 153s 153s Estimate Std. Error t value Pr(>|t|) 153s (Intercept) 18.3252 1.5452 11.86 1.1e-08 *** 153s corpProf -0.0436 0.1470 -0.30 0.77 153s corpProfLag 0.1614 0.1127 1.43 0.17 153s wages 0.8127 0.0436 18.65 2.8e-11 *** 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s 153s Residual standard error: 1.263 on 14 degrees of freedom 153s Number of observations: 18 Degrees of Freedom: 14 153s SSR: 22.337 MSE: 1.595 Root MSE: 1.263 153s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 153s 153s 153s 3SLS estimates for 'Investment' (equation 2) 153s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 153s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 153s gnpLag 153s 153s Estimate Std. Error t value Pr(>|t|) 153s (Intercept) 30.2418 8.3674 3.61 0.00282 ** 153s corpProf -0.0437 0.2341 -0.19 0.85457 153s corpProfLag 0.7856 0.1993 3.94 0.00147 ** 153s capitalLag -0.2065 0.0397 -5.20 0.00014 *** 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s 153s Residual standard error: 1.829 on 14 degrees of freedom 153s Number of observations: 18 Degrees of Freedom: 14 153s SSR: 46.838 MSE: 3.346 Root MSE: 1.829 153s Multiple R-Squared: 0.724 Adjusted R-Squared: 0.664 153s 153s 153s 3SLS estimates for 'PrivateWages' (equation 3) 153s Model Formula: privWage ~ gnp + gnpLag + trend 153s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 153s gnpLag 153s 153s Estimate Std. Error t value Pr(>|t|) 153s (Intercept) 0.4741 1.1280 0.42 0.67983 153s gnp 0.4268 0.0296 14.44 1.4e-10 *** 153s gnpLag 0.1767 0.0330 5.35 6.5e-05 *** 153s trend 0.1201 0.0290 4.14 0.00076 *** 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s 153s Residual standard error: 0.799 on 16 degrees of freedom 153s Number of observations: 20 Degrees of Freedom: 16 153s SSR: 10.218 MSE: 0.639 Root MSE: 0.799 153s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 153s 153s > residuals 153s Consumption Investment PrivateWages 153s 1 NA NA NA 153s 2 -0.8546 -2.1226 -1.1687 153s 3 -0.7611 0.3684 0.4670 153s 4 -1.1233 0.5912 1.3216 153s 5 0.0781 -1.6694 -0.2108 153s 6 0.6467 0.2952 -0.4776 153s 7 NA NA NA 153s 8 1.8444 1.4348 -0.8884 153s 9 1.8309 1.0020 0.1781 153s 10 NA 2.7265 1.0734 153s 11 -0.3652 -1.0581 -0.4134 153s 12 -1.3877 -0.6431 0.4203 153s 13 NA NA 0.0623 153s 14 -0.1818 2.4214 0.7091 153s 15 -0.6438 0.2168 0.5845 153s 16 -0.3417 NA 0.2455 153s 17 1.9583 2.4607 -0.6474 153s 18 -0.4806 -0.0468 0.9840 153s 19 -0.2563 -3.3855 -0.5930 153s 20 1.4832 1.1550 -0.2586 153s 21 1.4514 0.6086 -1.1446 153s 22 -1.2351 1.3453 0.5196 153s > fitted 153s Consumption Investment PrivateWages 153s 1 NA NA NA 153s 2 42.8 1.923 26.7 153s 3 45.8 1.532 28.8 153s 4 50.3 4.609 32.8 153s 5 50.5 4.669 34.1 153s 6 52.0 4.805 35.9 153s 7 NA NA NA 153s 8 54.4 2.765 38.8 153s 9 55.5 1.998 39.0 153s 10 NA 2.373 40.2 153s 11 55.4 2.058 38.3 153s 12 52.3 -2.757 34.1 153s 13 NA NA 28.9 153s 14 46.7 -7.521 27.8 153s 15 49.3 -3.217 30.0 153s 16 51.6 NA 33.0 153s 17 55.7 -0.361 37.4 153s 18 59.2 2.047 40.0 153s 19 57.8 1.485 38.8 153s 20 60.1 0.145 41.9 153s 21 63.5 2.691 46.1 153s 22 70.9 3.555 52.8 153s > predict 153s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 153s 1 NA NA NA NA 153s 2 42.8 0.548 41.7 43.9 153s 3 45.8 0.618 44.5 47.0 153s 4 50.3 0.411 49.5 51.2 153s 5 50.5 0.481 49.6 51.5 153s 6 52.0 0.490 51.0 52.9 153s 7 NA NA NA NA 153s 8 54.4 0.396 53.6 55.2 153s 9 55.5 0.467 54.5 56.4 153s 10 NA NA NA NA 153s 11 55.4 0.811 53.7 57.0 153s 12 52.3 0.775 50.7 53.8 153s 13 NA NA NA NA 153s 14 46.7 0.665 45.3 48.0 153s 15 49.3 0.463 48.4 50.3 153s 16 51.6 0.381 50.9 52.4 153s 17 55.7 0.428 54.9 56.6 153s 18 59.2 0.360 58.5 59.9 153s 19 57.8 0.492 56.8 58.7 153s 20 60.1 0.508 59.1 61.1 153s 21 63.5 0.499 62.5 64.6 153s 22 70.9 0.761 69.4 72.5 153s Investment.pred Investment.se.fit Investment.lwr Investment.upr 153s 1 NA NA NA NA 153s 2 1.923 1.079 -0.2526 4.098 153s 3 1.532 0.766 -0.0119 3.075 153s 4 4.609 0.668 3.2632 5.954 153s 5 4.669 0.566 3.5280 5.811 153s 6 4.805 0.543 3.7104 5.899 153s 7 NA NA NA NA 153s 8 2.765 0.447 1.8648 3.665 153s 9 1.998 0.651 0.6860 3.310 153s 10 2.373 0.710 0.9434 3.804 153s 11 2.058 1.237 -0.4350 4.551 153s 12 -2.757 1.139 -5.0532 -0.461 153s 13 NA NA NA NA 153s 14 -7.521 1.094 -9.7261 -5.317 153s 15 -3.217 0.648 -4.5217 -1.912 153s 16 NA NA NA NA 153s 17 -0.361 0.615 -1.6007 0.879 153s 18 2.047 0.417 1.2060 2.888 153s 19 1.485 0.684 0.1062 2.865 153s 20 0.145 0.699 -1.2632 1.553 153s 21 2.691 0.614 1.4548 3.928 153s 22 3.555 0.887 1.7674 5.342 153s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 153s 1 NA NA NA NA 153s 2 26.7 0.330 26.0 27.3 153s 3 28.8 0.336 28.2 29.5 153s 4 32.8 0.340 32.1 33.5 153s 5 34.1 0.251 33.6 34.6 153s 6 35.9 0.259 35.4 36.4 153s 7 NA NA NA NA 153s 8 38.8 0.253 38.3 39.3 153s 9 39.0 0.240 38.5 39.5 153s 10 40.2 0.236 39.8 40.7 153s 11 38.3 0.307 37.7 38.9 153s 12 34.1 0.313 33.4 34.7 153s 13 28.9 0.376 28.2 29.7 153s 14 27.8 0.327 27.1 28.4 153s 15 30.0 0.322 29.4 30.7 153s 16 33.0 0.270 32.4 33.5 153s 17 37.4 0.275 36.9 38.0 153s 18 40.0 0.216 39.6 40.5 153s 19 38.8 0.314 38.2 39.4 153s 20 41.9 0.296 41.3 42.5 153s 21 46.1 0.317 45.5 46.8 153s 22 52.8 0.480 51.8 53.7 153s > model.frame 153s [1] TRUE 153s > model.matrix 153s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 153s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 153s [3] "Numeric: lengths (696, 672) differ" 153s > nobs 153s [1] 56 153s > linearHypothesis 153s Linear hypothesis test (Theil's F test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 45 153s 2 44 1 2.29 0.14 153s Linear hypothesis test (F statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 45 153s 2 44 1 2.89 0.096 . 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s Linear hypothesis test (Chi^2 statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df Chisq Pr(>Chisq) 153s 1 45 153s 2 44 1 2.89 0.089 . 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s Linear hypothesis test (Theil's F test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s Consumption_corpProfLag - PrivateWages_trend = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 46 153s 2 44 2 2.3 0.11 153s Linear hypothesis test (F statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s Consumption_corpProfLag - PrivateWages_trend = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df F Pr(>F) 153s 1 46 153s 2 44 2 2.9 0.066 . 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s Linear hypothesis test (Chi^2 statistic of a Wald test) 153s 153s Hypothesis: 153s Consumption_corpProf + Investment_capitalLag = 0 153s Consumption_corpProfLag - PrivateWages_trend = 0 153s 153s Model 1: restricted model 153s Model 2: kleinModel 153s 153s Res.Df Df Chisq Pr(>Chisq) 153s 1 46 153s 2 44 2 5.79 0.055 . 153s --- 153s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 153s > logLik 153s 'log Lik.' -72.2 (df=18) 153s 'log Lik.' -83.4 (df=18) 153s Estimating function 153s Consumption_(Intercept) Consumption_corpProf 153s Consumption_2 -4.4102 -61.801 153s Consumption_3 -1.0169 -16.947 153s Consumption_4 0.6316 11.712 153s Consumption_5 -2.4849 -50.366 153s Consumption_6 1.3496 25.671 153s Consumption_8 6.2136 109.641 153s Consumption_9 5.5588 105.303 153s Consumption_11 -2.3690 -39.659 153s Consumption_12 -3.3344 -44.601 153s Consumption_14 0.8298 8.317 153s Consumption_15 -2.5803 -32.264 153s Consumption_16 -2.1088 -30.539 153s Consumption_17 7.9903 119.154 153s Consumption_18 -0.6538 -12.697 153s Consumption_19 -5.8714 -112.192 153s Consumption_20 4.4259 78.161 153s Consumption_21 2.2655 46.209 153s Consumption_22 -0.9489 -21.517 153s Investment_2 1.9674 27.570 153s Investment_3 -0.3392 -5.652 153s Investment_4 -0.5776 -10.712 153s Investment_5 1.5305 31.021 153s Investment_6 -0.2467 -4.692 153s Investment_8 -1.2650 -22.320 153s Investment_9 -0.8831 -16.728 153s Investment_10 0.0000 0.000 153s Investment_11 0.9353 15.658 153s Investment_12 0.5224 6.988 153s Investment_14 -2.2467 -22.520 153s Investment_15 -0.2344 -2.931 153s Investment_17 -2.2188 -33.088 153s Investment_18 -0.0466 -0.905 153s Investment_19 3.0409 58.107 153s Investment_20 -1.0335 -18.251 153s Investment_21 -0.5381 -10.975 153s Investment_22 -1.2437 -28.202 153s PrivateWages_2 -4.0943 -57.374 153s PrivateWages_3 1.5700 26.162 153s PrivateWages_4 3.6522 67.727 153s PrivateWages_5 -3.9696 -80.460 153s PrivateWages_6 -0.7099 -13.503 153s PrivateWages_8 2.2578 39.840 153s PrivateWages_9 2.5772 48.821 153s PrivateWages_10 0.0000 0.000 153s PrivateWages_11 -3.3861 -56.686 153s PrivateWages_12 -0.4354 -5.824 153s PrivateWages_13 0.0000 0.000 153s PrivateWages_14 4.5081 45.187 153s PrivateWages_15 -0.1430 -1.788 153s PrivateWages_16 -0.3534 -5.118 153s PrivateWages_17 3.6864 54.972 153s PrivateWages_18 0.1281 2.488 153s PrivateWages_19 -8.7578 -167.347 153s PrivateWages_20 1.9940 35.215 153s PrivateWages_21 -1.7982 -36.678 153s PrivateWages_22 2.6643 60.414 153s Consumption_corpProfLag Consumption_wages 153s Consumption_2 -56.01 -131.52 153s Consumption_3 -12.61 -32.39 153s Consumption_4 10.67 22.27 153s Consumption_5 -45.72 -95.92 153s Consumption_6 26.18 52.02 153s Consumption_8 121.79 248.60 153s Consumption_9 110.06 232.23 153s Consumption_11 -51.41 -102.11 153s Consumption_12 -52.02 -132.22 153s Consumption_14 5.81 27.65 153s Consumption_15 -28.90 -96.33 153s Consumption_16 -25.94 -84.65 153s Consumption_17 111.86 333.82 153s Consumption_18 -11.51 -31.13 153s Consumption_19 -101.57 -289.06 153s Consumption_20 67.72 214.91 153s Consumption_21 43.05 121.02 153s Consumption_22 -20.02 -57.69 153s Investment_2 24.99 58.67 153s Investment_3 -4.21 -10.80 153s Investment_4 -9.76 -20.36 153s Investment_5 28.16 59.08 153s Investment_6 -4.79 -9.51 153s Investment_8 -24.79 -50.61 153s Investment_9 -17.48 -36.89 153s Investment_10 0.00 0.00 153s Investment_11 20.30 40.31 153s Investment_12 8.15 20.72 153s Investment_14 -15.73 -74.88 153s Investment_15 -2.63 -8.75 153s Investment_17 -31.06 -92.70 153s Investment_18 -0.82 -2.22 153s Investment_19 52.61 149.71 153s Investment_20 -15.81 -50.18 153s Investment_21 -10.22 -28.74 153s Investment_22 -26.24 -75.61 153s PrivateWages_2 -52.00 -122.10 153s PrivateWages_3 19.47 50.00 153s PrivateWages_4 61.72 128.76 153s PrivateWages_5 -73.04 -153.23 153s PrivateWages_6 -13.77 -27.36 153s PrivateWages_8 44.25 90.33 153s PrivateWages_9 51.03 107.67 153s PrivateWages_10 0.00 0.00 153s PrivateWages_11 -73.48 -145.95 153s PrivateWages_12 -6.79 -17.27 153s PrivateWages_13 0.00 0.00 153s PrivateWages_14 31.56 150.24 153s PrivateWages_15 -1.60 -5.34 153s PrivateWages_16 -4.35 -14.19 153s PrivateWages_17 51.61 154.01 153s PrivateWages_18 2.25 6.10 153s PrivateWages_19 -151.51 -431.17 153s PrivateWages_20 30.51 96.82 153s PrivateWages_21 -34.17 -96.06 153s PrivateWages_22 56.22 161.97 153s Investment_(Intercept) Investment_corpProf 153s Consumption_2 1.9908 26.734 153s Consumption_3 0.4591 7.651 153s Consumption_4 -0.2851 -5.368 153s Consumption_5 1.1217 23.127 153s Consumption_6 -0.6092 -11.762 153s Consumption_8 -2.8049 -49.183 153s Consumption_9 -2.5093 -48.961 153s Consumption_11 1.0694 18.405 153s Consumption_12 1.5052 20.306 153s Consumption_14 -0.3746 -3.777 153s Consumption_15 1.1648 15.147 153s Consumption_16 0.0000 0.000 153s Consumption_17 -3.6069 -53.782 153s Consumption_18 0.2951 5.754 153s Consumption_19 2.6504 51.112 153s Consumption_20 -1.9979 -35.052 153s Consumption_21 -1.0227 -20.634 153s Consumption_22 0.4283 9.753 153s Investment_2 -1.8422 -24.739 153s Investment_3 0.3176 5.293 153s Investment_4 0.5409 10.184 153s Investment_5 -1.4331 -29.546 153s Investment_6 0.2310 4.459 153s Investment_8 1.1844 20.769 153s Investment_9 0.8269 16.134 153s Investment_10 2.3608 47.771 153s Investment_11 -0.8758 -15.072 153s Investment_12 -0.4892 -6.600 153s Investment_14 2.1037 21.212 153s Investment_15 0.2195 2.854 153s Investment_17 2.0776 30.979 153s Investment_18 0.0436 0.851 153s Investment_19 -2.8474 -54.911 153s Investment_20 0.9677 16.978 153s Investment_21 0.5038 10.165 153s Investment_22 1.1646 26.516 153s PrivateWages_2 2.2726 30.518 153s PrivateWages_3 -0.8714 -14.524 153s PrivateWages_4 -2.0272 -38.170 153s PrivateWages_5 2.2034 45.428 153s PrivateWages_6 0.3940 7.607 153s PrivateWages_8 -1.2532 -21.975 153s PrivateWages_9 -1.4305 -27.911 153s PrivateWages_10 -2.6709 -54.046 153s PrivateWages_11 1.8795 32.347 153s PrivateWages_12 0.2417 3.260 153s PrivateWages_13 0.0000 0.000 153s PrivateWages_14 -2.5023 -25.230 153s PrivateWages_15 0.0794 1.032 153s PrivateWages_16 0.0000 0.000 153s PrivateWages_17 -2.0461 -30.509 153s PrivateWages_18 -0.0711 -1.386 153s PrivateWages_19 4.8611 93.745 153s PrivateWages_20 -1.1068 -19.419 153s PrivateWages_21 0.9981 20.138 153s PrivateWages_22 -1.4788 -33.672 153s Investment_corpProfLag Investment_capitalLag 153s Consumption_2 25.283 363.92 153s Consumption_3 5.692 83.82 153s Consumption_4 -4.818 -52.60 153s Consumption_5 20.639 212.79 153s Consumption_6 -11.819 -117.39 153s Consumption_8 -54.976 -570.52 153s Consumption_9 -49.684 -520.93 153s Consumption_11 23.206 230.67 153s Consumption_12 23.481 326.17 153s Consumption_14 -2.622 -77.57 153s Consumption_15 13.045 235.28 153s Consumption_16 0.000 0.00 153s Consumption_17 -50.497 -713.09 153s Consumption_18 5.194 58.97 153s Consumption_19 45.852 534.85 153s Consumption_20 -30.568 -399.38 153s Consumption_21 -19.431 -205.77 153s Consumption_22 9.038 87.60 153s Investment_2 -23.396 -336.76 153s Investment_3 3.938 57.99 153s Investment_4 9.141 99.79 153s Investment_5 -26.369 -271.86 153s Investment_6 4.481 44.51 153s Investment_8 23.215 240.92 153s Investment_9 16.372 171.66 153s Investment_10 49.812 497.18 153s Investment_11 -19.004 -188.91 153s Investment_12 -7.631 -106.01 153s Investment_14 14.726 435.68 153s Investment_15 2.458 44.34 153s Investment_17 29.086 410.74 153s Investment_18 0.768 8.72 153s Investment_19 -49.260 -574.60 153s Investment_20 14.806 193.44 153s Investment_21 9.573 101.37 153s Investment_22 24.572 238.15 153s PrivateWages_2 28.862 415.43 153s PrivateWages_3 -10.806 -159.12 153s PrivateWages_4 -34.259 -374.01 153s PrivateWages_5 40.542 417.98 153s PrivateWages_6 7.644 75.93 153s PrivateWages_8 -24.563 -254.91 153s PrivateWages_9 -28.324 -296.97 153s PrivateWages_10 -56.356 -562.49 153s PrivateWages_11 40.785 405.41 153s PrivateWages_12 3.770 52.37 153s PrivateWages_13 0.000 0.00 153s PrivateWages_14 -17.516 -518.22 153s PrivateWages_15 0.889 16.03 153s PrivateWages_16 0.000 0.00 153s PrivateWages_17 -28.646 -404.52 153s PrivateWages_18 -1.251 -14.21 153s PrivateWages_19 84.097 980.97 153s PrivateWages_20 -16.934 -221.25 153s PrivateWages_21 18.964 200.82 153s PrivateWages_22 -31.204 -302.42 153s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 153s Consumption_2 -4.7927 -225.59 -215.2 153s Consumption_3 -1.1051 -54.79 -50.4 153s Consumption_4 0.6863 38.81 34.4 153s Consumption_5 -2.7004 -163.88 -154.5 153s Consumption_6 1.4666 88.89 83.7 153s Consumption_8 6.7526 405.14 432.2 153s Consumption_9 6.0409 376.16 389.0 153s Consumption_11 -2.5745 -164.03 -172.5 153s Consumption_12 -3.6236 -198.69 -221.8 153s Consumption_14 0.9017 37.99 39.9 153s Consumption_15 -2.8041 -143.62 -126.5 153s Consumption_16 -2.2917 -126.82 -113.9 153s Consumption_17 8.6833 498.37 472.4 153s Consumption_18 -0.7105 -47.73 -44.5 153s Consumption_19 -6.3806 -437.15 -414.7 153s Consumption_20 4.8097 321.50 292.9 153s Consumption_21 2.4620 184.32 171.1 153s Consumption_22 -1.0312 -89.59 -78.1 153s Investment_2 2.6290 123.75 118.0 153s Investment_3 -0.4532 -22.47 -20.7 153s Investment_4 -0.7719 -43.64 -38.7 153s Investment_5 2.0451 124.11 117.0 153s Investment_6 -0.3296 -19.98 -18.8 153s Investment_8 -1.6903 -101.41 -108.2 153s Investment_9 -1.1800 -73.48 -76.0 153s Investment_10 -3.3690 -217.54 -217.3 153s Investment_11 1.2498 79.63 83.7 153s Investment_12 0.6981 38.28 42.7 153s Investment_14 -3.0022 -126.47 -133.0 153s Investment_15 -0.3132 -16.04 -14.1 153s Investment_17 -2.9649 -170.17 -161.3 153s Investment_18 -0.0623 -4.18 -3.9 153s Investment_19 4.0635 278.40 264.1 153s Investment_20 -1.3810 -92.31 -84.1 153s Investment_21 -0.7190 -53.83 -50.0 153s Investment_22 -1.6619 -144.39 -125.8 153s PrivateWages_2 -8.0595 -379.36 -361.9 153s PrivateWages_3 3.0904 153.23 140.9 153s PrivateWages_4 7.1892 406.50 360.2 153s PrivateWages_5 -7.8142 -474.21 -447.0 153s PrivateWages_6 -1.3974 -84.70 -79.8 153s PrivateWages_8 4.4445 266.66 284.4 153s PrivateWages_9 5.0731 315.90 326.7 153s PrivateWages_10 9.4721 611.61 611.0 153s PrivateWages_11 -6.6655 -424.67 -446.6 153s PrivateWages_12 -0.8571 -46.99 -52.5 153s PrivateWages_13 -4.8476 -227.73 -258.9 153s PrivateWages_14 8.8741 373.85 393.1 153s PrivateWages_15 -0.2815 -14.42 -12.7 153s PrivateWages_16 -0.6957 -38.50 -34.6 153s PrivateWages_17 7.2565 416.48 394.8 153s PrivateWages_18 0.2522 16.94 15.8 153s PrivateWages_19 -17.2396 -1181.13 -1120.6 153s PrivateWages_20 3.9252 262.38 239.0 153s PrivateWages_21 -3.5398 -265.01 -246.0 153s PrivateWages_22 5.2446 455.65 397.0 153s PrivateWages_trend 153s Consumption_2 47.927 153s Consumption_3 9.946 153s Consumption_4 -5.491 153s Consumption_5 18.903 153s Consumption_6 -8.800 153s Consumption_8 -27.010 153s Consumption_9 -18.123 153s Consumption_11 2.574 153s Consumption_12 0.000 153s Consumption_14 1.803 153s Consumption_15 -8.412 153s Consumption_16 -9.167 153s Consumption_17 43.417 153s Consumption_18 -4.263 153s Consumption_19 -44.664 153s Consumption_20 38.478 153s Consumption_21 22.158 153s Consumption_22 -10.312 153s Investment_2 -26.290 153s Investment_3 4.079 153s Investment_4 6.175 153s Investment_5 -14.316 153s Investment_6 1.978 153s Investment_8 6.761 153s Investment_9 3.540 153s Investment_10 6.738 153s Investment_11 -1.250 153s Investment_12 0.000 153s Investment_14 -6.004 153s Investment_15 -0.940 153s Investment_17 -14.825 153s Investment_18 -0.374 153s Investment_19 28.444 153s Investment_20 -11.048 153s Investment_21 -6.471 153s Investment_22 -16.619 153s PrivateWages_2 80.595 153s PrivateWages_3 -27.814 153s PrivateWages_4 -57.514 153s PrivateWages_5 54.699 153s PrivateWages_6 8.384 153s PrivateWages_8 -17.778 153s PrivateWages_9 -15.219 153s PrivateWages_10 -18.944 153s PrivateWages_11 6.666 153s PrivateWages_12 0.000 153s PrivateWages_13 -4.848 153s PrivateWages_14 17.748 153s PrivateWages_15 -0.844 153s PrivateWages_16 -2.783 153s PrivateWages_17 36.283 153s PrivateWages_18 1.513 153s PrivateWages_19 -120.677 153s PrivateWages_20 31.402 153s PrivateWages_21 -31.858 153s PrivateWages_22 52.446 153s [1] TRUE 153s > Bread 153s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 153s [1,] 133.708 -4.1980 0.8576 153s [2,] -4.198 1.2100 -0.6653 153s [3,] 0.858 -0.6653 0.7119 153s [4,] -1.738 -0.1324 -0.0277 153s [5,] 125.235 3.6584 5.4171 153s [6,] -6.184 0.8150 -0.6677 153s [7,] 2.270 -0.5431 0.6187 153s [8,] -0.265 -0.0441 -0.0204 153s [9,] -39.027 0.3871 1.7425 153s [10,] 0.490 -0.0701 0.0456 153s [11,] 0.147 0.0648 -0.0766 153s [12,] 0.260 0.0523 0.0256 153s Consumption_wages Investment_(Intercept) Investment_corpProf 153s [1,] -1.73822 125.23 -6.18369 153s [2,] -0.13241 3.66 0.81500 153s [3,] -0.02768 5.42 -0.66769 153s [4,] 0.10634 -6.40 0.07260 153s [5,] -6.40260 3920.72 -66.16832 153s [6,] 0.07260 -66.17 3.06783 153s [7,] -0.07286 52.35 -2.32206 153s [8,] 0.03170 -18.13 0.25629 153s [9,] 0.06731 57.07 -0.51824 153s [10,] -0.00202 2.27 0.00785 153s [11,] 0.00109 -3.34 0.00101 153s [12,] -0.03773 -1.63 0.03241 153s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 153s [1,] 2.27003 -0.26469 -39.0267 153s [2,] -0.54312 -0.04408 0.3871 153s [3,] 0.61867 -0.02038 1.7425 153s [4,] -0.07286 0.03170 0.0673 153s [5,] 52.35486 -18.13066 57.0659 153s [6,] -2.32206 0.25629 -0.5182 153s [7,] 2.22379 -0.24386 -0.7311 153s [8,] -0.24386 0.08845 -0.1851 153s [9,] -0.73109 -0.18506 71.2482 153s [10,] 0.01103 -0.01288 -0.3220 153s [11,] 0.00202 0.01653 -0.8851 153s [12,] -0.04341 0.00871 0.7698 153s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 153s [1,] 0.49031 0.147339 0.260437 153s [2,] -0.07008 0.064790 0.052347 153s [3,] 0.04558 -0.076595 0.025629 153s [4,] -0.00202 0.001086 -0.037728 153s [5,] 2.27149 -3.339873 -1.627913 153s [6,] 0.00785 0.001013 0.032414 153s [7,] 0.01103 0.002018 -0.043407 153s [8,] -0.01288 0.016530 0.008714 153s [9,] -0.32199 -0.885080 0.769761 153s [10,] 0.04892 -0.044549 -0.013616 153s [11,] -0.04455 0.061046 0.000449 153s [12,] -0.01362 0.000449 0.047057 153s > 153s BEGIN TEST KleinI_noMat.R 153s 153s R version 4.3.2 (2023-10-31) -- "Eye Holes" 153s Copyright (C) 2023 The R Foundation for Statistical Computing 153s Platform: x86_64-pc-linux-gnu (64-bit) 153s 153s R is free software and comes with ABSOLUTELY NO WARRANTY. 153s You are welcome to redistribute it under certain conditions. 153s Type 'license()' or 'licence()' for distribution details. 153s 153s R is a collaborative project with many contributors. 153s Type 'contributors()' for more information and 153s 'citation()' on how to cite R or R packages in publications. 153s 153s Type 'demo()' for some demos, 'help()' for on-line help, or 153s 'help.start()' for an HTML browser interface to help. 153s Type 'q()' to quit R. 153s 153s > library( "systemfit" ) 153s Loading required package: Matrix 154s Loading required package: car 154s Loading required package: carData 154s Loading required package: lmtest 154s Loading required package: zoo 154s 154s Attaching package: ‘zoo’ 154s 154s The following objects are masked from ‘package:base’: 154s 154s as.Date, as.Date.numeric 154s 154s 154s Please cite the 'systemfit' package as: 154s 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/. 154s 154s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 154s https://r-forge.r-project.org/projects/systemfit/ 154s > options( warn = 1 ) 154s > options( digits = 3 ) 154s > 154s > data( "KleinI" ) 154s > eqConsump <- consump ~ corpProf + corpProfLag + wages 154s > eqInvest <- invest ~ corpProf + corpProfLag + capitalLag 154s > eqPrivWage <- privWage ~ gnp + gnpLag + trend 154s > inst <- ~ govExp + taxes + govWage + trend + capitalLag + corpProfLag + gnpLag 154s > system <- list( Consumption = eqConsump, Investment = eqInvest, 154s + PrivateWages = eqPrivWage ) 154s > restrict <- c( "Consumption_corpProf + Investment_capitalLag = 0" ) 154s > restrict2 <- c( restrict, "Consumption_corpProfLag - PrivateWages_trend = 0" ) 154s > 154s > for( dataNo in 1:5 ) { 154s + # set some values of some variables to NA 154s + if( dataNo == 2 ) { 154s + KleinI$gnpLag[ 7 ] <- NA 154s + } else if( dataNo == 3 ) { 154s + KleinI$wages[ 10 ] <- NA 154s + } else if( dataNo == 4 ) { 154s + KleinI$corpProf[ 13 ] <- NA 154s + } else if( dataNo == 5 ) { 154s + KleinI$invest[ 16 ] <- NA 154s + } 154s + 154s + # single-equation OLS 154s + lmConsump <- lm( eqConsump, data = KleinI ) 154s + lmInvest <- lm( eqInvest, data = KleinI ) 154s + lmPrivWage <- lm( eqPrivWage, data = KleinI ) 154s + 154s + for( methodNo in 1:5 ) { 154s + method <- c( "OLS", "2SLS", "SUR", "3SLS", "3SLS" )[ methodNo ] 154s + maxit <- ifelse( methodNo == 5, 500, 1 ) 154s + 154s + cat( "> \n> # ", ifelse( maxit == 1, "", "I" ), method, "\n", sep = "" ) 154s + if( method %in% c( "OLS", "WLS", "SUR" ) ) { 154s + kleinModel <- systemfit( system, method = method, data = KleinI, 154s + methodResidCov = ifelse( method == "OLS", "geomean", "noDfCor" ), 154s + maxit = maxit, useMatrix = FALSE ) 154s + } else { 154s + kleinModel <- systemfit( system, method = method, data = KleinI, 154s + inst = inst, methodResidCov = "noDfCor", maxit = maxit, 154s + useMatrix = FALSE ) 154s + } 154s + cat( "> summary\n" ) 154s + print( summary( kleinModel ) ) 154s + if( method == "OLS" ) { 154s + cat( "compare coef with single-equation OLS\n" ) 154s + print( all.equal( coef( kleinModel ), 154s + c( coef( lmConsump ), coef( lmInvest ), coef( lmPrivWage ) ), 154s + check.attributes = FALSE ) ) 154s + } 154s + cat( "> residuals\n" ) 154s + print( residuals( kleinModel ) ) 154s + cat( "> fitted\n" ) 154s + print( fitted( kleinModel ) ) 154s + cat( "> predict\n" ) 154s + print( predict( kleinModel, se.fit = TRUE, 154s + interval = ifelse( methodNo %in% c( 1, 4 ), "prediction", "confidence" ), 154s + useDfSys = methodNo %in% c( 1, 3, 5 ) ) ) 154s + cat( "> model.frame\n" ) 154s + if( methodNo == 1 ) { 154s + mfOls <- model.frame( kleinModel ) 154s + print( mfOls ) 154s + } else if( methodNo == 2 ) { 154s + mf2sls <- model.frame( kleinModel ) 154s + print( mf2sls ) 154s + } else if( methodNo == 3 ) { 154s + print( all.equal( mfOls, model.frame( kleinModel ) ) ) 154s + } else { 154s + print( all.equal( mf2sls, model.frame( kleinModel ) ) ) 154s + } 154s + cat( "> model.matrix\n" ) 154s + if( methodNo == 1 ) { 154s + mmOls <- model.matrix( kleinModel ) 154s + print( mmOls ) 154s + } else { 154s + print( all.equal( mmOls, model.matrix( kleinModel ) ) ) 154s + } 154s + cat( "> nobs\n" ) 154s + print( nobs( kleinModel ) ) 154s + cat( "> linearHypothesis\n" ) 154s + print( linearHypothesis( kleinModel, restrict ) ) 154s + print( linearHypothesis( kleinModel, restrict, test = "F" ) ) 154s + print( linearHypothesis( kleinModel, restrict, test = "Chisq" ) ) 154s + print( linearHypothesis( kleinModel, restrict2 ) ) 154s + print( linearHypothesis( kleinModel, restrict2, test = "F" ) ) 154s + print( linearHypothesis( kleinModel, restrict2, test = "Chisq" ) ) 154s + cat( "> logLik\n" ) 154s + print( logLik( kleinModel ) ) 154s + print( logLik( kleinModel, residCovDiag = TRUE ) ) 154s + if( method == "OLS" ) { 154s + cat( "compare log likelihood value with single-equation OLS\n" ) 154s + print( all.equal( logLik( kleinModel, residCovDiag = TRUE ), 154s + logLik( lmConsump ) + logLik( lmInvest ) + logLik( lmPrivWage ), 154s + check.attributes = FALSE ) ) 154s + } 154s + } 154s + } 154s > 154s > # OLS 154s > summary 154s 154s systemfit results 154s method: OLS 154s 154s N DF SSR detRCov OLS-R2 McElroy-R2 154s system 63 51 45.2 0.371 0.977 0.991 154s 154s N DF SSR MSE RMSE R2 Adj R2 154s Consumption 21 17 17.9 1.052 1.026 0.981 0.978 154s Investment 21 17 17.3 1.019 1.009 0.931 0.919 154s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 154s 154s The covariance matrix of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.0517 0.0611 -0.470 154s Investment 0.0611 1.0190 0.150 154s PrivateWages -0.4704 0.1497 0.589 154s 154s The correlations of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.0000 0.0591 -0.598 154s Investment 0.0591 1.0000 0.193 154s PrivateWages -0.5979 0.1933 1.000 154s 154s 154s OLS estimates for 'Consumption' (equation 1) 154s Model Formula: consump ~ corpProf + corpProfLag + wages 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 16.2366 1.3027 12.46 5.6e-10 *** 154s corpProf 0.1929 0.0912 2.12 0.049 * 154s corpProfLag 0.0899 0.0906 0.99 0.335 154s wages 0.7962 0.0399 19.93 3.2e-13 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.026 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 154s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 154s 154s 154s OLS estimates for 'Investment' (equation 2) 154s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 10.1258 5.4655 1.85 0.08137 . 154s corpProf 0.4796 0.0971 4.94 0.00012 *** 154s corpProfLag 0.3330 0.1009 3.30 0.00421 ** 154s capitalLag -0.1118 0.0267 -4.18 0.00062 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.009 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 154s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 154s 154s 154s OLS estimates for 'PrivateWages' (equation 3) 154s Model Formula: privWage ~ gnp + gnpLag + trend 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 1.4970 1.2700 1.18 0.25474 154s gnp 0.4395 0.0324 13.56 1.5e-10 *** 154s gnpLag 0.1461 0.0374 3.90 0.00114 ** 154s trend 0.1302 0.0319 4.08 0.00078 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 0.767 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 154s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 154s 154s compare coef with single-equation OLS 154s [1] TRUE 154s > residuals 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 -0.32389 -0.0668 -1.2942 154s 3 -1.25001 -0.0476 0.2957 154s 4 -1.56574 1.2467 1.1877 154s 5 -0.49350 -1.3512 -0.1358 154s 6 0.00761 0.4154 -0.4654 154s 7 0.86910 1.4923 -0.4838 154s 8 1.33848 0.7889 -0.7281 154s 9 1.05498 -0.6317 0.3392 154s 10 -0.58856 1.0830 1.1957 154s 11 0.28231 0.2791 -0.1508 154s 12 -0.22965 0.0369 0.5942 154s 13 -0.32213 0.3659 0.1027 154s 14 0.32228 0.2237 0.4503 154s 15 -0.05801 -0.1728 0.2816 154s 16 -0.03466 0.0101 0.0138 154s 17 1.61650 0.9719 -0.8508 154s 18 -0.43597 0.0516 0.9956 154s 19 0.21005 -2.5656 -0.4688 154s 20 0.98920 -0.6866 -0.3795 154s 21 0.78508 -0.7807 -1.0909 154s 22 -2.17345 -0.6623 0.5917 154s > fitted 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 42.2 -0.133 26.8 154s 3 46.3 1.948 29.0 154s 4 50.8 3.953 32.9 154s 5 51.1 4.351 34.0 154s 6 52.6 4.685 35.9 154s 7 54.2 4.108 37.9 154s 8 54.9 3.411 38.6 154s 9 56.2 3.632 38.9 154s 10 58.4 4.017 40.1 154s 11 54.7 0.721 38.1 154s 12 51.1 -3.437 33.9 154s 13 45.9 -6.566 28.9 154s 14 46.2 -5.324 28.0 154s 15 48.8 -2.827 30.3 154s 16 51.3 -1.310 33.2 154s 17 56.1 1.128 37.7 154s 18 59.1 1.948 40.0 154s 19 57.3 0.666 38.7 154s 20 60.6 1.987 42.0 154s 21 64.2 4.081 46.1 154s 22 71.9 5.562 52.7 154s > predict 154s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 154s 1 NA NA NA NA 154s 2 42.2 0.462 40.0 44.5 154s 3 46.3 0.518 43.9 48.6 154s 4 50.8 0.341 48.6 52.9 154s 5 51.1 0.396 48.9 53.3 154s 6 52.6 0.397 50.4 54.8 154s 7 54.2 0.359 52.0 56.4 154s 8 54.9 0.327 52.7 57.0 154s 9 56.2 0.350 54.1 58.4 154s 10 58.4 0.370 56.2 60.6 154s 11 54.7 0.606 52.3 57.1 154s 12 51.1 0.484 48.9 53.4 154s 13 45.9 0.629 43.5 48.3 154s 14 46.2 0.602 43.8 48.6 154s 15 48.8 0.374 46.6 50.9 154s 16 51.3 0.333 49.2 53.5 154s 17 56.1 0.366 53.9 58.3 154s 18 59.1 0.321 57.0 61.3 154s 19 57.3 0.371 55.1 59.5 154s 20 60.6 0.434 58.4 62.8 154s 21 64.2 0.425 62.0 66.4 154s 22 71.9 0.666 69.4 74.3 154s Investment.pred Investment.se.fit Investment.lwr Investment.upr 154s 1 NA NA NA NA 154s 2 -0.133 0.607 -2.498 2.231 154s 3 1.948 0.499 -0.313 4.208 154s 4 3.953 0.449 1.735 6.171 154s 5 4.351 0.371 2.192 6.510 154s 6 4.685 0.349 2.540 6.829 154s 7 4.108 0.329 1.976 6.239 154s 8 3.411 0.292 1.301 5.521 154s 9 3.632 0.389 1.460 5.804 154s 10 4.017 0.447 1.801 6.233 154s 11 0.721 0.601 -1.638 3.080 154s 12 -3.437 0.507 -5.704 -1.169 154s 13 -6.566 0.616 -8.940 -4.192 154s 14 -5.324 0.694 -7.783 -2.865 154s 15 -2.827 0.373 -4.988 -0.667 154s 16 -1.310 0.320 -3.436 0.816 154s 17 1.128 0.347 -1.015 3.271 154s 18 1.948 0.243 -0.136 4.033 154s 19 0.666 0.312 -1.456 2.787 154s 20 1.987 0.366 -0.169 4.143 154s 21 4.081 0.332 1.948 6.214 154s 22 5.562 0.461 3.334 7.790 154s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 154s 1 NA NA NA NA 154s 2 26.8 0.354 25.1 28.5 154s 3 29.0 0.355 27.3 30.7 154s 4 32.9 0.354 31.2 34.6 154s 5 34.0 0.269 32.4 35.7 154s 6 35.9 0.266 34.2 37.5 154s 7 37.9 0.266 36.3 39.5 154s 8 38.6 0.273 37.0 40.3 154s 9 38.9 0.261 37.2 40.5 154s 10 40.1 0.247 38.5 41.7 154s 11 38.1 0.354 36.4 39.7 154s 12 33.9 0.363 32.2 35.6 154s 13 28.9 0.429 27.1 30.7 154s 14 28.0 0.376 26.3 29.8 154s 15 30.3 0.371 28.6 32.0 154s 16 33.2 0.310 31.5 34.8 154s 17 37.7 0.305 36.0 39.3 154s 18 40.0 0.238 38.4 41.6 154s 19 38.7 0.357 37.0 40.4 154s 20 42.0 0.321 40.3 43.6 154s 21 46.1 0.335 44.4 47.8 154s 22 52.7 0.502 50.9 54.5 154s > model.frame 154s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 154s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 154s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 154s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 154s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 154s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 154s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 154s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 154s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 154s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 154s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 154s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 154s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 154s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 154s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 154s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 154s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 154s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 154s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 154s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 154s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 154s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 154s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 154s trend 154s 1 -11 154s 2 -10 154s 3 -9 154s 4 -8 154s 5 -7 154s 6 -6 154s 7 -5 154s 8 -4 154s 9 -3 154s 10 -2 154s 11 -1 154s 12 0 154s 13 1 154s 14 2 154s 15 3 154s 16 4 154s 17 5 154s 18 6 154s 19 7 154s 20 8 154s 21 9 154s 22 10 154s > model.matrix 154s Consumption_(Intercept) Consumption_corpProf 154s Consumption_2 1 12.4 154s Consumption_3 1 16.9 154s Consumption_4 1 18.4 154s Consumption_5 1 19.4 154s Consumption_6 1 20.1 154s Consumption_7 1 19.6 154s Consumption_8 1 19.8 154s Consumption_9 1 21.1 154s Consumption_10 1 21.7 154s Consumption_11 1 15.6 154s Consumption_12 1 11.4 154s Consumption_13 1 7.0 154s Consumption_14 1 11.2 154s Consumption_15 1 12.3 154s Consumption_16 1 14.0 154s Consumption_17 1 17.6 154s Consumption_18 1 17.3 154s Consumption_19 1 15.3 154s Consumption_20 1 19.0 154s Consumption_21 1 21.1 154s Consumption_22 1 23.5 154s Investment_2 0 0.0 154s Investment_3 0 0.0 154s Investment_4 0 0.0 154s Investment_5 0 0.0 154s Investment_6 0 0.0 154s Investment_7 0 0.0 154s Investment_8 0 0.0 154s Investment_9 0 0.0 154s Investment_10 0 0.0 154s Investment_11 0 0.0 154s Investment_12 0 0.0 154s Investment_13 0 0.0 154s Investment_14 0 0.0 154s Investment_15 0 0.0 154s Investment_16 0 0.0 154s Investment_17 0 0.0 154s Investment_18 0 0.0 154s Investment_19 0 0.0 154s Investment_20 0 0.0 154s Investment_21 0 0.0 154s Investment_22 0 0.0 154s PrivateWages_2 0 0.0 154s PrivateWages_3 0 0.0 154s PrivateWages_4 0 0.0 154s PrivateWages_5 0 0.0 154s PrivateWages_6 0 0.0 154s PrivateWages_7 0 0.0 154s PrivateWages_8 0 0.0 154s PrivateWages_9 0 0.0 154s PrivateWages_10 0 0.0 154s PrivateWages_11 0 0.0 154s PrivateWages_12 0 0.0 154s PrivateWages_13 0 0.0 154s PrivateWages_14 0 0.0 154s PrivateWages_15 0 0.0 154s PrivateWages_16 0 0.0 154s PrivateWages_17 0 0.0 154s PrivateWages_18 0 0.0 154s PrivateWages_19 0 0.0 154s PrivateWages_20 0 0.0 154s PrivateWages_21 0 0.0 154s PrivateWages_22 0 0.0 154s Consumption_corpProfLag Consumption_wages 154s Consumption_2 12.7 28.2 154s Consumption_3 12.4 32.2 154s Consumption_4 16.9 37.0 154s Consumption_5 18.4 37.0 154s Consumption_6 19.4 38.6 154s Consumption_7 20.1 40.7 154s Consumption_8 19.6 41.5 154s Consumption_9 19.8 42.9 154s Consumption_10 21.1 45.3 154s Consumption_11 21.7 42.1 154s Consumption_12 15.6 39.3 154s Consumption_13 11.4 34.3 154s Consumption_14 7.0 34.1 154s Consumption_15 11.2 36.6 154s Consumption_16 12.3 39.3 154s Consumption_17 14.0 44.2 154s Consumption_18 17.6 47.7 154s Consumption_19 17.3 45.9 154s Consumption_20 15.3 49.4 154s Consumption_21 19.0 53.0 154s Consumption_22 21.1 61.8 154s Investment_2 0.0 0.0 154s Investment_3 0.0 0.0 154s Investment_4 0.0 0.0 154s Investment_5 0.0 0.0 154s Investment_6 0.0 0.0 154s Investment_7 0.0 0.0 154s Investment_8 0.0 0.0 154s Investment_9 0.0 0.0 154s Investment_10 0.0 0.0 154s Investment_11 0.0 0.0 154s Investment_12 0.0 0.0 154s Investment_13 0.0 0.0 154s Investment_14 0.0 0.0 154s Investment_15 0.0 0.0 154s Investment_16 0.0 0.0 154s Investment_17 0.0 0.0 154s Investment_18 0.0 0.0 154s Investment_19 0.0 0.0 154s Investment_20 0.0 0.0 154s Investment_21 0.0 0.0 154s Investment_22 0.0 0.0 154s PrivateWages_2 0.0 0.0 154s PrivateWages_3 0.0 0.0 154s PrivateWages_4 0.0 0.0 154s PrivateWages_5 0.0 0.0 154s PrivateWages_6 0.0 0.0 154s PrivateWages_7 0.0 0.0 154s PrivateWages_8 0.0 0.0 154s PrivateWages_9 0.0 0.0 154s PrivateWages_10 0.0 0.0 154s PrivateWages_11 0.0 0.0 154s PrivateWages_12 0.0 0.0 154s PrivateWages_13 0.0 0.0 154s PrivateWages_14 0.0 0.0 154s PrivateWages_15 0.0 0.0 154s PrivateWages_16 0.0 0.0 154s PrivateWages_17 0.0 0.0 154s PrivateWages_18 0.0 0.0 154s PrivateWages_19 0.0 0.0 154s PrivateWages_20 0.0 0.0 154s PrivateWages_21 0.0 0.0 154s PrivateWages_22 0.0 0.0 154s Investment_(Intercept) Investment_corpProf 154s Consumption_2 0 0.0 154s Consumption_3 0 0.0 154s Consumption_4 0 0.0 154s Consumption_5 0 0.0 154s Consumption_6 0 0.0 154s Consumption_7 0 0.0 154s Consumption_8 0 0.0 154s Consumption_9 0 0.0 154s Consumption_10 0 0.0 154s Consumption_11 0 0.0 154s Consumption_12 0 0.0 154s Consumption_13 0 0.0 154s Consumption_14 0 0.0 154s Consumption_15 0 0.0 154s Consumption_16 0 0.0 154s Consumption_17 0 0.0 154s Consumption_18 0 0.0 154s Consumption_19 0 0.0 154s Consumption_20 0 0.0 154s Consumption_21 0 0.0 154s Consumption_22 0 0.0 154s Investment_2 1 12.4 154s Investment_3 1 16.9 154s Investment_4 1 18.4 154s Investment_5 1 19.4 154s Investment_6 1 20.1 154s Investment_7 1 19.6 154s Investment_8 1 19.8 154s Investment_9 1 21.1 154s Investment_10 1 21.7 154s Investment_11 1 15.6 154s Investment_12 1 11.4 154s Investment_13 1 7.0 154s Investment_14 1 11.2 154s Investment_15 1 12.3 154s Investment_16 1 14.0 154s Investment_17 1 17.6 154s Investment_18 1 17.3 154s Investment_19 1 15.3 154s Investment_20 1 19.0 154s Investment_21 1 21.1 154s Investment_22 1 23.5 154s PrivateWages_2 0 0.0 154s PrivateWages_3 0 0.0 154s PrivateWages_4 0 0.0 154s PrivateWages_5 0 0.0 154s PrivateWages_6 0 0.0 154s PrivateWages_7 0 0.0 154s PrivateWages_8 0 0.0 154s PrivateWages_9 0 0.0 154s PrivateWages_10 0 0.0 154s PrivateWages_11 0 0.0 154s PrivateWages_12 0 0.0 154s PrivateWages_13 0 0.0 154s PrivateWages_14 0 0.0 154s PrivateWages_15 0 0.0 154s PrivateWages_16 0 0.0 154s PrivateWages_17 0 0.0 154s PrivateWages_18 0 0.0 154s PrivateWages_19 0 0.0 154s PrivateWages_20 0 0.0 154s PrivateWages_21 0 0.0 154s PrivateWages_22 0 0.0 154s Investment_corpProfLag Investment_capitalLag 154s Consumption_2 0.0 0 154s Consumption_3 0.0 0 154s Consumption_4 0.0 0 154s Consumption_5 0.0 0 154s Consumption_6 0.0 0 154s Consumption_7 0.0 0 154s Consumption_8 0.0 0 154s Consumption_9 0.0 0 154s Consumption_10 0.0 0 154s Consumption_11 0.0 0 154s Consumption_12 0.0 0 154s Consumption_13 0.0 0 154s Consumption_14 0.0 0 154s Consumption_15 0.0 0 154s Consumption_16 0.0 0 154s Consumption_17 0.0 0 154s Consumption_18 0.0 0 154s Consumption_19 0.0 0 154s Consumption_20 0.0 0 154s Consumption_21 0.0 0 154s Consumption_22 0.0 0 154s Investment_2 12.7 183 154s Investment_3 12.4 183 154s Investment_4 16.9 184 154s Investment_5 18.4 190 154s Investment_6 19.4 193 154s Investment_7 20.1 198 154s Investment_8 19.6 203 154s Investment_9 19.8 208 154s Investment_10 21.1 211 154s Investment_11 21.7 216 154s Investment_12 15.6 217 154s Investment_13 11.4 213 154s Investment_14 7.0 207 154s Investment_15 11.2 202 154s Investment_16 12.3 199 154s Investment_17 14.0 198 154s Investment_18 17.6 200 154s Investment_19 17.3 202 154s Investment_20 15.3 200 154s Investment_21 19.0 201 154s Investment_22 21.1 204 154s PrivateWages_2 0.0 0 154s PrivateWages_3 0.0 0 154s PrivateWages_4 0.0 0 154s PrivateWages_5 0.0 0 154s PrivateWages_6 0.0 0 154s PrivateWages_7 0.0 0 154s PrivateWages_8 0.0 0 154s PrivateWages_9 0.0 0 154s PrivateWages_10 0.0 0 154s PrivateWages_11 0.0 0 154s PrivateWages_12 0.0 0 154s PrivateWages_13 0.0 0 154s PrivateWages_14 0.0 0 154s PrivateWages_15 0.0 0 154s PrivateWages_16 0.0 0 154s PrivateWages_17 0.0 0 154s PrivateWages_18 0.0 0 154s PrivateWages_19 0.0 0 154s PrivateWages_20 0.0 0 154s PrivateWages_21 0.0 0 154s PrivateWages_22 0.0 0 154s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 154s Consumption_2 0 0.0 0.0 154s Consumption_3 0 0.0 0.0 154s Consumption_4 0 0.0 0.0 154s Consumption_5 0 0.0 0.0 154s Consumption_6 0 0.0 0.0 154s Consumption_7 0 0.0 0.0 154s Consumption_8 0 0.0 0.0 154s Consumption_9 0 0.0 0.0 154s Consumption_10 0 0.0 0.0 154s Consumption_11 0 0.0 0.0 154s Consumption_12 0 0.0 0.0 154s Consumption_13 0 0.0 0.0 154s Consumption_14 0 0.0 0.0 154s Consumption_15 0 0.0 0.0 154s Consumption_16 0 0.0 0.0 154s Consumption_17 0 0.0 0.0 154s Consumption_18 0 0.0 0.0 154s Consumption_19 0 0.0 0.0 154s Consumption_20 0 0.0 0.0 154s Consumption_21 0 0.0 0.0 154s Consumption_22 0 0.0 0.0 154s Investment_2 0 0.0 0.0 154s Investment_3 0 0.0 0.0 154s Investment_4 0 0.0 0.0 154s Investment_5 0 0.0 0.0 154s Investment_6 0 0.0 0.0 154s Investment_7 0 0.0 0.0 154s Investment_8 0 0.0 0.0 154s Investment_9 0 0.0 0.0 154s Investment_10 0 0.0 0.0 154s Investment_11 0 0.0 0.0 154s Investment_12 0 0.0 0.0 154s Investment_13 0 0.0 0.0 154s Investment_14 0 0.0 0.0 154s Investment_15 0 0.0 0.0 154s Investment_16 0 0.0 0.0 154s Investment_17 0 0.0 0.0 154s Investment_18 0 0.0 0.0 154s Investment_19 0 0.0 0.0 154s Investment_20 0 0.0 0.0 154s Investment_21 0 0.0 0.0 154s Investment_22 0 0.0 0.0 154s PrivateWages_2 1 45.6 44.9 154s PrivateWages_3 1 50.1 45.6 154s PrivateWages_4 1 57.2 50.1 154s PrivateWages_5 1 57.1 57.2 154s PrivateWages_6 1 61.0 57.1 154s PrivateWages_7 1 64.0 61.0 154s PrivateWages_8 1 64.4 64.0 154s PrivateWages_9 1 64.5 64.4 154s PrivateWages_10 1 67.0 64.5 154s PrivateWages_11 1 61.2 67.0 154s PrivateWages_12 1 53.4 61.2 154s PrivateWages_13 1 44.3 53.4 154s PrivateWages_14 1 45.1 44.3 154s PrivateWages_15 1 49.7 45.1 154s PrivateWages_16 1 54.4 49.7 154s PrivateWages_17 1 62.7 54.4 154s PrivateWages_18 1 65.0 62.7 154s PrivateWages_19 1 60.9 65.0 154s PrivateWages_20 1 69.5 60.9 154s PrivateWages_21 1 75.7 69.5 154s PrivateWages_22 1 88.4 75.7 154s PrivateWages_trend 154s Consumption_2 0 154s Consumption_3 0 154s Consumption_4 0 154s Consumption_5 0 154s Consumption_6 0 154s Consumption_7 0 154s Consumption_8 0 154s Consumption_9 0 154s Consumption_10 0 154s Consumption_11 0 154s Consumption_12 0 154s Consumption_13 0 154s Consumption_14 0 154s Consumption_15 0 154s Consumption_16 0 154s Consumption_17 0 154s Consumption_18 0 154s Consumption_19 0 154s Consumption_20 0 154s Consumption_21 0 154s Consumption_22 0 154s Investment_2 0 154s Investment_3 0 154s Investment_4 0 154s Investment_5 0 154s Investment_6 0 154s Investment_7 0 154s Investment_8 0 154s Investment_9 0 154s Investment_10 0 154s Investment_11 0 154s Investment_12 0 154s Investment_13 0 154s Investment_14 0 154s Investment_15 0 154s Investment_16 0 154s Investment_17 0 154s Investment_18 0 154s Investment_19 0 154s Investment_20 0 154s Investment_21 0 154s Investment_22 0 154s PrivateWages_2 -10 154s PrivateWages_3 -9 154s PrivateWages_4 -8 154s PrivateWages_5 -7 154s PrivateWages_6 -6 154s PrivateWages_7 -5 154s PrivateWages_8 -4 154s PrivateWages_9 -3 154s PrivateWages_10 -2 154s PrivateWages_11 -1 154s PrivateWages_12 0 154s PrivateWages_13 1 154s PrivateWages_14 2 154s PrivateWages_15 3 154s PrivateWages_16 4 154s PrivateWages_17 5 154s PrivateWages_18 6 154s PrivateWages_19 7 154s PrivateWages_20 8 154s PrivateWages_21 9 154s PrivateWages_22 10 154s > nobs 154s [1] 63 154s > linearHypothesis 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 0.82 0.37 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 0.73 0.4 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 52 154s 2 51 1 0.73 0.39 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.42 0.66 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.37 0.69 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 53 154s 2 51 2 0.74 0.69 154s > logLik 154s 'log Lik.' -72.3 (df=13) 154s 'log Lik.' -77.9 (df=13) 154s compare log likelihood value with single-equation OLS 154s [1] TRUE 154s > 154s > # 2SLS 154s > summary 154s 154s systemfit results 154s method: 2SLS 154s 154s N DF SSR detRCov OLS-R2 McElroy-R2 154s system 63 51 61 0.288 0.969 0.992 154s 154s N DF SSR MSE RMSE R2 Adj R2 154s Consumption 21 17 21.9 1.290 1.136 0.977 0.973 154s Investment 21 17 29.0 1.709 1.307 0.885 0.865 154s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 154s 154s The covariance matrix of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.044 0.438 -0.385 154s Investment 0.438 1.383 0.193 154s PrivateWages -0.385 0.193 0.476 154s 154s The correlations of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.000 0.364 -0.546 154s Investment 0.364 1.000 0.237 154s PrivateWages -0.546 0.237 1.000 154s 154s 154s 2SLS estimates for 'Consumption' (equation 1) 154s Model Formula: consump ~ corpProf + corpProfLag + wages 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 16.5548 1.3208 12.53 5.2e-10 *** 154s corpProf 0.0173 0.1180 0.15 0.89 154s corpProfLag 0.2162 0.1073 2.02 0.06 . 154s wages 0.8102 0.0402 20.13 2.7e-13 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.136 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 21.925 MSE: 1.29 Root MSE: 1.136 154s Multiple R-Squared: 0.977 Adjusted R-Squared: 0.973 154s 154s 154s 2SLS estimates for 'Investment' (equation 2) 154s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 20.2782 7.5427 2.69 0.01555 * 154s corpProf 0.1502 0.1732 0.87 0.39792 154s corpProfLag 0.6159 0.1628 3.78 0.00148 ** 154s capitalLag -0.1578 0.0361 -4.37 0.00042 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.307 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 29.047 MSE: 1.709 Root MSE: 1.307 154s Multiple R-Squared: 0.885 Adjusted R-Squared: 0.865 154s 154s 154s 2SLS estimates for 'PrivateWages' (equation 3) 154s Model Formula: privWage ~ gnp + gnpLag + trend 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 1.5003 1.1478 1.31 0.20857 154s gnp 0.4389 0.0356 12.32 6.8e-10 *** 154s gnpLag 0.1467 0.0388 3.78 0.00150 ** 154s trend 0.1304 0.0291 4.47 0.00033 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 0.767 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 154s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 154s 154s > residuals 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 -0.46263 -1.320 -1.2940 154s 3 -0.61635 0.257 0.2981 154s 4 -1.30423 0.860 1.1918 154s 5 -0.24588 -1.594 -0.1361 154s 6 0.22948 0.259 -0.4634 154s 7 0.88538 1.207 -0.4824 154s 8 1.44189 0.969 -0.7284 154s 9 1.34190 0.113 0.3387 154s 10 -0.39403 1.796 1.1965 154s 11 -0.62564 -0.953 -0.1552 154s 12 -1.06543 -0.807 0.5882 154s 13 -1.33021 -0.895 0.0955 154s 14 0.61059 1.306 0.4487 154s 15 -0.14208 -0.151 0.2822 154s 16 0.00315 0.142 0.0145 154s 17 2.00337 1.749 -0.8478 154s 18 -0.60552 -0.192 0.9950 154s 19 -0.24771 -3.291 -0.4734 154s 20 1.38510 0.285 -0.3766 154s 21 1.03204 -0.104 -1.0893 154s 22 -1.89319 0.363 0.5974 154s > fitted 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 42.4 1.120 26.8 154s 3 45.6 1.643 29.0 154s 4 50.5 4.340 32.9 154s 5 50.8 4.594 34.0 154s 6 52.4 4.841 35.9 154s 7 54.2 4.393 37.9 154s 8 54.8 3.231 38.6 154s 9 56.0 2.887 38.9 154s 10 58.2 3.304 40.1 154s 11 55.6 1.953 38.1 154s 12 52.0 -2.593 33.9 154s 13 46.9 -5.305 28.9 154s 14 45.9 -6.406 28.1 154s 15 48.8 -2.849 30.3 154s 16 51.3 -1.442 33.2 154s 17 55.7 0.351 37.6 154s 18 59.3 2.192 40.0 154s 19 57.7 1.391 38.7 154s 20 60.2 1.015 42.0 154s 21 64.0 3.404 46.1 154s 22 71.6 4.537 52.7 154s > predict 154s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 154s 1 NA NA NA NA 154s 2 42.4 0.471 41.4 43.4 154s 3 45.6 0.577 44.4 46.8 154s 4 50.5 0.354 49.8 51.3 154s 5 50.8 0.405 50.0 51.7 154s 6 52.4 0.404 51.5 53.2 154s 7 54.2 0.359 53.5 55.0 154s 8 54.8 0.328 54.1 55.4 154s 9 56.0 0.368 55.2 56.7 154s 10 58.2 0.377 57.4 59.0 154s 11 55.6 0.728 54.1 57.2 154s 12 52.0 0.604 50.7 53.2 154s 13 46.9 0.765 45.3 48.5 154s 14 45.9 0.615 44.6 47.2 154s 15 48.8 0.374 48.1 49.6 154s 16 51.3 0.333 50.6 52.0 154s 17 55.7 0.409 54.8 56.6 154s 18 59.3 0.326 58.6 60.0 154s 19 57.7 0.414 56.9 58.6 154s 20 60.2 0.478 59.2 61.2 154s 21 64.0 0.446 63.0 64.9 154s 22 71.6 0.689 70.1 73.0 154s Investment.pred Investment.se.fit Investment.lwr Investment.upr 154s 1 NA NA NA NA 154s 2 1.120 0.865 -0.706 2.946 154s 3 1.643 0.594 0.390 2.895 154s 4 4.340 0.545 3.190 5.490 154s 5 4.594 0.443 3.660 5.527 154s 6 4.841 0.411 3.973 5.709 154s 7 4.393 0.399 3.550 5.235 154s 8 3.231 0.348 2.497 3.965 154s 9 2.887 0.542 1.744 4.030 154s 10 3.304 0.593 2.054 4.555 154s 11 1.953 0.855 0.148 3.757 154s 12 -2.593 0.679 -4.026 -1.160 154s 13 -5.305 0.876 -7.152 -3.457 154s 14 -6.406 0.916 -8.338 -4.473 154s 15 -2.849 0.435 -3.765 -1.932 154s 16 -1.442 0.376 -2.236 -0.649 154s 17 0.351 0.510 -0.724 1.426 154s 18 2.192 0.299 1.560 2.823 154s 19 1.391 0.464 0.411 2.371 154s 20 1.015 0.576 -0.201 2.230 154s 21 3.404 0.471 2.410 4.398 154s 22 4.537 0.675 3.114 5.961 154s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 154s 1 NA NA NA NA 154s 2 26.8 0.318 26.1 27.5 154s 3 29.0 0.330 28.3 29.7 154s 4 32.9 0.346 32.2 33.6 154s 5 34.0 0.242 33.5 34.5 154s 6 35.9 0.248 35.3 36.4 154s 7 37.9 0.244 37.4 38.4 154s 8 38.6 0.246 38.1 39.1 154s 9 38.9 0.235 38.4 39.4 154s 10 40.1 0.224 39.6 40.6 154s 11 38.1 0.350 37.3 38.8 154s 12 33.9 0.382 33.1 34.7 154s 13 28.9 0.454 27.9 29.9 154s 14 28.1 0.342 27.3 28.8 154s 15 30.3 0.335 29.6 31.0 154s 16 33.2 0.280 32.6 33.8 154s 17 37.6 0.291 37.0 38.3 154s 18 40.0 0.215 39.6 40.5 154s 19 38.7 0.356 37.9 39.4 154s 20 42.0 0.304 41.3 42.6 154s 21 46.1 0.306 45.4 46.7 154s 22 52.7 0.489 51.7 53.7 154s > model.frame 154s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 154s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 154s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 154s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 154s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 154s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 154s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 154s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 154s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 154s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 154s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 154s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 154s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 154s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 154s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 154s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 154s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 154s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 154s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 154s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 154s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 154s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 154s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 154s trend 154s 1 -11 154s 2 -10 154s 3 -9 154s 4 -8 154s 5 -7 154s 6 -6 154s 7 -5 154s 8 -4 154s 9 -3 154s 10 -2 154s 11 -1 154s 12 0 154s 13 1 154s 14 2 154s 15 3 154s 16 4 154s 17 5 154s 18 6 154s 19 7 154s 20 8 154s 21 9 154s 22 10 154s > model.matrix 154s [1] TRUE 154s > nobs 154s [1] 63 154s > linearHypothesis 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 1.08 0.3 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 1.29 0.26 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 52 154s 2 51 1 1.29 0.26 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.54 0.58 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.65 0.53 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 53 154s 2 51 2 1.3 0.52 154s > logLik 154s 'log Lik.' -76.3 (df=13) 154s 'log Lik.' -85.5 (df=13) 154s > 154s > # SUR 154s > summary 154s 154s systemfit results 154s method: SUR 154s 154s N DF SSR detRCov OLS-R2 McElroy-R2 154s system 63 51 46.5 0.158 0.977 0.993 154s 154s N DF SSR MSE RMSE R2 Adj R2 154s Consumption 21 17 18.1 1.065 1.032 0.981 0.977 154s Investment 21 17 17.6 1.036 1.018 0.930 0.918 154s PrivateWages 21 17 10.8 0.633 0.796 0.986 0.984 154s 154s The covariance matrix of the residuals used for estimation 154s Consumption Investment PrivateWages 154s Consumption 0.8514 0.0495 -0.381 154s Investment 0.0495 0.8249 0.121 154s PrivateWages -0.3808 0.1212 0.476 154s 154s The covariance matrix of the residuals 154s Consumption Investment PrivateWages 154s Consumption 0.8618 0.0766 -0.437 154s Investment 0.0766 0.8384 0.203 154s PrivateWages -0.4368 0.2027 0.513 154s 154s The correlations of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.0000 0.0901 -0.657 154s Investment 0.0901 1.0000 0.309 154s PrivateWages -0.6572 0.3092 1.000 154s 154s 154s SUR estimates for 'Consumption' (equation 1) 154s Model Formula: consump ~ corpProf + corpProfLag + wages 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 15.9805 1.1687 13.67 1.3e-10 *** 154s corpProf 0.2302 0.0767 3.00 0.008 ** 154s corpProfLag 0.0673 0.0769 0.87 0.394 154s wages 0.7962 0.0353 22.58 4.1e-14 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.032 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 18.098 MSE: 1.065 Root MSE: 1.032 154s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 154s 154s 154s SUR estimates for 'Investment' (equation 2) 154s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 12.9293 4.8014 2.69 0.01540 * 154s corpProf 0.4429 0.0861 5.15 8.1e-05 *** 154s corpProfLag 0.3655 0.0894 4.09 0.00077 *** 154s capitalLag -0.1253 0.0235 -5.34 5.4e-05 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.018 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 17.606 MSE: 1.036 Root MSE: 1.018 154s Multiple R-Squared: 0.93 Adjusted R-Squared: 0.918 154s 154s 154s SUR estimates for 'PrivateWages' (equation 3) 154s Model Formula: privWage ~ gnp + gnpLag + trend 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 1.6347 1.1173 1.46 0.16 154s gnp 0.4098 0.0273 15.04 3.0e-11 *** 154s gnpLag 0.1744 0.0312 5.59 3.2e-05 *** 154s trend 0.1558 0.0276 5.65 2.9e-05 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 0.796 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 10.763 MSE: 0.633 Root MSE: 0.796 154s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 154s 154s > residuals 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 -0.24064 -0.3522 -1.0960 154s 3 -1.34080 -0.1605 0.5818 154s 4 -1.61038 1.0687 1.5313 154s 5 -0.54147 -1.4707 -0.0220 154s 6 -0.04372 0.3299 -0.2587 154s 7 0.85234 1.4346 -0.3243 154s 8 1.30302 0.8306 -0.6674 154s 9 0.97574 -0.4918 0.3660 154s 10 -0.66060 1.2434 1.2682 154s 11 0.45069 0.2647 -0.3467 154s 12 -0.04295 0.0795 0.3057 154s 13 -0.06686 0.3369 -0.2602 154s 14 0.32177 0.4080 0.3434 154s 15 -0.00441 -0.1533 0.2628 154s 16 -0.01931 0.0158 -0.0216 154s 17 1.53656 1.0372 -0.7988 154s 18 -0.42317 0.0176 0.8550 154s 19 0.29041 -2.6364 -0.8217 154s 20 0.88685 -0.5822 -0.3869 154s 21 0.68839 -0.7015 -1.1838 154s 22 -2.31147 -0.5183 0.6742 154s > fitted 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 42.1 0.152 26.6 154s 3 46.3 2.060 28.7 154s 4 50.8 4.131 32.6 154s 5 51.1 4.471 33.9 154s 6 52.6 4.770 35.7 154s 7 54.2 4.165 37.7 154s 8 54.9 3.369 38.6 154s 9 56.3 3.492 38.8 154s 10 58.5 3.857 40.0 154s 11 54.5 0.735 38.2 154s 12 50.9 -3.479 34.2 154s 13 45.7 -6.537 29.3 154s 14 46.2 -5.508 28.2 154s 15 48.7 -2.847 30.3 154s 16 51.3 -1.316 33.2 154s 17 56.2 1.063 37.6 154s 18 59.1 1.982 40.1 154s 19 57.2 0.736 39.0 154s 20 60.7 1.882 42.0 154s 21 64.3 4.002 46.2 154s 22 72.0 5.418 52.6 154s > predict 154s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 154s 1 NA NA NA NA 154s 2 42.1 0.415 41.3 43.0 154s 3 46.3 0.449 45.4 47.2 154s 4 50.8 0.300 50.2 51.4 154s 5 51.1 0.348 50.4 51.8 154s 6 52.6 0.350 51.9 53.3 154s 7 54.2 0.317 53.6 54.9 154s 8 54.9 0.289 54.3 55.5 154s 9 56.3 0.309 55.7 56.9 154s 10 58.5 0.328 57.8 59.1 154s 11 54.5 0.516 53.5 55.6 154s 12 50.9 0.414 50.1 51.8 154s 13 45.7 0.544 44.6 46.8 154s 14 46.2 0.527 45.1 47.2 154s 15 48.7 0.332 48.0 49.4 154s 16 51.3 0.295 50.7 51.9 154s 17 56.2 0.319 55.5 56.8 154s 18 59.1 0.286 58.5 59.7 154s 19 57.2 0.323 56.6 57.9 154s 20 60.7 0.381 59.9 61.5 154s 21 64.3 0.381 63.5 65.1 154s 22 72.0 0.597 70.8 73.2 154s Investment.pred Investment.se.fit Investment.lwr Investment.upr 154s 1 NA NA NA NA 154s 2 0.152 0.536 -0.924 1.229 154s 3 2.060 0.446 1.166 2.955 154s 4 4.131 0.397 3.334 4.929 154s 5 4.471 0.329 3.809 5.132 154s 6 4.770 0.311 4.145 5.395 154s 7 4.165 0.294 3.575 4.756 154s 8 3.369 0.263 2.842 3.897 154s 9 3.492 0.347 2.796 4.188 154s 10 3.857 0.398 3.058 4.656 154s 11 0.735 0.539 -0.346 1.816 154s 12 -3.479 0.454 -4.390 -2.569 154s 13 -6.537 0.552 -7.646 -5.428 154s 14 -5.508 0.617 -6.747 -4.269 154s 15 -2.847 0.335 -3.519 -2.175 154s 16 -1.316 0.287 -1.892 -0.739 154s 17 1.063 0.311 0.439 1.686 154s 18 1.982 0.218 1.545 2.420 154s 19 0.736 0.279 0.176 1.296 154s 20 1.882 0.327 1.227 2.538 154s 21 4.002 0.297 3.405 4.598 154s 22 5.418 0.412 4.591 6.245 154s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 154s 1 NA NA NA NA 154s 2 26.6 0.313 26.0 27.2 154s 3 28.7 0.310 28.1 29.3 154s 4 32.6 0.305 32.0 33.2 154s 5 33.9 0.236 33.4 34.4 154s 6 35.7 0.233 35.2 36.1 154s 7 37.7 0.234 37.3 38.2 154s 8 38.6 0.239 38.1 39.0 154s 9 38.8 0.229 38.4 39.3 154s 10 40.0 0.219 39.6 40.5 154s 11 38.2 0.301 37.6 38.9 154s 12 34.2 0.308 33.6 34.8 154s 13 29.3 0.370 28.5 30.0 154s 14 28.2 0.332 27.5 28.8 154s 15 30.3 0.324 29.7 31.0 154s 16 33.2 0.271 32.7 33.8 154s 17 37.6 0.263 37.1 38.1 154s 18 40.1 0.211 39.7 40.6 154s 19 39.0 0.306 38.4 39.6 154s 20 42.0 0.280 41.4 42.5 154s 21 46.2 0.298 45.6 46.8 154s 22 52.6 0.445 51.7 53.5 154s > model.frame 154s [1] TRUE 154s > model.matrix 154s [1] TRUE 154s > nobs 154s [1] 63 154s > linearHypothesis 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 1.44 0.24 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 1.69 0.2 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 52 154s 2 51 1 1.69 0.19 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.77 0.47 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.91 0.41 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 53 154s 2 51 2 1.83 0.4 154s > logLik 154s 'log Lik.' -70 (df=18) 154s 'log Lik.' -79 (df=18) 154s > 154s > # 3SLS 154s > summary 154s 154s systemfit results 154s method: 3SLS 154s 154s N DF SSR detRCov OLS-R2 McElroy-R2 154s system 63 51 73.6 0.283 0.963 0.995 154s 154s N DF SSR MSE RMSE R2 Adj R2 154s Consumption 21 17 18.7 1.102 1.050 0.980 0.977 154s Investment 21 17 44.0 2.586 1.608 0.826 0.795 154s PrivateWages 21 17 10.9 0.642 0.801 0.986 0.984 154s 154s The covariance matrix of the residuals used for estimation 154s Consumption Investment PrivateWages 154s Consumption 1.044 0.438 -0.385 154s Investment 0.438 1.383 0.193 154s PrivateWages -0.385 0.193 0.476 154s 154s The covariance matrix of the residuals 154s Consumption Investment PrivateWages 154s Consumption 0.892 0.411 -0.394 154s Investment 0.411 2.093 0.403 154s PrivateWages -0.394 0.403 0.520 154s 154s The correlations of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.000 0.301 -0.578 154s Investment 0.301 1.000 0.386 154s PrivateWages -0.578 0.386 1.000 154s 154s 154s 3SLS estimates for 'Consumption' (equation 1) 154s Model Formula: consump ~ corpProf + corpProfLag + wages 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 16.4408 1.3045 12.60 4.7e-10 *** 154s corpProf 0.1249 0.1081 1.16 0.26 154s corpProfLag 0.1631 0.1004 1.62 0.12 154s wages 0.7901 0.0379 20.83 1.5e-13 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.05 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 18.727 MSE: 1.102 Root MSE: 1.05 154s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 154s 154s 154s 3SLS estimates for 'Investment' (equation 2) 154s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 28.1778 6.7938 4.15 0.00067 *** 154s corpProf -0.0131 0.1619 -0.08 0.93655 154s corpProfLag 0.7557 0.1529 4.94 0.00012 *** 154s capitalLag -0.1948 0.0325 -5.99 1.5e-05 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.608 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 43.954 MSE: 2.586 Root MSE: 1.608 154s Multiple R-Squared: 0.826 Adjusted R-Squared: 0.795 154s 154s 154s 3SLS estimates for 'PrivateWages' (equation 3) 154s Model Formula: privWage ~ gnp + gnpLag + trend 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 1.7972 1.1159 1.61 0.13 154s gnp 0.4005 0.0318 12.59 4.8e-10 *** 154s gnpLag 0.1813 0.0342 5.31 5.8e-05 *** 154s trend 0.1497 0.0279 5.36 5.2e-05 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 0.801 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 10.921 MSE: 0.642 Root MSE: 0.801 154s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 154s 154s > residuals 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 -0.4416 -2.1951 -1.20287 154s 3 -1.0150 0.1515 0.51834 154s 4 -1.5289 0.4406 1.50936 154s 5 -0.4985 -1.8667 -0.08743 154s 6 -0.0132 0.0713 -0.28089 154s 7 0.7759 1.0294 -0.33908 154s 8 1.3004 1.1011 -0.69282 154s 9 1.0993 0.5853 0.34494 154s 10 -0.5839 2.2952 1.27590 154s 11 -0.1917 -1.3443 -0.40414 154s 12 -0.5598 -0.9944 0.22151 154s 13 -0.6746 -1.3404 -0.36962 154s 14 0.5767 1.9316 0.31006 154s 15 -0.0211 -0.1217 0.27309 154s 16 0.0539 0.1847 0.00716 154s 17 1.8555 2.0937 -0.71866 154s 18 -0.4596 -0.3216 0.90582 154s 19 0.0613 -3.6314 -0.81881 154s 20 1.2602 0.7582 -0.26942 154s 21 0.9500 0.2428 -1.06125 154s 22 -1.9451 0.9302 0.87883 154s > fitted 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 42.3 1.99510 26.7 154s 3 46.0 1.74850 28.8 154s 4 50.7 4.75942 32.6 154s 5 51.1 4.86672 34.0 154s 6 52.6 5.02874 35.7 154s 7 54.3 4.57056 37.7 154s 8 54.9 3.09893 38.6 154s 9 56.2 2.41471 38.9 154s 10 58.4 2.80476 40.0 154s 11 55.2 2.34425 38.3 154s 12 51.5 -2.40558 34.3 154s 13 46.3 -4.85959 29.4 154s 14 45.9 -7.03164 28.2 154s 15 48.7 -2.87827 30.3 154s 16 51.2 -1.48466 33.2 154s 17 55.8 0.00629 37.5 154s 18 59.2 2.32164 40.1 154s 19 57.4 1.73138 39.0 154s 20 60.3 0.54175 41.9 154s 21 64.1 3.05716 46.1 154s 22 71.6 3.96979 52.4 154s > predict 154s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 154s 1 NA NA NA NA 154s 2 42.3 0.464 39.9 44.8 154s 3 46.0 0.541 43.5 48.5 154s 4 50.7 0.337 48.4 53.1 154s 5 51.1 0.385 48.7 53.5 154s 6 52.6 0.386 50.3 55.0 154s 7 54.3 0.349 52.0 56.7 154s 8 54.9 0.320 52.6 57.2 154s 9 56.2 0.355 53.9 58.5 154s 10 58.4 0.370 56.0 60.7 154s 11 55.2 0.682 52.6 57.8 154s 12 51.5 0.563 48.9 54.0 154s 13 46.3 0.719 43.6 49.0 154s 14 45.9 0.597 43.4 48.5 154s 15 48.7 0.370 46.4 51.1 154s 16 51.2 0.327 48.9 53.6 154s 17 55.8 0.391 53.5 58.2 154s 18 59.2 0.316 56.8 61.5 154s 19 57.4 0.389 55.1 59.8 154s 20 60.3 0.459 57.9 62.8 154s 21 64.1 0.438 61.7 66.4 154s 22 71.6 0.674 69.0 74.3 154s Investment.pred Investment.se.fit Investment.lwr Investment.upr 154s 1 NA NA NA NA 154s 2 1.99510 0.792 -1.787 5.777 154s 3 1.74850 0.585 -1.861 5.358 154s 4 4.75942 0.510 1.200 8.319 154s 5 4.86672 0.423 1.359 8.375 154s 6 5.02874 0.400 1.533 8.525 154s 7 4.57056 0.391 1.079 8.062 154s 8 3.09893 0.345 -0.371 6.568 154s 9 2.41471 0.511 -1.145 5.974 154s 10 2.80476 0.560 -0.788 6.397 154s 11 2.34425 0.839 -1.482 6.170 154s 12 -2.40558 0.673 -6.083 1.272 154s 13 -4.85959 0.862 -8.708 -1.011 154s 14 -7.03164 0.874 -10.893 -3.171 154s 15 -2.87827 0.433 -6.392 0.635 154s 16 -1.48466 0.375 -4.968 1.999 154s 17 0.00629 0.491 -3.541 3.554 154s 18 2.32164 0.294 -1.127 5.771 154s 19 1.73138 0.446 -1.789 5.252 154s 20 0.54175 0.547 -3.042 4.125 154s 21 3.05716 0.454 -0.468 6.582 154s 22 3.96979 0.642 0.317 7.623 154s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 154s 1 NA NA NA NA 154s 2 26.7 0.314 24.9 28.5 154s 3 28.8 0.318 27.0 30.6 154s 4 32.6 0.325 30.8 34.4 154s 5 34.0 0.235 32.2 35.7 154s 6 35.7 0.241 33.9 37.4 154s 7 37.7 0.238 36.0 39.5 154s 8 38.6 0.237 36.8 40.4 154s 9 38.9 0.227 37.1 40.6 154s 10 40.0 0.219 38.3 41.8 154s 11 38.3 0.317 36.5 40.1 154s 12 34.3 0.344 32.4 36.1 154s 13 29.4 0.419 27.5 31.3 154s 14 28.2 0.334 26.4 30.0 154s 15 30.3 0.320 28.5 32.1 154s 16 33.2 0.268 31.4 35.0 154s 17 37.5 0.269 35.7 39.3 154s 18 40.1 0.212 38.3 41.8 154s 19 39.0 0.331 37.2 40.8 154s 20 41.9 0.287 40.1 43.7 154s 21 46.1 0.301 44.3 47.9 154s 22 52.4 0.471 50.5 54.4 154s > model.frame 154s [1] TRUE 154s > model.matrix 154s [1] TRUE 154s > nobs 154s [1] 63 154s > linearHypothesis 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 0.29 0.59 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 0.39 0.54 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 52 154s 2 51 1 0.39 0.53 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.3 0.74 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.4 0.67 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 53 154s 2 51 2 0.8 0.67 154s > logLik 154s 'log Lik.' -76.1 (df=18) 154s 'log Lik.' -89.1 (df=18) 154s > 154s > # I3SLS 154s > summary 154s 154s systemfit results 154s method: iterated 3SLS 154s 154s convergence achieved after 20 iterations 154s 154s N DF SSR detRCov OLS-R2 McElroy-R2 154s system 63 51 128 0.509 0.936 0.996 154s 154s N DF SSR MSE RMSE R2 Adj R2 154s Consumption 21 17 19.2 1.130 1.063 0.980 0.976 154s Investment 21 17 95.7 5.627 2.372 0.621 0.554 154s PrivateWages 21 17 12.7 0.748 0.865 0.984 0.981 154s 154s The covariance matrix of the residuals used for estimation 154s Consumption Investment PrivateWages 154s Consumption 0.915 0.642 -0.435 154s Investment 0.642 4.555 0.734 154s PrivateWages -0.435 0.734 0.606 154s 154s The covariance matrix of the residuals 154s Consumption Investment PrivateWages 154s Consumption 0.915 0.642 -0.435 154s Investment 0.642 4.555 0.734 154s PrivateWages -0.435 0.734 0.606 154s 154s The correlations of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.000 0.314 -0.584 154s Investment 0.314 1.000 0.442 154s PrivateWages -0.584 0.442 1.000 154s 154s 154s 3SLS estimates for 'Consumption' (equation 1) 154s Model Formula: consump ~ corpProf + corpProfLag + wages 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 16.5590 1.2244 13.52 1.6e-10 *** 154s corpProf 0.1645 0.0962 1.71 0.105 154s corpProfLag 0.1766 0.0901 1.96 0.067 . 154s wages 0.7658 0.0348 22.03 6.1e-14 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.063 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 19.213 MSE: 1.13 Root MSE: 1.063 154s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 154s 154s 154s 3SLS estimates for 'Investment' (equation 2) 154s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 42.8959 10.5937 4.05 0.00083 *** 154s corpProf -0.3565 0.2602 -1.37 0.18838 154s corpProfLag 1.0113 0.2488 4.07 0.00081 *** 154s capitalLag -0.2602 0.0509 -5.12 8.6e-05 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 2.372 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 95.661 MSE: 5.627 Root MSE: 2.372 154s Multiple R-Squared: 0.621 Adjusted R-Squared: 0.554 154s 154s 154s 3SLS estimates for 'PrivateWages' (equation 3) 154s Model Formula: privWage ~ gnp + gnpLag + trend 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 2.6247 1.1956 2.20 0.042 * 154s gnp 0.3748 0.0311 12.05 9.4e-10 *** 154s gnpLag 0.1937 0.0324 5.98 1.5e-05 *** 154s trend 0.1679 0.0289 5.80 2.1e-05 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 0.865 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 12.719 MSE: 0.748 Root MSE: 0.865 154s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.981 154s 154s > residuals 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 -0.537 -3.95419 -1.2303 154s 3 -1.187 0.00151 0.5797 154s 4 -1.705 -0.22015 1.6794 154s 5 -0.734 -2.22753 -0.0260 154s 6 -0.251 -0.10866 -0.1362 154s 7 0.600 0.83218 -0.1837 154s 8 1.142 1.46624 -0.5825 154s 9 0.921 1.62030 0.4347 154s 10 -0.745 3.40013 1.4104 154s 11 -0.197 -2.15443 -0.4679 154s 12 -0.385 -1.62274 0.0106 154s 13 -0.390 -2.62869 -0.7363 154s 14 0.749 2.80517 0.0581 154s 15 0.112 -0.27710 0.1113 154s 16 0.170 0.13598 -0.1089 154s 17 1.925 2.76200 -0.6976 154s 18 -0.341 -0.53919 0.8651 154s 19 0.219 -4.32845 -1.0116 154s 20 1.383 1.71889 -0.2087 154s 21 1.028 1.06406 -0.9656 154s 22 -1.777 2.25466 1.2061 154s > fitted 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 42.4 3.754 26.7 154s 3 46.2 1.898 28.7 154s 4 50.9 5.420 32.4 154s 5 51.3 5.228 33.9 154s 6 52.9 5.209 35.5 154s 7 54.5 4.768 37.6 154s 8 55.1 2.734 38.5 154s 9 56.4 1.380 38.8 154s 10 58.5 1.700 39.9 154s 11 55.2 3.154 38.4 154s 12 51.3 -1.777 34.5 154s 13 46.0 -3.571 29.7 154s 14 45.8 -7.905 28.4 154s 15 48.6 -2.723 30.5 154s 16 51.1 -1.436 33.3 154s 17 55.8 -0.662 37.5 154s 18 59.0 2.539 40.1 154s 19 57.3 2.428 39.2 154s 20 60.2 -0.419 41.8 154s 21 64.0 2.236 46.0 154s 22 71.5 2.645 52.1 154s > predict 154s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 154s 1 NA NA NA NA 154s 2 42.4 0.434 41.6 43.3 154s 3 46.2 0.491 45.2 47.2 154s 4 50.9 0.309 50.3 51.5 154s 5 51.3 0.351 50.6 52.0 154s 6 52.9 0.352 52.1 53.6 154s 7 54.5 0.320 53.9 55.1 154s 8 55.1 0.293 54.5 55.6 154s 9 56.4 0.324 55.7 57.0 154s 10 58.5 0.340 57.9 59.2 154s 11 55.2 0.613 54.0 56.4 154s 12 51.3 0.506 50.3 52.3 154s 13 46.0 0.649 44.7 47.3 154s 14 45.8 0.546 44.7 46.8 154s 15 48.6 0.341 47.9 49.3 154s 16 51.1 0.301 50.5 51.7 154s 17 55.8 0.357 55.1 56.5 154s 18 59.0 0.293 58.5 59.6 154s 19 57.3 0.353 56.6 58.0 154s 20 60.2 0.421 59.4 61.1 154s 21 64.0 0.409 63.2 64.8 154s 22 71.5 0.630 70.2 72.7 154s Investment.pred Investment.se.fit Investment.lwr Investment.upr 154s 1 NA NA NA NA 154s 2 3.754 1.263 1.218 6.2906 154s 3 1.898 1.022 -0.153 3.9503 154s 4 5.420 0.853 3.709 7.1317 154s 5 5.228 0.727 3.767 6.6877 154s 6 5.209 0.703 3.797 6.6200 154s 7 4.768 0.688 3.387 6.1487 154s 8 2.734 0.615 1.499 3.9683 154s 9 1.380 0.852 -0.330 3.0893 154s 10 1.700 0.938 -0.184 3.5836 154s 11 3.154 1.437 0.269 6.0398 154s 12 -1.777 1.173 -4.133 0.5780 154s 13 -3.571 1.494 -6.570 -0.5725 154s 14 -7.905 1.479 -10.875 -4.9350 154s 15 -2.723 0.778 -4.285 -1.1613 154s 16 -1.436 0.672 -2.784 -0.0875 154s 17 -0.662 0.832 -2.333 1.0088 154s 18 2.539 0.522 1.491 3.5875 154s 19 2.428 0.753 0.918 3.9392 154s 20 -0.419 0.907 -2.240 1.4019 154s 21 2.236 0.775 0.679 3.7928 154s 22 2.645 1.076 0.486 4.8047 154s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 154s 1 NA NA NA NA 154s 2 26.7 0.340 26.0 27.4 154s 3 28.7 0.339 28.0 29.4 154s 4 32.4 0.340 31.7 33.1 154s 5 33.9 0.250 33.4 34.4 154s 6 35.5 0.258 35.0 36.1 154s 7 37.6 0.256 37.1 38.1 154s 8 38.5 0.252 38.0 39.0 154s 9 38.8 0.241 38.3 39.2 154s 10 39.9 0.239 39.4 40.4 154s 11 38.4 0.314 37.7 39.0 154s 12 34.5 0.342 33.8 35.2 154s 13 29.7 0.430 28.9 30.6 154s 14 28.4 0.361 27.7 29.2 154s 15 30.5 0.336 29.8 31.2 154s 16 33.3 0.281 32.7 33.9 154s 17 37.5 0.270 37.0 38.0 154s 18 40.1 0.231 39.7 40.6 154s 19 39.2 0.343 38.5 39.9 154s 20 41.8 0.294 41.2 42.4 154s 21 46.0 0.326 45.3 46.6 154s 22 52.1 0.501 51.1 53.1 154s > model.frame 154s [1] TRUE 154s > model.matrix 154s [1] TRUE 154s > nobs 154s [1] 63 154s > linearHypothesis 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 0.59 0.45 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 51 1 0.73 0.4 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 52 154s 2 51 1 0.73 0.39 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.72 0.49 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 53 154s 2 51 2 0.88 0.42 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 53 154s 2 51 2 1.77 0.41 154s > logLik 154s 'log Lik.' -82.3 (df=18) 154s 'log Lik.' -99.1 (df=18) 154s > 154s > # OLS 154s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 154s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 154s > summary 154s 154s systemfit results 154s method: OLS 154s 154s N DF SSR detRCov OLS-R2 McElroy-R2 154s system 62 50 44.9 0.372 0.977 0.991 154s 154s N DF SSR MSE RMSE R2 Adj R2 154s Consumption 21 17 17.88 1.052 1.03 0.981 0.978 154s Investment 21 17 17.32 1.019 1.01 0.931 0.919 154s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 154s 154s The covariance matrix of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.0703 -0.0161 -0.463 154s Investment -0.0161 0.9435 0.199 154s PrivateWages -0.4633 0.1993 0.609 154s 154s The correlations of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.0000 -0.0201 -0.575 154s Investment -0.0201 1.0000 0.264 154s PrivateWages -0.5747 0.2639 1.000 154s 154s 154s OLS estimates for 'Consumption' (equation 1) 154s Model Formula: consump ~ corpProf + corpProfLag + wages 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 16.2366 1.3141 12.36 6.4e-10 *** 154s corpProf 0.1929 0.0920 2.10 0.051 . 154s corpProfLag 0.0899 0.0914 0.98 0.339 154s wages 0.7962 0.0403 19.76 3.6e-13 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.026 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 154s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 154s 154s 154s OLS estimates for 'Investment' (equation 2) 154s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 10.1258 5.2592 1.93 0.07108 . 154s corpProf 0.4796 0.0934 5.13 8.3e-05 *** 154s corpProfLag 0.3330 0.0971 3.43 0.00318 ** 154s capitalLag -0.1118 0.0257 -4.35 0.00044 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.009 on 17 degrees of freedom 154s Number of observations: 21 Degrees of Freedom: 17 154s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 154s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 154s 154s 154s OLS estimates for 'PrivateWages' (equation 3) 154s Model Formula: privWage ~ gnp + gnpLag + trend 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 1.3550 1.3093 1.03 0.3161 154s gnp 0.4417 0.0331 13.33 4.4e-10 *** 154s gnpLag 0.1466 0.0381 3.85 0.0014 ** 154s trend 0.1244 0.0336 3.70 0.0020 ** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 0.78 on 16 degrees of freedom 154s Number of observations: 20 Degrees of Freedom: 16 154s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 154s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 154s 154s compare coef with single-equation OLS 154s [1] TRUE 154s > residuals 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 -0.32389 -0.0668 -1.3389 154s 3 -1.25001 -0.0476 0.2462 154s 4 -1.56574 1.2467 1.1255 154s 5 -0.49350 -1.3512 -0.1959 154s 6 0.00761 0.4154 -0.5284 154s 7 0.86910 1.4923 NA 154s 8 1.33848 0.7889 -0.7909 154s 9 1.05498 -0.6317 0.2819 154s 10 -0.58856 1.0830 1.1384 154s 11 0.28231 0.2791 -0.1904 154s 12 -0.22965 0.0369 0.5813 154s 13 -0.32213 0.3659 0.1206 154s 14 0.32228 0.2237 0.4773 154s 15 -0.05801 -0.1728 0.3035 154s 16 -0.03466 0.0101 0.0284 154s 17 1.61650 0.9719 -0.8517 154s 18 -0.43597 0.0516 0.9908 154s 19 0.21005 -2.5656 -0.4597 154s 20 0.98920 -0.6866 -0.3819 154s 21 0.78508 -0.7807 -1.1062 154s 22 -2.17345 -0.6623 0.5501 154s > fitted 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 42.2 -0.133 26.8 154s 3 46.3 1.948 29.1 154s 4 50.8 3.953 33.0 154s 5 51.1 4.351 34.1 154s 6 52.6 4.685 35.9 154s 7 54.2 4.108 NA 154s 8 54.9 3.411 38.7 154s 9 56.2 3.632 38.9 154s 10 58.4 4.017 40.2 154s 11 54.7 0.721 38.1 154s 12 51.1 -3.437 33.9 154s 13 45.9 -6.566 28.9 154s 14 46.2 -5.324 28.0 154s 15 48.8 -2.827 30.3 154s 16 51.3 -1.310 33.2 154s 17 56.1 1.128 37.7 154s 18 59.1 1.948 40.0 154s 19 57.3 0.666 38.7 154s 20 60.6 1.987 42.0 154s 21 64.2 4.081 46.1 154s 22 71.9 5.562 52.7 154s > predict 154s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 154s 1 NA NA NA NA 154s 2 42.2 0.466 40.0 44.5 154s 3 46.3 0.523 43.9 48.6 154s 4 50.8 0.344 48.6 52.9 154s 5 51.1 0.399 48.9 53.3 154s 6 52.6 0.401 50.4 54.8 154s 7 54.2 0.363 52.0 56.4 154s 8 54.9 0.330 52.7 57.0 154s 9 56.2 0.354 54.1 58.4 154s 10 58.4 0.373 56.2 60.6 154s 11 54.7 0.612 52.3 57.1 154s 12 51.1 0.489 48.8 53.4 154s 13 45.9 0.634 43.5 48.3 154s 14 46.2 0.608 43.8 48.6 154s 15 48.8 0.378 46.6 51.0 154s 16 51.3 0.336 49.2 53.5 154s 17 56.1 0.369 53.9 58.3 154s 18 59.1 0.324 57.0 61.3 154s 19 57.3 0.375 55.1 59.5 154s 20 60.6 0.437 58.4 62.9 154s 21 64.2 0.429 62.0 66.4 154s 22 71.9 0.672 69.4 74.3 154s Investment.pred Investment.se.fit Investment.lwr Investment.upr 154s 1 NA NA NA NA 154s 2 -0.133 0.584 -2.476 2.209 154s 3 1.948 0.480 -0.297 4.193 154s 4 3.953 0.432 1.748 6.159 154s 5 4.351 0.357 2.201 6.502 154s 6 4.685 0.336 2.548 6.821 154s 7 4.108 0.316 1.983 6.232 154s 8 3.411 0.281 1.306 5.516 154s 9 3.632 0.374 1.469 5.794 154s 10 4.017 0.430 1.813 6.221 154s 11 0.721 0.579 -1.616 3.058 154s 12 -3.437 0.488 -5.688 -1.185 154s 13 -6.566 0.592 -8.917 -4.215 154s 14 -5.324 0.667 -7.754 -2.893 154s 15 -2.827 0.359 -4.979 -0.675 154s 16 -1.310 0.308 -3.430 0.810 154s 17 1.128 0.334 -1.008 3.264 154s 18 1.948 0.234 -0.133 4.030 154s 19 0.666 0.300 -1.450 2.781 154s 20 1.987 0.353 -0.161 4.134 154s 21 4.081 0.319 1.954 6.207 154s 22 5.562 0.444 3.348 7.777 154s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 154s 1 NA NA NA NA 154s 2 26.8 0.366 25.1 28.6 154s 3 29.1 0.369 27.3 30.8 154s 4 33.0 0.372 31.2 34.7 154s 5 34.1 0.288 32.4 35.8 154s 6 35.9 0.287 34.3 37.6 154s 7 NA NA NA NA 154s 8 38.7 0.293 37.0 40.4 154s 9 38.9 0.279 37.3 40.6 154s 10 40.2 0.266 38.5 41.8 154s 11 38.1 0.365 36.4 39.8 154s 12 33.9 0.369 32.2 35.7 154s 13 28.9 0.438 27.1 30.7 154s 14 28.0 0.385 26.3 29.8 154s 15 30.3 0.379 28.6 32.0 154s 16 33.2 0.316 31.5 34.9 154s 17 37.7 0.310 36.0 39.3 154s 18 40.0 0.243 38.4 41.7 154s 19 38.7 0.363 36.9 40.4 154s 20 42.0 0.326 40.3 43.7 154s 21 46.1 0.341 44.4 47.8 154s 22 52.7 0.514 50.9 54.6 154s > model.frame 154s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 154s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 154s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 154s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 154s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 154s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 154s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 154s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 154s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 154s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 154s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 154s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 154s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 154s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 154s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 154s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 154s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 154s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 154s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 154s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 154s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 154s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 154s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 154s trend 154s 1 -11 154s 2 -10 154s 3 -9 154s 4 -8 154s 5 -7 154s 6 -6 154s 7 -5 154s 8 -4 154s 9 -3 154s 10 -2 154s 11 -1 154s 12 0 154s 13 1 154s 14 2 154s 15 3 154s 16 4 154s 17 5 154s 18 6 154s 19 7 154s 20 8 154s 21 9 154s 22 10 154s > model.matrix 154s Consumption_(Intercept) Consumption_corpProf 154s Consumption_2 1 12.4 154s Consumption_3 1 16.9 154s Consumption_4 1 18.4 154s Consumption_5 1 19.4 154s Consumption_6 1 20.1 154s Consumption_7 1 19.6 154s Consumption_8 1 19.8 154s Consumption_9 1 21.1 154s Consumption_10 1 21.7 154s Consumption_11 1 15.6 154s Consumption_12 1 11.4 154s Consumption_13 1 7.0 154s Consumption_14 1 11.2 154s Consumption_15 1 12.3 154s Consumption_16 1 14.0 154s Consumption_17 1 17.6 154s Consumption_18 1 17.3 154s Consumption_19 1 15.3 154s Consumption_20 1 19.0 154s Consumption_21 1 21.1 154s Consumption_22 1 23.5 154s Investment_2 0 0.0 154s Investment_3 0 0.0 154s Investment_4 0 0.0 154s Investment_5 0 0.0 154s Investment_6 0 0.0 154s Investment_7 0 0.0 154s Investment_8 0 0.0 154s Investment_9 0 0.0 154s Investment_10 0 0.0 154s Investment_11 0 0.0 154s Investment_12 0 0.0 154s Investment_13 0 0.0 154s Investment_14 0 0.0 154s Investment_15 0 0.0 154s Investment_16 0 0.0 154s Investment_17 0 0.0 154s Investment_18 0 0.0 154s Investment_19 0 0.0 154s Investment_20 0 0.0 154s Investment_21 0 0.0 154s Investment_22 0 0.0 154s PrivateWages_2 0 0.0 154s PrivateWages_3 0 0.0 154s PrivateWages_4 0 0.0 154s PrivateWages_5 0 0.0 154s PrivateWages_6 0 0.0 154s PrivateWages_8 0 0.0 154s PrivateWages_9 0 0.0 154s PrivateWages_10 0 0.0 154s PrivateWages_11 0 0.0 154s PrivateWages_12 0 0.0 154s PrivateWages_13 0 0.0 154s PrivateWages_14 0 0.0 154s PrivateWages_15 0 0.0 154s PrivateWages_16 0 0.0 154s PrivateWages_17 0 0.0 154s PrivateWages_18 0 0.0 154s PrivateWages_19 0 0.0 154s PrivateWages_20 0 0.0 154s PrivateWages_21 0 0.0 154s PrivateWages_22 0 0.0 154s Consumption_corpProfLag Consumption_wages 154s Consumption_2 12.7 28.2 154s Consumption_3 12.4 32.2 154s Consumption_4 16.9 37.0 154s Consumption_5 18.4 37.0 154s Consumption_6 19.4 38.6 154s Consumption_7 20.1 40.7 154s Consumption_8 19.6 41.5 154s Consumption_9 19.8 42.9 154s Consumption_10 21.1 45.3 154s Consumption_11 21.7 42.1 154s Consumption_12 15.6 39.3 154s Consumption_13 11.4 34.3 154s Consumption_14 7.0 34.1 154s Consumption_15 11.2 36.6 154s Consumption_16 12.3 39.3 154s Consumption_17 14.0 44.2 154s Consumption_18 17.6 47.7 154s Consumption_19 17.3 45.9 154s Consumption_20 15.3 49.4 154s Consumption_21 19.0 53.0 154s Consumption_22 21.1 61.8 154s Investment_2 0.0 0.0 154s Investment_3 0.0 0.0 154s Investment_4 0.0 0.0 154s Investment_5 0.0 0.0 154s Investment_6 0.0 0.0 154s Investment_7 0.0 0.0 154s Investment_8 0.0 0.0 154s Investment_9 0.0 0.0 154s Investment_10 0.0 0.0 154s Investment_11 0.0 0.0 154s Investment_12 0.0 0.0 154s Investment_13 0.0 0.0 154s Investment_14 0.0 0.0 154s Investment_15 0.0 0.0 154s Investment_16 0.0 0.0 154s Investment_17 0.0 0.0 154s Investment_18 0.0 0.0 154s Investment_19 0.0 0.0 154s Investment_20 0.0 0.0 154s Investment_21 0.0 0.0 154s Investment_22 0.0 0.0 154s PrivateWages_2 0.0 0.0 154s PrivateWages_3 0.0 0.0 154s PrivateWages_4 0.0 0.0 154s PrivateWages_5 0.0 0.0 154s PrivateWages_6 0.0 0.0 154s PrivateWages_8 0.0 0.0 154s PrivateWages_9 0.0 0.0 154s PrivateWages_10 0.0 0.0 154s PrivateWages_11 0.0 0.0 154s PrivateWages_12 0.0 0.0 154s PrivateWages_13 0.0 0.0 154s PrivateWages_14 0.0 0.0 154s PrivateWages_15 0.0 0.0 154s PrivateWages_16 0.0 0.0 154s PrivateWages_17 0.0 0.0 154s PrivateWages_18 0.0 0.0 154s PrivateWages_19 0.0 0.0 154s PrivateWages_20 0.0 0.0 154s PrivateWages_21 0.0 0.0 154s PrivateWages_22 0.0 0.0 154s Investment_(Intercept) Investment_corpProf 154s Consumption_2 0 0.0 154s Consumption_3 0 0.0 154s Consumption_4 0 0.0 154s Consumption_5 0 0.0 154s Consumption_6 0 0.0 154s Consumption_7 0 0.0 154s Consumption_8 0 0.0 154s Consumption_9 0 0.0 154s Consumption_10 0 0.0 154s Consumption_11 0 0.0 154s Consumption_12 0 0.0 154s Consumption_13 0 0.0 154s Consumption_14 0 0.0 154s Consumption_15 0 0.0 154s Consumption_16 0 0.0 154s Consumption_17 0 0.0 154s Consumption_18 0 0.0 154s Consumption_19 0 0.0 154s Consumption_20 0 0.0 154s Consumption_21 0 0.0 154s Consumption_22 0 0.0 154s Investment_2 1 12.4 154s Investment_3 1 16.9 154s Investment_4 1 18.4 154s Investment_5 1 19.4 154s Investment_6 1 20.1 154s Investment_7 1 19.6 154s Investment_8 1 19.8 154s Investment_9 1 21.1 154s Investment_10 1 21.7 154s Investment_11 1 15.6 154s Investment_12 1 11.4 154s Investment_13 1 7.0 154s Investment_14 1 11.2 154s Investment_15 1 12.3 154s Investment_16 1 14.0 154s Investment_17 1 17.6 154s Investment_18 1 17.3 154s Investment_19 1 15.3 154s Investment_20 1 19.0 154s Investment_21 1 21.1 154s Investment_22 1 23.5 154s PrivateWages_2 0 0.0 154s PrivateWages_3 0 0.0 154s PrivateWages_4 0 0.0 154s PrivateWages_5 0 0.0 154s PrivateWages_6 0 0.0 154s PrivateWages_8 0 0.0 154s PrivateWages_9 0 0.0 154s PrivateWages_10 0 0.0 154s PrivateWages_11 0 0.0 154s PrivateWages_12 0 0.0 154s PrivateWages_13 0 0.0 154s PrivateWages_14 0 0.0 154s PrivateWages_15 0 0.0 154s PrivateWages_16 0 0.0 154s PrivateWages_17 0 0.0 154s PrivateWages_18 0 0.0 154s PrivateWages_19 0 0.0 154s PrivateWages_20 0 0.0 154s PrivateWages_21 0 0.0 154s PrivateWages_22 0 0.0 154s Investment_corpProfLag Investment_capitalLag 154s Consumption_2 0.0 0 154s Consumption_3 0.0 0 154s Consumption_4 0.0 0 154s Consumption_5 0.0 0 154s Consumption_6 0.0 0 154s Consumption_7 0.0 0 154s Consumption_8 0.0 0 154s Consumption_9 0.0 0 154s Consumption_10 0.0 0 154s Consumption_11 0.0 0 154s Consumption_12 0.0 0 154s Consumption_13 0.0 0 154s Consumption_14 0.0 0 154s Consumption_15 0.0 0 154s Consumption_16 0.0 0 154s Consumption_17 0.0 0 154s Consumption_18 0.0 0 154s Consumption_19 0.0 0 154s Consumption_20 0.0 0 154s Consumption_21 0.0 0 154s Consumption_22 0.0 0 154s Investment_2 12.7 183 154s Investment_3 12.4 183 154s Investment_4 16.9 184 154s Investment_5 18.4 190 154s Investment_6 19.4 193 154s Investment_7 20.1 198 154s Investment_8 19.6 203 154s Investment_9 19.8 208 154s Investment_10 21.1 211 154s Investment_11 21.7 216 154s Investment_12 15.6 217 154s Investment_13 11.4 213 154s Investment_14 7.0 207 154s Investment_15 11.2 202 154s Investment_16 12.3 199 154s Investment_17 14.0 198 154s Investment_18 17.6 200 154s Investment_19 17.3 202 154s Investment_20 15.3 200 154s Investment_21 19.0 201 154s Investment_22 21.1 204 154s PrivateWages_2 0.0 0 154s PrivateWages_3 0.0 0 154s PrivateWages_4 0.0 0 154s PrivateWages_5 0.0 0 154s PrivateWages_6 0.0 0 154s PrivateWages_8 0.0 0 154s PrivateWages_9 0.0 0 154s PrivateWages_10 0.0 0 154s PrivateWages_11 0.0 0 154s PrivateWages_12 0.0 0 154s PrivateWages_13 0.0 0 154s PrivateWages_14 0.0 0 154s PrivateWages_15 0.0 0 154s PrivateWages_16 0.0 0 154s PrivateWages_17 0.0 0 154s PrivateWages_18 0.0 0 154s PrivateWages_19 0.0 0 154s PrivateWages_20 0.0 0 154s PrivateWages_21 0.0 0 154s PrivateWages_22 0.0 0 154s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 154s Consumption_2 0 0.0 0.0 154s Consumption_3 0 0.0 0.0 154s Consumption_4 0 0.0 0.0 154s Consumption_5 0 0.0 0.0 154s Consumption_6 0 0.0 0.0 154s Consumption_7 0 0.0 0.0 154s Consumption_8 0 0.0 0.0 154s Consumption_9 0 0.0 0.0 154s Consumption_10 0 0.0 0.0 154s Consumption_11 0 0.0 0.0 154s Consumption_12 0 0.0 0.0 154s Consumption_13 0 0.0 0.0 154s Consumption_14 0 0.0 0.0 154s Consumption_15 0 0.0 0.0 154s Consumption_16 0 0.0 0.0 154s Consumption_17 0 0.0 0.0 154s Consumption_18 0 0.0 0.0 154s Consumption_19 0 0.0 0.0 154s Consumption_20 0 0.0 0.0 154s Consumption_21 0 0.0 0.0 154s Consumption_22 0 0.0 0.0 154s Investment_2 0 0.0 0.0 154s Investment_3 0 0.0 0.0 154s Investment_4 0 0.0 0.0 154s Investment_5 0 0.0 0.0 154s Investment_6 0 0.0 0.0 154s Investment_7 0 0.0 0.0 154s Investment_8 0 0.0 0.0 154s Investment_9 0 0.0 0.0 154s Investment_10 0 0.0 0.0 154s Investment_11 0 0.0 0.0 154s Investment_12 0 0.0 0.0 154s Investment_13 0 0.0 0.0 154s Investment_14 0 0.0 0.0 154s Investment_15 0 0.0 0.0 154s Investment_16 0 0.0 0.0 154s Investment_17 0 0.0 0.0 154s Investment_18 0 0.0 0.0 154s Investment_19 0 0.0 0.0 154s Investment_20 0 0.0 0.0 154s Investment_21 0 0.0 0.0 154s Investment_22 0 0.0 0.0 154s PrivateWages_2 1 45.6 44.9 154s PrivateWages_3 1 50.1 45.6 154s PrivateWages_4 1 57.2 50.1 154s PrivateWages_5 1 57.1 57.2 154s PrivateWages_6 1 61.0 57.1 154s PrivateWages_8 1 64.4 64.0 154s PrivateWages_9 1 64.5 64.4 154s PrivateWages_10 1 67.0 64.5 154s PrivateWages_11 1 61.2 67.0 154s PrivateWages_12 1 53.4 61.2 154s PrivateWages_13 1 44.3 53.4 154s PrivateWages_14 1 45.1 44.3 154s PrivateWages_15 1 49.7 45.1 154s PrivateWages_16 1 54.4 49.7 154s PrivateWages_17 1 62.7 54.4 154s PrivateWages_18 1 65.0 62.7 154s PrivateWages_19 1 60.9 65.0 154s PrivateWages_20 1 69.5 60.9 154s PrivateWages_21 1 75.7 69.5 154s PrivateWages_22 1 88.4 75.7 154s PrivateWages_trend 154s Consumption_2 0 154s Consumption_3 0 154s Consumption_4 0 154s Consumption_5 0 154s Consumption_6 0 154s Consumption_7 0 154s Consumption_8 0 154s Consumption_9 0 154s Consumption_10 0 154s Consumption_11 0 154s Consumption_12 0 154s Consumption_13 0 154s Consumption_14 0 154s Consumption_15 0 154s Consumption_16 0 154s Consumption_17 0 154s Consumption_18 0 154s Consumption_19 0 154s Consumption_20 0 154s Consumption_21 0 154s Consumption_22 0 154s Investment_2 0 154s Investment_3 0 154s Investment_4 0 154s Investment_5 0 154s Investment_6 0 154s Investment_7 0 154s Investment_8 0 154s Investment_9 0 154s Investment_10 0 154s Investment_11 0 154s Investment_12 0 154s Investment_13 0 154s Investment_14 0 154s Investment_15 0 154s Investment_16 0 154s Investment_17 0 154s Investment_18 0 154s Investment_19 0 154s Investment_20 0 154s Investment_21 0 154s Investment_22 0 154s PrivateWages_2 -10 154s PrivateWages_3 -9 154s PrivateWages_4 -8 154s PrivateWages_5 -7 154s PrivateWages_6 -6 154s PrivateWages_8 -4 154s PrivateWages_9 -3 154s PrivateWages_10 -2 154s PrivateWages_11 -1 154s PrivateWages_12 0 154s PrivateWages_13 1 154s PrivateWages_14 2 154s PrivateWages_15 3 154s PrivateWages_16 4 154s PrivateWages_17 5 154s PrivateWages_18 6 154s PrivateWages_19 7 154s PrivateWages_20 8 154s PrivateWages_21 9 154s PrivateWages_22 10 154s > nobs 154s [1] 62 154s > linearHypothesis 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 51 154s 2 50 1 0.8 0.37 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 51 154s 2 50 1 0.72 0.4 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 51 154s 2 50 1 0.72 0.4 154s Linear hypothesis test (Theil's F test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 50 2 0.42 0.66 154s Linear hypothesis test (F statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df F Pr(>F) 154s 1 52 154s 2 50 2 0.37 0.69 154s Linear hypothesis test (Chi^2 statistic of a Wald test) 154s 154s Hypothesis: 154s Consumption_corpProf + Investment_capitalLag = 0 154s Consumption_corpProfLag - PrivateWages_trend = 0 154s 154s Model 1: restricted model 154s Model 2: kleinModel 154s 154s Res.Df Df Chisq Pr(>Chisq) 154s 1 52 154s 2 50 2 0.75 0.69 154s > logLik 154s 'log Lik.' -71.9 (df=13) 154s 'log Lik.' -77.1 (df=13) 154s compare log likelihood value with single-equation OLS 154s [1] "Mean relative difference: 0.000555" 154s > 154s > # 2SLS 154s > summary 154s 154s systemfit results 154s method: 2SLS 154s 154s N DF SSR detRCov OLS-R2 McElroy-R2 154s system 60 48 53.4 0.274 0.973 0.992 154s 154s N DF SSR MSE RMSE R2 Adj R2 154s Consumption 20 16 20.67 1.292 1.14 0.978 0.974 154s Investment 20 16 23.02 1.438 1.20 0.901 0.883 154s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 154s 154s The covariance matrix of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.034 0.309 -0.383 154s Investment 0.309 1.151 0.202 154s PrivateWages -0.383 0.202 0.487 154s 154s The correlations of the residuals 154s Consumption Investment PrivateWages 154s Consumption 1.000 0.284 -0.540 154s Investment 0.284 1.000 0.269 154s PrivateWages -0.540 0.269 1.000 154s 154s 154s 2SLS estimates for 'Consumption' (equation 1) 154s Model Formula: consump ~ corpProf + corpProfLag + wages 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 16.5093 1.3121 12.58 1.0e-09 *** 154s corpProf 0.0219 0.1159 0.19 0.85 154s corpProfLag 0.1931 0.1071 1.80 0.09 . 154s wages 0.8174 0.0408 20.05 9.2e-13 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.137 on 16 degrees of freedom 154s Number of observations: 20 Degrees of Freedom: 16 154s SSR: 20.671 MSE: 1.292 Root MSE: 1.137 154s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.974 154s 154s 154s 2SLS estimates for 'Investment' (equation 2) 154s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 17.843 6.850 2.60 0.01915 * 154s corpProf 0.217 0.155 1.40 0.18106 154s corpProfLag 0.542 0.148 3.65 0.00216 ** 154s capitalLag -0.145 0.033 -4.41 0.00044 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 1.199 on 16 degrees of freedom 154s Number of observations: 20 Degrees of Freedom: 16 154s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 154s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 154s 154s 154s 2SLS estimates for 'PrivateWages' (equation 3) 154s Model Formula: privWage ~ gnp + gnpLag + trend 154s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 154s gnpLag 154s 154s Estimate Std. Error t value Pr(>|t|) 154s (Intercept) 1.3431 1.1772 1.14 0.27070 154s gnp 0.4438 0.0358 12.39 1.3e-09 *** 154s gnpLag 0.1447 0.0389 3.72 0.00185 ** 154s trend 0.1238 0.0306 4.05 0.00093 *** 154s --- 154s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 154s 154s Residual standard error: 0.78 on 16 degrees of freedom 154s Number of observations: 20 Degrees of Freedom: 16 154s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 154s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 154s 154s > residuals 154s Consumption Investment PrivateWages 154s 1 NA NA NA 154s 2 -0.383 -1.0104 -1.3401 154s 3 -0.593 0.2478 0.2378 154s 4 -1.219 1.0621 1.1117 154s 5 -0.130 -1.4104 -0.1954 154s 6 0.354 0.4328 -0.5355 154s 7 NA NA NA 154s 8 1.551 1.0463 -0.7908 154s 9 1.440 0.0674 0.2831 154s 10 -0.286 1.7698 1.1353 154s 11 -0.453 -0.5912 -0.1765 155s 12 -0.994 -0.6318 0.6007 155s 13 -1.300 -0.6983 0.1443 155s 14 0.521 0.9724 0.4826 155s 15 -0.157 -0.1827 0.3016 155s 16 -0.014 0.1167 0.0261 155s 17 1.974 1.6266 -0.8614 155s 18 -0.576 -0.0525 0.9927 155s 19 -0.203 -3.0656 -0.4446 155s 20 1.342 0.1393 -0.3914 155s 21 1.039 -0.1305 -1.1115 155s 22 -1.912 0.2922 0.5312 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.3 0.810 26.8 155s 3 45.6 1.652 29.1 155s 4 50.4 4.138 33.0 155s 5 50.7 4.410 34.1 155s 6 52.2 4.667 35.9 155s 7 NA NA NA 155s 8 54.6 3.154 38.7 155s 9 55.9 2.933 38.9 155s 10 58.1 3.330 40.2 155s 11 55.5 1.591 38.1 155s 12 51.9 -2.768 33.9 155s 13 46.9 -5.502 28.9 155s 14 46.0 -6.072 28.0 155s 15 48.9 -2.817 30.3 155s 16 51.3 -1.417 33.2 155s 17 55.7 0.473 37.7 155s 18 59.3 2.053 40.0 155s 19 57.7 1.166 38.6 155s 20 60.3 1.161 42.0 155s 21 64.0 3.431 46.1 155s 22 71.6 4.608 52.8 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.3 0.473 41.3 43.3 155s 3 45.6 0.573 44.4 46.8 155s 4 50.4 0.366 49.6 51.2 155s 5 50.7 0.423 49.8 51.6 155s 6 52.2 0.426 51.3 53.1 155s 7 NA NA NA NA 155s 8 54.6 0.347 53.9 55.4 155s 9 55.9 0.384 55.0 56.7 155s 10 58.1 0.395 57.2 58.9 155s 11 55.5 0.729 53.9 57.0 155s 12 51.9 0.594 50.6 53.2 155s 13 46.9 0.752 45.3 48.5 155s 14 46.0 0.616 44.7 47.3 155s 15 48.9 0.373 48.1 49.6 155s 16 51.3 0.331 50.6 52.0 155s 17 55.7 0.403 54.9 56.6 155s 18 59.3 0.326 58.6 60.0 155s 19 57.7 0.411 56.8 58.6 155s 20 60.3 0.472 59.3 61.3 155s 21 64.0 0.443 63.0 64.9 155s 22 71.6 0.683 70.2 73.1 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 0.810 0.786 -0.8569 2.48 155s 3 1.652 0.541 0.5056 2.80 155s 4 4.138 0.511 3.0552 5.22 155s 5 4.410 0.421 3.5172 5.30 155s 6 4.667 0.395 3.8294 5.51 155s 7 NA NA NA NA 155s 8 3.154 0.327 2.4602 3.85 155s 9 2.933 0.489 1.8967 3.97 155s 10 3.330 0.537 2.1915 4.47 155s 11 1.591 0.786 -0.0748 3.26 155s 12 -2.768 0.615 -4.0716 -1.46 155s 13 -5.502 0.787 -7.1696 -3.83 155s 14 -6.072 0.842 -7.8568 -4.29 155s 15 -2.817 0.397 -3.6591 -1.98 155s 16 -1.417 0.343 -2.1436 -0.69 155s 17 0.473 0.457 -0.4954 1.44 155s 18 2.053 0.286 1.4471 2.66 155s 19 1.166 0.430 0.2549 2.08 155s 20 1.161 0.515 0.0698 2.25 155s 21 3.431 0.426 2.5282 4.33 155s 22 4.608 0.606 3.3223 5.89 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.328 26.1 27.5 155s 3 29.1 0.340 28.3 29.8 155s 4 33.0 0.360 32.2 33.8 155s 5 34.1 0.258 33.5 34.6 155s 6 35.9 0.266 35.4 36.5 155s 7 NA NA NA NA 155s 8 38.7 0.262 38.1 39.2 155s 9 38.9 0.250 38.4 39.4 155s 10 40.2 0.240 39.7 40.7 155s 11 38.1 0.355 37.3 38.8 155s 12 33.9 0.382 33.1 34.7 155s 13 28.9 0.456 27.9 29.8 155s 14 28.0 0.348 27.3 28.8 155s 15 30.3 0.339 29.6 31.0 155s 16 33.2 0.284 32.6 33.8 155s 17 37.7 0.293 37.0 38.3 155s 18 40.0 0.218 39.5 40.5 155s 19 38.6 0.358 37.9 39.4 155s 20 42.0 0.307 41.3 42.6 155s 21 46.1 0.310 45.5 46.8 155s 22 52.8 0.496 51.7 53.8 155s > model.frame 155s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 155s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 155s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 155s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 155s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 155s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 155s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 155s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 155s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 155s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 155s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 155s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 155s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 155s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 155s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 155s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 155s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 155s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 155s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 155s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 155s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 155s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 155s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 155s trend 155s 1 -11 155s 2 -10 155s 3 -9 155s 4 -8 155s 5 -7 155s 6 -6 155s 7 -5 155s 8 -4 155s 9 -3 155s 10 -2 155s 11 -1 155s 12 0 155s 13 1 155s 14 2 155s 15 3 155s 16 4 155s 17 5 155s 18 6 155s 19 7 155s 20 8 155s 21 9 155s 22 10 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 155s [3] "Numeric: lengths (744, 720) differ" 155s > nobs 155s [1] 60 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 48 1 0.95 0.34 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 48 1 1.05 0.31 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 49 155s 2 48 1 1.05 0.3 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 48 2 0.48 0.62 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 48 2 0.53 0.59 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 50 155s 2 48 2 1.06 0.59 155s > logLik 155s 'log Lik.' -72.2 (df=13) 155s 'log Lik.' -79.7 (df=13) 155s > 155s > # SUR 155s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: SUR 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 62 50 46.2 0.154 0.977 0.993 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 21 17 18.1 1.062 1.031 0.981 0.977 155s Investment 21 17 17.5 1.030 1.015 0.931 0.918 155s PrivateWages 20 16 10.6 0.663 0.814 0.987 0.984 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 0.8562 -0.0129 -0.371 155s Investment -0.0129 0.7548 0.159 155s PrivateWages -0.3706 0.1594 0.487 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 0.8684 0.0078 -0.442 155s Investment 0.0078 0.7702 0.237 155s PrivateWages -0.4416 0.2366 0.531 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.00000 0.00562 -0.651 155s Investment 0.00562 1.00000 0.372 155s PrivateWages -0.65109 0.37198 1.000 155s 155s 155s SUR estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.0647 1.1729 13.70 1.3e-10 *** 155s corpProf 0.2283 0.0775 2.94 0.0091 ** 155s corpProfLag 0.0723 0.0771 0.94 0.3615 155s wages 0.7930 0.0352 22.51 4.3e-14 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.031 on 17 degrees of freedom 155s Number of observations: 21 Degrees of Freedom: 17 155s SSR: 18.06 MSE: 1.062 Root MSE: 1.031 155s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 155s 155s 155s SUR estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 12.3516 4.5762 2.70 0.01520 * 155s corpProf 0.4461 0.0818 5.45 4.3e-05 *** 155s corpProfLag 0.3609 0.0849 4.25 0.00054 *** 155s capitalLag -0.1224 0.0223 -5.47 4.1e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.015 on 17 degrees of freedom 155s Number of observations: 21 Degrees of Freedom: 17 155s SSR: 17.514 MSE: 1.03 Root MSE: 1.015 155s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 155s 155s 155s SUR estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.5433 1.1371 1.36 0.19 155s gnp 0.4117 0.0279 14.77 9.6e-11 *** 155s gnpLag 0.1743 0.0317 5.50 4.8e-05 *** 155s trend 0.1550 0.0283 5.49 5.0e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.814 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.611 MSE: 0.663 Root MSE: 0.814 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.27628 -0.3003 -1.0910 155s 3 -1.35400 -0.1239 0.5795 155s 4 -1.62816 1.1154 1.5172 155s 5 -0.56494 -1.4358 -0.0341 155s 6 -0.06584 0.3581 -0.2772 155s 7 0.83245 1.4526 NA 155s 8 1.28855 0.8290 -0.6896 155s 9 0.96709 -0.5092 0.3445 155s 10 -0.66705 1.2210 1.2429 155s 11 0.41992 0.2497 -0.3602 155s 12 -0.05971 0.0470 0.3068 155s 13 -0.08649 0.3096 -0.2426 155s 14 0.33124 0.3652 0.3591 155s 15 -0.00604 -0.1652 0.2710 155s 16 -0.01478 0.0124 -0.0207 155s 17 1.55472 1.0339 -0.8117 155s 18 -0.41250 0.0255 0.8398 155s 19 0.29322 -2.6293 -0.8283 155s 20 0.91756 -0.5906 -0.4091 155s 21 0.71583 -0.7036 -1.2154 155s 22 -2.26223 -0.5283 0.6207 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.2 0.100 26.6 155s 3 46.4 2.024 28.7 155s 4 50.8 4.085 32.6 155s 5 51.2 4.436 33.9 155s 6 52.7 4.742 35.7 155s 7 54.3 4.147 NA 155s 8 54.9 3.371 38.6 155s 9 56.3 3.509 38.9 155s 10 58.5 3.879 40.1 155s 11 54.6 0.750 38.3 155s 12 51.0 -3.447 34.2 155s 13 45.7 -6.510 29.2 155s 14 46.2 -5.465 28.1 155s 15 48.7 -2.835 30.3 155s 16 51.3 -1.312 33.2 155s 17 56.1 1.066 37.6 155s 18 59.1 1.974 40.2 155s 19 57.2 0.729 39.0 155s 20 60.7 1.891 42.0 155s 21 64.3 4.004 46.2 155s 22 72.0 5.428 52.7 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.2 0.414 41.3 43.0 155s 3 46.4 0.451 45.4 47.3 155s 4 50.8 0.296 50.2 51.4 155s 5 51.2 0.342 50.5 51.9 155s 6 52.7 0.342 52.0 53.4 155s 7 54.3 0.309 53.6 54.9 155s 8 54.9 0.282 54.3 55.5 155s 9 56.3 0.303 55.7 56.9 155s 10 58.5 0.321 57.8 59.1 155s 11 54.6 0.515 53.5 55.6 155s 12 51.0 0.418 50.1 51.8 155s 13 45.7 0.548 44.6 46.8 155s 14 46.2 0.528 45.1 47.2 155s 15 48.7 0.333 48.0 49.4 155s 16 51.3 0.296 50.7 51.9 155s 17 56.1 0.321 55.5 56.8 155s 18 59.1 0.287 58.5 59.7 155s 19 57.2 0.325 56.6 57.9 155s 20 60.7 0.383 59.9 61.5 155s 21 64.3 0.382 63.5 65.1 155s 22 72.0 0.599 70.8 73.2 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 0.100 0.511 -0.926 1.127 155s 3 2.024 0.425 1.170 2.878 155s 4 4.085 0.378 3.325 4.845 155s 5 4.436 0.313 3.806 5.065 155s 6 4.742 0.296 4.147 5.336 155s 7 4.147 0.279 3.586 4.709 155s 8 3.371 0.250 2.868 3.874 155s 9 3.509 0.331 2.845 4.174 155s 10 3.879 0.380 3.116 4.642 155s 11 0.750 0.512 -0.279 1.779 155s 12 -3.447 0.433 -4.316 -2.578 155s 13 -6.510 0.527 -7.568 -5.451 155s 14 -5.465 0.587 -6.645 -4.285 155s 15 -2.835 0.320 -3.477 -2.193 155s 16 -1.312 0.274 -1.863 -0.761 155s 17 1.066 0.296 0.472 1.661 155s 18 1.974 0.208 1.558 2.391 155s 19 0.729 0.265 0.197 1.262 155s 20 1.891 0.311 1.266 2.515 155s 21 4.004 0.283 3.435 4.572 155s 22 5.428 0.393 4.640 6.217 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.6 0.318 26.0 27.2 155s 3 28.7 0.317 28.1 29.4 155s 4 32.6 0.315 32.0 33.2 155s 5 33.9 0.243 33.4 34.4 155s 6 35.7 0.242 35.2 36.2 155s 7 NA NA NA NA 155s 8 38.6 0.247 38.1 39.1 155s 9 38.9 0.236 38.4 39.3 155s 10 40.1 0.227 39.6 40.5 155s 11 38.3 0.306 37.6 38.9 155s 12 34.2 0.312 33.6 34.8 155s 13 29.2 0.376 28.5 30.0 155s 14 28.1 0.337 27.5 28.8 155s 15 30.3 0.328 29.7 31.0 155s 16 33.2 0.274 32.7 33.8 155s 17 37.6 0.266 37.1 38.1 155s 18 40.2 0.213 39.7 40.6 155s 19 39.0 0.310 38.4 39.7 155s 20 42.0 0.282 41.4 42.6 155s 21 46.2 0.300 45.6 46.8 155s 22 52.7 0.451 51.8 53.6 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] TRUE 155s > nobs 155s [1] 62 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 51 155s 2 50 1 1.39 0.24 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 51 155s 2 50 1 1.7 0.2 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 51 155s 2 50 1 1.7 0.19 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 52 155s 2 50 2 0.72 0.49 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 52 155s 2 50 2 0.87 0.42 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 52 155s 2 50 2 1.75 0.42 155s > logLik 155s 'log Lik.' -69.4 (df=18) 155s 'log Lik.' -78.2 (df=18) 155s > 155s > # 3SLS 155s > summary 155s 155s systemfit results 155s method: 3SLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 60 48 62.6 0.265 0.968 0.994 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 20 16 17.8 1.114 1.06 0.981 0.977 155s Investment 20 16 34.3 2.143 1.46 0.853 0.825 155s PrivateWages 20 16 10.5 0.656 0.81 0.987 0.984 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 1.034 0.309 -0.383 155s Investment 0.309 1.151 0.202 155s PrivateWages -0.383 0.202 0.487 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 0.891 0.304 -0.391 155s Investment 0.304 1.715 0.388 155s PrivateWages -0.391 0.388 0.525 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.246 -0.571 155s Investment 0.246 1.000 0.409 155s PrivateWages -0.571 0.409 1.000 155s 155s 155s 3SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.3668 1.3024 12.57 1.1e-09 *** 155s corpProf 0.1186 0.1073 1.10 0.29 155s corpProfLag 0.1448 0.1008 1.44 0.17 155s wages 0.8006 0.0391 20.47 6.7e-13 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.056 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 17.825 MSE: 1.114 Root MSE: 1.056 155s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 155s 155s 155s 3SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 24.8872 6.2956 3.95 0.00114 ** 155s corpProf 0.0702 0.1458 0.48 0.63648 155s corpProfLag 0.6688 0.1402 4.77 0.00021 *** 155s capitalLag -0.1786 0.0303 -5.90 2.3e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.464 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 34.295 MSE: 2.143 Root MSE: 1.464 155s Multiple R-Squared: 0.853 Adjusted R-Squared: 0.825 155s 155s 155s 3SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.6387 1.1457 1.43 0.17188 155s gnp 0.4062 0.0324 12.52 1.1e-09 *** 155s gnpLag 0.1784 0.0347 5.14 1.0e-04 *** 155s trend 0.1435 0.0292 4.91 0.00016 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.81 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.497 MSE: 0.656 Root MSE: 0.81 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.3538 -1.795 -1.2388 155s 3 -0.9465 0.154 0.4649 155s 4 -1.4189 0.678 1.4344 155s 5 -0.3546 -1.666 -0.1354 155s 6 0.1366 0.251 -0.3452 155s 7 NA NA NA 155s 8 1.4213 1.150 -0.7445 155s 9 1.2173 0.476 0.3001 155s 10 -0.4636 2.200 1.2232 155s 11 -0.0650 -0.962 -0.4104 155s 12 -0.5422 -0.808 0.2495 155s 13 -0.7092 -1.098 -0.3057 155s 14 0.4898 1.542 0.3497 155s 15 -0.0502 -0.155 0.2949 155s 16 0.0272 0.154 0.0214 155s 17 1.8311 1.932 -0.7322 155s 18 -0.4567 -0.180 0.9090 155s 19 0.0650 -3.381 -0.7795 155s 20 1.2135 0.557 -0.2847 155s 21 0.9466 0.167 -1.0812 155s 22 -1.9877 0.784 0.8102 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.3 1.595 26.7 155s 3 45.9 1.746 28.8 155s 4 50.6 4.522 32.7 155s 5 51.0 4.666 34.0 155s 6 52.5 4.849 35.7 155s 7 NA NA NA 155s 8 54.8 3.050 38.6 155s 9 56.1 2.524 38.9 155s 10 58.3 2.900 40.1 155s 11 55.1 1.962 38.3 155s 12 51.4 -2.592 34.3 155s 13 46.3 -5.102 29.3 155s 14 46.0 -6.642 28.2 155s 15 48.8 -2.845 30.3 155s 16 51.3 -1.454 33.2 155s 17 55.9 0.168 37.5 155s 18 59.2 2.180 40.1 155s 19 57.4 1.481 39.0 155s 20 60.4 0.743 41.9 155s 21 64.1 3.133 46.1 155s 22 71.7 4.116 52.5 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.3 0.468 39.8 44.7 155s 3 45.9 0.543 43.4 48.5 155s 4 50.6 0.352 48.3 53.0 155s 5 51.0 0.407 48.6 53.4 155s 6 52.5 0.411 50.1 54.9 155s 7 NA NA NA NA 155s 8 54.8 0.340 52.4 57.1 155s 9 56.1 0.372 53.7 58.5 155s 10 58.3 0.387 55.9 60.6 155s 11 55.1 0.687 52.4 57.7 155s 12 51.4 0.558 48.9 54.0 155s 13 46.3 0.713 43.6 49.0 155s 14 46.0 0.599 43.4 48.6 155s 15 48.8 0.368 46.4 51.1 155s 16 51.3 0.326 48.9 53.6 155s 17 55.9 0.388 53.5 58.3 155s 18 59.2 0.319 56.8 61.5 155s 19 57.4 0.391 55.0 59.8 155s 20 60.4 0.457 57.9 62.8 155s 21 64.1 0.437 61.6 66.5 155s 22 71.7 0.674 69.0 74.3 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 1.595 0.731 -1.8742 5.065 155s 3 1.746 0.533 -1.5566 5.050 155s 4 4.522 0.484 1.2530 7.791 155s 5 4.666 0.406 1.4458 7.887 155s 6 4.849 0.386 1.6390 8.058 155s 7 NA NA NA NA 155s 8 3.050 0.325 -0.1296 6.229 155s 9 2.524 0.467 -0.7334 5.782 155s 10 2.900 0.515 -0.3900 6.190 155s 11 1.962 0.769 -1.5438 5.467 155s 12 -2.592 0.608 -5.9519 0.769 155s 13 -5.102 0.774 -8.6129 -1.592 155s 14 -6.642 0.807 -10.1867 -3.098 155s 15 -2.845 0.395 -6.0599 0.370 155s 16 -1.454 0.341 -4.6409 1.733 155s 17 0.168 0.442 -3.0739 3.410 155s 18 2.180 0.281 -0.9807 5.340 155s 19 1.481 0.414 -1.7440 4.706 155s 20 0.743 0.492 -2.5310 4.017 155s 21 3.133 0.414 -0.0924 6.358 155s 22 4.116 0.583 0.7756 7.457 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.7 0.322 24.9 28.6 155s 3 28.8 0.328 27.0 30.7 155s 4 32.7 0.340 30.8 34.5 155s 5 34.0 0.250 32.2 35.8 155s 6 35.7 0.257 33.9 37.5 155s 7 NA NA NA NA 155s 8 38.6 0.254 36.8 40.4 155s 9 38.9 0.241 37.1 40.7 155s 10 40.1 0.235 38.3 41.9 155s 11 38.3 0.325 36.5 40.2 155s 12 34.3 0.349 32.4 36.1 155s 13 29.3 0.425 27.4 31.2 155s 14 28.2 0.340 26.3 30.0 155s 15 30.3 0.326 28.5 32.2 155s 16 33.2 0.272 31.4 35.0 155s 17 37.5 0.273 35.7 39.3 155s 18 40.1 0.214 38.3 41.9 155s 19 39.0 0.336 37.1 40.8 155s 20 41.9 0.290 40.1 43.7 155s 21 46.1 0.305 44.2 47.9 155s 22 52.5 0.479 50.5 54.5 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 155s [3] "Numeric: lengths (744, 720) differ" 155s > nobs 155s [1] 60 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 48 1 0.22 0.64 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 48 1 0.29 0.59 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 49 155s 2 48 1 0.29 0.59 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 48 2 0.29 0.75 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 48 2 0.38 0.68 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 50 155s 2 48 2 0.77 0.68 155s > logLik 155s 'log Lik.' -71.9 (df=18) 155s 'log Lik.' -82.9 (df=18) 155s > 155s > # I3SLS 155s > summary 155s 155s systemfit results 155s method: iterated 3SLS 155s 155s convergence achieved after 22 iterations 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 60 48 107 0.47 0.946 0.996 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 20 16 18.1 1.13 1.063 0.981 0.977 155s Investment 20 16 76.4 4.77 2.185 0.672 0.610 155s PrivateWages 20 16 12.3 0.77 0.877 0.984 0.982 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 0.905 0.509 -0.437 155s Investment 0.509 3.819 0.709 155s PrivateWages -0.437 0.709 0.616 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 0.905 0.509 -0.437 155s Investment 0.509 3.819 0.709 155s PrivateWages -0.437 0.709 0.616 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.274 -0.585 155s Investment 0.274 1.000 0.462 155s PrivateWages -0.585 0.462 1.000 155s 155s 155s 3SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.4728 1.2187 13.52 3.6e-10 *** 155s corpProf 0.1642 0.0952 1.73 0.10 155s corpProfLag 0.1552 0.0903 1.72 0.11 155s wages 0.7756 0.0356 21.82 2.5e-13 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.063 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 18.095 MSE: 1.131 Root MSE: 1.063 155s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 155s 155s 155s 3SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 38.7938 9.7249 3.99 0.00106 ** 155s corpProf -0.2501 0.2337 -1.07 0.30036 155s corpProfLag 0.9129 0.2271 4.02 0.00099 *** 155s capitalLag -0.2409 0.0469 -5.14 9.9e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 2.185 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 76.371 MSE: 4.773 Root MSE: 2.185 155s Multiple R-Squared: 0.672 Adjusted R-Squared: 0.61 155s 155s 155s 3SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 2.4620 1.2228 2.01 0.061 . 155s gnp 0.3776 0.0318 11.88 2.4e-09 *** 155s gnpLag 0.1937 0.0331 5.85 2.5e-05 *** 155s trend 0.1619 0.0300 5.40 5.9e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.877 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 12.318 MSE: 0.77 Root MSE: 0.877 155s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.982 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.4522 -3.4485 -1.2596 155s 3 -1.1470 0.0027 0.5437 155s 4 -1.6147 0.0274 1.6290 155s 5 -0.6117 -2.0392 -0.0707 155s 6 -0.1229 0.0457 -0.1859 155s 7 NA NA NA 155s 8 1.2461 1.4658 -0.6304 155s 9 1.0158 1.4202 0.3924 155s 10 -0.6460 3.2062 1.3671 155s 11 -0.0554 -1.7386 -0.4891 155s 12 -0.3472 -1.3793 0.0179 155s 13 -0.3947 -2.2646 -0.6968 155s 14 0.6536 2.4092 0.1021 155s 15 0.0821 -0.2787 0.1482 155s 16 0.1381 0.1196 -0.0796 155s 17 1.8826 2.5548 -0.6862 155s 18 -0.3415 -0.4009 0.8755 155s 19 0.2296 -4.0454 -0.9839 155s 20 1.3178 1.4481 -0.1989 155s 21 1.0065 0.9087 -0.9681 155s 22 -1.8388 1.9868 1.1734 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.4 3.249 26.8 155s 3 46.1 1.897 28.8 155s 4 50.8 5.173 32.5 155s 5 51.2 5.039 34.0 155s 6 52.7 5.054 35.6 155s 7 NA NA NA 155s 8 55.0 2.734 38.5 155s 9 56.3 1.580 38.8 155s 10 58.4 1.894 39.9 155s 11 55.1 2.739 38.4 155s 12 51.2 -2.021 34.5 155s 13 46.0 -3.935 29.7 155s 14 45.8 -7.509 28.4 155s 15 48.6 -2.721 30.5 155s 16 51.2 -1.420 33.3 155s 17 55.8 -0.455 37.5 155s 18 59.0 2.401 40.1 155s 19 57.3 2.145 39.2 155s 20 60.3 -0.148 41.8 155s 21 64.0 2.391 46.0 155s 22 71.5 2.913 52.1 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.4 0.437 41.5 43.2 155s 3 46.1 0.492 45.2 47.1 155s 4 50.8 0.321 50.2 51.5 155s 5 51.2 0.369 50.5 52.0 155s 6 52.7 0.372 52.0 53.5 155s 7 NA NA NA NA 155s 8 55.0 0.310 54.3 55.6 155s 9 56.3 0.338 55.6 57.0 155s 10 58.4 0.355 57.7 59.2 155s 11 55.1 0.618 53.8 56.3 155s 12 51.2 0.501 50.2 52.3 155s 13 46.0 0.642 44.7 47.3 155s 14 45.8 0.547 44.7 46.9 155s 15 48.6 0.340 47.9 49.3 155s 16 51.2 0.300 50.6 51.8 155s 17 55.8 0.354 55.1 56.5 155s 18 59.0 0.294 58.4 59.6 155s 19 57.3 0.354 56.6 58.0 155s 20 60.3 0.418 59.4 61.1 155s 21 64.0 0.407 63.2 64.8 155s 22 71.5 0.628 70.3 72.8 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 3.249 1.160 0.91672 5.580 155s 3 1.897 0.934 0.02009 3.775 155s 4 5.173 0.803 3.55865 6.787 155s 5 5.039 0.693 3.64486 6.433 155s 6 5.054 0.674 3.69840 6.410 155s 7 NA NA NA NA 155s 8 2.734 0.584 1.56002 3.908 155s 9 1.580 0.783 0.00466 3.155 155s 10 1.894 0.868 0.14846 3.639 155s 11 2.739 1.321 0.08241 5.395 155s 12 -2.021 1.064 -4.16036 0.119 155s 13 -3.935 1.349 -6.64712 -1.224 155s 14 -7.509 1.360 -10.24349 -4.775 155s 15 -2.721 0.712 -4.15288 -1.290 155s 16 -1.420 0.614 -2.65412 -0.185 155s 17 -0.455 0.751 -1.96433 1.055 155s 18 2.401 0.498 1.39939 3.402 155s 19 2.145 0.698 0.74152 3.549 155s 20 -0.148 0.816 -1.78957 1.493 155s 21 2.391 0.713 0.95855 3.824 155s 22 2.913 0.984 0.93419 4.892 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.347 26.1 27.5 155s 3 28.8 0.348 28.1 29.5 155s 4 32.5 0.354 31.8 33.2 155s 5 34.0 0.263 33.4 34.5 155s 6 35.6 0.274 35.0 36.1 155s 7 NA NA NA NA 155s 8 38.5 0.268 38.0 39.1 155s 9 38.8 0.256 38.3 39.3 155s 10 39.9 0.254 39.4 40.4 155s 11 38.4 0.323 37.7 39.0 155s 12 34.5 0.347 33.8 35.2 155s 13 29.7 0.435 28.8 30.6 155s 14 28.4 0.366 27.7 29.1 155s 15 30.5 0.341 29.8 31.1 155s 16 33.3 0.285 32.7 33.9 155s 17 37.5 0.275 36.9 38.0 155s 18 40.1 0.233 39.7 40.6 155s 19 39.2 0.346 38.5 39.9 155s 20 41.8 0.298 41.2 42.4 155s 21 46.0 0.329 45.3 46.6 155s 22 52.1 0.510 51.1 53.2 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 155s [3] "Numeric: lengths (744, 720) differ" 155s > nobs 155s [1] 60 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 48 1 0.4 0.53 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 48 1 0.5 0.49 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 49 155s 2 48 1 0.5 0.48 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 48 2 0.66 0.52 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 48 2 0.83 0.44 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 50 155s 2 48 2 1.66 0.44 155s > logLik 155s 'log Lik.' -77.6 (df=18) 155s 'log Lik.' -92.7 (df=18) 155s > 155s > # OLS 155s > summary 155s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s 155s systemfit results 155s method: OLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 61 49 44.5 0.382 0.977 0.99 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 20 16 17.48 1.093 1.04 0.981 0.978 155s Investment 21 17 17.32 1.019 1.01 0.931 0.919 155s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.124 0.034 -0.442 155s Investment 0.034 0.928 0.130 155s PrivateWages -0.442 0.130 0.563 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.0000 0.0266 -0.563 155s Investment 0.0266 1.0000 0.169 155s PrivateWages -0.5630 0.1689 1.000 155s 155s 155s OLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.1357 1.3571 11.89 2.4e-09 *** 155s corpProf 0.1994 0.0949 2.10 0.052 . 155s corpProfLag 0.0969 0.0944 1.03 0.320 155s wages 0.7940 0.0415 19.16 1.9e-12 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.045 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 17.481 MSE: 1.093 Root MSE: 1.045 155s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 155s 155s 155s OLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 10.1258 5.2164 1.94 0.06901 . 155s corpProf 0.4796 0.0927 5.17 7.6e-05 *** 155s corpProfLag 0.3330 0.0963 3.46 0.00299 ** 155s capitalLag -0.1118 0.0255 -4.38 0.00041 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.009 on 17 degrees of freedom 155s Number of observations: 21 Degrees of Freedom: 17 155s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 155s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 155s 155s 155s OLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3550 1.2591 1.08 0.2978 155s gnp 0.4417 0.0319 13.86 2.5e-10 *** 155s gnpLag 0.1466 0.0366 4.01 0.0010 ** 155s trend 0.1244 0.0323 3.85 0.0014 ** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.78 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 155s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 155s 155s compare coef with single-equation OLS 155s [1] TRUE 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.3304 -0.0668 -1.3389 155s 3 -1.2748 -0.0476 0.2462 155s 4 -1.6213 1.2467 1.1255 155s 5 -0.5661 -1.3512 -0.1959 155s 6 -0.0730 0.4154 -0.5284 155s 7 0.7915 1.4923 NA 155s 8 1.2648 0.7889 -0.7909 155s 9 0.9746 -0.6317 0.2819 155s 10 NA 1.0830 1.1384 155s 11 0.2225 0.2791 -0.1904 155s 12 -0.2256 0.0369 0.5813 155s 13 -0.2711 0.3659 0.1206 155s 14 0.3765 0.2237 0.4773 155s 15 -0.0349 -0.1728 0.3035 155s 16 -0.0243 0.0101 0.0284 155s 17 1.6023 0.9719 -0.8517 155s 18 -0.4658 0.0516 0.9908 155s 19 0.1914 -2.5656 -0.4597 155s 20 0.9683 -0.6866 -0.3819 155s 21 0.7325 -0.7807 -1.1062 155s 22 -2.2370 -0.6623 0.5501 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.2 -0.133 26.8 155s 3 46.3 1.948 29.1 155s 4 50.8 3.953 33.0 155s 5 51.2 4.351 34.1 155s 6 52.7 4.685 35.9 155s 7 54.3 4.108 NA 155s 8 54.9 3.411 38.7 155s 9 56.3 3.632 38.9 155s 10 NA 4.017 40.2 155s 11 54.8 0.721 38.1 155s 12 51.1 -3.437 33.9 155s 13 45.9 -6.566 28.9 155s 14 46.1 -5.324 28.0 155s 15 48.7 -2.827 30.3 155s 16 51.3 -1.310 33.2 155s 17 56.1 1.128 37.7 155s 18 59.2 1.948 40.0 155s 19 57.3 0.666 38.7 155s 20 60.6 1.987 42.0 155s 21 64.3 4.081 46.1 155s 22 71.9 5.562 52.7 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.2 0.478 39.9 44.5 155s 3 46.3 0.537 43.9 48.6 155s 4 50.8 0.364 48.6 53.0 155s 5 51.2 0.427 48.9 53.4 155s 6 52.7 0.433 50.4 54.9 155s 7 54.3 0.394 52.1 56.6 155s 8 54.9 0.360 52.7 57.2 155s 9 56.3 0.387 54.1 58.6 155s 10 NA NA NA NA 155s 11 54.8 0.635 52.3 57.2 155s 12 51.1 0.501 48.8 53.5 155s 13 45.9 0.656 43.4 48.4 155s 14 46.1 0.629 43.7 48.6 155s 15 48.7 0.389 46.5 51.0 155s 16 51.3 0.345 49.1 53.5 155s 17 56.1 0.379 53.9 58.3 155s 18 59.2 0.336 57.0 61.4 155s 19 57.3 0.385 55.1 59.5 155s 20 60.6 0.450 58.3 62.9 155s 21 64.3 0.448 62.0 66.6 155s 22 71.9 0.697 69.4 74.5 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 -0.133 0.579 -2.472 2.206 155s 3 1.948 0.476 -0.295 4.190 155s 4 3.953 0.428 1.750 6.157 155s 5 4.351 0.354 2.202 6.501 155s 6 4.685 0.333 2.548 6.821 155s 7 4.108 0.314 1.983 6.232 155s 8 3.411 0.279 1.306 5.516 155s 9 3.632 0.371 1.470 5.793 155s 10 4.017 0.426 1.815 6.219 155s 11 0.721 0.574 -1.613 3.054 155s 12 -3.437 0.484 -5.686 -1.188 155s 13 -6.566 0.588 -8.913 -4.219 155s 14 -5.324 0.662 -7.750 -2.898 155s 15 -2.827 0.356 -4.978 -0.676 155s 16 -1.310 0.305 -3.429 0.809 155s 17 1.128 0.332 -1.007 3.263 155s 18 1.948 0.232 -0.133 4.030 155s 19 0.666 0.298 -1.449 2.781 155s 20 1.987 0.350 -0.160 4.133 155s 21 4.081 0.317 1.955 6.207 155s 22 5.562 0.440 3.349 7.775 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.352 25.1 28.6 155s 3 29.1 0.355 27.3 30.8 155s 4 33.0 0.358 31.2 34.7 155s 5 34.1 0.277 32.4 35.8 155s 6 35.9 0.276 34.3 37.6 155s 7 NA NA NA NA 155s 8 38.7 0.282 37.0 40.4 155s 9 38.9 0.268 37.3 40.6 155s 10 40.2 0.255 38.5 41.8 155s 11 38.1 0.351 36.4 39.8 155s 12 33.9 0.355 32.2 35.6 155s 13 28.9 0.421 27.1 30.7 155s 14 28.0 0.370 26.3 29.8 155s 15 30.3 0.364 28.6 32.0 155s 16 33.2 0.304 31.5 34.9 155s 17 37.7 0.298 36.0 39.3 155s 18 40.0 0.233 38.4 41.6 155s 19 38.7 0.349 36.9 40.4 155s 20 42.0 0.314 40.3 43.7 155s 21 46.1 0.328 44.4 47.8 155s 22 52.7 0.494 50.9 54.6 155s > model.frame 155s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 155s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 155s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 155s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 155s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 155s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 155s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 155s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 155s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 155s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 155s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 155s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 155s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 155s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 155s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 155s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 155s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 155s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 155s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 155s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 155s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 155s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 155s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 155s trend 155s 1 -11 155s 2 -10 155s 3 -9 155s 4 -8 155s 5 -7 155s 6 -6 155s 7 -5 155s 8 -4 155s 9 -3 155s 10 -2 155s 11 -1 155s 12 0 155s 13 1 155s 14 2 155s 15 3 155s 16 4 155s 17 5 155s 18 6 155s 19 7 155s 20 8 155s 21 9 155s 22 10 155s > model.matrix 155s Consumption_(Intercept) Consumption_corpProf 155s Consumption_2 1 12.4 155s Consumption_3 1 16.9 155s Consumption_4 1 18.4 155s Consumption_5 1 19.4 155s Consumption_6 1 20.1 155s Consumption_7 1 19.6 155s Consumption_8 1 19.8 155s Consumption_9 1 21.1 155s Consumption_11 1 15.6 155s Consumption_12 1 11.4 155s Consumption_13 1 7.0 155s Consumption_14 1 11.2 155s Consumption_15 1 12.3 155s Consumption_16 1 14.0 155s Consumption_17 1 17.6 155s Consumption_18 1 17.3 155s Consumption_19 1 15.3 155s Consumption_20 1 19.0 155s Consumption_21 1 21.1 155s Consumption_22 1 23.5 155s Investment_2 0 0.0 155s Investment_3 0 0.0 155s Investment_4 0 0.0 155s Investment_5 0 0.0 155s Investment_6 0 0.0 155s Investment_7 0 0.0 155s Investment_8 0 0.0 155s Investment_9 0 0.0 155s Investment_10 0 0.0 155s Investment_11 0 0.0 155s Investment_12 0 0.0 155s Investment_13 0 0.0 155s Investment_14 0 0.0 155s Investment_15 0 0.0 155s Investment_16 0 0.0 155s Investment_17 0 0.0 155s Investment_18 0 0.0 155s Investment_19 0 0.0 155s Investment_20 0 0.0 155s Investment_21 0 0.0 155s Investment_22 0 0.0 155s PrivateWages_2 0 0.0 155s PrivateWages_3 0 0.0 155s PrivateWages_4 0 0.0 155s PrivateWages_5 0 0.0 155s PrivateWages_6 0 0.0 155s PrivateWages_8 0 0.0 155s PrivateWages_9 0 0.0 155s PrivateWages_10 0 0.0 155s PrivateWages_11 0 0.0 155s PrivateWages_12 0 0.0 155s PrivateWages_13 0 0.0 155s PrivateWages_14 0 0.0 155s PrivateWages_15 0 0.0 155s PrivateWages_16 0 0.0 155s PrivateWages_17 0 0.0 155s PrivateWages_18 0 0.0 155s PrivateWages_19 0 0.0 155s PrivateWages_20 0 0.0 155s PrivateWages_21 0 0.0 155s PrivateWages_22 0 0.0 155s Consumption_corpProfLag Consumption_wages 155s Consumption_2 12.7 28.2 155s Consumption_3 12.4 32.2 155s Consumption_4 16.9 37.0 155s Consumption_5 18.4 37.0 155s Consumption_6 19.4 38.6 155s Consumption_7 20.1 40.7 155s Consumption_8 19.6 41.5 155s Consumption_9 19.8 42.9 155s Consumption_11 21.7 42.1 155s Consumption_12 15.6 39.3 155s Consumption_13 11.4 34.3 155s Consumption_14 7.0 34.1 155s Consumption_15 11.2 36.6 155s Consumption_16 12.3 39.3 155s Consumption_17 14.0 44.2 155s Consumption_18 17.6 47.7 155s Consumption_19 17.3 45.9 155s Consumption_20 15.3 49.4 155s Consumption_21 19.0 53.0 155s Consumption_22 21.1 61.8 155s Investment_2 0.0 0.0 155s Investment_3 0.0 0.0 155s Investment_4 0.0 0.0 155s Investment_5 0.0 0.0 155s Investment_6 0.0 0.0 155s Investment_7 0.0 0.0 155s Investment_8 0.0 0.0 155s Investment_9 0.0 0.0 155s Investment_10 0.0 0.0 155s Investment_11 0.0 0.0 155s Investment_12 0.0 0.0 155s Investment_13 0.0 0.0 155s Investment_14 0.0 0.0 155s Investment_15 0.0 0.0 155s Investment_16 0.0 0.0 155s Investment_17 0.0 0.0 155s Investment_18 0.0 0.0 155s Investment_19 0.0 0.0 155s Investment_20 0.0 0.0 155s Investment_21 0.0 0.0 155s Investment_22 0.0 0.0 155s PrivateWages_2 0.0 0.0 155s PrivateWages_3 0.0 0.0 155s PrivateWages_4 0.0 0.0 155s PrivateWages_5 0.0 0.0 155s PrivateWages_6 0.0 0.0 155s PrivateWages_8 0.0 0.0 155s PrivateWages_9 0.0 0.0 155s PrivateWages_10 0.0 0.0 155s PrivateWages_11 0.0 0.0 155s PrivateWages_12 0.0 0.0 155s PrivateWages_13 0.0 0.0 155s PrivateWages_14 0.0 0.0 155s PrivateWages_15 0.0 0.0 155s PrivateWages_16 0.0 0.0 155s PrivateWages_17 0.0 0.0 155s PrivateWages_18 0.0 0.0 155s PrivateWages_19 0.0 0.0 155s PrivateWages_20 0.0 0.0 155s PrivateWages_21 0.0 0.0 155s PrivateWages_22 0.0 0.0 155s Investment_(Intercept) Investment_corpProf 155s Consumption_2 0 0.0 155s Consumption_3 0 0.0 155s Consumption_4 0 0.0 155s Consumption_5 0 0.0 155s Consumption_6 0 0.0 155s Consumption_7 0 0.0 155s Consumption_8 0 0.0 155s Consumption_9 0 0.0 155s Consumption_11 0 0.0 155s Consumption_12 0 0.0 155s Consumption_13 0 0.0 155s Consumption_14 0 0.0 155s Consumption_15 0 0.0 155s Consumption_16 0 0.0 155s Consumption_17 0 0.0 155s Consumption_18 0 0.0 155s Consumption_19 0 0.0 155s Consumption_20 0 0.0 155s Consumption_21 0 0.0 155s Consumption_22 0 0.0 155s Investment_2 1 12.4 155s Investment_3 1 16.9 155s Investment_4 1 18.4 155s Investment_5 1 19.4 155s Investment_6 1 20.1 155s Investment_7 1 19.6 155s Investment_8 1 19.8 155s Investment_9 1 21.1 155s Investment_10 1 21.7 155s Investment_11 1 15.6 155s Investment_12 1 11.4 155s Investment_13 1 7.0 155s Investment_14 1 11.2 155s Investment_15 1 12.3 155s Investment_16 1 14.0 155s Investment_17 1 17.6 155s Investment_18 1 17.3 155s Investment_19 1 15.3 155s Investment_20 1 19.0 155s Investment_21 1 21.1 155s Investment_22 1 23.5 155s PrivateWages_2 0 0.0 155s PrivateWages_3 0 0.0 155s PrivateWages_4 0 0.0 155s PrivateWages_5 0 0.0 155s PrivateWages_6 0 0.0 155s PrivateWages_8 0 0.0 155s PrivateWages_9 0 0.0 155s PrivateWages_10 0 0.0 155s PrivateWages_11 0 0.0 155s PrivateWages_12 0 0.0 155s PrivateWages_13 0 0.0 155s PrivateWages_14 0 0.0 155s PrivateWages_15 0 0.0 155s PrivateWages_16 0 0.0 155s PrivateWages_17 0 0.0 155s PrivateWages_18 0 0.0 155s PrivateWages_19 0 0.0 155s PrivateWages_20 0 0.0 155s PrivateWages_21 0 0.0 155s PrivateWages_22 0 0.0 155s Investment_corpProfLag Investment_capitalLag 155s Consumption_2 0.0 0 155s Consumption_3 0.0 0 155s Consumption_4 0.0 0 155s Consumption_5 0.0 0 155s Consumption_6 0.0 0 155s Consumption_7 0.0 0 155s Consumption_8 0.0 0 155s Consumption_9 0.0 0 155s Consumption_11 0.0 0 155s Consumption_12 0.0 0 155s Consumption_13 0.0 0 155s Consumption_14 0.0 0 155s Consumption_15 0.0 0 155s Consumption_16 0.0 0 155s Consumption_17 0.0 0 155s Consumption_18 0.0 0 155s Consumption_19 0.0 0 155s Consumption_20 0.0 0 155s Consumption_21 0.0 0 155s Consumption_22 0.0 0 155s Investment_2 12.7 183 155s Investment_3 12.4 183 155s Investment_4 16.9 184 155s Investment_5 18.4 190 155s Investment_6 19.4 193 155s Investment_7 20.1 198 155s Investment_8 19.6 203 155s Investment_9 19.8 208 155s Investment_10 21.1 211 155s Investment_11 21.7 216 155s Investment_12 15.6 217 155s Investment_13 11.4 213 155s Investment_14 7.0 207 155s Investment_15 11.2 202 155s Investment_16 12.3 199 155s Investment_17 14.0 198 155s Investment_18 17.6 200 155s Investment_19 17.3 202 155s Investment_20 15.3 200 155s Investment_21 19.0 201 155s Investment_22 21.1 204 155s PrivateWages_2 0.0 0 155s PrivateWages_3 0.0 0 155s PrivateWages_4 0.0 0 155s PrivateWages_5 0.0 0 155s PrivateWages_6 0.0 0 155s PrivateWages_8 0.0 0 155s PrivateWages_9 0.0 0 155s PrivateWages_10 0.0 0 155s PrivateWages_11 0.0 0 155s PrivateWages_12 0.0 0 155s PrivateWages_13 0.0 0 155s PrivateWages_14 0.0 0 155s PrivateWages_15 0.0 0 155s PrivateWages_16 0.0 0 155s PrivateWages_17 0.0 0 155s PrivateWages_18 0.0 0 155s PrivateWages_19 0.0 0 155s PrivateWages_20 0.0 0 155s PrivateWages_21 0.0 0 155s PrivateWages_22 0.0 0 155s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 155s Consumption_2 0 0.0 0.0 155s Consumption_3 0 0.0 0.0 155s Consumption_4 0 0.0 0.0 155s Consumption_5 0 0.0 0.0 155s Consumption_6 0 0.0 0.0 155s Consumption_7 0 0.0 0.0 155s Consumption_8 0 0.0 0.0 155s Consumption_9 0 0.0 0.0 155s Consumption_11 0 0.0 0.0 155s Consumption_12 0 0.0 0.0 155s Consumption_13 0 0.0 0.0 155s Consumption_14 0 0.0 0.0 155s Consumption_15 0 0.0 0.0 155s Consumption_16 0 0.0 0.0 155s Consumption_17 0 0.0 0.0 155s Consumption_18 0 0.0 0.0 155s Consumption_19 0 0.0 0.0 155s Consumption_20 0 0.0 0.0 155s Consumption_21 0 0.0 0.0 155s Consumption_22 0 0.0 0.0 155s Investment_2 0 0.0 0.0 155s Investment_3 0 0.0 0.0 155s Investment_4 0 0.0 0.0 155s Investment_5 0 0.0 0.0 155s Investment_6 0 0.0 0.0 155s Investment_7 0 0.0 0.0 155s Investment_8 0 0.0 0.0 155s Investment_9 0 0.0 0.0 155s Investment_10 0 0.0 0.0 155s Investment_11 0 0.0 0.0 155s Investment_12 0 0.0 0.0 155s Investment_13 0 0.0 0.0 155s Investment_14 0 0.0 0.0 155s Investment_15 0 0.0 0.0 155s Investment_16 0 0.0 0.0 155s Investment_17 0 0.0 0.0 155s Investment_18 0 0.0 0.0 155s Investment_19 0 0.0 0.0 155s Investment_20 0 0.0 0.0 155s Investment_21 0 0.0 0.0 155s Investment_22 0 0.0 0.0 155s PrivateWages_2 1 45.6 44.9 155s PrivateWages_3 1 50.1 45.6 155s PrivateWages_4 1 57.2 50.1 155s PrivateWages_5 1 57.1 57.2 155s PrivateWages_6 1 61.0 57.1 155s PrivateWages_8 1 64.4 64.0 155s PrivateWages_9 1 64.5 64.4 155s PrivateWages_10 1 67.0 64.5 155s PrivateWages_11 1 61.2 67.0 155s PrivateWages_12 1 53.4 61.2 155s PrivateWages_13 1 44.3 53.4 155s PrivateWages_14 1 45.1 44.3 155s PrivateWages_15 1 49.7 45.1 155s PrivateWages_16 1 54.4 49.7 155s PrivateWages_17 1 62.7 54.4 155s PrivateWages_18 1 65.0 62.7 155s PrivateWages_19 1 60.9 65.0 155s PrivateWages_20 1 69.5 60.9 155s PrivateWages_21 1 75.7 69.5 155s PrivateWages_22 1 88.4 75.7 155s PrivateWages_trend 155s Consumption_2 0 155s Consumption_3 0 155s Consumption_4 0 155s Consumption_5 0 155s Consumption_6 0 155s Consumption_7 0 155s Consumption_8 0 155s Consumption_9 0 155s Consumption_11 0 155s Consumption_12 0 155s Consumption_13 0 155s Consumption_14 0 155s Consumption_15 0 155s Consumption_16 0 155s Consumption_17 0 155s Consumption_18 0 155s Consumption_19 0 155s Consumption_20 0 155s Consumption_21 0 155s Consumption_22 0 155s Investment_2 0 155s Investment_3 0 155s Investment_4 0 155s Investment_5 0 155s Investment_6 0 155s Investment_7 0 155s Investment_8 0 155s Investment_9 0 155s Investment_10 0 155s Investment_11 0 155s Investment_12 0 155s Investment_13 0 155s Investment_14 0 155s Investment_15 0 155s Investment_16 0 155s Investment_17 0 155s Investment_18 0 155s Investment_19 0 155s Investment_20 0 155s Investment_21 0 155s Investment_22 0 155s PrivateWages_2 -10 155s PrivateWages_3 -9 155s PrivateWages_4 -8 155s PrivateWages_5 -7 155s PrivateWages_6 -6 155s PrivateWages_8 -4 155s PrivateWages_9 -3 155s PrivateWages_10 -2 155s PrivateWages_11 -1 155s PrivateWages_12 0 155s PrivateWages_13 1 155s PrivateWages_14 2 155s PrivateWages_15 3 155s PrivateWages_16 4 155s PrivateWages_17 5 155s PrivateWages_18 6 155s PrivateWages_19 7 155s PrivateWages_20 8 155s PrivateWages_21 9 155s PrivateWages_22 10 155s > nobs 155s [1] 61 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 49 1 0.87 0.35 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 49 1 0.8 0.38 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 50 155s 2 49 1 0.8 0.37 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 51 155s 2 49 2 0.48 0.62 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 51 155s 2 49 2 0.43 0.65 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 51 155s 2 49 2 0.87 0.65 155s > logLik 155s 'log Lik.' -71.7 (df=13) 155s 'log Lik.' -76.1 (df=13) 155s compare log likelihood value with single-equation OLS 155s [1] "Mean relative difference: 0.00159" 155s > 155s > # 2SLS 155s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: 2SLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 59 47 53.2 0.251 0.973 0.991 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 19 15 20.49 1.366 1.17 0.978 0.973 155s Investment 20 16 23.02 1.438 1.20 0.901 0.883 155s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.079 0.354 -0.383 155s Investment 0.354 1.047 0.107 155s PrivateWages -0.383 0.107 0.445 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.335 -0.556 155s Investment 0.335 1.000 0.149 155s PrivateWages -0.556 0.149 1.000 155s 155s 155s 2SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.4657 1.3505 12.19 3.5e-09 *** 155s corpProf 0.0243 0.1180 0.21 0.839 155s corpProfLag 0.1981 0.1087 1.82 0.088 . 155s wages 0.8159 0.0420 19.45 4.7e-12 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.169 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 20.493 MSE: 1.366 Root MSE: 1.169 155s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.973 155s 155s 155s 2SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 17.8425 6.5319 2.73 0.01478 * 155s corpProf 0.2167 0.1478 1.47 0.16189 155s corpProfLag 0.5416 0.1415 3.83 0.00149 ** 155s capitalLag -0.1455 0.0314 -4.63 0.00028 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.199 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 155s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 155s 155s 155s 2SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3431 1.1250 1.19 0.24995 155s gnp 0.4438 0.0342 12.97 6.6e-10 *** 155s gnpLag 0.1447 0.0371 3.90 0.00128 ** 155s trend 0.1238 0.0292 4.24 0.00063 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.78 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 155s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.39161 -1.0104 -1.3401 155s 3 -0.60524 0.2478 0.2378 155s 4 -1.24952 1.0621 1.1117 155s 5 -0.17101 -1.4104 -0.1954 155s 6 0.30841 0.4328 -0.5355 155s 7 NA NA NA 155s 8 1.50999 1.0463 -0.7908 155s 9 1.39649 0.0674 0.2831 155s 10 NA 1.7698 1.1353 155s 11 -0.49339 -0.5912 -0.1765 155s 12 -0.99824 -0.6318 0.6007 155s 13 -1.27965 -0.6983 0.1443 155s 14 0.55302 0.9724 0.4826 155s 15 -0.14553 -0.1827 0.3016 155s 16 -0.00773 0.1167 0.0261 155s 17 1.97001 1.6266 -0.8614 155s 18 -0.59152 -0.0525 0.9927 155s 19 -0.21481 -3.0656 -0.4446 155s 20 1.33575 0.1393 -0.3914 155s 21 1.01443 -0.1305 -1.1115 155s 22 -1.93986 0.2922 0.5312 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.3 0.810 26.8 155s 3 45.6 1.652 29.1 155s 4 50.4 4.138 33.0 155s 5 50.8 4.410 34.1 155s 6 52.3 4.667 35.9 155s 7 NA NA NA 155s 8 54.7 3.154 38.7 155s 9 55.9 2.933 38.9 155s 10 NA 3.330 40.2 155s 11 55.5 1.591 38.1 155s 12 51.9 -2.768 33.9 155s 13 46.9 -5.502 28.9 155s 14 45.9 -6.072 28.0 155s 15 48.8 -2.817 30.3 155s 16 51.3 -1.417 33.2 155s 17 55.7 0.473 37.7 155s 18 59.3 2.053 40.0 155s 19 57.7 1.166 38.6 155s 20 60.3 1.161 42.0 155s 21 64.0 3.431 46.1 155s 22 71.6 4.608 52.8 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.3 0.483 41.3 43.3 155s 3 45.6 0.586 44.4 46.9 155s 4 50.4 0.390 49.6 51.3 155s 5 50.8 0.456 49.8 51.7 155s 6 52.3 0.463 51.3 53.3 155s 7 NA NA NA NA 155s 8 54.7 0.382 53.9 55.5 155s 9 55.9 0.422 55.0 56.8 155s 10 NA NA NA NA 155s 11 55.5 0.742 53.9 57.1 155s 12 51.9 0.600 50.6 53.2 155s 13 46.9 0.770 45.2 48.5 155s 14 45.9 0.635 44.6 47.3 155s 15 48.8 0.383 48.0 49.7 155s 16 51.3 0.339 50.6 52.0 155s 17 55.7 0.410 54.9 56.6 155s 18 59.3 0.336 58.6 60.0 155s 19 57.7 0.418 56.8 58.6 155s 20 60.3 0.481 59.2 61.3 155s 21 64.0 0.462 63.0 65.0 155s 22 71.6 0.706 70.1 73.1 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 0.810 0.750 -0.77956 2.400 155s 3 1.652 0.516 0.55883 2.746 155s 4 4.138 0.487 3.10541 5.170 155s 5 4.410 0.402 3.55860 5.262 155s 6 4.667 0.377 3.86830 5.466 155s 7 NA NA NA NA 155s 8 3.154 0.312 2.49238 3.815 155s 9 2.933 0.466 1.94478 3.920 155s 10 3.330 0.512 2.24435 4.416 155s 11 1.591 0.749 0.00249 3.180 155s 12 -2.768 0.586 -4.01111 -1.525 155s 13 -5.502 0.750 -7.09222 -3.911 155s 14 -6.072 0.803 -7.77404 -4.371 155s 15 -2.817 0.379 -3.62002 -2.015 155s 16 -1.417 0.327 -2.10985 -0.723 155s 17 0.473 0.436 -0.45046 1.397 155s 18 2.053 0.272 1.47523 2.630 155s 19 1.166 0.410 0.29710 2.034 155s 20 1.161 0.491 0.12044 2.201 155s 21 3.431 0.406 2.57004 4.291 155s 22 4.608 0.578 3.38197 5.834 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.313 26.2 27.5 155s 3 29.1 0.325 28.4 29.8 155s 4 33.0 0.344 32.3 33.7 155s 5 34.1 0.246 33.6 34.6 155s 6 35.9 0.254 35.4 36.5 155s 7 NA NA NA NA 155s 8 38.7 0.251 38.2 39.2 155s 9 38.9 0.239 38.4 39.4 155s 10 40.2 0.229 39.7 40.7 155s 11 38.1 0.339 37.4 38.8 155s 12 33.9 0.365 33.1 34.7 155s 13 28.9 0.436 27.9 29.8 155s 14 28.0 0.333 27.3 28.7 155s 15 30.3 0.324 29.6 31.0 155s 16 33.2 0.271 32.6 33.7 155s 17 37.7 0.280 37.1 38.3 155s 18 40.0 0.208 39.6 40.4 155s 19 38.6 0.342 37.9 39.4 155s 20 42.0 0.293 41.4 42.6 155s 21 46.1 0.296 45.5 46.7 155s 22 52.8 0.474 51.8 53.8 155s > model.frame 155s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 155s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 155s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 155s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 155s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 155s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 155s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 155s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 155s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 155s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 155s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 155s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 155s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 155s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 155s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 155s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 155s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 155s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 155s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 155s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 155s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 155s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 155s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 155s trend 155s 1 -11 155s 2 -10 155s 3 -9 155s 4 -8 155s 5 -7 155s 6 -6 155s 7 -5 155s 8 -4 155s 9 -3 155s 10 -2 155s 11 -1 155s 12 0 155s 13 1 155s 14 2 155s 15 3 155s 16 4 155s 17 5 155s 18 6 155s 19 7 155s 20 8 155s 21 9 155s 22 10 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 155s [3] "Numeric: lengths (732, 708) differ" 155s > nobs 155s [1] 59 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.87 0.36 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.98 0.33 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 48 155s 2 47 1 0.98 0.32 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 0.43 0.65 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 0.49 0.61 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 49 155s 2 47 2 0.98 0.61 155s > logLik 155s 'log Lik.' -71.5 (df=13) 155s 'log Lik.' -78.7 (df=13) 155s > 155s > # SUR 155s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: SUR 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 61 49 45.4 0.151 0.977 0.992 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 20 16 17.6 1.102 1.050 0.981 0.977 155s Investment 21 17 17.5 1.029 1.015 0.931 0.918 155s PrivateWages 20 16 10.3 0.643 0.802 0.987 0.985 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 0.8871 0.0268 -0.349 155s Investment 0.0268 0.7328 0.103 155s PrivateWages -0.3492 0.1029 0.444 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 0.8852 0.0508 -0.406 155s Investment 0.0508 0.7313 0.161 155s PrivateWages -0.4063 0.1609 0.467 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.065 -0.635 155s Investment 0.065 1.000 0.262 155s PrivateWages -0.635 0.262 1.000 155s 155s 155s SUR estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.0876 1.2010 13.39 4.1e-10 *** 155s corpProf 0.2173 0.0799 2.72 0.015 * 155s corpProfLag 0.0694 0.0793 0.88 0.394 155s wages 0.7975 0.0360 22.15 2.0e-13 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.05 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 17.63 MSE: 1.102 Root MSE: 1.05 155s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 155s 155s 155s SUR estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 12.3518 4.5615 2.71 0.01493 * 155s corpProf 0.4511 0.0814 5.54 3.6e-05 *** 155s corpProfLag 0.3570 0.0846 4.22 0.00058 *** 155s capitalLag -0.1225 0.0223 -5.49 4.0e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.015 on 17 degrees of freedom 155s Number of observations: 21 Degrees of Freedom: 17 155s SSR: 17.5 MSE: 1.029 Root MSE: 1.015 155s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 155s 155s 155s SUR estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3964 1.0825 1.29 0.22 155s gnp 0.4177 0.0269 15.55 4.4e-11 *** 155s gnpLag 0.1709 0.0306 5.59 4.0e-05 *** 155s trend 0.1467 0.0272 5.40 5.9e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.802 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.284 MSE: 0.643 Root MSE: 0.802 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.2529 -0.2920 -1.15193 155s 3 -1.2998 -0.1392 0.50193 155s 4 -1.5662 1.1106 1.42026 155s 5 -0.4876 -1.4391 -0.09801 155s 6 0.0149 0.3556 -0.35678 155s 7 0.9002 1.4558 NA 155s 8 1.3535 0.8299 -0.74964 155s 9 1.0406 -0.5136 0.29355 155s 10 NA 1.2191 1.18544 155s 11 0.4417 0.2810 -0.36558 155s 12 -0.0892 0.0754 0.33733 155s 13 -0.1541 0.3429 -0.17490 155s 14 0.2984 0.3597 0.39941 155s 15 -0.0260 -0.1602 0.29441 155s 16 -0.0250 0.0130 -0.00177 155s 17 1.5671 1.0231 -0.81891 155s 18 -0.4089 0.0306 0.85516 155s 19 0.2819 -2.6153 -0.77184 155s 20 0.9257 -0.6030 -0.41040 155s 21 0.7415 -0.7118 -1.21679 155s 22 -2.2437 -0.5398 0.57166 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.2 0.092 26.7 155s 3 46.3 2.039 28.8 155s 4 50.8 4.089 32.7 155s 5 51.1 4.439 34.0 155s 6 52.6 4.744 35.8 155s 7 54.2 4.144 NA 155s 8 54.8 3.370 38.6 155s 9 56.3 3.514 38.9 155s 10 NA 3.881 40.1 155s 11 54.6 0.719 38.3 155s 12 51.0 -3.475 34.2 155s 13 45.8 -6.543 29.2 155s 14 46.2 -5.460 28.1 155s 15 48.7 -2.840 30.3 155s 16 51.3 -1.313 33.2 155s 17 56.1 1.077 37.6 155s 18 59.1 1.969 40.1 155s 19 57.2 0.715 39.0 155s 20 60.7 1.903 42.0 155s 21 64.3 4.012 46.2 155s 22 71.9 5.440 52.7 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.2 0.422 41.3 43.0 155s 3 46.3 0.462 45.4 47.2 155s 4 50.8 0.309 50.1 51.4 155s 5 51.1 0.359 50.4 51.8 155s 6 52.6 0.362 51.9 53.3 155s 7 54.2 0.328 53.5 54.9 155s 8 54.8 0.300 54.2 55.4 155s 9 56.3 0.323 55.6 56.9 155s 10 NA NA NA NA 155s 11 54.6 0.531 53.5 55.6 155s 12 51.0 0.427 50.1 51.8 155s 13 45.8 0.564 44.6 46.9 155s 14 46.2 0.543 45.1 47.3 155s 15 48.7 0.341 48.0 49.4 155s 16 51.3 0.302 50.7 51.9 155s 17 56.1 0.328 55.5 56.8 155s 18 59.1 0.294 58.5 59.7 155s 19 57.2 0.332 56.6 57.9 155s 20 60.7 0.392 59.9 61.5 155s 21 64.3 0.394 63.5 65.0 155s 22 71.9 0.615 70.7 73.2 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 0.092 0.508 -0.929 1.113 155s 3 2.039 0.421 1.193 2.885 155s 4 4.089 0.376 3.333 4.846 155s 5 4.439 0.311 3.813 5.065 155s 6 4.744 0.294 4.154 5.335 155s 7 4.144 0.277 3.587 4.701 155s 8 3.370 0.247 2.873 3.867 155s 9 3.514 0.328 2.855 4.172 155s 10 3.881 0.376 3.126 4.636 155s 11 0.719 0.508 -0.301 1.739 155s 12 -3.475 0.428 -4.336 -2.615 155s 13 -6.543 0.521 -7.590 -5.496 155s 14 -5.460 0.583 -6.632 -4.288 155s 15 -2.840 0.316 -3.474 -2.205 155s 16 -1.313 0.271 -1.857 -0.769 155s 17 1.077 0.293 0.488 1.666 155s 18 1.969 0.205 1.557 2.382 155s 19 0.715 0.263 0.187 1.244 155s 20 1.903 0.309 1.283 2.523 155s 21 4.012 0.280 3.449 4.574 155s 22 5.440 0.389 4.659 6.221 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.7 0.306 26.0 27.3 155s 3 28.8 0.305 28.2 29.4 155s 4 32.7 0.302 32.1 33.3 155s 5 34.0 0.231 33.5 34.5 155s 6 35.8 0.230 35.3 36.2 155s 7 NA NA NA NA 155s 8 38.6 0.233 38.2 39.1 155s 9 38.9 0.222 38.5 39.4 155s 10 40.1 0.213 39.7 40.5 155s 11 38.3 0.292 37.7 38.9 155s 12 34.2 0.300 33.6 34.8 155s 13 29.2 0.361 28.4 29.9 155s 14 28.1 0.322 27.5 28.7 155s 15 30.3 0.314 29.7 30.9 155s 16 33.2 0.263 32.7 33.7 155s 17 37.6 0.256 37.1 38.1 155s 18 40.1 0.204 39.7 40.6 155s 19 39.0 0.298 38.4 39.6 155s 20 42.0 0.272 41.5 42.6 155s 21 46.2 0.288 45.6 46.8 155s 22 52.7 0.431 51.9 53.6 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] TRUE 155s > nobs 155s [1] 61 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 49 1 1.01 0.32 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 50 155s 2 49 1 1.3 0.26 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 50 155s 2 49 1 1.3 0.25 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 51 155s 2 49 2 0.53 0.59 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 51 155s 2 49 2 0.69 0.51 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 51 155s 2 49 2 1.38 0.5 155s > logLik 155s 'log Lik.' -69.6 (df=18) 155s 'log Lik.' -76.9 (df=18) 155s > 155s > # 3SLS 155s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: 3SLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 59 47 59.5 0.241 0.97 0.994 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 19 15 18.1 1.203 1.097 0.980 0.977 155s Investment 20 16 31.1 1.945 1.395 0.866 0.841 155s PrivateWages 20 16 10.3 0.645 0.803 0.987 0.985 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 1.079 0.354 -0.383 155s Investment 0.354 1.047 0.107 155s PrivateWages -0.383 0.107 0.445 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 0.950 0.324 -0.395 155s Investment 0.324 1.385 0.242 155s PrivateWages -0.395 0.242 0.475 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.293 -0.582 155s Investment 0.293 1.000 0.292 155s PrivateWages -0.582 0.292 1.000 155s 155s 155s 3SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.5606 1.3295 12.46 2.6e-09 *** 155s corpProf 0.1100 0.1098 1.00 0.33 155s corpProfLag 0.1155 0.1007 1.15 0.27 155s wages 0.8086 0.0401 20.18 2.8e-12 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.097 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 18.051 MSE: 1.203 Root MSE: 1.097 155s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 155s 155s 155s 3SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 23.6871 6.1159 3.87 0.00135 ** 155s corpProf 0.1072 0.1414 0.76 0.45918 155s corpProfLag 0.6278 0.1361 4.61 0.00029 *** 155s capitalLag -0.1726 0.0295 -5.85 2.5e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.395 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 31.126 MSE: 1.945 Root MSE: 1.395 155s Multiple R-Squared: 0.866 Adjusted R-Squared: 0.841 155s 155s 155s 3SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3603 1.0927 1.24 0.23109 155s gnp 0.4117 0.0315 13.06 6.0e-10 *** 155s gnpLag 0.1782 0.0336 5.31 7.1e-05 *** 155s trend 0.1370 0.0280 4.89 0.00016 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.803 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.318 MSE: 0.645 Root MSE: 0.803 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.29542 -1.636 -1.2658 155s 3 -0.89033 0.135 0.4198 155s 4 -1.25669 0.777 1.3578 155s 5 -0.14000 -1.574 -0.2036 155s 6 0.37365 0.341 -0.4283 155s 7 NA NA NA 155s 8 1.63850 1.194 -0.8319 155s 9 1.44030 0.454 0.2186 155s 10 NA 2.192 1.1346 155s 11 0.17274 -0.750 -0.4603 155s 12 -0.49629 -0.698 0.2476 155s 13 -0.78384 -0.976 -0.2528 155s 14 0.32420 1.365 0.4028 155s 15 -0.10364 -0.170 0.3295 155s 16 -0.00105 0.140 0.0377 155s 17 1.84421 1.862 -0.7540 155s 18 -0.36893 -0.103 0.8827 155s 19 0.14129 -3.255 -0.7764 155s 20 1.23511 0.475 -0.3230 155s 21 1.06553 0.152 -1.1453 155s 22 -1.85709 0.746 0.6843 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.2 1.436 26.8 155s 3 45.9 1.765 28.9 155s 4 50.5 4.423 32.7 155s 5 50.7 4.574 34.1 155s 6 52.2 4.759 35.8 155s 7 NA NA NA 155s 8 54.6 3.006 38.7 155s 9 55.9 2.546 39.0 155s 10 NA 2.908 40.2 155s 11 54.8 1.750 38.4 155s 12 51.4 -2.702 34.3 155s 13 46.4 -5.224 29.3 155s 14 46.2 -6.465 28.1 155s 15 48.8 -2.830 30.3 155s 16 51.3 -1.440 33.2 155s 17 55.9 0.238 37.6 155s 18 59.1 2.103 40.1 155s 19 57.4 1.355 39.0 155s 20 60.4 0.825 41.9 155s 21 63.9 3.148 46.1 155s 22 71.6 4.154 52.6 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.2 0.475 39.6 44.7 155s 3 45.9 0.557 43.3 48.5 155s 4 50.5 0.372 48.0 52.9 155s 5 50.7 0.433 48.2 53.3 155s 6 52.2 0.438 49.7 54.7 155s 7 NA NA NA NA 155s 8 54.6 0.362 52.1 57.0 155s 9 55.9 0.401 53.4 58.3 155s 10 NA NA NA NA 155s 11 54.8 0.684 52.1 57.6 155s 12 51.4 0.563 48.8 54.0 155s 13 46.4 0.733 43.6 49.2 155s 14 46.2 0.612 43.5 48.9 155s 15 48.8 0.379 46.3 51.3 155s 16 51.3 0.334 48.9 53.7 155s 17 55.9 0.394 53.4 58.3 155s 18 59.1 0.322 56.6 61.5 155s 19 57.4 0.392 54.9 59.8 155s 20 60.4 0.462 57.8 62.9 155s 21 63.9 0.448 61.4 66.5 155s 22 71.6 0.686 68.8 74.3 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 1.436 0.709 -1.8811 4.754 155s 3 1.765 0.512 -1.3848 4.915 155s 4 4.423 0.470 1.3027 7.543 155s 5 4.574 0.392 1.5029 7.645 155s 6 4.759 0.370 1.7000 7.818 155s 7 NA NA NA NA 155s 8 3.006 0.306 -0.0214 6.033 155s 9 2.546 0.444 -0.5575 5.649 155s 10 2.908 0.488 -0.2245 6.041 155s 11 1.750 0.738 -1.5953 5.096 155s 12 -2.702 0.583 -5.9068 0.503 155s 13 -5.224 0.743 -8.5738 -1.874 155s 14 -6.465 0.780 -9.8530 -3.077 155s 15 -2.830 0.378 -5.8936 0.233 155s 16 -1.440 0.326 -4.4762 1.597 155s 17 0.238 0.426 -2.8533 3.329 155s 18 2.103 0.268 -0.9077 5.114 155s 19 1.355 0.399 -1.7201 4.431 155s 20 0.825 0.474 -2.2981 3.947 155s 21 3.148 0.393 0.0761 6.220 155s 22 4.154 0.555 0.9719 7.336 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.309 24.9 28.6 155s 3 28.9 0.315 27.1 30.7 155s 4 32.7 0.326 30.9 34.6 155s 5 34.1 0.236 32.3 35.9 155s 6 35.8 0.244 34.0 37.6 155s 7 NA NA NA NA 155s 8 38.7 0.237 37.0 40.5 155s 9 39.0 0.225 37.2 40.7 155s 10 40.2 0.219 38.4 41.9 155s 11 38.4 0.309 36.5 40.2 155s 12 34.3 0.336 32.4 36.1 155s 13 29.3 0.411 27.3 31.2 155s 14 28.1 0.326 26.3 29.9 155s 15 30.3 0.313 28.4 32.1 155s 16 33.2 0.262 31.4 35.0 155s 17 37.6 0.265 35.8 39.3 155s 18 40.1 0.205 38.4 41.9 155s 19 39.0 0.323 37.1 40.8 155s 20 41.9 0.282 40.1 43.7 155s 21 46.1 0.293 44.3 48.0 155s 22 52.6 0.463 50.7 54.6 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 155s [3] "Numeric: lengths (732, 708) differ" 155s > nobs 155s [1] 59 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.23 0.64 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.31 0.58 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 48 155s 2 47 1 0.31 0.58 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 0.5 0.61 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 0.68 0.51 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 49 155s 2 47 2 1.37 0.5 155s > logLik 155s 'log Lik.' -71 (df=18) 155s 'log Lik.' -81.1 (df=18) 155s > 155s > # I3SLS 155s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: iterated 3SLS 155s 155s convergence achieved after 15 iterations 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 59 47 81.3 0.349 0.958 0.995 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 19 15 18.1 1.209 1.100 0.980 0.976 155s Investment 20 16 52.0 3.250 1.803 0.776 0.735 155s PrivateWages 20 16 11.2 0.699 0.836 0.986 0.983 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 0.955 0.456 -0.421 155s Investment 0.456 2.294 0.375 155s PrivateWages -0.421 0.375 0.522 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 0.955 0.456 -0.421 155s Investment 0.456 2.294 0.375 155s PrivateWages -0.421 0.375 0.522 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.322 -0.582 155s Investment 0.322 1.000 0.341 155s PrivateWages -0.582 0.341 1.000 155s 155s 155s 3SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.8311 1.2489 13.48 8.7e-10 *** 155s corpProf 0.1468 0.0991 1.48 0.16 155s corpProfLag 0.0924 0.0906 1.02 0.32 155s wages 0.7945 0.0371 21.43 1.2e-12 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.1 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 18.14 MSE: 1.209 Root MSE: 1.1 155s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 155s 155s 155s 3SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 32.4128 8.2695 3.92 0.00122 ** 155s corpProf -0.0799 0.1934 -0.41 0.68498 155s corpProfLag 0.7607 0.1878 4.05 0.00093 *** 155s capitalLag -0.2114 0.0400 -5.29 7.4e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.803 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 51.999 MSE: 3.25 Root MSE: 1.803 155s Multiple R-Squared: 0.776 Adjusted R-Squared: 0.735 155s 155s 155s 3SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.5421 1.1496 1.34 0.19852 155s gnp 0.3936 0.0313 12.57 1.0e-09 *** 155s gnpLag 0.1945 0.0328 5.93 2.1e-05 *** 155s trend 0.1416 0.0286 4.95 0.00014 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.836 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 11.181 MSE: 0.699 Root MSE: 0.836 155s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.983 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.3309 -2.6308 -1.3061 155s 3 -1.0419 0.0146 0.4450 155s 4 -1.2918 0.4128 1.4338 155s 5 -0.1772 -1.7488 -0.2494 155s 6 0.3563 0.2807 -0.4066 155s 7 NA NA NA 155s 8 1.6778 1.4671 -0.8700 155s 9 1.4561 1.1068 0.1712 155s 10 NA 2.9002 1.1262 155s 11 0.4237 -1.0652 -0.6189 155s 12 -0.2711 -0.9488 0.0375 155s 13 -0.5643 -1.6241 -0.5055 155s 14 0.2845 1.8477 0.3080 155s 15 -0.0514 -0.2379 0.3003 155s 16 0.0521 0.1268 0.0141 155s 17 1.8733 2.2462 -0.7083 155s 18 -0.1962 -0.1724 0.8305 155s 19 0.3553 -3.5810 -0.9448 155s 20 1.3161 1.0343 -0.2738 155s 21 1.2055 0.6622 -1.1283 155s 22 -1.6327 1.5541 0.8257 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.2 2.431 26.8 155s 3 46.0 1.885 28.9 155s 4 50.5 4.787 32.7 155s 5 50.8 4.749 34.1 155s 6 52.2 4.819 35.8 155s 7 NA NA NA 155s 8 54.5 2.733 38.8 155s 9 55.8 1.893 39.0 155s 10 NA 2.200 40.2 155s 11 54.6 2.065 38.5 155s 12 51.2 -2.451 34.5 155s 13 46.2 -4.576 29.5 155s 14 46.2 -6.948 28.2 155s 15 48.8 -2.762 30.3 155s 16 51.2 -1.427 33.2 155s 17 55.8 -0.146 37.5 155s 18 58.9 2.172 40.2 155s 19 57.1 1.681 39.1 155s 20 60.3 0.266 41.9 155s 21 63.8 2.638 46.1 155s 22 71.3 3.346 52.5 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.2 0.446 41.3 43.1 155s 3 46.0 0.511 45.0 47.1 155s 4 50.5 0.340 49.8 51.2 155s 5 50.8 0.393 50.0 51.6 155s 6 52.2 0.396 51.4 53.0 155s 7 NA NA NA NA 155s 8 54.5 0.326 53.9 55.2 155s 9 55.8 0.362 55.1 56.6 155s 10 NA NA NA NA 155s 11 54.6 0.612 53.3 55.8 155s 12 51.2 0.511 50.1 52.2 155s 13 46.2 0.671 44.8 47.5 155s 14 46.2 0.563 45.1 47.3 155s 15 48.8 0.354 48.0 49.5 155s 16 51.2 0.311 50.6 51.9 155s 17 55.8 0.362 55.1 56.6 155s 18 58.9 0.297 58.3 59.5 155s 19 57.1 0.357 56.4 57.9 155s 20 60.3 0.427 59.4 61.1 155s 21 63.8 0.416 63.0 64.6 155s 22 71.3 0.640 70.0 72.6 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 2.431 0.970 0.4798 4.382 155s 3 1.885 0.745 0.3859 3.385 155s 4 4.787 0.664 3.4506 6.124 155s 5 4.749 0.562 3.6174 5.880 155s 6 4.819 0.537 3.7391 5.900 155s 7 NA NA NA NA 155s 8 2.733 0.446 1.8351 3.631 155s 9 1.893 0.620 0.6455 3.141 155s 10 2.200 0.684 0.8232 3.576 155s 11 2.065 1.055 -0.0569 4.187 155s 12 -2.451 0.845 -4.1517 -0.751 155s 13 -4.576 1.070 -6.7293 -2.423 155s 14 -6.948 1.103 -9.1676 -4.728 155s 15 -2.762 0.556 -3.8806 -1.644 155s 16 -1.427 0.480 -2.3919 -0.462 155s 17 -0.146 0.603 -1.3588 1.066 155s 18 2.172 0.390 1.3869 2.958 155s 19 1.681 0.563 0.5476 2.815 155s 20 0.266 0.661 -1.0634 1.595 155s 21 2.638 0.558 1.5144 3.761 155s 22 3.346 0.778 1.7808 4.911 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.326 26.2 27.5 155s 3 28.9 0.328 28.2 29.5 155s 4 32.7 0.334 32.0 33.3 155s 5 34.1 0.242 33.7 34.6 155s 6 35.8 0.252 35.3 36.3 155s 7 NA NA NA NA 155s 8 38.8 0.244 38.3 39.3 155s 9 39.0 0.232 38.6 39.5 155s 10 40.2 0.230 39.7 40.6 155s 11 38.5 0.308 37.9 39.1 155s 12 34.5 0.336 33.8 35.1 155s 13 29.5 0.420 28.7 30.4 155s 14 28.2 0.345 27.5 28.9 155s 15 30.3 0.325 29.6 31.0 155s 16 33.2 0.271 32.6 33.7 155s 17 37.5 0.267 37.0 38.0 155s 18 40.2 0.218 39.7 40.6 155s 19 39.1 0.331 38.5 39.8 155s 20 41.9 0.289 41.3 42.5 155s 21 46.1 0.311 45.5 46.8 155s 22 52.5 0.485 51.5 53.5 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 155s [3] "Numeric: lengths (732, 708) differ" 155s > nobs 155s [1] 59 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.28 0.6 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.37 0.55 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 48 155s 2 47 1 0.37 0.54 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 1.25 0.3 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 1.64 0.21 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 49 155s 2 47 2 3.28 0.19 155s > logLik 155s 'log Lik.' -74.5 (df=18) 155s 'log Lik.' -87.1 (df=18) 155s > 155s > # OLS 155s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: OLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 59 47 44.2 0.453 0.976 0.99 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 155s Investment 20 16 17.11 1.069 1.03 0.912 0.895 155s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.1939 0.0559 -0.474 155s Investment 0.0559 0.9839 0.140 155s PrivateWages -0.4745 0.1403 0.602 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.0000 0.0447 -0.568 155s Investment 0.0447 1.0000 0.169 155s PrivateWages -0.5680 0.1689 1.000 155s 155s 155s OLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.2957 1.4879 10.95 1.5e-08 *** 155s corpProf 0.1796 0.1162 1.55 0.14 155s corpProfLag 0.1032 0.0994 1.04 0.32 155s wages 0.7962 0.0433 18.39 1.1e-11 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.076 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 155s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 155s 155s 155s OLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 10.1813 5.3720 1.90 0.07627 . 155s corpProf 0.5003 0.1052 4.75 0.00022 *** 155s corpProfLag 0.3259 0.1003 3.25 0.00502 ** 155s capitalLag -0.1134 0.0265 -4.28 0.00057 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.034 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 17.109 MSE: 1.069 Root MSE: 1.034 155s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.895 155s 155s 155s OLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3550 1.3021 1.04 0.3135 155s gnp 0.4417 0.0330 13.40 4.1e-10 *** 155s gnpLag 0.1466 0.0379 3.87 0.0013 ** 155s trend 0.1244 0.0335 3.72 0.0019 ** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.78 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 155s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 155s 155s compare coef with single-equation OLS 155s [1] TRUE 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.3863 -0.000301 -1.3389 155s 3 -1.2484 -0.076489 0.2462 155s 4 -1.6040 1.221792 1.1255 155s 5 -0.5384 -1.377872 -0.1959 155s 6 -0.0413 0.386104 -0.5284 155s 7 0.8043 1.486279 NA 155s 8 1.2830 0.784055 -0.7909 155s 9 1.0142 -0.655354 0.2819 155s 10 NA 1.060871 1.1384 155s 11 0.1429 0.395249 -0.1904 155s 12 -0.3439 0.198005 0.5813 155s 13 NA NA 0.1206 155s 14 0.3199 0.312725 0.4773 155s 15 -0.1016 -0.084685 0.3035 155s 16 -0.0702 0.066194 0.0284 155s 17 1.6064 0.963697 -0.8517 155s 18 -0.4980 0.078506 0.9908 155s 19 0.1253 -2.496401 -0.4597 155s 20 0.9805 -0.711004 -0.3819 155s 21 0.7551 -0.820172 -1.1062 155s 22 -2.1992 -0.731199 0.5501 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.3 -0.200 26.8 155s 3 46.2 1.976 29.1 155s 4 50.8 3.978 33.0 155s 5 51.1 4.378 34.1 155s 6 52.6 4.714 35.9 155s 7 54.3 4.114 NA 155s 8 54.9 3.416 38.7 155s 9 56.3 3.655 38.9 155s 10 NA 4.039 40.2 155s 11 54.9 0.605 38.1 155s 12 51.2 -3.598 33.9 155s 13 NA NA 28.9 155s 14 46.2 -5.413 28.0 155s 15 48.8 -2.915 30.3 155s 16 51.4 -1.366 33.2 155s 17 56.1 1.136 37.7 155s 18 59.2 1.921 40.0 155s 19 57.4 0.596 38.7 155s 20 60.6 2.011 42.0 155s 21 64.2 4.120 46.1 155s 22 71.9 5.631 52.7 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.3 0.523 39.9 44.7 155s 3 46.2 0.560 43.8 48.7 155s 4 50.8 0.379 48.5 53.1 155s 5 51.1 0.448 48.8 53.5 155s 6 52.6 0.457 50.3 55.0 155s 7 54.3 0.408 52.0 56.6 155s 8 54.9 0.375 52.6 57.2 155s 9 56.3 0.418 54.0 58.6 155s 10 NA NA NA NA 155s 11 54.9 0.701 52.3 57.4 155s 12 51.2 0.638 48.7 53.8 155s 13 NA NA NA NA 155s 14 46.2 0.673 43.6 48.7 155s 15 48.8 0.453 46.5 51.2 155s 16 51.4 0.384 49.1 53.7 155s 17 56.1 0.391 53.8 58.4 155s 18 59.2 0.361 56.9 61.5 155s 19 57.4 0.449 55.0 59.7 155s 20 60.6 0.465 58.3 63.0 155s 21 64.2 0.468 61.9 66.6 155s 22 71.9 0.728 69.3 74.5 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 -0.200 0.613 -2.618 2.219 155s 3 1.976 0.494 -0.329 4.282 155s 4 3.978 0.444 1.714 6.242 155s 5 4.378 0.369 2.169 6.587 155s 6 4.714 0.349 2.519 6.909 155s 7 4.114 0.323 1.934 6.293 155s 8 3.416 0.287 1.257 5.575 155s 9 3.655 0.386 1.435 5.876 155s 10 4.039 0.441 1.777 6.301 155s 11 0.605 0.641 -1.843 3.053 155s 12 -3.598 0.606 -6.010 -1.186 155s 13 NA NA NA NA 155s 14 -5.413 0.708 -7.934 -2.892 155s 15 -2.915 0.412 -5.155 -0.676 155s 16 -1.366 0.336 -3.554 0.821 155s 17 1.136 0.342 -1.055 3.327 155s 18 1.921 0.246 -0.217 4.060 155s 19 0.596 0.341 -1.594 2.787 155s 20 2.011 0.364 -0.194 4.216 155s 21 4.120 0.337 1.932 6.308 155s 22 5.631 0.477 3.341 7.922 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.364 25.1 28.6 155s 3 29.1 0.367 27.3 30.8 155s 4 33.0 0.370 31.2 34.7 155s 5 34.1 0.286 32.4 35.8 155s 6 35.9 0.285 34.3 37.6 155s 7 NA NA NA NA 155s 8 38.7 0.292 37.0 40.4 155s 9 38.9 0.277 37.3 40.6 155s 10 40.2 0.264 38.5 41.8 155s 11 38.1 0.363 36.4 39.8 155s 12 33.9 0.367 32.2 35.7 155s 13 28.9 0.435 27.1 30.7 155s 14 28.0 0.383 26.3 29.8 155s 15 30.3 0.377 28.6 32.0 155s 16 33.2 0.315 31.5 34.9 155s 17 37.7 0.308 36.0 39.3 155s 18 40.0 0.241 38.4 41.7 155s 19 38.7 0.361 36.9 40.4 155s 20 42.0 0.324 40.3 43.7 155s 21 46.1 0.339 44.4 47.8 155s 22 52.7 0.511 50.9 54.6 155s > model.frame 155s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 155s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 155s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 155s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 155s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 155s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 155s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 155s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 155s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 155s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 155s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 155s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 155s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 155s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 155s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 155s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 155s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 155s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 155s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 155s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 155s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 155s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 155s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 155s trend 155s 1 -11 155s 2 -10 155s 3 -9 155s 4 -8 155s 5 -7 155s 6 -6 155s 7 -5 155s 8 -4 155s 9 -3 155s 10 -2 155s 11 -1 155s 12 0 155s 13 1 155s 14 2 155s 15 3 155s 16 4 155s 17 5 155s 18 6 155s 19 7 155s 20 8 155s 21 9 155s 22 10 155s > model.matrix 155s Consumption_(Intercept) Consumption_corpProf 155s Consumption_2 1 12.4 155s Consumption_3 1 16.9 155s Consumption_4 1 18.4 155s Consumption_5 1 19.4 155s Consumption_6 1 20.1 155s Consumption_7 1 19.6 155s Consumption_8 1 19.8 155s Consumption_9 1 21.1 155s Consumption_11 1 15.6 155s Consumption_12 1 11.4 155s Consumption_14 1 11.2 155s Consumption_15 1 12.3 155s Consumption_16 1 14.0 155s Consumption_17 1 17.6 155s Consumption_18 1 17.3 155s Consumption_19 1 15.3 155s Consumption_20 1 19.0 155s Consumption_21 1 21.1 155s Consumption_22 1 23.5 155s Investment_2 0 0.0 155s Investment_3 0 0.0 155s Investment_4 0 0.0 155s Investment_5 0 0.0 155s Investment_6 0 0.0 155s Investment_7 0 0.0 155s Investment_8 0 0.0 155s Investment_9 0 0.0 155s Investment_10 0 0.0 155s Investment_11 0 0.0 155s Investment_12 0 0.0 155s Investment_14 0 0.0 155s Investment_15 0 0.0 155s Investment_16 0 0.0 155s Investment_17 0 0.0 155s Investment_18 0 0.0 155s Investment_19 0 0.0 155s Investment_20 0 0.0 155s Investment_21 0 0.0 155s Investment_22 0 0.0 155s PrivateWages_2 0 0.0 155s PrivateWages_3 0 0.0 155s PrivateWages_4 0 0.0 155s PrivateWages_5 0 0.0 155s PrivateWages_6 0 0.0 155s PrivateWages_8 0 0.0 155s PrivateWages_9 0 0.0 155s PrivateWages_10 0 0.0 155s PrivateWages_11 0 0.0 155s PrivateWages_12 0 0.0 155s PrivateWages_13 0 0.0 155s PrivateWages_14 0 0.0 155s PrivateWages_15 0 0.0 155s PrivateWages_16 0 0.0 155s PrivateWages_17 0 0.0 155s PrivateWages_18 0 0.0 155s PrivateWages_19 0 0.0 155s PrivateWages_20 0 0.0 155s PrivateWages_21 0 0.0 155s PrivateWages_22 0 0.0 155s Consumption_corpProfLag Consumption_wages 155s Consumption_2 12.7 28.2 155s Consumption_3 12.4 32.2 155s Consumption_4 16.9 37.0 155s Consumption_5 18.4 37.0 155s Consumption_6 19.4 38.6 155s Consumption_7 20.1 40.7 155s Consumption_8 19.6 41.5 155s Consumption_9 19.8 42.9 155s Consumption_11 21.7 42.1 155s Consumption_12 15.6 39.3 155s Consumption_14 7.0 34.1 155s Consumption_15 11.2 36.6 155s Consumption_16 12.3 39.3 155s Consumption_17 14.0 44.2 155s Consumption_18 17.6 47.7 155s Consumption_19 17.3 45.9 155s Consumption_20 15.3 49.4 155s Consumption_21 19.0 53.0 155s Consumption_22 21.1 61.8 155s Investment_2 0.0 0.0 155s Investment_3 0.0 0.0 155s Investment_4 0.0 0.0 155s Investment_5 0.0 0.0 155s Investment_6 0.0 0.0 155s Investment_7 0.0 0.0 155s Investment_8 0.0 0.0 155s Investment_9 0.0 0.0 155s Investment_10 0.0 0.0 155s Investment_11 0.0 0.0 155s Investment_12 0.0 0.0 155s Investment_14 0.0 0.0 155s Investment_15 0.0 0.0 155s Investment_16 0.0 0.0 155s Investment_17 0.0 0.0 155s Investment_18 0.0 0.0 155s Investment_19 0.0 0.0 155s Investment_20 0.0 0.0 155s Investment_21 0.0 0.0 155s Investment_22 0.0 0.0 155s PrivateWages_2 0.0 0.0 155s PrivateWages_3 0.0 0.0 155s PrivateWages_4 0.0 0.0 155s PrivateWages_5 0.0 0.0 155s PrivateWages_6 0.0 0.0 155s PrivateWages_8 0.0 0.0 155s PrivateWages_9 0.0 0.0 155s PrivateWages_10 0.0 0.0 155s PrivateWages_11 0.0 0.0 155s PrivateWages_12 0.0 0.0 155s PrivateWages_13 0.0 0.0 155s PrivateWages_14 0.0 0.0 155s PrivateWages_15 0.0 0.0 155s PrivateWages_16 0.0 0.0 155s PrivateWages_17 0.0 0.0 155s PrivateWages_18 0.0 0.0 155s PrivateWages_19 0.0 0.0 155s PrivateWages_20 0.0 0.0 155s PrivateWages_21 0.0 0.0 155s PrivateWages_22 0.0 0.0 155s Investment_(Intercept) Investment_corpProf 155s Consumption_2 0 0.0 155s Consumption_3 0 0.0 155s Consumption_4 0 0.0 155s Consumption_5 0 0.0 155s Consumption_6 0 0.0 155s Consumption_7 0 0.0 155s Consumption_8 0 0.0 155s Consumption_9 0 0.0 155s Consumption_11 0 0.0 155s Consumption_12 0 0.0 155s Consumption_14 0 0.0 155s Consumption_15 0 0.0 155s Consumption_16 0 0.0 155s Consumption_17 0 0.0 155s Consumption_18 0 0.0 155s Consumption_19 0 0.0 155s Consumption_20 0 0.0 155s Consumption_21 0 0.0 155s Consumption_22 0 0.0 155s Investment_2 1 12.4 155s Investment_3 1 16.9 155s Investment_4 1 18.4 155s Investment_5 1 19.4 155s Investment_6 1 20.1 155s Investment_7 1 19.6 155s Investment_8 1 19.8 155s Investment_9 1 21.1 155s Investment_10 1 21.7 155s Investment_11 1 15.6 155s Investment_12 1 11.4 155s Investment_14 1 11.2 155s Investment_15 1 12.3 155s Investment_16 1 14.0 155s Investment_17 1 17.6 155s Investment_18 1 17.3 155s Investment_19 1 15.3 155s Investment_20 1 19.0 155s Investment_21 1 21.1 155s Investment_22 1 23.5 155s PrivateWages_2 0 0.0 155s PrivateWages_3 0 0.0 155s PrivateWages_4 0 0.0 155s PrivateWages_5 0 0.0 155s PrivateWages_6 0 0.0 155s PrivateWages_8 0 0.0 155s PrivateWages_9 0 0.0 155s PrivateWages_10 0 0.0 155s PrivateWages_11 0 0.0 155s PrivateWages_12 0 0.0 155s PrivateWages_13 0 0.0 155s PrivateWages_14 0 0.0 155s PrivateWages_15 0 0.0 155s PrivateWages_16 0 0.0 155s PrivateWages_17 0 0.0 155s PrivateWages_18 0 0.0 155s PrivateWages_19 0 0.0 155s PrivateWages_20 0 0.0 155s PrivateWages_21 0 0.0 155s PrivateWages_22 0 0.0 155s Investment_corpProfLag Investment_capitalLag 155s Consumption_2 0.0 0 155s Consumption_3 0.0 0 155s Consumption_4 0.0 0 155s Consumption_5 0.0 0 155s Consumption_6 0.0 0 155s Consumption_7 0.0 0 155s Consumption_8 0.0 0 155s Consumption_9 0.0 0 155s Consumption_11 0.0 0 155s Consumption_12 0.0 0 155s Consumption_14 0.0 0 155s Consumption_15 0.0 0 155s Consumption_16 0.0 0 155s Consumption_17 0.0 0 155s Consumption_18 0.0 0 155s Consumption_19 0.0 0 155s Consumption_20 0.0 0 155s Consumption_21 0.0 0 155s Consumption_22 0.0 0 155s Investment_2 12.7 183 155s Investment_3 12.4 183 155s Investment_4 16.9 184 155s Investment_5 18.4 190 155s Investment_6 19.4 193 155s Investment_7 20.1 198 155s Investment_8 19.6 203 155s Investment_9 19.8 208 155s Investment_10 21.1 211 155s Investment_11 21.7 216 155s Investment_12 15.6 217 155s Investment_14 7.0 207 155s Investment_15 11.2 202 155s Investment_16 12.3 199 155s Investment_17 14.0 198 155s Investment_18 17.6 200 155s Investment_19 17.3 202 155s Investment_20 15.3 200 155s Investment_21 19.0 201 155s Investment_22 21.1 204 155s PrivateWages_2 0.0 0 155s PrivateWages_3 0.0 0 155s PrivateWages_4 0.0 0 155s PrivateWages_5 0.0 0 155s PrivateWages_6 0.0 0 155s PrivateWages_8 0.0 0 155s PrivateWages_9 0.0 0 155s PrivateWages_10 0.0 0 155s PrivateWages_11 0.0 0 155s PrivateWages_12 0.0 0 155s PrivateWages_13 0.0 0 155s PrivateWages_14 0.0 0 155s PrivateWages_15 0.0 0 155s PrivateWages_16 0.0 0 155s PrivateWages_17 0.0 0 155s PrivateWages_18 0.0 0 155s PrivateWages_19 0.0 0 155s PrivateWages_20 0.0 0 155s PrivateWages_21 0.0 0 155s PrivateWages_22 0.0 0 155s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 155s Consumption_2 0 0.0 0.0 155s Consumption_3 0 0.0 0.0 155s Consumption_4 0 0.0 0.0 155s Consumption_5 0 0.0 0.0 155s Consumption_6 0 0.0 0.0 155s Consumption_7 0 0.0 0.0 155s Consumption_8 0 0.0 0.0 155s Consumption_9 0 0.0 0.0 155s Consumption_11 0 0.0 0.0 155s Consumption_12 0 0.0 0.0 155s Consumption_14 0 0.0 0.0 155s Consumption_15 0 0.0 0.0 155s Consumption_16 0 0.0 0.0 155s Consumption_17 0 0.0 0.0 155s Consumption_18 0 0.0 0.0 155s Consumption_19 0 0.0 0.0 155s Consumption_20 0 0.0 0.0 155s Consumption_21 0 0.0 0.0 155s Consumption_22 0 0.0 0.0 155s Investment_2 0 0.0 0.0 155s Investment_3 0 0.0 0.0 155s Investment_4 0 0.0 0.0 155s Investment_5 0 0.0 0.0 155s Investment_6 0 0.0 0.0 155s Investment_7 0 0.0 0.0 155s Investment_8 0 0.0 0.0 155s Investment_9 0 0.0 0.0 155s Investment_10 0 0.0 0.0 155s Investment_11 0 0.0 0.0 155s Investment_12 0 0.0 0.0 155s Investment_14 0 0.0 0.0 155s Investment_15 0 0.0 0.0 155s Investment_16 0 0.0 0.0 155s Investment_17 0 0.0 0.0 155s Investment_18 0 0.0 0.0 155s Investment_19 0 0.0 0.0 155s Investment_20 0 0.0 0.0 155s Investment_21 0 0.0 0.0 155s Investment_22 0 0.0 0.0 155s PrivateWages_2 1 45.6 44.9 155s PrivateWages_3 1 50.1 45.6 155s PrivateWages_4 1 57.2 50.1 155s PrivateWages_5 1 57.1 57.2 155s PrivateWages_6 1 61.0 57.1 155s PrivateWages_8 1 64.4 64.0 155s PrivateWages_9 1 64.5 64.4 155s PrivateWages_10 1 67.0 64.5 155s PrivateWages_11 1 61.2 67.0 155s PrivateWages_12 1 53.4 61.2 155s PrivateWages_13 1 44.3 53.4 155s PrivateWages_14 1 45.1 44.3 155s PrivateWages_15 1 49.7 45.1 155s PrivateWages_16 1 54.4 49.7 155s PrivateWages_17 1 62.7 54.4 155s PrivateWages_18 1 65.0 62.7 155s PrivateWages_19 1 60.9 65.0 155s PrivateWages_20 1 69.5 60.9 155s PrivateWages_21 1 75.7 69.5 155s PrivateWages_22 1 88.4 75.7 155s PrivateWages_trend 155s Consumption_2 0 155s Consumption_3 0 155s Consumption_4 0 155s Consumption_5 0 155s Consumption_6 0 155s Consumption_7 0 155s Consumption_8 0 155s Consumption_9 0 155s Consumption_11 0 155s Consumption_12 0 155s Consumption_14 0 155s Consumption_15 0 155s Consumption_16 0 155s Consumption_17 0 155s Consumption_18 0 155s Consumption_19 0 155s Consumption_20 0 155s Consumption_21 0 155s Consumption_22 0 155s Investment_2 0 155s Investment_3 0 155s Investment_4 0 155s Investment_5 0 155s Investment_6 0 155s Investment_7 0 155s Investment_8 0 155s Investment_9 0 155s Investment_10 0 155s Investment_11 0 155s Investment_12 0 155s Investment_14 0 155s Investment_15 0 155s Investment_16 0 155s Investment_17 0 155s Investment_18 0 155s Investment_19 0 155s Investment_20 0 155s Investment_21 0 155s Investment_22 0 155s PrivateWages_2 -10 155s PrivateWages_3 -9 155s PrivateWages_4 -8 155s PrivateWages_5 -7 155s PrivateWages_6 -6 155s PrivateWages_8 -4 155s PrivateWages_9 -3 155s PrivateWages_10 -2 155s PrivateWages_11 -1 155s PrivateWages_12 0 155s PrivateWages_13 1 155s PrivateWages_14 2 155s PrivateWages_15 3 155s PrivateWages_16 4 155s PrivateWages_17 5 155s PrivateWages_18 6 155s PrivateWages_19 7 155s PrivateWages_20 8 155s PrivateWages_21 9 155s PrivateWages_22 10 155s > nobs 155s [1] 59 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.33 0.57 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.31 0.58 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 48 155s 2 47 1 0.31 0.58 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 0.17 0.84 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 0.16 0.85 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 49 155s 2 47 2 0.33 0.85 155s > logLik 155s 'log Lik.' -69.6 (df=13) 155s 'log Lik.' -74.2 (df=13) 155s compare log likelihood value with single-equation OLS 155s [1] "Mean relative difference: 0.00099" 155s > 155s > # 2SLS 155s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: 2SLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 57 45 58.2 0.333 0.968 0.991 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 155s Investment 19 15 26.21 1.748 1.32 0.852 0.823 155s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.237 0.518 -0.408 155s Investment 0.518 1.263 0.113 155s PrivateWages -0.408 0.113 0.468 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.416 -0.538 155s Investment 0.416 1.000 0.139 155s PrivateWages -0.538 0.139 1.000 155s 155s 155s 2SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 17.2849 1.6018 10.79 3.6e-08 *** 155s corpProf -0.0770 0.1637 -0.47 0.645 155s corpProfLag 0.2327 0.1242 1.87 0.082 . 155s wages 0.8259 0.0459 17.98 4.5e-11 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.261 on 14 degrees of freedom 155s Number of observations: 18 Degrees of Freedom: 14 155s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 155s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 155s 155s 155s 2SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 18.4005 7.1627 2.57 0.02138 * 155s corpProf 0.1507 0.1905 0.79 0.44118 155s corpProfLag 0.5757 0.1634 3.52 0.00307 ** 155s capitalLag -0.1452 0.0339 -4.28 0.00065 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.322 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 26.213 MSE: 1.748 Root MSE: 1.322 155s Multiple R-Squared: 0.852 Adjusted R-Squared: 0.823 155s 155s 155s 2SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3431 1.1544 1.16 0.26172 155s gnp 0.4438 0.0351 12.64 9.7e-10 *** 155s gnpLag 0.1447 0.0381 3.80 0.00158 ** 155s trend 0.1238 0.0300 4.13 0.00078 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.78 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 155s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.6754 -1.23599 -1.3401 155s 3 -0.4627 0.32957 0.2378 155s 4 -1.1585 1.08894 1.1117 155s 5 -0.0305 -1.37017 -0.1954 155s 6 0.4693 0.48431 -0.5355 155s 7 NA NA NA 155s 8 1.6045 1.06811 -0.7908 155s 9 1.6018 0.16695 0.2831 155s 10 NA 1.86380 1.1353 155s 11 -0.9031 -0.92183 -0.1765 155s 12 -1.5948 -1.03217 0.6007 155s 13 NA NA 0.1443 155s 14 0.2854 0.85468 0.4826 155s 15 -0.4718 -0.36943 0.3016 155s 16 -0.2268 0.00554 0.0261 155s 17 2.0079 1.69566 -0.8614 155s 18 -0.7434 -0.12659 0.9927 155s 19 -0.5410 -3.26209 -0.4446 155s 20 1.4186 0.25579 -0.3914 155s 21 1.1462 -0.00185 -1.1115 155s 22 -1.7256 0.50679 0.5312 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.6 1.036 26.8 155s 3 45.5 1.570 29.1 155s 4 50.4 4.111 33.0 155s 5 50.6 4.370 34.1 155s 6 52.1 4.616 35.9 155s 7 NA NA NA 155s 8 54.6 3.132 38.7 155s 9 55.7 2.833 38.9 155s 10 NA 3.236 40.2 155s 11 55.9 1.922 38.1 155s 12 52.5 -2.368 33.9 155s 13 NA NA 28.9 155s 14 46.2 -5.955 28.0 155s 15 49.2 -2.631 30.3 155s 16 51.5 -1.306 33.2 155s 17 55.7 0.404 37.7 155s 18 59.4 2.127 40.0 155s 19 58.0 1.362 38.6 155s 20 60.2 1.044 42.0 155s 21 63.9 3.302 46.1 155s 22 71.4 4.393 52.8 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.6 0.571 41.4 43.8 155s 3 45.5 0.656 44.1 46.9 155s 4 50.4 0.431 49.4 51.3 155s 5 50.6 0.510 49.5 51.7 155s 6 52.1 0.521 51.0 53.2 155s 7 NA NA NA NA 155s 8 54.6 0.419 53.7 55.5 155s 9 55.7 0.496 54.6 56.8 155s 10 NA NA NA NA 155s 11 55.9 0.910 54.0 57.9 155s 12 52.5 0.869 50.6 54.4 155s 13 NA NA NA NA 155s 14 46.2 0.694 44.7 47.7 155s 15 49.2 0.487 48.1 50.2 155s 16 51.5 0.396 50.7 52.4 155s 17 55.7 0.445 54.7 56.6 155s 18 59.4 0.386 58.6 60.3 155s 19 58.0 0.548 56.9 59.2 155s 20 60.2 0.528 59.0 61.3 155s 21 63.9 0.515 62.8 65.0 155s 22 71.4 0.786 69.7 73.1 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 1.036 0.892 -0.865 2.937 155s 3 1.570 0.579 0.335 2.805 155s 4 4.111 0.531 2.979 5.243 155s 5 4.370 0.440 3.432 5.308 155s 6 4.616 0.416 3.729 5.502 155s 7 NA NA NA NA 155s 8 3.132 0.344 2.398 3.866 155s 9 2.833 0.533 1.696 3.970 155s 10 3.236 0.580 2.000 4.473 155s 11 1.922 0.959 -0.122 3.966 155s 12 -2.368 0.860 -4.201 -0.534 155s 13 NA NA NA NA 155s 14 -5.955 0.865 -7.799 -4.110 155s 15 -2.631 0.479 -3.652 -1.610 155s 16 -1.306 0.382 -2.120 -0.491 155s 17 0.404 0.487 -0.635 1.443 155s 18 2.127 0.319 1.447 2.806 155s 19 1.362 0.537 0.218 2.506 155s 20 1.044 0.566 -0.162 2.250 155s 21 3.302 0.486 2.265 4.339 155s 22 4.393 0.713 2.874 5.912 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.321 26.2 27.5 155s 3 29.1 0.334 28.4 29.8 155s 4 33.0 0.353 32.2 33.7 155s 5 34.1 0.253 33.6 34.6 155s 6 35.9 0.261 35.4 36.5 155s 7 NA NA NA NA 155s 8 38.7 0.257 38.1 39.2 155s 9 38.9 0.245 38.4 39.4 155s 10 40.2 0.235 39.7 40.7 155s 11 38.1 0.348 37.3 38.8 155s 12 33.9 0.374 33.1 34.7 155s 13 28.9 0.447 27.9 29.8 155s 14 28.0 0.341 27.3 28.7 155s 15 30.3 0.333 29.6 31.0 155s 16 33.2 0.278 32.6 33.8 155s 17 37.7 0.288 37.1 38.3 155s 18 40.0 0.214 39.6 40.5 155s 19 38.6 0.351 37.9 39.4 155s 20 42.0 0.301 41.4 42.6 155s 21 46.1 0.304 45.5 46.8 155s 22 52.8 0.486 51.7 53.8 155s > model.frame 155s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 155s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 155s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 155s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 155s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 155s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 155s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 155s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 155s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 155s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 155s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 155s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 155s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 155s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 155s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 155s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 155s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 155s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 155s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 155s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 155s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 155s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 155s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 155s trend 155s 1 -11 155s 2 -10 155s 3 -9 155s 4 -8 155s 5 -7 155s 6 -6 155s 7 -5 155s 8 -4 155s 9 -3 155s 10 -2 155s 11 -1 155s 12 0 155s 13 1 155s 14 2 155s 15 3 155s 16 4 155s 17 5 155s 18 6 155s 19 7 155s 20 8 155s 21 9 155s 22 10 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 155s [3] "Numeric: lengths (708, 684) differ" 155s > nobs 155s [1] 57 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 45 1 1.37 0.25 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 45 1 1.77 0.19 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 46 155s 2 45 1 1.77 0.18 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 45 2 0.69 0.51 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 45 2 0.89 0.42 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 47 155s 2 45 2 1.78 0.41 155s > logLik 155s 'log Lik.' -70.6 (df=13) 155s 'log Lik.' -78.7 (df=13) 155s > 155s > # SUR 155s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: SUR 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 59 47 45.1 0.168 0.976 0.992 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 155s Investment 20 16 17.3 1.083 1.041 0.911 0.894 155s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 0.9286 0.0435 -0.369 155s Investment 0.0435 0.7653 0.109 155s PrivateWages -0.3690 0.1091 0.468 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 0.9251 0.0748 -0.427 155s Investment 0.0748 0.7653 0.171 155s PrivateWages -0.4268 0.1706 0.492 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.0000 0.0888 -0.636 155s Investment 0.0888 1.0000 0.268 155s PrivateWages -0.6364 0.2678 1.000 155s 155s 155s SUR estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.2684 1.2781 12.73 1.9e-09 *** 155s corpProf 0.1942 0.0927 2.10 0.054 . 155s corpProfLag 0.0746 0.0819 0.91 0.377 155s wages 0.8011 0.0372 21.53 1.1e-12 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.08 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 155s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 155s 155s 155s SUR estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 12.6462 4.6500 2.72 0.01515 * 155s corpProf 0.4707 0.0916 5.14 9.9e-05 *** 155s corpProfLag 0.3519 0.0874 4.03 0.00097 *** 155s capitalLag -0.1253 0.0229 -5.47 5.1e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.041 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 17.325 MSE: 1.083 Root MSE: 1.041 155s Multiple R-Squared: 0.911 Adjusted R-Squared: 0.894 155s 155s 155s SUR estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3245 1.0946 1.21 0.24 155s gnp 0.4184 0.0260 16.08 2.7e-11 *** 155s gnpLag 0.1714 0.0307 5.59 4.1e-05 *** 155s trend 0.1455 0.0276 5.27 7.6e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.801 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.265 MSE: 0.642 Root MSE: 0.801 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.3146 -0.2419 -1.1439 155s 3 -1.2707 -0.1795 0.5080 155s 4 -1.5428 1.0691 1.4208 155s 5 -0.4489 -1.4778 -0.1000 155s 6 0.0588 0.3168 -0.3599 155s 7 0.9215 1.4450 NA 155s 8 1.3791 0.8287 -0.7561 155s 9 1.0901 -0.5272 0.2880 155s 10 NA 1.2089 1.1795 155s 11 0.3577 0.4081 -0.3681 155s 12 -0.2286 0.2569 0.3439 155s 13 NA NA -0.1574 155s 14 0.2172 0.4743 0.4225 155s 15 -0.1124 -0.0607 0.3154 155s 16 -0.0876 0.0761 0.0151 155s 17 1.5611 1.0205 -0.8084 155s 18 -0.4529 0.0580 0.8611 155s 19 0.1999 -2.5444 -0.7635 155s 20 0.9266 -0.6202 -0.4039 155s 21 0.7589 -0.7478 -1.2175 155s 22 -2.2135 -0.6029 0.5611 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.2 0.0419 26.6 155s 3 46.3 2.0795 28.8 155s 4 50.7 4.1309 32.7 155s 5 51.0 4.4778 34.0 155s 6 52.5 4.7832 35.8 155s 7 54.2 4.1550 NA 155s 8 54.8 3.3713 38.7 155s 9 56.2 3.5272 38.9 155s 10 NA 3.8911 40.1 155s 11 54.6 0.5919 38.3 155s 12 51.1 -3.6569 34.2 155s 13 NA NA 29.2 155s 14 46.3 -5.5743 28.1 155s 15 48.8 -2.9393 30.3 155s 16 51.4 -1.3761 33.2 155s 17 56.1 1.0795 37.6 155s 18 59.2 1.9420 40.1 155s 19 57.3 0.6444 39.0 155s 20 60.7 1.9202 42.0 155s 21 64.2 4.0478 46.2 155s 22 71.9 5.5029 52.7 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.2 0.448 41.3 43.1 155s 3 46.3 0.476 45.3 47.2 155s 4 50.7 0.318 50.1 51.4 155s 5 51.0 0.373 50.3 51.8 155s 6 52.5 0.378 51.8 53.3 155s 7 54.2 0.337 53.5 54.9 155s 8 54.8 0.310 54.2 55.4 155s 9 56.2 0.343 55.5 56.9 155s 10 NA NA NA NA 155s 11 54.6 0.567 53.5 55.8 155s 12 51.1 0.509 50.1 52.2 155s 13 NA NA NA NA 155s 14 46.3 0.573 45.1 47.4 155s 15 48.8 0.382 48.0 49.6 155s 16 51.4 0.328 50.7 52.0 155s 17 56.1 0.336 55.5 56.8 155s 18 59.2 0.309 58.5 59.8 155s 19 57.3 0.370 56.6 58.0 155s 20 60.7 0.401 59.9 61.5 155s 21 64.2 0.405 63.4 65.1 155s 22 71.9 0.633 70.6 73.2 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 0.0419 0.533 -1.0309 1.115 155s 3 2.0795 0.433 1.2082 2.951 155s 4 4.1309 0.387 3.3532 4.909 155s 5 4.4778 0.322 3.8307 5.125 155s 6 4.7832 0.305 4.1700 5.396 155s 7 4.1550 0.283 3.5852 4.725 155s 8 3.3713 0.253 2.8630 3.880 155s 9 3.5272 0.337 2.8488 4.206 155s 10 3.8911 0.386 3.1149 4.667 155s 11 0.5919 0.561 -0.5376 1.722 155s 12 -3.6569 0.530 -4.7223 -2.591 155s 13 NA NA NA NA 155s 14 -5.5743 0.618 -6.8176 -4.331 155s 15 -2.9393 0.362 -3.6671 -2.212 155s 16 -1.3761 0.296 -1.9710 -0.781 155s 17 1.0795 0.300 0.4763 1.683 155s 18 1.9420 0.216 1.5081 2.376 155s 19 0.6444 0.298 0.0451 1.244 155s 20 1.9202 0.318 1.2798 2.561 155s 21 4.0478 0.295 3.4537 4.642 155s 22 5.5029 0.417 4.6638 6.342 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.6 0.312 26.0 27.3 155s 3 28.8 0.312 28.2 29.4 155s 4 32.7 0.307 32.1 33.3 155s 5 34.0 0.237 33.5 34.5 155s 6 35.8 0.235 35.3 36.2 155s 7 NA NA NA NA 155s 8 38.7 0.239 38.2 39.1 155s 9 38.9 0.228 38.5 39.4 155s 10 40.1 0.218 39.7 40.6 155s 11 38.3 0.293 37.7 38.9 155s 12 34.2 0.290 33.6 34.7 155s 13 29.2 0.343 28.5 29.8 155s 14 28.1 0.321 27.4 28.7 155s 15 30.3 0.320 29.6 30.9 155s 16 33.2 0.268 32.6 33.7 155s 17 37.6 0.263 37.1 38.1 155s 18 40.1 0.207 39.7 40.6 155s 19 39.0 0.293 38.4 39.6 155s 20 42.0 0.279 41.4 42.6 155s 21 46.2 0.295 45.6 46.8 155s 22 52.7 0.435 51.9 53.6 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] TRUE 155s > nobs 155s [1] 59 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.41 0.52 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 47 1 0.52 0.47 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 48 155s 2 47 1 0.52 0.47 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 0.31 0.73 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 49 155s 2 47 2 0.4 0.67 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 49 155s 2 47 2 0.79 0.67 155s > logLik 155s 'log Lik.' -67.3 (df=18) 155s 'log Lik.' -74.9 (df=18) 155s > 155s > # 3SLS 155s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: 3SLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 57 45 66.8 0.361 0.963 0.993 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 18 14 22.6 1.616 1.271 0.974 0.968 155s Investment 19 15 34.1 2.277 1.509 0.807 0.769 155s PrivateWages 20 16 10.1 0.628 0.793 0.987 0.985 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 1.237 0.518 -0.408 155s Investment 0.518 1.263 0.113 155s PrivateWages -0.408 0.113 0.468 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.257 0.601 -0.421 155s Investment 0.601 1.601 0.214 155s PrivateWages -0.421 0.214 0.491 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.425 -0.537 155s Investment 0.425 1.000 0.239 155s PrivateWages -0.537 0.239 1.000 155s 155s 155s 3SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 18.2100 1.5273 11.92 1e-08 *** 155s corpProf -0.0639 0.1461 -0.44 0.67 155s corpProfLag 0.1687 0.1125 1.50 0.16 155s wages 0.8230 0.0431 19.07 2e-11 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.271 on 14 degrees of freedom 155s Number of observations: 18 Degrees of Freedom: 14 155s SSR: 22.626 MSE: 1.616 Root MSE: 1.271 155s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 155s 155s 155s 3SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 24.7534 6.5548 3.78 0.00183 ** 155s corpProf 0.0524 0.1807 0.29 0.77600 155s corpProfLag 0.6584 0.1551 4.24 0.00071 *** 155s capitalLag -0.1756 0.0311 -5.64 4.7e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.509 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 34.149 MSE: 2.277 Root MSE: 1.509 155s Multiple R-Squared: 0.807 Adjusted R-Squared: 0.769 155s 155s 155s 3SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 0.8154 1.0961 0.74 0.46772 155s gnp 0.4250 0.0299 14.19 1.7e-10 *** 155s gnpLag 0.1731 0.0331 5.23 8.3e-05 *** 155s trend 0.1255 0.0283 4.43 0.00042 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.793 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.054 MSE: 0.628 Root MSE: 0.793 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.8680 -1.857 -1.21010 155s 3 -0.7217 0.170 0.43075 155s 4 -1.1353 0.762 1.30899 155s 5 0.0755 -1.565 -0.20270 155s 6 0.6348 0.367 -0.46842 155s 7 NA NA NA 155s 8 1.7953 1.230 -0.85853 155s 9 1.7924 0.568 0.20422 155s 10 NA 2.308 1.09889 155s 11 -0.5211 -0.972 -0.39427 155s 12 -1.5560 -0.960 0.39889 155s 13 NA NA -0.00934 155s 14 -0.2384 1.327 0.59990 155s 15 -0.7342 -0.292 0.48094 155s 16 -0.4331 0.068 0.16188 155s 17 1.8775 1.932 -0.70448 155s 18 -0.6294 -0.154 0.95616 155s 19 -0.4252 -3.400 -0.62489 155s 20 1.3682 0.589 -0.29589 155s 21 1.3155 0.271 -1.14466 155s 22 -1.4276 0.942 0.55941 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.8 1.657 26.7 155s 3 45.7 1.730 28.9 155s 4 50.3 4.438 32.8 155s 5 50.5 4.565 34.1 155s 6 52.0 4.733 35.9 155s 7 NA NA NA 155s 8 54.4 2.970 38.8 155s 9 55.5 2.432 39.0 155s 10 NA 2.792 40.2 155s 11 55.5 1.972 38.3 155s 12 52.5 -2.440 34.1 155s 13 NA NA 29.0 155s 14 46.7 -6.427 27.9 155s 15 49.4 -2.708 30.1 155s 16 51.7 -1.368 33.0 155s 17 55.8 0.168 37.5 155s 18 59.3 2.154 40.0 155s 19 57.9 1.500 38.8 155s 20 60.2 0.711 41.9 155s 21 63.7 3.029 46.1 155s 22 71.1 3.958 52.7 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.8 0.542 39.8 45.7 155s 3 45.7 0.612 42.7 48.7 155s 4 50.3 0.407 47.5 53.2 155s 5 50.5 0.478 47.6 53.4 155s 6 52.0 0.488 49.0 54.9 155s 7 NA NA NA NA 155s 8 54.4 0.394 51.5 57.3 155s 9 55.5 0.464 52.6 58.4 155s 10 NA NA NA NA 155s 11 55.5 0.811 52.3 58.8 155s 12 52.5 0.773 49.3 55.6 155s 13 NA NA NA NA 155s 14 46.7 0.666 43.7 49.8 155s 15 49.4 0.463 46.5 52.3 155s 16 51.7 0.381 48.9 54.6 155s 17 55.8 0.424 52.9 58.7 155s 18 59.3 0.359 56.5 62.2 155s 19 57.9 0.492 55.0 60.8 155s 20 60.2 0.501 57.3 63.2 155s 21 63.7 0.491 60.8 66.6 155s 22 71.1 0.749 68.0 74.3 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 1.657 0.831 -2.015 5.329 155s 3 1.730 0.574 -1.711 5.171 155s 4 4.438 0.507 1.045 7.831 155s 5 4.565 0.426 1.223 7.907 155s 6 4.733 0.406 1.402 8.064 155s 7 NA NA NA NA 155s 8 2.970 0.334 -0.324 6.263 155s 9 2.432 0.501 -0.957 5.820 155s 10 2.792 0.544 -0.627 6.211 155s 11 1.972 0.937 -1.814 5.757 155s 12 -2.440 0.849 -6.131 1.250 155s 13 NA NA NA NA 155s 14 -6.427 0.836 -10.104 -2.750 155s 15 -2.708 0.477 -6.081 0.665 155s 16 -1.368 0.381 -4.685 1.949 155s 17 0.168 0.473 -3.202 3.538 155s 18 2.154 0.311 -1.130 5.438 155s 19 1.500 0.518 -1.900 4.900 155s 20 0.711 0.541 -2.705 4.127 155s 21 3.029 0.467 -0.338 6.395 155s 22 3.958 0.677 0.432 7.483 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.7 0.315 24.9 28.5 155s 3 28.9 0.322 27.1 30.7 155s 4 32.8 0.330 31.0 34.6 155s 5 34.1 0.241 32.3 35.9 155s 6 35.9 0.249 34.1 37.6 155s 7 NA NA NA NA 155s 8 38.8 0.243 37.0 40.5 155s 9 39.0 0.231 37.2 40.7 155s 10 40.2 0.225 38.5 41.9 155s 11 38.3 0.305 36.5 40.1 155s 12 34.1 0.317 32.3 35.9 155s 13 29.0 0.382 27.1 30.9 155s 14 27.9 0.321 26.1 29.7 155s 15 30.1 0.316 28.3 31.9 155s 16 33.0 0.265 31.3 34.8 155s 17 37.5 0.270 35.7 39.3 155s 18 40.0 0.207 38.3 41.8 155s 19 38.8 0.311 37.0 40.6 155s 20 41.9 0.287 40.1 43.7 155s 21 46.1 0.300 44.3 47.9 155s 22 52.7 0.463 50.8 54.7 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 155s [3] "Numeric: lengths (708, 684) differ" 155s > nobs 155s [1] 57 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 45 1 1.95 0.17 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 45 1 2.71 0.11 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 46 155s 2 45 1 2.71 0.1 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 45 2 1.78 0.18 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 45 2 2.48 0.095 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 47 155s 2 45 2 4.95 0.084 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s > logLik 155s 'log Lik.' -71.2 (df=18) 155s 'log Lik.' -81.7 (df=18) 155s > 155s > # I3SLS 155s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: iterated 3SLS 155s 155s convergence achieved after 9 iterations 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 57 45 75 0.422 0.959 0.993 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 18 14 22.7 1.622 1.273 0.973 0.968 155s Investment 19 15 42.1 2.809 1.676 0.762 0.715 155s PrivateWages 20 16 10.2 0.638 0.799 0.987 0.985 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 1.261 0.675 -0.439 155s Investment 0.675 1.949 0.237 155s PrivateWages -0.439 0.237 0.503 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.261 0.675 -0.439 155s Investment 0.675 1.949 0.237 155s PrivateWages -0.439 0.237 0.503 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.431 -0.550 155s Investment 0.431 1.000 0.239 155s PrivateWages -0.550 0.239 1.000 155s 155s 155s 3SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 18.5887 1.5250 12.19 7.6e-09 *** 155s corpProf -0.0438 0.1441 -0.30 0.77 155s corpProfLag 0.1456 0.1109 1.31 0.21 155s wages 0.8141 0.0428 19.01 2.1e-11 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.273 on 14 degrees of freedom 155s Number of observations: 18 Degrees of Freedom: 14 155s SSR: 22.704 MSE: 1.622 Root MSE: 1.273 155s Multiple R-Squared: 0.973 Adjusted R-Squared: 0.968 155s 155s 155s 3SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 29.4725 7.6857 3.83 0.0016 ** 155s corpProf -0.0183 0.2154 -0.09 0.9333 155s corpProfLag 0.7195 0.1850 3.89 0.0015 ** 155s capitalLag -0.1985 0.0366 -5.43 6.9e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.676 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 42.136 MSE: 2.809 Root MSE: 1.676 155s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.715 155s 155s 155s 3SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 0.5385 1.1055 0.49 0.63277 155s gnp 0.4251 0.0287 14.80 9.3e-11 *** 155s gnpLag 0.1776 0.0322 5.51 4.7e-05 *** 155s trend 0.1211 0.0283 4.28 0.00057 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.799 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.204 MSE: 0.638 Root MSE: 0.799 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.9524 -2.2888 -1.1837 155s 3 -0.8681 0.0698 0.4581 155s 4 -1.1653 0.5368 1.3199 155s 5 0.0601 -1.6917 -0.2194 155s 6 0.6426 0.2972 -0.4805 155s 7 NA NA NA 155s 8 1.8394 1.3723 -0.8931 155s 9 1.8275 0.8861 0.1723 155s 10 NA 2.6574 1.0707 155s 11 -0.3387 -0.9736 -0.4288 155s 12 -1.4550 -0.8630 0.3956 155s 13 NA NA 0.0277 155s 14 -0.3782 1.7151 0.6823 155s 15 -0.7768 -0.1993 0.5638 155s 16 -0.4606 0.1448 0.2281 155s 17 1.8605 2.1295 -0.6557 155s 18 -0.5262 -0.1493 0.9718 155s 19 -0.3047 -3.4730 -0.6148 155s 20 1.3992 0.8566 -0.2636 155s 21 1.4216 0.4910 -1.1472 155s 22 -1.2431 1.2792 0.5323 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.9 2.0888 26.7 155s 3 45.9 1.8302 28.8 155s 4 50.4 4.6632 32.8 155s 5 50.5 4.6917 34.1 155s 6 52.0 4.8028 35.9 155s 7 NA NA NA 155s 8 54.4 2.8277 38.8 155s 9 55.5 2.1139 39.0 155s 10 NA 2.4426 40.2 155s 11 55.3 1.9736 38.3 155s 12 52.4 -2.5370 34.1 155s 13 NA NA 29.0 155s 14 46.9 -6.8151 27.8 155s 15 49.5 -2.8007 30.0 155s 16 51.8 -1.4448 33.0 155s 17 55.8 -0.0295 37.5 155s 18 59.2 2.1493 40.0 155s 19 57.8 1.5730 38.8 155s 20 60.2 0.4434 41.9 155s 21 63.6 2.8090 46.1 155s 22 70.9 3.6208 52.8 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.9 0.541 41.8 43.9 155s 3 45.9 0.608 44.6 47.1 155s 4 50.4 0.403 49.6 51.2 155s 5 50.5 0.472 49.6 51.5 155s 6 52.0 0.481 51.0 52.9 155s 7 NA NA NA NA 155s 8 54.4 0.388 53.6 55.1 155s 9 55.5 0.458 54.6 56.4 155s 10 NA NA NA NA 155s 11 55.3 0.795 53.7 56.9 155s 12 52.4 0.762 50.8 53.9 155s 13 NA NA NA NA 155s 14 46.9 0.663 45.5 48.2 155s 15 49.5 0.462 48.5 50.4 155s 16 51.8 0.381 51.0 52.5 155s 17 55.8 0.423 55.0 56.7 155s 18 59.2 0.355 58.5 59.9 155s 19 57.8 0.484 56.8 58.8 155s 20 60.2 0.500 59.2 61.2 155s 21 63.6 0.490 62.6 64.6 155s 22 70.9 0.747 69.4 72.4 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 2.0888 0.985 0.105 4.072 155s 3 1.8302 0.708 0.404 3.257 155s 4 4.6632 0.612 3.430 5.897 155s 5 4.6917 0.519 3.645 5.738 155s 6 4.8028 0.498 3.800 5.806 155s 7 NA NA NA NA 155s 8 2.8277 0.410 2.003 3.653 155s 9 2.1139 0.599 0.908 3.320 155s 10 2.4426 0.651 1.131 3.754 155s 11 1.9736 1.138 -0.320 4.267 155s 12 -2.5370 1.038 -4.627 -0.447 155s 13 NA NA NA NA 155s 14 -6.8151 1.011 -8.851 -4.779 155s 15 -2.8007 0.587 -3.984 -1.617 155s 16 -1.4448 0.470 -2.392 -0.498 155s 17 -0.0295 0.573 -1.183 1.124 155s 18 2.1493 0.380 1.384 2.915 155s 19 1.5730 0.624 0.315 2.831 155s 20 0.4434 0.649 -0.864 1.751 155s 21 2.8090 0.565 1.671 3.947 155s 22 3.6208 0.814 1.982 5.260 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.7 0.322 26.0 27.3 155s 3 28.8 0.328 28.2 29.5 155s 4 32.8 0.332 32.1 33.4 155s 5 34.1 0.244 33.6 34.6 155s 6 35.9 0.252 35.4 36.4 155s 7 NA NA NA NA 155s 8 38.8 0.246 38.3 39.3 155s 9 39.0 0.234 38.6 39.5 155s 10 40.2 0.230 39.8 40.7 155s 11 38.3 0.299 37.7 38.9 155s 12 34.1 0.304 33.5 34.7 155s 13 29.0 0.366 28.2 29.7 155s 14 27.8 0.321 27.2 28.5 155s 15 30.0 0.317 29.4 30.7 155s 16 33.0 0.266 32.4 33.5 155s 17 37.5 0.270 36.9 38.0 155s 18 40.0 0.211 39.6 40.5 155s 19 38.8 0.305 38.2 39.4 155s 20 41.9 0.290 41.3 42.4 155s 21 46.1 0.309 45.5 46.8 155s 22 52.8 0.468 51.8 53.7 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 155s [3] "Numeric: lengths (708, 684) differ" 155s > nobs 155s [1] 57 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 45 1 2.17 0.15 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 45 1 2.84 0.099 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 46 155s 2 45 1 2.84 0.092 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 45 2 2.45 0.098 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 45 2 3.2 0.05 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 47 155s 2 45 2 6.4 0.041 * 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s > logLik 155s 'log Lik.' -72.7 (df=18) 155s 'log Lik.' -83.9 (df=18) 155s > 155s > # OLS 155s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: OLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 58 46 44.2 0.565 0.976 0.991 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 155s Investment 19 15 17.11 1.140 1.07 0.907 0.889 155s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.285 0.061 -0.511 155s Investment 0.061 1.059 0.151 155s PrivateWages -0.511 0.151 0.648 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.0000 0.0457 -0.568 155s Investment 0.0457 1.0000 0.168 155s PrivateWages -0.5681 0.1676 1.000 155s 155s 155s OLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.2957 1.5438 10.56 2.4e-08 *** 155s corpProf 0.1796 0.1206 1.49 0.16 155s corpProfLag 0.1032 0.1031 1.00 0.33 155s wages 0.7962 0.0449 17.73 1.8e-11 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.076 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 155s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 155s 155s 155s OLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 10.1724 5.5758 1.82 0.08808 . 155s corpProf 0.5004 0.1092 4.58 0.00036 *** 155s corpProfLag 0.3270 0.1052 3.11 0.00718 ** 155s capitalLag -0.1134 0.0275 -4.13 0.00090 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.068 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 17.105 MSE: 1.14 Root MSE: 1.068 155s Multiple R-Squared: 0.907 Adjusted R-Squared: 0.889 155s 155s 155s OLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3550 1.3512 1.00 0.3309 155s gnp 0.4417 0.0342 12.92 7e-10 *** 155s gnpLag 0.1466 0.0393 3.73 0.0018 ** 155s trend 0.1244 0.0347 3.58 0.0025 ** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.78 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 155s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 155s 155s compare coef with single-equation OLS 155s [1] TRUE 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.3863 0.00693 -1.3389 155s 3 -1.2484 -0.06954 0.2462 155s 4 -1.6040 1.22401 1.1255 155s 5 -0.5384 -1.37697 -0.1959 155s 6 -0.0413 0.38610 -0.5284 155s 7 0.8043 1.48598 NA 155s 8 1.2830 0.78465 -0.7909 155s 9 1.0142 -0.65483 0.2819 155s 10 NA 1.06018 1.1384 155s 11 0.1429 0.39508 -0.1904 155s 12 -0.3439 0.20479 0.5813 155s 13 NA NA 0.1206 155s 14 0.3199 0.32778 0.4773 155s 15 -0.1016 -0.07450 0.3035 155s 16 -0.0702 NA 0.0284 155s 17 1.6064 0.96998 -0.8517 155s 18 -0.4980 0.08124 0.9908 155s 19 0.1253 -2.49295 -0.4597 155s 20 0.9805 -0.70609 -0.3819 155s 21 0.7551 -0.81928 -1.1062 155s 22 -2.1992 -0.73256 0.5501 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.3 -0.207 26.8 155s 3 46.2 1.970 29.1 155s 4 50.8 3.976 33.0 155s 5 51.1 4.377 34.1 155s 6 52.6 4.714 35.9 155s 7 54.3 4.114 NA 155s 8 54.9 3.415 38.7 155s 9 56.3 3.655 38.9 155s 10 NA 4.040 40.2 155s 11 54.9 0.605 38.1 155s 12 51.2 -3.605 33.9 155s 13 NA NA 28.9 155s 14 46.2 -5.428 28.0 155s 15 48.8 -2.926 30.3 155s 16 51.4 NA 33.2 155s 17 56.1 1.130 37.7 155s 18 59.2 1.919 40.0 155s 19 57.4 0.593 38.7 155s 20 60.6 2.006 42.0 155s 21 64.2 4.119 46.1 155s 22 71.9 5.633 52.7 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.3 0.543 39.9 44.7 155s 3 46.2 0.581 43.8 48.7 155s 4 50.8 0.394 48.5 53.1 155s 5 51.1 0.465 48.8 53.5 155s 6 52.6 0.474 50.3 55.0 155s 7 54.3 0.423 52.0 56.6 155s 8 54.9 0.389 52.6 57.2 155s 9 56.3 0.434 54.0 58.6 155s 10 NA NA NA NA 155s 11 54.9 0.727 52.2 57.5 155s 12 51.2 0.662 48.7 53.8 155s 13 NA NA NA NA 155s 14 46.2 0.698 43.6 48.8 155s 15 48.8 0.470 46.4 51.2 155s 16 51.4 0.398 49.1 53.7 155s 17 56.1 0.405 53.8 58.4 155s 18 59.2 0.375 56.9 61.5 155s 19 57.4 0.466 55.0 59.7 155s 20 60.6 0.482 58.2 63.0 155s 21 64.2 0.485 61.9 66.6 155s 22 71.9 0.755 69.3 74.5 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 -0.207 0.645 -2.718 2.30 155s 3 1.970 0.523 -0.423 4.36 155s 4 3.976 0.462 1.634 6.32 155s 5 4.377 0.383 2.094 6.66 155s 6 4.714 0.362 2.444 6.98 155s 7 4.114 0.336 1.861 6.37 155s 8 3.415 0.298 1.184 5.65 155s 9 3.655 0.400 1.359 5.95 155s 10 4.040 0.458 1.701 6.38 155s 11 0.605 0.666 -1.928 3.14 155s 12 -3.605 0.637 -6.108 -1.10 155s 13 NA NA NA NA 155s 14 -5.428 0.767 -8.074 -2.78 155s 15 -2.926 0.453 -5.261 -0.59 155s 16 NA NA NA NA 155s 17 1.130 0.366 -1.142 3.40 155s 18 1.919 0.258 -0.293 4.13 155s 19 0.593 0.357 -1.674 2.86 155s 20 2.006 0.384 -0.278 4.29 155s 21 4.119 0.350 1.858 6.38 155s 22 5.633 0.495 3.263 8.00 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.378 25.1 28.6 155s 3 29.1 0.381 27.3 30.8 155s 4 33.0 0.384 31.2 34.7 155s 5 34.1 0.297 32.4 35.8 155s 6 35.9 0.296 34.2 37.6 155s 7 NA NA NA NA 155s 8 38.7 0.303 37.0 40.4 155s 9 38.9 0.288 37.2 40.6 155s 10 40.2 0.274 38.5 41.8 155s 11 38.1 0.377 36.3 39.8 155s 12 33.9 0.381 32.2 35.7 155s 13 28.9 0.452 27.1 30.7 155s 14 28.0 0.397 26.3 29.8 155s 15 30.3 0.391 28.5 32.1 155s 16 33.2 0.327 31.5 34.9 155s 17 37.7 0.320 36.0 39.3 155s 18 40.0 0.250 38.4 41.7 155s 19 38.7 0.375 36.9 40.4 155s 20 42.0 0.337 40.3 43.7 155s 21 46.1 0.352 44.4 47.8 155s 22 52.7 0.530 50.9 54.6 155s > model.frame 155s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 155s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 155s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 155s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 155s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 155s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 155s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 155s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 155s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 155s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 155s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 155s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 155s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 155s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 155s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 155s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 155s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 155s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 155s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 155s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 155s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 155s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 155s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 155s trend 155s 1 -11 155s 2 -10 155s 3 -9 155s 4 -8 155s 5 -7 155s 6 -6 155s 7 -5 155s 8 -4 155s 9 -3 155s 10 -2 155s 11 -1 155s 12 0 155s 13 1 155s 14 2 155s 15 3 155s 16 4 155s 17 5 155s 18 6 155s 19 7 155s 20 8 155s 21 9 155s 22 10 155s > model.matrix 155s Consumption_(Intercept) Consumption_corpProf 155s Consumption_2 1 12.4 155s Consumption_3 1 16.9 155s Consumption_4 1 18.4 155s Consumption_5 1 19.4 155s Consumption_6 1 20.1 155s Consumption_7 1 19.6 155s Consumption_8 1 19.8 155s Consumption_9 1 21.1 155s Consumption_11 1 15.6 155s Consumption_12 1 11.4 155s Consumption_14 1 11.2 155s Consumption_15 1 12.3 155s Consumption_16 1 14.0 155s Consumption_17 1 17.6 155s Consumption_18 1 17.3 155s Consumption_19 1 15.3 155s Consumption_20 1 19.0 155s Consumption_21 1 21.1 155s Consumption_22 1 23.5 155s Investment_2 0 0.0 155s Investment_3 0 0.0 155s Investment_4 0 0.0 155s Investment_5 0 0.0 155s Investment_6 0 0.0 155s Investment_7 0 0.0 155s Investment_8 0 0.0 155s Investment_9 0 0.0 155s Investment_10 0 0.0 155s Investment_11 0 0.0 155s Investment_12 0 0.0 155s Investment_14 0 0.0 155s Investment_15 0 0.0 155s Investment_17 0 0.0 155s Investment_18 0 0.0 155s Investment_19 0 0.0 155s Investment_20 0 0.0 155s Investment_21 0 0.0 155s Investment_22 0 0.0 155s PrivateWages_2 0 0.0 155s PrivateWages_3 0 0.0 155s PrivateWages_4 0 0.0 155s PrivateWages_5 0 0.0 155s PrivateWages_6 0 0.0 155s PrivateWages_8 0 0.0 155s PrivateWages_9 0 0.0 155s PrivateWages_10 0 0.0 155s PrivateWages_11 0 0.0 155s PrivateWages_12 0 0.0 155s PrivateWages_13 0 0.0 155s PrivateWages_14 0 0.0 155s PrivateWages_15 0 0.0 155s PrivateWages_16 0 0.0 155s PrivateWages_17 0 0.0 155s PrivateWages_18 0 0.0 155s PrivateWages_19 0 0.0 155s PrivateWages_20 0 0.0 155s PrivateWages_21 0 0.0 155s PrivateWages_22 0 0.0 155s Consumption_corpProfLag Consumption_wages 155s Consumption_2 12.7 28.2 155s Consumption_3 12.4 32.2 155s Consumption_4 16.9 37.0 155s Consumption_5 18.4 37.0 155s Consumption_6 19.4 38.6 155s Consumption_7 20.1 40.7 155s Consumption_8 19.6 41.5 155s Consumption_9 19.8 42.9 155s Consumption_11 21.7 42.1 155s Consumption_12 15.6 39.3 155s Consumption_14 7.0 34.1 155s Consumption_15 11.2 36.6 155s Consumption_16 12.3 39.3 155s Consumption_17 14.0 44.2 155s Consumption_18 17.6 47.7 155s Consumption_19 17.3 45.9 155s Consumption_20 15.3 49.4 155s Consumption_21 19.0 53.0 155s Consumption_22 21.1 61.8 155s Investment_2 0.0 0.0 155s Investment_3 0.0 0.0 155s Investment_4 0.0 0.0 155s Investment_5 0.0 0.0 155s Investment_6 0.0 0.0 155s Investment_7 0.0 0.0 155s Investment_8 0.0 0.0 155s Investment_9 0.0 0.0 155s Investment_10 0.0 0.0 155s Investment_11 0.0 0.0 155s Investment_12 0.0 0.0 155s Investment_14 0.0 0.0 155s Investment_15 0.0 0.0 155s Investment_17 0.0 0.0 155s Investment_18 0.0 0.0 155s Investment_19 0.0 0.0 155s Investment_20 0.0 0.0 155s Investment_21 0.0 0.0 155s Investment_22 0.0 0.0 155s PrivateWages_2 0.0 0.0 155s PrivateWages_3 0.0 0.0 155s PrivateWages_4 0.0 0.0 155s PrivateWages_5 0.0 0.0 155s PrivateWages_6 0.0 0.0 155s PrivateWages_8 0.0 0.0 155s PrivateWages_9 0.0 0.0 155s PrivateWages_10 0.0 0.0 155s PrivateWages_11 0.0 0.0 155s PrivateWages_12 0.0 0.0 155s PrivateWages_13 0.0 0.0 155s PrivateWages_14 0.0 0.0 155s PrivateWages_15 0.0 0.0 155s PrivateWages_16 0.0 0.0 155s PrivateWages_17 0.0 0.0 155s PrivateWages_18 0.0 0.0 155s PrivateWages_19 0.0 0.0 155s PrivateWages_20 0.0 0.0 155s PrivateWages_21 0.0 0.0 155s PrivateWages_22 0.0 0.0 155s Investment_(Intercept) Investment_corpProf 155s Consumption_2 0 0.0 155s Consumption_3 0 0.0 155s Consumption_4 0 0.0 155s Consumption_5 0 0.0 155s Consumption_6 0 0.0 155s Consumption_7 0 0.0 155s Consumption_8 0 0.0 155s Consumption_9 0 0.0 155s Consumption_11 0 0.0 155s Consumption_12 0 0.0 155s Consumption_14 0 0.0 155s Consumption_15 0 0.0 155s Consumption_16 0 0.0 155s Consumption_17 0 0.0 155s Consumption_18 0 0.0 155s Consumption_19 0 0.0 155s Consumption_20 0 0.0 155s Consumption_21 0 0.0 155s Consumption_22 0 0.0 155s Investment_2 1 12.4 155s Investment_3 1 16.9 155s Investment_4 1 18.4 155s Investment_5 1 19.4 155s Investment_6 1 20.1 155s Investment_7 1 19.6 155s Investment_8 1 19.8 155s Investment_9 1 21.1 155s Investment_10 1 21.7 155s Investment_11 1 15.6 155s Investment_12 1 11.4 155s Investment_14 1 11.2 155s Investment_15 1 12.3 155s Investment_17 1 17.6 155s Investment_18 1 17.3 155s Investment_19 1 15.3 155s Investment_20 1 19.0 155s Investment_21 1 21.1 155s Investment_22 1 23.5 155s PrivateWages_2 0 0.0 155s PrivateWages_3 0 0.0 155s PrivateWages_4 0 0.0 155s PrivateWages_5 0 0.0 155s PrivateWages_6 0 0.0 155s PrivateWages_8 0 0.0 155s PrivateWages_9 0 0.0 155s PrivateWages_10 0 0.0 155s PrivateWages_11 0 0.0 155s PrivateWages_12 0 0.0 155s PrivateWages_13 0 0.0 155s PrivateWages_14 0 0.0 155s PrivateWages_15 0 0.0 155s PrivateWages_16 0 0.0 155s PrivateWages_17 0 0.0 155s PrivateWages_18 0 0.0 155s PrivateWages_19 0 0.0 155s PrivateWages_20 0 0.0 155s PrivateWages_21 0 0.0 155s PrivateWages_22 0 0.0 155s Investment_corpProfLag Investment_capitalLag 155s Consumption_2 0.0 0 155s Consumption_3 0.0 0 155s Consumption_4 0.0 0 155s Consumption_5 0.0 0 155s Consumption_6 0.0 0 155s Consumption_7 0.0 0 155s Consumption_8 0.0 0 155s Consumption_9 0.0 0 155s Consumption_11 0.0 0 155s Consumption_12 0.0 0 155s Consumption_14 0.0 0 155s Consumption_15 0.0 0 155s Consumption_16 0.0 0 155s Consumption_17 0.0 0 155s Consumption_18 0.0 0 155s Consumption_19 0.0 0 155s Consumption_20 0.0 0 155s Consumption_21 0.0 0 155s Consumption_22 0.0 0 155s Investment_2 12.7 183 155s Investment_3 12.4 183 155s Investment_4 16.9 184 155s Investment_5 18.4 190 155s Investment_6 19.4 193 155s Investment_7 20.1 198 155s Investment_8 19.6 203 155s Investment_9 19.8 208 155s Investment_10 21.1 211 155s Investment_11 21.7 216 155s Investment_12 15.6 217 155s Investment_14 7.0 207 155s Investment_15 11.2 202 155s Investment_17 14.0 198 155s Investment_18 17.6 200 155s Investment_19 17.3 202 155s Investment_20 15.3 200 155s Investment_21 19.0 201 155s Investment_22 21.1 204 155s PrivateWages_2 0.0 0 155s PrivateWages_3 0.0 0 155s PrivateWages_4 0.0 0 155s PrivateWages_5 0.0 0 155s PrivateWages_6 0.0 0 155s PrivateWages_8 0.0 0 155s PrivateWages_9 0.0 0 155s PrivateWages_10 0.0 0 155s PrivateWages_11 0.0 0 155s PrivateWages_12 0.0 0 155s PrivateWages_13 0.0 0 155s PrivateWages_14 0.0 0 155s PrivateWages_15 0.0 0 155s PrivateWages_16 0.0 0 155s PrivateWages_17 0.0 0 155s PrivateWages_18 0.0 0 155s PrivateWages_19 0.0 0 155s PrivateWages_20 0.0 0 155s PrivateWages_21 0.0 0 155s PrivateWages_22 0.0 0 155s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 155s Consumption_2 0 0.0 0.0 155s Consumption_3 0 0.0 0.0 155s Consumption_4 0 0.0 0.0 155s Consumption_5 0 0.0 0.0 155s Consumption_6 0 0.0 0.0 155s Consumption_7 0 0.0 0.0 155s Consumption_8 0 0.0 0.0 155s Consumption_9 0 0.0 0.0 155s Consumption_11 0 0.0 0.0 155s Consumption_12 0 0.0 0.0 155s Consumption_14 0 0.0 0.0 155s Consumption_15 0 0.0 0.0 155s Consumption_16 0 0.0 0.0 155s Consumption_17 0 0.0 0.0 155s Consumption_18 0 0.0 0.0 155s Consumption_19 0 0.0 0.0 155s Consumption_20 0 0.0 0.0 155s Consumption_21 0 0.0 0.0 155s Consumption_22 0 0.0 0.0 155s Investment_2 0 0.0 0.0 155s Investment_3 0 0.0 0.0 155s Investment_4 0 0.0 0.0 155s Investment_5 0 0.0 0.0 155s Investment_6 0 0.0 0.0 155s Investment_7 0 0.0 0.0 155s Investment_8 0 0.0 0.0 155s Investment_9 0 0.0 0.0 155s Investment_10 0 0.0 0.0 155s Investment_11 0 0.0 0.0 155s Investment_12 0 0.0 0.0 155s Investment_14 0 0.0 0.0 155s Investment_15 0 0.0 0.0 155s Investment_17 0 0.0 0.0 155s Investment_18 0 0.0 0.0 155s Investment_19 0 0.0 0.0 155s Investment_20 0 0.0 0.0 155s Investment_21 0 0.0 0.0 155s Investment_22 0 0.0 0.0 155s PrivateWages_2 1 45.6 44.9 155s PrivateWages_3 1 50.1 45.6 155s PrivateWages_4 1 57.2 50.1 155s PrivateWages_5 1 57.1 57.2 155s PrivateWages_6 1 61.0 57.1 155s PrivateWages_8 1 64.4 64.0 155s PrivateWages_9 1 64.5 64.4 155s PrivateWages_10 1 67.0 64.5 155s PrivateWages_11 1 61.2 67.0 155s PrivateWages_12 1 53.4 61.2 155s PrivateWages_13 1 44.3 53.4 155s PrivateWages_14 1 45.1 44.3 155s PrivateWages_15 1 49.7 45.1 155s PrivateWages_16 1 54.4 49.7 155s PrivateWages_17 1 62.7 54.4 155s PrivateWages_18 1 65.0 62.7 155s PrivateWages_19 1 60.9 65.0 155s PrivateWages_20 1 69.5 60.9 155s PrivateWages_21 1 75.7 69.5 155s PrivateWages_22 1 88.4 75.7 155s PrivateWages_trend 155s Consumption_2 0 155s Consumption_3 0 155s Consumption_4 0 155s Consumption_5 0 155s Consumption_6 0 155s Consumption_7 0 155s Consumption_8 0 155s Consumption_9 0 155s Consumption_11 0 155s Consumption_12 0 155s Consumption_14 0 155s Consumption_15 0 155s Consumption_16 0 155s Consumption_17 0 155s Consumption_18 0 155s Consumption_19 0 155s Consumption_20 0 155s Consumption_21 0 155s Consumption_22 0 155s Investment_2 0 155s Investment_3 0 155s Investment_4 0 155s Investment_5 0 155s Investment_6 0 155s Investment_7 0 155s Investment_8 0 155s Investment_9 0 155s Investment_10 0 155s Investment_11 0 155s Investment_12 0 155s Investment_14 0 155s Investment_15 0 155s Investment_17 0 155s Investment_18 0 155s Investment_19 0 155s Investment_20 0 155s Investment_21 0 155s Investment_22 0 155s PrivateWages_2 -10 155s PrivateWages_3 -9 155s PrivateWages_4 -8 155s PrivateWages_5 -7 155s PrivateWages_6 -6 155s PrivateWages_8 -4 155s PrivateWages_9 -3 155s PrivateWages_10 -2 155s PrivateWages_11 -1 155s PrivateWages_12 0 155s PrivateWages_13 1 155s PrivateWages_14 2 155s PrivateWages_15 3 155s PrivateWages_16 4 155s PrivateWages_17 5 155s PrivateWages_18 6 155s PrivateWages_19 7 155s PrivateWages_20 8 155s PrivateWages_21 9 155s PrivateWages_22 10 155s > nobs 155s [1] 58 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 46 1 0.3 0.59 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 46 1 0.29 0.6 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 47 155s 2 46 1 0.29 0.59 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 46 2 0.16 0.85 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 46 2 0.15 0.86 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 48 155s 2 46 2 0.3 0.86 155s > logLik 155s 'log Lik.' -68.8 (df=13) 155s 'log Lik.' -73.3 (df=13) 155s compare log likelihood value with single-equation OLS 155s [1] "Mean relative difference: 0.0011" 155s > 155s > # 2SLS 155s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: 2SLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 56 44 57.9 0.391 0.968 0.992 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 155s Investment 18 14 25.85 1.847 1.36 0.847 0.815 155s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.307 0.540 -0.431 155s Investment 0.540 1.319 0.119 155s PrivateWages -0.431 0.119 0.496 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.414 -0.538 155s Investment 0.414 1.000 0.139 155s PrivateWages -0.538 0.139 1.000 155s 155s 155s 2SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 17.2849 1.6463 10.50 5.1e-08 *** 155s corpProf -0.0770 0.1683 -0.46 0.65 155s corpProfLag 0.2327 0.1276 1.82 0.09 . 155s wages 0.8259 0.0472 17.49 6.6e-11 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.261 on 14 degrees of freedom 155s Number of observations: 18 Degrees of Freedom: 14 155s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 155s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 155s 155s 155s 2SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 18.2571 7.3132 2.50 0.02564 * 155s corpProf 0.1564 0.1942 0.81 0.43408 155s corpProfLag 0.5714 0.1672 3.42 0.00417 ** 155s capitalLag -0.1446 0.0346 -4.18 0.00093 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.359 on 14 degrees of freedom 155s Number of observations: 18 Degrees of Freedom: 14 155s SSR: 25.852 MSE: 1.847 Root MSE: 1.359 155s Multiple R-Squared: 0.847 Adjusted R-Squared: 0.815 155s 155s 155s 2SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3431 1.1879 1.13 0.275 155s gnp 0.4438 0.0361 12.28 1.5e-09 *** 155s gnpLag 0.1447 0.0392 3.69 0.002 ** 155s trend 0.1238 0.0308 4.01 0.001 ** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.78 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 155s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.6754 -1.214 -1.3401 155s 3 -0.4627 0.325 0.2378 155s 4 -1.1585 1.094 1.1117 155s 5 -0.0305 -1.368 -0.1954 155s 6 0.4693 0.486 -0.5355 155s 7 NA NA NA 155s 8 1.6045 1.066 -0.7908 155s 9 1.6018 0.156 0.2831 155s 10 NA 1.853 1.1353 155s 11 -0.9031 -0.898 -0.1765 155s 12 -1.5948 -1.012 0.6007 155s 13 NA NA 0.1443 155s 14 0.2854 0.845 0.4826 155s 15 -0.4718 -0.365 0.3016 155s 16 -0.2268 NA 0.0261 155s 17 2.0079 1.685 -0.8614 155s 18 -0.7434 -0.121 0.9927 155s 19 -0.5410 -3.248 -0.4446 155s 20 1.4186 0.241 -0.3914 155s 21 1.1462 -0.013 -1.1115 155s 22 -1.7256 0.489 0.5312 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.6 1.014 26.8 155s 3 45.5 1.575 29.1 155s 4 50.4 4.106 33.0 155s 5 50.6 4.368 34.1 155s 6 52.1 4.614 35.9 155s 7 NA NA NA 155s 8 54.6 3.134 38.7 155s 9 55.7 2.844 38.9 155s 10 NA 3.247 40.2 155s 11 55.9 1.898 38.1 155s 12 52.5 -2.388 33.9 155s 13 NA NA 28.9 155s 14 46.2 -5.945 28.0 155s 15 49.2 -2.635 30.3 155s 16 51.5 NA 33.2 155s 17 55.7 0.415 37.7 155s 18 59.4 2.121 40.0 155s 19 58.0 1.348 38.6 155s 20 60.2 1.059 42.0 155s 21 63.9 3.313 46.1 155s 22 71.4 4.411 52.8 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.6 0.586 41.3 43.8 155s 3 45.5 0.674 44.0 46.9 155s 4 50.4 0.443 49.4 51.3 155s 5 50.6 0.524 49.5 51.8 155s 6 52.1 0.535 51.0 53.3 155s 7 NA NA NA NA 155s 8 54.6 0.431 53.7 55.5 155s 9 55.7 0.510 54.6 56.8 155s 10 NA NA NA NA 155s 11 55.9 0.936 53.9 57.9 155s 12 52.5 0.893 50.6 54.4 155s 13 NA NA NA NA 155s 14 46.2 0.713 44.7 47.7 155s 15 49.2 0.501 48.1 50.2 155s 16 51.5 0.407 50.7 52.4 155s 17 55.7 0.457 54.7 56.7 155s 18 59.4 0.397 58.6 60.3 155s 19 58.0 0.564 56.8 59.2 155s 20 60.2 0.543 59.0 61.3 155s 21 63.9 0.529 62.7 65.0 155s 22 71.4 0.808 69.7 73.2 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 1.014 0.919 -0.957 2.985 155s 3 1.575 0.602 0.284 2.867 155s 4 4.106 0.544 2.940 5.272 155s 5 4.368 0.450 3.402 5.333 155s 6 4.614 0.425 3.703 5.526 155s 7 NA NA NA NA 155s 8 3.134 0.352 2.380 3.889 155s 9 2.844 0.544 1.677 4.012 155s 10 3.247 0.592 1.976 4.518 155s 11 1.898 0.978 -0.200 3.996 155s 12 -2.388 0.886 -4.289 -0.488 155s 13 NA NA NA NA 155s 14 -5.945 0.916 -7.909 -3.980 155s 15 -2.635 0.518 -3.745 -1.525 155s 16 NA NA NA NA 155s 17 0.415 0.507 -0.671 1.501 155s 18 2.121 0.329 1.416 2.826 155s 19 1.348 0.551 0.166 2.529 155s 20 1.059 0.582 -0.189 2.306 155s 21 3.313 0.496 2.248 4.377 155s 22 4.411 0.728 2.850 5.971 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.8 0.330 26.1 27.5 155s 3 29.1 0.344 28.3 29.8 155s 4 33.0 0.363 32.2 33.8 155s 5 34.1 0.260 33.5 34.6 155s 6 35.9 0.268 35.4 36.5 155s 7 NA NA NA NA 155s 8 38.7 0.265 38.1 39.3 155s 9 38.9 0.252 38.4 39.5 155s 10 40.2 0.242 39.7 40.7 155s 11 38.1 0.358 37.3 38.8 155s 12 33.9 0.385 33.1 34.7 155s 13 28.9 0.460 27.9 29.8 155s 14 28.0 0.351 27.3 28.8 155s 15 30.3 0.343 29.6 31.0 155s 16 33.2 0.287 32.6 33.8 155s 17 37.7 0.296 37.0 38.3 155s 18 40.0 0.220 39.5 40.5 155s 19 38.6 0.361 37.9 39.4 155s 20 42.0 0.309 41.3 42.6 155s 21 46.1 0.312 45.4 46.8 155s 22 52.8 0.501 51.7 53.8 155s > model.frame 155s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 155s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 155s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 155s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 155s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 155s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 155s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 155s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 155s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 155s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 155s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 155s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 155s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 155s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 155s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 155s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 155s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 155s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 155s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 155s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 155s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 155s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 155s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 155s trend 155s 1 -11 155s 2 -10 155s 3 -9 155s 4 -8 155s 5 -7 155s 6 -6 155s 7 -5 155s 8 -4 155s 9 -3 155s 10 -2 155s 11 -1 155s 12 0 155s 13 1 155s 14 2 155s 15 3 155s 16 4 155s 17 5 155s 18 6 155s 19 7 155s 20 8 155s 21 9 155s 22 10 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 155s [3] "Numeric: lengths (696, 672) differ" 155s > nobs 155s [1] 56 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 45 155s 2 44 1 1.27 0.27 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 45 155s 2 44 1 1.66 0.2 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 45 155s 2 44 1 1.66 0.2 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 44 2 0.64 0.53 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 44 2 0.84 0.44 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 46 155s 2 44 2 1.68 0.43 155s > logLik 155s 'log Lik.' -69.5 (df=13) 155s 'log Lik.' -77.5 (df=13) 155s > 155s > # SUR 155s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: SUR 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 58 46 45.1 0.199 0.975 0.993 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 155s Investment 19 15 17.3 1.155 1.075 0.906 0.887 155s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 0.9830 0.0466 -0.391 155s Investment 0.0466 0.8101 0.115 155s PrivateWages -0.3906 0.1155 0.496 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 0.979 0.080 -0.452 155s Investment 0.080 0.810 0.181 155s PrivateWages -0.452 0.181 0.521 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.0000 0.0907 -0.636 155s Investment 0.0907 1.0000 0.267 155s PrivateWages -0.6362 0.2671 1.000 155s 155s 155s SUR estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 16.2670 1.3148 12.37 2.8e-09 *** 155s corpProf 0.1942 0.0954 2.04 0.06 . 155s corpProfLag 0.0747 0.0842 0.89 0.39 155s wages 0.8011 0.0383 20.93 1.6e-12 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.08 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 155s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 155s 155s 155s SUR estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 12.6390 4.7856 2.64 0.01852 * 155s corpProf 0.4708 0.0943 4.99 0.00016 *** 155s corpProfLag 0.3533 0.0907 3.89 0.00144 ** 155s capitalLag -0.1254 0.0236 -5.32 8.6e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.075 on 15 degrees of freedom 155s Number of observations: 19 Degrees of Freedom: 15 155s SSR: 17.321 MSE: 1.155 Root MSE: 1.075 155s Multiple R-Squared: 0.906 Adjusted R-Squared: 0.887 155s 155s 155s SUR estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 1.3264 1.1240 1.18 0.2552 155s gnp 0.4184 0.0268 15.63 4.1e-11 *** 155s gnpLag 0.1714 0.0315 5.43 5.5e-05 *** 155s trend 0.1456 0.0284 5.13 0.0001 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.801 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.266 MSE: 0.642 Root MSE: 0.801 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.3143 -0.2326 -1.1434 155s 3 -1.2700 -0.1705 0.5084 155s 4 -1.5426 1.0718 1.4211 155s 5 -0.4489 -1.4767 -0.0992 155s 6 0.0588 0.3167 -0.3594 155s 7 0.9213 1.4446 NA 155s 8 1.3789 0.8296 -0.7554 155s 9 1.0900 -0.5263 0.2887 155s 10 NA 1.2083 1.1800 155s 11 0.3569 0.4082 -0.3673 155s 12 -0.2288 0.2663 0.3445 155s 13 NA NA -0.1571 155s 14 0.2181 0.4946 0.4220 155s 15 -0.1120 -0.0470 0.3147 155s 16 -0.0872 NA 0.0145 155s 17 1.5615 1.0289 -0.8091 155s 18 -0.4530 0.0617 0.8608 155s 19 0.1997 -2.5397 -0.7635 155s 20 0.9268 -0.6136 -0.4046 155s 21 0.7588 -0.7465 -1.2179 155s 22 -2.2137 -0.6044 0.5606 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.2 0.0326 26.6 155s 3 46.3 2.0705 28.8 155s 4 50.7 4.1282 32.7 155s 5 51.0 4.4767 34.0 155s 6 52.5 4.7833 35.8 155s 7 54.2 4.1554 NA 155s 8 54.8 3.3704 38.7 155s 9 56.2 3.5263 38.9 155s 10 NA 3.8917 40.1 155s 11 54.6 0.5918 38.3 155s 12 51.1 -3.6663 34.2 155s 13 NA NA 29.2 155s 14 46.3 -5.5946 28.1 155s 15 48.8 -2.9530 30.3 155s 16 51.4 NA 33.2 155s 17 56.1 1.0711 37.6 155s 18 59.2 1.9383 40.1 155s 19 57.3 0.6397 39.0 155s 20 60.7 1.9136 42.0 155s 21 64.2 4.0465 46.2 155s 22 71.9 5.5044 52.7 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.2 0.460 41.3 43.1 155s 3 46.3 0.489 45.3 47.3 155s 4 50.7 0.328 50.1 51.4 155s 5 51.0 0.384 50.3 51.8 155s 6 52.5 0.389 51.8 53.3 155s 7 54.2 0.347 53.5 54.9 155s 8 54.8 0.319 54.2 55.5 155s 9 56.2 0.353 55.5 56.9 155s 10 NA NA NA NA 155s 11 54.6 0.583 53.5 55.8 155s 12 51.1 0.524 50.1 52.2 155s 13 NA NA NA NA 155s 14 46.3 0.589 45.1 47.5 155s 15 48.8 0.393 48.0 49.6 155s 16 51.4 0.337 50.7 52.1 155s 17 56.1 0.345 55.4 56.8 155s 18 59.2 0.318 58.5 59.8 155s 19 57.3 0.381 56.5 58.1 155s 20 60.7 0.413 59.8 61.5 155s 21 64.2 0.417 63.4 65.1 155s 22 71.9 0.651 70.6 73.2 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 0.0326 0.556 -1.0866 1.15 155s 3 2.0705 0.454 1.1575 2.98 155s 4 4.1282 0.399 3.3256 4.93 155s 5 4.4767 0.331 3.8101 5.14 155s 6 4.7833 0.314 4.1520 5.41 155s 7 4.1554 0.291 3.5687 4.74 155s 8 3.3704 0.260 2.8469 3.89 155s 9 3.5263 0.347 2.8278 4.22 155s 10 3.8917 0.397 3.0924 4.69 155s 11 0.5918 0.578 -0.5711 1.75 155s 12 -3.6663 0.551 -4.7762 -2.56 155s 13 NA NA NA NA 155s 14 -5.5946 0.661 -6.9261 -4.26 155s 15 -2.9530 0.392 -3.7430 -2.16 155s 16 NA NA NA NA 155s 17 1.0711 0.318 0.4315 1.71 155s 18 1.9383 0.225 1.4863 2.39 155s 19 0.6397 0.310 0.0165 1.26 155s 20 1.9136 0.333 1.2436 2.58 155s 21 4.0465 0.304 3.4345 4.66 155s 22 5.5044 0.429 4.6400 6.37 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.6 0.321 26.0 27.3 155s 3 28.8 0.321 28.1 29.4 155s 4 32.7 0.316 32.0 33.3 155s 5 34.0 0.244 33.5 34.5 155s 6 35.8 0.242 35.3 36.2 155s 7 NA NA NA NA 155s 8 38.7 0.246 38.2 39.2 155s 9 38.9 0.234 38.4 39.4 155s 10 40.1 0.225 39.7 40.6 155s 11 38.3 0.301 37.7 38.9 155s 12 34.2 0.298 33.6 34.8 155s 13 29.2 0.353 28.4 29.9 155s 14 28.1 0.330 27.4 28.7 155s 15 30.3 0.328 29.6 30.9 155s 16 33.2 0.275 32.6 33.7 155s 17 37.6 0.270 37.1 38.2 155s 18 40.1 0.213 39.7 40.6 155s 19 39.0 0.301 38.4 39.6 155s 20 42.0 0.287 41.4 42.6 155s 21 46.2 0.304 45.6 46.8 155s 22 52.7 0.448 51.8 53.6 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] TRUE 155s > nobs 155s [1] 58 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 46 1 0.4 0.53 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 47 155s 2 46 1 0.49 0.49 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 47 155s 2 46 1 0.49 0.48 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 46 2 0.31 0.74 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 48 155s 2 46 2 0.37 0.69 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 48 155s 2 46 2 0.75 0.69 155s > logLik 155s 'log Lik.' -66.4 (df=18) 155s 'log Lik.' -74.1 (df=18) 155s > 155s > # 3SLS 155s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: 3SLS 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 56 44 67.5 0.436 0.963 0.993 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 18 14 22.4 1.598 1.264 0.974 0.968 155s Investment 18 14 35.0 2.503 1.582 0.793 0.749 155s PrivateWages 20 16 10.1 0.629 0.793 0.987 0.985 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 1.307 0.540 -0.431 155s Investment 0.540 1.319 0.119 155s PrivateWages -0.431 0.119 0.496 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.309 0.638 -0.440 155s Investment 0.638 1.749 0.233 155s PrivateWages -0.440 0.233 0.519 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.422 -0.532 155s Investment 0.422 1.000 0.247 155s PrivateWages -0.532 0.247 1.000 155s 155s 155s 3SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 18.0338 1.5648 11.52 1.6e-08 *** 155s corpProf -0.0632 0.1500 -0.42 0.68 155s corpProfLag 0.1784 0.1154 1.55 0.14 155s wages 0.8224 0.0444 18.54 3.0e-11 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.264 on 14 degrees of freedom 155s Number of observations: 18 Degrees of Freedom: 14 155s SSR: 22.377 MSE: 1.598 Root MSE: 1.264 155s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 155s 155s 155s 3SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 24.6766 6.7008 3.68 0.00246 ** 155s corpProf 0.0472 0.1843 0.26 0.80149 155s corpProfLag 0.6874 0.1577 4.36 0.00065 *** 155s capitalLag -0.1776 0.0318 -5.59 6.7e-05 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.582 on 14 degrees of freedom 155s Number of observations: 18 Degrees of Freedom: 14 155s SSR: 35.037 MSE: 2.503 Root MSE: 1.582 155s Multiple R-Squared: 0.793 Adjusted R-Squared: 0.749 155s 155s 155s 3SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 0.7823 1.1254 0.70 0.49695 155s gnp 0.4257 0.0308 13.80 2.6e-10 *** 155s gnpLag 0.1728 0.0341 5.07 0.00011 *** 155s trend 0.1252 0.0291 4.30 0.00055 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.793 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.057 MSE: 0.629 Root MSE: 0.793 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.8058 -1.721 -1.20135 155s 3 -0.6573 0.337 0.43696 155s 4 -1.1124 0.810 1.31177 155s 5 0.0833 -1.544 -0.19794 155s 6 0.6334 0.368 -0.46596 155s 7 NA NA NA 155s 8 1.7939 1.245 -0.85614 155s 9 1.7891 0.593 0.20698 155s 10 NA 2.303 1.10034 155s 11 -0.5397 -1.015 -0.38801 155s 12 -1.5147 -0.846 0.40949 155s 13 NA NA 0.00602 155s 14 -0.1171 1.670 0.61306 155s 15 -0.6526 -0.075 0.49152 155s 16 -0.3617 NA 0.17066 155s 17 1.9331 2.086 -0.69991 155s 18 -0.6063 -0.101 0.96136 155s 19 -0.3990 -3.345 -0.61606 155s 20 1.4134 0.717 -0.29343 155s 21 1.3257 0.306 -1.14412 155s 22 -1.4340 0.935 0.55310 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.7 1.5213 26.7 155s 3 45.7 1.5632 28.9 155s 4 50.3 4.3898 32.8 155s 5 50.5 4.5444 34.1 155s 6 52.0 4.7320 35.9 155s 7 NA NA NA 155s 8 54.4 2.9547 38.8 155s 9 55.5 2.4075 39.0 155s 10 NA 2.7965 40.2 155s 11 55.5 2.0150 38.3 155s 12 52.4 -2.5541 34.1 155s 13 NA NA 29.0 155s 14 46.6 -6.7699 27.9 155s 15 49.4 -2.9250 30.1 155s 16 51.7 NA 33.0 155s 17 55.8 0.0139 37.5 155s 18 59.3 2.1013 40.0 155s 19 57.9 1.4453 38.8 155s 20 60.2 0.5828 41.9 155s 21 63.7 2.9944 46.1 155s 22 71.1 3.9651 52.7 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.7 0.555 39.7 45.7 155s 3 45.7 0.628 42.6 48.7 155s 4 50.3 0.418 47.5 53.2 155s 5 50.5 0.492 47.6 53.4 155s 6 52.0 0.501 49.0 54.9 155s 7 NA NA NA NA 155s 8 54.4 0.405 51.6 57.3 155s 9 55.5 0.477 52.6 58.4 155s 10 NA NA NA NA 155s 11 55.5 0.832 52.3 58.8 155s 12 52.4 0.792 49.2 55.6 155s 13 NA NA NA NA 155s 14 46.6 0.676 43.5 49.7 155s 15 49.4 0.470 46.5 52.2 155s 16 51.7 0.386 48.8 54.5 155s 17 55.8 0.433 52.9 58.6 155s 18 59.3 0.368 56.5 62.1 155s 19 57.9 0.504 55.0 60.8 155s 20 60.2 0.513 57.3 63.1 155s 21 63.7 0.505 60.8 66.6 155s 22 71.1 0.771 68.0 74.3 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 1.5213 0.857 -2.337 5.380 155s 3 1.5632 0.589 -2.058 5.184 155s 4 4.3898 0.519 0.819 7.961 155s 5 4.5444 0.436 1.025 8.064 155s 6 4.7320 0.415 1.224 8.240 155s 7 NA NA NA NA 155s 8 2.9547 0.342 -0.517 6.426 155s 9 2.4075 0.511 -1.158 5.973 155s 10 2.7965 0.556 -0.800 6.393 155s 11 2.0150 0.955 -1.948 5.978 155s 12 -2.5541 0.874 -6.431 1.323 155s 13 NA NA NA NA 155s 14 -6.7699 0.865 -10.637 -2.903 155s 15 -2.9250 0.503 -6.485 0.635 155s 16 NA NA NA NA 155s 17 0.0139 0.483 -3.534 3.561 155s 18 2.1013 0.320 -1.361 5.563 155s 19 1.4453 0.532 -2.134 5.025 155s 20 0.5828 0.550 -3.010 4.175 155s 21 2.9944 0.476 -0.549 6.538 155s 22 3.9651 0.692 0.261 7.669 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.7 0.324 24.9 28.5 155s 3 28.9 0.331 27.0 30.7 155s 4 32.8 0.339 31.0 34.6 155s 5 34.1 0.248 32.3 35.9 155s 6 35.9 0.256 34.1 37.6 155s 7 NA NA NA NA 155s 8 38.8 0.251 37.0 40.5 155s 9 39.0 0.238 37.2 40.7 155s 10 40.2 0.232 38.4 42.0 155s 11 38.3 0.314 36.5 40.1 155s 12 34.1 0.327 32.3 35.9 155s 13 29.0 0.393 27.1 30.9 155s 14 27.9 0.329 26.1 29.7 155s 15 30.1 0.324 28.3 31.9 155s 16 33.0 0.271 31.3 34.8 155s 17 37.5 0.277 35.7 39.3 155s 18 40.0 0.213 38.3 41.8 155s 19 38.8 0.320 37.0 40.6 155s 20 41.9 0.295 40.1 43.7 155s 21 46.1 0.309 44.3 47.9 155s 22 52.7 0.476 50.8 54.7 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 155s [3] "Numeric: lengths (696, 672) differ" 155s > nobs 155s [1] 56 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 45 155s 2 44 1 1.91 0.17 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 45 155s 2 44 1 2.6 0.11 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 45 155s 2 44 1 2.6 0.11 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 44 2 1.62 0.21 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 44 2 2.2 0.12 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 46 155s 2 44 2 4.41 0.11 155s > logLik 155s 'log Lik.' -70.1 (df=18) 155s 'log Lik.' -80.6 (df=18) 155s > 155s > # I3SLS 155s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 155s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 155s > summary 155s 155s systemfit results 155s method: iterated 3SLS 155s 155s convergence achieved after 10 iterations 155s 155s N DF SSR detRCov OLS-R2 McElroy-R2 155s system 56 44 79.4 0.55 0.956 0.994 155s 155s N DF SSR MSE RMSE R2 Adj R2 155s Consumption 18 14 22.3 1.595 1.263 0.974 0.968 155s Investment 18 14 46.8 3.346 1.829 0.724 0.664 155s PrivateWages 20 16 10.2 0.639 0.799 0.987 0.985 155s 155s The covariance matrix of the residuals used for estimation 155s Consumption Investment PrivateWages 155s Consumption 1.307 0.750 -0.452 155s Investment 0.750 2.318 0.272 155s PrivateWages -0.452 0.272 0.530 155s 155s The covariance matrix of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.307 0.750 -0.452 155s Investment 0.750 2.318 0.272 155s PrivateWages -0.452 0.272 0.530 155s 155s The correlations of the residuals 155s Consumption Investment PrivateWages 155s Consumption 1.000 0.424 -0.542 155s Investment 0.424 1.000 0.254 155s PrivateWages -0.542 0.254 1.000 155s 155s 155s 3SLS estimates for 'Consumption' (equation 1) 155s Model Formula: consump ~ corpProf + corpProfLag + wages 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 18.3252 1.5452 11.86 1.1e-08 *** 155s corpProf -0.0436 0.1470 -0.30 0.77 155s corpProfLag 0.1614 0.1127 1.43 0.17 155s wages 0.8127 0.0436 18.65 2.8e-11 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.263 on 14 degrees of freedom 155s Number of observations: 18 Degrees of Freedom: 14 155s SSR: 22.337 MSE: 1.595 Root MSE: 1.263 155s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 155s 155s 155s 3SLS estimates for 'Investment' (equation 2) 155s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 30.2418 8.3674 3.61 0.00282 ** 155s corpProf -0.0437 0.2341 -0.19 0.85457 155s corpProfLag 0.7856 0.1993 3.94 0.00147 ** 155s capitalLag -0.2065 0.0397 -5.20 0.00014 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 1.829 on 14 degrees of freedom 155s Number of observations: 18 Degrees of Freedom: 14 155s SSR: 46.838 MSE: 3.346 Root MSE: 1.829 155s Multiple R-Squared: 0.724 Adjusted R-Squared: 0.664 155s 155s 155s 3SLS estimates for 'PrivateWages' (equation 3) 155s Model Formula: privWage ~ gnp + gnpLag + trend 155s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 155s gnpLag 155s 155s Estimate Std. Error t value Pr(>|t|) 155s (Intercept) 0.4741 1.1280 0.42 0.67983 155s gnp 0.4268 0.0296 14.44 1.4e-10 *** 155s gnpLag 0.1767 0.0330 5.35 6.5e-05 *** 155s trend 0.1201 0.0290 4.14 0.00076 *** 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s 155s Residual standard error: 0.799 on 16 degrees of freedom 155s Number of observations: 20 Degrees of Freedom: 16 155s SSR: 10.218 MSE: 0.639 Root MSE: 0.799 155s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 155s 155s > residuals 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 -0.8546 -2.1226 -1.1687 155s 3 -0.7611 0.3684 0.4670 155s 4 -1.1233 0.5912 1.3216 155s 5 0.0781 -1.6694 -0.2108 155s 6 0.6467 0.2952 -0.4776 155s 7 NA NA NA 155s 8 1.8444 1.4348 -0.8884 155s 9 1.8309 1.0020 0.1781 155s 10 NA 2.7265 1.0734 155s 11 -0.3652 -1.0581 -0.4134 155s 12 -1.3877 -0.6431 0.4203 155s 13 NA NA 0.0623 155s 14 -0.1818 2.4214 0.7091 155s 15 -0.6438 0.2168 0.5845 155s 16 -0.3417 NA 0.2455 155s 17 1.9583 2.4607 -0.6474 155s 18 -0.4806 -0.0468 0.9840 155s 19 -0.2563 -3.3855 -0.5930 155s 20 1.4832 1.1550 -0.2586 155s 21 1.4514 0.6086 -1.1446 155s 22 -1.2351 1.3453 0.5196 155s > fitted 155s Consumption Investment PrivateWages 155s 1 NA NA NA 155s 2 42.8 1.923 26.7 155s 3 45.8 1.532 28.8 155s 4 50.3 4.609 32.8 155s 5 50.5 4.669 34.1 155s 6 52.0 4.805 35.9 155s 7 NA NA NA 155s 8 54.4 2.765 38.8 155s 9 55.5 1.998 39.0 155s 10 NA 2.373 40.2 155s 11 55.4 2.058 38.3 155s 12 52.3 -2.757 34.1 155s 13 NA NA 28.9 155s 14 46.7 -7.521 27.8 155s 15 49.3 -3.217 30.0 155s 16 51.6 NA 33.0 155s 17 55.7 -0.361 37.4 155s 18 59.2 2.047 40.0 155s 19 57.8 1.485 38.8 155s 20 60.1 0.145 41.9 155s 21 63.5 2.691 46.1 155s 22 70.9 3.555 52.8 155s > predict 155s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 155s 1 NA NA NA NA 155s 2 42.8 0.548 41.7 43.9 155s 3 45.8 0.618 44.5 47.0 155s 4 50.3 0.411 49.5 51.2 155s 5 50.5 0.481 49.6 51.5 155s 6 52.0 0.490 51.0 52.9 155s 7 NA NA NA NA 155s 8 54.4 0.396 53.6 55.2 155s 9 55.5 0.467 54.5 56.4 155s 10 NA NA NA NA 155s 11 55.4 0.811 53.7 57.0 155s 12 52.3 0.775 50.7 53.8 155s 13 NA NA NA NA 155s 14 46.7 0.665 45.3 48.0 155s 15 49.3 0.463 48.4 50.3 155s 16 51.6 0.381 50.9 52.4 155s 17 55.7 0.428 54.9 56.6 155s 18 59.2 0.360 58.5 59.9 155s 19 57.8 0.492 56.8 58.7 155s 20 60.1 0.508 59.1 61.1 155s 21 63.5 0.499 62.5 64.6 155s 22 70.9 0.761 69.4 72.5 155s Investment.pred Investment.se.fit Investment.lwr Investment.upr 155s 1 NA NA NA NA 155s 2 1.923 1.079 -0.2526 4.098 155s 3 1.532 0.766 -0.0119 3.075 155s 4 4.609 0.668 3.2632 5.954 155s 5 4.669 0.566 3.5280 5.811 155s 6 4.805 0.543 3.7104 5.899 155s 7 NA NA NA NA 155s 8 2.765 0.447 1.8648 3.665 155s 9 1.998 0.651 0.6860 3.310 155s 10 2.373 0.710 0.9434 3.804 155s 11 2.058 1.237 -0.4350 4.551 155s 12 -2.757 1.139 -5.0532 -0.461 155s 13 NA NA NA NA 155s 14 -7.521 1.094 -9.7261 -5.317 155s 15 -3.217 0.648 -4.5217 -1.912 155s 16 NA NA NA NA 155s 17 -0.361 0.615 -1.6007 0.879 155s 18 2.047 0.417 1.2060 2.888 155s 19 1.485 0.684 0.1062 2.865 155s 20 0.145 0.699 -1.2632 1.553 155s 21 2.691 0.614 1.4548 3.928 155s 22 3.555 0.887 1.7674 5.342 155s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 155s 1 NA NA NA NA 155s 2 26.7 0.330 26.0 27.3 155s 3 28.8 0.336 28.2 29.5 155s 4 32.8 0.340 32.1 33.5 155s 5 34.1 0.251 33.6 34.6 155s 6 35.9 0.259 35.4 36.4 155s 7 NA NA NA NA 155s 8 38.8 0.253 38.3 39.3 155s 9 39.0 0.240 38.5 39.5 155s 10 40.2 0.236 39.8 40.7 155s 11 38.3 0.307 37.7 38.9 155s 12 34.1 0.313 33.4 34.7 155s 13 28.9 0.376 28.2 29.7 155s 14 27.8 0.327 27.1 28.4 155s 15 30.0 0.322 29.4 30.7 155s 16 33.0 0.270 32.4 33.5 155s 17 37.4 0.275 36.9 38.0 155s 18 40.0 0.216 39.6 40.5 155s 19 38.8 0.314 38.2 39.4 155s 20 41.9 0.296 41.3 42.5 155s 21 46.1 0.317 45.5 46.8 155s 22 52.8 0.480 51.8 53.7 155s > model.frame 155s [1] TRUE 155s > model.matrix 155s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 155s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 155s [3] "Numeric: lengths (696, 672) differ" 155s > nobs 155s [1] 56 155s > linearHypothesis 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 45 155s 2 44 1 2.29 0.14 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 45 155s 2 44 1 2.89 0.096 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 45 155s 2 44 1 2.89 0.089 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s Linear hypothesis test (Theil's F test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 44 2 2.3 0.11 155s Linear hypothesis test (F statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df F Pr(>F) 155s 1 46 155s 2 44 2 2.9 0.066 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s Linear hypothesis test (Chi^2 statistic of a Wald test) 155s 155s Hypothesis: 155s Consumption_corpProf + Investment_capitalLag = 0 155s Consumption_corpProfLag - PrivateWages_trend = 0 155s 155s Model 1: restricted model 155s Model 2: kleinModel 155s 155s Res.Df Df Chisq Pr(>Chisq) 155s 1 46 155s 2 44 2 5.79 0.055 . 155s --- 155s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 155s > logLik 155s 'log Lik.' -72.2 (df=18) 155s 'log Lik.' -83.4 (df=18) 155s > 156s BEGIN TEST test_2sls.R 156s 156s R version 4.3.2 (2023-10-31) -- "Eye Holes" 156s Copyright (C) 2023 The R Foundation for Statistical Computing 156s Platform: x86_64-pc-linux-gnu (64-bit) 156s 156s R is free software and comes with ABSOLUTELY NO WARRANTY. 156s You are welcome to redistribute it under certain conditions. 156s Type 'license()' or 'licence()' for distribution details. 156s 156s R is a collaborative project with many contributors. 156s Type 'contributors()' for more information and 156s 'citation()' on how to cite R or R packages in publications. 156s 156s Type 'demo()' for some demos, 'help()' for on-line help, or 156s 'help.start()' for an HTML browser interface to help. 156s Type 'q()' to quit R. 156s 156s > library( systemfit ) 156s Loading required package: Matrix 157s Loading required package: car 157s Loading required package: carData 157s Loading required package: lmtest 157s Loading required package: zoo 157s 157s Attaching package: ‘zoo’ 157s 157s The following objects are masked from ‘package:base’: 157s 157s as.Date, as.Date.numeric 157s 157s 157s Please cite the 'systemfit' package as: 157s 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/. 157s 157s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 157s https://r-forge.r-project.org/projects/systemfit/ 157s > options( digits = 3 ) 157s > 157s > data( "Kmenta" ) 157s > useMatrix <- FALSE 157s > 157s > demand <- consump ~ price + income 157s > supply <- consump ~ price + farmPrice + trend 157s > inst <- ~ income + farmPrice + trend 157s > inst1 <- ~ income + farmPrice 157s > instlist <- list( inst1, inst ) 157s > system <- list( demand = demand, supply = supply ) 157s > restrm <- matrix(0,1,7) # restriction matrix "R" 157s > restrm[1,3] <- 1 157s > restrm[1,7] <- -1 157s > restrict <- "demand_income - supply_trend = 0" 157s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 157s > restr2m[1,3] <- 1 157s > restr2m[1,7] <- -1 157s > restr2m[2,2] <- -1 157s > restr2m[2,5] <- 1 157s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 157s > restrict2 <- c( "demand_income - supply_trend = 0", 157s + "- demand_price + supply_price = 0.5" ) 157s > tc <- matrix(0,7,6) 157s > tc[1,1] <- 1 157s > tc[2,2] <- 1 157s > tc[3,3] <- 1 157s > tc[4,4] <- 1 157s > tc[5,5] <- 1 157s > tc[6,6] <- 1 157s > tc[7,3] <- 1 157s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 157s > restr3m[1,2] <- -1 157s > restr3m[1,5] <- 1 157s > restr3q <- c( 0.5 ) # restriction vector "q" 2 157s > restrict3 <- "- C2 + C5 = 0.5" 157s > 157s > # It is not possible to estimate 2SLS with systemfit exactly 157s > # as EViews does, because EViews uses 157s > # methodResidCov == "geomean" for the coefficient covariance matrix and 157s > # methodResidCov == "noDfCor" for the residual covariance matrix. 157s > # systemfit uses always the same formulas for both calculations. 157s > 157s > ## *************** 2SLS estimation ************************ 157s > ## ************ 2SLS estimation (default)********************* 157s > fit2sls1 <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 157s + x = TRUE, useMatrix = useMatrix ) 157s > print( summary( fit2sls1 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 162 4.36 0.697 0.548 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 65.7 3.87 1.97 0.755 0.726 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.87 4.36 157s supply 4.36 6.04 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.902 157s supply 0.902 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 157s price -0.2436 0.0965 -2.52 0.022 * 157s income 0.3140 0.0469 6.69 3.8e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.966 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 157s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 157s price 0.2401 0.0999 2.40 0.0288 * 157s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 157s trend 0.2529 0.0997 2.54 0.0219 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2sls1 ) 157s [1] 40 157s > 157s > ## *************** 2SLS estimation (singleEqSigma=F)******************* 157s > fit2sls1s <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 157s + singleEqSigma = FALSE, useMatrix = useMatrix ) 157s > print( summary( fit2sls1s ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 162 4.36 0.697 0.548 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 65.7 3.87 1.97 0.755 0.726 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.87 4.36 157s supply 4.36 6.04 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.902 157s supply 0.902 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.633 8.935 10.59 6.6e-09 *** 157s price -0.244 0.109 -2.24 0.039 * 157s income 0.314 0.053 5.93 1.6e-05 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.966 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 157s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 10.8404 4.57 0.00032 *** 157s price 0.2401 0.0902 2.66 0.01706 * 157s farmPrice 0.2556 0.0426 5.99 1.9e-05 *** 157s trend 0.2529 0.0899 2.81 0.01253 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2sls1s ) 157s [1] 40 157s > 157s > ## ********************* 2SLS (useDfSys = TRUE) ***************** 157s > print( summary( fit2sls1, useDfSys = TRUE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 162 4.36 0.697 0.548 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 65.7 3.87 1.97 0.755 0.726 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.87 4.36 157s supply 4.36 6.04 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.902 157s supply 0.902 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 157s price -0.2436 0.0965 -2.52 0.017 * 157s income 0.3140 0.0469 6.69 1.3e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.966 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 157s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 157s price 0.2401 0.0999 2.40 0.02208 * 157s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 157s trend 0.2529 0.0997 2.54 0.01605 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2sls1 ) 157s [1] 40 157s > 157s > ## ********************* 2SLS (methodResidCov = "noDfCor" ) ***************** 157s > fit2sls1r <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 157s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 157s > print( summary( fit2sls1r ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 162 2.97 0.697 0.525 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 65.7 3.87 1.97 0.755 0.726 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.29 3.59 157s supply 3.59 4.83 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.902 157s supply 0.902 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.6333 7.3027 12.96 3.1e-10 *** 157s price -0.2436 0.0890 -2.74 0.014 * 157s income 0.3140 0.0433 7.25 1.3e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.966 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 157s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 10.7425 4.61 0.00029 *** 157s price 0.2401 0.0894 2.69 0.01623 * 157s farmPrice 0.2556 0.0423 6.05 1.7e-05 *** 157s trend 0.2529 0.0891 2.84 0.01188 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2sls1r ) 157s [1] 40 157s > 157s > ## *************** 2SLS (methodResidCov="noDfCor", singleEqSigma=F) ************* 157s > fit2sls1rs <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 157s + methodResidCov = "noDfCor", singleEqSigma = FALSE, useMatrix = useMatrix ) 157s > print( summary( fit2sls1rs ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 162 2.97 0.697 0.525 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 65.7 3.87 1.97 0.755 0.726 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.29 3.59 157s supply 3.59 4.83 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.902 157s supply 0.902 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.6333 8.1158 11.66 1.6e-09 *** 157s price -0.2436 0.0989 -2.46 0.025 * 157s income 0.3140 0.0481 6.53 5.2e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.966 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 157s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 9.8463 5.03 0.00012 *** 157s price 0.2401 0.0819 2.93 0.00980 ** 157s farmPrice 0.2556 0.0387 6.60 6.1e-06 *** 157s trend 0.2529 0.0817 3.10 0.00694 ** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2sls1rs ) 157s [1] 40 157s > 157s > ## ********************* 2SLS with restriction ******************** 157s > ## **************** 2SLS with restriction (default)******************** 157s > fit2sls2 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 157s + inst = inst, useMatrix = useMatrix ) 157s > print( summary( fit2sls2 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 166 3.6 0.691 0.553 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.749 0.719 157s supply 20 16 98.2 6.13 2.48 0.634 0.565 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.97 4.55 157s supply 4.55 6.13 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.923 157s supply 0.923 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.2816 8.8693 10.63 2.4e-12 *** 157s price -0.2247 0.1034 -2.17 0.037 * 157s income 0.2983 0.0454 6.57 1.6e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.991 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 157s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 48.1843 10.5384 4.57 6.1e-05 *** 157s price 0.2427 0.0896 2.71 0.011 * 157s farmPrice 0.2619 0.0411 6.38 2.8e-07 *** 157s trend 0.2983 0.0454 6.57 1.6e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.477 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 157s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 157s 157s > nobs( fit2sls2 ) 157s [1] 40 157s > # the same with symbolically specified restrictions 157s > fit2sls2Sym <- systemfit( system, "2SLS", data = Kmenta, 157s + restrict.matrix = restrict, inst = inst, useMatrix = useMatrix ) 157s > all.equal( fit2sls2, fit2sls2Sym ) 157s [1] "Component “call”: target, current do not match when deparsed" 157s > nobs( fit2sls2Sym ) 157s [1] 40 157s > 157s > ## ************* 2SLS with restriction (singleEqSigma=T) ***************** 157s > fit2sls2s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 157s + inst = inst, singleEqSigma = TRUE, x = TRUE, 157s + useMatrix = useMatrix ) 157s > print( summary( fit2sls2s ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 166 3.6 0.691 0.553 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.749 0.719 157s supply 20 16 98.2 6.13 2.48 0.634 0.565 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.97 4.55 157s supply 4.55 6.13 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.923 157s supply 0.923 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.2816 8.0090 11.77 1.5e-13 *** 157s price -0.2247 0.0946 -2.37 0.023 * 157s income 0.2983 0.0430 6.94 5.3e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.991 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 157s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 48.1843 11.8001 4.08 0.00025 *** 157s price 0.2427 0.1006 2.41 0.02135 * 157s farmPrice 0.2619 0.0459 5.70 2.1e-06 *** 157s trend 0.2983 0.0430 6.94 5.3e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.477 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 157s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 157s 157s > nobs( fit2sls2s ) 157s [1] 40 157s > 157s > ## ********************* 2SLS with restriction (useDfSys=T) ************** 157s > print( summary( fit2sls2, useDfSys = TRUE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 166 3.6 0.691 0.553 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.749 0.719 157s supply 20 16 98.2 6.13 2.48 0.634 0.565 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.97 4.55 157s supply 4.55 6.13 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.923 157s supply 0.923 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.2816 8.8693 10.63 2.4e-12 *** 157s price -0.2247 0.1034 -2.17 0.037 * 157s income 0.2983 0.0454 6.57 1.6e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.991 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 157s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 48.1843 10.5384 4.57 6.1e-05 *** 157s price 0.2427 0.0896 2.71 0.011 * 157s farmPrice 0.2619 0.0411 6.38 2.8e-07 *** 157s trend 0.2983 0.0454 6.57 1.6e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.477 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 157s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 157s 157s > nobs( fit2sls2 ) 157s [1] 40 157s > 157s > ## ********************* 2SLS with restriction (methodResidCov = "noDfCor") ************** 157s > fit2sls2r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 157s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 157s > print( summary( fit2sls2r ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 166 2.45 0.691 0.526 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.749 0.719 157s supply 20 16 98.2 6.13 2.48 0.634 0.565 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.37 3.75 157s supply 3.75 4.91 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.923 157s supply 0.923 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.2816 8.1771 11.53 2.7e-13 *** 157s price -0.2247 0.0954 -2.36 0.024 * 157s income 0.2983 0.0419 7.13 3.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.991 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 157s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 48.1843 9.7159 4.96 1.9e-05 *** 157s price 0.2427 0.0826 2.94 0.0059 ** 157s farmPrice 0.2619 0.0379 6.92 5.7e-08 *** 157s trend 0.2983 0.0419 7.13 3.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.477 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 157s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 157s 157s > nobs( fit2sls2r ) 157s [1] 40 157s > 157s > ## ******** 2SLS with restriction (methodResidCov="noDfCor", singleEqSigma=TRUE) ********* 157s > fit2sls2rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 157s + inst = inst, methodResidCov = "noDfCor", singleEqSigma = TRUE, 157s + useMatrix = useMatrix ) 157s > print( summary( fit2sls2rs ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 166 2.45 0.691 0.526 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.749 0.719 157s supply 20 16 98.2 6.13 2.48 0.634 0.565 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.37 3.75 157s supply 3.75 4.91 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.923 157s supply 0.923 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.2816 7.3834 12.77 1.6e-14 *** 157s price -0.2247 0.0871 -2.58 0.014 * 157s income 0.2983 0.0394 7.57 8.5e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.991 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 157s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 48.1843 10.5574 4.56 6.3e-05 *** 157s price 0.2427 0.0900 2.70 0.011 * 157s farmPrice 0.2619 0.0411 6.37 2.8e-07 *** 157s trend 0.2983 0.0394 7.57 8.5e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.477 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 157s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 157s 157s > nobs( fit2sls2rs ) 157s [1] 40 157s > 157s > ## ********************* 2SLS with restriction via restrict.regMat ****************** 157s > ## *************** 2SLS with restriction via restrict.regMat (default )*************** 157s > fit2sls3 <- systemfit( system, "2SLS", data = Kmenta, restrict.regMat = tc, 157s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 157s > print( summary( fit2sls3, useDfSys = TRUE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 166 2.45 0.691 0.526 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.749 0.719 157s supply 20 16 98.2 6.13 2.48 0.634 0.565 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.37 3.75 157s supply 3.75 4.91 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.923 157s supply 0.923 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.2816 8.1771 11.53 2.7e-13 *** 157s price -0.2247 0.0954 -2.36 0.024 * 157s income 0.2983 0.0419 7.13 3.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.991 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 157s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 48.1843 9.7159 4.96 1.9e-05 *** 157s price 0.2427 0.0826 2.94 0.0059 ** 157s farmPrice 0.2619 0.0379 6.92 5.7e-08 *** 157s trend 0.2983 0.0419 7.13 3.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.477 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 157s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 157s 157s > nobs( fit2sls3 ) 157s [1] 40 157s > 157s > 157s > ## ***************** 2SLS with 2 restrictions ******************* 157s > ## ************** 2SLS with 2 restrictions (default) ************** 157s > fit2sls4 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 157s + restrict.rhs = restr2q, inst = inst, useMatrix = useMatrix ) 157s > print( summary( fit2sls4 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 3.78 0.69 0.568 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.89 4.53 157s supply 4.53 6.25 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 157s price -0.2433 0.0663 -3.67 0.00081 *** 157s income 0.3027 0.0408 7.42 1.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 157s price 0.2567 0.0663 3.87 0.00045 *** 157s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 157s trend 0.3027 0.0408 7.42 1.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls4 ) 157s [1] 40 157s > # the same with symbolically specified restrictions 157s > fit2sls4Sym <- systemfit( system, "2SLS", data = Kmenta, 157s + restrict.matrix = restrict2, inst = inst, useMatrix = useMatrix ) 157s > all.equal( fit2sls4, fit2sls4Sym ) 157s [1] "Component “call”: target, current do not match when deparsed" 157s > nobs( fit2sls4Sym ) 157s [1] 40 157s > 157s > ## ************ 2SLS with 2 restrictions (singleEqSigma=T) ************** 157s > fit2sls4s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 157s + restrict.rhs = restr2q, inst = inst, singleEqSigma = TRUE, 157s + useMatrix = useMatrix ) 157s > print( summary( fit2sls4s ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 3.78 0.69 0.568 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.89 4.53 157s supply 4.53 6.25 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 6.3056 15.18 < 2e-16 *** 157s price -0.2433 0.0684 -3.56 0.0011 ** 157s income 0.3027 0.0394 7.69 5.1e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 8.3296 5.59 2.7e-06 *** 157s price 0.2567 0.0684 3.75 0.00064 *** 157s farmPrice 0.2637 0.0455 5.79 1.5e-06 *** 157s trend 0.3027 0.0394 7.69 5.1e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls4s ) 157s [1] 40 157s > 157s > ## ***************** 2SLS with 2 restrictions (useDfSys=T) ************** 157s > print( summary( fit2sls4, useDfSys = TRUE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 3.78 0.69 0.568 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.89 4.53 157s supply 4.53 6.25 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 157s price -0.2433 0.0663 -3.67 0.00081 *** 157s income 0.3027 0.0408 7.42 1.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 157s price 0.2567 0.0663 3.87 0.00045 *** 157s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 157s trend 0.3027 0.0408 7.42 1.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls4 ) 157s [1] 40 157s > 157s > ## ***************** 2SLS with 2 restrictions (methodResidCov="noDfCor") ************** 157s > fit2sls4r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 157s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 157s + x = TRUE, useMatrix = useMatrix ) 157s > print( summary( fit2sls4r ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 2.57 0.69 0.54 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.30 3.73 157s supply 3.73 5.00 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 6.0044 15.94 < 2e-16 *** 157s price -0.2433 0.0621 -3.92 0.00039 *** 157s income 0.3027 0.0382 7.93 2.5e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 7.3842 6.31 3.1e-07 *** 157s price 0.2567 0.0621 4.14 0.00021 *** 157s farmPrice 0.2637 0.0373 7.08 3.0e-08 *** 157s trend 0.3027 0.0382 7.93 2.5e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls4r ) 157s [1] 40 157s > 157s > ## ***** 2SLS with 2 restrictions (methodResidCov="noDfCor", singleEqSigma=T) ******* 157s > fit2sls4rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 157s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 157s + singleEqSigma = TRUE, useMatrix = useMatrix ) 157s > print( summary( fit2sls4rs ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 2.57 0.69 0.54 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.30 3.73 157s supply 3.73 5.00 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 5.7579 16.62 < 2e-16 *** 157s price -0.2433 0.0621 -3.92 4e-04 *** 157s income 0.3027 0.0360 8.40 6.6e-10 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 7.5360 6.18 4.5e-07 *** 157s price 0.2567 0.0621 4.13 0.00021 *** 157s farmPrice 0.2637 0.0407 6.47 1.8e-07 *** 157s trend 0.3027 0.0360 8.40 6.6e-10 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls4rs ) 157s [1] 40 157s > 157s > ## ************* 2SLS with 2 restrictions via R and restrict.regMat ****************** 157s > ## ******** 2SLS with 2 restrictions via R and restrict.regMat (default) ************* 157s > fit2sls5 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 157s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 157s + useMatrix = useMatrix ) 157s > print( summary( fit2sls5 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 3.78 0.69 0.568 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.89 4.53 157s supply 4.53 6.25 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 157s price -0.2433 0.0663 -3.67 0.00081 *** 157s income 0.3027 0.0408 7.42 1.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 157s price 0.2567 0.0663 3.87 0.00045 *** 157s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 157s trend 0.3027 0.0408 7.42 1.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls5 ) 157s [1] 40 157s > # the same with symbolically specified restrictions 157s > fit2sls5Sym <- systemfit( system, "2SLS", data = Kmenta, 157s + restrict.matrix = restrict3, restrict.regMat = tc, inst = inst, 157s + useMatrix = useMatrix ) 157s > all.equal( fit2sls5, fit2sls5Sym ) 157s [1] "Component “call”: target, current do not match when deparsed" 157s > nobs( fit2sls5Sym ) 157s [1] 40 157s > 157s > ## ******* 2SLS with 2 restrictions via R and restrict.regMat (singleEqSigma=T) ****** 157s > fit2sls5s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 157s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 157s + singleEqSigma = TRUE, useMatrix = useMatrix ) 157s > print( summary( fit2sls5s ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 3.78 0.69 0.568 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.89 4.53 157s supply 4.53 6.25 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 6.3056 15.18 < 2e-16 *** 157s price -0.2433 0.0684 -3.56 0.0011 ** 157s income 0.3027 0.0394 7.69 5.1e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 8.3296 5.59 2.7e-06 *** 157s price 0.2567 0.0684 3.75 0.00064 *** 157s farmPrice 0.2637 0.0455 5.79 1.5e-06 *** 157s trend 0.3027 0.0394 7.69 5.1e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls5s ) 157s [1] 40 157s > 157s > ## ********** 2SLS with 2 restrictions via R and restrict.regMat (useDfSys=T) ******* 157s > print( summary( fit2sls5, useDfSys = TRUE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 3.78 0.69 0.568 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.89 4.53 157s supply 4.53 6.25 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 157s price -0.2433 0.0663 -3.67 0.00081 *** 157s income 0.3027 0.0408 7.42 1.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 157s price 0.2567 0.0663 3.87 0.00045 *** 157s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 157s trend 0.3027 0.0408 7.42 1.1e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls5 ) 157s [1] 40 157s > 157s > ## ************* 2SLS with 2 restrictions via R and restrict.regMat (methodResidCov="noDfCor") ********* 157s > fit2sls5r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 157s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 157s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 157s > print( summary( fit2sls5r ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 2.57 0.69 0.54 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.30 3.73 157s supply 3.73 5.00 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 6.0044 15.94 < 2e-16 *** 157s price -0.2433 0.0621 -3.92 0.00039 *** 157s income 0.3027 0.0382 7.93 2.5e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 7.3842 6.31 3.1e-07 *** 157s price 0.2567 0.0621 4.14 0.00021 *** 157s farmPrice 0.2637 0.0373 7.08 3.0e-08 *** 157s trend 0.3027 0.0382 7.93 2.5e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls5r ) 157s [1] 40 157s > 157s > ## ** 2SLS with 2 restrictions via R and restrict.regMat (methodResidCov="noDfCor", singleEqSigma=T) ** 157s > fit2sls5rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 157s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 157s + methodResidCov = "noDfCor", singleEqSigma = TRUE, 157s + x = TRUE, useMatrix = useMatrix ) 157s > print( summary( fit2sls5rs ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 2.57 0.69 0.54 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.30 3.73 157s supply 3.73 5.00 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.919 157s supply 0.919 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 95.7059 5.7579 16.62 < 2e-16 *** 157s price -0.2433 0.0621 -3.92 4e-04 *** 157s income 0.3027 0.0360 8.40 6.6e-10 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.972 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 157s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.5637 7.5360 6.18 4.5e-07 *** 157s price 0.2567 0.0621 4.13 0.00021 *** 157s farmPrice 0.2637 0.0407 6.47 1.8e-07 *** 157s trend 0.3027 0.0360 8.40 6.6e-10 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.5 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 157s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 157s 157s > nobs( fit2sls5rs ) 157s [1] 40 157s > 157s > ## *********** 2SLS estimation with different instruments ************** 157s > ## ******* 2SLS estimation with different instruments (default) ********* 157s > fit2slsd1 <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 157s + useMatrix = useMatrix ) 157s > print( summary( fit2slsd1 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 164 9.25 0.694 0.512 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.748 0.719 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.97 3.84 157s supply 3.84 6.04 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.784 157s supply 0.784 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 157s price -0.4116 0.1448 -2.84 0.011 * 157s income 0.3617 0.0564 6.41 6.4e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.992 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 157s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 157s price 0.2401 0.0999 2.40 0.0288 * 157s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 157s trend 0.2529 0.0997 2.54 0.0219 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2slsd1 ) 157s [1] 40 157s > 157s > ## *********** 2SLS estimation with different instruments (singleEqSigma=F)***** 157s > fit2slsd1s <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 157s + singleEqSigma = FALSE, useMatrix = useMatrix ) 157s > print( summary( fit2slsd1s ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 164 9.25 0.694 0.512 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.748 0.719 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.97 3.84 157s supply 3.84 6.04 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.784 157s supply 0.784 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 106.7894 12.4749 8.56 1.4e-07 *** 157s price -0.4116 0.1622 -2.54 0.021 * 157s income 0.3617 0.0631 5.73 2.5e-05 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.992 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 157s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 10.8976 4.55 0.00033 *** 157s price 0.2401 0.0907 2.65 0.01755 * 157s farmPrice 0.2556 0.0429 5.96 2e-05 *** 157s trend 0.2529 0.0904 2.80 0.01292 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2slsd1s ) 157s [1] 40 157s > 157s > ## ********* 2SLS estimation with different instruments (useDfSys=T) ******* 157s > print( summary( fit2slsd1, useDfSys = TRUE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 164 9.25 0.694 0.512 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.748 0.719 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.97 3.84 157s supply 3.84 6.04 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.784 157s supply 0.784 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 157s price -0.4116 0.1448 -2.84 0.0076 ** 157s income 0.3617 0.0564 6.41 2.9e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.992 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 157s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 157s price 0.2401 0.0999 2.40 0.02208 * 157s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 157s trend 0.2529 0.0997 2.54 0.01605 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2slsd1 ) 157s [1] 40 157s > 157s > ## ********* 2SLS estimation with different instruments (methodResidCov="noDfCor") ****** 157s > fit2slsd1r <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 157s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 157s > print( summary( fit2slsd1r ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 164 6.29 0.694 0.5 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.748 0.719 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.37 3.16 157s supply 3.16 4.83 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.784 157s supply 0.784 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 106.789 10.274 10.39 8.8e-09 *** 157s price -0.412 0.134 -3.08 0.0068 ** 157s income 0.362 0.052 6.95 2.3e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.992 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 157s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 10.7425 4.61 0.00029 *** 157s price 0.2401 0.0894 2.69 0.01623 * 157s farmPrice 0.2556 0.0423 6.05 1.7e-05 *** 157s trend 0.2529 0.0891 2.84 0.01188 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2slsd1r ) 157s [1] 40 157s > 157s > ## 2SLS estimation with different instruments (methodResidCov="noDfCor",singleEqSigma=F) 157s > fit2slsd1r <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 157s + methodResidCov = "noDfCor", singleEqSigma = FALSE, 157s + useMatrix = useMatrix ) 157s > print( summary( fit2slsd1r ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 164 6.29 0.694 0.5 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.748 0.719 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.37 3.16 157s supply 3.16 4.83 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.784 157s supply 0.784 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 106.7894 11.3309 9.42 3.7e-08 *** 157s price -0.4116 0.1473 -2.79 0.012 * 157s income 0.3617 0.0574 6.31 7.9e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.992 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 157s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 9.8982 5.00 0.00013 *** 157s price 0.2401 0.0824 2.92 0.01012 * 157s farmPrice 0.2556 0.0389 6.56 6.5e-06 *** 157s trend 0.2529 0.0821 3.08 0.00718 ** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > nobs( fit2slsd1r ) 157s [1] 40 157s > 157s > ## **** 2SLS estimation with different instruments and restriction ******* 157s > ## ** 2SLS estimation with different instruments and restriction (default) **** 157s > fit2slsd2 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 157s + inst = instlist, useMatrix = useMatrix ) 157s > print( summary( fit2slsd2 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 165 4.89 0.693 0.56 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 64.4 3.79 1.95 0.760 0.731 157s supply 20 16 100.3 6.27 2.50 0.626 0.556 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.79 4.35 157s supply 4.35 6.27 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.891 157s supply 0.891 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 103.5936 11.8930 8.71 3.5e-10 *** 157s price -0.3449 0.1455 -2.37 0.024 * 157s income 0.3260 0.0511 6.38 2.8e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.947 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 157s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 47.3592 10.5362 4.49 7.7e-05 *** 157s price 0.2443 0.0894 2.73 0.0099 ** 157s farmPrice 0.2657 0.0411 6.47 2.1e-07 *** 157s trend 0.3260 0.0511 6.38 2.8e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.504 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 157s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 157s 157s > nobs( fit2slsd2 ) 157s [1] 40 157s > 157s > ## 2SLS estimation with different instruments and restriction (singleEqSigma=T) 157s > fit2slsd2s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 157s + inst = instlist, singleEqSigma = TRUE, useMatrix = useMatrix ) 157s > print( summary( fit2slsd2s ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 165 4.89 0.693 0.56 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 64.4 3.79 1.95 0.760 0.731 157s supply 20 16 100.3 6.27 2.50 0.626 0.556 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.79 4.35 157s supply 4.35 6.27 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.891 157s supply 0.891 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 103.5936 10.6344 9.74 2.3e-11 *** 157s price -0.3449 0.1327 -2.60 0.014 * 157s income 0.3260 0.0485 6.73 9.9e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.947 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 157s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 47.3592 11.9466 3.96 0.00036 *** 157s price 0.2443 0.1017 2.40 0.02188 * 157s farmPrice 0.2657 0.0465 5.71 2.0e-06 *** 157s trend 0.3260 0.0485 6.73 9.9e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.504 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 157s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 157s 157s > nobs( fit2slsd2s ) 157s [1] 40 157s > 157s > ## **** 2SLS estimation with different instruments and restriction (useDfSys=F) 157s > print( summary( fit2slsd2, useDfSys = FALSE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 165 4.89 0.693 0.56 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 64.4 3.79 1.95 0.760 0.731 157s supply 20 16 100.3 6.27 2.50 0.626 0.556 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.79 4.35 157s supply 4.35 6.27 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.891 157s supply 0.891 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 103.5936 11.8930 8.71 1.1e-07 *** 157s price -0.3449 0.1455 -2.37 0.03 * 157s income 0.3260 0.0511 6.38 6.9e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.947 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 157s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 47.3592 10.5362 4.49 0.00037 *** 157s price 0.2443 0.0894 2.73 0.01475 * 157s farmPrice 0.2657 0.0411 6.47 7.8e-06 *** 157s trend 0.3260 0.0511 6.38 9.1e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.504 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 157s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 157s 157s > nobs( fit2slsd2 ) 157s [1] 40 157s > 157s > ## **** 2SLS estimation with different instruments and restriction (methodResidCov="noDfCor") 157s > fit2slsd2r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 157s + inst = instlist, methodResidCov = "noDfCor", useMatrix = useMatrix ) 157s > print( summary( fit2slsd2r ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 165 3.32 0.693 0.537 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 64.4 3.79 1.95 0.760 0.731 157s supply 20 16 100.3 6.27 2.50 0.626 0.556 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.22 3.58 157s supply 3.58 5.02 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.891 157s supply 0.891 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 103.5936 10.9648 9.45 4.9e-11 *** 157s price -0.3449 0.1341 -2.57 0.015 * 157s income 0.3260 0.0471 6.92 5.7e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.947 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 157s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 47.3592 9.7139 4.88 2.5e-05 *** 157s price 0.2443 0.0824 2.96 0.0055 ** 157s farmPrice 0.2657 0.0379 7.01 4.3e-08 *** 157s trend 0.3260 0.0471 6.92 5.7e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.504 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 157s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 157s 157s > nobs( fit2slsd2r ) 157s [1] 40 157s > 157s > ## 2SLS estimation with different instr. and restr. (methodResidCov="noDfCor", singleEqSigma=T) 157s > fit2slsd2rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 157s + inst = instlist, methodResidCov = "noDfCor", singleEqSigma = TRUE, 157s + useMatrix = useMatrix ) 157s > print( summary( fit2slsd2rs ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 165 3.32 0.693 0.537 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 64.4 3.79 1.95 0.760 0.731 157s supply 20 16 100.3 6.27 2.50 0.626 0.556 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.22 3.58 157s supply 3.58 5.02 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.891 157s supply 0.891 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 103.5936 9.7929 10.58 2.7e-12 *** 157s price -0.3449 0.1220 -2.83 0.0078 ** 157s income 0.3260 0.0444 7.35 1.6e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.947 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 157s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 47.3592 10.6890 4.43 9.3e-05 *** 157s price 0.2443 0.0910 2.69 0.011 * 157s farmPrice 0.2657 0.0416 6.38 2.8e-07 *** 157s trend 0.3260 0.0444 7.35 1.6e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.504 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 157s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 157s 157s > nobs( fit2slsd2rs ) 157s [1] 40 157s > 157s > ## **** 2SLS estimation with different instruments and restriction via restrict.regMat * 157s > ## 2SLS estimation with different instruments and restriction via restrict.regMat (default) 157s > fit2slsd3 <- systemfit( system, "2SLS", data = Kmenta, restrict.regMat = tc, 157s + inst = instlist, useMatrix = useMatrix ) 157s > print( summary( fit2slsd3 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 165 4.89 0.693 0.56 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 64.4 3.79 1.95 0.760 0.731 157s supply 20 16 100.3 6.27 2.50 0.626 0.556 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.79 4.35 157s supply 4.35 6.27 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.891 157s supply 0.891 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 103.5936 11.8930 8.71 3.5e-10 *** 157s price -0.3449 0.1455 -2.37 0.024 * 157s income 0.3260 0.0511 6.38 2.8e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.947 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 157s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 47.3592 10.5362 4.49 7.7e-05 *** 157s price 0.2443 0.0894 2.73 0.0099 ** 157s farmPrice 0.2657 0.0411 6.47 2.1e-07 *** 157s trend 0.3260 0.0511 6.38 2.8e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.504 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 157s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 157s 157s > nobs( fit2slsd3 ) 157s [1] 40 157s > 157s > ## **** 2SLS estimation with different instr. and restr. via restrict.regMat (methodResidCov="noDfCor") 157s > fit2slsd3r <- systemfit( system, "2SLS", data = Kmenta, restrict.regMat = tc, 157s + inst = instlist, methodResidCov = "noDfCor", useMatrix = useMatrix ) 157s > print( summary( fit2slsd3r ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 165 3.32 0.693 0.537 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 64.4 3.79 1.95 0.760 0.731 157s supply 20 16 100.3 6.27 2.50 0.626 0.556 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.22 3.58 157s supply 3.58 5.02 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.891 157s supply 0.891 1.000 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 103.5936 10.9648 9.45 4.9e-11 *** 157s price -0.3449 0.1341 -2.57 0.015 * 157s income 0.3260 0.0471 6.92 5.7e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.947 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 157s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 47.3592 9.7139 4.88 2.5e-05 *** 157s price 0.2443 0.0824 2.96 0.0055 ** 157s farmPrice 0.2657 0.0379 7.01 4.3e-08 *** 157s trend 0.3260 0.0471 6.92 5.7e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.504 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 157s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 157s 157s > nobs( fit2slsd3r ) 157s [1] 40 157s > 157s > 157s > ## *********** estimations with a single regressor ************ 157s > fit2slsS1 <- systemfit( 157s + list( consump ~ price - 1, price ~ consump + trend ), "2SLS", 157s + data = Kmenta, inst = ~ farmPrice + trend + income, useMatrix = useMatrix ) 157s > print( summary( fit2slsS1 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 36 1544 179 -0.65 0.852 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s eq1 20 19 861 45.3 6.73 -2.213 -2.213 157s eq2 20 17 682 40.1 6.33 -0.022 -0.143 157s 157s The covariance matrix of the residuals 157s eq1 eq2 157s eq1 45.3 -40.5 157s eq2 -40.5 40.1 157s 157s The correlations of the residuals 157s eq1 eq2 157s eq1 1.00 -0.95 157s eq2 -0.95 1.00 157s 157s 157s 2SLS estimates for 'eq1' (equation 1) 157s Model Formula: consump ~ price - 1 157s Instruments: ~farmPrice + trend + income 157s 157s Estimate Std. Error t value Pr(>|t|) 157s price 1.006 0.015 66.9 <2e-16 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 6.734 on 19 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 19 157s SSR: 861.48 MSE: 45.341 Root MSE: 6.734 157s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 157s 157s 157s 2SLS estimates for 'eq2' (equation 2) 157s Model Formula: price ~ consump + trend 157s Instruments: ~farmPrice + trend + income 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 55.5365 46.2668 1.20 0.25 157s consump 0.4453 0.4622 0.96 0.35 157s trend -0.0426 0.2496 -0.17 0.87 157s 157s Residual standard error: 6.335 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 682.257 MSE: 40.133 Root MSE: 6.335 157s Multiple R-Squared: -0.022 Adjusted R-Squared: -0.143 157s 157s > nobs( fit2slsS1 ) 157s [1] 40 157s > fit2slsS2 <- systemfit( 157s + list( consump ~ price - 1, consump ~ trend - 1 ), "2SLS", 157s + data = Kmenta, inst = ~ farmPrice + price + income, useMatrix = useMatrix ) 157s > print( summary( fit2slsS2 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 38 47456 111148 -87.5 -5.28 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s eq1 20 19 861 45.3 6.73 -2.21 -2.21 157s eq2 20 19 46595 2452.3 49.52 -172.79 -172.79 157s 157s The covariance matrix of the residuals 157s eq1 eq2 157s eq1 45.34 -6.33 157s eq2 -6.33 2452.34 157s 157s The correlations of the residuals 157s eq1 eq2 157s eq1 1.0000 -0.0448 157s eq2 -0.0448 1.0000 157s 157s 157s 2SLS estimates for 'eq1' (equation 1) 157s Model Formula: consump ~ price - 1 157s Instruments: ~farmPrice + price + income 157s 157s Estimate Std. Error t value Pr(>|t|) 157s price 1.006 0.015 66.9 <2e-16 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 6.733 on 19 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 19 157s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 157s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 157s 157s 157s 2SLS estimates for 'eq2' (equation 2) 157s Model Formula: consump ~ trend - 1 157s Instruments: ~farmPrice + price + income 157s 157s Estimate Std. Error t value Pr(>|t|) 157s trend 7.578 0.934 8.11 1.4e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 49.521 on 19 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 19 157s SSR: 46594.549 MSE: 2452.345 Root MSE: 49.521 157s Multiple R-Squared: -172.786 Adjusted R-Squared: -172.786 157s 157s > nobs( fit2slsS2 ) 157s [1] 40 157s > fit2slsS3 <- systemfit( 157s + list( consump ~ trend - 1, price ~ trend - 1 ), "2SLS", 157s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 157s > print( summary( fit2slsS3 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 38 97978 687515 -104 -10.6 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s eq1 20 19 50950 2682 51.8 -189.0 -189.0 157s eq2 20 19 47028 2475 49.8 -69.5 -69.5 157s 157s The covariance matrix of the residuals 157s eq1 eq2 157s eq1 2682 2439 157s eq2 2439 2475 157s 157s The correlations of the residuals 157s eq1 eq2 157s eq1 1.000 0.989 157s eq2 0.989 1.000 157s 157s 157s 2SLS estimates for 'eq1' (equation 1) 157s Model Formula: consump ~ trend - 1 157s Instruments: ~income + farmPrice 157s 157s Estimate Std. Error t value Pr(>|t|) 157s trend 8.65 1.05 8.27 1e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 51.784 on 19 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 19 157s SSR: 50949.985 MSE: 2681.578 Root MSE: 51.784 157s Multiple R-Squared: -189.031 Adjusted R-Squared: -189.031 157s 157s 157s 2SLS estimates for 'eq2' (equation 2) 157s Model Formula: price ~ trend - 1 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s trend 7.318 0.929 7.88 2.1e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 49.751 on 19 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 19 157s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 157s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 157s 157s > nobs( fit2slsS3 ) 157s [1] 40 157s > fit2slsS4 <- systemfit( 157s + list( consump ~ trend - 1, price ~ trend - 1 ), "2SLS", 157s + data = Kmenta, inst = ~ farmPrice + trend + income, 157s + restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), useMatrix = useMatrix ) 157s > print( summary( fit2slsS4 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 39 93548 111736 -99 -1.03 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s eq1 20 19 46514 2448 49.5 -172.5 -172.5 157s eq2 20 19 47033 2475 49.8 -69.5 -69.5 157s 157s The covariance matrix of the residuals 157s eq1 eq2 157s eq1 2448 2439 157s eq2 2439 2475 157s 157s The correlations of the residuals 157s eq1 eq2 157s eq1 1.000 0.988 157s eq2 0.988 1.000 157s 157s 157s 2SLS estimates for 'eq1' (equation 1) 157s Model Formula: consump ~ trend - 1 157s Instruments: ~farmPrice + trend + income 157s 157s Estimate Std. Error t value Pr(>|t|) 157s trend 7.362 0.646 11.4 5.7e-14 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 49.478 on 19 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 19 157s SSR: 46514.283 MSE: 2448.12 Root MSE: 49.478 157s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 157s 157s 157s 2SLS estimates for 'eq2' (equation 2) 157s Model Formula: price ~ trend - 1 157s Instruments: ~farmPrice + trend + income 157s 157s Estimate Std. Error t value Pr(>|t|) 157s trend 7.362 0.646 11.4 5.7e-14 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 49.754 on 19 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 19 157s SSR: 47033.469 MSE: 2475.446 Root MSE: 49.754 157s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 157s 157s > nobs( fit2slsS4 ) 157s [1] 40 157s > fit2slsS5 <- systemfit( 157s + list( consump ~ 1, price ~ 1 ), "2SLS", 157s + data = Kmenta, inst = ~ farmPrice, useMatrix = useMatrix ) 157s > print( summary( fit2slsS1 ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 36 1544 179 -0.65 0.852 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s eq1 20 19 861 45.3 6.73 -2.213 -2.213 157s eq2 20 17 682 40.1 6.33 -0.022 -0.143 157s 157s The covariance matrix of the residuals 157s eq1 eq2 157s eq1 45.3 -40.5 157s eq2 -40.5 40.1 157s 157s The correlations of the residuals 157s eq1 eq2 157s eq1 1.00 -0.95 157s eq2 -0.95 1.00 157s 157s 157s 2SLS estimates for 'eq1' (equation 1) 157s Model Formula: consump ~ price - 1 157s Instruments: ~farmPrice + trend + income 157s 157s Estimate Std. Error t value Pr(>|t|) 157s price 1.006 0.015 66.9 <2e-16 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 6.734 on 19 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 19 157s SSR: 861.48 MSE: 45.341 Root MSE: 6.734 157s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 157s 157s 157s 2SLS estimates for 'eq2' (equation 2) 157s Model Formula: price ~ consump + trend 157s Instruments: ~farmPrice + trend + income 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 55.5365 46.2668 1.20 0.25 157s consump 0.4453 0.4622 0.96 0.35 157s trend -0.0426 0.2496 -0.17 0.87 157s 157s Residual standard error: 6.335 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 682.257 MSE: 40.133 Root MSE: 6.335 157s Multiple R-Squared: -0.022 Adjusted R-Squared: -0.143 157s 157s > 157s > 157s > ## **************** shorter summaries ********************** 157s > print( summary( fit2sls1, useDfSys = TRUE, residCov = FALSE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 162 4.36 0.697 0.548 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 65.7 3.87 1.97 0.755 0.726 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 157s price -0.2436 0.0965 -2.52 0.017 * 157s income 0.3140 0.0469 6.69 1.3e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.966 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 157s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 157s price 0.2401 0.0999 2.40 0.02208 * 157s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 157s trend 0.2529 0.0997 2.54 0.01605 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.458 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 157s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 157s 157s > 157s > print( summary( fit2sls1, equations = FALSE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 162 4.36 0.697 0.548 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 65.7 3.87 1.97 0.755 0.726 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.87 4.36 157s supply 4.36 6.04 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.902 157s supply 0.902 1.000 157s 157s 157s Coefficients: 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 157s demand_price -0.2436 0.0965 -2.52 0.0218 * 157s demand_income 0.3140 0.0469 6.69 3.8e-06 *** 157s supply_(Intercept) 49.5324 12.0105 4.12 0.0008 *** 157s supply_price 0.2401 0.0999 2.40 0.0288 * 157s supply_farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 157s supply_trend 0.2529 0.0997 2.54 0.0219 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s > 157s > print( summary( fit2sls1rs, residCov = FALSE, equations = FALSE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 162 2.97 0.697 0.525 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 65.7 3.87 1.97 0.755 0.726 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s 157s Coefficients: 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 94.6333 8.1158 11.66 1.6e-09 *** 157s demand_price -0.2436 0.0989 -2.46 0.02471 * 157s demand_income 0.3140 0.0481 6.53 5.2e-06 *** 157s supply_(Intercept) 49.5324 9.8463 5.03 0.00012 *** 157s supply_price 0.2401 0.0819 2.93 0.00980 ** 157s supply_farmPrice 0.2556 0.0387 6.60 6.1e-06 *** 157s supply_trend 0.2529 0.0817 3.10 0.00694 ** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s > 157s > print( summary( fit2sls2Sym, useDfSys = FALSE ), equations = FALSE ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 166 3.6 0.691 0.553 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.749 0.719 157s supply 20 16 98.2 6.13 2.48 0.634 0.565 157s 157s The covariance matrix of the residuals 157s demand supply 157s demand 3.97 4.55 157s supply 4.55 6.13 157s 157s The correlations of the residuals 157s demand supply 157s demand 1.000 0.923 157s supply 0.923 1.000 157s 157s 157s Coefficients: 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 94.2816 8.8693 10.63 6.3e-09 *** 157s demand_price -0.2247 0.1034 -2.17 0.04425 * 157s demand_income 0.2983 0.0454 6.57 4.8e-06 *** 157s supply_(Intercept) 48.1843 10.5384 4.57 0.00031 *** 157s supply_price 0.2427 0.0896 2.71 0.01551 * 157s supply_farmPrice 0.2619 0.0411 6.38 9.1e-06 *** 157s supply_trend 0.2983 0.0454 6.57 6.4e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s > 157s > print( summary( fit2sls2 ), residCov = FALSE ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 166 3.6 0.691 0.553 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.749 0.719 157s supply 20 16 98.2 6.13 2.48 0.634 0.565 157s 157s 157s 2SLS estimates for 'demand' (equation 1) 157s Model Formula: consump ~ price + income 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.2816 8.8693 10.63 2.4e-12 *** 157s price -0.2247 0.1034 -2.17 0.037 * 157s income 0.2983 0.0454 6.57 1.6e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 1.991 on 17 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 17 157s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 157s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 157s 157s 157s 2SLS estimates for 'supply' (equation 2) 157s Model Formula: consump ~ price + farmPrice + trend 157s Instruments: ~income + farmPrice + trend 157s 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 48.1843 10.5384 4.57 6.1e-05 *** 157s price 0.2427 0.0896 2.71 0.011 * 157s farmPrice 0.2619 0.0411 6.38 2.8e-07 *** 157s trend 0.2983 0.0454 6.57 1.6e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s 157s Residual standard error: 2.477 on 16 degrees of freedom 157s Number of observations: 20 Degrees of Freedom: 16 157s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 157s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 157s 157s > 157s > print( summary( fit2sls3, useDfSys = FALSE, residCov = FALSE, 157s + equations = FALSE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 166 2.45 0.691 0.526 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.749 0.719 157s supply 20 16 98.2 6.13 2.48 0.634 0.565 157s 157s 157s Coefficients: 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 94.2816 8.1771 11.53 1.8e-09 *** 157s demand_price -0.2247 0.0954 -2.36 0.03071 * 157s demand_income 0.2983 0.0419 7.13 1.7e-06 *** 157s supply_(Intercept) 48.1843 9.7159 4.96 0.00014 *** 157s supply_price 0.2427 0.0826 2.94 0.00966 ** 157s supply_farmPrice 0.2619 0.0379 6.92 3.5e-06 *** 157s supply_trend 0.2983 0.0419 7.13 2.4e-06 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s > 157s > print( summary( fit2sls4s ), equations = FALSE, residCov = FALSE ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 3.78 0.69 0.568 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s 157s Coefficients: 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 95.7059 6.3056 15.18 < 2e-16 *** 157s demand_price -0.2433 0.0684 -3.56 0.00110 ** 157s demand_income 0.3027 0.0394 7.69 5.1e-09 *** 157s supply_(Intercept) 46.5637 8.3296 5.59 2.7e-06 *** 157s supply_price 0.2567 0.0684 3.75 0.00064 *** 157s supply_farmPrice 0.2637 0.0455 5.79 1.5e-06 *** 157s supply_trend 0.3027 0.0394 7.69 5.1e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s > 157s > print( summary( fit2sls5r, equations = FALSE, residCov = FALSE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 35 166 2.57 0.69 0.54 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 66.1 3.89 1.97 0.754 0.725 157s supply 20 16 100.0 6.25 2.50 0.627 0.557 157s 157s 157s Coefficients: 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 95.7059 6.0044 15.94 < 2e-16 *** 157s demand_price -0.2433 0.0621 -3.92 0.00039 *** 157s demand_income 0.3027 0.0382 7.93 2.5e-09 *** 157s supply_(Intercept) 46.5637 7.3842 6.31 3.1e-07 *** 157s supply_price 0.2567 0.0621 4.14 0.00021 *** 157s supply_farmPrice 0.2637 0.0373 7.08 3.0e-08 *** 157s supply_trend 0.3027 0.0382 7.93 2.5e-09 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s > 157s > print( summary( fit2slsd1s ), residCov = FALSE, equations = FALSE ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 33 164 9.25 0.694 0.512 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 67.4 3.97 1.99 0.748 0.719 157s supply 20 16 96.6 6.04 2.46 0.640 0.572 157s 157s 157s Coefficients: 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 106.7894 12.4749 8.56 1.4e-07 *** 157s demand_price -0.4116 0.1622 -2.54 0.02121 * 157s demand_income 0.3617 0.0631 5.73 2.5e-05 *** 157s supply_(Intercept) 49.5324 10.8976 4.55 0.00033 *** 157s supply_price 0.2401 0.0907 2.65 0.01755 * 157s supply_farmPrice 0.2556 0.0429 5.96 2.0e-05 *** 157s supply_trend 0.2529 0.0904 2.80 0.01292 * 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s > 157s > print( summary( fit2slsd2, residCov = FALSE, equations = FALSE ) ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 165 4.89 0.693 0.56 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 64.4 3.79 1.95 0.760 0.731 157s supply 20 16 100.3 6.27 2.50 0.626 0.556 157s 157s 157s Coefficients: 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 103.5936 11.8930 8.71 3.5e-10 *** 157s demand_price -0.3449 0.1455 -2.37 0.0236 * 157s demand_income 0.3260 0.0511 6.38 2.8e-07 *** 157s supply_(Intercept) 47.3592 10.5362 4.49 7.7e-05 *** 157s supply_price 0.2443 0.0894 2.73 0.0099 ** 157s supply_farmPrice 0.2657 0.0411 6.47 2.1e-07 *** 157s supply_trend 0.3260 0.0511 6.38 2.8e-07 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s > 157s > print( summary( fit2slsd3r ), residCov = FALSE, equations = FALSE ) 157s 157s systemfit results 157s method: 2SLS 157s 157s N DF SSR detRCov OLS-R2 McElroy-R2 157s system 40 34 165 3.32 0.693 0.537 157s 157s N DF SSR MSE RMSE R2 Adj R2 157s demand 20 17 64.4 3.79 1.95 0.760 0.731 157s supply 20 16 100.3 6.27 2.50 0.626 0.556 157s 157s 157s Coefficients: 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 103.5936 10.9648 9.45 4.9e-11 *** 157s demand_price -0.3449 0.1341 -2.57 0.0147 * 157s demand_income 0.3260 0.0471 6.92 5.7e-08 *** 157s supply_(Intercept) 47.3592 9.7139 4.88 2.5e-05 *** 157s supply_price 0.2443 0.0824 2.96 0.0055 ** 157s supply_farmPrice 0.2657 0.0379 7.01 4.3e-08 *** 157s supply_trend 0.3260 0.0471 6.92 5.7e-08 *** 157s --- 157s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 157s > 157s > 157s > ## ****************** residuals ************************** 157s > print( residuals( fit2sls1 ) ) 157s demand supply 157s 1 0.843 -0.4348 157s 2 -0.698 -1.2131 157s 3 2.359 1.7090 157s 4 1.490 0.7956 157s 5 2.139 1.5942 157s 6 1.277 0.6595 157s 7 1.571 1.4346 157s 8 -3.066 -4.8724 157s 9 -1.125 -2.3975 157s 10 2.492 3.1427 157s 11 -0.108 0.0689 157s 12 -2.292 -1.3978 157s 13 -1.598 -1.1136 157s 14 -0.271 1.1684 157s 15 1.958 3.4865 157s 16 -3.430 -3.8285 157s 17 -0.313 0.6793 157s 18 -2.151 -2.7713 157s 19 1.592 2.6668 157s 20 -0.668 0.6235 157s > print( residuals( fit2sls1$eq[[ 1 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 157s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 157s 12 13 14 15 16 17 18 19 20 157s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 157s > 157s > print( residuals( fit2sls2s ) ) 157s demand supply 157s 1 0.678 -0.0135 157s 2 -0.777 -0.8544 157s 3 2.281 2.0245 157s 4 1.416 1.0692 157s 5 2.213 1.7598 157s 6 1.334 0.7923 157s 7 1.640 1.5342 157s 8 -2.994 -4.8544 157s 9 -1.072 -2.3959 157s 10 2.522 3.1637 157s 11 -0.330 0.1628 157s 12 -2.593 -1.2864 157s 13 -1.856 -1.0729 157s 14 -0.356 1.1087 157s 15 2.138 3.2597 157s 16 -3.282 -4.1265 157s 17 -0.076 0.3331 157s 18 -2.119 -3.0961 157s 19 1.690 2.3122 157s 20 -0.458 0.1799 157s > print( residuals( fit2sls2s$eq[[ 2 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 157s -0.0135 -0.8544 2.0245 1.0692 1.7598 0.7923 1.5342 -4.8544 -2.3959 3.1637 157s 11 12 13 14 15 16 17 18 19 20 157s 0.1628 -1.2864 -1.0729 1.1087 3.2597 -4.1265 0.3331 -3.0961 2.3122 0.1799 157s > 157s > print( residuals( fit2sls3 ) ) 157s demand supply 157s 1 0.678 -0.0135 157s 2 -0.777 -0.8544 157s 3 2.281 2.0245 157s 4 1.416 1.0692 157s 5 2.213 1.7598 157s 6 1.334 0.7923 157s 7 1.640 1.5342 157s 8 -2.994 -4.8544 157s 9 -1.072 -2.3959 157s 10 2.522 3.1637 157s 11 -0.330 0.1628 157s 12 -2.593 -1.2864 157s 13 -1.856 -1.0729 157s 14 -0.356 1.1087 157s 15 2.138 3.2597 157s 16 -3.282 -4.1265 157s 17 -0.076 0.3331 157s 18 -2.119 -3.0961 157s 19 1.690 2.3122 157s 20 -0.458 0.1799 157s > print( residuals( fit2sls3$eq[[ 1 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 157s 0.678 -0.777 2.281 1.416 2.213 1.334 1.640 -2.994 -1.072 2.522 -0.330 157s 12 13 14 15 16 17 18 19 20 157s -2.593 -1.856 -0.356 2.138 -3.282 -0.076 -2.119 1.690 -0.458 157s > 157s > print( residuals( fit2sls4r ) ) 157s demand supply 157s 1 0.729 0.0219 157s 2 -0.698 -0.8806 157s 3 2.349 2.0055 157s 4 1.496 1.0326 157s 5 2.165 1.7870 157s 6 1.310 0.7993 157s 7 1.635 1.5189 157s 8 -2.951 -4.9334 157s 9 -1.134 -2.3609 157s 10 2.397 3.2818 157s 11 -0.359 0.2857 157s 12 -2.524 -1.2257 157s 13 -1.745 -1.0782 157s 14 -0.349 1.1382 157s 15 2.022 3.2981 157s 16 -3.345 -4.1440 157s 17 -0.322 0.4686 157s 18 -2.075 -3.1779 157s 19 1.738 2.2072 157s 20 -0.339 -0.0444 157s > print( residuals( fit2sls4r$eq[[ 2 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 157s 0.0219 -0.8806 2.0055 1.0326 1.7870 0.7993 1.5189 -4.9334 -2.3609 3.2818 157s 11 12 13 14 15 16 17 18 19 20 157s 0.2857 -1.2257 -1.0782 1.1382 3.2981 -4.1440 0.4686 -3.1779 2.2072 -0.0444 157s > 157s > print( residuals( fit2sls5rs ) ) 157s demand supply 157s 1 0.729 0.0219 157s 2 -0.698 -0.8806 157s 3 2.349 2.0055 157s 4 1.496 1.0326 157s 5 2.165 1.7870 157s 6 1.310 0.7993 157s 7 1.635 1.5189 157s 8 -2.951 -4.9334 157s 9 -1.134 -2.3609 157s 10 2.397 3.2818 157s 11 -0.359 0.2857 157s 12 -2.524 -1.2257 157s 13 -1.745 -1.0782 157s 14 -0.349 1.1382 157s 15 2.022 3.2981 157s 16 -3.345 -4.1440 157s 17 -0.322 0.4686 157s 18 -2.075 -3.1779 157s 19 1.738 2.2072 157s 20 -0.339 -0.0444 157s > print( residuals( fit2sls5rs$eq[[ 1 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 157s 0.729 -0.698 2.349 1.496 2.165 1.310 1.635 -2.951 -1.134 2.397 -0.359 157s 12 13 14 15 16 17 18 19 20 157s -2.524 -1.745 -0.349 2.022 -3.345 -0.322 -2.075 1.738 -0.339 157s > 157s > print( residuals( fit2slsd1 ) ) 157s demand supply 157s 1 1.3775 -0.4348 157s 2 0.0125 -1.2131 157s 3 2.9728 1.7090 157s 4 2.2121 0.7956 157s 5 1.6920 1.5942 157s 6 1.0407 0.6595 157s 7 1.4768 1.4346 157s 8 -2.7583 -4.8724 157s 9 -1.6807 -2.3975 157s 10 1.4265 3.1427 157s 11 -0.2029 0.0689 157s 12 -1.5123 -1.3978 157s 13 -0.4958 -1.1136 157s 14 -0.1528 1.1684 157s 15 0.8692 3.4865 157s 16 -4.0547 -3.8285 157s 17 -2.5309 0.6793 157s 18 -1.8070 -2.7713 157s 19 1.9299 2.6668 157s 20 0.1853 0.6235 157s > print( residuals( fit2slsd1$eq[[ 2 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 157s -0.4348 -1.2131 1.7090 0.7956 1.5942 0.6595 1.4346 -4.8724 -2.3975 3.1427 157s 11 12 13 14 15 16 17 18 19 20 157s 0.0689 -1.3978 -1.1136 1.1684 3.4865 -3.8285 0.6793 -2.7713 2.6668 0.6235 157s > 157s > print( residuals( fit2slsd2r ) ) 157s demand supply 157s 1 0.996 0.2444 157s 2 -0.268 -0.6349 157s 3 2.715 2.2177 157s 4 1.936 1.2367 157s 5 1.907 1.8612 157s 6 1.184 0.8736 157s 7 1.609 1.5951 157s 8 -2.709 -4.8434 157s 9 -1.476 -2.3949 157s 10 1.705 3.1765 157s 11 -0.540 0.2202 157s 12 -2.167 -1.2182 157s 13 -1.150 -1.0480 157s 14 -0.316 1.0722 157s 15 1.395 3.1209 157s 16 -3.680 -4.3088 157s 17 -1.669 0.1212 157s 18 -1.829 -3.2948 157s 19 2.016 2.0952 157s 20 0.341 -0.0916 157s > print( residuals( fit2slsd2r$eq[[ 1 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 157s 0.996 -0.268 2.715 1.936 1.907 1.184 1.609 -2.709 -1.476 1.705 -0.540 157s 12 13 14 15 16 17 18 19 20 157s -2.167 -1.150 -0.316 1.395 -3.680 -1.669 -1.829 2.016 0.341 157s > 157s > 157s > ## *************** coefficients ********************* 157s > print( round( coef( fit2sls1s ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income supply_(Intercept) 157s 94.633 -0.244 0.314 49.532 157s supply_price supply_farmPrice supply_trend 157s 0.240 0.256 0.253 157s > print( round( coef( fit2sls1s$eq[[ 1 ]] ), digits = 6 ) ) 157s (Intercept) price income 157s 94.633 -0.244 0.314 157s > 157s > print( round( coef( fit2sls2 ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income supply_(Intercept) 157s 94.282 -0.225 0.298 48.184 157s supply_price supply_farmPrice supply_trend 157s 0.243 0.262 0.298 157s > print( round( coef( fit2sls2$eq[[ 2 ]] ), digits = 6 ) ) 157s (Intercept) price farmPrice trend 157s 48.184 0.243 0.262 0.298 157s > 157s > print( round( coef( fit2sls3 ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income supply_(Intercept) 157s 94.282 -0.225 0.298 48.184 157s supply_price supply_farmPrice supply_trend 157s 0.243 0.262 0.298 157s > print( round( coef( fit2sls3, modified.regMat = TRUE ), digits = 6 ) ) 157s C1 C2 C3 C4 C5 C6 157s 94.282 -0.225 0.298 48.184 0.243 0.262 157s > print( round( coef( fit2sls3$eq[[ 1 ]] ), digits = 6 ) ) 157s (Intercept) price income 157s 94.282 -0.225 0.298 157s > 157s > print( round( coef( fit2sls4s ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income supply_(Intercept) 157s 95.706 -0.243 0.303 46.564 157s supply_price supply_farmPrice supply_trend 157s 0.257 0.264 0.303 157s > print( round( coef( fit2sls4s$eq[[ 2 ]] ), digits = 6 ) ) 157s (Intercept) price farmPrice trend 157s 46.564 0.257 0.264 0.303 157s > 157s > print( round( coef( fit2sls5r ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income supply_(Intercept) 157s 95.706 -0.243 0.303 46.564 157s supply_price supply_farmPrice supply_trend 157s 0.257 0.264 0.303 157s > print( round( coef( fit2sls5r, modified.regMat = TRUE ), digits = 6 ) ) 157s C1 C2 C3 C4 C5 C6 157s 95.706 -0.243 0.303 46.564 0.257 0.264 157s > print( round( coef( fit2sls5r$eq[[ 2 ]] ), digits = 6 ) ) 157s (Intercept) price farmPrice trend 157s 46.564 0.257 0.264 0.303 157s > 157s > 157s > ## *************** coefficients with stats ********************* 157s > print( round( coef( summary( fit2sls1s ) ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 94.633 8.9352 10.59 0.000000 157s demand_price -0.244 0.1088 -2.24 0.038916 157s demand_income 0.314 0.0530 5.93 0.000016 157s supply_(Intercept) 49.532 10.8404 4.57 0.000315 157s supply_price 0.240 0.0902 2.66 0.017058 157s supply_farmPrice 0.256 0.0426 5.99 0.000019 157s supply_trend 0.253 0.0899 2.81 0.012528 157s > print( round( coef( summary( fit2sls1s$eq[[ 1 ]] ) ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.633 8.935 10.59 0.000000 157s price -0.244 0.109 -2.24 0.038916 157s income 0.314 0.053 5.93 0.000016 157s > 157s > print( round( coef( summary( fit2sls2, useDfSys = FALSE ) ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 94.282 8.8693 10.63 0.000000 157s demand_price -0.225 0.1034 -2.17 0.044246 157s demand_income 0.298 0.0454 6.57 0.000005 157s supply_(Intercept) 48.184 10.5384 4.57 0.000313 157s supply_price 0.243 0.0896 2.71 0.015508 157s supply_farmPrice 0.262 0.0411 6.38 0.000009 157s supply_trend 0.298 0.0454 6.57 0.000006 157s > print( round( coef( summary( fit2sls2$eq[[ 2 ]], useDfSys = FALSE ) ), 157s + digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 48.184 10.5384 4.57 0.000313 157s price 0.243 0.0896 2.71 0.015508 157s farmPrice 0.262 0.0411 6.38 0.000009 157s trend 0.298 0.0454 6.57 0.000006 157s > 157s > print( round( coef( summary( fit2sls3 ) ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 94.282 8.1771 11.53 0.000000 157s demand_price -0.225 0.0954 -2.36 0.024352 157s demand_income 0.298 0.0419 7.13 0.000000 157s supply_(Intercept) 48.184 9.7159 4.96 0.000019 157s supply_price 0.243 0.0826 2.94 0.005903 157s supply_farmPrice 0.262 0.0379 6.92 0.000000 157s supply_trend 0.298 0.0419 7.13 0.000000 157s > print( round( coef( summary( fit2sls3 ), modified.regMat = TRUE ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s C1 94.282 8.1771 11.53 0.000000 157s C2 -0.225 0.0954 -2.36 0.024352 157s C3 0.298 0.0419 7.13 0.000000 157s C4 48.184 9.7159 4.96 0.000019 157s C5 0.243 0.0826 2.94 0.005903 157s C6 0.262 0.0379 6.92 0.000000 157s > print( round( coef( summary( fit2sls3$eq[[ 1 ]] ) ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 94.282 8.1771 11.53 0.0000 157s price -0.225 0.0954 -2.36 0.0244 157s income 0.298 0.0419 7.13 0.0000 157s > 157s > print( round( coef( summary( fit2sls4s ) ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 95.706 6.3056 15.18 0.000000 157s demand_price -0.243 0.0684 -3.56 0.001104 157s demand_income 0.303 0.0394 7.69 0.000000 157s supply_(Intercept) 46.564 8.3296 5.59 0.000003 157s supply_price 0.257 0.0684 3.75 0.000635 157s supply_farmPrice 0.264 0.0455 5.79 0.000001 157s supply_trend 0.303 0.0394 7.69 0.000000 157s > print( round( coef( summary( fit2sls4s$eq[[ 2 ]] ) ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.564 8.3296 5.59 0.000003 157s price 0.257 0.0684 3.75 0.000635 157s farmPrice 0.264 0.0455 5.79 0.000001 157s trend 0.303 0.0394 7.69 0.000000 157s > 157s > print( round( coef( summary( fit2sls5r, useDfSys = FALSE ) ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s demand_(Intercept) 95.706 6.0044 15.94 0.000000 157s demand_price -0.243 0.0621 -3.92 0.001102 157s demand_income 0.303 0.0382 7.93 0.000000 157s supply_(Intercept) 46.564 7.3842 6.31 0.000010 157s supply_price 0.257 0.0621 4.14 0.000774 157s supply_farmPrice 0.264 0.0373 7.08 0.000003 157s supply_trend 0.303 0.0382 7.93 0.000001 157s > print( round( coef( summary( fit2sls5r, useDfSys = FALSE ), 157s + modified.regMat = TRUE ), digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s C1 95.706 6.0044 15.94 NA 157s C2 -0.243 0.0621 -3.92 NA 157s C3 0.303 0.0382 7.93 NA 157s C4 46.564 7.3842 6.31 NA 157s C5 0.257 0.0621 4.14 NA 157s C6 0.264 0.0373 7.08 NA 157s > print( round( coef( summary( fit2sls5r$eq[[ 2 ]], useDfSys = FALSE ) ), 157s + digits = 6 ) ) 157s Estimate Std. Error t value Pr(>|t|) 157s (Intercept) 46.564 7.3842 6.31 0.000010 157s price 0.257 0.0621 4.14 0.000774 157s farmPrice 0.264 0.0373 7.08 0.000003 157s trend 0.303 0.0382 7.93 0.000001 157s > 157s > 157s > ## *********** variance covariance matrix of the coefficients ******* 157s > print( round( vcov( fit2sls1s ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income 157s demand_(Intercept) 79.8371 -0.85694 0.06274 157s demand_price -0.8569 0.01185 -0.00336 157s demand_income 0.0627 -0.00336 0.00280 157s supply_(Intercept) 0.0000 0.00000 0.00000 157s supply_price 0.0000 0.00000 0.00000 157s supply_farmPrice 0.0000 0.00000 0.00000 157s supply_trend 0.0000 0.00000 0.00000 157s supply_(Intercept) supply_price supply_farmPrice 157s demand_(Intercept) 0.000 0.000000 0.000000 157s demand_price 0.000 0.000000 0.000000 157s demand_income 0.000 0.000000 0.000000 157s supply_(Intercept) 117.514 -0.892363 -0.263795 157s supply_price -0.892 0.008136 0.000763 157s supply_farmPrice -0.264 0.000763 0.001819 157s supply_trend -0.241 0.000472 0.001122 157s supply_trend 157s demand_(Intercept) 0.000000 157s demand_price 0.000000 157s demand_income 0.000000 157s supply_(Intercept) -0.240505 157s supply_price 0.000472 157s supply_farmPrice 0.001122 157s supply_trend 0.008090 157s > print( round( vcov( fit2sls1s$eq[[ 1 ]] ), digits = 6 ) ) 157s (Intercept) price income 157s (Intercept) 79.8371 -0.85694 0.06274 157s price -0.8569 0.01185 -0.00336 157s income 0.0627 -0.00336 0.00280 157s > 157s > print( round( vcov( fit2sls1r ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income 157s demand_(Intercept) 53.3287 -0.57241 0.04191 157s demand_price -0.5724 0.00791 -0.00225 157s demand_income 0.0419 -0.00225 0.00187 157s supply_(Intercept) 0.0000 0.00000 0.00000 157s supply_price 0.0000 0.00000 0.00000 157s supply_farmPrice 0.0000 0.00000 0.00000 157s supply_trend 0.0000 0.00000 0.00000 157s supply_(Intercept) supply_price supply_farmPrice 157s demand_(Intercept) 0.000 0.000000 0.000000 157s demand_price 0.000 0.000000 0.000000 157s demand_income 0.000 0.000000 0.000000 157s supply_(Intercept) 115.402 -0.876328 -0.259055 157s supply_price -0.876 0.007989 0.000749 157s supply_farmPrice -0.259 0.000749 0.001786 157s supply_trend -0.236 0.000463 0.001101 157s supply_trend 157s demand_(Intercept) 0.000000 157s demand_price 0.000000 157s demand_income 0.000000 157s supply_(Intercept) -0.236183 157s supply_price 0.000463 157s supply_farmPrice 0.001101 157s supply_trend 0.007945 157s > print( round( vcov( fit2sls1r$eq[[ 2 ]] ), digits = 6 ) ) 157s (Intercept) price farmPrice trend 157s (Intercept) 115.402 -0.876328 -0.259055 -0.236183 157s price -0.876 0.007989 0.000749 0.000463 157s farmPrice -0.259 0.000749 0.001786 0.001101 157s trend -0.236 0.000463 0.001101 0.007945 157s > 157s > print( round( vcov( fit2sls2 ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income 157s demand_(Intercept) 78.66379 -0.829021 0.046112 157s demand_price -0.82902 0.010698 -0.002471 157s demand_income 0.04611 -0.002471 0.002061 157s supply_(Intercept) -1.37081 0.073457 -0.061273 157s supply_price 0.00269 -0.000144 0.000120 157s supply_farmPrice 0.00639 -0.000343 0.000286 157s supply_trend 0.04611 -0.002471 0.002061 157s supply_(Intercept) supply_price supply_farmPrice 157s demand_(Intercept) -1.3708 0.002689 0.006393 157s demand_price 0.0735 -0.000144 -0.000343 157s demand_income -0.0613 0.000120 0.000286 157s supply_(Intercept) 111.0580 -0.872938 -0.236592 157s supply_price -0.8729 0.008032 0.000707 157s supply_farmPrice -0.2366 0.000707 0.001686 157s supply_trend -0.0613 0.000120 0.000286 157s supply_trend 157s demand_(Intercept) 0.046112 157s demand_price -0.002471 157s demand_income 0.002061 157s supply_(Intercept) -0.061273 157s supply_price 0.000120 157s supply_farmPrice 0.000286 157s supply_trend 0.002061 157s > print( round( vcov( fit2sls2$eq[[ 1 ]] ), digits = 6 ) ) 157s (Intercept) price income 157s (Intercept) 78.6638 -0.82902 0.04611 157s price -0.8290 0.01070 -0.00247 157s income 0.0461 -0.00247 0.00206 157s > 157s > print( round( vcov( fit2sls3 ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income 157s demand_(Intercept) 66.86423 -0.704668 0.039196 157s demand_price -0.70467 0.009094 -0.002100 157s demand_income 0.03920 -0.002100 0.001752 157s supply_(Intercept) -1.16519 0.062438 -0.052082 157s supply_price 0.00229 -0.000122 0.000102 157s supply_farmPrice 0.00543 -0.000291 0.000243 157s supply_trend 0.03920 -0.002100 0.001752 157s supply_(Intercept) supply_price supply_farmPrice 157s demand_(Intercept) -1.1652 0.002285 0.005434 157s demand_price 0.0624 -0.000122 -0.000291 157s demand_income -0.0521 0.000102 0.000243 157s supply_(Intercept) 94.3993 -0.741997 -0.201104 157s supply_price -0.7420 0.006827 0.000601 157s supply_farmPrice -0.2011 0.000601 0.001433 157s supply_trend -0.0521 0.000102 0.000243 157s supply_trend 157s demand_(Intercept) 0.039196 157s demand_price -0.002100 157s demand_income 0.001752 157s supply_(Intercept) -0.052082 157s supply_price 0.000102 157s supply_farmPrice 0.000243 157s supply_trend 0.001752 157s > print( round( vcov( fit2sls3, modified.regMat = TRUE ), digits = 6 ) ) 157s C1 C2 C3 C4 C5 C6 157s C1 66.86423 -0.704668 0.039196 -1.1652 0.002285 0.005434 157s C2 -0.70467 0.009094 -0.002100 0.0624 -0.000122 -0.000291 157s C3 0.03920 -0.002100 0.001752 -0.0521 0.000102 0.000243 157s C4 -1.16519 0.062438 -0.052082 94.3993 -0.741997 -0.201104 157s C5 0.00229 -0.000122 0.000102 -0.7420 0.006827 0.000601 157s C6 0.00543 -0.000291 0.000243 -0.2011 0.000601 0.001433 157s > print( round( vcov( fit2sls3$eq[[ 2 ]] ), digits = 6 ) ) 157s (Intercept) price farmPrice trend 157s (Intercept) 94.3993 -0.741997 -0.201104 -0.052082 157s price -0.7420 0.006827 0.000601 0.000102 157s farmPrice -0.2011 0.000601 0.001433 0.000243 157s trend -0.0521 0.000102 0.000243 0.001752 157s > 157s > print( round( vcov( fit2sls4s ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income 157s demand_(Intercept) 39.7610 -0.358128 -0.03842 157s demand_price -0.3581 0.004681 -0.00113 157s demand_income -0.0384 -0.001129 0.00155 157s supply_(Intercept) 39.6949 -0.480685 0.08595 157s supply_price -0.3581 0.004681 -0.00113 157s supply_farmPrice -0.0359 0.000252 0.00011 157s supply_trend -0.0384 -0.001129 0.00155 157s supply_(Intercept) supply_price supply_farmPrice 157s demand_(Intercept) 39.6949 -0.358128 -0.035932 157s demand_price -0.4807 0.004681 0.000252 157s demand_income 0.0859 -0.001129 0.000110 157s supply_(Intercept) 69.3817 -0.480685 -0.226588 157s supply_price -0.4807 0.004681 0.000252 157s supply_farmPrice -0.2266 0.000252 0.002072 157s supply_trend 0.0859 -0.001129 0.000110 157s supply_trend 157s demand_(Intercept) -0.03842 157s demand_price -0.00113 157s demand_income 0.00155 157s supply_(Intercept) 0.08595 157s supply_price -0.00113 157s supply_farmPrice 0.00011 157s supply_trend 0.00155 157s > print( round( vcov( fit2sls4s$eq[[ 1 ]] ), digits = 6 ) ) 157s (Intercept) price income 157s (Intercept) 39.7610 -0.35813 -0.03842 157s price -0.3581 0.00468 -0.00113 157s income -0.0384 -0.00113 0.00155 157s > 157s > print( round( vcov( fit2sls5r ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income 157s demand_(Intercept) 36.0523 -0.302514 -0.057288 157s demand_price -0.3025 0.003851 -0.000847 157s demand_income -0.0573 -0.000847 0.001456 157s supply_(Intercept) 34.1121 -0.397307 0.057684 157s supply_price -0.3025 0.003851 -0.000847 157s supply_farmPrice -0.0337 0.000218 0.000122 157s supply_trend -0.0573 -0.000847 0.001456 157s supply_(Intercept) supply_price supply_farmPrice 157s demand_(Intercept) 34.1121 -0.302514 -0.033671 157s demand_price -0.3973 0.003851 0.000218 157s demand_income 0.0577 -0.000847 0.000122 157s supply_(Intercept) 54.5267 -0.397307 -0.157170 157s supply_price -0.3973 0.003851 0.000218 157s supply_farmPrice -0.1572 0.000218 0.001388 157s supply_trend 0.0577 -0.000847 0.000122 157s supply_trend 157s demand_(Intercept) -0.057288 157s demand_price -0.000847 157s demand_income 0.001456 157s supply_(Intercept) 0.057684 157s supply_price -0.000847 157s supply_farmPrice 0.000122 157s supply_trend 0.001456 157s > print( round( vcov( fit2sls5r, modified.regMat = TRUE ), digits = 6 ) ) 157s C1 C2 C3 C4 C5 C6 157s C1 36.0523 -0.302514 -0.057288 34.1121 -0.302514 -0.033671 157s C2 -0.3025 0.003851 -0.000847 -0.3973 0.003851 0.000218 157s C3 -0.0573 -0.000847 0.001456 0.0577 -0.000847 0.000122 157s C4 34.1121 -0.397307 0.057684 54.5267 -0.397307 -0.157170 157s C5 -0.3025 0.003851 -0.000847 -0.3973 0.003851 0.000218 157s C6 -0.0337 0.000218 0.000122 -0.1572 0.000218 0.001388 157s > print( round( vcov( fit2sls5r$eq[[ 2 ]] ), digits = 6 ) ) 157s (Intercept) price farmPrice trend 157s (Intercept) 54.5267 -0.397307 -0.157170 0.057684 157s price -0.3973 0.003851 0.000218 -0.000847 157s farmPrice -0.1572 0.000218 0.001388 0.000122 157s trend 0.0577 -0.000847 0.000122 0.001456 157s > 157s > print( round( vcov( fit2slsd1 ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income 157s demand_(Intercept) 124.179 -1.51767 0.28519 157s demand_price -1.518 0.02098 -0.00595 157s demand_income 0.285 -0.00595 0.00318 157s supply_(Intercept) 0.000 0.00000 0.00000 157s supply_price 0.000 0.00000 0.00000 157s supply_farmPrice 0.000 0.00000 0.00000 157s supply_trend 0.000 0.00000 0.00000 157s supply_(Intercept) supply_price supply_farmPrice 157s demand_(Intercept) 0.000 0.000000 0.000000 157s demand_price 0.000 0.000000 0.000000 157s demand_income 0.000 0.000000 0.000000 157s supply_(Intercept) 144.253 -1.095410 -0.323818 157s supply_price -1.095 0.009987 0.000936 157s supply_farmPrice -0.324 0.000936 0.002233 157s supply_trend -0.295 0.000579 0.001377 157s supply_trend 157s demand_(Intercept) 0.000000 157s demand_price 0.000000 157s demand_income 0.000000 157s supply_(Intercept) -0.295229 157s supply_price 0.000579 157s supply_farmPrice 0.001377 157s supply_trend 0.009931 157s > print( round( vcov( fit2slsd1$eq[[ 1 ]] ), digits = 6 ) ) 157s (Intercept) price income 157s (Intercept) 124.179 -1.51767 0.28519 157s price -1.518 0.02098 -0.00595 157s income 0.285 -0.00595 0.00318 157s > 157s > print( round( vcov( fit2slsd2rs ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income 157s demand_(Intercept) 95.9017 -1.129212 0.176368 157s demand_price -1.1292 0.014881 -0.003682 157s demand_income 0.1764 -0.003682 0.001968 157s supply_(Intercept) -5.2430 0.109460 -0.058492 157s supply_price 0.0103 -0.000215 0.000115 157s supply_farmPrice 0.0245 -0.000510 0.000273 157s supply_trend 0.1764 -0.003682 0.001968 157s supply_(Intercept) supply_price supply_farmPrice 157s demand_(Intercept) -5.2430 0.010284 0.024451 157s demand_price 0.1095 -0.000215 -0.000510 157s demand_income -0.0585 0.000115 0.000273 157s supply_(Intercept) 114.2555 -0.898881 -0.243056 157s supply_price -0.8989 0.008273 0.000727 157s supply_farmPrice -0.2431 0.000727 0.001733 157s supply_trend -0.0585 0.000115 0.000273 157s supply_trend 157s demand_(Intercept) 0.176368 157s demand_price -0.003682 157s demand_income 0.001968 157s supply_(Intercept) -0.058492 157s supply_price 0.000115 157s supply_farmPrice 0.000273 157s supply_trend 0.001968 157s > print( round( vcov( fit2slsd2rs$eq[[ 2 ]] ), digits = 6 ) ) 157s (Intercept) price farmPrice trend 157s (Intercept) 114.2555 -0.898881 -0.243056 -0.058492 157s price -0.8989 0.008273 0.000727 0.000115 157s farmPrice -0.2431 0.000727 0.001733 0.000273 157s trend -0.0585 0.000115 0.000273 0.001968 157s > 157s > print( round( vcov( fit2slsd3 ), digits = 6 ) ) 157s demand_(Intercept) demand_price demand_income 157s demand_(Intercept) 141.4425 -1.640068 0.234151 157s demand_price -1.6401 0.021165 -0.004888 157s demand_income 0.2342 -0.004888 0.002612 157s supply_(Intercept) -6.9607 0.145321 -0.077656 157s supply_price 0.0137 -0.000285 0.000152 157s supply_farmPrice 0.0325 -0.000678 0.000362 157s supply_trend 0.2342 -0.004888 0.002612 157s supply_(Intercept) supply_price supply_farmPrice 157s demand_(Intercept) -6.9607 0.013653 0.032462 157s demand_price 0.1453 -0.000285 -0.000678 157s demand_income -0.0777 0.000152 0.000362 157s supply_(Intercept) 111.0123 -0.869653 -0.237751 157s supply_price -0.8697 0.007995 0.000708 157s supply_farmPrice -0.2378 0.000708 0.001688 157s supply_trend -0.0777 0.000152 0.000362 157s supply_trend 157s demand_(Intercept) 0.234151 157s demand_price -0.004888 157s demand_income 0.002612 157s supply_(Intercept) -0.077656 157s supply_price 0.000152 157s supply_farmPrice 0.000362 157s supply_trend 0.002612 157s > print( round( vcov( fit2slsd3, modified.regMat = TRUE ), digits = 6 ) ) 157s C1 C2 C3 C4 C5 C6 157s C1 141.4425 -1.640068 0.234151 -6.9607 0.013653 0.032462 157s C2 -1.6401 0.021165 -0.004888 0.1453 -0.000285 -0.000678 157s C3 0.2342 -0.004888 0.002612 -0.0777 0.000152 0.000362 157s C4 -6.9607 0.145321 -0.077656 111.0123 -0.869653 -0.237751 157s C5 0.0137 -0.000285 0.000152 -0.8697 0.007995 0.000708 157s C6 0.0325 -0.000678 0.000362 -0.2378 0.000708 0.001688 157s > print( round( vcov( fit2slsd3$eq[[ 1 ]] ), digits = 6 ) ) 157s (Intercept) price income 157s (Intercept) 141.442 -1.64007 0.23415 157s price -1.640 0.02116 -0.00489 157s income 0.234 -0.00489 0.00261 157s > 157s > 157s > ## *********** confidence intervals of coefficients ************* 157s > print( confint( fit2sls1 ) ) 157s 2.5 % 97.5 % 157s demand_(Intercept) 77.922 111.345 157s demand_price -0.447 -0.040 157s demand_income 0.215 0.413 157s supply_(Intercept) 24.071 74.994 157s supply_price 0.028 0.452 157s supply_farmPrice 0.155 0.356 157s supply_trend 0.042 0.464 157s > print( confint( fit2sls1$eq[[ 1 ]], level = 0.9 ) ) 157s 5 % 95 % 157s (Intercept) 80.854 108.412 157s price -0.411 -0.076 157s income 0.232 0.396 157s > 157s > print( confint( fit2sls2s, level = 0.9 ) ) 157s 5 % 95 % 157s demand_(Intercept) 78.005 110.558 157s demand_price -0.417 -0.032 157s demand_income 0.211 0.386 157s supply_(Intercept) 24.204 72.165 157s supply_price 0.038 0.447 157s supply_farmPrice 0.169 0.355 157s supply_trend 0.211 0.386 157s > print( confint( fit2sls2s$eq[[ 2 ]], level = 0.99 ) ) 157s 0.5 % 99.5 % 157s (Intercept) 15.989 80.380 157s price -0.032 0.517 157s farmPrice 0.137 0.387 157s trend 0.181 0.416 157s > 157s > print( confint( fit2sls3, level = 0.99, useDfSys = TRUE ) ) 157s 0.5 % 99.5 % 157s demand_(Intercept) 77.664 110.899 157s demand_price -0.419 -0.031 157s demand_income 0.213 0.383 157s supply_(Intercept) 28.439 67.929 157s supply_price 0.075 0.411 157s supply_farmPrice 0.185 0.339 157s supply_trend 0.213 0.383 157s > print( confint( fit2sls3$eq[[ 1 ]], level = 0.5, useDfSys = TRUE ) ) 157s 25 % 75 % 157s (Intercept) 88.71 99.857 157s price -0.29 -0.160 157s income 0.27 0.327 157s > 157s > print( confint( fit2sls4r, level = 0.5 ) ) 157s 25 % 75 % 157s demand_(Intercept) 83.516 107.895 157s demand_price -0.369 -0.117 157s demand_income 0.225 0.380 157s supply_(Intercept) 31.573 61.554 157s supply_price 0.131 0.383 157s supply_farmPrice 0.188 0.339 157s supply_trend 0.225 0.380 157s > print( confint( fit2sls4r$eq[[ 2 ]], level = 0.25 ) ) 157s 37.5 % 62.5 % 157s (Intercept) 44.192 48.935 157s price 0.237 0.277 157s farmPrice 0.252 0.276 157s trend 0.290 0.315 157s > 157s > print( confint( fit2sls5rs, level = 0.25 ) ) 157s 37.5 % 62.5 % 157s demand_(Intercept) 84.017 107.395 157s demand_price -0.369 -0.117 157s demand_income 0.230 0.376 157s supply_(Intercept) 31.265 61.863 157s supply_price 0.131 0.383 157s supply_farmPrice 0.181 0.346 157s supply_trend 0.230 0.376 157s > print( confint( fit2sls5rs$eq[[ 1 ]], level = 0.975 ) ) 157s 1.3 % 98.8 % 157s (Intercept) 82.221 109.191 157s price -0.389 -0.098 157s income 0.218 0.387 157s > 157s > print( confint( fit2slsd1, level = 0.975, useDfSys = TRUE ) ) 157s 1.3 % 98.8 % 157s demand_(Intercept) 84.118 129.461 157s demand_price -0.706 -0.117 157s demand_income 0.247 0.476 157s supply_(Intercept) 25.097 73.968 157s supply_price 0.037 0.443 157s supply_farmPrice 0.159 0.352 157s supply_trend 0.050 0.456 157s > print( confint( fit2slsd1$eq[[ 2 ]], level = 0.999, useDfSys = TRUE ) ) 157s 0.1 % 100 % 157s (Intercept) 6.163 92.901 157s price -0.121 0.601 157s farmPrice 0.085 0.426 157s trend -0.107 0.613 157s > 157s > print( confint( fit2slsd2r, level = 0.999 ) ) 157s 0.1 % 100 % 157s demand_(Intercept) 81.311 125.877 157s demand_price -0.617 -0.072 157s demand_income 0.230 0.422 157s supply_(Intercept) 27.618 67.100 157s supply_price 0.077 0.412 157s supply_farmPrice 0.189 0.343 157s supply_trend 0.230 0.422 157s > print( confint( fit2slsd2r$eq[[ 1 ]] ) ) 157s 2.5 % 97.5 % 157s (Intercept) 81.311 125.877 157s price -0.617 -0.072 157s income 0.230 0.422 157s > 157s > 157s > ## *********** fitted values ************* 157s > print( fitted( fit2sls1, se.fit = TRUE, interval = "prediction" ) ) 157s demand supply 157s 1 97.6 98.9 157s 2 99.9 100.4 157s 3 99.8 100.5 157s 4 100.0 100.7 157s 5 102.1 102.6 157s 6 102.0 102.6 157s 7 102.4 102.6 157s 8 103.0 104.8 157s 9 101.5 102.7 157s 10 100.3 99.7 157s 11 95.5 95.4 157s 12 94.7 93.8 157s 13 96.1 95.6 157s 14 99.0 97.6 157s 15 103.8 102.3 157s 16 103.7 104.1 157s 17 103.8 102.8 157s 18 102.1 102.7 157s 19 103.6 102.6 157s 20 106.9 105.6 157s > print( fitted( fit2sls1$eq[[ 1 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 12 13 157s 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 157s 14 15 16 17 18 19 20 157s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 157s > 157s > print( fitted( fit2sls2s ) ) 157s demand supply 157s 1 97.8 98.5 157s 2 100.0 100.0 157s 3 99.9 100.1 157s 4 100.1 100.4 157s 5 102.0 102.5 157s 6 101.9 102.5 157s 7 102.4 102.5 157s 8 102.9 104.8 157s 9 101.4 102.7 157s 10 100.3 99.7 157s 11 95.8 95.3 157s 12 95.0 93.7 157s 13 96.4 95.6 157s 14 99.1 97.6 157s 15 103.7 102.5 157s 16 103.5 104.4 157s 17 103.6 103.2 157s 18 102.0 103.0 157s 19 103.5 102.9 157s 20 106.7 106.1 157s > print( fitted( fit2sls2s$eq[[ 2 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 12 13 157s 98.5 100.0 100.1 100.4 102.5 102.5 102.5 104.8 102.7 99.7 95.3 93.7 95.6 157s 14 15 16 17 18 19 20 157s 97.6 102.5 104.4 103.2 103.0 102.9 106.1 157s > 157s > print( fitted( fit2sls3 ) ) 157s demand supply 157s 1 97.8 98.5 157s 2 100.0 100.0 157s 3 99.9 100.1 157s 4 100.1 100.4 157s 5 102.0 102.5 157s 6 101.9 102.5 157s 7 102.4 102.5 157s 8 102.9 104.8 157s 9 101.4 102.7 157s 10 100.3 99.7 157s 11 95.8 95.3 157s 12 95.0 93.7 157s 13 96.4 95.6 157s 14 99.1 97.6 157s 15 103.7 102.5 157s 16 103.5 104.4 157s 17 103.6 103.2 157s 18 102.0 103.0 157s 19 103.5 102.9 157s 20 106.7 106.1 157s > print( fitted( fit2sls3$eq[[ 1 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 12 13 157s 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 157s 14 15 16 17 18 19 20 157s 99.1 103.7 103.5 103.6 102.0 103.5 106.7 157s > 157s > print( fitted( fit2sls4r ) ) 157s demand supply 157s 1 97.8 98.5 157s 2 99.9 100.1 157s 3 99.8 100.2 157s 4 100.0 100.5 157s 5 102.1 102.5 157s 6 101.9 102.4 157s 7 102.4 102.5 157s 8 102.9 104.8 157s 9 101.5 102.7 157s 10 100.4 99.5 157s 11 95.8 95.1 157s 12 94.9 93.6 157s 13 96.3 95.6 157s 14 99.1 97.6 157s 15 103.8 102.5 157s 16 103.6 104.4 157s 17 103.8 103.1 157s 18 102.0 103.1 157s 19 103.5 103.0 157s 20 106.6 106.3 157s > print( fitted( fit2sls4r$eq[[ 2 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 12 13 157s 98.5 100.1 100.2 100.5 102.5 102.4 102.5 104.8 102.7 99.5 95.1 93.6 95.6 157s 14 15 16 17 18 19 20 157s 97.6 102.5 104.4 103.1 103.1 103.0 106.3 157s > 157s > print( fitted( fit2sls5rs ) ) 157s demand supply 157s 1 97.8 98.5 157s 2 99.9 100.1 157s 3 99.8 100.2 157s 4 100.0 100.5 157s 5 102.1 102.5 157s 6 101.9 102.4 157s 7 102.4 102.5 157s 8 102.9 104.8 157s 9 101.5 102.7 157s 10 100.4 99.5 157s 11 95.8 95.1 157s 12 94.9 93.6 157s 13 96.3 95.6 157s 14 99.1 97.6 157s 15 103.8 102.5 157s 16 103.6 104.4 157s 17 103.8 103.1 157s 18 102.0 103.1 157s 19 103.5 103.0 157s 20 106.6 106.3 157s > print( fitted( fit2sls5rs$eq[[ 1 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 12 13 157s 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 157s 14 15 16 17 18 19 20 157s 99.1 103.8 103.6 103.8 102.0 103.5 106.6 157s > 157s > print( fitted( fit2slsd1 ) ) 157s demand supply 157s 1 97.1 98.9 157s 2 99.2 100.4 157s 3 99.2 100.5 157s 4 99.3 100.7 157s 5 102.5 102.6 157s 6 102.2 102.6 157s 7 102.5 102.6 157s 8 102.7 104.8 157s 9 102.0 102.7 157s 10 101.4 99.7 157s 11 95.6 95.4 157s 12 93.9 93.8 157s 13 95.0 95.6 157s 14 98.9 97.6 157s 15 104.9 102.3 157s 16 104.3 104.1 157s 17 106.1 102.8 157s 18 101.7 102.7 157s 19 103.3 102.6 157s 20 106.0 105.6 157s > print( fitted( fit2slsd1$eq[[ 2 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 12 13 157s 98.9 100.4 100.5 100.7 102.6 102.6 102.6 104.8 102.7 99.7 95.4 93.8 95.6 157s 14 15 16 17 18 19 20 157s 97.6 102.3 104.1 102.8 102.7 102.6 105.6 157s > 157s > print( fitted( fit2slsd2r ) ) 157s demand supply 157s 1 97.5 98.2 157s 2 99.5 99.8 157s 3 99.4 99.9 157s 4 99.6 100.3 157s 5 102.3 102.4 157s 6 102.1 102.4 157s 7 102.4 102.4 157s 8 102.6 104.7 157s 9 101.8 102.7 157s 10 101.1 99.6 157s 11 96.0 95.2 157s 12 94.6 93.6 157s 13 95.7 95.6 157s 14 99.1 97.7 157s 15 104.4 102.7 157s 16 103.9 104.5 157s 17 105.2 103.4 157s 18 101.8 103.2 157s 19 103.2 103.1 157s 20 105.9 106.3 157s > print( fitted( fit2slsd2r$eq[[ 1 ]] ) ) 157s 1 2 3 4 5 6 7 8 9 10 11 12 13 157s 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 157s 14 15 16 17 18 19 20 157s 99.1 104.4 103.9 105.2 101.8 103.2 105.9 157s > 157s > 157s > ## *********** predicted values ************* 157s > predictData <- Kmenta 157s > predictData$consump <- NULL 157s > predictData$price <- Kmenta$price * 0.9 157s > predictData$income <- Kmenta$income * 1.1 157s > 157s > print( predict( fit2sls1, se.fit = TRUE, interval = "prediction" ) ) 157s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 157s 1 97.6 0.661 93.3 102.0 98.9 1.079 157s 2 99.9 0.600 95.5 104.2 100.4 1.064 157s 3 99.8 0.564 95.5 104.1 100.5 0.962 157s 4 100.0 0.605 95.7 104.4 100.7 0.938 157s 5 102.1 0.516 97.8 106.4 102.6 0.914 157s 6 102.0 0.474 97.7 106.2 102.6 0.808 157s 7 102.4 0.493 98.1 106.7 102.6 0.736 157s 8 103.0 0.615 98.6 107.3 104.8 0.994 157s 9 101.5 0.544 97.2 105.8 102.7 0.808 157s 10 100.3 0.822 95.8 104.8 99.7 1.023 157s 11 95.5 0.963 90.9 100.2 95.4 1.228 157s 12 94.7 1.006 90.1 99.4 93.8 1.428 157s 13 96.1 0.915 91.6 100.7 95.6 1.272 157s 14 99.0 0.518 94.7 103.3 97.6 0.917 157s 15 103.8 0.793 99.4 108.3 102.3 0.899 157s 16 103.7 0.636 99.3 108.0 104.1 0.936 157s 17 103.8 1.348 98.8 108.9 102.8 1.665 157s 18 102.1 0.549 97.8 106.4 102.7 0.988 157s 19 103.6 0.695 99.2 108.0 102.6 1.129 157s 20 106.9 1.306 101.9 111.9 105.6 1.733 157s supply.lwr supply.upr 157s 1 93.2 104.6 157s 2 94.7 106.1 157s 3 94.9 106.0 157s 4 95.1 106.3 157s 5 97.1 108.2 157s 6 97.1 108.1 157s 7 97.1 108.0 157s 8 99.2 110.4 157s 9 97.3 108.2 157s 10 94.0 105.3 157s 11 89.5 101.2 157s 12 87.8 99.8 157s 13 89.8 101.5 157s 14 92.0 103.1 157s 15 96.8 107.9 157s 16 98.5 109.6 157s 17 96.5 109.1 157s 18 97.1 108.3 157s 19 96.8 108.3 157s 20 99.2 112.0 157s > print( predict( fit2sls1$eq[[ 1 ]], se.fit = TRUE, interval = "prediction" ) ) 157s fit se.fit lwr upr 157s 1 97.6 0.661 93.3 102.0 157s 2 99.9 0.600 95.5 104.2 157s 3 99.8 0.564 95.5 104.1 157s 4 100.0 0.605 95.7 104.4 157s 5 102.1 0.516 97.8 106.4 157s 6 102.0 0.474 97.7 106.2 157s 7 102.4 0.493 98.1 106.7 157s 8 103.0 0.615 98.6 107.3 157s 9 101.5 0.544 97.2 105.8 157s 10 100.3 0.822 95.8 104.8 157s 11 95.5 0.963 90.9 100.2 157s 12 94.7 1.006 90.1 99.4 157s 13 96.1 0.915 91.6 100.7 157s 14 99.0 0.518 94.7 103.3 157s 15 103.8 0.793 99.4 108.3 157s 16 103.7 0.636 99.3 108.0 157s 17 103.8 1.348 98.8 108.9 157s 18 102.1 0.549 97.8 106.4 157s 19 103.6 0.695 99.2 108.0 157s 20 106.9 1.306 101.9 111.9 157s > 157s > print( predict( fit2sls2s, se.pred = TRUE, interval = "confidence", 157s + level = 0.999, newdata = predictData ) ) 157s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 157s 1 102.7 2.23 99.1 106 96.1 2.75 157s 2 105.2 2.23 101.6 109 97.5 2.64 157s 3 105.1 2.24 101.4 109 97.6 2.65 157s 4 105.4 2.23 101.8 109 97.9 2.62 157s 5 107.2 2.52 101.7 113 100.1 2.83 157s 6 107.1 2.46 101.9 112 100.0 2.77 157s 7 107.7 2.45 102.6 113 100.0 2.70 157s 8 108.5 2.41 103.6 113 102.2 2.65 157s 9 106.5 2.53 100.9 112 100.4 2.87 157s 10 105.0 2.66 98.7 111 97.4 3.10 157s 11 100.1 2.42 95.1 105 93.0 3.17 157s 12 99.5 2.22 96.0 103 91.3 3.14 157s 13 101.2 2.13 98.5 104 93.1 2.95 157s 14 104.0 2.32 99.7 108 95.3 2.91 157s 15 108.9 2.74 102.1 116 100.2 2.92 157s 16 108.9 2.62 102.7 115 102.0 2.79 157s 17 108.4 3.09 99.9 117 101.1 3.37 157s 18 107.5 2.36 102.9 112 100.5 2.65 157s 19 109.2 2.44 104.1 114 100.3 2.64 157s 20 113.0 2.67 106.6 119 103.3 2.58 157s supply.lwr supply.upr 157s 1 91.8 100.4 157s 2 94.3 100.8 157s 3 94.2 101.0 157s 4 94.8 101.0 157s 5 95.2 105.0 157s 6 95.6 104.5 157s 7 96.1 103.9 157s 8 98.9 105.6 157s 9 95.2 105.6 157s 10 90.7 104.1 157s 11 85.9 100.2 157s 12 84.4 98.3 157s 13 87.3 98.9 157s 14 89.7 100.8 157s 15 94.7 105.8 157s 16 97.3 106.6 157s 17 92.9 109.3 157s 18 97.1 103.9 157s 19 97.1 103.6 157s 20 100.7 105.9 157s > print( predict( fit2sls2s$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 157s + level = 0.999, newdata = predictData ) ) 157s fit se.pred lwr upr 157s 1 96.1 2.75 91.8 100.4 157s 2 97.5 2.64 94.3 100.8 157s 3 97.6 2.65 94.2 101.0 157s 4 97.9 2.62 94.8 101.0 157s 5 100.1 2.83 95.2 105.0 157s 6 100.0 2.77 95.6 104.5 157s 7 100.0 2.70 96.1 103.9 157s 8 102.2 2.65 98.9 105.6 157s 9 100.4 2.87 95.2 105.6 157s 10 97.4 3.10 90.7 104.1 157s 11 93.0 3.17 85.9 100.2 157s 12 91.3 3.14 84.4 98.3 157s 13 93.1 2.95 87.3 98.9 157s 14 95.3 2.91 89.7 100.8 157s 15 100.2 2.92 94.7 105.8 157s 16 102.0 2.79 97.3 106.6 157s 17 101.1 3.37 92.9 109.3 157s 18 100.5 2.65 97.1 103.9 157s 19 100.3 2.64 97.1 103.6 157s 20 103.3 2.58 100.7 105.9 157s > 157s > print( predict( fit2sls3, se.pred = TRUE, interval = "prediction", 157s + level = 0.975, useDfSys = TRUE ) ) 157s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 157s 1 97.8 2.09 92.9 103 98.5 2.55 157s 2 100.0 2.08 95.1 105 100.0 2.57 157s 3 99.9 2.07 95.0 105 100.1 2.55 157s 4 100.1 2.08 95.2 105 100.4 2.56 157s 5 102.0 2.06 97.2 107 102.5 2.58 157s 6 101.9 2.05 97.1 107 102.5 2.56 157s 7 102.4 2.05 97.5 107 102.5 2.55 157s 8 102.9 2.09 98.0 108 104.8 2.61 157s 9 101.4 2.07 96.6 106 102.7 2.57 157s 10 100.3 2.17 95.2 105 99.7 2.62 157s 11 95.8 2.20 90.6 101 95.3 2.67 157s 12 95.0 2.20 89.9 100 93.7 2.74 157s 13 96.4 2.17 91.3 101 95.6 2.69 157s 14 99.1 2.06 94.3 104 97.6 2.59 157s 15 103.7 2.14 98.7 109 102.5 2.56 157s 16 103.5 2.08 98.6 108 104.4 2.55 157s 17 103.6 2.40 98.0 109 103.2 2.78 157s 18 102.0 2.07 97.2 107 103.0 2.56 157s 19 103.5 2.11 98.6 108 102.9 2.59 157s 20 106.7 2.38 101.1 112 106.1 2.78 157s supply.lwr supply.upr 157s 1 92.5 104 157s 2 94.0 106 157s 3 94.1 106 157s 4 94.4 106 157s 5 96.4 109 157s 6 96.5 108 157s 7 96.5 108 157s 8 98.6 111 157s 9 96.7 109 157s 10 93.5 106 157s 11 89.0 102 157s 12 87.3 100 157s 13 89.3 102 157s 14 91.6 104 157s 15 96.5 109 157s 16 98.4 110 157s 17 96.7 110 157s 18 97.0 109 157s 19 96.8 109 157s 20 99.5 113 157s > print( predict( fit2sls3$eq[[ 1 ]], se.pred = TRUE, interval = "prediction", 157s + level = 0.975, useDfSys = TRUE ) ) 157s fit se.pred lwr upr 157s 1 97.8 2.09 92.9 103 157s 2 100.0 2.08 95.1 105 157s 3 99.9 2.07 95.0 105 157s 4 100.1 2.08 95.2 105 157s 5 102.0 2.06 97.2 107 157s 6 101.9 2.05 97.1 107 157s 7 102.4 2.05 97.5 107 157s 8 102.9 2.09 98.0 108 157s 9 101.4 2.07 96.6 106 157s 10 100.3 2.17 95.2 105 157s 11 95.8 2.20 90.6 101 157s 12 95.0 2.20 89.9 100 157s 13 96.4 2.17 91.3 101 157s 14 99.1 2.06 94.3 104 157s 15 103.7 2.14 98.7 109 157s 16 103.5 2.08 98.6 108 157s 17 103.6 2.40 98.0 109 157s 18 102.0 2.07 97.2 107 157s 19 103.5 2.11 98.6 108 157s 20 106.7 2.38 101.1 112 157s > 157s > print( predict( fit2sls4r, se.fit = TRUE, interval = "confidence", 157s + level = 0.25 ) ) 157s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 157s 1 97.8 0.602 97.6 97.9 98.5 0.586 157s 2 99.9 0.526 99.7 100.1 100.1 0.672 157s 3 99.8 0.508 99.7 100.0 100.2 0.621 157s 4 100.0 0.530 99.8 100.2 100.5 0.632 157s 5 102.1 0.488 101.9 102.2 102.5 0.704 157s 6 101.9 0.474 101.8 102.1 102.4 0.636 157s 7 102.4 0.498 102.2 102.5 102.5 0.587 157s 8 102.9 0.604 102.7 103.0 104.8 0.764 157s 9 101.5 0.502 101.3 101.6 102.7 0.656 157s 10 100.4 0.696 100.2 100.6 99.5 0.710 157s 11 95.8 0.928 95.5 96.1 95.1 0.885 157s 12 94.9 0.889 94.7 95.2 93.6 1.146 157s 13 96.3 0.739 96.0 96.5 95.6 1.052 157s 14 99.1 0.519 98.9 99.3 97.6 0.746 157s 15 103.8 0.626 103.6 104.0 102.5 0.637 157s 16 103.6 0.566 103.4 103.8 104.4 0.615 157s 17 103.8 0.942 103.5 104.1 103.1 1.153 157s 18 102.0 0.540 101.8 102.2 103.1 0.556 157s 19 103.5 0.677 103.3 103.7 103.0 0.631 157s 20 106.6 1.226 106.2 107.0 106.3 0.900 157s supply.lwr supply.upr 157s 1 98.3 98.7 157s 2 99.9 100.3 157s 3 100.0 100.4 157s 4 100.3 100.7 157s 5 102.2 102.7 157s 6 102.2 102.6 157s 7 102.3 102.7 157s 8 104.6 105.1 157s 9 102.5 102.9 157s 10 99.3 99.8 157s 11 94.9 95.4 157s 12 93.3 94.0 157s 13 95.3 96.0 157s 14 97.4 97.9 157s 15 102.3 102.7 157s 16 104.2 104.6 157s 17 102.7 103.4 157s 18 102.9 103.3 157s 19 102.8 103.2 157s 20 106.0 106.6 157s > print( predict( fit2sls4r$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 157s + level = 0.25 ) ) 157s fit se.fit lwr upr 157s 1 98.5 0.586 98.3 98.7 157s 2 100.1 0.672 99.9 100.3 157s 3 100.2 0.621 100.0 100.4 157s 4 100.5 0.632 100.3 100.7 157s 5 102.5 0.704 102.2 102.7 157s 6 102.4 0.636 102.2 102.6 157s 7 102.5 0.587 102.3 102.7 157s 8 104.8 0.764 104.6 105.1 157s 9 102.7 0.656 102.5 102.9 157s 10 99.5 0.710 99.3 99.8 157s 11 95.1 0.885 94.9 95.4 157s 12 93.6 1.146 93.3 94.0 157s 13 95.6 1.052 95.3 96.0 157s 14 97.6 0.746 97.4 97.9 157s 15 102.5 0.637 102.3 102.7 157s 16 104.4 0.615 104.2 104.6 157s 17 103.1 1.153 102.7 103.4 157s 18 103.1 0.556 102.9 103.3 157s 19 103.0 0.631 102.8 103.2 157s 20 106.3 0.900 106.0 106.6 157s > 157s > print( predict( fit2sls5rs, se.fit = TRUE, se.pred = TRUE, 157s + interval = "prediction", level = 0.5, newdata = predictData ) ) 157s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 157s 1 102.8 0.713 2.10 101.4 104 95.9 157s 2 105.4 0.742 2.11 103.9 107 97.4 157s 3 105.3 0.751 2.11 103.8 107 97.5 157s 4 105.5 0.749 2.11 104.1 107 97.8 157s 5 107.5 1.080 2.25 105.9 109 99.9 157s 6 107.4 1.031 2.23 105.9 109 99.9 157s 7 107.9 1.040 2.23 106.4 109 99.9 157s 8 108.7 1.044 2.23 107.1 110 102.1 157s 9 106.8 1.073 2.24 105.2 108 100.2 157s 10 105.3 1.188 2.30 103.8 107 97.2 157s 11 100.3 1.013 2.22 98.8 102 92.8 157s 12 99.7 0.770 2.12 98.2 101 91.1 157s 13 101.3 0.584 2.06 99.9 103 93.0 157s 14 104.3 0.833 2.14 102.8 106 95.1 157s 15 109.2 1.310 2.37 107.6 111 100.1 157s 16 109.1 1.214 2.32 107.6 111 101.8 157s 17 108.9 1.582 2.53 107.1 111 100.8 157s 18 107.7 0.958 2.19 106.2 109 100.4 157s 19 109.4 1.111 2.26 107.9 111 100.3 157s 20 113.2 1.529 2.50 111.5 115 103.4 157s supply.se.fit supply.se.pred supply.lwr supply.upr 157s 1 0.746 2.61 94.1 97.7 157s 2 0.628 2.58 95.6 99.1 157s 3 0.642 2.58 95.7 99.3 157s 4 0.607 2.57 96.0 99.5 157s 5 0.978 2.68 98.1 101.8 157s 6 0.881 2.65 98.1 101.7 157s 7 0.786 2.62 98.1 101.7 157s 8 0.780 2.62 100.4 103.9 157s 9 1.031 2.70 98.4 102.1 157s 10 1.212 2.78 95.3 99.1 157s 11 1.339 2.84 90.8 94.7 157s 12 1.478 2.90 89.1 93.1 157s 13 1.292 2.81 91.1 94.9 157s 14 1.123 2.74 93.2 97.0 157s 15 1.105 2.73 98.2 101.9 157s 16 0.996 2.69 100.0 103.7 157s 17 1.636 2.99 98.8 102.9 157s 18 0.777 2.62 98.7 102.2 157s 19 0.775 2.62 98.5 102.1 157s 20 0.600 2.57 101.6 105.1 157s > print( predict( fit2sls5rs$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 157s + interval = "prediction", level = 0.5, newdata = predictData ) ) 157s fit se.fit se.pred lwr upr 157s 1 102.8 0.713 2.10 101.4 104 157s 2 105.4 0.742 2.11 103.9 107 157s 3 105.3 0.751 2.11 103.8 107 157s 4 105.5 0.749 2.11 104.1 107 157s 5 107.5 1.080 2.25 105.9 109 157s 6 107.4 1.031 2.23 105.9 109 157s 7 107.9 1.040 2.23 106.4 109 157s 8 108.7 1.044 2.23 107.1 110 157s 9 106.8 1.073 2.24 105.2 108 157s 10 105.3 1.188 2.30 103.8 107 157s 11 100.3 1.013 2.22 98.8 102 157s 12 99.7 0.770 2.12 98.2 101 157s 13 101.3 0.584 2.06 99.9 103 157s 14 104.3 0.833 2.14 102.8 106 157s 15 109.2 1.310 2.37 107.6 111 157s 16 109.1 1.214 2.32 107.6 111 157s 17 108.9 1.582 2.53 107.1 111 157s 18 107.7 0.958 2.19 106.2 109 157s 19 109.4 1.111 2.26 107.9 111 157s 20 113.2 1.529 2.50 111.5 115 157s > 157s > print( predict( fit2slsd1, se.fit = TRUE, se.pred = TRUE, 157s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 157s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 157s 1 97.1 0.751 2.13 95.1 99.2 98.9 157s 2 99.2 0.757 2.13 97.1 101.2 100.4 157s 3 99.2 0.692 2.11 97.3 101.1 100.5 157s 4 99.3 0.766 2.13 97.2 101.4 100.7 157s 5 102.5 0.595 2.08 100.9 104.2 102.6 157s 6 102.2 0.503 2.05 100.8 103.6 102.6 157s 7 102.5 0.503 2.05 101.1 103.9 102.6 157s 8 102.7 0.653 2.10 100.9 104.4 104.8 157s 9 102.0 0.655 2.10 100.2 103.8 102.7 157s 10 101.4 1.074 2.26 98.5 104.3 99.7 157s 11 95.6 0.978 2.22 93.0 98.3 95.4 157s 12 93.9 1.134 2.29 90.8 97.0 93.8 157s 13 95.0 1.162 2.31 91.9 98.2 95.6 157s 14 98.9 0.530 2.06 97.5 100.4 97.6 157s 15 104.9 1.061 2.26 102.0 107.8 102.3 157s 16 104.3 0.757 2.13 102.2 106.3 104.1 157s 17 106.1 1.963 2.80 100.7 111.4 102.8 157s 18 101.7 0.597 2.08 100.1 103.4 102.7 157s 19 103.3 0.736 2.12 101.3 105.3 102.6 157s 20 106.0 1.430 2.45 102.1 110.0 105.6 157s supply.se.fit supply.se.pred supply.lwr supply.upr 157s 1 1.079 2.68 96.0 101.9 157s 2 1.064 2.68 97.5 103.3 157s 3 0.962 2.64 97.8 103.1 157s 4 0.938 2.63 98.1 103.3 157s 5 0.914 2.62 100.1 105.1 157s 6 0.808 2.59 100.4 104.8 157s 7 0.736 2.57 100.5 104.6 157s 8 0.994 2.65 102.1 107.5 157s 9 0.808 2.59 100.5 105.0 157s 10 1.023 2.66 96.9 102.5 157s 11 1.228 2.75 92.0 98.7 157s 12 1.428 2.84 89.9 97.7 157s 13 1.272 2.77 92.2 99.1 157s 14 0.917 2.62 95.1 100.1 157s 15 0.899 2.62 99.9 104.8 157s 16 0.936 2.63 101.5 106.6 157s 17 1.665 2.97 98.3 107.4 157s 18 0.988 2.65 100.0 105.4 157s 19 1.129 2.70 99.5 105.6 157s 20 1.733 3.01 100.9 110.3 157s > print( predict( fit2slsd1$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 157s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 157s fit se.fit se.pred lwr upr 157s 1 98.9 1.079 2.68 96.0 101.9 157s 2 100.4 1.064 2.68 97.5 103.3 157s 3 100.5 0.962 2.64 97.8 103.1 157s 4 100.7 0.938 2.63 98.1 103.3 157s 5 102.6 0.914 2.62 100.1 105.1 157s 6 102.6 0.808 2.59 100.4 104.8 157s 7 102.6 0.736 2.57 100.5 104.6 157s 8 104.8 0.994 2.65 102.1 107.5 157s 9 102.7 0.808 2.59 100.5 105.0 157s 10 99.7 1.023 2.66 96.9 102.5 157s 11 95.4 1.228 2.75 92.0 98.7 157s 12 93.8 1.428 2.84 89.9 97.7 157s 13 95.6 1.272 2.77 92.2 99.1 157s 14 97.6 0.917 2.62 95.1 100.1 157s 15 102.3 0.899 2.62 99.9 104.8 157s 16 104.1 0.936 2.63 101.5 106.6 157s 17 102.8 1.665 2.97 98.3 107.4 157s 18 102.7 0.988 2.65 100.0 105.4 157s 19 102.6 1.129 2.70 99.5 105.6 157s 20 105.6 1.733 3.01 100.9 110.3 157s > 157s > print( predict( fit2slsd2r, se.fit = TRUE, interval = "prediction", 157s + level = 0.9, newdata = predictData ) ) 157s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 157s 1 104 1.34 99.8 108 95.8 1.026 157s 2 106 1.27 102.3 110 97.3 0.786 157s 3 106 1.32 102.2 110 97.4 0.804 157s 4 106 1.27 102.4 110 97.7 0.734 157s 5 109 2.06 104.2 114 100.0 1.130 157s 6 109 1.92 104.1 113 99.9 1.014 157s 7 109 1.86 104.7 114 99.9 0.893 157s 8 110 1.67 105.4 114 102.2 0.765 157s 9 108 2.12 103.4 113 100.4 1.187 157s 10 107 2.45 101.9 112 97.4 1.525 157s 11 102 1.85 97.1 106 92.9 1.627 157s 12 101 1.26 96.6 104 91.2 1.587 157s 13 102 0.98 98.3 106 93.1 1.314 157s 14 105 1.63 101.1 110 95.3 1.253 157s 15 111 2.53 105.6 116 100.4 1.269 157s 16 111 2.23 105.7 116 102.1 1.075 157s 17 111 3.28 104.9 118 101.3 1.888 157s 18 109 1.59 104.5 113 100.7 0.796 157s 19 110 1.70 106.1 115 100.5 0.772 157s 20 114 1.87 109.4 119 103.6 0.656 157s supply.lwr supply.upr 157s 1 91.2 100.4 157s 2 92.8 101.7 157s 3 93.0 101.9 157s 4 93.3 102.1 157s 5 95.3 104.6 157s 6 95.4 104.5 157s 7 95.4 104.4 157s 8 97.8 106.6 157s 9 95.7 105.1 157s 10 92.5 102.4 157s 11 87.9 98.0 157s 12 86.2 96.2 157s 13 88.3 97.9 157s 14 90.5 100.0 157s 15 95.6 105.1 157s 16 97.5 106.7 157s 17 96.0 106.6 157s 18 96.2 105.1 157s 19 96.1 105.0 157s 20 99.2 107.9 157s > print( predict( fit2slsd2r$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 157s + level = 0.9, newdata = predictData ) ) 157s fit se.fit lwr upr 157s 1 104 1.34 99.8 108 157s 2 106 1.27 102.3 110 157s 3 106 1.32 102.2 110 157s 4 106 1.27 102.4 110 157s 5 109 2.06 104.2 114 157s 6 109 1.92 104.1 113 157s 7 109 1.86 104.7 114 157s 8 110 1.67 105.4 114 157s 9 108 2.12 103.4 113 157s 10 107 2.45 101.9 112 157s 11 102 1.85 97.1 106 157s 12 101 1.26 96.6 104 157s 13 102 0.98 98.3 106 157s 14 105 1.63 101.1 110 157s 15 111 2.53 105.6 116 157s 16 111 2.23 105.7 116 157s 17 111 3.28 104.9 118 157s 18 109 1.59 104.5 113 157s 19 110 1.70 106.1 115 157s 20 114 1.87 109.4 119 157s > 157s > # predict just one observation 157s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 157s + trend = 25 ) 157s > 157s > print( predict( fit2sls1rs, newdata = smallData ) ) 157s demand.pred supply.pred 157s 1 110 118 157s > print( predict( fit2sls1rs$eq[[ 1 ]], newdata = smallData ) ) 157s fit 157s 1 110 157s > 157s > print( predict( fit2sls2, se.fit = TRUE, level = 0.9, 157s + newdata = smallData ) ) 157s demand.pred demand.se.fit supply.pred supply.se.fit 157s 1 110 2.79 119 3.18 157s > print( predict( fit2sls2$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 157s + newdata = smallData ) ) 157s fit se.pred 157s 1 110 3.42 157s > 157s > print( predict( fit2sls3, interval = "prediction", level = 0.975, 157s + newdata = smallData ) ) 157s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 157s 1 110 102 117 119 110 128 157s > print( predict( fit2sls3$eq[[ 1 ]], interval = "confidence", level = 0.8, 157s + newdata = smallData ) ) 157s fit lwr upr 157s 1 110 106 113 157s > 157s > print( predict( fit2sls4r, se.fit = TRUE, interval = "confidence", 157s + level = 0.999, newdata = smallData ) ) 157s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 157s 1 109 2.24 101 118 119 2.09 157s supply.lwr supply.upr 157s 1 112 127 157s > print( predict( fit2sls4r$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 157s + level = 0.75, newdata = smallData ) ) 157s fit se.pred lwr upr 157s 1 119 3.26 115 123 157s > 157s > print( predict( fit2sls5s, se.fit = TRUE, interval = "prediction", 157s + newdata = smallData ) ) 157s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 157s 1 109 2.26 103 116 119 2.33 157s supply.lwr supply.upr 157s 1 112 126 157s > print( predict( fit2sls5s$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 157s + newdata = smallData ) ) 157s fit se.pred lwr upr 157s 1 109 3 105 114 157s > 157s > print( predict( fit2slsd3, se.fit = TRUE, se.pred = TRUE, 157s + interval = "prediction", level = 0.5, newdata = smallData ) ) 157s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 157s 1 108 3.33 3.86 105 110 119 157s supply.se.fit supply.se.pred supply.lwr supply.upr 157s 1 3.2 4.07 116 122 157s > print( predict( fit2slsd3$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 157s + interval = "confidence", level = 0.25, newdata = smallData ) ) 157s fit se.fit se.pred lwr upr 157s 1 108 3.33 3.86 107 109 157s > 157s > 157s > ## ************ correlation of predicted values *************** 157s > print( correlation.systemfit( fit2sls1, 1, 2 ) ) 157s [,1] 157s [1,] 0 157s [2,] 0 157s [3,] 0 157s [4,] 0 157s [5,] 0 157s [6,] 0 157s [7,] 0 157s [8,] 0 157s [9,] 0 157s [10,] 0 157s [11,] 0 157s [12,] 0 157s [13,] 0 157s [14,] 0 157s [15,] 0 157s [16,] 0 157s [17,] 0 157s [18,] 0 157s [19,] 0 157s [20,] 0 157s > 157s > print( correlation.systemfit( fit2sls2s, 2, 1 ) ) 157s [,1] 157s [1,] 0.413453 157s [2,] 0.153759 157s [3,] 0.152962 157s [4,] 0.112671 157s [5,] -0.071442 157s [6,] -0.053943 157s [7,] -0.050961 157s [8,] -0.005442 157s [9,] -0.000476 157s [10,] -0.001894 157s [11,] 0.047351 157s [12,] 0.064973 157s [13,] 0.024591 157s [14,] -0.028036 157s [15,] 0.175326 157s [16,] 0.254878 157s [17,] 0.104540 157s [18,] 0.065579 157s [19,] 0.147008 157s [20,] 0.124593 157s > 157s > print( correlation.systemfit( fit2sls3, 1, 2 ) ) 157s [,1] 157s [1,] 0.44877 157s [2,] 0.16875 157s [3,] 0.16850 157s [4,] 0.12519 157s [5,] -0.08079 157s [6,] -0.06096 157s [7,] -0.05780 157s [8,] -0.00618 157s [9,] -0.00054 157s [10,] -0.00214 157s [11,] 0.05454 157s [12,] 0.07607 157s [13,] 0.02868 157s [14,] -0.03197 157s [15,] 0.19899 157s [16,] 0.28551 157s [17,] 0.11838 157s [18,] 0.07184 157s [19,] 0.16271 157s [20,] 0.13995 157s > 157s > print( correlation.systemfit( fit2sls4r, 2, 1 ) ) 157s [,1] 157s [1,] 0.4078 157s [2,] 0.2866 157s [3,] 0.2528 157s [4,] 0.2836 157s [5,] -0.0300 157s [6,] -0.0537 157s [7,] -0.0627 157s [8,] 0.1044 157s [9,] 0.1003 157s [10,] 0.4530 157s [11,] 0.1293 157s [12,] 0.0184 157s [13,] 0.0449 157s [14,] -0.0409 157s [15,] 0.4229 157s [16,] 0.2649 157s [17,] 0.6554 157s [18,] 0.2693 157s [19,] 0.3831 157s [20,] 0.5784 157s > 157s > print( correlation.systemfit( fit2sls5rs, 1, 2 ) ) 157s [,1] 157s [1,] 0.38438 157s [2,] 0.30697 157s [3,] 0.26690 157s [4,] 0.30163 157s [5,] -0.02768 157s [6,] -0.05086 157s [7,] -0.05895 157s [8,] 0.10102 157s [9,] 0.10072 157s [10,] 0.45547 157s [11,] 0.10817 157s [12,] 0.00552 157s [13,] 0.04219 157s [14,] -0.04054 157s [15,] 0.42100 157s [16,] 0.24974 157s [17,] 0.65722 157s [18,] 0.24286 157s [19,] 0.34336 157s [20,] 0.54717 157s > 157s > print( correlation.systemfit( fit2slsd1, 2, 1 ) ) 157s [,1] 157s [1,] 0 157s [2,] 0 157s [3,] 0 157s [4,] 0 157s [5,] 0 157s [6,] 0 157s [7,] 0 157s [8,] 0 157s [9,] 0 157s [10,] 0 157s [11,] 0 157s [12,] 0 157s [13,] 0 157s [14,] 0 157s [15,] 0 157s [16,] 0 157s [17,] 0 157s [18,] 0 157s [19,] 0 157s [20,] 0 157s > 157s > print( correlation.systemfit( fit2slsd2r, 1, 2 ) ) 157s [,1] 157s [1,] 0.51320 157s [2,] 0.27263 157s [3,] 0.26221 157s [4,] 0.21307 157s [5,] -0.11973 157s [6,] -0.08282 157s [7,] -0.06158 157s [8,] -0.00225 157s [9,] -0.00103 157s [10,] -0.00892 157s [11,] 0.04576 157s [12,] 0.08710 157s [13,] 0.03423 157s [14,] -0.03425 157s [15,] 0.25625 157s [16,] 0.35070 157s [17,] 0.17505 157s [18,] -0.02443 157s [19,] 0.07277 157s [20,] 0.05142 157s > 157s > 157s > ## ************ Log-Likelihood values *************** 157s > print( logLik( fit2sls1 ) ) 157s 'log Lik.' -67.6 (df=8) 157s > print( logLik( fit2sls1, residCovDiag = TRUE ) ) 157s 'log Lik.' -84.4 (df=8) 157s > 157s > print( logLik( fit2sls2s ) ) 157s 'log Lik.' -65.7 (df=7) 157s > print( logLik( fit2sls2s, residCovDiag = TRUE ) ) 157s 'log Lik.' -84.8 (df=7) 157s > 157s > print( logLik( fit2sls3 ) ) 157s 'log Lik.' -65.7 (df=7) 157s > print( logLik( fit2sls3, residCovDiag = TRUE ) ) 157s 'log Lik.' -84.8 (df=7) 157s > 157s > print( logLik( fit2sls4r ) ) 157s 'log Lik.' -66.2 (df=6) 157s > print( logLik( fit2sls4r, residCovDiag = TRUE ) ) 157s 'log Lik.' -84.8 (df=6) 157s > 157s > print( logLik( fit2sls5rs ) ) 157s 'log Lik.' -66.2 (df=6) 157s > print( logLik( fit2sls5rs, residCovDiag = TRUE ) ) 157s 'log Lik.' -84.8 (df=6) 157s > 157s > print( logLik( fit2slsd1 ) ) 157s 'log Lik.' -75.1 (df=8) 157s > print( logLik( fit2slsd1, residCovDiag = TRUE ) ) 157s 'log Lik.' -84.7 (df=8) 157s > 157s > print( logLik( fit2slsd2r ) ) 157s 'log Lik.' -68.8 (df=7) 157s > print( logLik( fit2slsd2r, residCovDiag = TRUE ) ) 157s 'log Lik.' -84.6 (df=7) 157s > 157s > 157s > ## ************** F tests **************** 157s > # testing first restriction 157s > print( linearHypothesis( fit2sls1, restrm ) ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0.06 0.8 157s > linearHypothesis( fit2sls1, restrict ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0.06 0.8 157s > 157s > print( linearHypothesis( fit2sls1s, restrm ) ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1s 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0.07 0.79 157s > linearHypothesis( fit2sls1s, restrict ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1s 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0.07 0.79 157s > 157s > print( linearHypothesis( fit2sls1, restrm ) ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0.06 0.8 157s > linearHypothesis( fit2sls1, restrict ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0.06 0.8 157s > 157s > print( linearHypothesis( fit2sls1r, restrm ) ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1r 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0.08 0.78 157s > linearHypothesis( fit2sls1r, restrict ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1r 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0.08 0.78 157s > 157s > # testing second restriction 157s > restrOnly2m <- matrix(0,1,7) 157s > restrOnly2q <- 0.5 157s > restrOnly2m[1,2] <- -1 157s > restrOnly2m[1,5] <- 1 157s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 157s > # first restriction not imposed 157s > print( linearHypothesis( fit2sls1, restrOnly2m, restrOnly2q ) ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0 0.96 157s > linearHypothesis( fit2sls1, restrictOnly2 ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df F Pr(>F) 157s 1 34 157s 2 33 1 0 0.96 157s > 157s > # first restriction imposed 157s > print( linearHypothesis( fit2sls2, restrOnly2m, restrOnly2q ) ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls2 157s 157s Res.Df Df F Pr(>F) 157s 1 35 157s 2 34 1 0.01 0.92 157s > linearHypothesis( fit2sls2, restrictOnly2 ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls2 157s 157s Res.Df Df F Pr(>F) 157s 1 35 157s 2 34 1 0.01 0.92 157s > 157s > print( linearHypothesis( fit2sls2r, restrOnly2m, restrOnly2q ) ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls2r 157s 157s Res.Df Df F Pr(>F) 157s 1 35 157s 2 34 1 0.01 0.91 157s > linearHypothesis( fit2sls2r, restrictOnly2 ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls2r 157s 157s Res.Df Df F Pr(>F) 157s 1 35 157s 2 34 1 0.01 0.91 157s > 157s > print( linearHypothesis( fit2sls3, restrOnly2m, restrOnly2q ) ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls3 157s 157s Res.Df Df F Pr(>F) 157s 1 35 157s 2 34 1 0.01 0.91 157s > linearHypothesis( fit2sls3, restrictOnly2 ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls3 157s 157s Res.Df Df F Pr(>F) 157s 1 35 157s 2 34 1 0.01 0.91 157s > 157s > # testing both of the restrictions 157s > print( linearHypothesis( fit2sls1, restr2m, restr2q ) ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df F Pr(>F) 157s 1 35 157s 2 33 2 0.04 0.97 157s > linearHypothesis( fit2sls1, restrict2 ) 157s Linear hypothesis test (Theil's F test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df F Pr(>F) 157s 1 35 157s 2 33 2 0.04 0.97 157s > 157s > 157s > ## ************** Wald tests **************** 157s > # testing first restriction 157s > print( linearHypothesis( fit2sls1, restrm, test = "Chisq" ) ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.31 0.58 157s > linearHypothesis( fit2sls1, restrict, test = "Chisq" ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.31 0.58 157s > 157s > print( linearHypothesis( fit2sls1s, restrm, test = "Chisq" ) ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1s 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.34 0.56 157s > linearHypothesis( fit2sls1s, restrict, test = "Chisq" ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1s 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.34 0.56 157s > 157s > print( linearHypothesis( fit2sls1, restrm, test = "Chisq" ) ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.31 0.58 157s > linearHypothesis( fit2sls1, restrict, test = "Chisq" ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.31 0.58 157s > 157s > print( linearHypothesis( fit2sls1r, restrm, test = "Chisq" ) ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1r 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.38 0.54 157s > linearHypothesis( fit2sls1r, restrict, test = "Chisq" ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s 157s Model 1: restricted model 157s Model 2: fit2sls1r 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.38 0.54 157s > 157s > # testing second restriction 157s > # first restriction not imposed 157s > print( linearHypothesis( fit2sls1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.01 0.91 157s > linearHypothesis( fit2sls1, restrictOnly2, test = "Chisq" ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 34 157s 2 33 1 0.01 0.91 157s > # first restriction imposed 157s > print( linearHypothesis( fit2sls2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls2 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 35 157s 2 34 1 0.06 0.81 157s > linearHypothesis( fit2sls2, restrictOnly2, test = "Chisq" ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls2 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 35 157s 2 34 1 0.06 0.81 157s > 157s > print( linearHypothesis( fit2sls2r, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls2r 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 35 157s 2 34 1 0.07 0.8 157s > linearHypothesis( fit2sls2r, restrictOnly2, test = "Chisq" ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls2r 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 35 157s 2 34 1 0.07 0.8 157s > 157s > print( linearHypothesis( fit2sls3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls3 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 35 157s 2 34 1 0.07 0.8 157s > linearHypothesis( fit2sls3, restrictOnly2, test = "Chisq" ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls3 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 35 157s 2 34 1 0.07 0.8 157s > 157s > # testing both of the restrictions 157s > print( linearHypothesis( fit2sls1, restr2m, restr2q, test = "Chisq" ) ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 35 157s 2 33 2 0.35 0.84 157s > linearHypothesis( fit2sls1, restrict2, test = "Chisq" ) 157s Linear hypothesis test (Chi^2 statistic of a Wald test) 157s 157s Hypothesis: 157s demand_income - supply_trend = 0 157s - demand_price + supply_price = 0.5 157s 157s Model 1: restricted model 157s Model 2: fit2sls1 157s 157s Res.Df Df Chisq Pr(>Chisq) 157s 1 35 157s 2 33 2 0.35 0.84 157s > 157s > 157s > ## **************** model frame ************************ 157s > print( mf <- model.frame( fit2sls1 ) ) 157s consump price income farmPrice trend 157s 1 98.5 100.3 87.4 98.0 1 157s 2 99.2 104.3 97.6 99.1 2 157s 3 102.2 103.4 96.7 99.1 3 157s 4 101.5 104.5 98.2 98.1 4 157s 5 104.2 98.0 99.8 110.8 5 157s 6 103.2 99.5 100.5 108.2 6 157s 7 104.0 101.1 103.2 105.6 7 157s 8 99.9 104.8 107.8 109.8 8 157s 9 100.3 96.4 96.6 108.7 9 157s 10 102.8 91.2 88.9 100.6 10 157s 11 95.4 93.1 75.1 81.0 11 157s 12 92.4 98.8 76.9 68.6 12 157s 13 94.5 102.9 84.6 70.9 13 157s 14 98.8 98.8 90.6 81.4 14 157s 15 105.8 95.1 103.1 102.3 15 157s 16 100.2 98.5 105.1 105.0 16 157s 17 103.5 86.5 96.4 110.5 17 157s 18 99.9 104.0 104.4 92.5 18 157s 19 105.2 105.8 110.7 89.3 19 157s 20 106.2 113.5 127.1 93.0 20 157s > print( mf1 <- model.frame( fit2sls1$eq[[ 1 ]] ) ) 157s consump price income 157s 1 98.5 100.3 87.4 157s 2 99.2 104.3 97.6 157s 3 102.2 103.4 96.7 157s 4 101.5 104.5 98.2 157s 5 104.2 98.0 99.8 157s 6 103.2 99.5 100.5 157s 7 104.0 101.1 103.2 157s 8 99.9 104.8 107.8 157s 9 100.3 96.4 96.6 157s 10 102.8 91.2 88.9 157s 11 95.4 93.1 75.1 157s 12 92.4 98.8 76.9 157s 13 94.5 102.9 84.6 157s 14 98.8 98.8 90.6 157s 15 105.8 95.1 103.1 157s 16 100.2 98.5 105.1 157s 17 103.5 86.5 96.4 157s 18 99.9 104.0 104.4 157s 19 105.2 105.8 110.7 157s 20 106.2 113.5 127.1 157s > print( attributes( mf1 )$terms ) 157s consump ~ price + income 157s attr(,"variables") 157s list(consump, price, income) 157s attr(,"factors") 157s price income 157s consump 0 0 157s price 1 0 157s income 0 1 157s attr(,"term.labels") 157s [1] "price" "income" 157s attr(,"order") 157s [1] 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, income) 157s attr(,"dataClasses") 157s consump price income 157s "numeric" "numeric" "numeric" 157s > print( mf2 <- model.frame( fit2sls1$eq[[ 2 ]] ) ) 157s consump price farmPrice trend 157s 1 98.5 100.3 98.0 1 157s 2 99.2 104.3 99.1 2 157s 3 102.2 103.4 99.1 3 157s 4 101.5 104.5 98.1 4 157s 5 104.2 98.0 110.8 5 157s 6 103.2 99.5 108.2 6 157s 7 104.0 101.1 105.6 7 157s 8 99.9 104.8 109.8 8 157s 9 100.3 96.4 108.7 9 157s 10 102.8 91.2 100.6 10 157s 11 95.4 93.1 81.0 11 157s 12 92.4 98.8 68.6 12 157s 13 94.5 102.9 70.9 13 157s 14 98.8 98.8 81.4 14 157s 15 105.8 95.1 102.3 15 157s 16 100.2 98.5 105.0 16 157s 17 103.5 86.5 110.5 17 157s 18 99.9 104.0 92.5 18 157s 19 105.2 105.8 89.3 19 157s 20 106.2 113.5 93.0 20 157s > print( attributes( mf2 )$terms ) 157s consump ~ price + farmPrice + trend 157s attr(,"variables") 157s list(consump, price, farmPrice, trend) 157s attr(,"factors") 157s price farmPrice trend 157s consump 0 0 0 157s price 1 0 0 157s farmPrice 0 1 0 157s trend 0 0 1 157s attr(,"term.labels") 157s [1] "price" "farmPrice" "trend" 157s attr(,"order") 157s [1] 1 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, farmPrice, trend) 157s attr(,"dataClasses") 157s consump price farmPrice trend 157s "numeric" "numeric" "numeric" "numeric" 157s > 157s > print( all.equal( mf, model.frame( fit2sls2s ) ) ) 157s [1] TRUE 157s > print( all.equal( mf2, model.frame( fit2sls2s$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > 157s > print( all.equal( mf, model.frame( fit2sls3 ) ) ) 157s [1] TRUE 157s > print( all.equal( mf1, model.frame( fit2sls3$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > 157s > print( all.equal( mf, model.frame( fit2sls4r ) ) ) 157s [1] TRUE 157s > print( all.equal( mf2, model.frame( fit2sls4r$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > 157s > print( all.equal( mf, model.frame( fit2sls5rs ) ) ) 157s [1] TRUE 157s > print( all.equal( mf1, model.frame( fit2sls5rs$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > 157s > fit2sls1$eq[[ 1 ]]$modelInst 157s income farmPrice trend 157s 1 87.4 98.0 1 157s 2 97.6 99.1 2 157s 3 96.7 99.1 3 157s 4 98.2 98.1 4 157s 5 99.8 110.8 5 157s 6 100.5 108.2 6 157s 7 103.2 105.6 7 157s 8 107.8 109.8 8 157s 9 96.6 108.7 9 157s 10 88.9 100.6 10 157s 11 75.1 81.0 11 157s 12 76.9 68.6 12 157s 13 84.6 70.9 13 157s 14 90.6 81.4 14 157s 15 103.1 102.3 15 157s 16 105.1 105.0 16 157s 17 96.4 110.5 17 157s 18 104.4 92.5 18 157s 19 110.7 89.3 19 157s 20 127.1 93.0 20 157s > fit2sls1$eq[[ 2 ]]$modelInst 157s income farmPrice trend 157s 1 87.4 98.0 1 157s 2 97.6 99.1 2 157s 3 96.7 99.1 3 157s 4 98.2 98.1 4 157s 5 99.8 110.8 5 157s 6 100.5 108.2 6 157s 7 103.2 105.6 7 157s 8 107.8 109.8 8 157s 9 96.6 108.7 9 157s 10 88.9 100.6 10 157s 11 75.1 81.0 11 157s 12 76.9 68.6 12 157s 13 84.6 70.9 13 157s 14 90.6 81.4 14 157s 15 103.1 102.3 15 157s 16 105.1 105.0 16 157s 17 96.4 110.5 17 157s 18 104.4 92.5 18 157s 19 110.7 89.3 19 157s 20 127.1 93.0 20 157s > 157s > fit2sls2s$eq[[ 1 ]]$modelInst 157s income farmPrice trend 157s 1 87.4 98.0 1 157s 2 97.6 99.1 2 157s 3 96.7 99.1 3 157s 4 98.2 98.1 4 157s 5 99.8 110.8 5 157s 6 100.5 108.2 6 157s 7 103.2 105.6 7 157s 8 107.8 109.8 8 157s 9 96.6 108.7 9 157s 10 88.9 100.6 10 157s 11 75.1 81.0 11 157s 12 76.9 68.6 12 157s 13 84.6 70.9 13 157s 14 90.6 81.4 14 157s 15 103.1 102.3 15 157s 16 105.1 105.0 16 157s 17 96.4 110.5 17 157s 18 104.4 92.5 18 157s 19 110.7 89.3 19 157s 20 127.1 93.0 20 157s > fit2sls2s$eq[[ 2 ]]$modelInst 157s income farmPrice trend 157s 1 87.4 98.0 1 157s 2 97.6 99.1 2 157s 3 96.7 99.1 3 157s 4 98.2 98.1 4 157s 5 99.8 110.8 5 157s 6 100.5 108.2 6 157s 7 103.2 105.6 7 157s 8 107.8 109.8 8 157s 9 96.6 108.7 9 157s 10 88.9 100.6 10 157s 11 75.1 81.0 11 157s 12 76.9 68.6 12 157s 13 84.6 70.9 13 157s 14 90.6 81.4 14 157s 15 103.1 102.3 15 157s 16 105.1 105.0 16 157s 17 96.4 110.5 17 157s 18 104.4 92.5 18 157s 19 110.7 89.3 19 157s 20 127.1 93.0 20 157s > 157s > fit2sls5rs$eq[[ 1 ]]$modelInst 157s income farmPrice trend 157s 1 87.4 98.0 1 157s 2 97.6 99.1 2 157s 3 96.7 99.1 3 157s 4 98.2 98.1 4 157s 5 99.8 110.8 5 157s 6 100.5 108.2 6 157s 7 103.2 105.6 7 157s 8 107.8 109.8 8 157s 9 96.6 108.7 9 157s 10 88.9 100.6 10 157s 11 75.1 81.0 11 157s 12 76.9 68.6 12 157s 13 84.6 70.9 13 157s 14 90.6 81.4 14 157s 15 103.1 102.3 15 157s 16 105.1 105.0 16 157s 17 96.4 110.5 17 157s 18 104.4 92.5 18 157s 19 110.7 89.3 19 157s 20 127.1 93.0 20 157s > fit2sls5rs$eq[[ 2 ]]$modelInst 157s income farmPrice trend 157s 1 87.4 98.0 1 157s 2 97.6 99.1 2 157s 3 96.7 99.1 3 157s 4 98.2 98.1 4 157s 5 99.8 110.8 5 157s 6 100.5 108.2 6 157s 7 103.2 105.6 7 157s 8 107.8 109.8 8 157s 9 96.6 108.7 9 157s 10 88.9 100.6 10 157s 11 75.1 81.0 11 157s 12 76.9 68.6 12 157s 13 84.6 70.9 13 157s 14 90.6 81.4 14 157s 15 103.1 102.3 15 157s 16 105.1 105.0 16 157s 17 96.4 110.5 17 157s 18 104.4 92.5 18 157s 19 110.7 89.3 19 157s 20 127.1 93.0 20 157s > 157s > 157s > ## **************** model matrix ************************ 157s > # with x (returnModelMatrix) = TRUE 157s > print( !is.null( fit2sls1$eq[[ 1 ]]$x ) ) 157s [1] TRUE 157s > print( mm <- model.matrix( fit2sls1 ) ) 157s demand_(Intercept) demand_price demand_income supply_(Intercept) 157s demand_1 1 100.3 87.4 0 157s demand_2 1 104.3 97.6 0 157s demand_3 1 103.4 96.7 0 157s demand_4 1 104.5 98.2 0 157s demand_5 1 98.0 99.8 0 157s demand_6 1 99.5 100.5 0 157s demand_7 1 101.1 103.2 0 157s demand_8 1 104.8 107.8 0 157s demand_9 1 96.4 96.6 0 157s demand_10 1 91.2 88.9 0 157s demand_11 1 93.1 75.1 0 157s demand_12 1 98.8 76.9 0 157s demand_13 1 102.9 84.6 0 157s demand_14 1 98.8 90.6 0 157s demand_15 1 95.1 103.1 0 157s demand_16 1 98.5 105.1 0 157s demand_17 1 86.5 96.4 0 157s demand_18 1 104.0 104.4 0 157s demand_19 1 105.8 110.7 0 157s demand_20 1 113.5 127.1 0 157s supply_1 0 0.0 0.0 1 157s supply_2 0 0.0 0.0 1 157s supply_3 0 0.0 0.0 1 157s supply_4 0 0.0 0.0 1 157s supply_5 0 0.0 0.0 1 157s supply_6 0 0.0 0.0 1 157s supply_7 0 0.0 0.0 1 157s supply_8 0 0.0 0.0 1 157s supply_9 0 0.0 0.0 1 157s supply_10 0 0.0 0.0 1 157s supply_11 0 0.0 0.0 1 157s supply_12 0 0.0 0.0 1 157s supply_13 0 0.0 0.0 1 157s supply_14 0 0.0 0.0 1 157s supply_15 0 0.0 0.0 1 157s supply_16 0 0.0 0.0 1 157s supply_17 0 0.0 0.0 1 157s supply_18 0 0.0 0.0 1 157s supply_19 0 0.0 0.0 1 157s supply_20 0 0.0 0.0 1 157s supply_price supply_farmPrice supply_trend 157s demand_1 0.0 0.0 0 157s demand_2 0.0 0.0 0 157s demand_3 0.0 0.0 0 157s demand_4 0.0 0.0 0 157s demand_5 0.0 0.0 0 157s demand_6 0.0 0.0 0 157s demand_7 0.0 0.0 0 157s demand_8 0.0 0.0 0 157s demand_9 0.0 0.0 0 157s demand_10 0.0 0.0 0 157s demand_11 0.0 0.0 0 157s demand_12 0.0 0.0 0 157s demand_13 0.0 0.0 0 157s demand_14 0.0 0.0 0 157s demand_15 0.0 0.0 0 157s demand_16 0.0 0.0 0 157s demand_17 0.0 0.0 0 157s demand_18 0.0 0.0 0 157s demand_19 0.0 0.0 0 157s demand_20 0.0 0.0 0 157s supply_1 100.3 98.0 1 157s supply_2 104.3 99.1 2 157s supply_3 103.4 99.1 3 157s supply_4 104.5 98.1 4 157s supply_5 98.0 110.8 5 157s supply_6 99.5 108.2 6 157s supply_7 101.1 105.6 7 157s supply_8 104.8 109.8 8 157s supply_9 96.4 108.7 9 157s supply_10 91.2 100.6 10 157s supply_11 93.1 81.0 11 157s supply_12 98.8 68.6 12 157s supply_13 102.9 70.9 13 157s supply_14 98.8 81.4 14 157s supply_15 95.1 102.3 15 157s supply_16 98.5 105.0 16 157s supply_17 86.5 110.5 17 157s supply_18 104.0 92.5 18 157s supply_19 105.8 89.3 19 157s supply_20 113.5 93.0 20 157s > print( mm1 <- model.matrix( fit2sls1$eq[[ 1 ]] ) ) 157s (Intercept) price income 157s 1 1 100.3 87.4 157s 2 1 104.3 97.6 157s 3 1 103.4 96.7 157s 4 1 104.5 98.2 157s 5 1 98.0 99.8 157s 6 1 99.5 100.5 157s 7 1 101.1 103.2 157s 8 1 104.8 107.8 157s 9 1 96.4 96.6 157s 10 1 91.2 88.9 157s 11 1 93.1 75.1 157s 12 1 98.8 76.9 157s 13 1 102.9 84.6 157s 14 1 98.8 90.6 157s 15 1 95.1 103.1 157s 16 1 98.5 105.1 157s 17 1 86.5 96.4 157s 18 1 104.0 104.4 157s 19 1 105.8 110.7 157s 20 1 113.5 127.1 157s attr(,"assign") 157s [1] 0 1 2 157s > print( mm2 <- model.matrix( fit2sls1$eq[[ 2 ]] ) ) 157s (Intercept) price farmPrice trend 157s 1 1 100.3 98.0 1 157s 2 1 104.3 99.1 2 157s 3 1 103.4 99.1 3 157s 4 1 104.5 98.1 4 157s 5 1 98.0 110.8 5 157s 6 1 99.5 108.2 6 157s 7 1 101.1 105.6 7 157s 8 1 104.8 109.8 8 157s 9 1 96.4 108.7 9 157s 10 1 91.2 100.6 10 157s 11 1 93.1 81.0 11 157s 12 1 98.8 68.6 12 157s 13 1 102.9 70.9 13 157s 14 1 98.8 81.4 14 157s 15 1 95.1 102.3 15 157s 16 1 98.5 105.0 16 157s 17 1 86.5 110.5 17 157s 18 1 104.0 92.5 18 157s 19 1 105.8 89.3 19 157s 20 1 113.5 93.0 20 157s attr(,"assign") 157s [1] 0 1 2 3 157s > 157s > # with x (returnModelMatrix) = FALSE 157s > print( all.equal( mm, model.matrix( fit2sls1s ) ) ) 157s [1] TRUE 157s > print( all.equal( mm1, model.matrix( fit2sls1s$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > print( all.equal( mm2, model.matrix( fit2sls1s$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > print( !is.null( fit2sls1s$eq[[ 1 ]]$x ) ) 157s [1] FALSE 157s > 157s > # with x (returnModelMatrix) = TRUE 157s > print( !is.null( fit2sls2s$eq[[ 1 ]]$x ) ) 157s [1] TRUE 157s > print( all.equal( mm, model.matrix( fit2sls2s ) ) ) 157s [1] TRUE 157s > print( all.equal( mm1, model.matrix( fit2sls2s$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > print( all.equal( mm2, model.matrix( fit2sls2s$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > 157s > # with x (returnModelMatrix) = FALSE 157s > print( all.equal( mm, model.matrix( fit2sls2Sym ) ) ) 157s [1] TRUE 157s > print( all.equal( mm1, model.matrix( fit2sls2Sym$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > print( all.equal( mm2, model.matrix( fit2sls2Sym$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > print( !is.null( fit2sls2Sym$eq[[ 1 ]]$x ) ) 157s [1] FALSE 157s > 157s > # with x (returnModelMatrix) = FALSE 157s > print( all.equal( mm, model.matrix( fit2sls3 ) ) ) 157s [1] TRUE 157s > print( all.equal( mm1, model.matrix( fit2sls3$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > print( all.equal( mm2, model.matrix( fit2sls3$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > print( !is.null( fit2sls3$eq[[ 1 ]]$x ) ) 157s [1] FALSE 157s > 157s > # with x (returnModelMatrix) = TRUE 157s > print( !is.null( fit2sls4r$eq[[ 1 ]]$x ) ) 157s [1] TRUE 157s > print( all.equal( mm, model.matrix( fit2sls4r ) ) ) 157s [1] TRUE 157s > print( all.equal( mm1, model.matrix( fit2sls4r$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > print( all.equal( mm2, model.matrix( fit2sls4r$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > 157s > # with x (returnModelMatrix) = FALSE 157s > print( all.equal( mm, model.matrix( fit2sls4s ) ) ) 157s [1] TRUE 157s > print( all.equal( mm1, model.matrix( fit2sls4s$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > print( all.equal( mm2, model.matrix( fit2sls4s$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > print( !is.null( fit2sls4s$eq[[ 1 ]]$x ) ) 157s [1] FALSE 157s > 157s > # with x (returnModelMatrix) = TRUE 157s > print( !is.null( fit2sls5rs$eq[[ 1 ]]$x ) ) 157s [1] TRUE 157s > print( all.equal( mm, model.matrix( fit2sls5rs ) ) ) 157s [1] TRUE 157s > print( all.equal( mm1, model.matrix( fit2sls5rs$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > print( all.equal( mm2, model.matrix( fit2sls5rs$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > 157s > # with x (returnModelMatrix) = FALSE 157s > print( all.equal( mm, model.matrix( fit2sls5r ) ) ) 157s [1] TRUE 157s > print( all.equal( mm1, model.matrix( fit2sls5r$eq[[ 1 ]] ) ) ) 157s [1] TRUE 157s > print( all.equal( mm2, model.matrix( fit2sls5r$eq[[ 2 ]] ) ) ) 157s [1] TRUE 157s > print( !is.null( fit2sls5r$eq[[ 1 ]]$x ) ) 157s [1] FALSE 157s > 157s > # matrices of instrumental variables 157s > model.matrix( fit2sls1, which = "z" ) 157s demand_(Intercept) demand_income demand_farmPrice demand_trend 157s demand_1 1 87.4 98.0 1 157s demand_2 1 97.6 99.1 2 157s demand_3 1 96.7 99.1 3 157s demand_4 1 98.2 98.1 4 157s demand_5 1 99.8 110.8 5 157s demand_6 1 100.5 108.2 6 157s demand_7 1 103.2 105.6 7 157s demand_8 1 107.8 109.8 8 157s demand_9 1 96.6 108.7 9 157s demand_10 1 88.9 100.6 10 157s demand_11 1 75.1 81.0 11 157s demand_12 1 76.9 68.6 12 157s demand_13 1 84.6 70.9 13 157s demand_14 1 90.6 81.4 14 157s demand_15 1 103.1 102.3 15 157s demand_16 1 105.1 105.0 16 157s demand_17 1 96.4 110.5 17 157s demand_18 1 104.4 92.5 18 157s demand_19 1 110.7 89.3 19 157s demand_20 1 127.1 93.0 20 157s supply_1 0 0.0 0.0 0 157s supply_2 0 0.0 0.0 0 157s supply_3 0 0.0 0.0 0 157s supply_4 0 0.0 0.0 0 157s supply_5 0 0.0 0.0 0 157s supply_6 0 0.0 0.0 0 157s supply_7 0 0.0 0.0 0 157s supply_8 0 0.0 0.0 0 157s supply_9 0 0.0 0.0 0 157s supply_10 0 0.0 0.0 0 157s supply_11 0 0.0 0.0 0 157s supply_12 0 0.0 0.0 0 157s supply_13 0 0.0 0.0 0 157s supply_14 0 0.0 0.0 0 157s supply_15 0 0.0 0.0 0 157s supply_16 0 0.0 0.0 0 157s supply_17 0 0.0 0.0 0 157s supply_18 0 0.0 0.0 0 157s supply_19 0 0.0 0.0 0 157s supply_20 0 0.0 0.0 0 157s supply_(Intercept) supply_income supply_farmPrice supply_trend 157s demand_1 0 0.0 0.0 0 157s demand_2 0 0.0 0.0 0 157s demand_3 0 0.0 0.0 0 157s demand_4 0 0.0 0.0 0 157s demand_5 0 0.0 0.0 0 157s demand_6 0 0.0 0.0 0 157s demand_7 0 0.0 0.0 0 157s demand_8 0 0.0 0.0 0 157s demand_9 0 0.0 0.0 0 157s demand_10 0 0.0 0.0 0 157s demand_11 0 0.0 0.0 0 157s demand_12 0 0.0 0.0 0 157s demand_13 0 0.0 0.0 0 157s demand_14 0 0.0 0.0 0 157s demand_15 0 0.0 0.0 0 157s demand_16 0 0.0 0.0 0 157s demand_17 0 0.0 0.0 0 157s demand_18 0 0.0 0.0 0 157s demand_19 0 0.0 0.0 0 157s demand_20 0 0.0 0.0 0 157s supply_1 1 87.4 98.0 1 157s supply_2 1 97.6 99.1 2 157s supply_3 1 96.7 99.1 3 157s supply_4 1 98.2 98.1 4 157s supply_5 1 99.8 110.8 5 157s supply_6 1 100.5 108.2 6 157s supply_7 1 103.2 105.6 7 157s supply_8 1 107.8 109.8 8 157s supply_9 1 96.6 108.7 9 157s supply_10 1 88.9 100.6 10 157s supply_11 1 75.1 81.0 11 157s supply_12 1 76.9 68.6 12 157s supply_13 1 84.6 70.9 13 157s supply_14 1 90.6 81.4 14 157s supply_15 1 103.1 102.3 15 157s supply_16 1 105.1 105.0 16 157s supply_17 1 96.4 110.5 17 157s supply_18 1 104.4 92.5 18 157s supply_19 1 110.7 89.3 19 157s supply_20 1 127.1 93.0 20 157s > model.matrix( fit2sls1$eq[[ 1 ]], which = "z" ) 157s (Intercept) income farmPrice trend 157s 1 1 87.4 98.0 1 157s 2 1 97.6 99.1 2 157s 3 1 96.7 99.1 3 157s 4 1 98.2 98.1 4 157s 5 1 99.8 110.8 5 157s 6 1 100.5 108.2 6 157s 7 1 103.2 105.6 7 157s 8 1 107.8 109.8 8 157s 9 1 96.6 108.7 9 157s 10 1 88.9 100.6 10 157s 11 1 75.1 81.0 11 157s 12 1 76.9 68.6 12 157s 13 1 84.6 70.9 13 157s 14 1 90.6 81.4 14 157s 15 1 103.1 102.3 15 157s 16 1 105.1 105.0 16 157s 17 1 96.4 110.5 17 157s 18 1 104.4 92.5 18 157s 19 1 110.7 89.3 19 157s 20 1 127.1 93.0 20 157s attr(,"assign") 157s [1] 0 1 2 3 157s > model.matrix( fit2sls1$eq[[ 2 ]], which = "z" ) 157s (Intercept) income farmPrice trend 157s 1 1 87.4 98.0 1 157s 2 1 97.6 99.1 2 157s 3 1 96.7 99.1 3 157s 4 1 98.2 98.1 4 157s 5 1 99.8 110.8 5 157s 6 1 100.5 108.2 6 157s 7 1 103.2 105.6 7 157s 8 1 107.8 109.8 8 157s 9 1 96.6 108.7 9 157s 10 1 88.9 100.6 10 157s 11 1 75.1 81.0 11 157s 12 1 76.9 68.6 12 157s 13 1 84.6 70.9 13 157s 14 1 90.6 81.4 14 157s 15 1 103.1 102.3 15 157s 16 1 105.1 105.0 16 157s 17 1 96.4 110.5 17 157s 18 1 104.4 92.5 18 157s 19 1 110.7 89.3 19 157s 20 1 127.1 93.0 20 157s attr(,"assign") 157s [1] 0 1 2 3 157s > 157s > # matrices of fitted regressors 157s > model.matrix( fit2sls5r, which = "xHat" ) 157s demand_(Intercept) demand_price demand_income supply_(Intercept) 157s demand_1 1 99.6 87.4 0 157s demand_2 1 105.1 97.6 0 157s demand_3 1 103.8 96.7 0 157s demand_4 1 104.5 98.2 0 157s demand_5 1 98.7 99.8 0 157s demand_6 1 99.6 100.5 0 157s demand_7 1 102.0 103.2 0 157s demand_8 1 102.2 107.8 0 157s demand_9 1 94.6 96.6 0 157s demand_10 1 92.7 88.9 0 157s demand_11 1 92.4 75.1 0 157s demand_12 1 98.9 76.9 0 157s demand_13 1 102.2 84.6 0 157s demand_14 1 100.3 90.6 0 157s demand_15 1 97.6 103.1 0 157s demand_16 1 96.9 105.1 0 157s demand_17 1 87.7 96.4 0 157s demand_18 1 101.1 104.4 0 157s demand_19 1 106.1 110.7 0 157s demand_20 1 114.4 127.1 0 157s supply_1 0 0.0 0.0 1 157s supply_2 0 0.0 0.0 1 157s supply_3 0 0.0 0.0 1 157s supply_4 0 0.0 0.0 1 157s supply_5 0 0.0 0.0 1 157s supply_6 0 0.0 0.0 1 157s supply_7 0 0.0 0.0 1 157s supply_8 0 0.0 0.0 1 157s supply_9 0 0.0 0.0 1 157s supply_10 0 0.0 0.0 1 157s supply_11 0 0.0 0.0 1 157s supply_12 0 0.0 0.0 1 157s supply_13 0 0.0 0.0 1 157s supply_14 0 0.0 0.0 1 157s supply_15 0 0.0 0.0 1 157s supply_16 0 0.0 0.0 1 157s supply_17 0 0.0 0.0 1 157s supply_18 0 0.0 0.0 1 157s supply_19 0 0.0 0.0 1 157s supply_20 0 0.0 0.0 1 157s supply_price supply_farmPrice supply_trend 157s demand_1 0.0 0.0 0 157s demand_2 0.0 0.0 0 157s demand_3 0.0 0.0 0 157s demand_4 0.0 0.0 0 157s demand_5 0.0 0.0 0 157s demand_6 0.0 0.0 0 157s demand_7 0.0 0.0 0 157s demand_8 0.0 0.0 0 157s demand_9 0.0 0.0 0 157s demand_10 0.0 0.0 0 157s demand_11 0.0 0.0 0 157s demand_12 0.0 0.0 0 157s demand_13 0.0 0.0 0 157s demand_14 0.0 0.0 0 157s demand_15 0.0 0.0 0 157s demand_16 0.0 0.0 0 157s demand_17 0.0 0.0 0 157s demand_18 0.0 0.0 0 157s demand_19 0.0 0.0 0 157s demand_20 0.0 0.0 0 157s supply_1 99.6 98.0 1 157s supply_2 105.1 99.1 2 157s supply_3 103.8 99.1 3 157s supply_4 104.5 98.1 4 157s supply_5 98.7 110.8 5 157s supply_6 99.6 108.2 6 157s supply_7 102.0 105.6 7 157s supply_8 102.2 109.8 8 157s supply_9 94.6 108.7 9 157s supply_10 92.7 100.6 10 157s supply_11 92.4 81.0 11 157s supply_12 98.9 68.6 12 157s supply_13 102.2 70.9 13 157s supply_14 100.3 81.4 14 157s supply_15 97.6 102.3 15 157s supply_16 96.9 105.0 16 157s supply_17 87.7 110.5 17 157s supply_18 101.1 92.5 18 157s supply_19 106.1 89.3 19 157s supply_20 114.4 93.0 20 157s > model.matrix( fit2sls5r$eq[[ 1 ]], which = "xHat" ) 157s (Intercept) price income 157s 1 1 99.6 87.4 157s 2 1 105.1 97.6 157s 3 1 103.8 96.7 157s 4 1 104.5 98.2 157s 5 1 98.7 99.8 157s 6 1 99.6 100.5 157s 7 1 102.0 103.2 157s 8 1 102.2 107.8 157s 9 1 94.6 96.6 157s 10 1 92.7 88.9 157s 11 1 92.4 75.1 157s 12 1 98.9 76.9 157s 13 1 102.2 84.6 157s 14 1 100.3 90.6 157s 15 1 97.6 103.1 157s 16 1 96.9 105.1 157s 17 1 87.7 96.4 157s 18 1 101.1 104.4 157s 19 1 106.1 110.7 157s 20 1 114.4 127.1 157s > model.matrix( fit2sls5r$eq[[ 2 ]], which = "xHat" ) 157s (Intercept) price farmPrice trend 157s 1 1 99.6 98.0 1 157s 2 1 105.1 99.1 2 157s 3 1 103.8 99.1 3 157s 4 1 104.5 98.1 4 157s 5 1 98.7 110.8 5 157s 6 1 99.6 108.2 6 157s 7 1 102.0 105.6 7 157s 8 1 102.2 109.8 8 157s 9 1 94.6 108.7 9 157s 10 1 92.7 100.6 10 157s 11 1 92.4 81.0 11 157s 12 1 98.9 68.6 12 157s 13 1 102.2 70.9 13 157s 14 1 100.3 81.4 14 157s 15 1 97.6 102.3 15 157s 16 1 96.9 105.0 16 157s 17 1 87.7 110.5 17 157s 18 1 101.1 92.5 18 157s 19 1 106.1 89.3 19 157s 20 1 114.4 93.0 20 157s > 157s > 157s > ## **************** formulas ************************ 157s > formula( fit2sls1 ) 157s $demand 157s consump ~ price + income 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s 157s > formula( fit2sls1$eq[[ 1 ]] ) 157s consump ~ price + income 157s > 157s > formula( fit2sls2s ) 157s $demand 157s consump ~ price + income 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s 157s > formula( fit2sls2s$eq[[ 2 ]] ) 157s consump ~ price + farmPrice + trend 157s > 157s > formula( fit2sls3 ) 157s $demand 157s consump ~ price + income 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s 157s > formula( fit2sls3$eq[[ 1 ]] ) 157s consump ~ price + income 157s > 157s > formula( fit2sls4r ) 157s $demand 157s consump ~ price + income 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s 157s > formula( fit2sls4r$eq[[ 2 ]] ) 157s consump ~ price + farmPrice + trend 157s > 157s > formula( fit2sls5rs ) 157s $demand 157s consump ~ price + income 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s 157s > formula( fit2sls5rs$eq[[ 1 ]] ) 157s consump ~ price + income 157s > 157s > formula( fit2slsd1 ) 157s $demand 157s consump ~ price + income 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s 157s > formula( fit2slsd1$eq[[ 2 ]] ) 157s consump ~ price + farmPrice + trend 157s > 157s > formula( fit2slsd2r ) 157s $demand 157s consump ~ price + income 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s 157s > formula( fit2slsd2r$eq[[ 1 ]] ) 157s consump ~ price + income 157s > 157s > 157s > ## **************** model terms ******************* 157s > terms( fit2sls1 ) 157s $demand 157s consump ~ price + income 157s attr(,"variables") 157s list(consump, price, income) 157s attr(,"factors") 157s price income 157s consump 0 0 157s price 1 0 157s income 0 1 157s attr(,"term.labels") 157s [1] "price" "income" 157s attr(,"order") 157s [1] 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, income) 157s attr(,"dataClasses") 157s consump price income 157s "numeric" "numeric" "numeric" 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s attr(,"variables") 157s list(consump, price, farmPrice, trend) 157s attr(,"factors") 157s price farmPrice trend 157s consump 0 0 0 157s price 1 0 0 157s farmPrice 0 1 0 157s trend 0 0 1 157s attr(,"term.labels") 157s [1] "price" "farmPrice" "trend" 157s attr(,"order") 157s [1] 1 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, farmPrice, trend) 157s attr(,"dataClasses") 157s consump price farmPrice trend 157s "numeric" "numeric" "numeric" "numeric" 157s 157s > terms( fit2sls1$eq[[ 1 ]] ) 157s consump ~ price + income 157s attr(,"variables") 157s list(consump, price, income) 157s attr(,"factors") 157s price income 157s consump 0 0 157s price 1 0 157s income 0 1 157s attr(,"term.labels") 157s [1] "price" "income" 157s attr(,"order") 157s [1] 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, income) 157s attr(,"dataClasses") 157s consump price income 157s "numeric" "numeric" "numeric" 157s > 157s > terms( fit2sls2s ) 157s $demand 157s consump ~ price + income 157s attr(,"variables") 157s list(consump, price, income) 157s attr(,"factors") 157s price income 157s consump 0 0 157s price 1 0 157s income 0 1 157s attr(,"term.labels") 157s [1] "price" "income" 157s attr(,"order") 157s [1] 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, income) 157s attr(,"dataClasses") 157s consump price income 157s "numeric" "numeric" "numeric" 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s attr(,"variables") 157s list(consump, price, farmPrice, trend) 157s attr(,"factors") 157s price farmPrice trend 157s consump 0 0 0 157s price 1 0 0 157s farmPrice 0 1 0 157s trend 0 0 1 157s attr(,"term.labels") 157s [1] "price" "farmPrice" "trend" 157s attr(,"order") 157s [1] 1 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, farmPrice, trend) 157s attr(,"dataClasses") 157s consump price farmPrice trend 157s "numeric" "numeric" "numeric" "numeric" 157s 157s > terms( fit2sls2s$eq[[ 2 ]] ) 157s consump ~ price + farmPrice + trend 157s attr(,"variables") 157s list(consump, price, farmPrice, trend) 157s attr(,"factors") 157s price farmPrice trend 157s consump 0 0 0 157s price 1 0 0 157s farmPrice 0 1 0 157s trend 0 0 1 157s attr(,"term.labels") 157s [1] "price" "farmPrice" "trend" 157s attr(,"order") 157s [1] 1 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, farmPrice, trend) 157s attr(,"dataClasses") 157s consump price farmPrice trend 157s "numeric" "numeric" "numeric" "numeric" 157s > 157s > terms( fit2sls3 ) 157s $demand 157s consump ~ price + income 157s attr(,"variables") 157s list(consump, price, income) 157s attr(,"factors") 157s price income 157s consump 0 0 157s price 1 0 157s income 0 1 157s attr(,"term.labels") 157s [1] "price" "income" 157s attr(,"order") 157s [1] 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, income) 157s attr(,"dataClasses") 157s consump price income 157s "numeric" "numeric" "numeric" 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s attr(,"variables") 157s list(consump, price, farmPrice, trend) 157s attr(,"factors") 157s price farmPrice trend 157s consump 0 0 0 157s price 1 0 0 157s farmPrice 0 1 0 157s trend 0 0 1 157s attr(,"term.labels") 157s [1] "price" "farmPrice" "trend" 157s attr(,"order") 157s [1] 1 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, farmPrice, trend) 157s attr(,"dataClasses") 157s consump price farmPrice trend 157s "numeric" "numeric" "numeric" "numeric" 157s 157s > terms( fit2sls3$eq[[ 1 ]] ) 157s consump ~ price + income 157s attr(,"variables") 157s list(consump, price, income) 157s attr(,"factors") 157s price income 157s consump 0 0 157s price 1 0 157s income 0 1 157s attr(,"term.labels") 157s [1] "price" "income" 157s attr(,"order") 157s [1] 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, income) 157s attr(,"dataClasses") 157s consump price income 157s "numeric" "numeric" "numeric" 157s > 157s > terms( fit2sls4r ) 157s $demand 157s consump ~ price + income 157s attr(,"variables") 157s list(consump, price, income) 157s attr(,"factors") 157s price income 157s consump 0 0 157s price 1 0 157s income 0 1 157s attr(,"term.labels") 157s [1] "price" "income" 157s attr(,"order") 157s [1] 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, income) 157s attr(,"dataClasses") 157s consump price income 157s "numeric" "numeric" "numeric" 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s attr(,"variables") 157s list(consump, price, farmPrice, trend) 157s attr(,"factors") 157s price farmPrice trend 157s consump 0 0 0 157s price 1 0 0 157s farmPrice 0 1 0 157s trend 0 0 1 157s attr(,"term.labels") 157s [1] "price" "farmPrice" "trend" 157s attr(,"order") 157s [1] 1 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, farmPrice, trend) 157s attr(,"dataClasses") 157s consump price farmPrice trend 157s "numeric" "numeric" "numeric" "numeric" 157s 157s > terms( fit2sls4r$eq[[ 2 ]] ) 157s consump ~ price + farmPrice + trend 157s attr(,"variables") 157s list(consump, price, farmPrice, trend) 157s attr(,"factors") 157s price farmPrice trend 157s consump 0 0 0 157s price 1 0 0 157s farmPrice 0 1 0 157s trend 0 0 1 157s attr(,"term.labels") 157s [1] "price" "farmPrice" "trend" 157s attr(,"order") 157s [1] 1 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, farmPrice, trend) 157s attr(,"dataClasses") 157s consump price farmPrice trend 157s "numeric" "numeric" "numeric" "numeric" 157s > 157s > terms( fit2sls5rs ) 157s $demand 157s consump ~ price + income 157s attr(,"variables") 157s list(consump, price, income) 157s attr(,"factors") 157s price income 157s consump 0 0 157s price 1 0 157s income 0 1 157s attr(,"term.labels") 157s [1] "price" "income" 157s attr(,"order") 157s [1] 1 1 157s attr(,"intercept") 157s [1] 1 157s attr(,"response") 157s [1] 1 157s attr(,".Environment") 157s 157s attr(,"predvars") 157s list(consump, price, income) 157s attr(,"dataClasses") 157s consump price income 157s "numeric" "numeric" "numeric" 157s 157s $supply 157s consump ~ price + farmPrice + trend 157s attr(,"variables") 157s list(consump, price, farmPrice, trend) 157s attr(,"factors") 157s price farmPrice trend 157s consump 0 0 0 158s price 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "price" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 1 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(consump, price, farmPrice, trend) 158s attr(,"dataClasses") 158s consump price farmPrice trend 158s "numeric" "numeric" "numeric" "numeric" 158s 158s > terms( fit2sls5rs$eq[[ 1 ]] ) 158s consump ~ price + income 158s attr(,"variables") 158s list(consump, price, income) 158s attr(,"factors") 158s price income 158s consump 0 0 158s price 1 0 158s income 0 1 158s attr(,"term.labels") 158s [1] "price" "income" 158s attr(,"order") 158s [1] 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 1 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(consump, price, income) 158s attr(,"dataClasses") 158s consump price income 158s "numeric" "numeric" "numeric" 158s > 158s > terms( fit2slsd1 ) 158s $demand 158s consump ~ price + income 158s attr(,"variables") 158s list(consump, price, income) 158s attr(,"factors") 158s price income 158s consump 0 0 158s price 1 0 158s income 0 1 158s attr(,"term.labels") 158s [1] "price" "income" 158s attr(,"order") 158s [1] 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 1 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(consump, price, income) 158s attr(,"dataClasses") 158s consump price income 158s "numeric" "numeric" "numeric" 158s 158s $supply 158s consump ~ price + farmPrice + trend 158s attr(,"variables") 158s list(consump, price, farmPrice, trend) 158s attr(,"factors") 158s price farmPrice trend 158s consump 0 0 0 158s price 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "price" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 1 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(consump, price, farmPrice, trend) 158s attr(,"dataClasses") 158s consump price farmPrice trend 158s "numeric" "numeric" "numeric" "numeric" 158s 158s > terms( fit2slsd1$eq[[ 2 ]] ) 158s consump ~ price + farmPrice + trend 158s attr(,"variables") 158s list(consump, price, farmPrice, trend) 158s attr(,"factors") 158s price farmPrice trend 158s consump 0 0 0 158s price 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "price" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 1 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(consump, price, farmPrice, trend) 158s attr(,"dataClasses") 158s consump price farmPrice trend 158s "numeric" "numeric" "numeric" "numeric" 158s > 158s > terms( fit2slsd2r ) 158s $demand 158s consump ~ price + income 158s attr(,"variables") 158s list(consump, price, income) 158s attr(,"factors") 158s price income 158s consump 0 0 158s price 1 0 158s income 0 1 158s attr(,"term.labels") 158s [1] "price" "income" 158s attr(,"order") 158s [1] 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 1 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(consump, price, income) 158s attr(,"dataClasses") 158s consump price income 158s "numeric" "numeric" "numeric" 158s 158s $supply 158s consump ~ price + farmPrice + trend 158s attr(,"variables") 158s list(consump, price, farmPrice, trend) 158s attr(,"factors") 158s price farmPrice trend 158s consump 0 0 0 158s price 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "price" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 1 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(consump, price, farmPrice, trend) 158s attr(,"dataClasses") 158s consump price farmPrice trend 158s "numeric" "numeric" "numeric" "numeric" 158s 158s > terms( fit2slsd2r$eq[[ 1 ]] ) 158s consump ~ price + income 158s attr(,"variables") 158s list(consump, price, income) 158s attr(,"factors") 158s price income 158s consump 0 0 158s price 1 0 158s income 0 1 158s attr(,"term.labels") 158s [1] "price" "income" 158s attr(,"order") 158s [1] 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 1 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(consump, price, income) 158s attr(,"dataClasses") 158s consump price income 158s "numeric" "numeric" "numeric" 158s > 158s > 158s > ## **************** terms of instruments ******************* 158s > fit2sls1$eq[[ 1 ]]$termsInst 158s ~income + farmPrice + trend 158s attr(,"variables") 158s list(income, farmPrice, trend) 158s attr(,"factors") 158s income farmPrice trend 158s income 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "income" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 0 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(income, farmPrice, trend) 158s attr(,"dataClasses") 158s income farmPrice trend 158s "numeric" "numeric" "numeric" 158s > 158s > fit2sls2s$eq[[ 2 ]]$termsInst 158s ~income + farmPrice + trend 158s attr(,"variables") 158s list(income, farmPrice, trend) 158s attr(,"factors") 158s income farmPrice trend 158s income 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "income" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 0 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(income, farmPrice, trend) 158s attr(,"dataClasses") 158s income farmPrice trend 158s "numeric" "numeric" "numeric" 158s > 158s > fit2sls3$eq[[ 1 ]]$termsInst 158s ~income + farmPrice + trend 158s attr(,"variables") 158s list(income, farmPrice, trend) 158s attr(,"factors") 158s income farmPrice trend 158s income 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "income" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 0 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(income, farmPrice, trend) 158s attr(,"dataClasses") 158s income farmPrice trend 158s "numeric" "numeric" "numeric" 158s > 158s > fit2sls4r$eq[[ 2 ]]$termsInst 158s ~income + farmPrice + trend 158s attr(,"variables") 158s list(income, farmPrice, trend) 158s attr(,"factors") 158s income farmPrice trend 158s income 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "income" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 0 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(income, farmPrice, trend) 158s attr(,"dataClasses") 158s income farmPrice trend 158s "numeric" "numeric" "numeric" 158s > 158s > fit2sls5rs$eq[[ 1 ]]$termsInst 158s ~income + farmPrice + trend 158s attr(,"variables") 158s list(income, farmPrice, trend) 158s attr(,"factors") 158s income farmPrice trend 158s income 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "income" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 0 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(income, farmPrice, trend) 158s attr(,"dataClasses") 158s income farmPrice trend 158s "numeric" "numeric" "numeric" 158s > 158s > fit2slsd1$eq[[ 2 ]]$termsInst 158s ~income + farmPrice + trend 158s attr(,"variables") 158s list(income, farmPrice, trend) 158s attr(,"factors") 158s income farmPrice trend 158s income 1 0 0 158s farmPrice 0 1 0 158s trend 0 0 1 158s attr(,"term.labels") 158s [1] "income" "farmPrice" "trend" 158s attr(,"order") 158s [1] 1 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 0 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(income, farmPrice, trend) 158s attr(,"dataClasses") 158s income farmPrice trend 158s "numeric" "numeric" "numeric" 158s > 158s > fit2slsd2r$eq[[ 1 ]]$termsInst 158s ~income + farmPrice 158s attr(,"variables") 158s list(income, farmPrice) 158s attr(,"factors") 158s income farmPrice 158s income 1 0 158s farmPrice 0 1 158s attr(,"term.labels") 158s [1] "income" "farmPrice" 158s attr(,"order") 158s [1] 1 1 158s attr(,"intercept") 158s [1] 1 158s attr(,"response") 158s [1] 0 158s attr(,".Environment") 158s 158s attr(,"predvars") 158s list(income, farmPrice) 158s attr(,"dataClasses") 158s income farmPrice 158s "numeric" "numeric" 158s > 158s > 158s > ## **************** estfun ************************ 158s > library( "sandwich" ) 158s > 158s > estfun( fit2sls1 ) 158s demand_(Intercept) demand_price demand_income supply_(Intercept) 158s demand_1 0.6738 67.13 58.89 0.000 158s demand_2 -0.4897 -51.48 -47.80 0.000 158s demand_3 2.4440 253.65 236.33 0.000 158s demand_4 1.4958 156.35 146.88 0.000 158s demand_5 2.2975 226.65 229.29 0.000 158s demand_6 1.3235 131.89 133.02 0.000 158s demand_7 1.7917 182.70 184.90 0.000 158s demand_8 -3.6818 -376.41 -396.90 0.000 158s demand_9 -1.5729 -148.80 -151.94 0.000 158s demand_10 2.8552 264.73 253.83 0.000 158s demand_11 -0.2736 -25.29 -20.55 0.000 158s demand_12 -2.2634 -223.89 -174.06 0.000 158s demand_13 -1.7795 -181.80 -150.55 0.000 158s demand_14 0.0991 9.93 8.98 0.000 158s demand_15 2.5674 250.64 264.70 0.000 158s demand_16 -3.8102 -369.18 -400.45 0.000 158s demand_17 -0.0206 -1.81 -1.99 0.000 158s demand_18 -2.8715 -290.19 -299.78 0.000 158s demand_19 1.6632 176.41 184.12 0.000 158s demand_20 -0.4478 -51.23 -56.92 0.000 158s supply_1 0.0000 0.00 0.00 -0.268 158s supply_2 0.0000 0.00 0.00 -1.418 158s supply_3 0.0000 0.00 0.00 1.625 158s supply_4 0.0000 0.00 0.00 0.790 158s supply_5 0.0000 0.00 0.00 1.438 158s supply_6 0.0000 0.00 0.00 0.613 158s supply_7 0.0000 0.00 0.00 1.217 158s supply_8 0.0000 0.00 0.00 -4.265 158s supply_9 0.0000 0.00 0.00 -1.956 158s supply_10 0.0000 0.00 0.00 2.785 158s supply_11 0.0000 0.00 0.00 0.233 158s supply_12 0.0000 0.00 0.00 -1.426 158s supply_13 0.0000 0.00 0.00 -0.935 158s supply_14 0.0000 0.00 0.00 0.803 158s supply_15 0.0000 0.00 0.00 2.886 158s supply_16 0.0000 0.00 0.00 -3.454 158s supply_17 0.0000 0.00 0.00 0.391 158s supply_18 0.0000 0.00 0.00 -2.061 158s supply_19 0.0000 0.00 0.00 2.596 158s supply_20 0.0000 0.00 0.00 0.406 158s supply_price supply_farmPrice supply_trend 158s demand_1 0.0 0.0 0.000 158s demand_2 0.0 0.0 0.000 158s demand_3 0.0 0.0 0.000 158s demand_4 0.0 0.0 0.000 158s demand_5 0.0 0.0 0.000 158s demand_6 0.0 0.0 0.000 158s demand_7 0.0 0.0 0.000 158s demand_8 0.0 0.0 0.000 158s demand_9 0.0 0.0 0.000 158s demand_10 0.0 0.0 0.000 158s demand_11 0.0 0.0 0.000 158s demand_12 0.0 0.0 0.000 158s demand_13 0.0 0.0 0.000 158s demand_14 0.0 0.0 0.000 158s demand_15 0.0 0.0 0.000 158s demand_16 0.0 0.0 0.000 158s demand_17 0.0 0.0 0.000 158s demand_18 0.0 0.0 0.000 158s demand_19 0.0 0.0 0.000 158s demand_20 0.0 0.0 0.000 158s supply_1 -26.7 -26.3 -0.268 158s supply_2 -149.1 -140.5 -2.836 158s supply_3 168.7 161.1 4.876 158s supply_4 82.6 77.5 3.159 158s supply_5 141.9 159.3 7.190 158s supply_6 61.1 66.4 3.680 158s supply_7 124.1 128.5 8.520 158s supply_8 -436.1 -468.3 -34.122 158s supply_9 -185.0 -212.6 -17.602 158s supply_10 258.2 280.1 27.848 158s supply_11 21.5 18.8 2.558 158s supply_12 -141.0 -97.8 -17.107 158s supply_13 -95.5 -66.3 -12.152 158s supply_14 80.6 65.4 11.246 158s supply_15 281.7 295.2 43.286 158s supply_16 -334.7 -362.7 -55.267 158s supply_17 34.3 43.2 6.650 158s supply_18 -208.3 -190.7 -37.106 158s supply_19 275.4 231.8 49.327 158s supply_20 46.5 37.8 8.122 158s > round( colSums( estfun( fit2sls1 ) ), digits = 7 ) 158s demand_(Intercept) demand_price demand_income supply_(Intercept) 158s 0 0 0 0 158s supply_price supply_farmPrice supply_trend 158s 0 0 0 158s > 158s > estfun( fit2sls1s ) 158s demand_(Intercept) demand_price demand_income supply_(Intercept) 158s demand_1 0.6738 67.13 58.89 0.000 158s demand_2 -0.4897 -51.48 -47.80 0.000 158s demand_3 2.4440 253.65 236.33 0.000 158s demand_4 1.4958 156.35 146.88 0.000 158s demand_5 2.2975 226.65 229.29 0.000 158s demand_6 1.3235 131.89 133.02 0.000 158s demand_7 1.7917 182.70 184.90 0.000 158s demand_8 -3.6818 -376.41 -396.90 0.000 158s demand_9 -1.5729 -148.80 -151.94 0.000 158s demand_10 2.8552 264.73 253.83 0.000 158s demand_11 -0.2736 -25.29 -20.55 0.000 158s demand_12 -2.2634 -223.89 -174.06 0.000 158s demand_13 -1.7795 -181.80 -150.55 0.000 158s demand_14 0.0991 9.93 8.98 0.000 158s demand_15 2.5674 250.64 264.70 0.000 158s demand_16 -3.8102 -369.18 -400.45 0.000 158s demand_17 -0.0206 -1.81 -1.99 0.000 158s demand_18 -2.8715 -290.19 -299.78 0.000 158s demand_19 1.6632 176.41 184.12 0.000 158s demand_20 -0.4478 -51.23 -56.92 0.000 158s supply_1 0.0000 0.00 0.00 -0.268 158s supply_2 0.0000 0.00 0.00 -1.418 158s supply_3 0.0000 0.00 0.00 1.625 158s supply_4 0.0000 0.00 0.00 0.790 158s supply_5 0.0000 0.00 0.00 1.438 158s supply_6 0.0000 0.00 0.00 0.613 158s supply_7 0.0000 0.00 0.00 1.217 158s supply_8 0.0000 0.00 0.00 -4.265 158s supply_9 0.0000 0.00 0.00 -1.956 158s supply_10 0.0000 0.00 0.00 2.785 158s supply_11 0.0000 0.00 0.00 0.233 158s supply_12 0.0000 0.00 0.00 -1.426 158s supply_13 0.0000 0.00 0.00 -0.935 158s supply_14 0.0000 0.00 0.00 0.803 158s supply_15 0.0000 0.00 0.00 2.886 158s supply_16 0.0000 0.00 0.00 -3.454 158s supply_17 0.0000 0.00 0.00 0.391 158s supply_18 0.0000 0.00 0.00 -2.061 158s supply_19 0.0000 0.00 0.00 2.596 158s supply_20 0.0000 0.00 0.00 0.406 158s supply_price supply_farmPrice supply_trend 158s demand_1 0.0 0.0 0.000 158s demand_2 0.0 0.0 0.000 158s demand_3 0.0 0.0 0.000 158s demand_4 0.0 0.0 0.000 158s demand_5 0.0 0.0 0.000 158s demand_6 0.0 0.0 0.000 158s demand_7 0.0 0.0 0.000 158s demand_8 0.0 0.0 0.000 158s demand_9 0.0 0.0 0.000 158s demand_10 0.0 0.0 0.000 158s demand_11 0.0 0.0 0.000 158s demand_12 0.0 0.0 0.000 158s demand_13 0.0 0.0 0.000 158s demand_14 0.0 0.0 0.000 158s demand_15 0.0 0.0 0.000 158s demand_16 0.0 0.0 0.000 158s demand_17 0.0 0.0 0.000 158s demand_18 0.0 0.0 0.000 158s demand_19 0.0 0.0 0.000 158s demand_20 0.0 0.0 0.000 158s supply_1 -26.7 -26.3 -0.268 158s supply_2 -149.1 -140.5 -2.836 158s supply_3 168.7 161.1 4.876 158s supply_4 82.6 77.5 3.159 158s supply_5 141.9 159.3 7.190 158s supply_6 61.1 66.4 3.680 158s supply_7 124.1 128.5 8.520 158s supply_8 -436.1 -468.3 -34.122 158s supply_9 -185.0 -212.6 -17.602 158s supply_10 258.2 280.1 27.848 158s supply_11 21.5 18.8 2.558 158s supply_12 -141.0 -97.8 -17.107 158s supply_13 -95.5 -66.3 -12.152 158s supply_14 80.6 65.4 11.246 158s supply_15 281.7 295.2 43.286 158s supply_16 -334.7 -362.7 -55.267 158s supply_17 34.3 43.2 6.650 158s supply_18 -208.3 -190.7 -37.106 158s supply_19 275.4 231.8 49.327 158s supply_20 46.5 37.8 8.122 158s > round( colSums( estfun( fit2sls1s ) ), digits = 7 ) 158s demand_(Intercept) demand_price demand_income supply_(Intercept) 158s 0 0 0 0 158s supply_price supply_farmPrice supply_trend 158s 0 0 0 158s > 158s > estfun( fit2sls1r ) 158s demand_(Intercept) demand_price demand_income supply_(Intercept) 158s demand_1 0.6738 67.13 58.89 0.000 158s demand_2 -0.4897 -51.48 -47.80 0.000 158s demand_3 2.4440 253.65 236.33 0.000 158s demand_4 1.4958 156.35 146.88 0.000 158s demand_5 2.2975 226.65 229.29 0.000 158s demand_6 1.3235 131.89 133.02 0.000 158s demand_7 1.7917 182.70 184.90 0.000 158s demand_8 -3.6818 -376.41 -396.90 0.000 158s demand_9 -1.5729 -148.80 -151.94 0.000 158s demand_10 2.8552 264.73 253.83 0.000 158s demand_11 -0.2736 -25.29 -20.55 0.000 158s demand_12 -2.2634 -223.89 -174.06 0.000 158s demand_13 -1.7795 -181.80 -150.55 0.000 158s demand_14 0.0991 9.93 8.98 0.000 158s demand_15 2.5674 250.64 264.70 0.000 158s demand_16 -3.8102 -369.18 -400.45 0.000 158s demand_17 -0.0206 -1.81 -1.99 0.000 158s demand_18 -2.8715 -290.19 -299.78 0.000 158s demand_19 1.6632 176.41 184.12 0.000 158s demand_20 -0.4478 -51.23 -56.92 0.000 158s supply_1 0.0000 0.00 0.00 -0.268 158s supply_2 0.0000 0.00 0.00 -1.418 158s supply_3 0.0000 0.00 0.00 1.625 158s supply_4 0.0000 0.00 0.00 0.790 158s supply_5 0.0000 0.00 0.00 1.438 158s supply_6 0.0000 0.00 0.00 0.613 158s supply_7 0.0000 0.00 0.00 1.217 158s supply_8 0.0000 0.00 0.00 -4.265 158s supply_9 0.0000 0.00 0.00 -1.956 158s supply_10 0.0000 0.00 0.00 2.785 158s supply_11 0.0000 0.00 0.00 0.233 158s supply_12 0.0000 0.00 0.00 -1.426 158s supply_13 0.0000 0.00 0.00 -0.935 158s supply_14 0.0000 0.00 0.00 0.803 158s supply_15 0.0000 0.00 0.00 2.886 158s supply_16 0.0000 0.00 0.00 -3.454 158s supply_17 0.0000 0.00 0.00 0.391 158s supply_18 0.0000 0.00 0.00 -2.061 158s supply_19 0.0000 0.00 0.00 2.596 158s supply_20 0.0000 0.00 0.00 0.406 158s supply_price supply_farmPrice supply_trend 158s demand_1 0.0 0.0 0.000 158s demand_2 0.0 0.0 0.000 158s demand_3 0.0 0.0 0.000 158s demand_4 0.0 0.0 0.000 158s demand_5 0.0 0.0 0.000 158s demand_6 0.0 0.0 0.000 158s demand_7 0.0 0.0 0.000 158s demand_8 0.0 0.0 0.000 158s demand_9 0.0 0.0 0.000 158s demand_10 0.0 0.0 0.000 158s demand_11 0.0 0.0 0.000 158s demand_12 0.0 0.0 0.000 158s demand_13 0.0 0.0 0.000 158s demand_14 0.0 0.0 0.000 158s demand_15 0.0 0.0 0.000 158s demand_16 0.0 0.0 0.000 158s demand_17 0.0 0.0 0.000 158s demand_18 0.0 0.0 0.000 158s demand_19 0.0 0.0 0.000 158s demand_20 0.0 0.0 0.000 158s supply_1 -26.7 -26.3 -0.268 158s supply_2 -149.1 -140.5 -2.836 158s supply_3 168.7 161.1 4.876 158s supply_4 82.6 77.5 3.159 158s supply_5 141.9 159.3 7.190 158s supply_6 61.1 66.4 3.680 158s supply_7 124.1 128.5 8.520 158s supply_8 -436.1 -468.3 -34.122 158s supply_9 -185.0 -212.6 -17.602 158s supply_10 258.2 280.1 27.848 158s supply_11 21.5 18.8 2.558 158s supply_12 -141.0 -97.8 -17.107 158s supply_13 -95.5 -66.3 -12.152 158s supply_14 80.6 65.4 11.246 158s supply_15 281.7 295.2 43.286 158s supply_16 -334.7 -362.7 -55.267 158s supply_17 34.3 43.2 6.650 158s supply_18 -208.3 -190.7 -37.106 158s supply_19 275.4 231.8 49.327 158s supply_20 46.5 37.8 8.122 158s > round( colSums( estfun( fit2sls1r ) ), digits = 7 ) 158s demand_(Intercept) demand_price demand_income supply_(Intercept) 158s 0 0 0 0 158s supply_price supply_farmPrice supply_trend 158s 0 0 0 158s > 158s > 158s > ## **************** bread ************************ 158s > bread( fit2sls1 ) 158s demand_(Intercept) demand_price demand_income 158s demand_(Intercept) 649.07 -6.9669 0.5100 158s demand_price -6.97 0.0963 -0.0273 158s demand_income 0.51 -0.0273 0.0228 158s supply_(Intercept) 0.00 0.0000 0.0000 158s supply_price 0.00 0.0000 0.0000 158s supply_farmPrice 0.00 0.0000 0.0000 158s supply_trend 0.00 0.0000 0.0000 158s supply_(Intercept) supply_price supply_farmPrice 158s demand_(Intercept) 0.00 0.00000 0.00000 158s demand_price 0.00 0.00000 0.00000 158s demand_income 0.00 0.00000 0.00000 158s supply_(Intercept) 955.38 -7.25488 -2.14464 158s supply_price -7.25 0.06614 0.00620 158s supply_farmPrice -2.14 0.00620 0.01479 158s supply_trend -1.96 0.00384 0.00912 158s supply_trend 158s demand_(Intercept) 0.00000 158s demand_price 0.00000 158s demand_income 0.00000 158s supply_(Intercept) -1.95529 158s supply_price 0.00384 158s supply_farmPrice 0.00912 158s supply_trend 0.06577 158s > 158s > bread( fit2sls1s ) 158s demand_(Intercept) demand_price demand_income 158s demand_(Intercept) 649.07 -6.9669 0.5100 158s demand_price -6.97 0.0963 -0.0273 158s demand_income 0.51 -0.0273 0.0228 158s supply_(Intercept) 0.00 0.0000 0.0000 158s supply_price 0.00 0.0000 0.0000 158s supply_farmPrice 0.00 0.0000 0.0000 158s supply_trend 0.00 0.0000 0.0000 158s supply_(Intercept) supply_price supply_farmPrice 158s demand_(Intercept) 0.00 0.00000 0.00000 158s demand_price 0.00 0.00000 0.00000 158s demand_income 0.00 0.00000 0.00000 158s supply_(Intercept) 955.38 -7.25488 -2.14464 158s supply_price -7.25 0.06614 0.00620 158s supply_farmPrice -2.14 0.00620 0.01479 158s supply_trend -1.96 0.00384 0.00912 158s supply_trend 158s demand_(Intercept) 0.00000 158s demand_price 0.00000 158s demand_income 0.00000 158s supply_(Intercept) -1.95529 158s supply_price 0.00384 158s supply_farmPrice 0.00912 158s supply_trend 0.06577 158s > 158s > bread( fit2sls1r ) 158s demand_(Intercept) demand_price demand_income 158s demand_(Intercept) 649.07 -6.9669 0.5100 158s demand_price -6.97 0.0963 -0.0273 158s demand_income 0.51 -0.0273 0.0228 158s supply_(Intercept) 0.00 0.0000 0.0000 158s supply_price 0.00 0.0000 0.0000 158s supply_farmPrice 0.00 0.0000 0.0000 158s supply_trend 0.00 0.0000 0.0000 158s supply_(Intercept) supply_price supply_farmPrice 158s demand_(Intercept) 0.00 0.00000 0.00000 158s demand_price 0.00 0.00000 0.00000 158s demand_income 0.00 0.00000 0.00000 158s supply_(Intercept) 955.38 -7.25488 -2.14464 158s supply_price -7.25 0.06614 0.00620 158s supply_farmPrice -2.14 0.00620 0.01479 158s supply_trend -1.96 0.00384 0.00912 158s supply_trend 158s demand_(Intercept) 0.00000 158s demand_price 0.00000 158s demand_income 0.00000 158s supply_(Intercept) -1.95529 158s supply_price 0.00384 158s supply_farmPrice 0.00912 158s supply_trend 0.06577 158s > 158s BEGIN TEST test_3sls.R 158s 158s R version 4.3.2 (2023-10-31) -- "Eye Holes" 158s Copyright (C) 2023 The R Foundation for Statistical Computing 158s Platform: x86_64-pc-linux-gnu (64-bit) 158s 158s R is free software and comes with ABSOLUTELY NO WARRANTY. 158s You are welcome to redistribute it under certain conditions. 158s Type 'license()' or 'licence()' for distribution details. 158s 158s R is a collaborative project with many contributors. 158s Type 'contributors()' for more information and 158s 'citation()' on how to cite R or R packages in publications. 158s 158s Type 'demo()' for some demos, 'help()' for on-line help, or 158s 'help.start()' for an HTML browser interface to help. 158s Type 'q()' to quit R. 158s 158s > library( systemfit ) 158s Loading required package: Matrix 159s Loading required package: car 159s Loading required package: carData 159s Loading required package: lmtest 159s Loading required package: zoo 159s 159s Attaching package: ‘zoo’ 159s 159s The following objects are masked from ‘package:base’: 159s 159s as.Date, as.Date.numeric 159s 159s 159s Please cite the 'systemfit' package as: 159s 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/. 159s 159s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 159s https://r-forge.r-project.org/projects/systemfit/ 159s > options( digits = 3 ) 159s > 159s > data( "Kmenta" ) 159s > useMatrix <- FALSE 159s > 159s > demand <- consump ~ price + income 159s > supply <- consump ~ price + farmPrice + trend 159s > inst <- ~ income + farmPrice + trend 159s > inst1 <- ~ income + farmPrice 159s > instlist <- list( inst1, inst ) 159s > system <- list( demand = demand, supply = supply ) 159s > restrm <- matrix(0,1,7) # restriction matrix "R" 159s > restrm[1,3] <- 1 159s > restrm[1,7] <- -1 159s > restrict <- "demand_income - supply_trend = 0" 159s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 159s > restr2m[1,3] <- 1 159s > restr2m[1,7] <- -1 159s > restr2m[2,2] <- -1 159s > restr2m[2,5] <- 1 159s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 159s > restrict2 <- c( "demand_income - supply_trend = 0", 159s + "- demand_price + supply_price = 0.5" ) 159s > tc <- matrix(0,7,6) 159s > tc[1,1] <- 1 159s > tc[2,2] <- 1 159s > tc[3,3] <- 1 159s > tc[4,4] <- 1 159s > tc[5,5] <- 1 159s > tc[6,6] <- 1 159s > tc[7,3] <- 1 159s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 159s > restr3m[1,2] <- -1 159s > restr3m[1,5] <- 1 159s > restr3q <- c( 0.5 ) # restriction vector "q" 2 159s > restrict3 <- "- C2 + C5 = 0.5" 159s > 159s > 159s > ## *************** 3SLS estimation ************************ 159s > fit3sls <- list() 159s > formulas <- c( "GLS", "IV", "Schmidt", "GMM", "EViews" ) 159s > for( i in seq( along = formulas ) ) { 159s + fit3sls[[ i ]] <- list() 159s + 159s + print( "***************************************************" ) 159s + print( paste( "3SLS formula:", formulas[ i ] ) ) 159s + print( "************* 3SLS *********************************" ) 159s + fit3sls[[ i ]]$e1 <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, method3sls = formulas[ i ], useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e1 ) ) 159s + 159s + print( "********************* 3SLS EViews-like *****************" ) 159s + fit3sls[[ i ]]$e1e <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, methodResidCov = "noDfCor", method3sls = formulas[ i ], 159s + useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e1e, useDfSys = TRUE ) ) 159s + 159s + print( "********************* 3SLS with methodResidCov = Theil *****************" ) 159s + fit3sls[[ i ]]$e1c <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, methodResidCov = "Theil", method3sls = formulas[ i ], 159s + x = TRUE, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e1c, useDfSys = TRUE ) ) 159s + 159s + print( "*************** W3SLS with methodResidCov = Theil *****************" ) 159s + fit3sls[[ i ]]$e1wc <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, methodResidCov = "Theil", method3sls = formulas[ i ], 159s + residCovWeighted = TRUE, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e1wc, useDfSys = TRUE ) ) 159s + 159s + 159s + print( "*************** 3SLS with restriction *****************" ) 159s + fit3sls[[ i ]]$e2 <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.matrix = restrm, method3sls = formulas[ i ], 159s + x = TRUE, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e2 ) ) 159s + # the same with symbolically specified restrictions 159s + fit3sls[[ i ]]$e2Sym <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.matrix = restrict, method3sls = formulas[ i ], 159s + x = TRUE, useMatrix = useMatrix ) 159s + print( all.equal( fit3sls[[ i ]]$e2, fit3sls[[ i ]]$e2Sym ) ) 159s + 159s + print( "************** 3SLS with restriction (EViews-like) *****************" ) 159s + fit3sls[[ i ]]$e2e <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restrm, 159s + method3sls = formulas[ i ], useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e2e, useDfSys = TRUE ) ) 159s + print( nobs( fit3sls[[i]]$e2e )) 159s + 159s + print( "*************** W3SLS with restriction *****************" ) 159s + fit3sls[[ i ]]$e2w <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.matrix = restrm, method3sls = formulas[ i ], 159s + residCovWeighted = TRUE, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e2w ) ) 159s + 159s + 159s + print( "*************** 3SLS with restriction via restrict.regMat ********************" ) 159s + fit3sls[[ i ]]$e3 <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.regMat = tc, method3sls = formulas[ i ], 159s + useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e3 ) ) 159s + 159s + print( "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" ) 159s + fit3sls[[ i ]]$e3e <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, methodResidCov = "noDfCor", restrict.regMat = tc, 159s + method3sls = formulas[ i ], x = TRUE, 159s + useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e3e, useDfSys = TRUE ) ) 159s + 159s + print( "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" ) 159s + fit3sls[[ i ]]$e3we <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, methodResidCov = "noDfCor", restrict.regMat = tc, 159s + method3sls = formulas[ i ], residCovWeighted = TRUE, 159s + useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e3we, useDfSys = TRUE ) ) 159s + 159s + 159s + print( "*************** 3SLS with 2 restrictions **********************" ) 159s + fit3sls[[ i ]]$e4 <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.matrix = restr2m, restrict.rhs = restr2q, 159s + method3sls = formulas[ i ], x = TRUE, 159s + useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e4 ) ) 159s + # the same with symbolically specified restrictions 159s + fit3sls[[ i ]]$e4Sym <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.matrix = restrict2, method3sls = formulas[ i ], 159s + x = TRUE, useMatrix = useMatrix ) 159s + print( all.equal( fit3sls[[ i ]]$e4, fit3sls[[ i ]]$e4Sym ) ) 159s + 159s + print( "*************** 3SLS with 2 restrictions (EViews-like) ************" ) 159s + fit3sls[[ i ]]$e4e <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restr2m, 159s + restrict.rhs = restr2q, method3sls = formulas[ i ], 159s + useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e4e, useDfSys = TRUE ) ) 159s + 159s + print( "********** W3SLS with 2 (symbolic) restrictions ***************" ) 159s + fit3sls[[ i ]]$e4wSym <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.matrix = restrict2, method3sls = formulas[ i ], 159s + residCovWeighted = TRUE, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e4wSym ) ) 159s + 159s + 159s + print( "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" ) 159s + fit3sls[[ i ]]$e5 <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.regMat = tc, restrict.matrix = restr3m, 159s + restrict.rhs = restr3q, method3sls = formulas[ i ], 159s + useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e5 ) ) 159s + # the same with symbolically specified restrictions 159s + fit3sls[[ i ]]$e5Sym <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.regMat = tc, restrict.matrix = restrict3, 159s + method3sls = formulas[ i ], useMatrix = useMatrix ) 159s + print( all.equal( fit3sls[[ i ]]$e5, fit3sls[[ i ]]$e5Sym ) ) 159s + 159s + print( "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" ) 159s + fit3sls[[ i ]]$e5e <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.regMat = tc, methodResidCov = "noDfCor", 159s + restrict.matrix = restr3m, restrict.rhs = restr3q, 159s + method3sls = formulas[ i ], x = TRUE, 159s + useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e5e, useDfSys = TRUE ) ) 159s + 159s + print( "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" ) 159s + fit3sls[[ i ]]$e5we <- systemfit( system, "3SLS", data = Kmenta, 159s + inst = inst, restrict.regMat = tc, methodResidCov = "noDfCor", 159s + restrict.matrix = restr3m, restrict.rhs = restr3q, method3sls = formulas[ i ], 159s + residCovWeighted = TRUE, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$e5we, useDfSys = TRUE ) ) 159s + 159s + ## *********** estimations with a single regressor ************ 159s + fit3sls[[ i ]]$S1 <- systemfit( 159s + list( farmPrice ~ consump - 1, price ~ consump + trend ), "3SLS", 159s + data = Kmenta, inst = ~ trend + income, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$S1 ) ) 159s + fit3sls[[ i ]]$S2 <- systemfit( 159s + list( consump ~ farmPrice - 1, consump ~ trend - 1 ), "3SLS", 159s + data = Kmenta, inst = ~ price + income, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$S2 ) ) 159s + fit3sls[[ i ]]$S3 <- systemfit( 159s + list( consump ~ trend - 1, farmPrice ~ trend - 1 ), "3SLS", 159s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$S3 ) ) 159s + fit3sls[[ i ]]$S4 <- systemfit( 159s + list( consump ~ farmPrice - 1, price ~ trend - 1 ), "3SLS", 159s + data = Kmenta, inst = ~ farmPrice + trend + income, 159s + restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$S4 ) ) 159s + fit3sls[[ i ]]$S5 <- systemfit( 159s + list( consump ~ 1, price ~ 1 ), "3SLS", 159s + data = Kmenta, inst = ~ income, useMatrix = useMatrix ) 159s + print( summary( fit3sls[[ i ]]$S5 ) ) 159s + } 159s [1] "***************************************************" 159s [1] "3SLS formula: GLS" 159s [1] "************* 3SLS *********************************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 174 1.03 0.676 0.786 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 107.9 6.75 2.60 0.598 0.522 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.87 4.36 159s supply 4.36 6.04 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 5.00 159s supply 5.00 6.74 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.00 0.98 159s supply 0.98 1.00 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 159s price -0.2436 0.0965 -2.52 0.022 * 159s income 0.3140 0.0469 6.69 3.8e-06 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 159s price 0.2286 0.0997 2.29 0.03571 * 159s farmPrice 0.2282 0.0440 5.19 9e-05 *** 159s trend 0.3611 0.0729 4.95 0.00014 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.597 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 159s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 159s 159s [1] "********************* 3SLS EViews-like *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 173 0.719 0.677 0.748 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 107.2 6.70 2.59 0.600 0.525 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.29 3.59 159s supply 3.59 4.83 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.29 4.11 159s supply 4.11 5.36 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.979 159s supply 0.979 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 159s price -0.2436 0.0890 -2.74 0.0099 ** 159s income 0.3140 0.0433 7.25 2.5e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 159s price 0.2289 0.0892 2.57 0.015 * 159s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 159s trend 0.3579 0.0652 5.49 4.3e-06 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.589 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 159s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 159s 159s [1] "********************* 3SLS with methodResidCov = Theil *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 174 -0.718 0.675 0.922 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 108.7 6.79 2.61 0.594 0.518 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.87 4.50 159s supply 4.50 6.04 159s 159s warning: this covariance matrix is NOT positive semidefinit! 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 5.2 159s supply 5.20 6.8 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.981 159s supply 0.981 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 159s price -0.2436 0.0965 -2.52 0.017 * 159s income 0.3140 0.0469 6.69 1.3e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 159s price 0.2282 0.0997 2.29 0.02855 * 159s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 159s trend 0.3648 0.0707 5.16 1.1e-05 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.607 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 159s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 159s 159s [1] "*************** W3SLS with methodResidCov = Theil *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 174 -0.718 0.675 0.922 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 108.7 6.79 2.61 0.594 0.518 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.87 4.50 159s supply 4.50 6.04 159s 159s warning: this covariance matrix is NOT positive semidefinit! 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 5.2 159s supply 5.20 6.8 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.981 159s supply 0.981 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 159s price -0.2436 0.0965 -2.52 0.017 * 159s income 0.3140 0.0469 6.69 1.3e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 159s price 0.2282 0.0997 2.29 0.02855 * 159s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 159s trend 0.3648 0.0707 5.16 1.1e-05 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.607 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 159s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 159s 159s [1] "*************** 3SLS with restriction *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 173 1.27 0.678 0.722 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.8 3.99 2.00 0.747 0.717 159s supply 20 16 104.8 6.55 2.56 0.609 0.536 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.97 4.55 159s supply 4.55 6.13 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.99 4.98 159s supply 4.98 6.55 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.975 159s supply 0.975 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 159s price -0.222 0.096 -2.31 0.027 * 159s income 0.296 0.045 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.997 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 159s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 159s price 0.2193 0.1002 2.19 0.036 * 159s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 159s trend 0.2956 0.0450 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.559 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 159s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 159s 159s [1] "Component “call”: target, current do not match when deparsed" 159s [1] "************** 3SLS with restriction (EViews-like) *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 171 0.887 0.68 0.678 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.5 3.97 1.99 0.748 0.719 159s supply 20 16 104.0 6.50 2.55 0.612 0.539 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.37 3.75 159s supply 3.75 4.91 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.37 4.08 159s supply 4.08 5.20 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.974 159s supply 0.974 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 159s price -0.2243 0.0888 -2.53 0.016 * 159s income 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.992 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 159s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 159s price 0.2207 0.0896 2.46 0.019 * 159s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 159s trend 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.55 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 159s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 159s 159s [1] 40 159s [1] "*************** W3SLS with restriction *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 173 1.24 0.677 0.725 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 68.1 4.00 2.00 0.746 0.716 159s supply 20 16 105.2 6.57 2.56 0.608 0.534 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.93 4.56 159s supply 4.56 6.15 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 4.00 5.01 159s supply 5.01 6.57 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.976 159s supply 0.976 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 159s price -0.2194 0.0954 -2.3 0.028 * 159s income 0.2938 0.0445 6.6 1.4e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.001 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 159s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 159s price 0.2184 0.1003 2.18 0.036 * 159s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 159s trend 0.2938 0.0445 6.60 1.4e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.564 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 159s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 159s 159s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 173 1.27 0.678 0.722 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.8 3.99 2.00 0.747 0.717 159s supply 20 16 104.8 6.55 2.56 0.609 0.536 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.97 4.55 159s supply 4.55 6.13 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.99 4.98 159s supply 4.98 6.55 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.975 159s supply 0.975 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 159s price -0.222 0.096 -2.31 0.027 * 159s income 0.296 0.045 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.997 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 159s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 159s price 0.2193 0.1002 2.19 0.036 * 159s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 159s trend 0.2956 0.0450 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.559 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 159s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 159s 159s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 171 0.887 0.68 0.678 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.5 3.97 1.99 0.748 0.719 159s supply 20 16 104.0 6.50 2.55 0.612 0.539 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.37 3.75 159s supply 3.75 4.91 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.37 4.08 159s supply 4.08 5.20 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.974 159s supply 0.974 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 159s price -0.2243 0.0888 -2.53 0.016 * 159s income 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.992 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 159s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 159s price 0.2207 0.0896 2.46 0.019 * 159s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 159s trend 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.55 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 159s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 159s 159s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 172 0.873 0.679 0.681 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.7 3.98 2.00 0.748 0.718 159s supply 20 16 104.3 6.52 2.55 0.611 0.538 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.35 3.76 159s supply 3.76 4.92 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.38 4.10 159s supply 4.10 5.22 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.975 159s supply 0.975 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 159s price -0.2225 0.0883 -2.52 0.017 * 159s income 0.2964 0.0416 7.13 3.1e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.995 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 159s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 159s price 0.2201 0.0897 2.45 0.019 * 159s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 159s trend 0.2964 0.0416 7.13 3.1e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.553 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 159s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 159s 159s [1] "*************** 3SLS with 2 restrictions **********************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 171 1.74 0.681 0.696 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.8 3.87 1.97 0.755 0.726 159s supply 20 16 105.4 6.59 2.57 0.607 0.533 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.89 4.53 159s supply 4.53 6.25 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 4.87 159s supply 4.87 6.59 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 159s price -0.2457 0.0891 -2.76 0.0092 ** 159s income 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.967 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 159s price 0.2543 0.0891 2.85 0.0072 ** 159s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 159s trend 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.566 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 159s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 159s 159s [1] "Component “call”: target, current do not match when deparsed" 159s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 170 1.19 0.683 0.658 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.6 3.86 1.96 0.755 0.727 159s supply 20 16 104.6 6.54 2.56 0.610 0.537 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.30 3.73 159s supply 3.73 5.00 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.28 4.00 159s supply 4.00 5.23 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 159s price -0.2494 0.0812 -3.07 0.0041 ** 159s income 0.3248 0.0209 15.57 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.964 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 159s price 0.2506 0.0812 3.09 0.0039 ** 159s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 159s trend 0.3248 0.0209 15.57 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.557 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 159s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 159s 159s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 172 1.74 0.68 0.697 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.9 3.88 1.97 0.754 0.725 159s supply 20 16 105.7 6.60 2.57 0.606 0.532 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.88 4.55 159s supply 4.55 6.27 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.88 4.88 159s supply 4.88 6.60 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 159s price -0.2443 0.0892 -2.74 0.0096 ** 159s income 0.3234 0.0229 14.14 4.4e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.969 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 159s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 159s price 0.2557 0.0892 2.87 0.0069 ** 159s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 159s trend 0.3234 0.0229 14.14 4.4e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.57 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 159s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 159s 159s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 171 1.74 0.681 0.696 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.8 3.87 1.97 0.755 0.726 159s supply 20 16 105.4 6.59 2.57 0.607 0.533 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.89 4.53 159s supply 4.53 6.25 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 4.87 159s supply 4.87 6.59 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 159s price -0.2457 0.0891 -2.76 0.0092 ** 159s income 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.967 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 159s price 0.2543 0.0891 2.85 0.0072 ** 159s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 159s trend 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.566 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 159s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 159s 159s [1] "Component “call”: target, current do not match when deparsed" 159s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 170 1.19 0.683 0.658 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.6 3.86 1.96 0.755 0.727 159s supply 20 16 104.6 6.54 2.56 0.610 0.537 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.30 3.73 159s supply 3.73 5.00 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.28 4.00 159s supply 4.00 5.23 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 159s price -0.2494 0.0812 -3.07 0.0041 ** 159s income 0.3248 0.0209 15.57 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.964 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 159s price 0.2506 0.0812 3.09 0.0039 ** 159s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 159s trend 0.3248 0.0209 15.57 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.557 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 159s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 159s 159s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 170 1.19 0.682 0.659 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.6 3.86 1.97 0.755 0.726 159s supply 20 16 104.8 6.55 2.56 0.609 0.536 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.30 3.75 159s supply 3.75 5.01 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.28 4.00 159s supply 4.00 5.24 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 159s price -0.2484 0.0812 -3.06 0.0042 ** 159s income 0.3246 0.0205 15.81 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.965 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 159s price 0.2516 0.0812 3.10 0.0038 ** 159s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 159s trend 0.3246 0.0205 15.81 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.559 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 159s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 36 3690 5613 0.012 0.368 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 2132 112.2 10.59 0.305 0.305 159s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 112.2 -44.8 159s eq2 -44.8 56.8 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 112.2 -68.3 159s eq2 -68.3 91.7 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.000 -0.674 159s eq2 -0.674 1.000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: farmPrice ~ consump - 1 159s Instruments: ~trend + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s consump 0.9588 0.0235 40.9 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 10.592 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 159s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: price ~ consump + trend 159s Instruments: ~trend + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) -92.192 49.896 -1.85 0.0821 . 159s consump 1.953 0.499 3.92 0.0011 ** 159s trend -0.469 0.247 -1.90 0.0743 . 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 9.574 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 159s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 38 56326 283068 -104 -10.6 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 2313 122 11.0 -7.63 -7.63 159s eq2 20 19 54013 2843 53.3 -200.46 -200.46 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 121 -255 159s eq2 -255 2953 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 122 -251 159s eq2 -251 2843 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.000 -0.433 159s eq2 -0.433 1.000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: consump ~ farmPrice - 1 159s Instruments: ~price + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 11.034 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 159s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: consump ~ trend - 1 159s Instruments: ~price + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s trend 9.02 1.13 8 1.7e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 53.318 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 159s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 38 167069 397886 -49.1 -0.82 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 76692 4036 63.5 -285.0 -285.0 159s eq2 20 19 90377 4757 69.0 -28.5 -28.5 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 2682 2547 159s eq2 2547 2741 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 4036 4336 159s eq2 4336 4757 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.000 0.928 159s eq2 0.928 1.000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: consump ~ trend - 1 159s Instruments: ~income + farmPrice 159s 159s Estimate Std. Error t value Pr(>|t|) 159s trend 4.162 0.723 5.75 1.5e-05 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 63.533 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 159s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: farmPrice ~ trend - 1 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s trend 3.274 0.676 4.84 0.00011 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 68.969 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 159s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 39 161126 1162329 -171 -17.4 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 3553 187 13.7 -12.3 -12.3 159s eq2 20 19 157573 8293 91.1 -235.2 -235.2 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 208 -731 159s eq2 -731 8271 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 187 -623 159s eq2 -623 8293 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.000 -0.121 159s eq2 -0.121 1.000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: consump ~ farmPrice - 1 159s Instruments: ~farmPrice + trend + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 13.675 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 159s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: price ~ trend - 1 159s Instruments: ~farmPrice + trend + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s trend 1.1122 0.0272 40.8 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 91.068 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 159s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 38 935 491 0 0 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 268 14.1 3.76 0 0 159s eq2 20 19 667 35.1 5.93 0 0 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 14.11 2.18 159s eq2 2.18 35.12 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 14.11 2.18 159s eq2 2.18 35.12 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.0000 0.0981 159s eq2 0.0981 1.0000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: consump ~ 1 159s Instruments: ~income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 100.90 0.84 120 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 3.756 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 159s Multiple R-Squared: 0 Adjusted R-Squared: 0 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: price ~ 1 159s Instruments: ~income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 100.02 1.33 75.5 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 5.926 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 159s Multiple R-Squared: 0 Adjusted R-Squared: 0 159s 159s [1] "***************************************************" 159s [1] "3SLS formula: IV" 159s [1] "************* 3SLS *********************************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 174 1.03 0.676 0.786 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 107.9 6.75 2.60 0.598 0.522 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.87 4.36 159s supply 4.36 6.04 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 5.00 159s supply 5.00 6.74 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.00 0.98 159s supply 0.98 1.00 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 159s price -0.2436 0.0965 -2.52 0.022 * 159s income 0.3140 0.0469 6.69 3.8e-06 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 159s price 0.2286 0.0997 2.29 0.03571 * 159s farmPrice 0.2282 0.0440 5.19 9e-05 *** 159s trend 0.3611 0.0729 4.95 0.00014 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.597 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 159s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 159s 159s [1] "********************* 3SLS EViews-like *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 173 0.719 0.677 0.748 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 107.2 6.70 2.59 0.600 0.525 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.29 3.59 159s supply 3.59 4.83 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.29 4.11 159s supply 4.11 5.36 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.979 159s supply 0.979 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 159s price -0.2436 0.0890 -2.74 0.0099 ** 159s income 0.3140 0.0433 7.25 2.5e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 159s price 0.2289 0.0892 2.57 0.015 * 159s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 159s trend 0.3579 0.0652 5.49 4.3e-06 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.589 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 159s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 159s 159s [1] "********************* 3SLS with methodResidCov = Theil *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 174 -0.718 0.675 0.922 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 108.7 6.79 2.61 0.594 0.518 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.87 4.50 159s supply 4.50 6.04 159s 159s warning: this covariance matrix is NOT positive semidefinit! 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 5.2 159s supply 5.20 6.8 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.981 159s supply 0.981 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 159s price -0.2436 0.0965 -2.52 0.017 * 159s income 0.3140 0.0469 6.69 1.3e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 159s price 0.2282 0.0997 2.29 0.02855 * 159s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 159s trend 0.3648 0.0707 5.16 1.1e-05 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.607 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 159s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 159s 159s [1] "*************** W3SLS with methodResidCov = Theil *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 174 -0.718 0.675 0.922 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 108.7 6.79 2.61 0.594 0.518 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.87 4.50 159s supply 4.50 6.04 159s 159s warning: this covariance matrix is NOT positive semidefinit! 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 5.2 159s supply 5.20 6.8 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.981 159s supply 0.981 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 159s price -0.2436 0.0965 -2.52 0.017 * 159s income 0.3140 0.0469 6.69 1.3e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 159s price 0.2282 0.0997 2.29 0.02855 * 159s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 159s trend 0.3648 0.0707 5.16 1.1e-05 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.607 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 159s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 159s 159s [1] "*************** 3SLS with restriction *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 173 1.27 0.678 0.722 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.8 3.99 2.00 0.747 0.717 159s supply 20 16 104.8 6.55 2.56 0.609 0.536 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.97 4.55 159s supply 4.55 6.13 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.99 4.98 159s supply 4.98 6.55 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.975 159s supply 0.975 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 159s price -0.222 0.096 -2.31 0.027 * 159s income 0.296 0.045 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.997 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 159s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 159s price 0.2193 0.1002 2.19 0.036 * 159s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 159s trend 0.2956 0.0450 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.559 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 159s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 159s 159s [1] "Component “call”: target, current do not match when deparsed" 159s [1] "************** 3SLS with restriction (EViews-like) *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 171 0.887 0.68 0.678 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.5 3.97 1.99 0.748 0.719 159s supply 20 16 104.0 6.50 2.55 0.612 0.539 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.37 3.75 159s supply 3.75 4.91 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.37 4.08 159s supply 4.08 5.20 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.974 159s supply 0.974 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 159s price -0.2243 0.0888 -2.53 0.016 * 159s income 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.992 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 159s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 159s price 0.2207 0.0896 2.46 0.019 * 159s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 159s trend 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.55 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 159s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 159s 159s [1] 40 159s [1] "*************** W3SLS with restriction *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 173 1.24 0.677 0.725 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 68.1 4.00 2.00 0.746 0.716 159s supply 20 16 105.2 6.57 2.56 0.608 0.534 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.93 4.56 159s supply 4.56 6.15 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 4.00 5.01 159s supply 5.01 6.57 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.976 159s supply 0.976 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 159s price -0.2194 0.0954 -2.3 0.028 * 159s income 0.2938 0.0445 6.6 1.4e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.001 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 159s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 159s price 0.2184 0.1003 2.18 0.036 * 159s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 159s trend 0.2938 0.0445 6.60 1.4e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.564 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 159s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 159s 159s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 173 1.27 0.678 0.722 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.8 3.99 2.00 0.747 0.717 159s supply 20 16 104.8 6.55 2.56 0.609 0.536 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.97 4.55 159s supply 4.55 6.13 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.99 4.98 159s supply 4.98 6.55 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.975 159s supply 0.975 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 159s price -0.222 0.096 -2.31 0.027 * 159s income 0.296 0.045 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.997 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 159s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 159s price 0.2193 0.1002 2.19 0.036 * 159s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 159s trend 0.2956 0.0450 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.559 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 159s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 159s 159s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 171 0.887 0.68 0.678 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.5 3.97 1.99 0.748 0.719 159s supply 20 16 104.0 6.50 2.55 0.612 0.539 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.37 3.75 159s supply 3.75 4.91 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.37 4.08 159s supply 4.08 5.20 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.974 159s supply 0.974 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 159s price -0.2243 0.0888 -2.53 0.016 * 159s income 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.992 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 159s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 159s price 0.2207 0.0896 2.46 0.019 * 159s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 159s trend 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.55 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 159s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 159s 159s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 172 0.873 0.679 0.681 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.7 3.98 2.00 0.748 0.718 159s supply 20 16 104.3 6.52 2.55 0.611 0.538 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.35 3.76 159s supply 3.76 4.92 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.38 4.10 159s supply 4.10 5.22 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.975 159s supply 0.975 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 159s price -0.2225 0.0883 -2.52 0.017 * 159s income 0.2964 0.0416 7.13 3.1e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.995 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 159s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 159s price 0.2201 0.0897 2.45 0.019 * 159s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 159s trend 0.2964 0.0416 7.13 3.1e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.553 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 159s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 159s 159s [1] "*************** 3SLS with 2 restrictions **********************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 171 1.74 0.681 0.696 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.8 3.87 1.97 0.755 0.726 159s supply 20 16 105.4 6.59 2.57 0.607 0.533 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.89 4.53 159s supply 4.53 6.25 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 4.87 159s supply 4.87 6.59 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 159s price -0.2457 0.0891 -2.76 0.0092 ** 159s income 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.967 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 159s price 0.2543 0.0891 2.85 0.0072 ** 159s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 159s trend 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.566 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 159s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 159s 159s [1] "Component “call”: target, current do not match when deparsed" 159s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 170 1.19 0.683 0.658 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.6 3.86 1.96 0.755 0.727 159s supply 20 16 104.6 6.54 2.56 0.610 0.537 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.30 3.73 159s supply 3.73 5.00 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.28 4.00 159s supply 4.00 5.23 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 159s price -0.2494 0.0812 -3.07 0.0041 ** 159s income 0.3248 0.0209 15.57 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.964 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 159s price 0.2506 0.0812 3.09 0.0039 ** 159s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 159s trend 0.3248 0.0209 15.57 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.557 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 159s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 159s 159s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 172 1.74 0.68 0.697 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.9 3.88 1.97 0.754 0.725 159s supply 20 16 105.7 6.60 2.57 0.606 0.532 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.88 4.55 159s supply 4.55 6.27 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.88 4.88 159s supply 4.88 6.60 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 159s price -0.2443 0.0892 -2.74 0.0096 ** 159s income 0.3234 0.0229 14.14 4.4e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.969 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 159s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 159s price 0.2557 0.0892 2.87 0.0069 ** 159s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 159s trend 0.3234 0.0229 14.14 4.4e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.57 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 159s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 159s 159s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 171 1.74 0.681 0.696 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.8 3.87 1.97 0.755 0.726 159s supply 20 16 105.4 6.59 2.57 0.607 0.533 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.89 4.53 159s supply 4.53 6.25 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 4.87 159s supply 4.87 6.59 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 159s price -0.2457 0.0891 -2.76 0.0092 ** 159s income 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.967 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 159s price 0.2543 0.0891 2.85 0.0072 ** 159s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 159s trend 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.566 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 159s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 159s 159s [1] "Component “call”: target, current do not match when deparsed" 159s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 170 1.19 0.683 0.658 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.6 3.86 1.96 0.755 0.727 159s supply 20 16 104.6 6.54 2.56 0.610 0.537 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.30 3.73 159s supply 3.73 5.00 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.28 4.00 159s supply 4.00 5.23 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 159s price -0.2494 0.0812 -3.07 0.0041 ** 159s income 0.3248 0.0209 15.57 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.964 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 159s price 0.2506 0.0812 3.09 0.0039 ** 159s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 159s trend 0.3248 0.0209 15.57 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.557 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 159s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 159s 159s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 170 1.19 0.682 0.659 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.6 3.86 1.97 0.755 0.726 159s supply 20 16 104.8 6.55 2.56 0.609 0.536 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.30 3.75 159s supply 3.75 5.01 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.28 4.00 159s supply 4.00 5.24 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 159s price -0.2484 0.0812 -3.06 0.0042 ** 159s income 0.3246 0.0205 15.81 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.965 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 159s price 0.2516 0.0812 3.10 0.0038 ** 159s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 159s trend 0.3246 0.0205 15.81 < 2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.559 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 159s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 36 3690 5613 0.012 0.368 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 2132 112.2 10.59 0.305 0.305 159s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 112.2 -44.8 159s eq2 -44.8 56.8 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 112.2 -68.3 159s eq2 -68.3 91.7 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.000 -0.674 159s eq2 -0.674 1.000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: farmPrice ~ consump - 1 159s Instruments: ~trend + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s consump 0.9588 0.0235 40.9 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 10.592 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 159s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: price ~ consump + trend 159s Instruments: ~trend + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) -92.192 49.896 -1.85 0.0821 . 159s consump 1.953 0.499 3.92 0.0011 ** 159s trend -0.469 0.247 -1.90 0.0743 . 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 9.574 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 159s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 38 56326 283068 -104 -10.6 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 2313 122 11.0 -7.63 -7.63 159s eq2 20 19 54013 2843 53.3 -200.46 -200.46 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 121 -255 159s eq2 -255 2953 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 122 -251 159s eq2 -251 2843 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.000 -0.433 159s eq2 -0.433 1.000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: consump ~ farmPrice - 1 159s Instruments: ~price + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 11.034 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 159s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: consump ~ trend - 1 159s Instruments: ~price + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s trend 9.02 1.13 8 1.7e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 53.318 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 159s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 38 167069 397886 -49.1 -0.82 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 76692 4036 63.5 -285.0 -285.0 159s eq2 20 19 90377 4757 69.0 -28.5 -28.5 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 2682 2547 159s eq2 2547 2741 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 4036 4336 159s eq2 4336 4757 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.000 0.928 159s eq2 0.928 1.000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: consump ~ trend - 1 159s Instruments: ~income + farmPrice 159s 159s Estimate Std. Error t value Pr(>|t|) 159s trend 4.162 0.723 5.75 1.5e-05 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 63.533 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 159s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: farmPrice ~ trend - 1 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s trend 3.274 0.676 4.84 0.00011 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 68.969 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 159s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 39 161126 1162329 -171 -17.4 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 3553 187 13.7 -12.3 -12.3 159s eq2 20 19 157573 8293 91.1 -235.2 -235.2 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 208 -731 159s eq2 -731 8271 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 187 -623 159s eq2 -623 8293 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.000 -0.121 159s eq2 -0.121 1.000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: consump ~ farmPrice - 1 159s Instruments: ~farmPrice + trend + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 13.675 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 159s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: price ~ trend - 1 159s Instruments: ~farmPrice + trend + income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s trend 1.1122 0.0272 40.8 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 91.068 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 159s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 159s 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 38 935 491 0 0 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s eq1 20 19 268 14.1 3.76 0 0 159s eq2 20 19 667 35.1 5.93 0 0 159s 159s The covariance matrix of the residuals used for estimation 159s eq1 eq2 159s eq1 14.11 2.18 159s eq2 2.18 35.12 159s 159s The covariance matrix of the residuals 159s eq1 eq2 159s eq1 14.11 2.18 159s eq2 2.18 35.12 159s 159s The correlations of the residuals 159s eq1 eq2 159s eq1 1.0000 0.0981 159s eq2 0.0981 1.0000 159s 159s 159s 3SLS estimates for 'eq1' (equation 1) 159s Model Formula: consump ~ 1 159s Instruments: ~income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 100.90 0.84 120 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 3.756 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 159s Multiple R-Squared: 0 Adjusted R-Squared: 0 159s 159s 159s 3SLS estimates for 'eq2' (equation 2) 159s Model Formula: price ~ 1 159s Instruments: ~income 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 100.02 1.33 75.5 <2e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 5.926 on 19 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 19 159s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 159s Multiple R-Squared: 0 Adjusted R-Squared: 0 159s 159s [1] "***************************************************" 159s [1] "3SLS formula: Schmidt" 159s [1] "************* 3SLS *********************************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 174 1.03 0.676 0.786 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 107.9 6.75 2.60 0.598 0.522 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.87 4.36 159s supply 4.36 6.04 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 5.00 159s supply 5.00 6.74 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.00 0.98 159s supply 0.98 1.00 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 159s price -0.2436 0.0965 -2.52 0.022 * 159s income 0.3140 0.0469 6.69 3.8e-06 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 159s price 0.2286 0.0997 2.29 0.03571 * 159s farmPrice 0.2282 0.0440 5.19 9e-05 *** 159s trend 0.3611 0.0729 4.95 0.00014 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.597 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 159s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 159s 159s [1] "********************* 3SLS EViews-like *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 173 0.719 0.677 0.748 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 107.2 6.70 2.59 0.600 0.525 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.29 3.59 159s supply 3.59 4.83 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.29 4.11 159s supply 4.11 5.36 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.979 159s supply 0.979 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 159s price -0.2436 0.0890 -2.74 0.0099 ** 159s income 0.3140 0.0433 7.25 2.5e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 159s price 0.2289 0.0892 2.57 0.015 * 159s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 159s trend 0.3579 0.0652 5.49 4.3e-06 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.589 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 159s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 159s 159s [1] "********************* 3SLS with methodResidCov = Theil *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 174 -0.718 0.675 0.922 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 108.7 6.79 2.61 0.594 0.518 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.87 4.50 159s supply 4.50 6.04 159s 159s warning: this covariance matrix is NOT positive semidefinit! 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 5.2 159s supply 5.20 6.8 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.981 159s supply 0.981 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 159s price -0.2436 0.0965 -2.52 0.017 * 159s income 0.3140 0.0469 6.69 1.3e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 159s price 0.2282 0.0997 2.29 0.02855 * 159s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 159s trend 0.3648 0.0707 5.16 1.1e-05 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.607 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 159s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 159s 159s [1] "*************** W3SLS with methodResidCov = Theil *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 33 174 -0.718 0.675 0.922 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.7 3.87 1.97 0.755 0.726 159s supply 20 16 108.7 6.79 2.61 0.594 0.518 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.87 4.50 159s supply 4.50 6.04 159s 159s warning: this covariance matrix is NOT positive semidefinit! 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 5.2 159s supply 5.20 6.8 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.981 159s supply 0.981 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 159s price -0.2436 0.0965 -2.52 0.017 * 159s income 0.3140 0.0469 6.69 1.3e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.966 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 159s price 0.2282 0.0997 2.29 0.02855 * 159s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 159s trend 0.3648 0.0707 5.16 1.1e-05 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.607 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 159s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 159s 159s [1] "*************** 3SLS with restriction *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 173 1.27 0.678 0.722 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.8 3.99 2.00 0.747 0.717 159s supply 20 16 104.8 6.55 2.56 0.609 0.536 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.97 4.55 159s supply 4.55 6.13 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.99 4.98 159s supply 4.98 6.55 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.975 159s supply 0.975 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 159s price -0.222 0.096 -2.31 0.027 * 159s income 0.296 0.045 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.997 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 159s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 159s price 0.2193 0.1002 2.19 0.036 * 159s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 159s trend 0.2956 0.0450 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.559 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 159s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 159s 159s [1] "Component “call”: target, current do not match when deparsed" 159s [1] "************** 3SLS with restriction (EViews-like) *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 171 0.887 0.68 0.678 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.5 3.97 1.99 0.748 0.719 159s supply 20 16 104.0 6.50 2.55 0.612 0.539 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.37 3.75 159s supply 3.75 4.91 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.37 4.08 159s supply 4.08 5.20 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.974 159s supply 0.974 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 159s price -0.2243 0.0888 -2.53 0.016 * 159s income 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.992 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 159s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 159s price 0.2207 0.0896 2.46 0.019 * 159s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 159s trend 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.55 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 159s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 159s 159s [1] 40 159s [1] "*************** W3SLS with restriction *****************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 173 1.24 0.677 0.725 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 68.1 4.00 2.00 0.746 0.716 159s supply 20 16 105.2 6.57 2.56 0.608 0.534 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.93 4.56 159s supply 4.56 6.15 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 4.00 5.01 159s supply 5.01 6.57 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.976 159s supply 0.976 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 159s price -0.2194 0.0954 -2.3 0.028 * 159s income 0.2938 0.0445 6.6 1.4e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.001 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 159s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 159s price 0.2184 0.1003 2.18 0.036 * 159s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 159s trend 0.2938 0.0445 6.60 1.4e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.564 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 159s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 159s 159s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 173 1.27 0.678 0.722 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.8 3.99 2.00 0.747 0.717 159s supply 20 16 104.8 6.55 2.56 0.609 0.536 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.97 4.55 159s supply 4.55 6.13 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.99 4.98 159s supply 4.98 6.55 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.975 159s supply 0.975 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 159s price -0.222 0.096 -2.31 0.027 * 159s income 0.296 0.045 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.997 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 159s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 159s price 0.2193 0.1002 2.19 0.036 * 159s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 159s trend 0.2956 0.0450 6.57 1.6e-07 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.559 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 159s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 159s 159s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 171 0.887 0.68 0.678 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.5 3.97 1.99 0.748 0.719 159s supply 20 16 104.0 6.50 2.55 0.612 0.539 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.37 3.75 159s supply 3.75 4.91 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.37 4.08 159s supply 4.08 5.20 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.974 159s supply 0.974 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 159s price -0.2243 0.0888 -2.53 0.016 * 159s income 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.992 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 159s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 159s price 0.2207 0.0896 2.46 0.019 * 159s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 159s trend 0.2979 0.0420 7.10 3.4e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.55 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 159s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 159s 159s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 34 172 0.873 0.679 0.681 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 67.7 3.98 2.00 0.748 0.718 159s supply 20 16 104.3 6.52 2.55 0.611 0.538 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.35 3.76 159s supply 3.76 4.92 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.38 4.10 159s supply 4.10 5.22 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.975 159s supply 0.975 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 159s price -0.2225 0.0883 -2.52 0.017 * 159s income 0.2964 0.0416 7.13 3.1e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.995 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 159s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 159s price 0.2201 0.0897 2.45 0.019 * 159s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 159s trend 0.2964 0.0416 7.13 3.1e-08 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.553 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 159s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 159s 159s [1] "*************** 3SLS with 2 restrictions **********************" 159s 159s systemfit results 159s method: 3SLS 159s 159s N DF SSR detRCov OLS-R2 McElroy-R2 159s system 40 35 171 1.74 0.681 0.696 159s 159s N DF SSR MSE RMSE R2 Adj R2 159s demand 20 17 65.8 3.87 1.97 0.755 0.726 159s supply 20 16 105.4 6.59 2.57 0.607 0.533 159s 159s The covariance matrix of the residuals used for estimation 159s demand supply 159s demand 3.89 4.53 159s supply 4.53 6.25 159s 159s The covariance matrix of the residuals 159s demand supply 159s demand 3.87 4.87 159s supply 4.87 6.59 159s 159s The correlations of the residuals 159s demand supply 159s demand 1.000 0.965 159s supply 0.965 1.000 159s 159s 159s 3SLS estimates for 'demand' (equation 1) 159s Model Formula: consump ~ price + income 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 159s price -0.2457 0.0891 -2.76 0.0092 ** 159s income 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 1.967 on 17 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 17 159s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 159s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 159s 159s 159s 3SLS estimates for 'supply' (equation 2) 159s Model Formula: consump ~ price + farmPrice + trend 159s Instruments: ~income + farmPrice + trend 159s 159s Estimate Std. Error t value Pr(>|t|) 159s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 159s price 0.2543 0.0891 2.85 0.0072 ** 159s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 159s trend 0.3236 0.0233 13.91 8.9e-16 *** 159s --- 159s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 159s 159s Residual standard error: 2.566 on 16 degrees of freedom 159s Number of observations: 20 Degrees of Freedom: 16 159s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 159s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 159s 159s [1] "Component “call”: target, current do not match when deparsed" 159s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 170 1.19 0.683 0.658 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.6 3.86 1.96 0.755 0.727 160s supply 20 16 104.6 6.54 2.56 0.610 0.537 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.30 3.73 160s supply 3.73 5.00 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.28 4.00 160s supply 4.00 5.23 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 160s price -0.2494 0.0812 -3.07 0.0041 ** 160s income 0.3248 0.0209 15.57 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.964 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 160s price 0.2506 0.0812 3.09 0.0039 ** 160s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 160s trend 0.3248 0.0209 15.57 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.557 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 160s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 160s 160s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 172 1.74 0.68 0.697 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.9 3.88 1.97 0.754 0.725 160s supply 20 16 105.7 6.60 2.57 0.606 0.532 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.88 4.55 160s supply 4.55 6.27 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.88 4.88 160s supply 4.88 6.60 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 160s price -0.2443 0.0892 -2.74 0.0096 ** 160s income 0.3234 0.0229 14.14 4.4e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.969 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 160s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 160s price 0.2557 0.0892 2.87 0.0069 ** 160s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 160s trend 0.3234 0.0229 14.14 4.4e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.57 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 160s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 160s 160s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 171 1.74 0.681 0.696 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.8 3.87 1.97 0.755 0.726 160s supply 20 16 105.4 6.59 2.57 0.607 0.533 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.89 4.53 160s supply 4.53 6.25 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 4.87 160s supply 4.87 6.59 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 160s price -0.2457 0.0891 -2.76 0.0092 ** 160s income 0.3236 0.0233 13.91 8.9e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.967 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 160s price 0.2543 0.0891 2.85 0.0072 ** 160s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 160s trend 0.3236 0.0233 13.91 8.9e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.566 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 160s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 160s 160s [1] "Component “call”: target, current do not match when deparsed" 160s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 170 1.19 0.683 0.658 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.6 3.86 1.96 0.755 0.727 160s supply 20 16 104.6 6.54 2.56 0.610 0.537 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.30 3.73 160s supply 3.73 5.00 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.28 4.00 160s supply 4.00 5.23 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 160s price -0.2494 0.0812 -3.07 0.0041 ** 160s income 0.3248 0.0209 15.57 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.964 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 160s price 0.2506 0.0812 3.09 0.0039 ** 160s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 160s trend 0.3248 0.0209 15.57 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.557 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 160s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 160s 160s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 170 1.19 0.682 0.659 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.6 3.86 1.97 0.755 0.726 160s supply 20 16 104.8 6.55 2.56 0.609 0.536 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.30 3.75 160s supply 3.75 5.01 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.28 4.00 160s supply 4.00 5.24 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 160s price -0.2484 0.0812 -3.06 0.0042 ** 160s income 0.3246 0.0205 15.81 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.965 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 160s price 0.2516 0.0812 3.10 0.0038 ** 160s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 160s trend 0.3246 0.0205 15.81 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.559 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 160s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 36 3690 5613 0.012 0.368 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 2132 112.2 10.59 0.305 0.305 160s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 112.2 -44.8 160s eq2 -44.8 56.8 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 112.2 -68.3 160s eq2 -68.3 91.7 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 -0.674 160s eq2 -0.674 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: farmPrice ~ consump - 1 160s Instruments: ~trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s consump 0.9588 0.0235 40.9 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 10.592 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 160s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: price ~ consump + trend 160s Instruments: ~trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) -92.192 49.896 -1.85 0.0821 . 160s consump 1.953 0.499 3.92 0.0011 ** 160s trend -0.469 0.247 -1.90 0.0743 . 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 9.574 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 160s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 38 56326 283068 -104 -10.6 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 2313 122 11.0 -7.63 -7.63 160s eq2 20 19 54013 2843 53.3 -200.46 -200.46 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 121 -255 160s eq2 -255 2953 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 122 -251 160s eq2 -251 2843 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 -0.433 160s eq2 -0.433 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ farmPrice - 1 160s Instruments: ~price + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 11.034 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 160s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: consump ~ trend - 1 160s Instruments: ~price + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 9.02 1.13 8 1.7e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 53.318 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 160s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 38 167069 397886 -49.1 -0.82 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 76692 4036 63.5 -285.0 -285.0 160s eq2 20 19 90377 4757 69.0 -28.5 -28.5 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 2682 2547 160s eq2 2547 2741 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 4036 4336 160s eq2 4336 4757 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 0.928 160s eq2 0.928 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ trend - 1 160s Instruments: ~income + farmPrice 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 4.162 0.723 5.75 1.5e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 63.533 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 160s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: farmPrice ~ trend - 1 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 3.274 0.676 4.84 0.00011 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 68.969 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 160s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 39 161126 1162329 -171 -17.4 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 3553 187 13.7 -12.3 -12.3 160s eq2 20 19 157573 8293 91.1 -235.2 -235.2 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 208 -731 160s eq2 -731 8271 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 187 -623 160s eq2 -623 8293 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 -0.121 160s eq2 -0.121 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ farmPrice - 1 160s Instruments: ~farmPrice + trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 13.675 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 160s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: price ~ trend - 1 160s Instruments: ~farmPrice + trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 1.1122 0.0272 40.8 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 91.068 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 160s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 38 935 491 0 0 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 268 14.1 3.76 0 0 160s eq2 20 19 667 35.1 5.93 0 0 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 14.11 2.18 160s eq2 2.18 35.12 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 14.11 2.18 160s eq2 2.18 35.12 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.0000 0.0981 160s eq2 0.0981 1.0000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ 1 160s Instruments: ~income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 100.90 0.84 120 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 3.756 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 160s Multiple R-Squared: 0 Adjusted R-Squared: 0 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: price ~ 1 160s Instruments: ~income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 100.02 1.33 75.5 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 5.926 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 160s Multiple R-Squared: 0 Adjusted R-Squared: 0 160s 160s [1] "***************************************************" 160s [1] "3SLS formula: GMM" 160s [1] "************* 3SLS *********************************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 174 1.03 0.676 0.786 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 107.9 6.75 2.60 0.598 0.522 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 4.36 160s supply 4.36 6.04 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.00 160s supply 5.00 6.74 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.00 0.98 160s supply 0.98 1.00 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 160s price -0.2436 0.0965 -2.52 0.022 * 160s income 0.3140 0.0469 6.69 3.8e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 160s price 0.2286 0.0997 2.29 0.03571 * 160s farmPrice 0.2282 0.0440 5.19 9e-05 *** 160s trend 0.3611 0.0729 4.95 0.00014 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.597 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 160s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 160s 160s [1] "********************* 3SLS EViews-like *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 173 0.719 0.677 0.748 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 107.2 6.70 2.59 0.600 0.525 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.29 3.59 160s supply 3.59 4.83 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.29 4.11 160s supply 4.11 5.36 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.979 160s supply 0.979 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 160s price -0.2436 0.0890 -2.74 0.0099 ** 160s income 0.3140 0.0433 7.25 2.5e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 160s price 0.2289 0.0892 2.57 0.015 * 160s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 160s trend 0.3579 0.0652 5.49 4.3e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.589 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 160s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 160s 160s [1] "********************* 3SLS with methodResidCov = Theil *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 174 -0.718 0.675 0.922 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 108.7 6.79 2.61 0.594 0.518 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 4.50 160s supply 4.50 6.04 160s 160s warning: this covariance matrix is NOT positive semidefinit! 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.2 160s supply 5.20 6.8 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.981 160s supply 0.981 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 160s price -0.2436 0.0965 -2.52 0.017 * 160s income 0.3140 0.0469 6.69 1.3e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 160s price 0.2282 0.0997 2.29 0.02855 * 160s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 160s trend 0.3648 0.0707 5.16 1.1e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.607 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 160s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 160s 160s [1] "*************** W3SLS with methodResidCov = Theil *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 174 -0.718 0.675 0.922 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 108.7 6.79 2.61 0.594 0.518 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 4.50 160s supply 4.50 6.04 160s 160s warning: this covariance matrix is NOT positive semidefinit! 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.2 160s supply 5.20 6.8 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.981 160s supply 0.981 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 160s price -0.2436 0.0965 -2.52 0.017 * 160s income 0.3140 0.0469 6.69 1.3e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 160s price 0.2282 0.0997 2.29 0.02855 * 160s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 160s trend 0.3648 0.0707 5.16 1.1e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.607 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 160s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 160s 160s [1] "*************** 3SLS with restriction *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 173 1.27 0.678 0.722 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.8 3.99 2.00 0.747 0.717 160s supply 20 16 104.8 6.55 2.56 0.609 0.536 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.97 4.55 160s supply 4.55 6.13 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.99 4.98 160s supply 4.98 6.55 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.975 160s supply 0.975 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 160s price -0.222 0.096 -2.31 0.027 * 160s income 0.296 0.045 6.57 1.6e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.997 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 160s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 160s price 0.2193 0.1002 2.19 0.036 * 160s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 160s trend 0.2956 0.0450 6.57 1.6e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.559 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 160s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 160s 160s [1] "Component “call”: target, current do not match when deparsed" 160s [1] "************** 3SLS with restriction (EViews-like) *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 171 0.887 0.68 0.678 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.5 3.97 1.99 0.748 0.719 160s supply 20 16 104.0 6.50 2.55 0.612 0.539 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.37 3.75 160s supply 3.75 4.91 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.37 4.08 160s supply 4.08 5.20 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.974 160s supply 0.974 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 160s price -0.2243 0.0888 -2.53 0.016 * 160s income 0.2979 0.0420 7.10 3.4e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.992 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 160s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 160s price 0.2207 0.0896 2.46 0.019 * 160s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 160s trend 0.2979 0.0420 7.10 3.4e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.55 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 160s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 160s 160s [1] 40 160s [1] "*************** W3SLS with restriction *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 173 1.24 0.677 0.725 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 68.1 4.00 2.00 0.746 0.716 160s supply 20 16 105.2 6.57 2.56 0.608 0.534 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.93 4.56 160s supply 4.56 6.15 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.00 5.01 160s supply 5.01 6.57 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.976 160s supply 0.976 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 160s price -0.2194 0.0954 -2.3 0.028 * 160s income 0.2938 0.0445 6.6 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.001 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 160s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 160s price 0.2184 0.1003 2.18 0.036 * 160s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 160s trend 0.2938 0.0445 6.60 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.564 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 160s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 160s 160s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 173 1.27 0.678 0.722 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.8 3.99 2.00 0.747 0.717 160s supply 20 16 104.8 6.55 2.56 0.609 0.536 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.97 4.55 160s supply 4.55 6.13 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.99 4.98 160s supply 4.98 6.55 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.975 160s supply 0.975 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 160s price -0.222 0.096 -2.31 0.027 * 160s income 0.296 0.045 6.57 1.6e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.997 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 160s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 160s price 0.2193 0.1002 2.19 0.036 * 160s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 160s trend 0.2956 0.0450 6.57 1.6e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.559 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 160s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 160s 160s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 171 0.887 0.68 0.678 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.5 3.97 1.99 0.748 0.719 160s supply 20 16 104.0 6.50 2.55 0.612 0.539 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.37 3.75 160s supply 3.75 4.91 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.37 4.08 160s supply 4.08 5.20 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.974 160s supply 0.974 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 160s price -0.2243 0.0888 -2.53 0.016 * 160s income 0.2979 0.0420 7.10 3.4e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.992 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 160s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 160s price 0.2207 0.0896 2.46 0.019 * 160s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 160s trend 0.2979 0.0420 7.10 3.4e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.55 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 160s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 160s 160s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 172 0.873 0.679 0.681 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.7 3.98 2.00 0.748 0.718 160s supply 20 16 104.3 6.52 2.55 0.611 0.538 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.35 3.76 160s supply 3.76 4.92 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.38 4.10 160s supply 4.10 5.22 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.975 160s supply 0.975 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 160s price -0.2225 0.0883 -2.52 0.017 * 160s income 0.2964 0.0416 7.13 3.1e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.995 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 160s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 160s price 0.2201 0.0897 2.45 0.019 * 160s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 160s trend 0.2964 0.0416 7.13 3.1e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.553 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 160s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 160s 160s [1] "*************** 3SLS with 2 restrictions **********************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 171 1.74 0.681 0.696 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.8 3.87 1.97 0.755 0.726 160s supply 20 16 105.4 6.59 2.57 0.607 0.533 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.89 4.53 160s supply 4.53 6.25 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 4.87 160s supply 4.87 6.59 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 160s price -0.2457 0.0891 -2.76 0.0092 ** 160s income 0.3236 0.0233 13.91 8.9e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.967 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 160s price 0.2543 0.0891 2.85 0.0072 ** 160s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 160s trend 0.3236 0.0233 13.91 8.9e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.566 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 160s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 160s 160s [1] "Component “call”: target, current do not match when deparsed" 160s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 170 1.19 0.683 0.658 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.6 3.86 1.96 0.755 0.727 160s supply 20 16 104.6 6.54 2.56 0.610 0.537 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.30 3.73 160s supply 3.73 5.00 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.28 4.00 160s supply 4.00 5.23 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 160s price -0.2494 0.0812 -3.07 0.0041 ** 160s income 0.3248 0.0209 15.57 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.964 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 160s price 0.2506 0.0812 3.09 0.0039 ** 160s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 160s trend 0.3248 0.0209 15.57 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.557 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 160s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 160s 160s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 172 1.74 0.68 0.697 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.9 3.88 1.97 0.754 0.725 160s supply 20 16 105.7 6.60 2.57 0.606 0.532 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.88 4.55 160s supply 4.55 6.27 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.88 4.88 160s supply 4.88 6.60 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 160s price -0.2443 0.0892 -2.74 0.0096 ** 160s income 0.3234 0.0229 14.14 4.4e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.969 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 160s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 160s price 0.2557 0.0892 2.87 0.0069 ** 160s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 160s trend 0.3234 0.0229 14.14 4.4e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.57 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 160s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 160s 160s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 171 1.74 0.681 0.696 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.8 3.87 1.97 0.755 0.726 160s supply 20 16 105.4 6.59 2.57 0.607 0.533 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.89 4.53 160s supply 4.53 6.25 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 4.87 160s supply 4.87 6.59 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 160s price -0.2457 0.0891 -2.76 0.0092 ** 160s income 0.3236 0.0233 13.91 8.9e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.967 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 160s price 0.2543 0.0891 2.85 0.0072 ** 160s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 160s trend 0.3236 0.0233 13.91 8.9e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.566 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 160s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 160s 160s [1] "Component “call”: target, current do not match when deparsed" 160s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 170 1.19 0.683 0.658 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.6 3.86 1.96 0.755 0.727 160s supply 20 16 104.6 6.54 2.56 0.610 0.537 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.30 3.73 160s supply 3.73 5.00 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.28 4.00 160s supply 4.00 5.23 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 160s price -0.2494 0.0812 -3.07 0.0041 ** 160s income 0.3248 0.0209 15.57 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.964 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 160s price 0.2506 0.0812 3.09 0.0039 ** 160s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 160s trend 0.3248 0.0209 15.57 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.557 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 160s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 160s 160s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 170 1.19 0.682 0.659 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.6 3.86 1.97 0.755 0.726 160s supply 20 16 104.8 6.55 2.56 0.609 0.536 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.30 3.75 160s supply 3.75 5.01 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.28 4.00 160s supply 4.00 5.24 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.965 160s supply 0.965 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 160s price -0.2484 0.0812 -3.06 0.0042 ** 160s income 0.3246 0.0205 15.81 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.965 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 160s price 0.2516 0.0812 3.10 0.0038 ** 160s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 160s trend 0.3246 0.0205 15.81 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.559 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 160s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 36 3690 5613 0.012 0.368 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 2132 112.2 10.59 0.305 0.305 160s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 112.2 -44.8 160s eq2 -44.8 56.8 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 112.2 -68.3 160s eq2 -68.3 91.7 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 -0.674 160s eq2 -0.674 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: farmPrice ~ consump - 1 160s Instruments: ~trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s consump 0.9588 0.0235 40.9 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 10.592 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 160s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: price ~ consump + trend 160s Instruments: ~trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) -92.192 49.896 -1.85 0.0821 . 160s consump 1.953 0.499 3.92 0.0011 ** 160s trend -0.469 0.247 -1.90 0.0743 . 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 9.574 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 160s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 38 56326 283068 -104 -10.6 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 2313 122 11.0 -7.63 -7.63 160s eq2 20 19 54013 2843 53.3 -200.46 -200.46 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 121 -255 160s eq2 -255 2953 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 122 -251 160s eq2 -251 2843 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 -0.433 160s eq2 -0.433 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ farmPrice - 1 160s Instruments: ~price + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 11.034 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 160s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: consump ~ trend - 1 160s Instruments: ~price + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 9.02 1.13 8 1.7e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 53.318 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 160s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 38 167069 397886 -49.1 -0.82 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 76692 4036 63.5 -285.0 -285.0 160s eq2 20 19 90377 4757 69.0 -28.5 -28.5 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 2682 2547 160s eq2 2547 2741 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 4036 4336 160s eq2 4336 4757 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 0.928 160s eq2 0.928 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ trend - 1 160s Instruments: ~income + farmPrice 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 4.162 0.723 5.75 1.5e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 63.533 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 160s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: farmPrice ~ trend - 1 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 3.274 0.676 4.84 0.00011 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 68.969 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 160s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 39 161126 1162329 -171 -17.4 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 3553 187 13.7 -12.3 -12.3 160s eq2 20 19 157573 8293 91.1 -235.2 -235.2 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 208 -731 160s eq2 -731 8271 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 187 -623 160s eq2 -623 8293 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 -0.121 160s eq2 -0.121 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ farmPrice - 1 160s Instruments: ~farmPrice + trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 13.675 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 160s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: price ~ trend - 1 160s Instruments: ~farmPrice + trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 1.1122 0.0272 40.8 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 91.068 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 160s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 38 935 491 0 0 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 268 14.1 3.76 0 0 160s eq2 20 19 667 35.1 5.93 0 0 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 14.11 2.18 160s eq2 2.18 35.12 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 14.11 2.18 160s eq2 2.18 35.12 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.0000 0.0981 160s eq2 0.0981 1.0000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ 1 160s Instruments: ~income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 100.90 0.84 120 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 3.756 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 160s Multiple R-Squared: 0 Adjusted R-Squared: 0 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: price ~ 1 160s Instruments: ~income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 100.02 1.33 75.5 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 5.926 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 160s Multiple R-Squared: 0 Adjusted R-Squared: 0 160s 160s [1] "***************************************************" 160s [1] "3SLS formula: EViews" 160s [1] "************* 3SLS *********************************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 174 1.03 0.676 0.786 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 107.9 6.75 2.60 0.598 0.522 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 4.36 160s supply 4.36 6.04 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.00 160s supply 5.00 6.74 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.00 0.98 160s supply 0.98 1.00 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 160s price -0.2436 0.0965 -2.52 0.022 * 160s income 0.3140 0.0469 6.69 3.8e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 160s price 0.2286 0.0997 2.29 0.03571 * 160s farmPrice 0.2282 0.0440 5.19 9e-05 *** 160s trend 0.3611 0.0729 4.95 0.00014 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.597 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 160s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 160s 160s [1] "********************* 3SLS EViews-like *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 173 0.719 0.677 0.748 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 107.2 6.70 2.59 0.600 0.525 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.29 3.59 160s supply 3.59 4.83 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.29 4.11 160s supply 4.11 5.36 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.979 160s supply 0.979 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 160s price -0.2436 0.0890 -2.74 0.0099 ** 160s income 0.3140 0.0433 7.25 2.5e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 160s price 0.2289 0.0892 2.57 0.015 * 160s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 160s trend 0.3579 0.0652 5.49 4.3e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.589 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 160s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 160s 160s [1] "********************* 3SLS with methodResidCov = Theil *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 174 -0.718 0.675 0.922 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 108.7 6.79 2.61 0.594 0.518 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 4.50 160s supply 4.50 6.04 160s 160s warning: this covariance matrix is NOT positive semidefinit! 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.2 160s supply 5.20 6.8 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.981 160s supply 0.981 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 160s price -0.2436 0.0965 -2.52 0.017 * 160s income 0.3140 0.0469 6.69 1.3e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 160s price 0.2282 0.0997 2.29 0.02855 * 160s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 160s trend 0.3648 0.0707 5.16 1.1e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.607 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 160s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 160s 160s [1] "*************** W3SLS with methodResidCov = Theil *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 174 -0.718 0.675 0.922 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 108.7 6.79 2.61 0.594 0.518 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 4.50 160s supply 4.50 6.04 160s 160s warning: this covariance matrix is NOT positive semidefinit! 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.2 160s supply 5.20 6.8 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.981 160s supply 0.981 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 160s price -0.2436 0.0965 -2.52 0.017 * 160s income 0.3140 0.0469 6.69 1.3e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 160s price 0.2282 0.0997 2.29 0.02855 * 160s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 160s trend 0.3648 0.0707 5.16 1.1e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.607 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 160s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 160s 160s [1] "*************** 3SLS with restriction *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 173 1.27 0.678 0.722 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.8 3.99 2.00 0.747 0.717 160s supply 20 16 104.8 6.55 2.56 0.609 0.536 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.97 4.55 160s supply 4.55 6.13 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.99 4.98 160s supply 4.98 6.55 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.975 160s supply 0.975 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 160s price -0.222 0.096 -2.31 0.027 * 160s income 0.296 0.045 6.57 1.6e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.997 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 160s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 160s price 0.2193 0.1002 2.19 0.036 * 160s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 160s trend 0.2956 0.0450 6.57 1.6e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.559 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 160s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 160s 160s [1] "Component “call”: target, current do not match when deparsed" 160s [1] "************** 3SLS with restriction (EViews-like) *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 171 0.887 0.68 0.678 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.5 3.97 1.99 0.748 0.719 160s supply 20 16 104.0 6.50 2.55 0.612 0.539 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.37 3.75 160s supply 3.75 4.91 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.37 4.08 160s supply 4.08 5.20 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.974 160s supply 0.974 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 160s price -0.2243 0.0888 -2.53 0.016 * 160s income 0.2979 0.0420 7.10 3.4e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.992 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 160s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 160s price 0.2207 0.0896 2.46 0.019 * 160s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 160s trend 0.2979 0.0420 7.10 3.4e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.55 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 160s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 160s 160s [1] 40 160s [1] "*************** W3SLS with restriction *****************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 173 1.24 0.677 0.725 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 68.1 4.00 2.00 0.746 0.716 160s supply 20 16 105.2 6.57 2.56 0.608 0.534 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.93 4.56 160s supply 4.56 6.15 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.00 5.01 160s supply 5.01 6.57 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.976 160s supply 0.976 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 160s price -0.2194 0.0954 -2.3 0.028 * 160s income 0.2938 0.0445 6.6 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.001 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 160s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 160s price 0.2184 0.1003 2.18 0.036 * 160s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 160s trend 0.2938 0.0445 6.60 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.564 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 160s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 160s 160s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 173 1.27 0.678 0.722 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.8 3.99 2.00 0.747 0.717 160s supply 20 16 104.8 6.55 2.56 0.609 0.536 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.97 4.55 160s supply 4.55 6.13 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.99 4.98 160s supply 4.98 6.55 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.975 160s supply 0.975 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 160s price -0.222 0.096 -2.31 0.027 * 160s income 0.296 0.045 6.57 1.6e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.997 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 160s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 160s price 0.2193 0.1002 2.19 0.036 * 160s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 160s trend 0.2956 0.0450 6.57 1.6e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.559 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 160s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 160s 160s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 171 0.887 0.68 0.678 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.5 3.97 1.99 0.748 0.719 160s supply 20 16 104.0 6.50 2.55 0.612 0.539 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.37 3.75 160s supply 3.75 4.91 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.37 4.08 160s supply 4.08 5.20 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.974 160s supply 0.974 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 160s price -0.2243 0.0888 -2.53 0.016 * 160s income 0.2979 0.0420 7.10 3.4e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.992 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 160s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 160s price 0.2207 0.0896 2.46 0.019 * 160s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 160s trend 0.2979 0.0420 7.10 3.4e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.55 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 160s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 160s 160s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 172 0.873 0.679 0.681 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 67.7 3.98 2.00 0.748 0.718 160s supply 20 16 104.3 6.52 2.55 0.611 0.538 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.35 3.76 160s supply 3.76 4.92 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.38 4.10 160s supply 4.10 5.22 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.975 160s supply 0.975 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 160s price -0.2225 0.0883 -2.52 0.017 * 160s income 0.2964 0.0416 7.13 3.1e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.995 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 160s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 160s price 0.2201 0.0897 2.45 0.019 * 160s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 160s trend 0.2964 0.0416 7.13 3.1e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.553 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 160s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 160s 160s [1] "*************** 3SLS with 2 restrictions **********************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 442 31.1 0.176 -0.052 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 164 9.66 3.11 0.388 0.316 160s supply 20 16 278 17.36 4.17 -0.036 -0.230 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.89 4.53 160s supply 4.53 6.25 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 9.66 11.7 160s supply 11.69 17.4 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.903 160s supply 0.903 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 91.2986 7.9234 11.52 1.8e-13 *** 160s price -0.4494 0.0891 -5.04 1.4e-05 *** 160s income 0.5592 0.0233 24.04 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 3.108 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 164.177 MSE: 9.657 Root MSE: 3.108 160s Multiple R-Squared: 0.388 Adjusted R-Squared: 0.316 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) -1.8394 8.1797 -0.22 0.82 160s price 0.5506 0.0891 6.18 4.5e-07 *** 160s farmPrice 0.4325 0.0241 17.95 < 2e-16 *** 160s trend 0.5592 0.0233 24.04 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 4.167 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 277.77 MSE: 17.361 Root MSE: 4.167 160s Multiple R-Squared: -0.036 Adjusted R-Squared: -0.23 160s 160s [1] "Component “call”: target, current do not match when deparsed" 160s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 439 21.3 0.18 -0.18 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 169 9.93 3.15 0.370 0.296 160s supply 20 16 271 16.91 4.11 -0.009 -0.198 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.30 3.73 160s supply 3.73 5.00 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 8.44 9.64 160s supply 9.64 13.53 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.902 160s supply 0.902 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 93.2926 7.3154 12.75 1.0e-14 *** 160s price -0.4781 0.0812 -5.89 1.1e-06 *** 160s income 0.5683 0.0209 27.24 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 3.152 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 168.882 MSE: 9.934 Root MSE: 3.152 160s Multiple R-Squared: 0.37 Adjusted R-Squared: 0.296 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 0.6559 7.5503 0.09 0.93 160s price 0.5219 0.0812 6.43 2.1e-07 *** 160s farmPrice 0.4355 0.0212 20.49 < 2e-16 *** 160s trend 0.5683 0.0209 27.24 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 4.112 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 270.595 MSE: 16.912 Root MSE: 4.112 160s Multiple R-Squared: -0.009 Adjusted R-Squared: -0.198 160s 160s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 448 31.2 0.165 -0.057 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 166 9.77 3.13 0.38 0.307 160s supply 20 16 281 17.59 4.19 -0.05 -0.246 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.88 4.55 160s supply 4.55 6.27 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 9.77 11.9 160s supply 11.86 17.6 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.905 160s supply 0.905 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 90.6391 7.9088 11.46 2.1e-13 *** 160s price -0.4438 0.0892 -4.98 1.7e-05 *** 160s income 0.5603 0.0229 24.50 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 3.126 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 166.148 MSE: 9.773 Root MSE: 3.126 160s Multiple R-Squared: 0.38 Adjusted R-Squared: 0.307 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) -2.5480 8.1522 -0.31 0.76 160s price 0.5562 0.0892 6.24 3.7e-07 *** 160s farmPrice 0.4340 0.0237 18.33 < 2e-16 *** 160s trend 0.5603 0.0229 24.50 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 4.194 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 281.4 MSE: 17.587 Root MSE: 4.194 160s Multiple R-Squared: -0.05 Adjusted R-Squared: -0.246 160s 160s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 442 31.1 0.176 -0.052 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 164 9.66 3.11 0.388 0.316 160s supply 20 16 278 17.36 4.17 -0.036 -0.230 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.89 4.53 160s supply 4.53 6.25 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 9.66 11.7 160s supply 11.69 17.4 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.903 160s supply 0.903 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 91.2986 7.9234 11.52 1.8e-13 *** 160s price -0.4494 0.0891 -5.04 1.4e-05 *** 160s income 0.5592 0.0233 24.04 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 3.108 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 164.177 MSE: 9.657 Root MSE: 3.108 160s Multiple R-Squared: 0.388 Adjusted R-Squared: 0.316 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) -1.8394 8.1797 -0.22 0.82 160s price 0.5506 0.0891 6.18 4.5e-07 *** 160s farmPrice 0.4325 0.0241 17.95 < 2e-16 *** 160s trend 0.5592 0.0233 24.04 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 4.167 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 277.77 MSE: 17.361 Root MSE: 4.167 160s Multiple R-Squared: -0.036 Adjusted R-Squared: -0.23 160s 160s [1] "Component “call”: target, current do not match when deparsed" 160s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 439 21.3 0.18 -0.18 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 169 9.93 3.15 0.370 0.296 160s supply 20 16 271 16.91 4.11 -0.009 -0.198 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.30 3.73 160s supply 3.73 5.00 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 8.44 9.64 160s supply 9.64 13.53 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.902 160s supply 0.902 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 93.2926 7.3154 12.75 1.0e-14 *** 160s price -0.4781 0.0812 -5.89 1.1e-06 *** 160s income 0.5683 0.0209 27.24 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 3.152 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 168.882 MSE: 9.934 Root MSE: 3.152 160s Multiple R-Squared: 0.37 Adjusted R-Squared: 0.296 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 0.6559 7.5503 0.09 0.93 160s price 0.5219 0.0812 6.43 2.1e-07 *** 160s farmPrice 0.4355 0.0212 20.49 < 2e-16 *** 160s trend 0.5683 0.0209 27.24 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 4.112 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 270.595 MSE: 16.912 Root MSE: 4.112 160s Multiple R-Squared: -0.009 Adjusted R-Squared: -0.198 160s 160s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 444 21.3 0.172 -0.188 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 171 10.0 3.17 0.363 0.289 160s supply 20 16 274 17.1 4.13 -0.020 -0.212 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.30 3.75 160s supply 3.75 5.01 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 8.53 9.77 160s supply 9.77 13.68 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.904 160s supply 0.904 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.7628 7.3058 12.70 1.2e-14 *** 160s price -0.4740 0.0812 -5.84 1.3e-06 *** 160s income 0.5694 0.0205 27.74 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 3.168 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 170.659 MSE: 10.039 Root MSE: 3.168 160s Multiple R-Squared: 0.363 Adjusted R-Squared: 0.289 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 0.0845 7.5314 0.01 0.99 160s price 0.5260 0.0812 6.48 1.8e-07 *** 160s farmPrice 0.4370 0.0209 20.91 < 2e-16 *** 160s trend 0.5694 0.0205 27.74 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 4.135 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 273.568 MSE: 17.098 Root MSE: 4.135 160s Multiple R-Squared: -0.02 Adjusted R-Squared: -0.212 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 36 3690 5613 0.012 0.368 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 2132 112.2 10.59 0.305 0.305 160s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 112.2 -44.8 160s eq2 -44.8 56.8 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 112.2 -68.3 160s eq2 -68.3 91.7 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 -0.674 160s eq2 -0.674 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: farmPrice ~ consump - 1 160s Instruments: ~trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s consump 0.9588 0.0235 40.9 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 10.592 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 160s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: price ~ consump + trend 160s Instruments: ~trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) -92.192 49.896 -1.85 0.0821 . 160s consump 1.953 0.499 3.92 0.0011 ** 160s trend -0.469 0.247 -1.90 0.0743 . 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 9.574 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 160s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 38 56326 283068 -104 -10.6 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 2313 122 11.0 -7.63 -7.63 160s eq2 20 19 54013 2843 53.3 -200.46 -200.46 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 121 -255 160s eq2 -255 2953 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 122 -251 160s eq2 -251 2843 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 -0.433 160s eq2 -0.433 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ farmPrice - 1 160s Instruments: ~price + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 11.034 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 160s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: consump ~ trend - 1 160s Instruments: ~price + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 9.02 1.13 8 1.7e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 53.318 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 160s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 38 167069 397886 -49.1 -0.82 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 76692 4036 63.5 -285.0 -285.0 160s eq2 20 19 90377 4757 69.0 -28.5 -28.5 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 2682 2547 160s eq2 2547 2741 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 4036 4336 160s eq2 4336 4757 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 0.928 160s eq2 0.928 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ trend - 1 160s Instruments: ~income + farmPrice 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 4.162 0.723 5.75 1.5e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 63.533 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 160s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: farmPrice ~ trend - 1 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 3.274 0.676 4.84 0.00011 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 68.969 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 160s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 39 161126 1162329 -171 -17.4 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 3553 187 13.7 -12.3 -12.3 160s eq2 20 19 157573 8293 91.1 -235.2 -235.2 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 208 -731 160s eq2 -731 8271 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 187 -623 160s eq2 -623 8293 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.000 -0.121 160s eq2 -0.121 1.000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ farmPrice - 1 160s Instruments: ~farmPrice + trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 13.675 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 160s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: price ~ trend - 1 160s Instruments: ~farmPrice + trend + income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s trend 1.1122 0.0272 40.8 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 91.068 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 160s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 160s 160s 160s systemfit results 160s method: 3SLS 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 38 935 491 0 0 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s eq1 20 19 268 14.1 3.76 0 0 160s eq2 20 19 667 35.1 5.93 0 0 160s 160s The covariance matrix of the residuals used for estimation 160s eq1 eq2 160s eq1 14.11 2.18 160s eq2 2.18 35.12 160s 160s The covariance matrix of the residuals 160s eq1 eq2 160s eq1 14.11 2.18 160s eq2 2.18 35.12 160s 160s The correlations of the residuals 160s eq1 eq2 160s eq1 1.0000 0.0981 160s eq2 0.0981 1.0000 160s 160s 160s 3SLS estimates for 'eq1' (equation 1) 160s Model Formula: consump ~ 1 160s Instruments: ~income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 100.90 0.84 120 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 3.756 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 160s Multiple R-Squared: 0 Adjusted R-Squared: 0 160s 160s 160s 3SLS estimates for 'eq2' (equation 2) 160s Model Formula: price ~ 1 160s Instruments: ~income 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 100.02 1.33 75.5 <2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 5.926 on 19 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 19 160s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 160s Multiple R-Squared: 0 Adjusted R-Squared: 0 160s 160s > 160s > ## ******************** iterated 3SLS ********************** 160s > fit3slsi <- list() 160s > formulas <- c( "GLS", "IV", "Schmidt", "GMM", "EViews" ) 160s > for( i in seq( along = formulas ) ) { 160s + fit3slsi[[ i ]] <- list() 160s + 160s + print( "***************************************************" ) 160s + print( paste( "3SLS formula:", formulas[ i ] ) ) 160s + print( "************* 3SLS *********************************" ) 160s + fit3slsi[[ i ]]$e1 <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, method3sls = formulas[ i ], maxiter = 100, 160s + useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e1 ) ) 160s + 160s + print( "********************* iterated 3SLS EViews-like ****************" ) 160s + fit3slsi[[ i ]]$e1e <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, methodResidCov = "noDfCor", method3sls = formulas[ i ], 160s + maxiter = 100, useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e1e, useDfSys = TRUE ) ) 160s + 160s + print( "************** iterated 3SLS with methodResidCov = Theil **************" ) 160s + fit3slsi[[ i ]]$e1c <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, methodResidCov = "Theil", method3sls = formulas[ i ], 160s + maxiter = 100, x = TRUE, useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e1c, useDfSys = TRUE ) ) 160s + 160s + print( "**************** iterated W3SLS EViews-like ****************" ) 160s + fit3slsi[[ i ]]$e1we <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, methodResidCov = "noDfCor", method3sls = formulas[ i ], 160s + maxiter = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e1we, useDfSys = TRUE ) ) 160s + 160s + 160s + print( "******* iterated 3SLS with restriction *****************" ) 160s + fit3slsi[[ i ]]$e2 <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, restrict.matrix = restrm, method3sls = formulas[ i ], 160s + maxiter = 100, x = TRUE, useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e2 ) ) 160s + 160s + print( "********* iterated 3SLS with restriction (EViews-like) *********" ) 160s + fit3slsi[[ i ]]$e2e <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restrm, 160s + method3sls = formulas[ i ], maxiter = 100, useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e2e, useDfSys = TRUE ) ) 160s + 160s + print( "******** iterated W3SLS with restriction (EViews-like) *********" ) 160s + fit3slsi[[ i ]]$e2we <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restrm, 160s + method3sls = formulas[ i ], maxiter = 100, residCovWeighted = TRUE, 160s + useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e2we, useDfSys = TRUE ) ) 160s + 160s + 160s + print( "********* iterated 3SLS with restriction via restrict.regMat *****************" ) 160s + fit3slsi[[ i ]]$e3 <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, restrict.regMat = tc, method3sls = formulas[ i ], 160s + maxiter = 100, useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e3 ) ) 160s + 160s + print( "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" ) 160s + fit3slsi[[ i ]]$e3e <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, methodResidCov = "noDfCor", restrict.regMat = tc, 160s + method3sls = formulas[ i ], maxiter = 100, x = TRUE, 160s + useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e3e, useDfSys = TRUE ) ) 160s + 160s + print( "***** iterated W3SLS with restriction via restrict.regMat ********" ) 160s + fit3slsi[[ i ]]$e3w <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, restrict.regMat = tc, method3sls = formulas[ i ], maxiter = 100, 160s + residCovWeighted = TRUE, x = TRUE, useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e3w ) ) 160s + 160s + 160s + print( "******** iterated 3SLS with 2 restrictions *********************" ) 160s + fit3slsi[[ i ]]$e4 <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, restrict.matrix = restr2m, restrict.rhs = restr2q, 160s + method3sls = formulas[ i ], maxiter = 100, x = TRUE, 160s + useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e4 ) ) 160s + 160s + print( "********* iterated 3SLS with 2 restrictions (EViews-like) *******" ) 160s + fit3slsi[[ i ]]$e4e <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restr2m, 160s + restrict.rhs = restr2q, method3sls = formulas[ i ], maxiter = 100, 160s + useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e4e, useDfSys = TRUE ) ) 160s + 160s + print( "******** iterated W3SLS with 2 restrictions (EViews-like) *******" ) 160s + fit3slsi[[ i ]]$e4we <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restr2m, 160s + restrict.rhs = restr2q, method3sls = formulas[ i ], maxiter = 100, 160s + residCovWeighted = TRUE, useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e4we, useDfSys = TRUE ) ) 160s + 160s + 160s + print( "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" ) 160s + fit3slsi[[ i ]]$e5 <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, restrict.regMat = tc, restrict.matrix = restr3m, 160s + restrict.rhs = restr3q, method3sls = formulas[ i ], maxiter = 100, 160s + useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e5 ) ) 160s + 160s + print( "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" ) 160s + fit3slsi[[ i ]]$e5e <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, restrict.regMat = tc, methodResidCov = "noDfCor", 160s + restrict.matrix = restr3m, restrict.rhs = restr3q, 160s + method3sls = formulas[ i ], maxiter = 100, useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e5e, useDfSys = TRUE ) ) 160s + 160s + print( "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" ) 160s + fit3slsi[[ i ]]$e5w <- systemfit( system, "3SLS", data = Kmenta, 160s + inst = inst, restrict.regMat = tc, restrict.matrix = restr3m, 160s + restrict.rhs = restr3q, method3sls = formulas[ i ], maxiter = 100, 160s + residCovWeighted = TRUE, x = TRUE, 160s + useMatrix = useMatrix ) 160s + print( summary( fit3slsi[[ i ]]$e5w ) ) 160s + } 160s [1] "***************************************************" 160s [1] "3SLS formula: GLS" 160s [1] "************* 3SLS *********************************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 178 0.983 0.668 0.814 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 112.4 7.03 2.65 0.581 0.502 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 5.12 160s supply 5.12 7.03 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.12 160s supply 5.12 7.03 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 160s price -0.2436 0.0965 -2.52 0.022 * 160s income 0.3140 0.0469 6.69 3.8e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 160s price 0.2266 0.1075 2.11 0.05110 . 160s farmPrice 0.2234 0.0468 4.78 0.00021 *** 160s trend 0.3800 0.0720 5.28 7.5e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.651 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 160s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 160s 160s [1] "********************* iterated 3SLS EViews-like ****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 177 0.667 0.67 0.782 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 111.3 6.96 2.64 0.585 0.507 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 160s price -0.2436 0.0890 -2.74 0.0099 ** 160s income 0.3140 0.0433 7.25 2.5e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 160s price 0.2271 0.0956 2.37 0.024 * 160s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 160s trend 0.3756 0.0641 5.86 1.5e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.637 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 160s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 160s 160s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 179 -0.818 0.665 0.957 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 113.8 7.11 2.67 0.576 0.496 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 5.32 160s supply 5.32 7.11 160s 160s warning: this covariance matrix is NOT positive semidefinit! 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.32 160s supply 5.32 7.11 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 160s price -0.2436 0.0965 -2.52 0.017 * 160s income 0.3140 0.0469 6.69 1.3e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 160s price 0.2261 0.1081 2.09 0.04425 * 160s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 160s trend 0.3851 0.0693 5.55 3.6e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.667 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 160s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 160s 160s [1] "**************** iterated W3SLS EViews-like ****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 177 0.667 0.67 0.782 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 111.3 6.96 2.64 0.585 0.507 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 160s price -0.2436 0.0890 -2.74 0.0099 ** 160s income 0.3140 0.0433 7.25 2.5e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 160s price 0.2271 0.0956 2.37 0.024 * 160s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 160s trend 0.3756 0.0641 5.86 1.5e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.637 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 160s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 160s 160s [1] "******* iterated 3SLS with restriction *****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 17 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 240 0.56 0.553 0.819 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 98.4 5.79 2.41 0.633 0.590 160s supply 20 16 141.1 8.82 2.97 0.474 0.375 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 160s price -0.1064 0.1023 -1.04 0.31 160s income 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.406 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 160s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 160s price 0.1833 0.1189 1.54 0.13 160s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 160s trend 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.97 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 160s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 160s 160s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 20 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 237 0.364 0.557 0.755 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 99.3 5.84 2.42 0.630 0.586 160s supply 20 16 138.1 8.63 2.94 0.485 0.388 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 160s price -0.1043 0.0958 -1.09 0.28 160s income 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.417 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 160s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 160s price 0.1851 0.1053 1.76 0.088 . 160s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 160s trend 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.938 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 160s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 160s 160s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 20 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 237 0.364 0.557 0.755 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 99.3 5.84 2.42 0.630 0.586 160s supply 20 16 138.1 8.63 2.94 0.485 0.388 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 160s price -0.1043 0.0958 -1.09 0.28 160s income 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.417 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 160s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 160s price 0.1851 0.1053 1.76 0.088 . 160s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 160s trend 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.938 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 160s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 160s 160s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 17 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 240 0.56 0.553 0.819 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 98.4 5.79 2.41 0.633 0.590 160s supply 20 16 141.1 8.82 2.97 0.474 0.375 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 160s price -0.1064 0.1023 -1.04 0.31 160s income 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.406 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 160s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 160s price 0.1833 0.1189 1.54 0.13 160s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 160s trend 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.97 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 160s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 160s 160s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 20 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 237 0.364 0.557 0.755 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 99.3 5.84 2.42 0.630 0.586 160s supply 20 16 138.1 8.63 2.94 0.485 0.388 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 160s price -0.1043 0.0958 -1.09 0.28 160s income 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.417 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 160s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 160s price 0.1851 0.1053 1.76 0.088 . 160s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 160s trend 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.938 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 160s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 160s 160s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 17 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 240 0.56 0.553 0.819 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 98.4 5.79 2.41 0.633 0.590 160s supply 20 16 141.1 8.82 2.97 0.474 0.375 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 160s price -0.1064 0.1023 -1.04 0.31 160s income 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.406 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 160s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 160s price 0.1833 0.1189 1.54 0.13 160s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 160s trend 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.97 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 160s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 160s 160s [1] "******** iterated 3SLS with 2 restrictions *********************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 9 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 185 1.76 0.655 0.71 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 69.9 4.11 2.03 0.739 0.709 160s supply 20 16 114.8 7.18 2.68 0.572 0.491 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.00 0.97 160s supply 0.97 1.00 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 160s price -0.2007 0.0920 -2.18 0.036 * 160s income 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.028 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 160s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 160s price 0.2993 0.0920 3.25 0.0025 ** 160s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 160s trend 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.679 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 160s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 160s 160s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 8 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 179 1.19 0.666 0.668 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 68.3 4.02 2.00 0.745 0.715 160s supply 20 16 110.8 6.92 2.63 0.587 0.509 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.968 160s supply 0.968 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 160s price -0.2168 0.0835 -2.6 0.014 * 160s income 0.3199 0.0168 19.1 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.004 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 160s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 160s price 0.2832 0.0835 3.39 0.0017 ** 160s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 160s trend 0.3199 0.0168 19.07 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.631 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 160s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 160s 160s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 8 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 179 1.19 0.666 0.668 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 68.3 4.02 2.00 0.745 0.715 160s supply 20 16 110.8 6.92 2.63 0.587 0.509 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.968 160s supply 0.968 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 160s price -0.2168 0.0835 -2.6 0.014 * 160s income 0.3199 0.0168 19.1 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.004 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 160s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 160s price 0.2832 0.0835 3.39 0.0017 ** 160s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 160s trend 0.3199 0.0168 19.07 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.631 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 160s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 160s 160s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 9 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 185 1.76 0.655 0.71 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 69.9 4.11 2.03 0.739 0.709 160s supply 20 16 114.8 7.18 2.68 0.572 0.491 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.00 0.97 160s supply 0.97 1.00 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 160s price -0.2007 0.0920 -2.18 0.036 * 160s income 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.028 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 160s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 160s price 0.2993 0.0920 3.25 0.0025 ** 160s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 160s trend 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.679 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 160s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 160s 160s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 8 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 179 1.19 0.666 0.668 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 68.3 4.02 2.00 0.745 0.715 160s supply 20 16 110.8 6.92 2.63 0.587 0.509 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.968 160s supply 0.968 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 160s price -0.2168 0.0835 -2.6 0.014 * 160s income 0.3199 0.0168 19.1 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.004 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 160s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 160s price 0.2832 0.0835 3.39 0.0017 ** 160s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 160s trend 0.3199 0.0168 19.07 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.631 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 160s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 160s 160s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 9 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 185 1.76 0.655 0.71 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 69.9 4.11 2.03 0.739 0.709 160s supply 20 16 114.8 7.18 2.68 0.572 0.491 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.00 0.97 160s supply 0.97 1.00 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 160s price -0.2007 0.0920 -2.18 0.036 * 160s income 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.028 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 160s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 160s price 0.2993 0.0920 3.25 0.0025 ** 160s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 160s trend 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.679 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 160s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 160s 160s [1] "***************************************************" 160s [1] "3SLS formula: IV" 160s [1] "************* 3SLS *********************************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 178 0.983 0.668 0.814 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 112.4 7.03 2.65 0.581 0.502 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 5.12 160s supply 5.12 7.03 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.12 160s supply 5.12 7.03 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 160s price -0.2436 0.0965 -2.52 0.022 * 160s income 0.3140 0.0469 6.69 3.8e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 160s price 0.2266 0.1075 2.11 0.05110 . 160s farmPrice 0.2234 0.0468 4.78 0.00021 *** 160s trend 0.3800 0.0720 5.28 7.5e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.651 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 160s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 160s 160s [1] "********************* iterated 3SLS EViews-like ****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 177 0.667 0.67 0.782 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 111.3 6.96 2.64 0.585 0.507 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 160s price -0.2436 0.0890 -2.74 0.0099 ** 160s income 0.3140 0.0433 7.25 2.5e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 160s price 0.2271 0.0956 2.37 0.024 * 160s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 160s trend 0.3756 0.0641 5.86 1.5e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.637 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 160s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 160s 160s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 179 -0.818 0.665 0.957 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 113.8 7.11 2.67 0.576 0.496 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 5.32 160s supply 5.32 7.11 160s 160s warning: this covariance matrix is NOT positive semidefinit! 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.32 160s supply 5.32 7.11 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 160s price -0.2436 0.0965 -2.52 0.017 * 160s income 0.3140 0.0469 6.69 1.3e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 160s price 0.2261 0.1081 2.09 0.04425 * 160s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 160s trend 0.3851 0.0693 5.55 3.6e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.667 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 160s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 160s 160s [1] "**************** iterated W3SLS EViews-like ****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 177 0.667 0.67 0.782 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 111.3 6.96 2.64 0.585 0.507 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 160s price -0.2436 0.0890 -2.74 0.0099 ** 160s income 0.3140 0.0433 7.25 2.5e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 160s price 0.2271 0.0956 2.37 0.024 * 160s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 160s trend 0.3756 0.0641 5.86 1.5e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.637 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 160s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 160s 160s [1] "******* iterated 3SLS with restriction *****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 17 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 240 0.56 0.553 0.819 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 98.4 5.79 2.41 0.633 0.590 160s supply 20 16 141.1 8.82 2.97 0.474 0.375 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 160s price -0.1064 0.1023 -1.04 0.31 160s income 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.406 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 160s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 160s price 0.1833 0.1189 1.54 0.13 160s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 160s trend 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.97 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 160s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 160s 160s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 20 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 237 0.364 0.557 0.755 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 99.3 5.84 2.42 0.630 0.586 160s supply 20 16 138.1 8.63 2.94 0.485 0.388 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 160s price -0.1043 0.0958 -1.09 0.28 160s income 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.417 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 160s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 160s price 0.1851 0.1053 1.76 0.088 . 160s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 160s trend 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.938 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 160s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 160s 160s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 20 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 237 0.364 0.557 0.755 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 99.3 5.84 2.42 0.630 0.586 160s supply 20 16 138.1 8.63 2.94 0.485 0.388 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 160s price -0.1043 0.0958 -1.09 0.28 160s income 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.417 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 160s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 160s price 0.1851 0.1053 1.76 0.088 . 160s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 160s trend 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.938 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 160s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 160s 160s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 17 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 240 0.56 0.553 0.819 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 98.4 5.79 2.41 0.633 0.590 160s supply 20 16 141.1 8.82 2.97 0.474 0.375 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 160s price -0.1064 0.1023 -1.04 0.31 160s income 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.406 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 160s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 160s price 0.1833 0.1189 1.54 0.13 160s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 160s trend 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.97 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 160s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 160s 160s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 20 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 237 0.364 0.557 0.755 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 99.3 5.84 2.42 0.630 0.586 160s supply 20 16 138.1 8.63 2.94 0.485 0.388 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.96 5.82 160s supply 5.82 6.90 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 160s price -0.1043 0.0958 -1.09 0.28 160s income 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.417 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 160s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 160s price 0.1851 0.1053 1.76 0.088 . 160s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 160s trend 0.1979 0.0299 6.61 1.4e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.938 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 160s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 160s 160s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 17 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 240 0.56 0.553 0.819 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 98.4 5.79 2.41 0.633 0.590 160s supply 20 16 141.1 8.82 2.97 0.474 0.375 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 160s price -0.1064 0.1023 -1.04 0.31 160s income 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.406 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 160s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 160s price 0.1833 0.1189 1.54 0.13 160s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 160s trend 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.97 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 160s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 160s 160s [1] "******** iterated 3SLS with 2 restrictions *********************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 9 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 185 1.76 0.655 0.71 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 69.9 4.11 2.03 0.739 0.709 160s supply 20 16 114.8 7.18 2.68 0.572 0.491 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.00 0.97 160s supply 0.97 1.00 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 160s price -0.2007 0.0920 -2.18 0.036 * 160s income 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.028 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 160s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 160s price 0.2993 0.0920 3.25 0.0025 ** 160s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 160s trend 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.679 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 160s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 160s 160s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 8 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 179 1.19 0.666 0.668 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 68.3 4.02 2.00 0.745 0.715 160s supply 20 16 110.8 6.92 2.63 0.587 0.509 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.968 160s supply 0.968 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 160s price -0.2168 0.0835 -2.6 0.014 * 160s income 0.3199 0.0168 19.1 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.004 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 160s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 160s price 0.2832 0.0835 3.39 0.0017 ** 160s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 160s trend 0.3199 0.0168 19.07 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.631 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 160s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 160s 160s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 8 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 179 1.19 0.666 0.668 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 68.3 4.02 2.00 0.745 0.715 160s supply 20 16 110.8 6.92 2.63 0.587 0.509 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.968 160s supply 0.968 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 160s price -0.2168 0.0835 -2.6 0.014 * 160s income 0.3199 0.0168 19.1 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.004 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 160s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 160s price 0.2832 0.0835 3.39 0.0017 ** 160s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 160s trend 0.3199 0.0168 19.07 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.631 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 160s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 160s 160s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 9 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 185 1.76 0.655 0.71 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 69.9 4.11 2.03 0.739 0.709 160s supply 20 16 114.8 7.18 2.68 0.572 0.491 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.00 0.97 160s supply 0.97 1.00 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 160s price -0.2007 0.0920 -2.18 0.036 * 160s income 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.028 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 160s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 160s price 0.2993 0.0920 3.25 0.0025 ** 160s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 160s trend 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.679 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 160s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 160s 160s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 8 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 179 1.19 0.666 0.668 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 68.3 4.02 2.00 0.745 0.715 160s supply 20 16 110.8 6.92 2.63 0.587 0.509 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.41 4.21 160s supply 4.21 5.54 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.968 160s supply 0.968 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 160s price -0.2168 0.0835 -2.6 0.014 * 160s income 0.3199 0.0168 19.1 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.004 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 160s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 160s price 0.2832 0.0835 3.39 0.0017 ** 160s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 160s trend 0.3199 0.0168 19.07 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.631 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 160s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 160s 160s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 9 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 35 185 1.76 0.655 0.71 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 69.9 4.11 2.03 0.739 0.709 160s supply 20 16 114.8 7.18 2.68 0.572 0.491 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 4.11 5.27 160s supply 5.27 7.18 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.00 0.97 160s supply 0.97 1.00 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 160s price -0.2007 0.0920 -2.18 0.036 * 160s income 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.028 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 160s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 160s price 0.2993 0.0920 3.25 0.0025 ** 160s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 160s trend 0.3159 0.0192 16.42 < 2e-16 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.679 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 160s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 160s 160s [1] "***************************************************" 160s [1] "3SLS formula: Schmidt" 160s [1] "************* 3SLS *********************************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 178 0.983 0.668 0.814 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 112.4 7.03 2.65 0.581 0.502 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 5.12 160s supply 5.12 7.03 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.12 160s supply 5.12 7.03 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 160s price -0.2436 0.0965 -2.52 0.022 * 160s income 0.3140 0.0469 6.69 3.8e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 160s price 0.2266 0.1075 2.11 0.05110 . 160s farmPrice 0.2234 0.0468 4.78 0.00021 *** 160s trend 0.3800 0.0720 5.28 7.5e-05 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.651 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 160s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 160s 160s [1] "********************* iterated 3SLS EViews-like ****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 177 0.667 0.67 0.782 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 111.3 6.96 2.64 0.585 0.507 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 160s price -0.2436 0.0890 -2.74 0.0099 ** 160s income 0.3140 0.0433 7.25 2.5e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 160s price 0.2271 0.0956 2.37 0.024 * 160s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 160s trend 0.3756 0.0641 5.86 1.5e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.637 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 160s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 160s 160s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 179 -0.818 0.665 0.957 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 113.8 7.11 2.67 0.576 0.496 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.87 5.32 160s supply 5.32 7.11 160s 160s warning: this covariance matrix is NOT positive semidefinit! 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.87 5.32 160s supply 5.32 7.11 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 160s price -0.2436 0.0965 -2.52 0.017 * 160s income 0.3140 0.0469 6.69 1.3e-07 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 160s price 0.2261 0.1081 2.09 0.04425 * 160s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 160s trend 0.3851 0.0693 5.55 3.6e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.667 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 160s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 160s 160s [1] "**************** iterated W3SLS EViews-like ****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 6 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 33 177 0.667 0.67 0.782 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 65.7 3.87 1.97 0.755 0.726 160s supply 20 16 111.3 6.96 2.64 0.585 0.507 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 3.29 4.20 160s supply 4.20 5.57 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.982 160s supply 0.982 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 160s price -0.2436 0.0890 -2.74 0.0099 ** 160s income 0.3140 0.0433 7.25 2.5e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 1.966 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 160s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 160s price 0.2271 0.0956 2.37 0.024 * 160s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 160s trend 0.3756 0.0641 5.86 1.5e-06 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.637 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 160s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 160s 160s [1] "******* iterated 3SLS with restriction *****************" 160s 160s systemfit results 160s method: iterated 3SLS 160s 160s convergence achieved after 17 iterations 160s 160s N DF SSR detRCov OLS-R2 McElroy-R2 160s system 40 34 240 0.56 0.553 0.819 160s 160s N DF SSR MSE RMSE R2 Adj R2 160s demand 20 17 98.4 5.79 2.41 0.633 0.590 160s supply 20 16 141.1 8.82 2.97 0.474 0.375 160s 160s The covariance matrix of the residuals used for estimation 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The covariance matrix of the residuals 160s demand supply 160s demand 5.79 7.11 160s supply 7.11 8.82 160s 160s The correlations of the residuals 160s demand supply 160s demand 1.000 0.995 160s supply 0.995 1.000 160s 160s 160s 3SLS estimates for 'demand' (equation 1) 160s Model Formula: consump ~ price + income 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 160s price -0.1064 0.1023 -1.04 0.31 160s income 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.406 on 17 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 17 160s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 160s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 160s 160s 160s 3SLS estimates for 'supply' (equation 2) 160s Model Formula: consump ~ price + farmPrice + trend 160s Instruments: ~income + farmPrice + trend 160s 160s Estimate Std. Error t value Pr(>|t|) 160s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 160s price 0.1833 0.1189 1.54 0.13 160s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 160s trend 0.1996 0.0297 6.73 9.9e-08 *** 160s --- 160s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 160s 160s Residual standard error: 2.97 on 16 degrees of freedom 160s Number of observations: 20 Degrees of Freedom: 16 160s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 160s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 160s 160s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 20 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 237 0.364 0.557 0.755 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 99.3 5.84 2.42 0.630 0.586 161s supply 20 16 138.1 8.63 2.94 0.485 0.388 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 161s price -0.1043 0.0958 -1.09 0.28 161s income 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.417 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 161s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 161s price 0.1851 0.1053 1.76 0.088 . 161s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 161s trend 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.938 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 161s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 161s 161s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 20 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 237 0.364 0.557 0.755 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 99.3 5.84 2.42 0.630 0.586 161s supply 20 16 138.1 8.63 2.94 0.485 0.388 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 161s price -0.1043 0.0958 -1.09 0.28 161s income 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.417 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 161s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 161s price 0.1851 0.1053 1.76 0.088 . 161s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 161s trend 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.938 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 161s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 161s 161s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 17 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 240 0.56 0.553 0.819 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 98.4 5.79 2.41 0.633 0.590 161s supply 20 16 141.1 8.82 2.97 0.474 0.375 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 161s price -0.1064 0.1023 -1.04 0.31 161s income 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.406 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 161s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 161s price 0.1833 0.1189 1.54 0.13 161s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 161s trend 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.97 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 161s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 161s 161s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 20 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 237 0.364 0.557 0.755 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 99.3 5.84 2.42 0.630 0.586 161s supply 20 16 138.1 8.63 2.94 0.485 0.388 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 161s price -0.1043 0.0958 -1.09 0.28 161s income 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.417 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 161s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 161s price 0.1851 0.1053 1.76 0.088 . 161s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 161s trend 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.938 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 161s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 161s 161s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 17 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 240 0.56 0.553 0.819 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 98.4 5.79 2.41 0.633 0.590 161s supply 20 16 141.1 8.82 2.97 0.474 0.375 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 161s price -0.1064 0.1023 -1.04 0.31 161s income 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.406 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 161s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 161s price 0.1833 0.1189 1.54 0.13 161s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 161s trend 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.97 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 161s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 161s 161s [1] "******** iterated 3SLS with 2 restrictions *********************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 9 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 185 1.76 0.655 0.71 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 69.9 4.11 2.03 0.739 0.709 161s supply 20 16 114.8 7.18 2.68 0.572 0.491 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.00 0.97 161s supply 0.97 1.00 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 161s price -0.2007 0.0920 -2.18 0.036 * 161s income 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.028 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 161s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 161s price 0.2993 0.0920 3.25 0.0025 ** 161s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 161s trend 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.679 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 161s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 161s 161s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 8 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 179 1.19 0.666 0.668 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 68.3 4.02 2.00 0.745 0.715 161s supply 20 16 110.8 6.92 2.63 0.587 0.509 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.968 161s supply 0.968 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 161s price -0.2168 0.0835 -2.6 0.014 * 161s income 0.3199 0.0168 19.1 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.004 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 161s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 161s price 0.2832 0.0835 3.39 0.0017 ** 161s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 161s trend 0.3199 0.0168 19.07 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.631 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 161s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 161s 161s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 8 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 179 1.19 0.666 0.668 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 68.3 4.02 2.00 0.745 0.715 161s supply 20 16 110.8 6.92 2.63 0.587 0.509 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.968 161s supply 0.968 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 161s price -0.2168 0.0835 -2.6 0.014 * 161s income 0.3199 0.0168 19.1 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.004 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 161s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 161s price 0.2832 0.0835 3.39 0.0017 ** 161s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 161s trend 0.3199 0.0168 19.07 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.631 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 161s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 161s 161s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 9 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 185 1.76 0.655 0.71 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 69.9 4.11 2.03 0.739 0.709 161s supply 20 16 114.8 7.18 2.68 0.572 0.491 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.00 0.97 161s supply 0.97 1.00 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 161s price -0.2007 0.0920 -2.18 0.036 * 161s income 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.028 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 161s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 161s price 0.2993 0.0920 3.25 0.0025 ** 161s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 161s trend 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.679 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 161s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 161s 161s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 8 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 179 1.19 0.666 0.668 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 68.3 4.02 2.00 0.745 0.715 161s supply 20 16 110.8 6.92 2.63 0.587 0.509 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.968 161s supply 0.968 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 161s price -0.2168 0.0835 -2.6 0.014 * 161s income 0.3199 0.0168 19.1 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.004 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 161s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 161s price 0.2832 0.0835 3.39 0.0017 ** 161s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 161s trend 0.3199 0.0168 19.07 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.631 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 161s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 161s 161s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 9 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 185 1.76 0.655 0.71 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 69.9 4.11 2.03 0.739 0.709 161s supply 20 16 114.8 7.18 2.68 0.572 0.491 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.00 0.97 161s supply 0.97 1.00 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 161s price -0.2007 0.0920 -2.18 0.036 * 161s income 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.028 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 161s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 161s price 0.2993 0.0920 3.25 0.0025 ** 161s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 161s trend 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.679 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 161s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 161s 161s [1] "***************************************************" 161s [1] "3SLS formula: GMM" 161s [1] "************* 3SLS *********************************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 6 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 178 0.983 0.668 0.814 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 65.7 3.87 1.97 0.755 0.726 161s supply 20 16 112.4 7.03 2.65 0.581 0.502 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.87 5.12 161s supply 5.12 7.03 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.87 5.12 161s supply 5.12 7.03 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.982 161s supply 0.982 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 161s price -0.2436 0.0965 -2.52 0.022 * 161s income 0.3140 0.0469 6.69 3.8e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.966 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 161s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 161s price 0.2266 0.1075 2.11 0.05110 . 161s farmPrice 0.2234 0.0468 4.78 0.00021 *** 161s trend 0.3800 0.0720 5.28 7.5e-05 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.651 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 161s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 161s 161s [1] "********************* iterated 3SLS EViews-like ****************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 6 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 177 0.667 0.67 0.782 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 65.7 3.87 1.97 0.755 0.726 161s supply 20 16 111.3 6.96 2.64 0.585 0.507 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.29 4.20 161s supply 4.20 5.57 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.29 4.20 161s supply 4.20 5.57 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.982 161s supply 0.982 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 161s price -0.2436 0.0890 -2.74 0.0099 ** 161s income 0.3140 0.0433 7.25 2.5e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.966 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 161s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 161s price 0.2271 0.0956 2.37 0.024 * 161s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 161s trend 0.3756 0.0641 5.86 1.5e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.637 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 161s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 161s 161s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 6 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 179 -0.818 0.665 0.957 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 65.7 3.87 1.97 0.755 0.726 161s supply 20 16 113.8 7.11 2.67 0.576 0.496 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.87 5.32 161s supply 5.32 7.11 161s 161s warning: this covariance matrix is NOT positive semidefinit! 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.87 5.32 161s supply 5.32 7.11 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.982 161s supply 0.982 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 161s price -0.2436 0.0965 -2.52 0.017 * 161s income 0.3140 0.0469 6.69 1.3e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.966 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 161s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 161s price 0.2261 0.1081 2.09 0.04425 * 161s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 161s trend 0.3851 0.0693 5.55 3.6e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.667 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 161s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 161s 161s [1] "**************** iterated W3SLS EViews-like ****************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 6 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 177 0.667 0.67 0.782 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 65.7 3.87 1.97 0.755 0.726 161s supply 20 16 111.3 6.96 2.64 0.585 0.507 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.29 4.20 161s supply 4.20 5.57 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.29 4.20 161s supply 4.20 5.57 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.982 161s supply 0.982 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 161s price -0.2436 0.0890 -2.74 0.0099 ** 161s income 0.3140 0.0433 7.25 2.5e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.966 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 161s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 161s price 0.2271 0.0956 2.37 0.024 * 161s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 161s trend 0.3756 0.0641 5.86 1.5e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.637 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 161s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 161s 161s [1] "******* iterated 3SLS with restriction *****************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 17 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 240 0.56 0.553 0.819 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 98.4 5.79 2.41 0.633 0.590 161s supply 20 16 141.1 8.82 2.97 0.474 0.375 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 161s price -0.1064 0.1023 -1.04 0.31 161s income 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.406 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 161s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 161s price 0.1833 0.1189 1.54 0.13 161s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 161s trend 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.97 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 161s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 161s 161s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 20 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 237 0.364 0.557 0.755 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 99.3 5.84 2.42 0.630 0.586 161s supply 20 16 138.1 8.63 2.94 0.485 0.388 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 161s price -0.1043 0.0958 -1.09 0.28 161s income 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.417 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 161s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 161s price 0.1851 0.1053 1.76 0.088 . 161s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 161s trend 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.938 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 161s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 161s 161s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 20 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 237 0.364 0.557 0.755 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 99.3 5.84 2.42 0.630 0.586 161s supply 20 16 138.1 8.63 2.94 0.485 0.388 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 161s price -0.1043 0.0958 -1.09 0.28 161s income 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.417 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 161s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 161s price 0.1851 0.1053 1.76 0.088 . 161s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 161s trend 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.938 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 161s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 161s 161s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 17 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 240 0.56 0.553 0.819 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 98.4 5.79 2.41 0.633 0.590 161s supply 20 16 141.1 8.82 2.97 0.474 0.375 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 161s price -0.1064 0.1023 -1.04 0.31 161s income 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.406 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 161s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 161s price 0.1833 0.1189 1.54 0.13 161s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 161s trend 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.97 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 161s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 161s 161s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 20 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 237 0.364 0.557 0.755 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 99.3 5.84 2.42 0.630 0.586 161s supply 20 16 138.1 8.63 2.94 0.485 0.388 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 161s price -0.1043 0.0958 -1.09 0.28 161s income 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.417 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 161s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 161s price 0.1851 0.1053 1.76 0.088 . 161s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 161s trend 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.938 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 161s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 161s 161s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 17 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 240 0.56 0.553 0.819 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 98.4 5.79 2.41 0.633 0.590 161s supply 20 16 141.1 8.82 2.97 0.474 0.375 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 161s price -0.1064 0.1023 -1.04 0.31 161s income 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.406 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 161s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 161s price 0.1833 0.1189 1.54 0.13 161s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 161s trend 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.97 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 161s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 161s 161s [1] "******** iterated 3SLS with 2 restrictions *********************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 9 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 185 1.76 0.655 0.71 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 69.9 4.11 2.03 0.739 0.709 161s supply 20 16 114.8 7.18 2.68 0.572 0.491 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.00 0.97 161s supply 0.97 1.00 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 161s price -0.2007 0.0920 -2.18 0.036 * 161s income 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.028 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 161s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 161s price 0.2993 0.0920 3.25 0.0025 ** 161s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 161s trend 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.679 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 161s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 161s 161s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 8 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 179 1.19 0.666 0.668 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 68.3 4.02 2.00 0.745 0.715 161s supply 20 16 110.8 6.92 2.63 0.587 0.509 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.968 161s supply 0.968 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 161s price -0.2168 0.0835 -2.6 0.014 * 161s income 0.3199 0.0168 19.1 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.004 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 161s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 161s price 0.2832 0.0835 3.39 0.0017 ** 161s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 161s trend 0.3199 0.0168 19.07 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.631 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 161s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 161s 161s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 8 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 179 1.19 0.666 0.668 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 68.3 4.02 2.00 0.745 0.715 161s supply 20 16 110.8 6.92 2.63 0.587 0.509 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.968 161s supply 0.968 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 161s price -0.2168 0.0835 -2.6 0.014 * 161s income 0.3199 0.0168 19.1 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.004 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 161s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 161s price 0.2832 0.0835 3.39 0.0017 ** 161s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 161s trend 0.3199 0.0168 19.07 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.631 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 161s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 161s 161s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 9 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 185 1.76 0.655 0.71 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 69.9 4.11 2.03 0.739 0.709 161s supply 20 16 114.8 7.18 2.68 0.572 0.491 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.00 0.97 161s supply 0.97 1.00 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 161s price -0.2007 0.0920 -2.18 0.036 * 161s income 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.028 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 161s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 161s price 0.2993 0.0920 3.25 0.0025 ** 161s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 161s trend 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.679 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 161s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 161s 161s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 8 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 179 1.19 0.666 0.668 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 68.3 4.02 2.00 0.745 0.715 161s supply 20 16 110.8 6.92 2.63 0.587 0.509 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.41 4.21 161s supply 4.21 5.54 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.968 161s supply 0.968 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 161s price -0.2168 0.0835 -2.6 0.014 * 161s income 0.3199 0.0168 19.1 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.004 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 161s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 161s price 0.2832 0.0835 3.39 0.0017 ** 161s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 161s trend 0.3199 0.0168 19.07 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.631 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 161s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 161s 161s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 9 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 185 1.76 0.655 0.71 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 69.9 4.11 2.03 0.739 0.709 161s supply 20 16 114.8 7.18 2.68 0.572 0.491 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.11 5.27 161s supply 5.27 7.18 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.00 0.97 161s supply 0.97 1.00 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 161s price -0.2007 0.0920 -2.18 0.036 * 161s income 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.028 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 161s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 161s price 0.2993 0.0920 3.25 0.0025 ** 161s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 161s trend 0.3159 0.0192 16.42 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.679 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 161s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 161s 161s [1] "***************************************************" 161s [1] "3SLS formula: EViews" 161s [1] "************* 3SLS *********************************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 6 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 178 0.983 0.668 0.814 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 65.7 3.87 1.97 0.755 0.726 161s supply 20 16 112.4 7.03 2.65 0.581 0.502 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.87 5.12 161s supply 5.12 7.03 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.87 5.12 161s supply 5.12 7.03 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.982 161s supply 0.982 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 161s price -0.2436 0.0965 -2.52 0.022 * 161s income 0.3140 0.0469 6.69 3.8e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.966 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 161s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 161s price 0.2266 0.1075 2.11 0.05110 . 161s farmPrice 0.2234 0.0468 4.78 0.00021 *** 161s trend 0.3800 0.0720 5.28 7.5e-05 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.651 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 161s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 161s 161s [1] "********************* iterated 3SLS EViews-like ****************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 6 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 177 0.667 0.67 0.782 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 65.7 3.87 1.97 0.755 0.726 161s supply 20 16 111.3 6.96 2.64 0.585 0.507 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.29 4.20 161s supply 4.20 5.57 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.29 4.20 161s supply 4.20 5.57 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.982 161s supply 0.982 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 161s price -0.2436 0.0890 -2.74 0.0099 ** 161s income 0.3140 0.0433 7.25 2.5e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.966 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 161s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 161s price 0.2271 0.0956 2.37 0.024 * 161s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 161s trend 0.3756 0.0641 5.86 1.5e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.637 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 161s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 161s 161s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 6 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 179 -0.818 0.665 0.957 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 65.7 3.87 1.97 0.755 0.726 161s supply 20 16 113.8 7.11 2.67 0.576 0.496 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.87 5.32 161s supply 5.32 7.11 161s 161s warning: this covariance matrix is NOT positive semidefinit! 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.87 5.32 161s supply 5.32 7.11 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.982 161s supply 0.982 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 161s price -0.2436 0.0965 -2.52 0.017 * 161s income 0.3140 0.0469 6.69 1.3e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.966 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 161s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 161s price 0.2261 0.1081 2.09 0.04425 * 161s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 161s trend 0.3851 0.0693 5.55 3.6e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.667 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 161s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 161s 161s [1] "**************** iterated W3SLS EViews-like ****************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 6 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 177 0.667 0.67 0.782 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 65.7 3.87 1.97 0.755 0.726 161s supply 20 16 111.3 6.96 2.64 0.585 0.507 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.29 4.20 161s supply 4.20 5.57 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.29 4.20 161s supply 4.20 5.57 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.982 161s supply 0.982 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 161s price -0.2436 0.0890 -2.74 0.0099 ** 161s income 0.3140 0.0433 7.25 2.5e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.966 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 161s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 161s price 0.2271 0.0956 2.37 0.024 * 161s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 161s trend 0.3756 0.0641 5.86 1.5e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.637 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 161s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 161s 161s [1] "******* iterated 3SLS with restriction *****************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 17 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 240 0.56 0.553 0.819 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 98.4 5.79 2.41 0.633 0.590 161s supply 20 16 141.1 8.82 2.97 0.474 0.375 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 161s price -0.1064 0.1023 -1.04 0.31 161s income 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.406 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 161s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 161s price 0.1833 0.1189 1.54 0.13 161s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 161s trend 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.97 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 161s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 161s 161s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 20 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 237 0.364 0.557 0.755 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 99.3 5.84 2.42 0.630 0.586 161s supply 20 16 138.1 8.63 2.94 0.485 0.388 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 161s price -0.1043 0.0958 -1.09 0.28 161s income 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.417 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 161s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 161s price 0.1851 0.1053 1.76 0.088 . 161s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 161s trend 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.938 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 161s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 161s 161s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 20 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 237 0.364 0.557 0.755 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 99.3 5.84 2.42 0.630 0.586 161s supply 20 16 138.1 8.63 2.94 0.485 0.388 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 161s price -0.1043 0.0958 -1.09 0.28 161s income 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.417 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 161s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 161s price 0.1851 0.1053 1.76 0.088 . 161s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 161s trend 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.938 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 161s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 161s 161s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 17 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 240 0.56 0.553 0.819 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 98.4 5.79 2.41 0.633 0.590 161s supply 20 16 141.1 8.82 2.97 0.474 0.375 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 161s price -0.1064 0.1023 -1.04 0.31 161s income 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.406 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 161s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 161s price 0.1833 0.1189 1.54 0.13 161s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 161s trend 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.97 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 161s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 161s 161s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 20 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 237 0.364 0.557 0.755 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 99.3 5.84 2.42 0.630 0.586 161s supply 20 16 138.1 8.63 2.94 0.485 0.388 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.96 5.82 161s supply 5.82 6.90 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 161s price -0.1043 0.0958 -1.09 0.28 161s income 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.417 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 161s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 161s price 0.1851 0.1053 1.76 0.088 . 161s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 161s trend 0.1979 0.0299 6.61 1.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.938 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 161s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 161s 161s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 17 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 240 0.56 0.553 0.819 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 98.4 5.79 2.41 0.633 0.590 161s supply 20 16 141.1 8.82 2.97 0.474 0.375 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 5.79 7.11 161s supply 7.11 8.82 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.995 161s supply 0.995 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 161s price -0.1064 0.1023 -1.04 0.31 161s income 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.406 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 161s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 161s price 0.1833 0.1189 1.54 0.13 161s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 161s trend 0.1996 0.0297 6.73 9.9e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.97 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 161s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 161s 161s [1] "******** iterated 3SLS with 2 restrictions *********************" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s warning: convergence not achieved after 100 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 1194 34.7 -1.23 0.688 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 274 16.1 4.02 -0.024 -0.144 161s supply 20 16 920 57.5 7.58 -2.431 -3.074 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 16.1 29.9 161s supply 29.9 57.5 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 16.1 29.9 161s supply 29.9 57.5 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.981 161s supply 0.981 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 43.5261 10.3602 4.20 0.00017 *** 161s price 0.2553 0.1380 1.85 0.07275 . 161s income 0.3264 0.0424 7.71 4.8e-09 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 4.018 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 274.43 MSE: 16.143 Root MSE: 4.018 161s Multiple R-Squared: -0.024 Adjusted R-Squared: -0.144 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) -49.0143 9.6115 -5.10 1.2e-05 *** 161s price 1.2553 0.1380 9.10 9.5e-11 *** 161s farmPrice 0.2166 0.0573 3.78 0.00058 *** 161s trend 0.3264 0.0424 7.71 4.8e-09 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 7.582 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 919.812 MSE: 57.488 Root MSE: 7.582 161s Multiple R-Squared: -2.431 Adjusted R-Squared: -3.074 161s 161s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 66 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 615 20.5 -0.147 0.48 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 151 8.87 2.98 0.437 0.371 161s supply 20 16 464 29.00 5.38 -0.731 -1.055 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 7.54 12.4 161s supply 12.43 23.2 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 7.54 12.4 161s supply 12.43 23.2 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.939 161s supply 0.939 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.3925 9.6792 7.07 3.1e-08 *** 161s price -0.0907 0.1236 -0.73 0.47 161s income 0.4263 0.0385 11.08 5.4e-13 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.979 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 150.821 MSE: 8.872 Root MSE: 2.979 161s Multiple R-Squared: 0.437 Adjusted R-Squared: 0.371 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) -27.3424 9.5498 -2.86 0.007 ** 161s price 0.9093 0.1236 7.36 1.3e-08 *** 161s farmPrice 0.3396 0.0498 6.82 6.5e-08 *** 161s trend 0.4263 0.0385 11.08 5.4e-13 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 5.385 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 464.036 MSE: 29.002 Root MSE: 5.385 161s Multiple R-Squared: -0.731 Adjusted R-Squared: -1.055 161s 161s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 66 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 615 20.5 -0.147 0.48 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 151 8.87 2.98 0.437 0.371 161s supply 20 16 464 29.00 5.38 -0.731 -1.055 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 7.54 12.4 161s supply 12.43 23.2 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 7.54 12.4 161s supply 12.43 23.2 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.939 161s supply 0.939 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.3925 9.6792 7.07 3.1e-08 *** 161s price -0.0907 0.1236 -0.73 0.47 161s income 0.4263 0.0385 11.08 5.4e-13 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.979 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 150.821 MSE: 8.872 Root MSE: 2.979 161s Multiple R-Squared: 0.437 Adjusted R-Squared: 0.371 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) -27.3423 9.5498 -2.86 0.007 ** 161s price 0.9093 0.1236 7.36 1.3e-08 *** 161s farmPrice 0.3396 0.0498 6.82 6.5e-08 *** 161s trend 0.4263 0.0385 11.08 5.4e-13 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 5.385 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 464.036 MSE: 29.002 Root MSE: 5.385 161s Multiple R-Squared: -0.731 Adjusted R-Squared: -1.055 161s 161s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s warning: convergence not achieved after 100 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 1194 34.7 -1.23 0.688 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 274 16.1 4.02 -0.024 -0.144 161s supply 20 16 920 57.5 7.58 -2.431 -3.074 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 16.1 29.9 161s supply 29.9 57.5 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 16.1 29.9 161s supply 29.9 57.5 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.981 161s supply 0.981 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 43.5261 10.3602 4.20 0.00017 *** 161s price 0.2553 0.1380 1.85 0.07275 . 161s income 0.3264 0.0424 7.71 4.8e-09 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 4.018 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 274.43 MSE: 16.143 Root MSE: 4.018 161s Multiple R-Squared: -0.024 Adjusted R-Squared: -0.144 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) -49.0143 9.6115 -5.10 1.2e-05 *** 161s price 1.2553 0.1380 9.10 9.5e-11 *** 161s farmPrice 0.2166 0.0573 3.78 0.00058 *** 161s trend 0.3264 0.0424 7.71 4.8e-09 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 7.582 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 919.812 MSE: 57.488 Root MSE: 7.582 161s Multiple R-Squared: -2.431 Adjusted R-Squared: -3.074 161s 161s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s convergence achieved after 66 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 615 20.5 -0.147 0.48 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 151 8.87 2.98 0.437 0.371 161s supply 20 16 464 29.00 5.38 -0.731 -1.055 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 7.54 12.4 161s supply 12.43 23.2 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 7.54 12.4 161s supply 12.43 23.2 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.939 161s supply 0.939 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 68.3925 9.6792 7.07 3.1e-08 *** 161s price -0.0907 0.1236 -0.73 0.47 161s income 0.4263 0.0385 11.08 5.4e-13 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.979 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 150.821 MSE: 8.872 Root MSE: 2.979 161s Multiple R-Squared: 0.437 Adjusted R-Squared: 0.371 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) -27.3424 9.5498 -2.86 0.007 ** 161s price 0.9093 0.1236 7.36 1.3e-08 *** 161s farmPrice 0.3396 0.0498 6.82 6.5e-08 *** 161s trend 0.4263 0.0385 11.08 5.4e-13 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 5.385 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 464.036 MSE: 29.002 Root MSE: 5.385 161s Multiple R-Squared: -0.731 Adjusted R-Squared: -1.055 161s 161s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 161s 161s systemfit results 161s method: iterated 3SLS 161s 161s warning: convergence not achieved after 100 iterations 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 1194 34.7 -1.23 0.688 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 274 16.1 4.02 -0.024 -0.144 161s supply 20 16 920 57.5 7.58 -2.431 -3.074 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 16.1 29.9 161s supply 29.9 57.5 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 16.1 29.9 161s supply 29.9 57.5 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.981 161s supply 0.981 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 43.5261 10.3602 4.20 0.00017 *** 161s price 0.2553 0.1380 1.85 0.07275 . 161s income 0.3264 0.0424 7.71 4.8e-09 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 4.018 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 274.43 MSE: 16.143 Root MSE: 4.018 161s Multiple R-Squared: -0.024 Adjusted R-Squared: -0.144 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) -49.0142 9.6115 -5.10 1.2e-05 *** 161s price 1.2553 0.1380 9.10 9.5e-11 *** 161s farmPrice 0.2166 0.0573 3.78 0.00058 *** 161s trend 0.3264 0.0424 7.71 4.8e-09 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 7.582 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 919.811 MSE: 57.488 Root MSE: 7.582 161s Multiple R-Squared: -2.431 Adjusted R-Squared: -3.074 161s 161s > 161s > ## **************** 3SLS with different instruments ************* 161s > fit3slsd <- list() 161s > formulas <- c( "GLS", "IV", "Schmidt", "GMM", "EViews" ) 161s > for( i in seq( along = formulas ) ) { 161s + fit3slsd[[ i ]] <- list() 161s + 161s + print( "***************************************************" ) 161s + print( paste( "3SLS formula:", formulas[ i ] ) ) 161s + print( "************* 3SLS with different instruments **************" ) 161s + fit3slsd[[ i ]]$e1 <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, method3sls = formulas[ i ], useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e1 ) ) 161s + 161s + print( "******* 3SLS with different instruments (EViews-like) **********" ) 161s + fit3slsd[[ i ]]$e1e <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, methodResidCov = "noDfCor", method3sls = formulas[ i ], 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e1e, useDfSys = TRUE ) ) 161s + 161s + print( "**** 3SLS with different instruments and methodResidCov = Theil ***" ) 161s + fit3slsd[[ i ]]$e1c <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, methodResidCov = "Theil", method3sls = formulas[ i ], 161s + x = TRUE, useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e1c, useDfSys = TRUE ) ) 161s + 161s + print( "************* W3SLS with different instruments **************" ) 161s + fit3slsd[[ i ]]$e1w <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, method3sls = formulas[ i ], residCovWeighted = TRUE, 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e1w ) ) 161s + 161s + 161s + print( "******* 3SLS with different instruments and restriction ********" ) 161s + fit3slsd[[ i ]]$e2 <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, restrict.matrix = restrm, method3sls = formulas[ i ], 161s + x = TRUE, useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e2 ) ) 161s + 161s + print( "** 3SLS with different instruments and restriction (EViews-like) *" ) 161s + fit3slsd[[ i ]]$e2e <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, methodResidCov = "noDfCor", restrict.matrix = restrm, 161s + method3sls = formulas[ i ], useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e2e, useDfSys = TRUE ) ) 161s + 161s + print( "** W3SLS with different instruments and restriction (EViews-like) *" ) 161s + fit3slsd[[ i ]]$e2we <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, methodResidCov = "noDfCor", restrict.matrix = restrm, 161s + method3sls = formulas[ i ], residCovWeighted = TRUE, 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e2we, useDfSys = TRUE ) ) 161s + 161s + 161s + print( "** 3SLS with different instruments and restriction via restrict.regMat *******" ) 161s + fit3slsd[[ i ]]$e3 <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, restrict.regMat = tc, method3sls = formulas[ i ], 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e3 ) ) 161s + 161s + print( "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" ) 161s + fit3slsd[[ i ]]$e3e <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, methodResidCov = "noDfCor", restrict.regMat = tc, 161s + method3sls = formulas[ i ], x = TRUE, 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e3e, useDfSys = TRUE ) ) 161s + 161s + print( "** W3SLS with different instr. and restr. via restrict.regMat ****" ) 161s + fit3slsd[[ i ]]$e3w <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, restrict.regMat = tc, method3sls = formulas[ i ], 161s + residCovWeighted = TRUE, x = TRUE, 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e3w ) ) 161s + 161s + 161s + print( "****** 3SLS with different instruments and 2 restrictions *********" ) 161s + fit3slsd[[ i ]]$e4 <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, restrict.matrix = restr2m, restrict.rhs = restr2q, 161s + method3sls = formulas[ i ], x = TRUE, 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e4 ) ) 161s + 161s + print( "** 3SLS with different instruments and 2 restrictions (EViews-like) *" ) 161s + fit3slsd[[ i ]]$e4e <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, methodResidCov = "noDfCor", restrict.matrix = restr2m, 161s + restrict.rhs = restr2q, method3sls = formulas[ i ], 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e4e, useDfSys = TRUE ) ) 161s + 161s + print( "**** W3SLS with different instruments and 2 restrictions *********" ) 161s + fit3slsd[[ i ]]$e4w <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, restrict.matrix = restr2m, restrict.rhs = restr2q, 161s + method3sls = formulas[ i ], residCovWeighted = TRUE, 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e4w ) ) 161s + 161s + 161s + print( " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" ) 161s + fit3slsd[[ i ]]$e5 <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, restrict.regMat = tc, restrict.matrix = restr3m, 161s + restrict.rhs = restr3q, method3sls = formulas[ i ], 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e5 ) ) 161s + 161s + print( "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" ) 161s + fit3slsd[[ i ]]$e5e <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, restrict.regMat = tc, methodResidCov = "noDfCor", 161s + restrict.matrix = restr3m, restrict.rhs = restr3q, 161s + method3sls = formulas[ i ], x = TRUE, 161s + useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e5e, useDfSys = TRUE ) ) 161s + 161s + print( "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" ) 161s + fit3slsd[[ i ]]$e5we <- systemfit( system, "3SLS", data = Kmenta, 161s + inst = instlist, restrict.regMat = tc, methodResidCov = "noDfCor", 161s + restrict.matrix = restr3m, restrict.rhs = restr3q, method3sls = formulas[ i ], 161s + residCovWeighted = TRUE, useMatrix = useMatrix ) 161s + print( summary( fit3slsd[[ i ]]$e5we, useDfSys = TRUE ) ) 161s + } 161s [1] "***************************************************" 161s [1] "3SLS formula: GLS" 161s [1] "************* 3SLS with different instruments **************" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 170 13.4 0.683 0.52 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 67.4 3.97 1.99 0.748 0.719 161s supply 20 16 102.4 6.40 2.53 0.618 0.546 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.97 3.84 161s supply 3.84 6.04 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.97 3.47 161s supply 3.47 6.40 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.688 161s supply 0.688 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 161s price -0.4116 0.1448 -2.84 0.011 * 161s income 0.3617 0.0564 6.41 6.4e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.992 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 161s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 46.9385 11.5390 4.07 0.0009 *** 161s price 0.2744 0.0897 3.06 0.0075 ** 161s farmPrice 0.2521 0.0470 5.36 6.4e-05 *** 161s trend 0.2048 0.0781 2.62 0.0185 * 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.53 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 102.443 MSE: 6.403 Root MSE: 2.53 161s Multiple R-Squared: 0.618 Adjusted R-Squared: 0.546 161s 161s [1] "******* 3SLS with different instruments (EViews-like) **********" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 170 9 0.684 0.511 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 67.4 3.97 1.99 0.748 0.719 161s supply 20 16 102.2 6.39 2.53 0.619 0.547 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.37 3.16 161s supply 3.16 4.83 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.37 2.87 161s supply 2.87 5.11 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.691 161s supply 0.691 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 161s price -0.412 0.134 -3.08 0.0041 ** 161s income 0.362 0.052 6.95 6.0e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.992 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 161s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 47.0160 10.3208 4.56 6.8e-05 *** 161s price 0.2734 0.0802 3.41 0.0017 ** 161s farmPrice 0.2522 0.0421 6.00 9.8e-07 *** 161s trend 0.2062 0.0699 2.95 0.0058 ** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.527 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 102.203 MSE: 6.388 Root MSE: 2.527 161s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 161s 161s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 170 12.7 0.683 0.502 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 67.4 3.97 1.99 0.748 0.719 161s supply 20 16 102.7 6.42 2.53 0.617 0.545 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.97 3.96 161s supply 3.96 6.04 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.97 3.57 161s supply 3.57 6.42 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.685 161s supply 0.685 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 161s price -0.4116 0.1448 -2.84 0.0076 ** 161s income 0.3617 0.0564 6.41 2.9e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.992 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 161s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 46.8512 11.5060 4.07 0.00027 *** 161s price 0.2756 0.0889 3.10 0.00395 ** 161s farmPrice 0.2520 0.0470 5.36 6.4e-06 *** 161s trend 0.2032 0.0765 2.66 0.01204 * 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.534 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 102.718 MSE: 6.42 Root MSE: 2.534 161s Multiple R-Squared: 0.617 Adjusted R-Squared: 0.545 161s 161s [1] "************* W3SLS with different instruments **************" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 170 13.4 0.683 0.52 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 67.4 3.97 1.99 0.748 0.719 161s supply 20 16 102.4 6.40 2.53 0.618 0.546 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.97 3.84 161s supply 3.84 6.04 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.97 3.47 161s supply 3.47 6.40 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.688 161s supply 0.688 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 161s price -0.4116 0.1448 -2.84 0.011 * 161s income 0.3617 0.0564 6.41 6.4e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.992 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 161s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 46.9385 11.5390 4.07 0.0009 *** 161s price 0.2744 0.0897 3.06 0.0075 ** 161s farmPrice 0.2521 0.0470 5.36 6.4e-05 *** 161s trend 0.2048 0.0781 2.62 0.0185 * 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.53 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 102.443 MSE: 6.403 Root MSE: 2.53 161s Multiple R-Squared: 0.618 Adjusted R-Squared: 0.546 161s 161s [1] "******* 3SLS with different instruments and restriction ********" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 201 2.72 0.626 0.685 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 72.3 4.25 2.06 0.730 0.699 161s supply 20 16 128.3 8.02 2.83 0.521 0.432 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.79 4.35 161s supply 4.35 6.27 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.25 5.60 161s supply 5.60 8.02 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.959 161s supply 0.959 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 88.9456 6.3475 14.01 1.1e-15 *** 161s price -0.1778 0.0812 -2.19 0.036 * 161s income 0.3049 0.0474 6.43 2.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.062 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 72.262 MSE: 4.251 Root MSE: 2.062 161s Multiple R-Squared: 0.73 Adjusted R-Squared: 0.699 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 40.2918 11.2022 3.60 0.001 ** 161s price 0.3613 0.0785 4.60 5.6e-05 *** 161s farmPrice 0.2201 0.0453 4.86 2.6e-05 *** 161s trend 0.3049 0.0474 6.43 2.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.832 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 128.304 MSE: 8.019 Root MSE: 2.832 161s Multiple R-Squared: 0.521 Adjusted R-Squared: 0.432 161s 161s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 200 1.75 0.627 0.651 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 72.7 4.28 2.07 0.729 0.697 161s supply 20 16 127.0 7.94 2.82 0.526 0.437 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.22 3.58 161s supply 3.58 5.02 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.64 4.62 161s supply 4.62 6.35 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.961 161s supply 0.961 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 88.7634 5.8428 15.19 < 2e-16 *** 161s price -0.1738 0.0737 -2.36 0.024 * 161s income 0.3027 0.0432 7.00 4.5e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.068 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 72.717 MSE: 4.277 Root MSE: 2.068 161s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 40.8177 10.0564 4.06 0.00027 *** 161s price 0.3569 0.0705 5.06 1.4e-05 *** 161s farmPrice 0.2195 0.0403 5.45 4.4e-06 *** 161s trend 0.3027 0.0432 7.00 4.5e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.818 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 127.044 MSE: 7.94 Root MSE: 2.818 161s Multiple R-Squared: 0.526 Adjusted R-Squared: 0.437 161s 161s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 199 1.77 0.629 0.65 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 72.4 4.26 2.06 0.730 0.698 161s supply 20 16 126.7 7.92 2.81 0.527 0.439 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.24 3.60 161s supply 3.60 5.06 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.62 4.60 161s supply 4.60 6.34 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.961 161s supply 0.961 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 88.9298 5.9083 15.05 < 2e-16 *** 161s price -0.1760 0.0746 -2.36 0.024 * 161s income 0.3032 0.0434 6.99 4.6e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.064 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 72.435 MSE: 4.261 Root MSE: 2.064 161s Multiple R-Squared: 0.73 Adjusted R-Squared: 0.698 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 40.8325 10.1094 4.04 0.00029 *** 161s price 0.3562 0.0711 5.01 1.7e-05 *** 161s farmPrice 0.2200 0.0405 5.43 4.8e-06 *** 161s trend 0.3032 0.0434 6.99 4.6e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.814 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 126.74 MSE: 7.921 Root MSE: 2.814 161s Multiple R-Squared: 0.527 Adjusted R-Squared: 0.439 161s 161s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 201 2.72 0.626 0.685 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 72.3 4.25 2.06 0.730 0.699 161s supply 20 16 128.3 8.02 2.83 0.521 0.432 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.79 4.35 161s supply 4.35 6.27 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.25 5.60 161s supply 5.60 8.02 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.959 161s supply 0.959 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 88.9456 6.3475 14.01 1.1e-15 *** 161s price -0.1778 0.0812 -2.19 0.036 * 161s income 0.3049 0.0474 6.43 2.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.062 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 72.262 MSE: 4.251 Root MSE: 2.062 161s Multiple R-Squared: 0.73 Adjusted R-Squared: 0.699 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 40.2918 11.2022 3.60 0.001 ** 161s price 0.3613 0.0785 4.60 5.6e-05 *** 161s farmPrice 0.2201 0.0453 4.86 2.6e-05 *** 161s trend 0.3049 0.0474 6.43 2.4e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.832 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 128.304 MSE: 8.019 Root MSE: 2.832 161s Multiple R-Squared: 0.521 Adjusted R-Squared: 0.432 161s 161s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 200 1.75 0.627 0.651 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 72.7 4.28 2.07 0.729 0.697 161s supply 20 16 127.0 7.94 2.82 0.526 0.437 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.22 3.58 161s supply 3.58 5.02 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.64 4.62 161s supply 4.62 6.35 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.961 161s supply 0.961 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 88.7634 5.8428 15.19 < 2e-16 *** 161s price -0.1738 0.0737 -2.36 0.024 * 161s income 0.3027 0.0432 7.00 4.5e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.068 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 72.717 MSE: 4.277 Root MSE: 2.068 161s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 40.8177 10.0564 4.06 0.00027 *** 161s price 0.3569 0.0705 5.06 1.4e-05 *** 161s farmPrice 0.2195 0.0403 5.45 4.4e-06 *** 161s trend 0.3027 0.0432 7.00 4.5e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.818 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 127.044 MSE: 7.94 Root MSE: 2.818 161s Multiple R-Squared: 0.526 Adjusted R-Squared: 0.437 161s 161s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 200 2.75 0.627 0.684 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 71.9 4.23 2.06 0.732 0.700 161s supply 20 16 127.9 8.00 2.83 0.523 0.433 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.81 4.36 161s supply 4.36 6.34 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.23 5.58 161s supply 5.58 7.99 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.958 161s supply 0.958 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 89.1391 6.4318 13.86 1.6e-15 *** 161s price -0.1803 0.0823 -2.19 0.035 * 161s income 0.3055 0.0476 6.42 2.5e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.057 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 71.945 MSE: 4.232 Root MSE: 2.057 161s Multiple R-Squared: 0.732 Adjusted R-Squared: 0.7 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 40.3187 11.2699 3.58 0.0011 ** 161s price 0.3604 0.0792 4.55 6.5e-05 *** 161s farmPrice 0.2207 0.0456 4.84 2.8e-05 *** 161s trend 0.3055 0.0476 6.42 2.5e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.828 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 127.918 MSE: 7.995 Root MSE: 2.828 161s Multiple R-Squared: 0.523 Adjusted R-Squared: 0.433 161s 161s [1] "****** 3SLS with different instruments and 2 restrictions *********" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 211 2.1 0.606 0.71 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 77.9 4.58 2.14 0.709 0.675 161s supply 20 16 133.2 8.32 2.88 0.503 0.410 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.79 4.45 161s supply 4.45 6.06 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.58 6.01 161s supply 6.01 8.32 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.972 161s supply 0.972 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 86.4443 5.3770 16.08 <2e-16 *** 161s price -0.1371 0.0504 -2.72 0.01 * 161s income 0.2888 0.0182 15.89 <2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.141 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 77.945 MSE: 4.585 Root MSE: 2.141 161s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 41.8618 5.4316 7.71 4.8e-09 *** 161s price 0.3629 0.0504 7.20 2.1e-08 *** 161s farmPrice 0.2040 0.0205 9.96 9.4e-12 *** 161s trend 0.2888 0.0182 15.89 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.885 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 133.177 MSE: 8.324 Root MSE: 2.885 161s Multiple R-Squared: 0.503 Adjusted R-Squared: 0.41 161s 161s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 210 1.42 0.609 0.668 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 77.9 4.58 2.14 0.709 0.675 161s supply 20 16 132.0 8.25 2.87 0.508 0.415 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.22 3.67 161s supply 3.67 4.85 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.90 4.93 161s supply 4.93 6.60 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.972 161s supply 0.972 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 86.3521 4.9704 17.4 <2e-16 *** 161s price -0.1376 0.0458 -3.0 0.0049 ** 161s income 0.2902 0.0168 17.3 <2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.141 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 77.912 MSE: 4.583 Root MSE: 2.141 161s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 41.6089 4.9950 8.33 8.0e-10 *** 161s price 0.3624 0.0458 7.91 2.6e-09 *** 161s farmPrice 0.2069 0.0184 11.27 3.4e-13 *** 161s trend 0.2902 0.0168 17.27 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.872 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 131.997 MSE: 8.25 Root MSE: 2.872 161s Multiple R-Squared: 0.508 Adjusted R-Squared: 0.415 161s 161s [1] "**** W3SLS with different instruments and 2 restrictions *********" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 214 2.1 0.601 0.713 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 78.9 4.64 2.15 0.706 0.671 161s supply 20 16 135.2 8.45 2.91 0.496 0.401 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.75 4.46 161s supply 4.46 6.04 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.64 6.09 161s supply 6.09 8.45 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.973 161s supply 0.973 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 85.9516 5.1136 16.81 <2e-16 *** 161s price -0.1318 0.0479 -2.75 0.0093 ** 161s income 0.2884 0.0171 16.86 <2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.154 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 78.853 MSE: 4.638 Root MSE: 2.154 161s Multiple R-Squared: 0.706 Adjusted R-Squared: 0.671 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 41.4498 5.1591 8.03 1.9e-09 *** 161s price 0.3682 0.0479 7.69 5.0e-09 *** 161s farmPrice 0.2028 0.0193 10.50 2.3e-12 *** 161s trend 0.2884 0.0171 16.86 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.907 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 135.215 MSE: 8.451 Root MSE: 2.907 161s Multiple R-Squared: 0.496 Adjusted R-Squared: 0.401 161s 161s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 211 2.1 0.606 0.71 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 77.9 4.58 2.14 0.709 0.675 161s supply 20 16 133.2 8.32 2.88 0.503 0.410 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.79 4.45 161s supply 4.45 6.06 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 4.58 6.01 161s supply 6.01 8.32 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.972 161s supply 0.972 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 86.4443 5.3770 16.08 <2e-16 *** 161s price -0.1371 0.0504 -2.72 0.01 * 161s income 0.2888 0.0182 15.89 <2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.141 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 77.945 MSE: 4.585 Root MSE: 2.141 161s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 41.8618 5.4316 7.71 4.8e-09 *** 161s price 0.3629 0.0504 7.20 2.1e-08 *** 161s farmPrice 0.2040 0.0205 9.96 9.4e-12 *** 161s trend 0.2888 0.0182 15.89 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.885 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 133.177 MSE: 8.324 Root MSE: 2.885 161s Multiple R-Squared: 0.503 Adjusted R-Squared: 0.41 161s 161s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 210 1.42 0.609 0.668 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 77.9 4.58 2.14 0.709 0.675 161s supply 20 16 132.0 8.25 2.87 0.508 0.415 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.22 3.67 161s supply 3.67 4.85 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.90 4.93 161s supply 4.93 6.60 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.972 161s supply 0.972 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 86.3521 4.9704 17.4 <2e-16 *** 161s price -0.1376 0.0458 -3.0 0.0049 ** 161s income 0.2902 0.0168 17.3 <2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.141 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 77.912 MSE: 4.583 Root MSE: 2.141 161s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 41.6089 4.9950 8.33 8.0e-10 *** 161s price 0.3624 0.0458 7.91 2.6e-09 *** 161s farmPrice 0.2069 0.0184 11.27 3.4e-13 *** 161s trend 0.2902 0.0168 17.27 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.872 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 131.997 MSE: 8.25 Root MSE: 2.872 161s Multiple R-Squared: 0.508 Adjusted R-Squared: 0.415 161s 161s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 35 212 1.42 0.604 0.671 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 78.7 4.63 2.15 0.706 0.672 161s supply 20 16 133.7 8.36 2.89 0.501 0.408 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.19 3.68 161s supply 3.68 4.83 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.94 4.99 161s supply 4.99 6.69 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.973 161s supply 0.973 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 85.9108 4.7598 18.05 <2e-16 *** 161s price -0.1329 0.0438 -3.03 0.0045 ** 161s income 0.2900 0.0159 18.18 <2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.152 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 78.713 MSE: 4.63 Root MSE: 2.152 161s Multiple R-Squared: 0.706 Adjusted R-Squared: 0.672 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 41.2362 4.7784 8.63 3.5e-10 *** 161s price 0.3671 0.0438 8.38 7.0e-10 *** 161s farmPrice 0.2060 0.0174 11.81 9.1e-14 *** 161s trend 0.2900 0.0159 18.18 < 2e-16 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.891 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 133.715 MSE: 8.357 Root MSE: 2.891 161s Multiple R-Squared: 0.501 Adjusted R-Squared: 0.408 161s 161s [1] "***************************************************" 161s [1] "3SLS formula: IV" 161s [1] "************* 3SLS with different instruments **************" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 174 2.12 0.675 0.659 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 67.4 3.97 1.99 0.748 0.719 161s supply 20 16 106.6 6.66 2.58 0.602 0.528 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.97 3.84 161s supply 3.84 6.04 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.97 4.93 161s supply 4.93 6.66 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.959 161s supply 0.959 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 161s price -0.4116 0.1448 -2.84 0.011 * 161s income 0.3617 0.0564 6.41 6.4e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.992 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 161s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 57.2953 11.7078 4.89 0.00016 *** 161s price 0.1373 0.0979 1.40 0.17978 161s farmPrice 0.2660 0.0483 5.51 4.8e-05 *** 161s trend 0.3970 0.0672 5.91 2.2e-05 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.582 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 161s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 161s 161s [1] "******* 3SLS with different instruments (EViews-like) **********" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 173 1.51 0.677 0.612 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 67.4 3.97 1.99 0.748 0.719 161s supply 20 16 105.7 6.61 2.57 0.606 0.532 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.37 3.16 161s supply 3.16 4.83 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.37 4.04 161s supply 4.04 5.29 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.957 161s supply 0.957 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 161s price -0.412 0.134 -3.08 0.0041 ** 161s income 0.362 0.052 6.95 6.0e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.992 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 161s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 57.0636 10.4717 5.45 4.9e-06 *** 161s price 0.1403 0.0875 1.60 0.12 161s farmPrice 0.2657 0.0432 6.15 6.2e-07 *** 161s trend 0.3927 0.0601 6.53 2.0e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.571 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 105.735 MSE: 6.608 Root MSE: 2.571 161s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 161s 161s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 175 0.321 0.673 0.655 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 67.4 3.97 1.99 0.748 0.719 161s supply 20 16 107.7 6.73 2.59 0.598 0.523 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.97 3.96 161s supply 3.96 6.04 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.97 5.14 161s supply 5.14 6.73 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.962 161s supply 0.962 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 161s price -0.4116 0.1448 -2.84 0.0076 ** 161s income 0.3617 0.0564 6.41 2.9e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.992 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 161s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 57.5567 11.6867 4.92 2.3e-05 *** 161s price 0.1338 0.0977 1.37 0.18 161s farmPrice 0.2664 0.0484 5.51 4.1e-06 *** 161s trend 0.4018 0.0644 6.24 4.8e-07 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.594 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 107.679 MSE: 6.73 Root MSE: 2.594 161s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 161s 161s [1] "************* W3SLS with different instruments **************" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 33 174 2.12 0.675 0.659 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 67.4 3.97 1.99 0.748 0.719 161s supply 20 16 106.6 6.66 2.58 0.602 0.528 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.97 3.84 161s supply 3.84 6.04 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 3.97 4.93 161s supply 4.93 6.66 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.959 161s supply 0.959 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 161s price -0.4116 0.1448 -2.84 0.011 * 161s income 0.3617 0.0564 6.41 6.4e-06 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 1.992 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 161s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 57.2953 11.7078 4.89 0.00016 *** 161s price 0.1373 0.0979 1.40 0.17978 161s farmPrice 0.2660 0.0483 5.51 4.8e-05 *** 161s trend 0.3970 0.0672 5.91 2.2e-05 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 2.582 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 161s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 161s 161s [1] "******* 3SLS with different instruments and restriction ********" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 397 11.4 0.26 -0.128 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 175 10.3 3.20 0.349 0.273 161s supply 20 16 223 13.9 3.73 0.170 0.014 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.79 4.35 161s supply 4.35 6.27 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 10.3 11.5 161s supply 11.5 13.9 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.959 161s supply 0.959 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 137.2061 12.4591 11.01 9.3e-13 *** 161s price -0.8101 0.1734 -4.67 4.5e-05 *** 161s income 0.4585 0.0659 6.96 5.0e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 3.204 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 174.513 MSE: 10.265 Root MSE: 3.204 161s Multiple R-Squared: 0.349 Adjusted R-Squared: 0.273 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 81.1339 9.1968 8.82 2.6e-10 *** 161s price -0.1765 0.0892 -1.98 0.056 . 161s farmPrice 0.3374 0.0591 5.71 2.1e-06 *** 161s trend 0.4585 0.0659 6.96 5.0e-08 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 3.73 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 222.562 MSE: 13.91 Root MSE: 3.73 161s Multiple R-Squared: 0.17 Adjusted R-Squared: 0.014 161s 161s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 161s 161s systemfit results 161s method: 3SLS 161s 161s N DF SSR detRCov OLS-R2 McElroy-R2 161s system 40 34 365 7.14 0.319 -0.166 161s 161s N DF SSR MSE RMSE R2 Adj R2 161s demand 20 17 163 9.57 3.09 0.393 0.322 161s supply 20 16 202 12.65 3.56 0.245 0.104 161s 161s The covariance matrix of the residuals used for estimation 161s demand supply 161s demand 3.22 3.58 161s supply 3.58 5.02 161s 161s The covariance matrix of the residuals 161s demand supply 161s demand 8.13 8.67 161s supply 8.67 10.12 161s 161s The correlations of the residuals 161s demand supply 161s demand 1.000 0.956 161s supply 0.956 1.000 161s 161s 161s 3SLS estimates for 'demand' (equation 1) 161s Model Formula: consump ~ price + income 161s Instruments: ~income + farmPrice 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 134.9751 11.3086 11.94 1.0e-13 *** 161s price -0.7834 0.1565 -5.01 1.7e-05 *** 161s income 0.4539 0.0598 7.60 8.0e-09 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 3.093 on 17 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 17 161s SSR: 162.635 MSE: 9.567 Root MSE: 3.093 161s Multiple R-Squared: 0.393 Adjusted R-Squared: 0.322 161s 161s 161s 3SLS estimates for 'supply' (equation 2) 161s Model Formula: consump ~ price + farmPrice + trend 161s Instruments: ~income + farmPrice + trend 161s 161s Estimate Std. Error t value Pr(>|t|) 161s (Intercept) 78.1824 8.5029 9.19 9.6e-11 *** 161s price -0.1415 0.0807 -1.75 0.089 . 161s farmPrice 0.3322 0.0524 6.34 3.1e-07 *** 161s trend 0.4539 0.0598 7.60 8.0e-09 *** 161s --- 161s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 161s 161s Residual standard error: 3.557 on 16 degrees of freedom 161s Number of observations: 20 Degrees of Freedom: 16 161s SSR: 202.39 MSE: 12.649 Root MSE: 3.557 161s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.104 161s 161s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 351 6.72 0.345 -0.118 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 156 9.18 3.03 0.418 0.349 162s supply 20 16 195 12.20 3.49 0.272 0.135 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.24 3.60 162s supply 3.60 5.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 7.81 8.34 162s supply 8.34 9.76 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.955 162s supply 0.955 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 133.7954 11.2810 11.86 1.2e-13 *** 162s price -0.7678 0.1558 -4.93 2.1e-05 *** 162s income 0.4501 0.0595 7.56 8.8e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.031 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 156.133 MSE: 9.184 Root MSE: 3.031 162s Multiple R-Squared: 0.418 Adjusted R-Squared: 0.349 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 77.4097 8.6219 8.98 1.7e-10 *** 162s price -0.1304 0.0814 -1.60 0.12 162s farmPrice 0.3292 0.0523 6.29 3.6e-07 *** 162s trend 0.4501 0.0595 7.56 8.8e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.493 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 195.256 MSE: 12.204 Root MSE: 3.493 162s Multiple R-Squared: 0.272 Adjusted R-Squared: 0.135 162s 162s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 397 11.4 0.26 -0.128 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 175 10.3 3.20 0.349 0.273 162s supply 20 16 223 13.9 3.73 0.170 0.014 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.35 162s supply 4.35 6.27 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 10.3 11.5 162s supply 11.5 13.9 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.959 162s supply 0.959 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 137.2061 12.4591 11.01 9.3e-13 *** 162s price -0.8101 0.1734 -4.67 4.5e-05 *** 162s income 0.4585 0.0659 6.96 5.0e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.204 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 174.513 MSE: 10.265 Root MSE: 3.204 162s Multiple R-Squared: 0.349 Adjusted R-Squared: 0.273 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 81.1339 9.1968 8.82 2.6e-10 *** 162s price -0.1765 0.0892 -1.98 0.056 . 162s farmPrice 0.3374 0.0591 5.71 2.1e-06 *** 162s trend 0.4585 0.0659 6.96 5.0e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.73 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 222.562 MSE: 13.91 Root MSE: 3.73 162s Multiple R-Squared: 0.17 Adjusted R-Squared: 0.014 162s 162s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 365 7.14 0.319 -0.166 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 163 9.57 3.09 0.393 0.322 162s supply 20 16 202 12.65 3.56 0.245 0.104 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.58 162s supply 3.58 5.02 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 8.13 8.67 162s supply 8.67 10.12 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.956 162s supply 0.956 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 134.9751 11.3086 11.94 1.0e-13 *** 162s price -0.7834 0.1565 -5.01 1.7e-05 *** 162s income 0.4539 0.0598 7.60 8.0e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.093 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 162.635 MSE: 9.567 Root MSE: 3.093 162s Multiple R-Squared: 0.393 Adjusted R-Squared: 0.322 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 78.1824 8.5029 9.19 9.6e-11 *** 162s price -0.1415 0.0807 -1.75 0.089 . 162s farmPrice 0.3322 0.0524 6.34 3.1e-07 *** 162s trend 0.4539 0.0598 7.60 8.0e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.557 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 202.39 MSE: 12.649 Root MSE: 3.557 162s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.104 162s 162s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 378 10.5 0.295 -0.071 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 166 9.74 3.12 0.382 0.309 162s supply 20 16 212 13.26 3.64 0.209 0.060 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.81 4.36 162s supply 4.36 6.34 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 9.75 10.9 162s supply 10.89 13.3 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.958 162s supply 0.958 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 135.6740 12.4146 10.93 1.1e-12 *** 162s price -0.7901 0.1723 -4.59 5.9e-05 *** 162s income 0.4537 0.0655 6.92 5.6e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.122 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 165.668 MSE: 9.745 Root MSE: 3.122 162s Multiple R-Squared: 0.382 Adjusted R-Squared: 0.309 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 80.0613 9.3724 8.54 5.6e-10 *** 162s price -0.1614 0.0902 -1.79 0.082 . 162s farmPrice 0.3335 0.0590 5.65 2.4e-06 *** 162s trend 0.4537 0.0655 6.92 5.6e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.642 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 212.177 MSE: 13.261 Root MSE: 3.642 162s Multiple R-Squared: 0.209 Adjusted R-Squared: 0.06 162s 162s [1] "****** 3SLS with different instruments and 2 restrictions *********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 362 6.33 0.325 0.259 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 149 8.79 2.96 0.443 0.377 162s supply 20 16 213 13.30 3.65 0.206 0.058 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.45 162s supply 4.45 6.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 8.79 10.5 162s supply 10.51 13.3 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.973 162s supply 0.973 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 135.467 10.955 12.37 2.5e-14 *** 162s price -0.727 0.116 -6.27 3.4e-07 *** 162s income 0.391 0.018 21.77 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.964 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 149.387 MSE: 8.787 Root MSE: 2.964 162s Multiple R-Squared: 0.443 Adjusted R-Squared: 0.377 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 92.2897 11.0352 8.36 7.3e-10 *** 162s price -0.2272 0.1160 -1.96 0.058 . 162s farmPrice 0.2817 0.0209 13.47 2.0e-15 *** 162s trend 0.3913 0.0180 21.77 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.647 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 212.786 MSE: 13.299 Root MSE: 3.647 162s Multiple R-Squared: 0.206 Adjusted R-Squared: 0.058 162s 162s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 306 3.37 0.43 0.248 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 127 7.5 2.74 0.525 0.469 162s supply 20 16 178 11.2 3.34 0.334 0.210 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.67 162s supply 3.67 4.85 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 6.37 7.31 162s supply 7.31 8.92 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.97 162s supply 0.97 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 130.7296 9.6847 13.50 2.0e-15 *** 162s price -0.6671 0.1009 -6.61 1.2e-07 *** 162s income 0.3782 0.0159 23.74 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.738 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 127.413 MSE: 7.495 Root MSE: 2.738 162s Multiple R-Squared: 0.525 Adjusted R-Squared: 0.469 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 87.4510 9.7547 8.96 1.4e-10 *** 162s price -0.1671 0.1009 -1.66 0.11 162s farmPrice 0.2710 0.0183 14.81 < 2e-16 *** 162s trend 0.3782 0.0159 23.74 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.34 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 178.456 MSE: 11.154 Root MSE: 3.34 162s Multiple R-Squared: 0.334 Adjusted R-Squared: 0.21 162s 162s [1] "**** W3SLS with different instruments and 2 restrictions *********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 467 8.98 0.128 0.113 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 193 11.3 3.37 0.282 0.197 162s supply 20 16 275 17.2 4.14 -0.025 -0.217 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.75 4.46 162s supply 4.46 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 11.3 13.6 162s supply 13.6 17.2 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.977 162s supply 0.977 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 143.4678 11.2566 12.75 1.0e-14 *** 162s price -0.8203 0.1194 -6.87 5.6e-08 *** 162s income 0.4047 0.0168 24.13 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.366 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 192.561 MSE: 11.327 Root MSE: 3.366 162s Multiple R-Squared: 0.282 Adjusted R-Squared: 0.197 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 100.3734 11.3093 8.88 1.7e-10 *** 162s price -0.3203 0.1194 -2.68 0.011 * 162s farmPrice 0.2930 0.0198 14.79 < 2e-16 *** 162s trend 0.4047 0.0168 24.13 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 4.144 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 274.775 MSE: 17.173 Root MSE: 4.144 162s Multiple R-Squared: -0.025 Adjusted R-Squared: -0.217 162s 162s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 362 6.33 0.325 0.259 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 149 8.79 2.96 0.443 0.377 162s supply 20 16 213 13.30 3.65 0.206 0.058 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.45 162s supply 4.45 6.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 8.79 10.5 162s supply 10.51 13.3 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.973 162s supply 0.973 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 135.467 10.955 12.37 2.5e-14 *** 162s price -0.727 0.116 -6.27 3.4e-07 *** 162s income 0.391 0.018 21.77 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.964 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 149.387 MSE: 8.787 Root MSE: 2.964 162s Multiple R-Squared: 0.443 Adjusted R-Squared: 0.377 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 92.2897 11.0352 8.36 7.3e-10 *** 162s price -0.2272 0.1160 -1.96 0.058 . 162s farmPrice 0.2817 0.0209 13.47 2.0e-15 *** 162s trend 0.3913 0.0180 21.77 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.647 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 212.786 MSE: 13.299 Root MSE: 3.647 162s Multiple R-Squared: 0.206 Adjusted R-Squared: 0.058 162s 162s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 306 3.37 0.43 0.248 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 127 7.5 2.74 0.525 0.469 162s supply 20 16 178 11.2 3.34 0.334 0.210 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.67 162s supply 3.67 4.85 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 6.37 7.31 162s supply 7.31 8.92 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.97 162s supply 0.97 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 130.7296 9.6847 13.50 2.0e-15 *** 162s price -0.6671 0.1009 -6.61 1.2e-07 *** 162s income 0.3782 0.0159 23.74 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.738 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 127.413 MSE: 7.495 Root MSE: 2.738 162s Multiple R-Squared: 0.525 Adjusted R-Squared: 0.469 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 87.4510 9.7547 8.96 1.4e-10 *** 162s price -0.1671 0.1009 -1.66 0.11 162s farmPrice 0.2710 0.0183 14.81 < 2e-16 *** 162s trend 0.3782 0.0159 23.74 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.34 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 178.456 MSE: 11.154 Root MSE: 3.34 162s Multiple R-Squared: 0.334 Adjusted R-Squared: 0.21 162s 162s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 365 4.27 0.319 0.127 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 153 8.97 3.00 0.431 0.364 162s supply 20 16 213 13.29 3.65 0.207 0.058 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.19 3.68 162s supply 3.68 4.83 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 7.63 8.77 162s supply 8.77 10.64 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.973 162s supply 0.973 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 136.2729 9.8523 13.83 8.9e-16 *** 162s price -0.7306 0.1027 -7.11 2.7e-08 *** 162s income 0.3865 0.0149 25.95 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.996 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 152.579 MSE: 8.975 Root MSE: 2.996 162s Multiple R-Squared: 0.431 Adjusted R-Squared: 0.364 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 93.0701 9.9030 9.40 4.2e-11 *** 162s price -0.2306 0.1027 -2.24 0.031 * 162s farmPrice 0.2777 0.0174 15.99 < 2e-16 *** 162s trend 0.3865 0.0149 25.95 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.646 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 212.723 MSE: 13.295 Root MSE: 3.646 162s Multiple R-Squared: 0.207 Adjusted R-Squared: 0.058 162s 162s [1] "***************************************************" 162s [1] "3SLS formula: Schmidt" 162s [1] "************* 3SLS with different instruments **************" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 164 9.25 0.694 0.512 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 96.6 6.04 2.46 0.640 0.572 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.784 162s supply 0.784 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 162s price -0.4116 0.1448 -2.84 0.011 * 162s income 0.3617 0.0564 6.41 6.4e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 162s price 0.2401 0.0999 2.40 0.0288 * 162s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 162s trend 0.2529 0.0997 2.54 0.0219 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.458 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 162s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 162s 162s [1] "******* 3SLS with different instruments (EViews-like) **********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 164 6.29 0.694 0.5 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 96.6 6.04 2.46 0.640 0.572 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.37 3.16 162s supply 3.16 4.83 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.37 3.16 162s supply 3.16 4.83 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.784 162s supply 0.784 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 162s price -0.412 0.134 -3.08 0.0041 ** 162s income 0.362 0.052 6.95 6.0e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 162s price 0.2401 0.0894 2.69 0.0112 * 162s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 162s trend 0.2529 0.0891 2.84 0.0077 ** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.458 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 162s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 162s 162s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 164 8.24 0.694 0.481 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 96.6 6.04 2.46 0.640 0.572 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.97 3.96 162s supply 3.96 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 3.96 162s supply 3.96 6.04 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.784 162s supply 0.784 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 162s price -0.4116 0.1448 -2.84 0.0076 ** 162s income 0.3617 0.0564 6.41 2.9e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 162s price 0.2401 0.0999 2.40 0.02208 * 162s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 162s trend 0.2529 0.0997 2.54 0.01605 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.458 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 162s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 162s 162s [1] "************* W3SLS with different instruments **************" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 164 9.25 0.694 0.512 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 96.6 6.04 2.46 0.640 0.572 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.784 162s supply 0.784 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 162s price -0.4116 0.1448 -2.84 0.011 * 162s income 0.3617 0.0564 6.41 6.4e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 162s price 0.2401 0.0999 2.40 0.0288 * 162s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 162s trend 0.2529 0.0997 2.54 0.0219 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.458 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 162s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 162s 162s [1] "******* 3SLS with different instruments and restriction ********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 175 2.68 0.673 0.665 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 65 3.82 1.96 0.758 0.729 162s supply 20 16 110 6.90 2.63 0.588 0.511 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.35 162s supply 4.35 6.27 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.82 4.87 162s supply 4.87 6.90 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.948 162s supply 0.948 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 95.0869 9.9882 9.52 4.0e-11 *** 162s price -0.2583 0.1296 -1.99 0.054 . 162s income 0.3244 0.0534 6.08 6.8e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.955 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 64.961 MSE: 3.821 Root MSE: 1.955 162s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.729 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 45.4891 12.9647 3.51 0.0013 ** 162s price 0.2929 0.1164 2.52 0.0167 * 162s farmPrice 0.2350 0.0490 4.80 3.1e-05 *** 162s trend 0.3244 0.0534 6.08 6.8e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.627 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 110.382 MSE: 6.899 Root MSE: 2.627 162s Multiple R-Squared: 0.588 Adjusted R-Squared: 0.511 162s 162s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 175 1.75 0.673 0.636 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 65.2 3.83 1.96 0.757 0.728 162s supply 20 16 110.0 6.88 2.62 0.590 0.513 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.58 162s supply 3.58 5.02 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.26 4.02 162s supply 4.02 5.50 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.95 162s supply 0.95 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 94.845 9.149 10.37 4.6e-12 *** 162s price -0.254 0.119 -2.14 0.039 * 162s income 0.323 0.049 6.58 1.5e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.958 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 65.171 MSE: 3.834 Root MSE: 1.958 162s Multiple R-Squared: 0.757 Adjusted R-Squared: 0.728 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 45.7348 11.5558 3.96 0.00037 *** 162s price 0.2913 0.1036 2.81 0.00814 ** 162s farmPrice 0.2343 0.0438 5.35 6.0e-06 *** 162s trend 0.3226 0.0490 6.58 1.5e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.622 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 110.035 MSE: 6.877 Root MSE: 2.622 162s Multiple R-Squared: 0.59 Adjusted R-Squared: 0.513 162s 162s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 175 1.76 0.674 0.635 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 65.1 3.83 1.96 0.757 0.729 162s supply 20 16 109.9 6.87 2.62 0.590 0.513 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.24 3.60 162s supply 3.60 5.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.25 4.02 162s supply 4.02 5.50 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.949 162s supply 0.949 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 94.9533 9.1511 10.38 4.5e-12 *** 162s price -0.2555 0.1186 -2.15 0.038 * 162s income 0.3229 0.0491 6.58 1.5e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.957 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 65.09 MSE: 3.829 Root MSE: 1.957 162s Multiple R-Squared: 0.757 Adjusted R-Squared: 0.729 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 45.7433 11.6043 3.94 0.00038 *** 162s price 0.2908 0.1039 2.80 0.00839 ** 162s farmPrice 0.2347 0.0440 5.34 6.2e-06 *** 162s trend 0.3229 0.0491 6.58 1.5e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.621 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 109.922 MSE: 6.87 Root MSE: 2.621 162s Multiple R-Squared: 0.59 Adjusted R-Squared: 0.513 162s 162s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 175 2.68 0.673 0.665 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 65 3.82 1.96 0.758 0.729 162s supply 20 16 110 6.90 2.63 0.588 0.511 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.35 162s supply 4.35 6.27 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.82 4.87 162s supply 4.87 6.90 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.948 162s supply 0.948 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 95.0869 9.9882 9.52 4.0e-11 *** 162s price -0.2583 0.1296 -1.99 0.054 . 162s income 0.3244 0.0534 6.08 6.8e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.955 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 64.961 MSE: 3.821 Root MSE: 1.955 162s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.729 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 45.4891 12.9647 3.51 0.0013 ** 162s price 0.2929 0.1164 2.52 0.0167 * 162s farmPrice 0.2350 0.0490 4.80 3.1e-05 *** 162s trend 0.3244 0.0534 6.08 6.8e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.627 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 110.382 MSE: 6.899 Root MSE: 2.627 162s Multiple R-Squared: 0.588 Adjusted R-Squared: 0.511 162s 162s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 175 1.75 0.673 0.636 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 65.2 3.83 1.96 0.757 0.728 162s supply 20 16 110.0 6.88 2.62 0.590 0.513 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.58 162s supply 3.58 5.02 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.26 4.02 162s supply 4.02 5.50 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.95 162s supply 0.95 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 94.845 9.149 10.37 4.6e-12 *** 162s price -0.254 0.119 -2.14 0.039 * 162s income 0.323 0.049 6.58 1.5e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.958 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 65.171 MSE: 3.834 Root MSE: 1.958 162s Multiple R-Squared: 0.757 Adjusted R-Squared: 0.728 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 45.7348 11.5558 3.96 0.00037 *** 162s price 0.2913 0.1036 2.81 0.00814 ** 162s farmPrice 0.2343 0.0438 5.35 6.0e-06 *** 162s trend 0.3226 0.0490 6.58 1.5e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.622 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 110.035 MSE: 6.877 Root MSE: 2.622 162s Multiple R-Squared: 0.59 Adjusted R-Squared: 0.513 162s 162s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 175 2.7 0.673 0.664 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 64.9 3.82 1.95 0.758 0.730 162s supply 20 16 110.2 6.89 2.62 0.589 0.512 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.81 4.36 162s supply 4.36 6.34 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.82 4.86 162s supply 4.86 6.89 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.947 162s supply 0.947 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 95.2108 9.9899 9.53 3.9e-11 *** 162s price -0.2599 0.1296 -2.00 0.053 . 162s income 0.3248 0.0535 6.08 6.9e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.954 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 64.876 MSE: 3.816 Root MSE: 1.954 162s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.73 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 45.5042 13.0242 3.49 0.0013 ** 162s price 0.2923 0.1167 2.50 0.0172 * 162s farmPrice 0.2354 0.0492 4.78 3.3e-05 *** 162s trend 0.3248 0.0535 6.08 6.9e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.625 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 110.241 MSE: 6.89 Root MSE: 2.625 162s Multiple R-Squared: 0.589 Adjusted R-Squared: 0.512 162s 162s [1] "****** 3SLS with different instruments and 2 restrictions *********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 178 1.92 0.667 0.696 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.5 3.97 1.99 0.748 0.719 162s supply 20 16 110.9 6.93 2.63 0.586 0.509 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.45 162s supply 4.45 6.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 5.06 162s supply 5.06 6.93 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.964 162s supply 0.964 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 93.3937 10.2477 9.11 9.1e-11 *** 162s price -0.2208 0.1165 -1.90 0.066 . 162s income 0.3033 0.0257 11.78 9.9e-14 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.993 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.513 MSE: 3.971 Root MSE: 1.993 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.0104 10.4895 4.67 4.3e-05 *** 162s price 0.2792 0.1165 2.40 0.022 * 162s farmPrice 0.2150 0.0247 8.70 2.8e-10 *** 162s trend 0.3033 0.0257 11.78 9.9e-14 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.633 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 110.934 MSE: 6.933 Root MSE: 2.633 162s Multiple R-Squared: 0.586 Adjusted R-Squared: 0.509 162s 162s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 178 1.3 0.668 0.659 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.6 3.98 1.99 0.748 0.718 162s supply 20 16 110.7 6.92 2.63 0.587 0.510 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.67 162s supply 3.67 4.85 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.38 4.17 162s supply 4.17 5.53 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.965 162s supply 0.965 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 93.210 9.365 9.95 9.6e-12 *** 162s price -0.219 0.105 -2.09 0.044 * 162s income 0.304 0.023 13.19 3.8e-15 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.994 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.616 MSE: 3.977 Root MSE: 1.994 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 48.6930 9.6005 5.07 1.3e-05 *** 162s price 0.2806 0.1052 2.67 0.011 * 162s farmPrice 0.2168 0.0216 10.02 8.1e-12 *** 162s trend 0.3038 0.0230 13.19 3.8e-15 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.63 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 110.672 MSE: 6.917 Root MSE: 2.63 162s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.51 162s 162s [1] "**** W3SLS with different instruments and 2 restrictions *********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 179 1.92 0.666 0.698 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.7 3.98 2.00 0.747 0.718 162s supply 20 16 111.6 6.98 2.64 0.584 0.506 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.75 4.46 162s supply 4.46 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.98 5.09 162s supply 5.09 6.98 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.965 162s supply 0.965 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 93.180 10.378 8.98 1.3e-10 *** 162s price -0.218 0.118 -1.85 0.073 . 162s income 0.303 0.025 12.11 4.5e-14 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.996 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.719 MSE: 3.983 Root MSE: 1.996 162s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.718 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 48.8549 10.5929 4.61 5.1e-05 *** 162s price 0.2817 0.1182 2.38 0.023 * 162s farmPrice 0.2141 0.0239 8.94 1.5e-10 *** 162s trend 0.3030 0.0250 12.11 4.5e-14 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.641 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 111.614 MSE: 6.976 Root MSE: 2.641 162s Multiple R-Squared: 0.584 Adjusted R-Squared: 0.506 162s 162s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 178 1.92 0.667 0.696 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.5 3.97 1.99 0.748 0.719 162s supply 20 16 110.9 6.93 2.63 0.586 0.509 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.45 162s supply 4.45 6.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 5.06 162s supply 5.06 6.93 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.964 162s supply 0.964 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 93.3937 10.2477 9.11 9.1e-11 *** 162s price -0.2208 0.1165 -1.90 0.066 . 162s income 0.3033 0.0257 11.78 9.9e-14 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.993 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.513 MSE: 3.971 Root MSE: 1.993 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.0104 10.4895 4.67 4.3e-05 *** 162s price 0.2792 0.1165 2.40 0.022 * 162s farmPrice 0.2150 0.0247 8.70 2.8e-10 *** 162s trend 0.3033 0.0257 11.78 9.9e-14 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.633 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 110.934 MSE: 6.933 Root MSE: 2.633 162s Multiple R-Squared: 0.586 Adjusted R-Squared: 0.509 162s 162s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 178 1.3 0.668 0.659 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.6 3.98 1.99 0.748 0.718 162s supply 20 16 110.7 6.92 2.63 0.587 0.510 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.67 162s supply 3.67 4.85 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.38 4.17 162s supply 4.17 5.53 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.965 162s supply 0.965 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 93.210 9.365 9.95 9.6e-12 *** 162s price -0.219 0.105 -2.09 0.044 * 162s income 0.304 0.023 13.19 3.8e-15 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.994 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.616 MSE: 3.977 Root MSE: 1.994 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 48.6930 9.6005 5.07 1.3e-05 *** 162s price 0.2806 0.1052 2.67 0.011 * 162s farmPrice 0.2168 0.0216 10.02 8.1e-12 *** 162s trend 0.3038 0.0230 13.19 3.8e-15 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.63 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 110.672 MSE: 6.917 Root MSE: 2.63 162s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.51 162s 162s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 179 1.3 0.666 0.661 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.8 3.99 2.00 0.747 0.717 162s supply 20 16 111.2 6.95 2.64 0.585 0.507 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.19 3.68 162s supply 3.68 4.83 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.39 4.19 162s supply 4.19 5.56 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.965 162s supply 0.965 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 93.0165 9.4718 9.82 1.4e-11 *** 162s price -0.2172 0.1066 -2.04 0.049 * 162s income 0.3036 0.0224 13.56 1.8e-15 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.997 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.8 MSE: 3.988 Root MSE: 1.997 162s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 48.5496 9.6886 5.01 1.6e-05 *** 162s price 0.2828 0.1066 2.65 0.012 * 162s farmPrice 0.2161 0.0210 10.30 3.9e-12 *** 162s trend 0.3036 0.0224 13.56 1.8e-15 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.637 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 111.249 MSE: 6.953 Root MSE: 2.637 162s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 162s 162s [1] "***************************************************" 162s [1] "3SLS formula: GMM" 162s [1] "************* 3SLS with different instruments **************" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 164 9.25 0.694 0.512 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 96.6 6.04 2.46 0.640 0.572 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.784 162s supply 0.784 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 162s price -0.4116 0.1448 -2.84 0.011 * 162s income 0.3617 0.0564 6.41 6.4e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 162s price 0.2401 0.0999 2.40 0.0288 * 162s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 162s trend 0.2529 0.0997 2.54 0.0219 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.458 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 162s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 162s 162s [1] "******* 3SLS with different instruments (EViews-like) **********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 164 6.29 0.694 0.5 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 96.6 6.04 2.46 0.640 0.572 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.37 3.16 162s supply 3.16 4.83 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.37 3.16 162s supply 3.16 4.83 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.784 162s supply 0.784 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 162s price -0.412 0.134 -3.08 0.0041 ** 162s income 0.362 0.052 6.95 6.0e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 162s price 0.2401 0.0894 2.69 0.0112 * 162s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 162s trend 0.2529 0.0891 2.84 0.0077 ** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.458 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 162s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 162s 162s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 164 8.24 0.694 0.481 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 96.6 6.04 2.46 0.640 0.572 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.97 3.96 162s supply 3.96 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 3.96 162s supply 3.96 6.04 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.784 162s supply 0.784 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 162s price -0.4116 0.1448 -2.84 0.0076 ** 162s income 0.3617 0.0564 6.41 2.9e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 162s price 0.2401 0.0999 2.40 0.02208 * 162s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 162s trend 0.2529 0.0997 2.54 0.01605 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.458 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 162s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 162s 162s [1] "************* W3SLS with different instruments **************" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 164 9.25 0.694 0.512 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 96.6 6.04 2.46 0.640 0.572 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.784 162s supply 0.784 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 162s price -0.4116 0.1448 -2.84 0.011 * 162s income 0.3617 0.0564 6.41 6.4e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 162s price 0.2401 0.0999 2.40 0.0288 * 162s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 162s trend 0.2529 0.0997 2.54 0.0219 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.458 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 162s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 162s 162s [1] "******* 3SLS with different instruments and restriction ********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 166 2.78 0.691 0.636 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 63.4 3.73 1.93 0.764 0.736 162s supply 20 16 102.2 6.39 2.53 0.619 0.547 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.35 162s supply 4.35 6.27 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.73 4.59 162s supply 4.59 6.39 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.94 162s supply 0.94 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 100.1363 8.6083 11.63 2.1e-13 *** 162s price -0.3244 0.1114 -2.91 0.0063 ** 162s income 0.3405 0.0509 6.69 1.1e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.931 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 63.395 MSE: 3.729 Root MSE: 1.931 162s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.7623 12.2354 4.07 0.00027 *** 162s price 0.2366 0.1018 2.33 0.02617 * 162s farmPrice 0.2473 0.0474 5.22 9.0e-06 *** 162s trend 0.3405 0.0509 6.69 1.1e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.527 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.181 MSE: 6.386 Root MSE: 2.527 162s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 162s 162s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 165 1.84 0.691 0.608 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 63.4 3.73 1.93 0.764 0.736 162s supply 20 16 102.1 6.38 2.53 0.619 0.548 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.58 162s supply 3.58 5.02 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.17 3.79 162s supply 3.79 5.10 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.941 162s supply 0.941 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 99.9363 7.9106 12.63 2.1e-14 *** 162s price -0.3212 0.1019 -3.15 0.0034 ** 162s income 0.3393 0.0466 7.28 2.0e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.931 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 63.37 MSE: 3.728 Root MSE: 1.931 162s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.8516 10.9418 4.56 6.4e-05 *** 162s price 0.2364 0.0910 2.60 0.014 * 162s farmPrice 0.2467 0.0423 5.83 1.4e-06 *** 162s trend 0.3393 0.0466 7.28 2.0e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.526 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.07 MSE: 6.379 Root MSE: 2.526 162s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 162s 162s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 165 1.85 0.691 0.608 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 63.4 3.73 1.93 0.764 0.736 162s supply 20 16 102.1 6.38 2.53 0.619 0.548 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.24 3.60 162s supply 3.60 5.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.17 3.78 162s supply 3.78 5.10 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.941 162s supply 0.941 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 99.9706 7.9399 12.59 2.4e-14 *** 162s price -0.3217 0.1023 -3.15 0.0034 ** 162s income 0.3394 0.0467 7.26 2.1e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.931 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 63.372 MSE: 3.728 Root MSE: 1.931 162s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.8336 10.9955 4.53 6.9e-05 *** 162s price 0.2364 0.0915 2.59 0.014 * 162s farmPrice 0.2469 0.0425 5.80 1.6e-06 *** 162s trend 0.3394 0.0467 7.26 2.1e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.526 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.073 MSE: 6.38 Root MSE: 2.526 162s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 162s 162s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 166 2.78 0.691 0.636 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 63.4 3.73 1.93 0.764 0.736 162s supply 20 16 102.2 6.39 2.53 0.619 0.547 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.35 162s supply 4.35 6.27 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.73 4.59 162s supply 4.59 6.39 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.94 162s supply 0.94 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 100.1363 8.6083 11.63 2.1e-13 *** 162s price -0.3244 0.1114 -2.91 0.0063 ** 162s income 0.3405 0.0509 6.69 1.1e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.931 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 63.395 MSE: 3.729 Root MSE: 1.931 162s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.7623 12.2354 4.07 0.00027 *** 162s price 0.2366 0.1018 2.33 0.02617 * 162s farmPrice 0.2473 0.0474 5.22 9.0e-06 *** 162s trend 0.3405 0.0509 6.69 1.1e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.527 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.181 MSE: 6.386 Root MSE: 2.527 162s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 162s 162s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 165 1.84 0.691 0.608 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 63.4 3.73 1.93 0.764 0.736 162s supply 20 16 102.1 6.38 2.53 0.619 0.548 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.58 162s supply 3.58 5.02 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.17 3.79 162s supply 3.79 5.10 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.941 162s supply 0.941 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 99.9363 7.9106 12.63 2.1e-14 *** 162s price -0.3212 0.1019 -3.15 0.0034 ** 162s income 0.3393 0.0466 7.28 2.0e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.931 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 63.37 MSE: 3.728 Root MSE: 1.931 162s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.8516 10.9418 4.56 6.4e-05 *** 162s price 0.2364 0.0910 2.60 0.014 * 162s farmPrice 0.2467 0.0423 5.83 1.4e-06 *** 162s trend 0.3393 0.0466 7.28 2.0e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.526 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.07 MSE: 6.379 Root MSE: 2.526 162s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 162s 162s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 166 2.79 0.691 0.635 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 63.4 3.73 1.93 0.764 0.736 162s supply 20 16 102.2 6.39 2.53 0.619 0.547 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.81 4.36 162s supply 4.36 6.34 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.73 4.59 162s supply 4.59 6.39 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.94 162s supply 0.94 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 100.174 8.646 11.59 2.4e-13 *** 162s price -0.325 0.112 -2.91 0.0064 ** 162s income 0.341 0.051 6.67 1.2e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.931 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 63.398 MSE: 3.729 Root MSE: 1.931 162s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.7425 12.3029 4.04 0.00029 *** 162s price 0.2367 0.1023 2.31 0.02691 * 162s farmPrice 0.2474 0.0477 5.19 9.8e-06 *** 162s trend 0.3406 0.0510 6.67 1.2e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.527 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.183 MSE: 6.386 Root MSE: 2.527 162s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 162s 162s [1] "****** 3SLS with different instruments and 2 restrictions *********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 165 1.89 0.692 0.677 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 64.1 3.77 1.94 0.761 0.733 162s supply 20 16 101.2 6.32 2.52 0.623 0.552 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.45 162s supply 4.45 6.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.77 4.68 162s supply 4.68 6.32 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.96 162s supply 0.96 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 98.8949 8.2696 11.96 6.4e-14 *** 162s price -0.2870 0.0909 -3.16 0.0033 ** 162s income 0.3148 0.0224 14.04 4.4e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.941 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 64.072 MSE: 3.769 Root MSE: 1.941 162s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 54.6693 8.4422 6.48 1.8e-07 *** 162s price 0.2130 0.0909 2.34 0.025 * 162s farmPrice 0.2237 0.0228 9.82 1.3e-11 *** 162s trend 0.3148 0.0224 14.04 4.4e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.515 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 101.181 MSE: 6.324 Root MSE: 2.515 162s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 162s 162s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 165 1.28 0.692 0.642 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 64.1 3.77 1.94 0.761 0.733 162s supply 20 16 101.1 6.32 2.51 0.623 0.552 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.67 162s supply 3.67 4.85 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.21 3.86 162s supply 3.86 5.06 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.96 162s supply 0.96 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 98.6650 7.5755 13.02 5.6e-15 *** 162s price -0.2845 0.0822 -3.46 0.0014 ** 162s income 0.3146 0.0203 15.52 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.942 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 64.111 MSE: 3.771 Root MSE: 1.942 162s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 54.3281 7.7347 7.02 3.6e-08 *** 162s price 0.2155 0.0822 2.62 0.013 * 162s farmPrice 0.2247 0.0201 11.16 4.4e-13 *** 162s trend 0.3146 0.0203 15.52 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.514 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 101.149 MSE: 6.322 Root MSE: 2.514 162s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 162s 162s [1] "**** W3SLS with different instruments and 2 restrictions *********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 165 1.89 0.692 0.677 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 64.1 3.77 1.94 0.761 0.733 162s supply 20 16 101.3 6.33 2.52 0.622 0.551 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.75 4.46 162s supply 4.46 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.77 4.69 162s supply 4.69 6.33 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.96 162s supply 0.96 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 98.9360 8.2215 12.03 5.4e-14 *** 162s price -0.2872 0.0907 -3.17 0.0032 ** 162s income 0.3147 0.0215 14.64 2.2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.941 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 64.08 MSE: 3.769 Root MSE: 1.941 162s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 54.7520 8.3733 6.54 1.5e-07 *** 162s price 0.2128 0.0907 2.35 0.025 * 162s farmPrice 0.2231 0.0218 10.24 4.5e-12 *** 162s trend 0.3147 0.0215 14.64 2.2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.516 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 101.278 MSE: 6.33 Root MSE: 2.516 162s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 162s 162s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 165 1.89 0.692 0.677 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 64.1 3.77 1.94 0.761 0.733 162s supply 20 16 101.2 6.32 2.52 0.623 0.552 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.45 162s supply 4.45 6.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.77 4.68 162s supply 4.68 6.32 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.96 162s supply 0.96 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 98.8949 8.2696 11.96 6.4e-14 *** 162s price -0.2870 0.0909 -3.16 0.0033 ** 162s income 0.3148 0.0224 14.04 4.4e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.941 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 64.072 MSE: 3.769 Root MSE: 1.941 162s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 54.6693 8.4422 6.48 1.8e-07 *** 162s price 0.2130 0.0909 2.34 0.025 * 162s farmPrice 0.2237 0.0228 9.82 1.3e-11 *** 162s trend 0.3148 0.0224 14.04 4.4e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.515 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 101.181 MSE: 6.324 Root MSE: 2.515 162s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 162s 162s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 165 1.28 0.692 0.642 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 64.1 3.77 1.94 0.761 0.733 162s supply 20 16 101.1 6.32 2.51 0.623 0.552 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.67 162s supply 3.67 4.85 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.21 3.86 162s supply 3.86 5.06 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.96 162s supply 0.96 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 98.6650 7.5755 13.02 5.6e-15 *** 162s price -0.2845 0.0822 -3.46 0.0014 ** 162s income 0.3146 0.0203 15.52 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.942 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 64.111 MSE: 3.771 Root MSE: 1.942 162s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 54.3281 7.7347 7.02 3.6e-08 *** 162s price 0.2155 0.0822 2.62 0.013 * 162s farmPrice 0.2247 0.0201 11.16 4.4e-13 *** 162s trend 0.3146 0.0203 15.52 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.514 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 101.149 MSE: 6.322 Root MSE: 2.514 162s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 162s 162s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 165 1.28 0.692 0.643 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 64.1 3.77 1.94 0.761 0.733 162s supply 20 16 101.2 6.33 2.52 0.622 0.552 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.19 3.68 162s supply 3.68 4.83 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.21 3.87 162s supply 3.87 5.06 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.96 162s supply 0.96 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 98.6980 7.5376 13.09 4.9e-15 *** 162s price -0.2847 0.0820 -3.47 0.0014 ** 162s income 0.3145 0.0195 16.13 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.942 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 64.117 MSE: 3.772 Root MSE: 1.942 162s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 54.3972 7.6824 7.08 3.0e-08 *** 162s price 0.2153 0.0820 2.62 0.013 * 162s farmPrice 0.2242 0.0193 11.60 1.5e-13 *** 162s trend 0.3145 0.0195 16.13 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.515 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 101.231 MSE: 6.327 Root MSE: 2.515 162s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.552 162s 162s [1] "***************************************************" 162s [1] "3SLS formula: EViews" 162s [1] "************* 3SLS with different instruments **************" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 174 2.12 0.675 0.659 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 106.6 6.66 2.58 0.602 0.528 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 4.93 162s supply 4.93 6.66 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.959 162s supply 0.959 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 162s price -0.4116 0.1448 -2.84 0.011 * 162s income 0.3617 0.0564 6.41 6.4e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.2953 11.5390 4.97 0.00014 *** 162s price 0.1373 0.0897 1.53 0.14529 162s farmPrice 0.2660 0.0470 5.66 3.6e-05 *** 162s trend 0.3970 0.0781 5.08 0.00011 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.582 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 162s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 162s 162s [1] "******* 3SLS with different instruments (EViews-like) **********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 173 1.51 0.677 0.612 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 105.7 6.61 2.57 0.606 0.532 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.37 3.16 162s supply 3.16 4.83 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.37 4.04 162s supply 4.04 5.29 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.957 162s supply 0.957 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 162s price -0.412 0.134 -3.08 0.0041 ** 162s income 0.362 0.052 6.95 6.0e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.0636 10.3208 5.53 3.9e-06 *** 162s price 0.1403 0.0802 1.75 0.089 . 162s farmPrice 0.2657 0.0421 6.32 3.8e-07 *** 162s trend 0.3927 0.0699 5.62 3.0e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.571 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 105.735 MSE: 6.608 Root MSE: 2.571 162s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 162s 162s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 175 0.321 0.673 0.655 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 107.7 6.73 2.59 0.598 0.523 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.97 3.96 162s supply 3.96 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 5.14 162s supply 5.14 6.73 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.962 162s supply 0.962 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 162s price -0.4116 0.1448 -2.84 0.0076 ** 162s income 0.3617 0.0564 6.41 2.9e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.5567 11.5060 5.00 1.8e-05 *** 162s price 0.1338 0.0889 1.50 0.14 162s farmPrice 0.2664 0.0470 5.66 2.6e-06 *** 162s trend 0.4018 0.0765 5.26 8.7e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.594 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 107.679 MSE: 6.73 Root MSE: 2.594 162s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 162s 162s [1] "************* W3SLS with different instruments **************" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 174 2.12 0.675 0.659 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.4 3.97 1.99 0.748 0.719 162s supply 20 16 106.6 6.66 2.58 0.602 0.528 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.97 3.84 162s supply 3.84 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.97 4.93 162s supply 4.93 6.66 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.959 162s supply 0.959 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 162s price -0.4116 0.1448 -2.84 0.011 * 162s income 0.3617 0.0564 6.41 6.4e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.2953 11.5390 4.97 0.00014 *** 162s price 0.1373 0.0897 1.53 0.14529 162s farmPrice 0.2660 0.0470 5.66 3.6e-05 *** 162s trend 0.3970 0.0781 5.08 0.00011 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.582 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 162s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 162s 162s [1] "******* 3SLS with different instruments and restriction ********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 174 3.39 0.676 0.542 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 71.1 4.18 2.04 0.735 0.704 162s supply 20 16 102.6 6.41 2.53 0.617 0.546 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.35 162s supply 4.35 6.27 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 4.18 4.84 162s supply 4.84 6.41 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.935 162s supply 0.935 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 109.4916 6.3475 17.25 < 2e-16 *** 162s price -0.4470 0.0812 -5.50 3.8e-06 *** 162s income 0.3703 0.0474 7.81 4.3e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.045 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 71.077 MSE: 4.181 Root MSE: 2.045 162s Multiple R-Squared: 0.735 Adjusted R-Squared: 0.704 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.6795 11.2022 5.15 1.1e-05 *** 162s price 0.1324 0.0785 1.69 0.1 162s farmPrice 0.2700 0.0453 5.97 9.5e-07 *** 162s trend 0.3703 0.0474 7.81 4.3e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.532 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.574 MSE: 6.411 Root MSE: 2.532 162s Multiple R-Squared: 0.617 Adjusted R-Squared: 0.546 162s 162s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 173 2.29 0.678 0.515 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 70.5 4.15 2.04 0.737 0.706 162s supply 20 16 102.2 6.38 2.53 0.619 0.548 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.58 162s supply 3.58 5.02 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.53 3.96 162s supply 3.96 5.11 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.934 162s supply 0.934 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 109.1085 5.8428 18.67 < 2e-16 *** 162s price -0.4422 0.0737 -6.00 8.6e-07 *** 162s income 0.3693 0.0432 8.54 5.6e-10 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.037 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 70.515 MSE: 4.148 Root MSE: 2.037 162s Multiple R-Squared: 0.737 Adjusted R-Squared: 0.706 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.2679 10.0564 5.69 2.1e-06 *** 162s price 0.1375 0.0705 1.95 0.06 . 162s farmPrice 0.2691 0.0403 6.68 1.1e-07 *** 162s trend 0.3693 0.0432 8.54 5.6e-10 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.527 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.156 MSE: 6.385 Root MSE: 2.527 162s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 162s 162s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 173 2.29 0.678 0.515 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 70.5 4.15 2.04 0.737 0.706 162s supply 20 16 102.1 6.38 2.53 0.619 0.548 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.24 3.60 162s supply 3.60 5.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.52 3.96 162s supply 3.96 5.11 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.934 162s supply 0.934 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 109.0818 5.9083 18.46 < 2e-16 *** 162s price -0.4418 0.0746 -5.92 1.1e-06 *** 162s income 0.3692 0.0434 8.51 6.2e-10 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.036 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 70.475 MSE: 4.146 Root MSE: 2.036 162s Multiple R-Squared: 0.737 Adjusted R-Squared: 0.706 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.2616 10.1094 5.66 2.4e-06 *** 162s price 0.1376 0.0711 1.94 0.061 . 162s farmPrice 0.2690 0.0405 6.64 1.3e-07 *** 162s trend 0.3692 0.0434 8.51 6.2e-10 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.527 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.135 MSE: 6.383 Root MSE: 2.527 162s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 162s 162s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 174 3.39 0.676 0.542 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 71.1 4.18 2.04 0.735 0.704 162s supply 20 16 102.6 6.41 2.53 0.617 0.546 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.35 162s supply 4.35 6.27 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 4.18 4.84 162s supply 4.84 6.41 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.935 162s supply 0.935 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 109.4916 6.3475 17.25 < 2e-16 *** 162s price -0.4470 0.0812 -5.50 3.8e-06 *** 162s income 0.3703 0.0474 7.81 4.3e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.045 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 71.077 MSE: 4.181 Root MSE: 2.045 162s Multiple R-Squared: 0.735 Adjusted R-Squared: 0.704 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.6795 11.2022 5.15 1.1e-05 *** 162s price 0.1324 0.0785 1.69 0.1 162s farmPrice 0.2700 0.0453 5.97 9.5e-07 *** 162s trend 0.3703 0.0474 7.81 4.3e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.532 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.574 MSE: 6.411 Root MSE: 2.532 162s Multiple R-Squared: 0.617 Adjusted R-Squared: 0.546 162s 162s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 173 2.29 0.678 0.515 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 70.5 4.15 2.04 0.737 0.706 162s supply 20 16 102.2 6.38 2.53 0.619 0.548 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.58 162s supply 3.58 5.02 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.53 3.96 162s supply 3.96 5.11 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.934 162s supply 0.934 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 109.1085 5.8428 18.67 < 2e-16 *** 162s price -0.4422 0.0737 -6.00 8.6e-07 *** 162s income 0.3693 0.0432 8.54 5.6e-10 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.037 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 70.515 MSE: 4.148 Root MSE: 2.037 162s Multiple R-Squared: 0.737 Adjusted R-Squared: 0.706 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.2679 10.0564 5.69 2.1e-06 *** 162s price 0.1375 0.0705 1.95 0.06 . 162s farmPrice 0.2691 0.0403 6.68 1.1e-07 *** 162s trend 0.3693 0.0432 8.54 5.6e-10 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.527 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.156 MSE: 6.385 Root MSE: 2.527 162s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 162s 162s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 174 3.38 0.676 0.543 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 71 4.18 2.04 0.735 0.704 162s supply 20 16 103 6.41 2.53 0.618 0.546 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.81 4.36 162s supply 4.36 6.34 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 4.18 4.84 162s supply 4.84 6.41 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.935 162s supply 0.935 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 109.4522 6.4318 17.02 < 2e-16 *** 162s price -0.4465 0.0823 -5.42 4.8e-06 *** 162s income 0.3702 0.0476 7.78 4.8e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.044 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 71.017 MSE: 4.177 Root MSE: 2.044 162s Multiple R-Squared: 0.735 Adjusted R-Squared: 0.704 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 57.6669 11.2699 5.12 1.2e-05 *** 162s price 0.1326 0.0792 1.67 0.1 162s farmPrice 0.2699 0.0456 5.92 1.1e-06 *** 162s trend 0.3702 0.0476 7.78 4.8e-09 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.532 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 102.539 MSE: 6.409 Root MSE: 2.532 162s Multiple R-Squared: 0.618 Adjusted R-Squared: 0.546 162s 162s [1] "****** 3SLS with different instruments and 2 restrictions *********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 358 32.4 0.333 -0.013 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 141 8.32 2.88 0.472 0.410 162s supply 20 16 216 13.53 3.68 0.193 0.042 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.45 162s supply 4.45 6.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 8.32 8.95 162s supply 8.95 13.53 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.844 162s supply 0.844 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 108.5837 5.3770 20.2 < 2e-16 *** 162s price -0.6034 0.0504 -12.0 6.2e-14 *** 162s income 0.5399 0.0182 29.7 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.884 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 141.436 MSE: 8.32 Root MSE: 2.884 162s Multiple R-Squared: 0.472 Adjusted R-Squared: 0.41 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 14.7043 5.4316 2.71 0.01 * 162s price 0.3966 0.0504 7.87 3e-09 *** 162s farmPrice 0.4228 0.0205 20.65 <2e-16 *** 162s trend 0.5399 0.0182 29.71 <2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.678 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 216.4 MSE: 13.525 Root MSE: 3.678 162s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 162s 162s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 359 21.9 0.331 -0.059 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 143 8.38 2.90 0.468 0.406 162s supply 20 16 216 13.52 3.68 0.193 0.042 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.67 162s supply 3.67 4.85 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 7.13 7.43 162s supply 7.43 10.82 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.846 162s supply 0.846 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 107.9852 4.9704 21.7 < 2e-16 *** 162s price -0.5994 0.0458 -13.1 4.9e-15 *** 162s income 0.5420 0.0168 32.2 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.896 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 142.542 MSE: 8.385 Root MSE: 2.896 162s Multiple R-Squared: 0.468 Adjusted R-Squared: 0.406 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 14.4922 4.9950 2.90 0.0064 ** 162s price 0.4006 0.0458 8.75 2.5e-10 *** 162s farmPrice 0.4207 0.0184 22.92 < 2e-16 *** 162s trend 0.5420 0.0168 32.25 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.677 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 216.315 MSE: 13.52 Root MSE: 3.677 162s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 162s 162s [1] "**** W3SLS with different instruments and 2 restrictions *********" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 364 32.3 0.322 -0.022 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 143 8.43 2.90 0.466 0.403 162s supply 20 16 220 13.78 3.71 0.178 0.024 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.75 4.46 162s supply 4.46 6.04 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 8.43 9.15 162s supply 9.15 13.78 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.00 0.85 162s supply 0.85 1.00 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 107.9125 5.1136 21.1 < 2e-16 *** 162s price -0.5996 0.0479 -12.5 1.7e-14 *** 162s income 0.5430 0.0171 31.7 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.903 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 143.236 MSE: 8.426 Root MSE: 2.903 162s Multiple R-Squared: 0.466 Adjusted R-Squared: 0.403 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 13.9658 5.1591 2.71 0.01 * 162s price 0.4004 0.0479 8.36 7.3e-10 *** 162s farmPrice 0.4263 0.0193 22.08 < 2e-16 *** 162s trend 0.5430 0.0171 31.74 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.712 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 220.468 MSE: 13.779 Root MSE: 3.712 162s Multiple R-Squared: 0.178 Adjusted R-Squared: 0.024 162s 162s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 358 32.4 0.333 -0.013 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 141 8.32 2.88 0.472 0.410 162s supply 20 16 216 13.53 3.68 0.193 0.042 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.79 4.45 162s supply 4.45 6.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 8.32 8.95 162s supply 8.95 13.53 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.844 162s supply 0.844 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 108.5837 5.3770 20.2 < 2e-16 *** 162s price -0.6034 0.0504 -12.0 6.2e-14 *** 162s income 0.5399 0.0182 29.7 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.884 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 141.436 MSE: 8.32 Root MSE: 2.884 162s Multiple R-Squared: 0.472 Adjusted R-Squared: 0.41 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 14.7043 5.4316 2.71 0.01 * 162s price 0.3966 0.0504 7.87 3e-09 *** 162s farmPrice 0.4228 0.0205 20.65 <2e-16 *** 162s trend 0.5399 0.0182 29.71 <2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.678 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 216.4 MSE: 13.525 Root MSE: 3.678 162s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 162s 162s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 359 21.9 0.331 -0.059 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 143 8.38 2.90 0.468 0.406 162s supply 20 16 216 13.52 3.68 0.193 0.042 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.22 3.67 162s supply 3.67 4.85 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 7.13 7.43 162s supply 7.43 10.82 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.846 162s supply 0.846 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 107.9852 4.9704 21.7 < 2e-16 *** 162s price -0.5994 0.0458 -13.1 4.9e-15 *** 162s income 0.5420 0.0168 32.2 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.896 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 142.542 MSE: 8.385 Root MSE: 2.896 162s Multiple R-Squared: 0.468 Adjusted R-Squared: 0.406 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 14.4922 4.9950 2.90 0.0064 ** 162s price 0.4006 0.0458 8.75 2.5e-10 *** 162s farmPrice 0.4207 0.0184 22.92 < 2e-16 *** 162s trend 0.5420 0.0168 32.25 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.677 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 216.315 MSE: 13.52 Root MSE: 3.677 162s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 162s 162s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 364 21.8 0.321 -0.069 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 144 8.49 2.91 0.462 0.399 162s supply 20 16 220 13.76 3.71 0.179 0.025 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.19 3.68 162s supply 3.68 4.83 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 7.21 7.59 162s supply 7.59 11.00 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.852 162s supply 0.852 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 107.3179 4.7598 22.6 < 2e-16 *** 162s price -0.5955 0.0438 -13.6 1.6e-15 *** 162s income 0.5449 0.0159 34.2 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.913 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 144.274 MSE: 8.487 Root MSE: 2.913 162s Multiple R-Squared: 0.462 Adjusted R-Squared: 0.399 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 13.7761 4.7784 2.88 0.0067 ** 162s price 0.4045 0.0438 9.23 6.6e-11 *** 162s farmPrice 0.4237 0.0174 24.30 < 2e-16 *** 162s trend 0.5449 0.0159 34.17 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.709 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 220.081 MSE: 13.755 Root MSE: 3.709 162s Multiple R-Squared: 0.179 Adjusted R-Squared: 0.025 162s 162s > 162s > 162s > ## **************** shorter summaries ********************** 162s > print( summary( fit3sls[[ 2 ]]$e1c, equations = FALSE ) ) 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 174 -0.718 0.675 0.922 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 65.7 3.87 1.97 0.755 0.726 162s supply 20 16 108.7 6.79 2.61 0.594 0.518 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.87 4.50 162s supply 4.50 6.04 162s 162s warning: this covariance matrix is NOT positive semidefinit! 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.87 5.2 162s supply 5.20 6.8 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.981 162s supply 0.981 1.000 162s 162s 162s Coefficients: 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 162s demand_price -0.2436 0.0965 -2.52 0.02183 * 162s demand_income 0.3140 0.0469 6.69 3.8e-06 *** 162s supply_(Intercept) 52.2869 11.8853 4.40 0.00045 *** 162s supply_price 0.2282 0.0997 2.29 0.03595 * 162s supply_farmPrice 0.2272 0.0438 5.19 8.9e-05 *** 162s supply_trend 0.3648 0.0707 5.16 9.5e-05 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( summary( fit3sls[[ 3 ]]$e2e ), residCov = FALSE ) 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 171 0.887 0.68 0.678 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.5 3.97 1.99 0.748 0.719 162s supply 20 16 104.0 6.50 2.55 0.612 0.539 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 162s price -0.2243 0.0888 -2.53 0.016 * 162s income 0.2979 0.0420 7.10 3.4e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.992 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 162s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 162s price 0.2207 0.0896 2.46 0.019 * 162s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 162s trend 0.2979 0.0420 7.10 3.4e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.55 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 162s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 162s 162s > 162s > print( summary( fit3sls[[ 4 ]]$e3, useDfSys = FALSE ), residCov = FALSE ) 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 173 1.27 0.678 0.722 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 67.8 3.99 2.00 0.747 0.717 162s supply 20 16 104.8 6.55 2.56 0.609 0.536 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 94.222 8.015 11.76 1.4e-09 *** 162s price -0.222 0.096 -2.31 0.034 * 162s income 0.296 0.045 6.57 4.8e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.997 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 162s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 55.9604 11.5777 4.83 0.00018 *** 162s price 0.2193 0.1002 2.19 0.04374 * 162s farmPrice 0.2060 0.0403 5.11 0.00011 *** 162s trend 0.2956 0.0450 6.57 6.5e-06 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.559 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 162s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 162s 162s > 162s > print( summary( fit3sls[[ 5 ]]$e4e, equations = FALSE ), 162s + equations = FALSE ) 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 439 21.3 0.18 -0.18 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 169 9.93 3.15 0.370 0.296 162s supply 20 16 271 16.91 4.11 -0.009 -0.198 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.30 3.73 162s supply 3.73 5.00 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 8.44 9.64 162s supply 9.64 13.53 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.902 162s supply 0.902 1.000 162s 162s 162s Coefficients: 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 93.2926 7.3154 12.75 1.0e-14 *** 162s demand_price -0.4781 0.0812 -5.89 1.1e-06 *** 162s demand_income 0.5683 0.0209 27.24 < 2e-16 *** 162s supply_(Intercept) 0.6559 7.5503 0.09 0.93 162s supply_price 0.5219 0.0812 6.43 2.1e-07 *** 162s supply_farmPrice 0.4355 0.0212 20.49 < 2e-16 *** 162s supply_trend 0.5683 0.0209 27.24 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( summary( fit3sls[[ 1 ]]$e4wSym, residCov = FALSE ), 162s + equations = FALSE ) 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 172 1.74 0.68 0.697 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 65.9 3.88 1.97 0.754 0.725 162s supply 20 16 105.7 6.60 2.57 0.606 0.532 162s 162s 162s Coefficients: 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 162s demand_price -0.2443 0.0892 -2.74 0.0096 ** 162s demand_income 0.3234 0.0229 14.14 4.4e-16 *** 162s supply_(Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 162s supply_price 0.2557 0.0892 2.87 0.0069 ** 162s supply_farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 162s supply_trend 0.3234 0.0229 14.14 4.4e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( summary( fit3sls[[ 2 ]]$e5, residCov = FALSE ), residCov = TRUE ) 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 171 1.74 0.681 0.696 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 65.8 3.87 1.97 0.755 0.726 162s supply 20 16 105.4 6.59 2.57 0.607 0.533 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.89 4.53 162s supply 4.53 6.25 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.87 4.87 162s supply 4.87 6.59 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.965 162s supply 0.965 1.000 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 162s price -0.2457 0.0891 -2.76 0.0092 ** 162s income 0.3236 0.0233 13.91 8.9e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 1.967 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 162s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 162s price 0.2543 0.0891 2.85 0.0072 ** 162s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 162s trend 0.3236 0.0233 13.91 8.9e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.566 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 162s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 162s 162s > 162s > print( summary( fit3slsi[[ 3 ]]$e3e, residCov = FALSE, 162s + equations = FALSE ) ) 162s 162s systemfit results 162s method: iterated 3SLS 162s 162s convergence achieved after 20 iterations 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 237 0.364 0.557 0.755 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 99.3 5.84 2.42 0.630 0.586 162s supply 20 16 138.1 8.63 2.94 0.485 0.388 162s 162s 162s Coefficients: 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 162s demand_price -0.1043 0.0958 -1.09 0.284 162s demand_income 0.1979 0.0299 6.61 1.4e-07 *** 162s supply_(Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 162s supply_price 0.1851 0.1053 1.76 0.088 . 162s supply_farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 162s supply_trend 0.1979 0.0299 6.61 1.4e-07 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( summary( fit3slsi[[ 4 ]]$e1we ), equations = FALSE, residCov = FALSE ) 162s 162s systemfit results 162s method: iterated 3SLS 162s 162s convergence achieved after 6 iterations 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 33 177 0.667 0.67 0.782 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 65.7 3.87 1.97 0.755 0.726 162s supply 20 16 111.3 6.96 2.64 0.585 0.507 162s 162s 162s Coefficients: 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 94.6333 7.3027 12.96 3.1e-10 *** 162s demand_price -0.2436 0.0890 -2.74 0.01402 * 162s demand_income 0.3140 0.0433 7.25 1.3e-06 *** 162s supply_(Intercept) 52.5527 11.3956 4.61 0.00029 *** 162s supply_price 0.2271 0.0956 2.37 0.03043 * 162s supply_farmPrice 0.2245 0.0416 5.39 6.0e-05 *** 162s supply_trend 0.3756 0.0641 5.86 2.4e-05 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( summary( fit3slsd[[ 5 ]]$e4, residCov = FALSE ) ) 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 35 358 32.4 0.333 -0.013 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 141 8.32 2.88 0.472 0.410 162s supply 20 16 216 13.53 3.68 0.193 0.042 162s 162s 162s 3SLS estimates for 'demand' (equation 1) 162s Model Formula: consump ~ price + income 162s Instruments: ~income + farmPrice 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 108.5837 5.3770 20.2 < 2e-16 *** 162s price -0.6034 0.0504 -12.0 6.2e-14 *** 162s income 0.5399 0.0182 29.7 < 2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 2.884 on 17 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 17 162s SSR: 141.436 MSE: 8.32 Root MSE: 2.884 162s Multiple R-Squared: 0.472 Adjusted R-Squared: 0.41 162s 162s 162s 3SLS estimates for 'supply' (equation 2) 162s Model Formula: consump ~ price + farmPrice + trend 162s Instruments: ~income + farmPrice + trend 162s 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 14.7043 5.4316 2.71 0.01 * 162s price 0.3966 0.0504 7.87 3e-09 *** 162s farmPrice 0.4228 0.0205 20.65 <2e-16 *** 162s trend 0.5399 0.0182 29.71 <2e-16 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s 162s Residual standard error: 3.678 on 16 degrees of freedom 162s Number of observations: 20 Degrees of Freedom: 16 162s SSR: 216.4 MSE: 13.525 Root MSE: 3.678 162s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 162s 162s > 162s > print( summary( fit3slsd[[ 1 ]]$e2we, equations = FALSE ) ) 162s 162s systemfit results 162s method: 3SLS 162s 162s N DF SSR detRCov OLS-R2 McElroy-R2 162s system 40 34 199 1.77 0.629 0.65 162s 162s N DF SSR MSE RMSE R2 Adj R2 162s demand 20 17 72.4 4.26 2.06 0.730 0.698 162s supply 20 16 126.7 7.92 2.81 0.527 0.439 162s 162s The covariance matrix of the residuals used for estimation 162s demand supply 162s demand 3.24 3.60 162s supply 3.60 5.06 162s 162s The covariance matrix of the residuals 162s demand supply 162s demand 3.62 4.60 162s supply 4.60 6.34 162s 162s The correlations of the residuals 162s demand supply 162s demand 1.000 0.961 162s supply 0.961 1.000 162s 162s 162s Coefficients: 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 88.9298 5.9083 15.05 < 2e-16 *** 162s demand_price -0.1760 0.0746 -2.36 0.02415 * 162s demand_income 0.3032 0.0434 6.99 4.6e-08 *** 162s supply_(Intercept) 40.8325 10.1094 4.04 0.00029 *** 162s supply_price 0.3562 0.0711 5.01 1.7e-05 *** 162s supply_farmPrice 0.2200 0.0405 5.43 4.8e-06 *** 162s supply_trend 0.3032 0.0434 6.99 4.6e-08 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > 162s > ## ****************** residuals ************************** 162s > print( residuals( fit3sls[[ 1 ]]$e1c ) ) 162s demand supply 162s 1 0.843 0.670 162s 2 -0.698 -0.142 162s 3 2.359 2.659 162s 4 1.490 1.618 162s 5 2.139 2.588 162s 6 1.277 1.485 162s 7 1.571 2.093 162s 8 -3.066 -4.163 162s 9 -1.125 -1.929 162s 10 2.492 3.207 162s 11 -0.108 -0.513 162s 12 -2.292 -2.375 162s 13 -1.598 -2.089 162s 14 -0.271 0.330 162s 15 1.958 3.086 162s 16 -3.430 -4.225 162s 17 -0.313 0.185 162s 18 -2.151 -3.680 162s 19 1.592 1.576 162s 20 -0.668 -0.382 162s > print( residuals( fit3sls[[ 1 ]]$e1c$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 162s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 162s 12 13 14 15 16 17 18 19 20 162s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 162s > 162s > print( residuals( fit3sls[[ 4 ]]$e1wc ) ) 162s demand supply 162s 1 0.843 0.670 162s 2 -0.698 -0.142 162s 3 2.359 2.659 162s 4 1.490 1.618 162s 5 2.139 2.588 162s 6 1.277 1.485 162s 7 1.571 2.093 162s 8 -3.066 -4.163 162s 9 -1.125 -1.929 162s 10 2.492 3.207 162s 11 -0.108 -0.513 162s 12 -2.292 -2.375 162s 13 -1.598 -2.089 162s 14 -0.271 0.330 162s 15 1.958 3.086 162s 16 -3.430 -4.225 162s 17 -0.313 0.185 162s 18 -2.151 -3.680 162s 19 1.592 1.576 162s 20 -0.668 -0.382 162s > print( residuals( fit3sls[[ 4 ]]$e1wc$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 162s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 162s 12 13 14 15 16 17 18 19 20 162s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 162s > 162s > print( residuals( fit3sls[[ 2 ]]$e2e ) ) 162s demand supply 162s 1 0.6744 0.0619 162s 2 -0.7785 -0.6344 162s 3 2.2797 2.2267 162s 4 1.4140 1.2428 162s 5 2.2144 2.4566 162s 6 1.3352 1.3851 162s 7 1.6419 2.0264 162s 8 -2.9923 -4.0603 162s 9 -1.0710 -1.8419 162s 10 2.5226 3.1787 162s 11 -0.3346 -0.8086 162s 12 -2.5999 -2.7819 162s 13 -1.8617 -2.3572 162s 14 -0.3584 0.2840 162s 15 2.1419 3.4511 162s 16 -3.2786 -3.7199 162s 17 -0.0706 0.7656 162s 18 -2.1179 -3.2218 162s 19 1.6924 2.0576 162s 20 -0.4528 0.2893 162s > print( residuals( fit3sls[[ 2 ]]$e2e$eq[[ 2 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 162s 0.0619 -0.6344 2.2267 1.2428 2.4566 1.3851 2.0264 -4.0603 -1.8419 3.1787 162s 11 12 13 14 15 16 17 18 19 20 162s -0.8086 -2.7819 -2.3572 0.2840 3.4511 -3.7199 0.7656 -3.2218 2.0576 0.2893 162s > 162s > print( residuals( fit3sls[[ 3 ]]$e3 ) ) 162s demand supply 162s 1 0.6499 0.045 162s 2 -0.7902 -0.639 162s 3 2.2682 2.223 162s 4 1.4031 1.239 162s 5 2.2253 2.490 162s 6 1.3437 1.414 162s 7 1.6522 2.051 162s 8 -2.9817 -4.013 162s 9 -1.0632 -1.808 162s 10 2.5270 3.179 162s 11 -0.3675 -0.872 162s 12 -2.6445 -2.878 162s 13 -1.8999 -2.437 162s 14 -0.3711 0.237 162s 15 2.1685 3.474 162s 16 -3.2566 -3.680 162s 17 -0.0355 0.809 162s 18 -2.1131 -3.213 162s 19 1.7070 2.060 162s 20 -0.4215 0.319 162s > print( residuals( fit3sls[[ 3 ]]$e3$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 162s 0.6499 -0.7902 2.2682 1.4031 2.2253 1.3437 1.6522 -2.9817 -1.0632 2.5270 162s 11 12 13 14 15 16 17 18 19 20 162s -0.3675 -2.6445 -1.8999 -0.3711 2.1685 -3.2566 -0.0355 -2.1131 1.7070 -0.4215 162s > 162s > print( residuals( fit3sls[[ 4 ]]$e4e ) ) 162s demand supply 162s 1 0.9543 0.278 162s 2 -0.6734 -0.586 162s 3 2.3881 2.272 162s 4 1.5091 1.252 162s 5 2.1028 2.356 162s 6 1.2414 1.271 162s 7 1.5161 1.894 162s 8 -3.1487 -4.421 162s 9 -1.1358 -1.958 162s 10 2.5334 3.368 162s 11 0.0936 -0.275 162s 12 -2.0762 -2.176 162s 13 -1.4415 -1.951 162s 14 -0.2039 0.559 162s 15 1.8691 3.353 162s 16 -3.5213 -4.003 162s 17 -0.3804 0.692 162s 18 -2.2018 -3.453 162s 19 1.4834 1.817 162s 20 -0.9080 -0.289 162s > print( residuals( fit3sls[[ 4 ]]$e4e$eq[[ 2 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 162s 0.278 -0.586 2.272 1.252 2.356 1.271 1.894 -4.421 -1.958 3.368 -0.275 162s 12 13 14 15 16 17 18 19 20 162s -2.176 -1.951 0.559 3.353 -4.003 0.692 -3.453 1.817 -0.289 162s > 162s > print( residuals( fit3sls[[ 5 ]]$e5 ) ) 162s demand supply 162s 1 3.391 2.137 162s 2 0.160 -0.366 162s 3 3.267 2.508 162s 4 2.250 1.132 162s 5 1.168 1.398 162s 6 0.434 0.165 162s 7 0.397 0.594 162s 8 -4.607 -7.911 162s 9 -1.631 -2.964 162s 10 2.800 5.323 162s 11 3.967 4.833 162s 12 2.518 3.479 162s 13 2.169 1.774 162s 14 1.169 3.182 162s 15 -0.415 2.626 162s 16 -5.608 -6.508 162s 17 -2.817 0.433 162s 18 -3.012 -5.580 162s 19 -0.454 -0.427 162s 20 -5.146 -5.829 162s > print( residuals( fit3sls[[ 5 ]]$e5$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 162s 3.391 0.160 3.267 2.250 1.168 0.434 0.397 -4.607 -1.631 2.800 3.967 162s 12 13 14 15 16 17 18 19 20 162s 2.518 2.169 1.169 -0.415 -5.608 -2.817 -3.012 -0.454 -5.146 162s > 162s > print( residuals( fit3slsi[[ 2 ]]$e3e ) ) 162s demand supply 162s 1 -0.376 -0.761 162s 2 -1.281 -1.123 162s 3 1.786 1.809 162s 4 0.942 0.878 162s 5 2.683 3.039 162s 6 1.699 1.899 162s 7 2.083 2.477 162s 8 -2.534 -3.021 162s 9 -0.736 -1.093 162s 10 2.713 3.153 162s 11 -1.748 -2.334 162s 12 -4.518 -5.058 162s 13 -3.502 -4.191 162s 14 -0.901 -0.705 162s 15 3.286 4.209 162s 16 -2.334 -2.514 162s 17 1.438 2.113 162s 18 -1.911 -2.680 162s 19 2.320 2.490 162s 20 0.889 1.412 162s > print( residuals( fit3slsi[[ 2 ]]$e3e$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 162s -0.376 -1.281 1.786 0.942 2.683 1.699 2.083 -2.534 -0.736 2.713 -1.748 162s 12 13 14 15 16 17 18 19 20 162s -4.518 -3.502 -0.901 3.286 -2.334 1.438 -1.911 2.320 0.889 162s > 162s > print( residuals( fit3slsi[[ 1 ]]$e2we ) ) 162s demand supply 162s 1 -0.376 -0.761 162s 2 -1.281 -1.123 162s 3 1.786 1.809 162s 4 0.942 0.878 162s 5 2.683 3.039 162s 6 1.699 1.899 162s 7 2.083 2.477 162s 8 -2.534 -3.021 162s 9 -0.736 -1.093 162s 10 2.713 3.153 162s 11 -1.748 -2.334 162s 12 -4.518 -5.058 162s 13 -3.502 -4.191 162s 14 -0.901 -0.705 162s 15 3.286 4.209 162s 16 -2.334 -2.514 162s 17 1.438 2.113 162s 18 -1.911 -2.680 162s 19 2.320 2.490 162s 20 0.889 1.412 162s > print( residuals( fit3slsi[[ 1 ]]$e2we$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 162s -0.376 -1.281 1.786 0.942 2.683 1.699 2.083 -2.534 -0.736 2.713 -1.748 162s 12 13 14 15 16 17 18 19 20 162s -4.518 -3.502 -0.901 3.286 -2.334 1.438 -1.911 2.320 0.889 162s > 162s > print( residuals( fit3slsd[[ 3 ]]$e4 ) ) 162s demand supply 162s 1 0.7282 0.088 162s 2 -0.7938 -0.850 162s 3 2.2722 2.054 162s 4 1.3947 1.007 162s 5 2.2092 2.526 162s 6 1.3211 1.378 162s 7 1.6076 1.935 162s 8 -3.0646 -4.397 162s 9 -1.0534 -1.692 162s 10 2.6003 3.674 162s 11 -0.1888 -0.319 162s 12 -2.4839 -2.564 162s 13 -1.8018 -2.397 162s 14 -0.3164 0.423 162s 15 2.1290 3.682 162s 16 -3.3141 -3.704 162s 17 -0.0169 1.445 162s 18 -2.1692 -3.473 162s 19 1.6008 1.716 162s 20 -0.6603 -0.530 162s > print( residuals( fit3slsd[[ 3 ]]$e4$eq[[ 2 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 162s 0.088 -0.850 2.054 1.007 2.526 1.378 1.935 -4.397 -1.692 3.674 -0.319 162s 12 13 14 15 16 17 18 19 20 162s -2.564 -2.397 0.423 3.682 -3.704 1.445 -3.473 1.716 -0.530 162s > 162s > print( residuals( fit3slsd[[ 5 ]]$e5we ) ) 162s demand supply 162s 1 3.290 2.057 162s 2 0.781 0.154 162s 3 3.754 2.921 162s 4 2.915 1.707 162s 5 0.906 1.148 162s 6 0.394 0.120 162s 7 0.632 0.775 162s 8 -3.766 -7.138 162s 9 -2.167 -3.402 162s 10 1.391 4.066 162s 11 2.631 3.690 162s 12 2.043 3.077 162s 13 2.405 2.007 162s 14 0.885 2.914 162s 15 -1.051 2.024 162s 16 -5.729 -6.584 162s 17 -4.810 -1.328 162s 18 -2.329 -4.924 162s 19 0.576 0.472 162s 20 -2.753 -3.755 162s > print( residuals( fit3slsd[[ 5 ]]$e5we$eq[[ 2 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 162s 2.057 0.154 2.921 1.707 1.148 0.120 0.775 -7.138 -3.402 4.066 3.690 162s 12 13 14 15 16 17 18 19 20 162s 3.077 2.007 2.914 2.024 -6.584 -1.328 -4.924 0.472 -3.755 162s > 162s > 162s > ## *************** coefficients ********************* 162s > print( round( coef( fit3sls[[ 3 ]]$e1c ), digits = 6 ) ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 94.633 -0.244 0.314 52.287 162s supply_price supply_farmPrice supply_trend 162s 0.228 0.227 0.365 162s > print( round( coef( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]] ), digits = 6 ) ) 162s (Intercept) price farmPrice trend 162s 52.287 0.228 0.227 0.365 162s > 162s > print( round( coef( fit3slsi[[ 4 ]]$e2 ), digits = 6 ) ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 92.074 -0.106 0.200 68.855 162s supply_price supply_farmPrice supply_trend 162s 0.183 0.120 0.200 162s > print( round( coef( fit3slsi[[ 5 ]]$e2$eq[[ 1 ]] ), digits = 6 ) ) 162s (Intercept) price income 162s 92.074 -0.106 0.200 162s > 162s > print( round( coef( fit3sls[[ 2 ]]$e2w ), digits = 6 ) ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 94.182 -0.219 0.294 56.254 162s supply_price supply_farmPrice supply_trend 162s 0.218 0.204 0.294 162s > print( round( coef( fit3sls[[ 3 ]]$e2w$eq[[ 1 ]] ), digits = 6 ) ) 162s (Intercept) price income 162s 94.182 -0.219 0.294 162s > 162s > print( round( coef( fit3slsd[[ 5 ]]$e3e ), digits = 6 ) ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 109.109 -0.442 0.369 57.268 162s supply_price supply_farmPrice supply_trend 162s 0.137 0.269 0.369 162s > print( round( coef( fit3slsd[[ 5 ]]$e3e, modified.regMat = TRUE ), digits = 6 ) ) 162s C1 C2 C3 C4 C5 C6 162s 109.109 -0.442 0.369 57.268 0.137 0.269 162s > print( round( coef( fit3slsd[[ 1 ]]$e3e$eq[[ 2 ]] ), digits = 6 ) ) 162s (Intercept) price farmPrice trend 162s 40.818 0.357 0.219 0.303 162s > 162s > print( round( coef( fit3slsd[[ 4 ]]$e3w ), digits = 6 ) ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 100.174 -0.325 0.341 49.743 162s supply_price supply_farmPrice supply_trend 162s 0.237 0.247 0.341 162s > print( round( coef( fit3slsd[[ 4 ]]$e3w, modified.regMat = TRUE ), digits = 6 ) ) 162s C1 C2 C3 C4 C5 C6 162s 100.174 -0.325 0.341 49.743 0.237 0.247 162s > print( round( coef( fit3slsd[[ 5 ]]$e3w$eq[[ 2 ]] ), digits = 6 ) ) 162s (Intercept) price farmPrice trend 162s 57.667 0.133 0.270 0.370 162s > 162s > print( round( coef( fit3sls[[ 1 ]]$e4 ), digits = 6 ) ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 93.907 -0.246 0.324 49.905 162s supply_price supply_farmPrice supply_trend 162s 0.254 0.229 0.324 162s > print( round( coef( fit3sls[[ 2 ]]$e4$eq[[ 1 ]] ), digits = 6 ) ) 162s (Intercept) price income 162s 93.907 -0.246 0.324 162s > 162s > print( round( coef( fit3slsi[[ 2 ]]$e4we ), digits = 6 ) ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 91.390 -0.217 0.320 47.579 162s supply_price supply_farmPrice supply_trend 162s 0.283 0.224 0.320 162s > print( round( coef( fit3slsi[[ 1 ]]$e4we$eq[[ 1 ]] ), digits = 6 ) ) 162s (Intercept) price income 162s 91.390 -0.217 0.320 162s > 162s > print( round( coef( fit3slsi[[ 2 ]]$e5e ), digits = 6 ) ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 91.390 -0.217 0.320 47.579 162s supply_price supply_farmPrice supply_trend 162s 0.283 0.224 0.320 162s > print( round( coef( fit3slsi[[ 2 ]]$e5e, modified.regMat = TRUE ), digits = 6 ) ) 162s C1 C2 C3 C4 C5 C6 162s 91.390 -0.217 0.320 47.579 0.283 0.224 162s > print( round( coef( fit3slsi[[ 3 ]]$e5e$eq[[ 2 ]] ), digits = 6 ) ) 162s (Intercept) price farmPrice trend 162s 47.579 0.283 0.224 0.320 162s > 162s > 162s > ## *************** coefficients with stats ********************* 162s > print( round( coef( summary( fit3sls[[ 3 ]]$e1c, useDfSys = FALSE ) ), 162s + digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 94.633 7.9208 11.95 0.000000 162s demand_price -0.244 0.0965 -2.52 0.021832 162s demand_income 0.314 0.0469 6.69 0.000004 162s supply_(Intercept) 52.287 11.8853 4.40 0.000448 162s supply_price 0.228 0.0997 2.29 0.035951 162s supply_farmPrice 0.227 0.0438 5.19 0.000089 162s supply_trend 0.365 0.0707 5.16 0.000095 162s > print( round( coef( summary( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]], useDfSys = FALSE ) ), 162s + digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 52.287 11.8853 4.40 0.000448 162s price 0.228 0.0997 2.29 0.035951 162s farmPrice 0.227 0.0438 5.19 0.000089 162s trend 0.365 0.0707 5.16 0.000095 162s > 162s > print( round( coef( summary( fit3slsd[[ 2 ]]$e1w, useDfSys = FALSE ) ), 162s + digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 106.789 11.1435 9.58 0.000000 162s demand_price -0.412 0.1448 -2.84 0.011271 162s demand_income 0.362 0.0564 6.41 0.000006 162s supply_(Intercept) 57.295 11.7078 4.89 0.000162 162s supply_price 0.137 0.0979 1.40 0.179781 162s supply_farmPrice 0.266 0.0483 5.51 0.000048 162s supply_trend 0.397 0.0672 5.91 0.000022 162s > print( round( coef( summary( fit3slsd[[ 3 ]]$e1w$eq[[ 2 ]], useDfSys = FALSE ) ), 162s + digits = 3 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 49.532 12.011 4.12 0.001 162s price 0.240 0.100 2.40 0.029 162s farmPrice 0.256 0.047 5.41 0.000 162s trend 0.253 0.100 2.54 0.022 162s > 162s > print( round( coef( summary( fit3slsi[[ 4 ]]$e2 ) ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 92.074 9.6303 9.56 0.000000 162s demand_price -0.106 0.1023 -1.04 0.305469 162s demand_income 0.200 0.0297 6.73 0.000000 162s supply_(Intercept) 68.855 12.4839 5.52 0.000004 162s supply_price 0.183 0.1189 1.54 0.132354 162s supply_farmPrice 0.120 0.0260 4.63 0.000051 162s supply_trend 0.200 0.0297 6.73 0.000000 162s > print( round( coef( summary( fit3slsi[[ 5 ]]$e2$eq[[ 1 ]] ) ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 92.074 9.6303 9.56 0.000 162s price -0.106 0.1023 -1.04 0.305 162s income 0.200 0.0297 6.73 0.000 162s > 162s > print( round( coef( summary( fit3slsd[[ 5 ]]$e3e, useDfSys = FALSE ) ), 162s + digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 109.109 5.8428 18.67 0.000000 162s demand_price -0.442 0.0737 -6.00 0.000014 162s demand_income 0.369 0.0432 8.54 0.000000 162s supply_(Intercept) 57.268 10.0564 5.69 0.000033 162s supply_price 0.137 0.0705 1.95 0.069081 162s supply_farmPrice 0.269 0.0403 6.68 0.000005 162s supply_trend 0.369 0.0432 8.54 0.000000 162s > print( round( coef( summary( fit3slsd[[ 5 ]]$e3e, useDfSys = FALSE ), 162s + modified.regMat = TRUE ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s C1 109.109 5.8428 18.67 NA 162s C2 -0.442 0.0737 -6.00 NA 162s C3 0.369 0.0432 8.54 NA 162s C4 57.268 10.0564 5.69 NA 162s C5 0.137 0.0705 1.95 NA 162s C6 0.269 0.0403 6.68 NA 162s > print( round( coef( summary( fit3slsd[[ 1 ]]$e3e$eq[[ 2 ]], useDfSys = FALSE ) ), 162s + digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 40.818 10.0564 4.06 0.000912 162s price 0.357 0.0705 5.06 0.000116 162s farmPrice 0.219 0.0403 5.45 0.000053 162s trend 0.303 0.0432 7.00 0.000003 162s > 162s > print( round( coef( summary( fit3slsi[[ 4 ]]$e3w, useDfSys = FALSE ) ), 162s + digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 92.074 9.6303 9.56 0.000000 162s demand_price -0.106 0.1023 -1.04 0.312700 162s demand_income 0.200 0.0297 6.73 0.000004 162s supply_(Intercept) 68.855 12.4839 5.52 0.000047 162s supply_price 0.183 0.1189 1.54 0.142642 162s supply_farmPrice 0.120 0.0260 4.63 0.000278 162s supply_trend 0.200 0.0297 6.73 0.000005 162s > print( round( coef( summary( fit3slsi[[ 4 ]]$e3w, useDfSys = FALSE ), 162s + modified.regMat = TRUE ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s C1 92.074 9.6303 9.56 NA 162s C2 -0.106 0.1023 -1.04 NA 162s C3 0.200 0.0297 6.73 NA 162s C4 68.855 12.4839 5.52 NA 162s C5 0.183 0.1189 1.54 NA 162s C6 0.120 0.0260 4.63 NA 162s > print( round( coef( summary( fit3slsi[[ 5 ]]$e3w$eq[[ 2 ]], useDfSys = FALSE ) ), 162s + digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 68.855 12.4839 5.52 0.000047 162s price 0.183 0.1189 1.54 0.142642 162s farmPrice 0.120 0.0260 4.63 0.000278 162s trend 0.200 0.0297 6.73 0.000005 162s > 162s > print( round( coef( summary( fit3sls[[ 1 ]]$e4 ) ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 93.907 7.9234 11.85 0.000000 162s demand_price -0.246 0.0891 -2.76 0.009212 162s demand_income 0.324 0.0233 13.91 0.000000 162s supply_(Intercept) 49.905 8.1797 6.10 0.000001 162s supply_price 0.254 0.0891 2.85 0.007217 162s supply_farmPrice 0.229 0.0241 9.52 0.000000 162s supply_trend 0.324 0.0233 13.91 0.000000 162s > print( round( coef( summary( fit3sls[[ 2 ]]$e4$eq[[ 1 ]] ) ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 93.907 7.9234 11.85 0.00000 162s price -0.246 0.0891 -2.76 0.00921 162s income 0.324 0.0233 13.91 0.00000 162s > 162s > print( round( coef( summary( fit3slsi[[ 2 ]]$e5e ) ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 91.390 7.3161 12.49 0.00000 162s demand_price -0.217 0.0835 -2.60 0.01365 162s demand_income 0.320 0.0168 19.07 0.00000 162s supply_(Intercept) 47.579 7.4268 6.41 0.00000 162s supply_price 0.283 0.0835 3.39 0.00174 162s supply_farmPrice 0.224 0.0168 13.36 0.00000 162s supply_trend 0.320 0.0168 19.07 0.00000 162s > print( round( coef( summary( fit3slsi[[ 2 ]]$e5e ), modified.regMat = TRUE ), 162s + digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s C1 91.390 7.3161 12.49 0.00000 162s C2 -0.217 0.0835 -2.60 0.01365 162s C3 0.320 0.0168 19.07 0.00000 162s C4 47.579 7.4268 6.41 0.00000 162s C5 0.283 0.0835 3.39 0.00174 162s C6 0.224 0.0168 13.36 0.00000 162s > print( round( coef( summary( fit3slsi[[ 3 ]]$e5e$eq[[ 2 ]] ) ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 47.579 7.4268 6.41 0.00000 162s price 0.283 0.0835 3.39 0.00174 162s farmPrice 0.224 0.0168 13.36 0.00000 162s trend 0.320 0.0168 19.07 0.00000 162s > 162s > print( round( coef( summary( fit3sls[[ 2 ]]$e5we ) ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s demand_(Intercept) 94.083 7.3058 12.88 0.00000 162s demand_price -0.248 0.0812 -3.06 0.00424 162s demand_income 0.325 0.0205 15.81 0.00000 162s supply_(Intercept) 50.019 7.5314 6.64 0.00000 162s supply_price 0.252 0.0812 3.10 0.00383 162s supply_farmPrice 0.231 0.0209 11.05 0.00000 162s supply_trend 0.325 0.0205 15.81 0.00000 162s > print( round( coef( summary( fit3sls[[ 2 ]]$e5we ), modified.regMat = TRUE ), 162s + digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s C1 94.083 7.3058 12.88 0.00000 162s C2 -0.248 0.0812 -3.06 0.00424 162s C3 0.325 0.0205 15.81 0.00000 162s C4 50.019 7.5314 6.64 0.00000 162s C5 0.252 0.0812 3.10 0.00383 162s C6 0.231 0.0209 11.05 0.00000 162s > print( round( coef( summary( fit3sls[[ 3 ]]$e5we$eq[[ 2 ]] ) ), digits = 6 ) ) 162s Estimate Std. Error t value Pr(>|t|) 162s (Intercept) 50.019 7.5314 6.64 0.00000 162s price 0.252 0.0812 3.10 0.00383 162s farmPrice 0.231 0.0209 11.05 0.00000 162s trend 0.325 0.0205 15.81 0.00000 162s > 162s > 162s > ## *********** variance covariance matrix of the coefficients ******* 162s > print( round( vcov( fit3sls[[ 3 ]]$e1c ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 62.7397 -0.67342 0.04930 162s demand_price -0.6734 0.00931 -0.00264 162s demand_income 0.0493 -0.00264 0.00220 162s supply_(Intercept) 65.2708 -0.36561 -0.29198 162s supply_price -0.6979 0.00620 0.00079 162s supply_farmPrice 0.0423 -0.00227 0.00189 162s supply_trend 0.0638 -0.00342 0.00285 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 65.271 -0.69790 0.04230 162s demand_price -0.366 0.00620 -0.00227 162s demand_income -0.292 0.00079 0.00189 162s supply_(Intercept) 141.261 -1.08251 -0.29300 162s supply_price -1.083 0.00993 0.00080 162s supply_farmPrice -0.293 0.00080 0.00192 162s supply_trend -0.417 0.00110 0.00263 162s supply_trend 162s demand_(Intercept) 0.06383 162s demand_price -0.00342 162s demand_income 0.00285 162s supply_(Intercept) -0.41674 162s supply_price 0.00110 162s supply_farmPrice 0.00263 162s supply_trend 0.00500 162s > print( round( vcov( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]] ), digits = 5 ) ) 162s (Intercept) price farmPrice trend 162s (Intercept) 141.261 -1.08251 -0.29300 -0.41674 162s price -1.083 0.00993 0.00080 0.00110 162s farmPrice -0.293 0.00080 0.00192 0.00263 162s trend -0.417 0.00110 0.00263 0.00500 162s > 162s > print( round( vcov( fit3sls[[ 4 ]]$e2 ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 64.2351 -0.68447 0.04535 162s demand_price -0.6845 0.00921 -0.00243 162s demand_income 0.0454 -0.00243 0.00203 162s supply_(Intercept) 67.0281 -0.42600 -0.24804 162s supply_price -0.7080 0.00641 0.00069 162s supply_farmPrice 0.0366 -0.00196 0.00164 162s supply_trend 0.0454 -0.00243 0.00203 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 67.028 -0.70800 0.03661 162s demand_price -0.426 0.00641 -0.00196 162s demand_income -0.248 0.00069 0.00164 162s supply_(Intercept) 134.043 -1.07653 -0.24277 162s supply_price -1.077 0.01003 0.00068 162s supply_farmPrice -0.243 0.00068 0.00163 162s supply_trend -0.248 0.00069 0.00164 162s supply_trend 162s demand_(Intercept) 0.04535 162s demand_price -0.00243 162s demand_income 0.00203 162s supply_(Intercept) -0.24804 162s supply_price 0.00069 162s supply_farmPrice 0.00164 162s supply_trend 0.00203 162s > print( round( vcov( fit3sls[[ 5 ]]$e2$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 64.2351 -0.68447 0.04535 162s price -0.6845 0.00921 -0.00243 162s income 0.0454 -0.00243 0.00203 162s > 162s > print( round( vcov( fit3sls[[ 5 ]]$e3e ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 54.6190 -0.58283 0.03940 162s demand_price -0.5828 0.00789 -0.00211 162s demand_income 0.0394 -0.00211 0.00176 162s supply_(Intercept) 55.1360 -0.34396 -0.21065 162s supply_price -0.5835 0.00527 0.00058 162s supply_farmPrice 0.0310 -0.00166 0.00139 162s supply_trend 0.0394 -0.00211 0.00176 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 55.136 -0.58348 0.03102 162s demand_price -0.344 0.00527 -0.00166 162s demand_income -0.211 0.00058 0.00139 162s supply_(Intercept) 108.147 -0.86360 -0.19987 162s supply_price -0.864 0.00803 0.00056 162s supply_farmPrice -0.200 0.00056 0.00134 162s supply_trend -0.211 0.00058 0.00139 162s supply_trend 162s demand_(Intercept) 0.03940 162s demand_price -0.00211 162s demand_income 0.00176 162s supply_(Intercept) -0.21065 162s supply_price 0.00058 162s supply_farmPrice 0.00139 162s supply_trend 0.00176 162s > print( round( vcov( fit3sls[[ 5 ]]$e3e, modified.regMat = TRUE ), digits = 5 ) ) 162s C1 C2 C3 C4 C5 C6 162s C1 54.6190 -0.58283 0.03940 55.136 -0.58348 0.03102 162s C2 -0.5828 0.00789 -0.00211 -0.344 0.00527 -0.00166 162s C3 0.0394 -0.00211 0.00176 -0.211 0.00058 0.00139 162s C4 55.1360 -0.34396 -0.21065 108.147 -0.86360 -0.19987 162s C5 -0.5835 0.00527 0.00058 -0.864 0.00803 0.00056 162s C6 0.0310 -0.00166 0.00139 -0.200 0.00056 0.00134 162s > print( round( vcov( fit3sls[[ 1 ]]$e3e$eq[[ 2 ]] ), digits = 5 ) ) 162s (Intercept) price farmPrice trend 162s (Intercept) 108.147 -0.86360 -0.19987 -0.21065 162s price -0.864 0.00803 0.00056 0.00058 162s farmPrice -0.200 0.00056 0.00134 0.00139 162s trend -0.211 0.00058 0.00139 0.00176 162s > 162s > print( round( vcov( fit3sls[[ 1 ]]$e4 ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 62.7805 -0.68439 0.06014 162s demand_price -0.6844 0.00794 -0.00113 162s demand_income 0.0601 -0.00113 0.00054 162s supply_(Intercept) 63.2287 -0.69892 0.07078 162s supply_price -0.6844 0.00794 -0.00113 162s supply_farmPrice 0.0499 -0.00087 0.00038 162s supply_trend 0.0601 -0.00113 0.00054 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 63.2287 -0.68439 0.04986 162s demand_price -0.6989 0.00794 -0.00087 162s demand_income 0.0708 -0.00113 0.00038 162s supply_(Intercept) 66.9073 -0.69892 0.02657 162s supply_price -0.6989 0.00794 -0.00087 162s supply_farmPrice 0.0266 -0.00087 0.00058 162s supply_trend 0.0708 -0.00113 0.00038 162s supply_trend 162s demand_(Intercept) 0.06014 162s demand_price -0.00113 162s demand_income 0.00054 162s supply_(Intercept) 0.07078 162s supply_price -0.00113 162s supply_farmPrice 0.00038 162s supply_trend 0.00054 162s > print( round( vcov( fit3sls[[ 2 ]]$e4$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 62.7805 -0.68439 0.06014 162s price -0.6844 0.00794 -0.00113 162s income 0.0601 -0.00113 0.00054 162s > 162s > print( round( vcov( fit3sls[[ 3 ]]$e4wSym ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 62.5490 -0.68436 0.06248 162s demand_price -0.6844 0.00795 -0.00113 162s demand_income 0.0625 -0.00113 0.00052 162s supply_(Intercept) 62.9766 -0.69799 0.07241 162s supply_price -0.6844 0.00795 -0.00113 162s supply_farmPrice 0.0522 -0.00088 0.00037 162s supply_trend 0.0625 -0.00113 0.00052 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 62.9766 -0.68436 0.05220 162s demand_price -0.6980 0.00795 -0.00088 162s demand_income 0.0724 -0.00113 0.00037 162s supply_(Intercept) 66.4588 -0.69799 0.03007 162s supply_price -0.6980 0.00795 -0.00088 162s supply_farmPrice 0.0301 -0.00088 0.00056 162s supply_trend 0.0724 -0.00113 0.00037 162s supply_trend 162s demand_(Intercept) 0.06248 162s demand_price -0.00113 162s demand_income 0.00052 162s supply_(Intercept) 0.07241 162s supply_price -0.00113 162s supply_farmPrice 0.00037 162s supply_trend 0.00052 162s > print( round( vcov( fit3sls[[ 4 ]]$e4wSym$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 62.5490 -0.68436 0.06248 162s price -0.6844 0.00795 -0.00113 162s income 0.0625 -0.00113 0.00052 162s > 162s > print( round( vcov( fit3sls[[ 2 ]]$e5e ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 53.5147 -0.57537 0.04304 162s demand_price -0.5754 0.00659 -0.00085 162s demand_income 0.0430 -0.00085 0.00044 162s supply_(Intercept) 53.9493 -0.58881 0.05259 162s supply_price -0.5754 0.00659 -0.00085 162s supply_farmPrice 0.0345 -0.00063 0.00029 162s supply_trend 0.0430 -0.00085 0.00044 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 53.9493 -0.57537 0.03449 162s demand_price -0.5888 0.00659 -0.00063 162s demand_income 0.0526 -0.00085 0.00029 162s supply_(Intercept) 57.0063 -0.58881 0.01639 162s supply_price -0.5888 0.00659 -0.00063 162s supply_farmPrice 0.0164 -0.00063 0.00045 162s supply_trend 0.0526 -0.00085 0.00029 162s supply_trend 162s demand_(Intercept) 0.04304 162s demand_price -0.00085 162s demand_income 0.00044 162s supply_(Intercept) 0.05259 162s supply_price -0.00085 162s supply_farmPrice 0.00029 162s supply_trend 0.00044 162s > print( round( vcov( fit3sls[[ 2 ]]$e5e, modified.regMat = TRUE ), digits = 5 ) ) 162s C1 C2 C3 C4 C5 C6 162s C1 53.5147 -0.57537 0.04304 53.9493 -0.57537 0.03449 162s C2 -0.5754 0.00659 -0.00085 -0.5888 0.00659 -0.00063 162s C3 0.0430 -0.00085 0.00044 0.0526 -0.00085 0.00029 162s C4 53.9493 -0.58881 0.05259 57.0063 -0.58881 0.01639 162s C5 -0.5754 0.00659 -0.00085 -0.5888 0.00659 -0.00063 162s C6 0.0345 -0.00063 0.00029 0.0164 -0.00063 0.00045 162s > print( round( vcov( fit3sls[[ 3 ]]$e5e$eq[[ 2 ]] ), digits = 5 ) ) 162s (Intercept) price farmPrice trend 162s (Intercept) 57.0063 -0.58881 0.01639 0.05259 162s price -0.5888 0.00659 -0.00063 -0.00085 162s farmPrice 0.0164 -0.00063 0.00045 0.00029 162s trend 0.0526 -0.00085 0.00029 0.00044 162s > 162s > print( round( vcov( fit3slsi[[ 4 ]]$e1e ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 53.3287 -0.57241 0.04191 162s demand_price -0.5724 0.00791 -0.00225 162s demand_income 0.0419 -0.00225 0.00187 162s supply_(Intercept) 60.8329 -0.34075 -0.27213 162s supply_price -0.6504 0.00578 0.00074 162s supply_farmPrice 0.0394 -0.00211 0.00176 162s supply_trend 0.0595 -0.00319 0.00266 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 60.833 -0.65044 0.03942 162s demand_price -0.341 0.00578 -0.00211 162s demand_income -0.272 0.00074 0.00176 162s supply_(Intercept) 129.860 -0.99616 -0.26688 162s supply_price -0.996 0.00915 0.00073 162s supply_farmPrice -0.267 0.00073 0.00173 162s supply_trend -0.396 0.00107 0.00255 162s supply_trend 162s demand_(Intercept) 0.05949 162s demand_price -0.00319 162s demand_income 0.00266 162s supply_(Intercept) -0.39621 162s supply_price 0.00107 162s supply_farmPrice 0.00255 162s supply_trend 0.00411 162s > print( round( vcov( fit3slsi[[ 3 ]]$e1e$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 53.3287 -0.57241 0.04191 162s price -0.5724 0.00791 -0.00225 162s income 0.0419 -0.00225 0.00187 162s > 162s > print( round( vcov( fit3slsi[[ 5 ]]$e1we ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 53.3287 -0.57241 0.04191 162s demand_price -0.5724 0.00791 -0.00225 162s demand_income 0.0419 -0.00225 0.00187 162s supply_(Intercept) 60.8329 -0.34075 -0.27213 162s supply_price -0.6504 0.00578 0.00074 162s supply_farmPrice 0.0394 -0.00211 0.00176 162s supply_trend 0.0595 -0.00319 0.00266 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 60.833 -0.65044 0.03942 162s demand_price -0.341 0.00578 -0.00211 162s demand_income -0.272 0.00074 0.00176 162s supply_(Intercept) 129.860 -0.99616 -0.26688 162s supply_price -0.996 0.00915 0.00073 162s supply_farmPrice -0.267 0.00073 0.00173 162s supply_trend -0.396 0.00107 0.00255 162s supply_trend 162s demand_(Intercept) 0.05949 162s demand_price -0.00319 162s demand_income 0.00266 162s supply_(Intercept) -0.39621 162s supply_price 0.00107 162s supply_farmPrice 0.00255 162s supply_trend 0.00411 162s > print( round( vcov( fit3slsi[[ 1 ]]$e1we$eq[[ 2 ]] ), digits = 5 ) ) 162s (Intercept) price farmPrice trend 162s (Intercept) 129.860 -0.99616 -0.26688 -0.39621 162s price -0.996 0.00915 0.00073 0.00107 162s farmPrice -0.267 0.00073 0.00173 0.00255 162s trend -0.396 0.00107 0.00255 0.00411 162s > 162s > print( round( vcov( fit3slsi[[ 5 ]]$e2e ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 79.5917 -0.81281 0.02003 162s demand_price -0.8128 0.00917 -0.00107 162s demand_income 0.0200 -0.00107 0.00090 162s supply_(Intercept) 90.3437 -0.79178 -0.11134 162s supply_price -0.9184 0.00888 0.00031 162s supply_farmPrice 0.0165 -0.00088 0.00074 162s supply_trend 0.0200 -0.00107 0.00090 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 90.3437 -0.91836 0.01646 162s demand_price -0.7918 0.00888 -0.00088 162s demand_income -0.1113 0.00031 0.00074 162s supply_(Intercept) 124.3894 -1.13680 -0.09494 162s supply_price -1.1368 0.01108 0.00026 162s supply_farmPrice -0.0949 0.00026 0.00063 162s supply_trend -0.1113 0.00031 0.00074 162s supply_trend 162s demand_(Intercept) 0.02003 162s demand_price -0.00107 162s demand_income 0.00090 162s supply_(Intercept) -0.11134 162s supply_price 0.00031 162s supply_farmPrice 0.00074 162s supply_trend 0.00090 162s > print( round( vcov( fit3slsi[[ 4 ]]$e2e$eq[[ 2 ]] ), digits = 5 ) ) 162s (Intercept) price farmPrice trend 162s (Intercept) 124.3894 -1.13680 -0.09494 -0.11134 162s price -1.1368 0.01108 0.00026 0.00031 162s farmPrice -0.0949 0.00026 0.00063 0.00074 162s trend -0.1113 0.00031 0.00074 0.00090 162s > 162s > print( round( vcov( fit3slsi[[ 1 ]]$e3 ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 92.7431 -0.94355 0.01968 162s demand_price -0.9435 0.01046 -0.00105 162s demand_income 0.0197 -0.00105 0.00088 162s supply_(Intercept) 110.7701 -0.99345 -0.11331 162s supply_price -1.1222 0.01091 0.00031 162s supply_farmPrice 0.0168 -0.00090 0.00075 162s supply_trend 0.0197 -0.00105 0.00088 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 110.770 -1.12223 0.01680 162s demand_price -0.993 0.01091 -0.00090 162s demand_income -0.113 0.00031 0.00075 162s supply_(Intercept) 155.849 -1.44407 -0.10125 162s supply_price -1.444 0.01413 0.00028 162s supply_farmPrice -0.101 0.00028 0.00067 162s supply_trend -0.113 0.00031 0.00075 162s supply_trend 162s demand_(Intercept) 0.01968 162s demand_price -0.00105 162s demand_income 0.00088 162s supply_(Intercept) -0.11331 162s supply_price 0.00031 162s supply_farmPrice 0.00075 162s supply_trend 0.00088 162s > print( round( vcov( fit3slsi[[ 1 ]]$e3, modified.regMat = TRUE ), digits = 5 ) ) 162s C1 C2 C3 C4 C5 C6 162s C1 92.7431 -0.94355 0.01968 110.770 -1.12223 0.01680 162s C2 -0.9435 0.01046 -0.00105 -0.993 0.01091 -0.00090 162s C3 0.0197 -0.00105 0.00088 -0.113 0.00031 0.00075 162s C4 110.7701 -0.99345 -0.11331 155.849 -1.44407 -0.10125 162s C5 -1.1222 0.01091 0.00031 -1.444 0.01413 0.00028 162s C6 0.0168 -0.00090 0.00075 -0.101 0.00028 0.00067 162s > print( round( vcov( fit3slsi[[ 5 ]]$e3$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 92.7431 -0.94355 0.01968 162s price -0.9435 0.01046 -0.00105 162s income 0.0197 -0.00105 0.00088 162s > 162s > print( round( vcov( fit3slsi[[ 2 ]]$e4e ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 53.5249 -0.60193 0.07023 162s demand_price -0.6019 0.00697 -0.00098 162s demand_income 0.0702 -0.00098 0.00028 162s supply_(Intercept) 53.7695 -0.60749 0.07383 162s supply_price -0.6019 0.00697 -0.00098 162s supply_farmPrice 0.0611 -0.00082 0.00022 162s supply_trend 0.0702 -0.00098 0.00028 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 53.7695 -0.60193 0.06114 162s demand_price -0.6075 0.00697 -0.00082 162s demand_income 0.0738 -0.00098 0.00022 162s supply_(Intercept) 55.1575 -0.60749 0.05283 162s supply_price -0.6075 0.00697 -0.00082 162s supply_farmPrice 0.0528 -0.00082 0.00028 162s supply_trend 0.0738 -0.00098 0.00022 162s supply_trend 162s demand_(Intercept) 0.07023 162s demand_price -0.00098 162s demand_income 0.00028 162s supply_(Intercept) 0.07383 162s supply_price -0.00098 162s supply_farmPrice 0.00022 162s supply_trend 0.00028 162s > print( round( vcov( fit3slsi[[ 1 ]]$e4e$eq[[ 2 ]] ), digits = 5 ) ) 162s (Intercept) price farmPrice trend 162s (Intercept) 55.1575 -0.60749 0.05283 0.07383 162s price -0.6075 0.00697 -0.00082 -0.00098 162s farmPrice 0.0528 -0.00082 0.00028 0.00022 162s trend 0.0738 -0.00098 0.00022 0.00028 162s > 162s > print( round( vcov( fit3slsi[[ 3 ]]$e5 ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 62.6857 -0.71803 0.09573 162s demand_price -0.7180 0.00846 -0.00132 162s demand_income 0.0957 -0.00132 0.00037 162s supply_(Intercept) 62.7317 -0.72119 0.09909 162s supply_price -0.7180 0.00846 -0.00132 162s supply_farmPrice 0.0863 -0.00115 0.00030 162s supply_trend 0.0957 -0.00132 0.00037 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 62.7317 -0.71803 0.08635 162s demand_price -0.7212 0.00846 -0.00115 162s demand_income 0.0991 -0.00132 0.00030 162s supply_(Intercept) 64.1668 -0.72119 0.07539 162s supply_price -0.7212 0.00846 -0.00115 162s supply_farmPrice 0.0754 -0.00115 0.00038 162s supply_trend 0.0991 -0.00132 0.00030 162s supply_trend 162s demand_(Intercept) 0.09573 162s demand_price -0.00132 162s demand_income 0.00037 162s supply_(Intercept) 0.09909 162s supply_price -0.00132 162s supply_farmPrice 0.00030 162s supply_trend 0.00037 162s > print( round( vcov( fit3slsi[[ 3 ]]$e5, modified.regMat = TRUE ), digits = 5 ) ) 162s C1 C2 C3 C4 C5 C6 162s C1 62.6857 -0.71803 0.09573 62.7317 -0.71803 0.08635 162s C2 -0.7180 0.00846 -0.00132 -0.7212 0.00846 -0.00115 162s C3 0.0957 -0.00132 0.00037 0.0991 -0.00132 0.00030 162s C4 62.7317 -0.72119 0.09909 64.1668 -0.72119 0.07539 162s C5 -0.7180 0.00846 -0.00132 -0.7212 0.00846 -0.00115 162s C6 0.0863 -0.00115 0.00030 0.0754 -0.00115 0.00038 162s > print( round( vcov( fit3slsi[[ 2 ]]$e5$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 62.6857 -0.71803 0.09573 162s price -0.7180 0.00846 -0.00132 162s income 0.0957 -0.00132 0.00037 162s > 162s > print( round( vcov( fit3slsi[[ 5 ]]$e5w ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 107.334 -1.39936 0.34281 162s demand_price -1.399 0.01904 -0.00518 162s demand_income 0.343 -0.00518 0.00179 162s supply_(Intercept) 95.422 -1.22389 0.29205 162s supply_price -1.399 0.01904 -0.00518 162s supply_farmPrice 0.439 -0.00648 0.00214 162s supply_trend 0.343 -0.00518 0.00179 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 95.422 -1.39936 0.43918 162s demand_price -1.224 0.01904 -0.00648 162s demand_income 0.292 -0.00518 0.00214 162s supply_(Intercept) 92.381 -1.22389 0.30881 162s supply_price -1.224 0.01904 -0.00648 162s supply_farmPrice 0.309 -0.00648 0.00328 162s supply_trend 0.292 -0.00518 0.00214 162s supply_trend 162s demand_(Intercept) 0.34281 162s demand_price -0.00518 162s demand_income 0.00179 162s supply_(Intercept) 0.29205 162s supply_price -0.00518 162s supply_farmPrice 0.00214 162s supply_trend 0.00179 162s > print( round( vcov( fit3slsi[[ 5 ]]$e5w, modified.regMat = TRUE ), digits = 5 ) ) 162s C1 C2 C3 C4 C5 C6 162s C1 107.334 -1.39936 0.34281 95.422 -1.39936 0.43918 162s C2 -1.399 0.01904 -0.00518 -1.224 0.01904 -0.00648 162s C3 0.343 -0.00518 0.00179 0.292 -0.00518 0.00214 162s C4 95.422 -1.22389 0.29205 92.381 -1.22389 0.30881 162s C5 -1.399 0.01904 -0.00518 -1.224 0.01904 -0.00648 162s C6 0.439 -0.00648 0.00214 0.309 -0.00648 0.00328 162s > print( round( vcov( fit3slsi[[ 4 ]]$e5w$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 62.6858 -0.71803 0.09573 162s price -0.7180 0.00846 -0.00132 162s income 0.0957 -0.00132 0.00037 162s > 162s > print( round( vcov( fit3slsd[[ 5 ]]$e1c ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 124.179 -1.51767 0.28519 162s demand_price -1.518 0.02098 -0.00595 162s demand_income 0.285 -0.00595 0.00318 162s supply_(Intercept) 45.831 -0.16114 -0.30261 162s supply_price -0.564 0.00477 0.00089 162s supply_farmPrice 0.157 -0.00365 0.00213 162s supply_trend -0.416 0.00351 0.00066 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 45.831 -0.56422 0.15696 162s demand_price -0.161 0.00477 -0.00365 162s demand_income -0.303 0.00089 0.00213 162s supply_(Intercept) 132.389 -0.93831 -0.33973 162s supply_price -0.938 0.00791 0.00115 162s supply_farmPrice -0.340 0.00115 0.00221 162s supply_trend -0.515 0.00349 0.00108 162s supply_trend 162s demand_(Intercept) -0.41585 162s demand_price 0.00351 162s demand_income 0.00066 162s supply_(Intercept) -0.51541 162s supply_price 0.00349 162s supply_farmPrice 0.00108 162s supply_trend 0.00585 162s > print( round( vcov( fit3slsd[[ 2 ]]$e1c$eq[[ 2 ]] ), digits = 5 ) ) 162s (Intercept) price farmPrice trend 162s (Intercept) 136.580 -1.06234 -0.24479 -0.60682 162s price -0.994 0.00955 -0.00011 0.00471 162s farmPrice -0.334 0.00098 0.00234 0.00096 162s trend -0.438 0.00119 0.00284 0.00415 162s > 162s > print( round( vcov( fit3slsd[[ 1 ]]$e2 ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 40.2908 -0.42351 0.02315 162s demand_price -0.4235 0.00660 -0.00242 162s demand_income 0.0232 -0.00242 0.00225 162s supply_(Intercept) 23.1539 0.17811 -0.41781 162s supply_price -0.2648 0.00059 0.00211 162s supply_farmPrice 0.0342 -0.00220 0.00190 162s supply_trend 0.0232 -0.00242 0.00225 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 23.154 -0.26482 0.03423 162s demand_price 0.178 0.00059 -0.00220 162s demand_income -0.418 0.00211 0.00190 162s supply_(Intercept) 125.488 -0.81757 -0.40378 162s supply_price -0.818 0.00616 0.00186 162s supply_farmPrice -0.404 0.00186 0.00205 162s supply_trend -0.418 0.00211 0.00190 162s supply_trend 162s demand_(Intercept) 0.02315 162s demand_price -0.00242 162s demand_income 0.00225 162s supply_(Intercept) -0.41781 162s supply_price 0.00211 162s supply_farmPrice 0.00190 162s supply_trend 0.00225 162s > print( round( vcov( fit3slsd[[ 3 ]]$e2$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 99.763 -1.2027 0.21239 162s price -1.203 0.0168 -0.00490 162s income 0.212 -0.0049 0.00285 162s > 162s > print( round( vcov( fit3slsd[[ 5 ]]$e2we ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 34.9080 -0.36232 0.01530 162s demand_price -0.3623 0.00556 -0.00199 162s demand_income 0.0153 -0.00199 0.00188 162s supply_(Intercept) 20.3293 0.13409 -0.34409 162s supply_price -0.2272 0.00057 0.00174 162s supply_farmPrice 0.0249 -0.00176 0.00155 162s supply_trend 0.0153 -0.00199 0.00188 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 20.329 -0.22716 0.02494 162s demand_price 0.134 0.00057 -0.00176 162s demand_income -0.344 0.00174 0.00155 162s supply_(Intercept) 102.201 -0.66897 -0.32522 162s supply_price -0.669 0.00505 0.00150 162s supply_farmPrice -0.325 0.00150 0.00164 162s supply_trend -0.344 0.00174 0.00155 162s supply_trend 162s demand_(Intercept) 0.01530 162s demand_price -0.00199 162s demand_income 0.00188 162s supply_(Intercept) -0.34409 162s supply_price 0.00174 162s supply_farmPrice 0.00155 162s supply_trend 0.00188 162s > print( round( vcov( fit3slsd[[ 3 ]]$e2we$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 83.743 -1.0065 0.17519 162s price -1.006 0.0141 -0.00410 162s income 0.175 -0.0041 0.00241 162s > 162s > print( round( vcov( fit3slsd[[ 2 ]]$e3 ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 155.228 -2.21373 0.68055 162s demand_price -1.929 0.03005 -0.01103 162s demand_income 0.389 -0.00812 0.00434 162s supply_(Intercept) 120.424 -1.33693 0.13854 162s supply_price -1.546 0.02054 -0.00522 162s supply_farmPrice 0.314 -0.00655 0.00350 162s supply_trend 0.389 -0.00812 0.00434 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) -25.183 -0.42614 0.63002 162s demand_price 0.811 0.00271 -0.01000 162s demand_income -0.572 0.00159 0.00380 162s supply_(Intercept) 84.582 -0.95409 0.10043 162s supply_price -0.279 0.00796 -0.00478 162s supply_farmPrice -0.521 0.00147 0.00350 162s supply_trend -0.572 0.00159 0.00380 162s supply_trend 162s demand_(Intercept) 0.68055 162s demand_price -0.01103 162s demand_income 0.00434 162s supply_(Intercept) 0.13854 162s supply_price -0.00522 162s supply_farmPrice 0.00350 162s supply_trend 0.00434 162s > print( round( vcov( fit3slsd[[ 2 ]]$e3, modified.regMat = TRUE ), digits = 5 ) ) 162s C1 C2 C3 C4 C5 C6 162s C1 155.228 -2.21373 0.68055 -25.183 -0.42614 0.63002 162s C2 -1.929 0.03005 -0.01103 0.811 0.00271 -0.01000 162s C3 0.389 -0.00812 0.00434 -0.572 0.00159 0.00380 162s C4 120.424 -1.33693 0.13854 84.582 -0.95409 0.10043 162s C5 -1.546 0.02054 -0.00522 -0.279 0.00796 -0.00478 162s C6 0.314 -0.00655 0.00350 -0.521 0.00147 0.00350 162s > print( round( vcov( fit3slsd[[ 4 ]]$e3$eq[[ 2 ]] ), digits = 5 ) ) 162s (Intercept) price farmPrice trend 162s (Intercept) 149.704 -1.13641 -0.33425 -0.32676 162s price -1.136 0.01036 0.00094 0.00091 162s farmPrice -0.334 0.00094 0.00225 0.00216 162s trend -0.327 0.00091 0.00216 0.00259 162s > 162s > print( round( vcov( fit3slsd[[ 3 ]]$e4 ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 105.016 -1.17085 0.12591 162s demand_price -1.171 0.01356 -0.00191 162s demand_income 0.126 -0.00191 0.00066 162s supply_(Intercept) 106.127 -1.19320 0.13778 162s supply_price -1.171 0.01356 -0.00191 162s supply_farmPrice 0.102 -0.00148 0.00047 162s supply_trend 0.126 -0.00191 0.00066 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 106.1266 -1.17085 0.10227 162s demand_price -1.1932 0.01356 -0.00148 162s demand_income 0.1378 -0.00191 0.00047 162s supply_(Intercept) 110.0305 -1.19320 0.08453 162s supply_price -1.1932 0.01356 -0.00148 162s supply_farmPrice 0.0845 -0.00148 0.00061 162s supply_trend 0.1378 -0.00191 0.00047 162s supply_trend 162s demand_(Intercept) 0.12591 162s demand_price -0.00191 162s demand_income 0.00066 162s supply_(Intercept) 0.13778 162s supply_price -0.00191 162s supply_farmPrice 0.00047 162s supply_trend 0.00066 162s > print( round( vcov( fit3slsd[[ 5 ]]$e4$eq[[ 1 ]] ), digits = 5 ) ) 162s (Intercept) price income 162s (Intercept) 28.9118 -0.25481 -0.03319 162s price -0.2548 0.00254 0.00001 162s income -0.0332 0.00001 0.00033 162s > 162s > print( round( vcov( fit3slsd[[ 4 ]]$e5e ), digits = 5 ) ) 162s demand_(Intercept) demand_price demand_income 162s demand_(Intercept) 57.3878 -0.60414 0.03280 162s demand_price -0.6041 0.00675 -0.00073 162s demand_income 0.0328 -0.00073 0.00041 162s supply_(Intercept) 57.4828 -0.61352 0.04167 162s supply_price -0.6041 0.00675 -0.00073 162s supply_farmPrice 0.0288 -0.00056 0.00028 162s supply_trend 0.0328 -0.00073 0.00041 162s supply_(Intercept) supply_price supply_farmPrice 162s demand_(Intercept) 57.4828 -0.60414 0.02879 162s demand_price -0.6135 0.00675 -0.00056 162s demand_income 0.0417 -0.00073 0.00028 162s supply_(Intercept) 59.8263 -0.61352 0.01389 162s supply_price -0.6135 0.00675 -0.00056 162s supply_farmPrice 0.0139 -0.00056 0.00041 162s supply_trend 0.0417 -0.00073 0.00028 162s supply_trend 162s demand_(Intercept) 0.03280 162s demand_price -0.00073 162s demand_income 0.00041 162s supply_(Intercept) 0.04167 162s supply_price -0.00073 162s supply_farmPrice 0.00028 162s supply_trend 0.00041 162s > print( round( vcov( fit3slsd[[ 4 ]]$e5e, modified.regMat = TRUE ), digits = 5 ) ) 162s C1 C2 C3 C4 C5 C6 162s C1 57.3878 -0.60414 0.03280 57.4828 -0.60414 0.02879 162s C2 -0.6041 0.00675 -0.00073 -0.6135 0.00675 -0.00056 162s C3 0.0328 -0.00073 0.00041 0.0417 -0.00073 0.00028 162s C4 57.4828 -0.61352 0.04167 59.8263 -0.61352 0.01389 162s C5 -0.6041 0.00675 -0.00073 -0.6135 0.00675 -0.00056 162s C6 0.0288 -0.00056 0.00028 0.0139 -0.00056 0.00041 162s > print( round( vcov( fit3slsd[[ 1 ]]$e5e$eq[[ 2 ]] ), digits = 5 ) ) 162s (Intercept) price farmPrice trend 162s (Intercept) 24.9502 -0.21066 -0.03490 -0.02530 162s price -0.2107 0.00210 0.00000 0.00004 162s farmPrice -0.0349 0.00000 0.00034 0.00018 162s trend -0.0253 0.00004 0.00018 0.00028 162s > 162s > 162s > ## *********** confidence intervals of coefficients ************* 162s > print( confint( fit3sls[[ 1 ]]$e1c, useDfSys = TRUE ) ) 162s 2.5 % 97.5 % 162s demand_(Intercept) 78.518 110.748 162s demand_price -0.440 -0.047 162s demand_income 0.218 0.409 162s supply_(Intercept) 28.106 76.468 162s supply_price 0.025 0.431 162s supply_farmPrice 0.138 0.316 162s supply_trend 0.221 0.509 162s > print( confint( fit3sls[[ 1 ]]$e1c$eq[[ 1 ]], level = 0.9, useDfSys = TRUE ) ) 162s 5 % 95 % 162s (Intercept) 81.228 108.038 162s price -0.407 -0.080 162s income 0.235 0.393 162s > 162s > print( confint( fit3sls[[ 2 ]]$e2e, level = 0.9, useDfSys = TRUE ) ) 162s 5 % 95 % 162s demand_(Intercept) 79.254 109.293 162s demand_price -0.405 -0.044 162s demand_income 0.213 0.383 162s supply_(Intercept) 34.318 76.586 162s supply_price 0.039 0.403 162s supply_farmPrice 0.135 0.284 162s supply_trend 0.213 0.383 162s > print( confint( fit3sls[[ 2 ]]$e2e$eq[[ 2 ]], level = 0.99, useDfSys = TRUE ) ) 162s 0.5 % 99.5 % 162s (Intercept) 27.079 83.826 162s price -0.024 0.465 162s farmPrice 0.110 0.309 162s trend 0.183 0.412 162s > 162s > print( confint( fit3sls[[ 3 ]]$e3, level = 0.99 ) ) 162s 0.5 % 99.5 % 162s demand_(Intercept) 77.934 110.509 162s demand_price -0.417 -0.026 162s demand_income 0.204 0.387 162s supply_(Intercept) 32.432 79.489 162s supply_price 0.016 0.423 162s supply_farmPrice 0.124 0.288 162s supply_trend 0.204 0.387 162s > print( confint( fit3sls[[ 3 ]]$e3$eq[[ 1 ]], level = 0.5 ) ) 162s 25 % 75 % 162s (Intercept) 88.757 99.686 162s price -0.287 -0.156 162s income 0.265 0.326 162s > 162s > print( confint( fit3sls[[ 5 ]]$e3we, level = 0.99 ) ) 162s 0.5 % 99.5 % 162s demand_(Intercept) 79.280 109.202 162s demand_price -0.402 -0.043 162s demand_income 0.212 0.381 162s supply_(Intercept) 34.570 76.815 162s supply_price 0.038 0.402 162s supply_farmPrice 0.134 0.282 162s supply_trend 0.212 0.381 162s > print( confint( fit3sls[[ 5 ]]$e3we$eq[[ 1 ]], level = 0.5 ) ) 162s 25 % 75 % 162s (Intercept) 89.222 99.260 162s price -0.283 -0.162 162s income 0.268 0.325 162s > 162s > print( confint( fit3sls[[ 4 ]]$e4e, level = 0.5, useDfSys = TRUE ) ) 162s 25 % 75 % 162s demand_(Intercept) 79.319 109.021 162s demand_price -0.414 -0.085 162s demand_income 0.282 0.367 162s supply_(Intercept) 34.758 65.413 162s supply_price 0.086 0.415 162s supply_farmPrice 0.188 0.274 162s supply_trend 0.282 0.367 162s > print( confint( fit3sls[[ 4 ]]$e4e$eq[[ 2 ]], level = 0.25, useDfSys = TRUE ) ) 162s 37.5 % 62.5 % 162s (Intercept) 47.661 52.510 162s price 0.224 0.277 162s farmPrice 0.224 0.238 162s trend 0.318 0.331 162s > 162s > print( confint( fit3sls[[ 5 ]]$e5, level = 0.25 ) ) 162s 37.5 % 62.5 % 162s demand_(Intercept) 75.213 107.384 162s demand_price -0.630 -0.268 162s demand_income 0.512 0.606 162s supply_(Intercept) -18.445 14.766 162s supply_price 0.370 0.732 162s supply_farmPrice 0.384 0.481 162s supply_trend 0.512 0.606 162s > print( confint( fit3sls[[ 5 ]]$e5$eq[[ 1 ]], level = 0.975 ) ) 162s 1.3 % 98.8 % 162s (Intercept) 72.742 109.855 162s price -0.658 -0.241 162s income 0.505 0.614 162s > 162s > print( confint( fit3slsi[[ 2 ]]$e3e, level = 0.975, useDfSys = TRUE ) ) 162s 1.3 % 98.8 % 162s demand_(Intercept) 73.905 110.166 162s demand_price -0.299 0.090 162s demand_income 0.137 0.259 162s supply_(Intercept) 45.617 90.949 162s supply_price -0.029 0.399 162s supply_farmPrice 0.073 0.175 162s supply_trend 0.137 0.259 162s > print( confint( fit3slsi[[ 2 ]]$e3e$eq[[ 1 ]], level = 0.999, useDfSys = TRUE ) ) 162s 0.1 % 100 % 162s (Intercept) 59.912 124.159 162s price -0.449 0.241 162s income 0.090 0.306 162s > 162s > print( confint( fit3slsi[[ 1 ]]$e5w, level = 0.975, useDfSys = TRUE ) ) 162s 1.3 % 98.8 % 162s demand_(Intercept) 74.084 106.230 162s demand_price -0.387 -0.014 162s demand_income 0.277 0.355 162s supply_(Intercept) 30.219 62.743 162s supply_price 0.113 0.486 162s supply_farmPrice 0.179 0.259 162s supply_trend 0.277 0.355 162s > print( confint( fit3slsi[[ 1 ]]$e5w$eq[[ 1 ]], level = 0.999, useDfSys = TRUE ) ) 162s 0.1 % 100 % 162s (Intercept) 61.724 118.590 162s price -0.531 0.130 162s income 0.247 0.385 162s > 162s > print( confint( fit3slsd[[ 3 ]]$e4, level = 0.999 ) ) 162s 0.1 % 100 % 162s demand_(Intercept) 72.590 114.198 162s demand_price -0.457 0.016 162s demand_income 0.251 0.356 162s supply_(Intercept) 27.716 70.305 162s supply_price 0.043 0.516 162s supply_farmPrice 0.165 0.265 162s supply_trend 0.251 0.356 162s > print( confint( fit3slsd[[ 3 ]]$e4$eq[[ 2 ]] ) ) 162s 2.5 % 97.5 % 162s (Intercept) 27.716 70.305 162s price 0.043 0.516 162s farmPrice 0.165 0.265 162s trend 0.251 0.356 162s > 162s > print( confint( fit3slsd[[ 2 ]]$e4w, level = 0.999 ) ) 162s 0.1 % 100 % 162s demand_(Intercept) 120.616 166.320 162s demand_price -1.063 -0.578 162s demand_income 0.371 0.439 162s supply_(Intercept) 77.414 123.333 162s supply_price -0.563 -0.078 162s supply_farmPrice 0.253 0.333 162s supply_trend 0.371 0.439 162s > print( confint( fit3slsd[[ 2 ]]$e4w$eq[[ 2 ]] ) ) 162s 2.5 % 97.5 % 162s (Intercept) 77.414 123.333 162s price -0.563 -0.078 162s farmPrice 0.253 0.333 162s trend 0.371 0.439 162s > 162s > 162s > ## *********** fitted values ************* 162s > print( fitted( fit3sls[[ 2 ]]$e1c ) ) 162s demand supply 162s 1 97.6 97.8 162s 2 99.9 99.3 162s 3 99.8 99.5 162s 4 100.0 99.9 162s 5 102.1 101.7 162s 6 102.0 101.8 162s 7 102.4 101.9 162s 8 103.0 104.1 162s 9 101.5 102.3 162s 10 100.3 99.6 162s 11 95.5 95.9 162s 12 94.7 94.8 162s 13 96.1 96.6 162s 14 99.0 98.4 162s 15 103.8 102.7 162s 16 103.7 104.4 162s 17 103.8 103.3 162s 18 102.1 103.6 162s 19 103.6 103.6 162s 20 106.9 106.6 162s > print( fitted( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 12 13 162s 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 162s 14 15 16 17 18 19 20 162s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 162s > 162s > print( fitted( fit3sls[[ 1 ]]$e1wc ) ) 162s demand supply 162s 1 97.6 97.8 162s 2 99.9 99.3 162s 3 99.8 99.5 162s 4 100.0 99.9 162s 5 102.1 101.7 162s 6 102.0 101.8 162s 7 102.4 101.9 162s 8 103.0 104.1 162s 9 101.5 102.3 162s 10 100.3 99.6 162s 11 95.5 95.9 162s 12 94.7 94.8 162s 13 96.1 96.6 162s 14 99.0 98.4 162s 15 103.8 102.7 162s 16 103.7 104.4 162s 17 103.8 103.3 162s 18 102.1 103.6 162s 19 103.6 103.6 162s 20 106.9 106.6 162s > print( fitted( fit3sls[[ 1 ]]$e1wc$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 12 13 162s 97.6 99.9 99.8 100.0 102.1 102.0 102.4 103.0 101.5 100.3 95.5 94.7 96.1 162s 14 15 16 17 18 19 20 162s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 162s > 162s > print( fitted( fit3sls[[ 3 ]]$e2e ) ) 162s demand supply 162s 1 97.8 98.4 162s 2 100.0 99.8 162s 3 99.9 99.9 162s 4 100.1 100.3 162s 5 102.0 101.8 162s 6 101.9 101.9 162s 7 102.4 102.0 162s 8 102.9 104.0 162s 9 101.4 102.2 162s 10 100.3 99.6 162s 11 95.8 96.2 162s 12 95.0 95.2 162s 13 96.4 96.9 162s 14 99.1 98.5 162s 15 103.7 102.3 162s 16 103.5 103.9 162s 17 103.6 102.8 162s 18 102.0 103.2 162s 19 103.5 103.2 162s 20 106.7 105.9 162s > print( fitted( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 12 13 162s 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 162s 14 15 16 17 18 19 20 162s 98.5 102.3 103.9 102.8 103.2 103.2 105.9 162s > 162s > print( fitted( fit3sls[[ 4 ]]$e3 ) ) 162s demand supply 162s 1 97.8 98.4 162s 2 100.0 99.8 162s 3 99.9 99.9 162s 4 100.1 100.3 162s 5 102.0 101.7 162s 6 101.9 101.8 162s 7 102.3 101.9 162s 8 102.9 103.9 162s 9 101.4 102.2 162s 10 100.3 99.6 162s 11 95.8 96.3 162s 12 95.1 95.3 162s 13 96.4 97.0 162s 14 99.1 98.5 162s 15 103.6 102.3 162s 16 103.5 103.9 162s 17 103.6 102.7 162s 18 102.0 103.1 162s 19 103.5 103.2 162s 20 106.7 105.9 162s > print( fitted( fit3sls[[ 4 ]]$e3$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 12 13 162s 97.8 100.0 99.9 100.1 102.0 101.9 102.3 102.9 101.4 100.3 95.8 95.1 96.4 162s 14 15 16 17 18 19 20 162s 99.1 103.6 103.5 103.6 102.0 103.5 106.7 162s > 162s > print( fitted( fit3sls[[ 5 ]]$e4e ) ) 162s demand supply 162s 1 95.0 96.3 162s 2 98.9 99.4 162s 3 98.8 99.5 162s 4 99.1 100.2 162s 5 103.2 102.9 162s 6 102.9 103.1 162s 7 103.6 103.4 162s 8 104.5 107.7 162s 9 102.1 103.4 162s 10 100.2 97.8 162s 11 91.5 90.8 162s 12 89.8 88.9 162s 13 92.2 92.6 162s 14 97.6 95.6 162s 15 106.4 103.4 162s 16 105.9 106.9 162s 17 106.7 103.6 162s 18 102.9 105.4 162s 19 105.6 105.5 162s 20 111.3 111.7 162s > print( fitted( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 12 13 162s 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 162s 14 15 16 17 18 19 20 162s 95.6 103.4 106.9 103.6 105.4 105.5 111.7 162s > 162s > print( fitted( fit3sls[[ 1 ]]$e5 ) ) 162s demand supply 162s 1 97.5 98.2 162s 2 99.9 99.8 162s 3 99.8 99.9 162s 4 100.0 100.3 162s 5 102.1 101.9 162s 6 102.0 102.0 162s 7 102.5 102.1 162s 8 103.1 104.3 162s 9 101.5 102.3 162s 10 100.3 99.4 162s 11 95.3 95.7 162s 12 94.5 94.6 162s 13 96.0 96.5 162s 14 99.0 98.2 162s 15 103.9 102.4 162s 16 103.7 104.2 162s 17 103.9 102.7 162s 18 102.1 103.4 162s 19 103.7 103.4 162s 20 107.2 106.6 162s > print( fitted( fit3sls[[ 1 ]]$e5$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 12 13 162s 97.5 99.9 99.8 100.0 102.1 102.0 102.5 103.1 101.5 100.3 95.3 94.5 96.0 162s 14 15 16 17 18 19 20 162s 99.0 103.9 103.7 103.9 102.1 103.7 107.2 162s > 162s > print( fitted( fit3slsi[[ 3 ]]$e3e ) ) 162s demand supply 162s 1 98.9 99.2 162s 2 100.5 100.3 162s 3 100.4 100.4 162s 4 100.6 100.6 162s 5 101.6 101.2 162s 6 101.5 101.3 162s 7 101.9 101.5 162s 8 102.4 102.9 162s 9 101.1 101.4 162s 10 100.1 99.7 162s 11 97.2 97.8 162s 12 96.9 97.5 162s 13 98.0 98.7 162s 14 99.7 99.5 162s 15 102.5 101.6 162s 16 102.6 102.7 162s 17 102.1 101.4 162s 18 101.8 102.6 162s 19 102.9 102.7 162s 20 105.3 104.8 162s > print( fitted( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 12 13 162s 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 162s 14 15 16 17 18 19 20 162s 99.7 102.5 102.6 102.1 101.8 102.9 105.3 162s > 162s > print( fitted( fit3slsd[[ 4 ]]$e4 ) ) 162s demand supply 162s 1 97.6 98.3 162s 2 99.7 99.7 162s 3 99.7 99.8 162s 4 99.8 100.1 162s 5 102.2 101.9 162s 6 102.0 102.0 162s 7 102.4 102.0 162s 8 102.8 104.1 162s 9 101.6 102.4 162s 10 100.7 99.8 162s 11 95.8 96.1 162s 12 94.8 94.8 162s 13 96.0 96.5 162s 14 99.1 98.3 162s 15 104.1 102.5 162s 16 103.7 104.2 162s 17 104.4 103.2 162s 18 101.9 103.2 162s 19 103.4 103.2 162s 20 106.3 105.9 162s > print( fitted( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 12 13 162s 98.3 99.7 99.8 100.1 101.9 102.0 102.0 104.1 102.4 99.8 96.1 94.8 96.5 162s 14 15 16 17 18 19 20 162s 98.3 102.5 104.2 103.2 103.2 103.2 105.9 162s > 162s > print( fitted( fit3slsd[[ 2 ]]$e3w ) ) 162s demand supply 162s 1 96.1 97.0 162s 2 97.6 97.2 162s 3 97.8 97.8 162s 4 97.7 97.7 162s 5 103.5 103.5 162s 6 102.7 102.8 162s 7 102.6 102.1 162s 8 101.8 103.4 162s 9 103.3 104.8 162s 10 103.9 103.4 162s 11 96.2 97.0 162s 12 92.5 92.4 162s 13 92.7 93.0 162s 14 98.8 97.6 162s 15 107.3 105.6 162s 16 105.6 106.4 162s 17 111.1 110.7 162s 18 100.9 102.3 162s 19 102.3 101.4 162s 20 103.7 101.8 162s > print( fitted( fit3slsd[[ 2 ]]$e3w$eq[[ 2 ]] ) ) 162s 1 2 3 4 5 6 7 8 9 10 11 12 13 162s 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 162s 14 15 16 17 18 19 20 162s 97.6 105.6 106.4 110.7 102.3 101.4 101.8 162s > 162s > 162s > ## *********** predicted values ************* 162s > predictData <- Kmenta 162s > predictData$consump <- NULL 162s > predictData$price <- Kmenta$price * 0.9 162s > predictData$income <- Kmenta$income * 1.1 162s > 162s > print( predict( fit3sls[[ 2 ]]$e1c, se.fit = TRUE, interval = "prediction", 162s + useDfSys = TRUE ) ) 162s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 162s 1 97.6 0.661 93.4 101.9 97.8 0.826 162s 2 99.9 0.600 95.7 104.1 99.3 0.825 162s 3 99.8 0.564 95.6 104.0 99.5 0.755 162s 4 100.0 0.605 95.8 104.2 99.9 0.783 162s 5 102.1 0.516 98.0 106.2 101.7 0.669 162s 6 102.0 0.474 97.9 106.1 101.8 0.620 162s 7 102.4 0.493 98.3 106.5 101.9 0.608 162s 8 103.0 0.615 98.8 107.2 104.1 0.889 162s 9 101.5 0.544 97.3 105.6 102.3 0.753 162s 10 100.3 0.822 96.0 104.7 99.6 1.022 162s 11 95.5 0.963 91.1 100.0 95.9 1.172 162s 12 94.7 1.006 90.2 99.2 94.8 1.289 162s 13 96.1 0.915 91.7 100.5 96.6 1.114 162s 14 99.0 0.518 94.9 103.2 98.4 0.751 162s 15 103.8 0.793 99.5 108.2 102.7 0.863 162s 16 103.7 0.636 99.5 107.9 104.4 0.902 162s 17 103.8 1.348 99.0 108.7 103.3 1.636 162s 18 102.1 0.549 97.9 106.2 103.6 0.807 162s 19 103.6 0.695 99.4 107.9 103.6 0.898 162s 20 106.9 1.306 102.1 111.7 106.6 1.613 162s supply.lwr supply.upr 162s 1 92.3 103 162s 2 93.8 105 162s 3 94.0 105 162s 4 94.3 105 162s 5 96.2 107 162s 6 96.3 107 162s 7 96.5 107 162s 8 98.5 110 162s 9 96.8 108 162s 10 93.9 105 162s 11 90.1 102 162s 12 88.9 101 162s 13 90.9 102 162s 14 92.9 104 162s 15 97.1 108 162s 16 98.8 110 162s 17 97.1 110 162s 18 98.1 109 162s 19 98.0 109 162s 20 100.4 113 162s > print( predict( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 162s + useDfSys = TRUE ) ) 162s fit se.fit lwr upr 162s 1 97.6 0.661 93.4 101.9 162s 2 99.9 0.600 95.7 104.1 162s 3 99.8 0.564 95.6 104.0 162s 4 100.0 0.605 95.8 104.2 162s 5 102.1 0.516 98.0 106.2 162s 6 102.0 0.474 97.9 106.1 162s 7 102.4 0.493 98.3 106.5 162s 8 103.0 0.615 98.8 107.2 162s 9 101.5 0.544 97.3 105.6 162s 10 100.3 0.822 96.0 104.7 162s 11 95.5 0.963 91.1 100.0 162s 12 94.7 1.006 90.2 99.2 162s 13 96.1 0.915 91.7 100.5 162s 14 99.0 0.518 94.9 103.2 162s 15 103.8 0.793 99.5 108.2 162s 16 103.7 0.636 99.5 107.9 162s 17 103.8 1.348 99.0 108.7 162s 18 102.1 0.549 97.9 106.2 162s 19 103.6 0.695 99.4 107.9 162s 20 106.9 1.306 102.1 111.7 162s > 162s > print( predict( fit3sls[[ 3 ]]$e2e, se.pred = TRUE, interval = "confidence", 162s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 162s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 162s 1 102.7 2.20 99.3 106 96.2 2.78 162s 2 105.2 2.21 101.8 109 97.5 2.68 162s 3 105.1 2.22 101.6 109 97.7 2.69 162s 4 105.4 2.21 101.9 109 98.0 2.67 162s 5 107.2 2.47 101.9 112 99.6 2.80 162s 6 107.1 2.43 102.1 112 99.7 2.76 162s 7 107.7 2.42 102.8 113 99.7 2.72 162s 8 108.5 2.38 103.7 113 101.6 2.66 162s 9 106.5 2.48 101.2 112 100.1 2.85 162s 10 105.0 2.59 99.1 111 97.6 3.04 162s 11 100.1 2.36 95.5 105 94.2 3.07 162s 12 99.5 2.19 96.3 103 93.0 3.00 162s 13 101.2 2.11 98.7 104 94.6 2.85 162s 14 104.0 2.29 100.0 108 96.3 2.84 162s 15 108.9 2.68 102.4 115 100.2 2.90 162s 16 108.8 2.57 103.0 115 101.8 2.81 162s 17 108.4 2.99 100.4 116 100.8 3.28 162s 18 107.5 2.34 103.1 112 100.9 2.66 162s 19 109.2 2.42 104.3 114 100.8 2.64 162s 20 113.0 2.63 106.8 119 103.4 2.62 162s supply.lwr supply.upr 162s 1 92.2 100.2 162s 2 94.6 100.5 162s 3 94.6 100.7 162s 4 95.1 100.8 162s 5 95.4 103.8 162s 6 95.8 103.5 162s 7 96.3 103.1 162s 8 98.9 104.4 162s 9 95.4 104.7 162s 10 91.6 103.6 162s 11 88.0 100.4 162s 12 87.3 98.7 162s 13 90.1 99.2 162s 14 91.8 100.8 162s 15 95.3 105.2 162s 16 97.5 106.0 162s 17 93.4 108.3 162s 18 98.1 103.6 162s 19 98.4 103.2 162s 20 101.2 105.6 162s > print( predict( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 162s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 162s fit se.pred lwr upr 162s 1 96.2 2.78 92.2 100.2 162s 2 97.5 2.68 94.6 100.5 162s 3 97.7 2.69 94.6 100.7 162s 4 98.0 2.67 95.1 100.8 162s 5 99.6 2.80 95.4 103.8 162s 6 99.7 2.76 95.8 103.5 162s 7 99.7 2.72 96.3 103.1 162s 8 101.6 2.66 98.9 104.4 162s 9 100.1 2.85 95.4 104.7 162s 10 97.6 3.04 91.6 103.6 162s 11 94.2 3.07 88.0 100.4 162s 12 93.0 3.00 87.3 98.7 162s 13 94.6 2.85 90.1 99.2 162s 14 96.3 2.84 91.8 100.8 162s 15 100.2 2.90 95.3 105.2 162s 16 101.8 2.81 97.5 106.0 162s 17 100.8 3.28 93.4 108.3 162s 18 100.9 2.66 98.1 103.6 162s 19 100.8 2.64 98.4 103.2 162s 20 103.4 2.62 101.2 105.6 162s > 162s > print( predict( fit3sls[[ 5 ]]$e2w, se.pred = TRUE, interval = "confidence", 162s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 162s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 162s 1 102.6 2.24 99.0 106 96.3 2.84 162s 2 105.1 2.24 101.5 109 97.6 2.72 162s 3 105.0 2.25 101.3 109 97.7 2.73 162s 4 105.3 2.24 101.6 109 98.0 2.71 162s 5 107.1 2.54 101.5 113 99.6 2.88 162s 6 107.0 2.49 101.7 112 99.6 2.82 162s 7 107.6 2.48 102.3 113 99.7 2.77 162s 8 108.3 2.44 103.3 113 101.6 2.70 162s 9 106.4 2.55 100.7 112 100.0 2.94 162s 10 104.9 2.67 98.5 111 97.6 3.17 162s 11 100.1 2.43 95.1 105 94.3 3.20 162s 12 99.5 2.23 96.0 103 93.2 3.11 162s 13 101.2 2.14 98.5 104 94.8 2.92 162s 14 104.0 2.33 99.6 108 96.4 2.92 162s 15 108.7 2.77 101.8 116 100.2 2.99 162s 16 108.7 2.65 102.5 115 101.7 2.88 162s 17 108.3 3.12 99.7 117 100.8 3.45 162s 18 107.4 2.39 102.7 112 100.9 2.70 162s 19 109.1 2.48 103.8 114 100.8 2.67 162s 20 112.9 2.71 106.3 119 103.4 2.65 162s supply.lwr supply.upr 162s 1 91.8 100.7 162s 2 94.3 100.8 162s 3 94.3 101.1 162s 4 94.8 101.1 162s 5 94.9 104.3 162s 6 95.4 103.9 162s 7 95.9 103.5 162s 8 98.5 104.7 162s 9 94.9 105.2 162s 10 90.9 104.4 162s 11 87.4 101.2 162s 12 86.9 99.5 162s 13 89.7 99.8 162s 14 91.4 101.4 162s 15 94.7 105.8 162s 16 97.0 106.5 162s 17 92.5 109.1 162s 18 97.8 103.9 162s 19 98.1 103.5 162s 20 101.0 105.9 162s > print( predict( fit3sls[[ 5 ]]$e2w$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 162s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 162s fit se.pred lwr upr 162s 1 96.3 2.84 91.8 100.7 162s 2 97.6 2.72 94.3 100.8 162s 3 97.7 2.73 94.3 101.1 162s 4 98.0 2.71 94.8 101.1 162s 5 99.6 2.88 94.9 104.3 162s 6 99.6 2.82 95.4 103.9 162s 7 99.7 2.77 95.9 103.5 162s 8 101.6 2.70 98.5 104.7 162s 9 100.0 2.94 94.9 105.2 162s 10 97.6 3.17 90.9 104.4 162s 11 94.3 3.20 87.4 101.2 162s 12 93.2 3.11 86.9 99.5 162s 13 94.8 2.92 89.7 99.8 162s 14 96.4 2.92 91.4 101.4 162s 15 100.2 2.99 94.7 105.8 162s 16 101.7 2.88 97.0 106.5 162s 17 100.8 3.45 92.5 109.1 162s 18 100.9 2.70 97.8 103.9 162s 19 100.8 2.67 98.1 103.5 162s 20 103.4 2.65 101.0 105.9 162s > 162s > print( predict( fit3sls[[ 4 ]]$e3, se.pred = TRUE, interval = "prediction", 162s + level = 0.975 ) ) 162s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 162s 1 97.8 2.10 92.9 103 98.4 2.64 162s 2 100.0 2.09 95.1 105 99.8 2.66 162s 3 99.9 2.08 95.0 105 99.9 2.65 162s 4 100.1 2.09 95.2 105 100.3 2.66 162s 5 102.0 2.06 97.2 107 101.7 2.65 162s 6 101.9 2.05 97.1 107 101.8 2.63 162s 7 102.3 2.06 97.5 107 101.9 2.63 162s 8 102.9 2.09 98.0 108 103.9 2.71 162s 9 101.4 2.07 96.6 106 102.2 2.67 162s 10 100.3 2.16 95.2 105 99.6 2.76 162s 11 95.8 2.21 90.6 101 96.3 2.80 162s 12 95.1 2.22 89.9 100 95.3 2.84 162s 13 96.4 2.19 91.3 102 97.0 2.78 162s 14 99.1 2.06 94.3 104 98.5 2.67 162s 15 103.6 2.15 98.6 109 102.3 2.68 162s 16 103.5 2.09 98.6 108 103.9 2.68 162s 17 103.6 2.41 97.9 109 102.7 3.00 162s 18 102.0 2.07 97.2 107 103.1 2.66 162s 19 103.5 2.12 98.6 108 103.2 2.69 162s 20 106.7 2.39 101.1 112 105.9 2.98 162s supply.lwr supply.upr 162s 1 92.2 105 162s 2 93.6 106 162s 3 93.7 106 162s 4 94.0 107 162s 5 95.5 108 162s 6 95.7 108 162s 7 95.8 108 162s 8 97.6 110 162s 9 95.9 108 162s 10 93.2 106 162s 11 89.7 103 162s 12 88.6 102 162s 13 90.5 103 162s 14 92.3 105 162s 15 96.0 109 162s 16 97.6 110 162s 17 95.7 110 162s 18 96.9 109 162s 19 96.9 109 162s 20 98.9 113 162s > print( predict( fit3sls[[ 4 ]]$e3$eq[[ 1 ]], se.pred = TRUE, interval = "prediction", 162s + level = 0.975 ) ) 162s fit se.pred lwr upr 162s 1 97.8 2.10 92.9 103 162s 2 100.0 2.09 95.1 105 162s 3 99.9 2.08 95.0 105 162s 4 100.1 2.09 95.2 105 162s 5 102.0 2.06 97.2 107 162s 6 101.9 2.05 97.1 107 162s 7 102.3 2.06 97.5 107 162s 8 102.9 2.09 98.0 108 162s 9 101.4 2.07 96.6 106 162s 10 100.3 2.16 95.2 105 162s 11 95.8 2.21 90.6 101 162s 12 95.1 2.22 89.9 100 162s 13 96.4 2.19 91.3 102 162s 14 99.1 2.06 94.3 104 162s 15 103.6 2.15 98.6 109 162s 16 103.5 2.09 98.6 108 162s 17 103.6 2.41 97.9 109 162s 18 102.0 2.07 97.2 107 162s 19 103.5 2.12 98.6 108 162s 20 106.7 2.39 101.1 112 162s > 162s > print( predict( fit3sls[[ 5 ]]$e4e, se.fit = TRUE, interval = "confidence", 162s + level = 0.25, useDfSys = TRUE ) ) 162s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 162s 1 95.0 0.465 94.8 95.1 96.3 0.536 162s 2 98.9 0.532 98.7 99.1 99.4 0.663 162s 3 98.8 0.497 98.6 99.0 99.5 0.613 162s 4 99.1 0.541 99.0 99.3 100.2 0.662 162s 5 103.2 0.450 103.0 103.3 102.9 0.593 162s 6 102.9 0.417 102.7 103.0 103.1 0.543 162s 7 103.6 0.420 103.5 103.8 103.4 0.524 162s 8 104.5 0.525 104.3 104.6 107.7 0.634 162s 9 102.1 0.494 101.9 102.2 103.4 0.660 162s 10 100.2 0.760 100.0 100.4 97.8 0.895 162s 11 91.5 0.660 91.3 91.7 90.8 0.736 162s 12 89.8 0.563 89.6 89.9 88.9 0.742 162s 13 92.2 0.597 92.0 92.4 92.6 0.806 162s 14 97.6 0.426 97.4 97.7 95.6 0.568 162s 15 106.4 0.619 106.2 106.6 103.4 0.721 162s 16 105.9 0.476 105.8 106.1 106.9 0.608 162s 17 106.7 1.159 106.3 107.1 103.6 1.414 162s 18 102.9 0.494 102.7 103.0 105.4 0.582 162s 19 105.6 0.574 105.4 105.8 105.5 0.676 162s 20 111.3 1.030 110.9 111.6 111.7 1.146 162s supply.lwr supply.upr 162s 1 96.1 96.4 162s 2 99.1 99.6 162s 3 99.3 99.7 162s 4 100.0 100.4 162s 5 102.7 103.1 162s 6 102.9 103.3 162s 7 103.2 103.5 162s 8 107.5 107.9 162s 9 103.2 103.7 162s 10 97.5 98.0 162s 11 90.5 91.0 162s 12 88.7 89.1 162s 13 92.4 92.9 162s 14 95.4 95.8 162s 15 103.1 103.6 162s 16 106.7 107.0 162s 17 103.1 104.0 162s 18 105.3 105.6 162s 19 105.3 105.8 162s 20 111.4 112.1 162s > print( predict( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 162s + level = 0.25, useDfSys = TRUE ) ) 162s fit se.fit lwr upr 162s 1 96.3 0.536 96.1 96.4 162s 2 99.4 0.663 99.1 99.6 162s 3 99.5 0.613 99.3 99.7 162s 4 100.2 0.662 100.0 100.4 162s 5 102.9 0.593 102.7 103.1 162s 6 103.1 0.543 102.9 103.3 162s 7 103.4 0.524 103.2 103.5 162s 8 107.7 0.634 107.5 107.9 162s 9 103.4 0.660 103.2 103.7 162s 10 97.8 0.895 97.5 98.0 162s 11 90.8 0.736 90.5 91.0 162s 12 88.9 0.742 88.7 89.1 162s 13 92.6 0.806 92.4 92.9 162s 14 95.6 0.568 95.4 95.8 162s 15 103.4 0.721 103.1 103.6 162s 16 106.9 0.608 106.7 107.0 162s 17 103.6 1.414 103.1 104.0 162s 18 105.4 0.582 105.3 105.6 162s 19 105.5 0.676 105.3 105.8 162s 20 111.7 1.146 111.4 112.1 162s > 162s > print( predict( fit3sls[[ 1 ]]$e5, se.fit = TRUE, se.pred = TRUE, 162s + interval = "prediction", level = 0.5, newdata = predictData ) ) 162s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 162s 1 102.8 0.957 2.19 101.3 104 95.7 162s 2 105.6 0.829 2.13 104.1 107 97.1 162s 3 105.5 0.869 2.15 104.0 107 97.3 162s 4 105.8 0.823 2.13 104.3 107 97.6 162s 5 107.8 1.308 2.36 106.2 109 99.4 162s 6 107.7 1.213 2.31 106.1 109 99.4 162s 7 108.3 1.145 2.28 106.7 110 99.5 162s 8 109.1 0.984 2.20 107.6 111 101.7 162s 9 107.0 1.372 2.40 105.3 109 99.8 162s 10 105.4 1.659 2.57 103.6 107 97.1 162s 11 100.1 1.365 2.39 98.4 102 93.3 162s 12 99.4 0.969 2.19 97.9 101 92.1 162s 13 101.3 0.752 2.11 99.8 103 93.9 162s 14 104.3 1.112 2.26 102.8 106 95.7 162s 15 109.6 1.580 2.52 107.9 111 100.0 162s 16 109.6 1.368 2.40 107.9 111 101.7 162s 17 109.1 2.136 2.90 107.1 111 100.5 162s 18 108.1 0.966 2.19 106.6 110 100.8 162s 19 109.9 0.980 2.20 108.4 111 100.7 162s 20 114.1 0.997 2.21 112.6 116 103.7 162s supply.se.fit supply.se.pred supply.lwr supply.upr 162s 1 0.959 2.74 93.8 97.5 162s 2 0.742 2.67 95.3 99.0 162s 3 0.791 2.69 95.4 99.1 162s 4 0.735 2.67 95.8 99.4 162s 5 1.280 2.87 97.4 101.3 162s 6 1.159 2.82 97.5 101.3 162s 7 1.031 2.77 97.6 101.4 162s 8 0.867 2.71 99.8 103.5 162s 9 1.416 2.93 97.8 101.8 162s 10 1.724 3.09 95.0 99.2 162s 11 1.457 2.95 91.3 95.4 162s 12 1.102 2.79 90.2 94.0 162s 13 0.894 2.72 92.1 95.8 162s 14 1.092 2.79 93.8 97.6 162s 15 1.516 2.98 98.0 102.0 162s 16 1.321 2.89 99.7 103.7 162s 17 2.297 3.44 98.2 102.9 162s 18 0.847 2.70 98.9 102.6 162s 19 0.743 2.67 98.9 102.6 162s 20 0.589 2.63 101.9 105.5 162s > print( predict( fit3sls[[ 1 ]]$e5$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 162s + interval = "prediction", level = 0.5, newdata = predictData ) ) 162s fit se.fit se.pred lwr upr 162s 1 102.8 0.957 2.19 101.3 104 162s 2 105.6 0.829 2.13 104.1 107 162s 3 105.5 0.869 2.15 104.0 107 162s 4 105.8 0.823 2.13 104.3 107 162s 5 107.8 1.308 2.36 106.2 109 162s 6 107.7 1.213 2.31 106.1 109 162s 7 108.3 1.145 2.28 106.7 110 162s 8 109.1 0.984 2.20 107.6 111 162s 9 107.0 1.372 2.40 105.3 109 162s 10 105.4 1.659 2.57 103.6 107 162s 11 100.1 1.365 2.39 98.4 102 162s 12 99.4 0.969 2.19 97.9 101 162s 13 101.3 0.752 2.11 99.8 103 162s 14 104.3 1.112 2.26 102.8 106 162s 15 109.6 1.580 2.52 107.9 111 162s 16 109.6 1.368 2.40 107.9 111 162s 17 109.1 2.136 2.90 107.1 111 162s 18 108.1 0.966 2.19 106.6 110 162s 19 109.9 0.980 2.20 108.4 111 162s 20 114.1 0.997 2.21 112.6 116 162s > 162s > print( predict( fit3slsi[[ 3 ]]$e3e, se.fit = TRUE, se.pred = TRUE, 162s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 162s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 162s 1 98.9 0.590 2.49 97.3 100.5 99.2 162s 2 100.5 0.643 2.50 98.7 102.2 100.3 162s 3 100.4 0.602 2.49 98.7 102.0 100.4 162s 4 100.6 0.653 2.50 98.8 102.3 100.6 162s 5 101.6 0.548 2.48 100.1 103.1 101.2 162s 6 101.5 0.512 2.47 100.1 102.9 101.3 162s 7 101.9 0.524 2.47 100.5 103.3 101.5 162s 8 102.4 0.667 2.51 100.6 104.3 102.9 162s 9 101.1 0.599 2.49 99.5 102.7 101.4 162s 10 100.1 0.928 2.59 97.6 102.6 99.7 162s 11 97.2 0.898 2.58 94.7 99.6 97.8 162s 12 96.9 0.767 2.54 94.8 99.0 97.5 162s 13 98.0 0.745 2.53 96.0 100.1 98.7 162s 14 99.7 0.536 2.48 98.2 101.1 99.5 162s 15 102.5 0.745 2.53 100.5 104.5 101.6 162s 16 102.6 0.589 2.49 101.0 104.2 102.7 162s 17 102.1 1.376 2.78 98.3 105.8 101.4 162s 18 101.8 0.615 2.49 100.2 103.5 102.6 162s 19 102.9 0.738 2.53 100.9 104.9 102.7 162s 20 105.3 1.357 2.77 101.6 109.0 104.8 162s supply.se.fit supply.se.pred supply.lwr supply.upr 162s 1 0.638 3.01 97.5 101.0 162s 2 0.752 3.03 98.3 102.4 162s 3 0.700 3.02 98.4 102.3 162s 4 0.761 3.03 98.6 102.7 162s 5 0.649 3.01 99.4 103.0 162s 6 0.610 3.00 99.7 103.0 162s 7 0.613 3.00 99.8 103.2 162s 8 0.829 3.05 100.7 105.2 162s 9 0.731 3.03 99.4 103.4 162s 10 1.092 3.13 96.7 102.6 162s 11 1.037 3.12 94.9 100.6 162s 12 0.902 3.07 95.0 99.9 162s 13 0.855 3.06 96.4 101.1 162s 14 0.670 3.01 97.6 101.3 162s 15 0.812 3.05 99.4 103.8 162s 16 0.707 3.02 100.8 104.7 162s 17 1.584 3.34 97.1 105.7 162s 18 0.740 3.03 100.6 104.6 162s 19 0.852 3.06 100.4 105.1 162s 20 1.564 3.33 100.6 109.1 162s > print( predict( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 162s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 162s fit se.fit se.pred lwr upr 162s 1 98.9 0.590 2.49 97.3 100.5 162s 2 100.5 0.643 2.50 98.7 102.2 162s 3 100.4 0.602 2.49 98.7 102.0 162s 4 100.6 0.653 2.50 98.8 102.3 162s 5 101.6 0.548 2.48 100.1 103.1 162s 6 101.5 0.512 2.47 100.1 102.9 162s 7 101.9 0.524 2.47 100.5 103.3 162s 8 102.4 0.667 2.51 100.6 104.3 162s 9 101.1 0.599 2.49 99.5 102.7 162s 10 100.1 0.928 2.59 97.6 102.6 162s 11 97.2 0.898 2.58 94.7 99.6 162s 12 96.9 0.767 2.54 94.8 99.0 162s 13 98.0 0.745 2.53 96.0 100.1 162s 14 99.7 0.536 2.48 98.2 101.1 162s 15 102.5 0.745 2.53 100.5 104.5 162s 16 102.6 0.589 2.49 101.0 104.2 162s 17 102.1 1.376 2.78 98.3 105.8 162s 18 101.8 0.615 2.49 100.2 103.5 162s 19 102.9 0.738 2.53 100.9 104.9 162s 20 105.3 1.357 2.77 101.6 109.0 162s > 162s > print( predict( fit3slsi[[ 1 ]]$e5w, se.fit = TRUE, se.pred = TRUE, 162s + interval = "prediction", level = 0.5, newdata = predictData ) ) 162s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 162s 1 102.4 0.986 2.25 100.9 104 95.3 162s 2 105.2 0.851 2.20 103.7 107 96.9 162s 3 105.1 0.896 2.22 103.6 107 97.0 162s 4 105.4 0.844 2.20 103.9 107 97.4 162s 5 107.1 1.351 2.44 105.5 109 98.7 162s 6 107.1 1.250 2.38 105.5 109 98.9 162s 7 107.8 1.173 2.34 106.2 109 99.0 162s 8 108.7 0.983 2.25 107.2 110 101.3 162s 9 106.3 1.420 2.48 104.6 108 99.1 162s 10 104.6 1.713 2.65 102.8 106 96.2 162s 11 99.4 1.372 2.45 97.8 101 92.8 162s 12 99.0 0.965 2.25 97.5 101 91.9 162s 13 101.0 0.768 2.17 99.5 102 93.8 162s 14 103.8 1.149 2.33 102.2 105 95.3 162s 15 108.8 1.631 2.60 107.0 111 99.2 162s 16 108.9 1.405 2.47 107.2 111 101.1 162s 17 108.0 2.211 3.00 106.0 110 99.4 162s 18 107.7 0.978 2.25 106.1 109 100.4 162s 19 109.5 0.964 2.25 108.0 111 100.5 162s 20 113.8 0.818 2.19 112.3 115 103.7 162s supply.se.fit supply.se.pred supply.lwr supply.upr 162s 1 0.987 2.85 93.3 97.2 162s 2 0.772 2.79 95.0 98.8 162s 3 0.824 2.80 95.1 98.9 162s 4 0.767 2.79 95.5 99.3 162s 5 1.341 3.00 96.7 100.8 162s 6 1.215 2.94 96.9 100.9 162s 7 1.084 2.89 97.1 101.0 162s 8 0.907 2.83 99.4 103.2 162s 9 1.483 3.06 97.0 101.2 162s 10 1.795 3.22 94.1 98.4 162s 11 1.455 3.05 90.7 94.8 162s 12 1.002 2.86 90.0 93.9 162s 13 0.805 2.80 91.9 95.7 162s 14 1.087 2.89 93.4 97.3 162s 15 1.585 3.11 97.1 101.4 162s 16 1.383 3.01 99.0 103.1 162s 17 2.399 3.60 96.9 101.8 162s 18 0.883 2.82 98.5 102.4 162s 19 0.770 2.79 98.6 102.4 162s 20 0.616 2.75 101.9 105.6 162s > print( predict( fit3slsi[[ 1 ]]$e5w$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 162s + interval = "prediction", level = 0.5, newdata = predictData ) ) 162s fit se.fit se.pred lwr upr 162s 1 102.4 0.986 2.25 100.9 104 162s 2 105.2 0.851 2.20 103.7 107 162s 3 105.1 0.896 2.22 103.6 107 162s 4 105.4 0.844 2.20 103.9 107 162s 5 107.1 1.351 2.44 105.5 109 162s 6 107.1 1.250 2.38 105.5 109 162s 7 107.8 1.173 2.34 106.2 109 162s 8 108.7 0.983 2.25 107.2 110 162s 9 106.3 1.420 2.48 104.6 108 162s 10 104.6 1.713 2.65 102.8 106 162s 11 99.4 1.372 2.45 97.8 101 162s 12 99.0 0.965 2.25 97.5 101 162s 13 101.0 0.768 2.17 99.5 102 162s 14 103.8 1.149 2.33 102.2 105 162s 15 108.8 1.631 2.60 107.0 111 162s 16 108.9 1.405 2.47 107.2 111 162s 17 108.0 2.211 3.00 106.0 110 162s 18 107.7 0.978 2.25 106.1 109 162s 19 109.5 0.964 2.25 108.0 111 162s 20 113.8 0.818 2.19 112.3 115 162s > 162s > print( predict( fit3slsd[[ 4 ]]$e4, se.fit = TRUE, interval = "prediction", 162s + level = 0.9, newdata = predictData ) ) 162s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 162s 1 103 0.972 99.6 107 96.1 0.980 162s 2 106 0.820 102.2 109 97.5 0.751 162s 3 106 0.863 102.1 109 97.6 0.801 162s 4 106 0.813 102.4 109 97.9 0.741 162s 5 108 1.305 104.2 112 99.8 1.287 162s 6 108 1.206 104.1 112 99.8 1.164 162s 7 109 1.132 104.7 112 99.9 1.035 162s 8 109 0.960 105.5 113 101.8 0.857 162s 9 107 1.377 103.4 111 100.3 1.422 162s 10 106 1.688 101.8 110 97.8 1.748 162s 11 101 1.415 96.8 105 94.1 1.490 162s 12 100 1.004 96.3 104 92.7 1.115 162s 13 102 0.766 98.1 105 94.4 0.891 162s 14 105 1.124 101.0 109 96.2 1.107 162s 15 110 1.575 105.8 114 100.5 1.523 162s 16 110 1.355 105.9 114 102.1 1.318 162s 17 110 2.158 105.0 115 101.3 2.305 162s 18 108 0.947 104.5 112 101.0 0.843 162s 19 110 0.953 106.3 114 100.9 0.735 162s 20 114 0.974 109.9 117 103.5 0.583 162s supply.lwr supply.upr 162s 1 91.6 100.7 162s 2 93.0 101.9 162s 3 93.2 102.1 162s 4 93.5 102.3 162s 5 95.0 104.6 162s 6 95.2 104.5 162s 7 95.3 104.5 162s 8 97.3 106.3 162s 9 95.4 105.2 162s 10 92.6 103.0 162s 11 89.2 99.0 162s 12 88.1 97.4 162s 13 89.8 98.9 162s 14 91.6 100.9 162s 15 95.5 105.5 162s 16 97.3 106.9 162s 17 95.6 107.1 162s 18 96.5 105.5 162s 19 96.5 105.3 162s 20 99.2 107.9 162s > print( predict( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 162s + level = 0.9, newdata = predictData ) ) 162s fit se.fit lwr upr 162s 1 96.1 0.980 91.6 100.7 162s 2 97.5 0.751 93.0 101.9 162s 3 97.6 0.801 93.2 102.1 162s 4 97.9 0.741 93.5 102.3 162s 5 99.8 1.287 95.0 104.6 162s 6 99.8 1.164 95.2 104.5 162s 7 99.9 1.035 95.3 104.5 162s 8 101.8 0.857 97.3 106.3 162s 9 100.3 1.422 95.4 105.2 162s 10 97.8 1.748 92.6 103.0 162s 11 94.1 1.490 89.2 99.0 162s 12 92.7 1.115 88.1 97.4 162s 13 94.4 0.891 89.8 98.9 162s 14 96.2 1.107 91.6 100.9 162s 15 100.5 1.523 95.5 105.5 162s 16 102.1 1.318 97.3 106.9 162s 17 101.3 2.305 95.6 107.1 162s 18 101.0 0.843 96.5 105.5 162s 19 100.9 0.735 96.5 105.3 162s 20 103.5 0.583 99.2 107.9 162s > 162s > print( predict( fit3slsd[[ 2 ]]$e3w, se.fit = TRUE, se.pred = TRUE, 162s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 162s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 162s 1 96.1 0.832 3.23 93.8 98.3 97.0 162s 2 97.6 0.849 3.24 95.3 99.9 97.2 162s 3 97.8 0.771 3.22 95.7 99.9 97.8 162s 4 97.7 0.857 3.24 95.3 100.0 97.7 162s 5 103.5 0.648 3.19 101.8 105.3 103.5 162s 6 102.7 0.519 3.16 101.3 104.1 102.8 162s 7 102.6 0.499 3.16 101.3 104.0 102.1 162s 8 101.8 0.627 3.18 100.1 103.5 103.4 162s 9 103.3 0.714 3.20 101.3 105.2 104.8 162s 10 103.9 1.172 3.33 100.7 107.1 103.4 162s 11 96.2 0.920 3.25 93.7 98.7 97.0 162s 12 92.5 1.261 3.37 89.1 95.9 92.4 162s 13 92.7 1.364 3.41 89.0 96.5 93.0 162s 14 98.8 0.528 3.17 97.3 100.2 97.6 162s 15 107.3 1.245 3.36 103.9 110.7 105.6 162s 16 105.6 0.856 3.24 103.2 107.9 106.4 162s 17 111.1 2.310 3.88 104.8 117.4 110.7 162s 18 100.9 0.592 3.18 99.2 102.5 102.3 162s 19 102.3 0.700 3.20 100.4 104.2 101.4 162s 20 103.7 1.350 3.40 100.0 107.4 101.8 162s supply.se.fit supply.se.pred supply.lwr supply.upr 162s 1 0.791 3.73 94.8 99.2 162s 2 0.857 3.74 94.8 99.5 162s 3 0.776 3.72 95.7 99.9 162s 4 0.825 3.73 95.5 100.0 162s 5 0.817 3.73 101.2 105.7 162s 6 0.713 3.71 100.9 104.8 162s 7 0.644 3.70 100.4 103.9 162s 8 0.858 3.74 101.0 105.7 162s 9 0.962 3.77 102.2 107.4 162s 10 1.040 3.79 100.6 106.3 162s 11 1.083 3.80 94.1 100.0 162s 12 1.633 3.99 88.0 96.9 162s 13 1.568 3.96 88.7 97.3 162s 14 0.871 3.74 95.2 100.0 162s 15 1.029 3.78 102.8 108.4 162s 16 1.056 3.79 103.6 109.3 162s 17 2.050 4.18 105.1 116.2 162s 18 0.687 3.71 100.4 104.2 162s 19 0.773 3.72 99.3 103.5 162s 20 1.300 3.87 98.3 105.4 162s > print( predict( fit3slsd[[ 2 ]]$e3w$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 162s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 162s fit se.fit se.pred lwr upr 162s 1 96.1 0.832 3.23 93.8 98.3 162s 2 97.6 0.849 3.24 95.3 99.9 162s 3 97.8 0.771 3.22 95.7 99.9 162s 4 97.7 0.857 3.24 95.3 100.0 162s 5 103.5 0.648 3.19 101.8 105.3 162s 6 102.7 0.519 3.16 101.3 104.1 162s 7 102.6 0.499 3.16 101.3 104.0 162s 8 101.8 0.627 3.18 100.1 103.5 162s 9 103.3 0.714 3.20 101.3 105.2 162s 10 103.9 1.172 3.33 100.7 107.1 162s 11 96.2 0.920 3.25 93.7 98.7 162s 12 92.5 1.261 3.37 89.1 95.9 162s 13 92.7 1.364 3.41 89.0 96.5 162s 14 98.8 0.528 3.17 97.3 100.2 162s 15 107.3 1.245 3.36 103.9 110.7 162s 16 105.6 0.856 3.24 103.2 107.9 162s 17 111.1 2.310 3.88 104.8 117.4 162s 18 100.9 0.592 3.18 99.2 102.5 162s 19 102.3 0.700 3.20 100.4 104.2 162s 20 103.7 1.350 3.40 100.0 107.4 162s > 162s > 162s > # predict just one observation 162s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 162s + trend = 25 ) 162s > 162s > print( predict( fit3sls[[ 3 ]]$e1c, newdata = smallData ) ) 162s demand.pred supply.pred 162s 1 110 118 162s > print( predict( fit3sls[[ 3 ]]$e1c$eq[[ 1 ]], newdata = smallData ) ) 162s fit 162s 1 110 162s > 162s > print( predict( fit3sls[[ 4 ]]$e2e, se.fit = TRUE, level = 0.9, 162s + newdata = smallData ) ) 162s demand.pred demand.se.fit supply.pred supply.se.fit 162s 1 110 2.34 117 3.29 162s > print( predict( fit3sls[[ 5 ]]$e2e$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 162s + newdata = smallData ) ) 162s fit se.pred 162s 1 110 3.07 162s > 162s > print( predict( fit3sls[[ 1]]$e3, interval = "prediction", level = 0.975, 162s + newdata = smallData ) ) 162s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 162s 1 110 102 117 117 106 127 162s > print( predict( fit3sls[[ 1 ]]$e3$eq[[ 1 ]], interval = "confidence", level = 0.8, 162s + newdata = smallData ) ) 162s fit lwr upr 162s 1 110 106 113 162s > 162s > print( predict( fit3sls[[ 4]]$e3we, interval = "prediction", level = 0.975, 162s + newdata = smallData ) ) 162s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 162s 1 110 103 117 117 107 126 162s > print( predict( fit3sls[[ 4 ]]$e3we$eq[[ 1 ]], interval = "confidence", level = 0.8, 162s + newdata = smallData ) ) 162s fit lwr upr 162s 1 110 107 113 162s > 162s > print( predict( fit3sls[[ 2 ]]$e4e, se.fit = TRUE, interval = "confidence", 162s + level = 0.999, newdata = smallData ) ) 162s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 162s 1 110 2.14 103 118 119 2.25 162s supply.lwr supply.upr 162s 1 110 127 162s > print( predict( fit3sls[[ 2 ]]$e4e$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 162s + level = 0.75, newdata = smallData ) ) 162s fit se.pred lwr upr 162s 1 119 3.41 115 123 162s > 162s > print( predict( fit3sls[[ 3 ]]$e5, se.fit = TRUE, interval = "prediction", 162s + newdata = smallData ) ) 162s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 162s 1 111 2.3 104 117 119 2.44 162s supply.lwr supply.upr 162s 1 111 126 162s > print( predict( fit3sls[[ 3 ]]$e5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 162s + newdata = smallData ) ) 162s fit se.pred lwr upr 162s 1 111 3.02 106 115 162s > 162s > print( predict( fit3slsi[[ 4 ]]$e3e, se.fit = TRUE, se.pred = TRUE, 162s + interval = "prediction", level = 0.5, newdata = smallData ) ) 162s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 162s 1 108 2.75 3.66 106 111 112 162s supply.se.fit supply.se.pred supply.lwr supply.upr 162s 1 3.46 4.54 109 115 162s > print( predict( fit3slsd[[ 5 ]]$e4$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 162s + interval = "confidence", level = 0.25, newdata = smallData ) ) 162s fit se.fit se.pred lwr upr 162s 1 111 1.85 3.42 111 112 162s > 162s > print( predict( fit3slsd[[ 2 ]]$e2we, se.fit = TRUE, se.pred = TRUE, 162s + interval = "prediction", level = 0.5, newdata = smallData ) ) 162s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 162s 1 101 2.76 4.1 98.7 104 111 162s supply.se.fit supply.se.pred supply.lwr supply.upr 162s 1 2.79 4.47 108 114 162s > print( predict( fit3slsi[[ 3 ]]$e4we$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 162s + interval = "confidence", level = 0.25, newdata = smallData ) ) 162s fit se.fit se.pred lwr upr 162s 1 111 2.03 2.86 111 112 162s > 162s > 162s > ## ************ correlation of predicted values *************** 162s > print( correlation.systemfit( fit3sls[[ 1 ]]$e1c, 2, 1 ) ) 162s [,1] 162s [1,] 0.880 162s [2,] 0.881 162s [3,] 0.886 162s [4,] 0.901 162s [5,] 0.866 162s [6,] 0.881 162s [7,] 0.892 162s [8,] 0.887 162s [9,] 0.901 162s [10,] 0.924 162s [11,] 0.925 162s [12,] 0.916 162s [13,] 0.910 162s [14,] 0.885 162s [15,] 0.909 162s [16,] 0.921 162s [17,] 0.928 162s [18,] 0.845 162s [19,] 0.890 162s [20,] 0.920 162s > 162s > print( correlation.systemfit( fit3sls[[ 2 ]]$e2e, 1, 2 ) ) 162s [,1] 162s [1,] 0.935 162s [2,] 0.927 162s [3,] 0.923 162s [4,] 0.921 162s [5,] 0.876 162s [6,] 0.884 162s [7,] 0.894 162s [8,] 0.875 162s [9,] 0.890 162s [10,] 0.917 162s [11,] 0.911 162s [12,] 0.898 162s [13,] 0.892 162s [14,] 0.871 162s [15,] 0.905 162s [16,] 0.945 162s [17,] 0.926 162s [18,] 0.908 162s [19,] 0.915 162s [20,] 0.926 162s > 162s > print( correlation.systemfit( fit3sls[[ 5 ]]$e2w, 2, 1 ) ) 162s [,1] 162s [1,] 0.932 162s [2,] 0.928 162s [3,] 0.925 162s [4,] 0.923 162s [5,] 0.882 162s [6,] 0.890 162s [7,] 0.899 162s [8,] 0.880 162s [9,] 0.895 162s [10,] 0.921 162s [11,] 0.914 162s [12,] 0.900 162s [13,] 0.895 162s [14,] 0.876 162s [15,] 0.905 162s [16,] 0.947 162s [17,] 0.928 162s [18,] 0.915 162s [19,] 0.916 162s [20,] 0.928 162s > 162s > print( correlation.systemfit( fit3sls[[ 3 ]]$e3, 2, 1 ) ) 162s [,1] 162s [1,] 0.931 162s [2,] 0.925 162s [3,] 0.922 162s [4,] 0.920 162s [5,] 0.877 162s [6,] 0.884 162s [7,] 0.894 162s [8,] 0.875 162s [9,] 0.890 162s [10,] 0.917 162s [11,] 0.910 162s [12,] 0.896 162s [13,] 0.891 162s [14,] 0.871 162s [15,] 0.903 162s [16,] 0.944 162s [17,] 0.925 162s [18,] 0.911 162s [19,] 0.913 162s [20,] 0.925 162s > 162s > print( correlation.systemfit( fit3sls[[ 4 ]]$e4e, 1, 2 ) ) 162s [,1] 162s [1,] 0.924 162s [2,] 0.933 162s [3,] 0.933 162s [4,] 0.938 162s [5,] 0.862 162s [6,] 0.868 162s [7,] 0.874 162s [8,] 0.879 162s [9,] 0.883 162s [10,] 0.943 162s [11,] 0.830 162s [12,] 0.744 162s [13,] 0.826 162s [14,] 0.834 162s [15,] 0.952 162s [16,] 0.918 162s [17,] 0.954 162s [18,] 0.930 162s [19,] 0.890 162s [20,] 0.893 162s > 162s > print( correlation.systemfit( fit3sls[[ 5 ]]$e5, 2, 1 ) ) 162s [,1] 162s [1,] 0.922 162s [2,] 0.935 162s [3,] 0.934 162s [4,] 0.939 162s [5,] 0.863 162s [6,] 0.868 162s [7,] 0.874 162s [8,] 0.876 162s [9,] 0.884 162s [10,] 0.942 162s [11,] 0.824 162s [12,] 0.747 162s [13,] 0.830 162s [14,] 0.833 162s [15,] 0.952 162s [16,] 0.919 162s [17,] 0.955 162s [18,] 0.928 162s [19,] 0.886 162s [20,] 0.888 162s > 162s > print( correlation.systemfit( fit3slsi[[ 2 ]]$e3e, 1, 2 ) ) 162s [,1] 162s [1,] 0.982 162s [2,] 0.994 162s [3,] 0.993 162s [4,] 0.992 162s [5,] 0.990 162s [6,] 0.990 162s [7,] 0.991 162s [8,] 0.978 162s [9,] 0.984 162s [10,] 0.992 162s [11,] 0.991 162s [12,] 0.985 162s [13,] 0.986 162s [14,] 0.980 162s [15,] 0.976 162s [16,] 0.994 162s [17,] 0.992 162s [18,] 0.987 162s [19,] 0.990 162s [20,] 0.991 162s > 162s > print( correlation.systemfit( fit3slsi[[ 4 ]]$e5w, 1, 2 ) ) 162s [,1] 162s [1,] 0.962 162s [2,] 0.975 162s [3,] 0.974 162s [4,] 0.976 162s [5,] 0.946 162s [6,] 0.948 162s [7,] 0.951 162s [8,] 0.944 162s [9,] 0.952 162s [10,] 0.976 162s [11,] 0.912 162s [12,] 0.871 162s [13,] 0.926 162s [14,] 0.927 162s [15,] 0.979 162s [16,] 0.968 162s [17,] 0.981 162s [18,] 0.970 162s [19,] 0.947 162s [20,] 0.943 162s > 162s > print( correlation.systemfit( fit3slsd[[ 3 ]]$e4, 2, 1 ) ) 162s [,1] 162s [1,] 0.932 162s [2,] 0.954 162s [3,] 0.952 162s [4,] 0.957 162s [5,] 0.892 162s [6,] 0.887 162s [7,] 0.887 162s [8,] 0.905 162s [9,] 0.914 162s [10,] 0.963 162s [11,] 0.860 162s [12,] 0.779 162s [13,] 0.878 162s [14,] 0.852 162s [15,] 0.968 162s [16,] 0.938 162s [17,] 0.973 162s [18,] 0.946 162s [19,] 0.913 162s [20,] 0.921 162s > 162s > 162s > ## ************ Log-Likelihood values *************** 162s > print( logLik( fit3sls[[ 1 ]]$e1c ) ) 162s 'log Lik.' -53 (df=10) 162s > print( logLik( fit3sls[[ 1 ]]$e1c, residCovDiag = TRUE ) ) 162s 'log Lik.' -85.6 (df=10) 162s > 162s > print( logLik( fit3sls[[ 2 ]]$e2e ) ) 162s 'log Lik.' -55.6 (df=9) 162s > print( logLik( fit3sls[[ 2 ]]$e2e, residCovDiag = TRUE ) ) 162s 'log Lik.' -85.4 (df=9) 162s > 162s > print( logLik( fit3sls[[ 3 ]]$e3 ) ) 162s 'log Lik.' -55.3 (df=9) 162s > print( logLik( fit3sls[[ 3 ]]$e3, residCovDiag = TRUE ) ) 162s 'log Lik.' -85.5 (df=9) 162s > 162s > print( logLik( fit3sls[[ 4 ]]$e4e ) ) 162s 'log Lik.' -58.5 (df=8) 162s > print( logLik( fit3sls[[ 4 ]]$e4e, residCovDiag = TRUE ) ) 162s 'log Lik.' -85.2 (df=8) 162s > 162s > print( logLik( fit3sls[[ 2 ]]$e4wSym ) ) 162s 'log Lik.' -58.5 (df=8) 162s > print( logLik( fit3sls[[ 2 ]]$e4wSym, residCovDiag = TRUE ) ) 162s 'log Lik.' -85.3 (df=8) 162s > 162s > print( logLik( fit3sls[[ 5 ]]$e5 ) ) 162s 'log Lik.' -87.3 (df=8) 162s > print( logLik( fit3sls[[ 5 ]]$e5, residCovDiag = TRUE ) ) 162s 'log Lik.' -104 (df=8) 162s > 162s > print( logLik( fit3slsi[[ 2 ]]$e3e ) ) 162s 'log Lik.' -46.7 (df=9) 162s > print( logLik( fit3slsi[[ 2 ]]$e3e, residCovDiag = TRUE ) ) 162s 'log Lik.' -92.1 (df=9) 162s > 162s > print( logLik( fit3slsi[[ 1 ]]$e1we ) ) 162s 'log Lik.' -52.7 (df=10) 162s > print( logLik( fit3slsi[[ 1 ]]$e1we, residCovDiag = TRUE ) ) 162s 'log Lik.' -85.8 (df=10) 162s > 162s > print( logLik( fit3slsd[[ 3 ]]$e4 ) ) 162s 'log Lik.' -59.4 (df=8) 162s > print( logLik( fit3slsd[[ 3 ]]$e4, residCovDiag = TRUE ) ) 162s 'log Lik.' -86.1 (df=8) 162s > 162s > print( logLik( fit3slsd[[ 5 ]]$e2we ) ) 162s 'log Lik.' -65 (df=9) 162s > print( logLik( fit3slsd[[ 5 ]]$e2we, residCovDiag = TRUE ) ) 162s 'log Lik.' -85.7 (df=9) 162s > 162s > 162s > ## ************** F tests **************** 162s > # testing first restriction 162s > print( linearHypothesis( fit3sls[[ 1 ]]$e1, restrm ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[1]]$e1 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 1.69 0.2 162s > linearHypothesis( fit3sls[[ 1 ]]$e1, restrict ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[1]]$e1 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 1.69 0.2 162s > 162s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restrm ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[2]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 1.52 0.23 162s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[2]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 1.52 0.23 162s > 162s > print( linearHypothesis( fit3sls[[ 3 ]]$e1c, restrm ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[3]]$e1c 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 2.47 0.13 162s > linearHypothesis( fit3sls[[ 3 ]]$e1c, restrict ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[3]]$e1c 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 2.47 0.13 162s > 162s > print( linearHypothesis( fit3slsi[[ 4 ]]$e1, restrm ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[4]]$e1 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 4.75 0.037 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > linearHypothesis( fit3slsi[[ 4 ]]$e1, restrict ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[4]]$e1 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 4.75 0.037 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrm ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[5]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.18 0.68 162s > linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrict ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[5]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.18 0.68 162s > 162s > print( linearHypothesis( fit3slsd[[ 2 ]]$e1w, restrm ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[2]]$e1w 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.51 0.48 162s > linearHypothesis( fit3slsd[[ 2 ]]$e1w, restrict ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[2]]$e1w 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.51 0.48 162s > 162s > # testing second restriction 162s > restrOnly2m <- matrix(0,1,7) 162s > restrOnly2q <- 0.5 162s > restrOnly2m[1,2] <- -1 162s > restrOnly2m[1,5] <- 1 162s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 162s > # first restriction not imposed 162s > print( linearHypothesis( fit3sls[[ 5 ]]$e1c, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[5]]$e1c 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.17 0.69 162s > linearHypothesis( fit3sls[[ 5 ]]$e1c, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[5]]$e1c 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.17 0.69 162s > 162s > print( linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[1]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.13 0.72 162s > linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[1]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.13 0.72 162s > 162s > print( linearHypothesis( fit3slsi[[ 3 ]]$e1we, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[3]]$e1we 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.13 0.72 162s > linearHypothesis( fit3slsi[[ 3 ]]$e1we, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[3]]$e1we 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.13 0.72 162s > 162s > print( linearHypothesis( fit3slsd[[ 2 ]]$e1, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[2]]$e1 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.25 0.62 162s > linearHypothesis( fit3slsd[[ 2 ]]$e1, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[2]]$e1 162s 162s Res.Df Df F Pr(>F) 162s 1 34 162s 2 33 1 0.25 0.62 162s > 162s > # first restriction imposed 162s > print( linearHypothesis( fit3sls[[ 4 ]]$e2, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[4]]$e2 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.81 0.38 162s > linearHypothesis( fit3sls[[ 4 ]]$e2, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[4]]$e2 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.81 0.38 162s > 162s > print( linearHypothesis( fit3sls[[ 4 ]]$e3, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[4]]$e3 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.81 0.38 162s > linearHypothesis( fit3sls[[ 4 ]]$e3, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[4]]$e3 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.81 0.38 162s > 162s > print( linearHypothesis( fit3sls[[ 1 ]]$e2w, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[1]]$e2w 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.9 0.35 162s > linearHypothesis( fit3sls[[ 1 ]]$e2w, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[1]]$e2w 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.9 0.35 162s > 162s > print( linearHypothesis( fit3sls[[ 1 ]]$e3we, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[1]]$e3we 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.75 0.39 162s > linearHypothesis( fit3sls[[ 1 ]]$e3we, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[1]]$e3we 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.75 0.39 162s > 162s > print( linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[5]]$e2e 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 15.1 0.00044 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[5]]$e2e 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 15.1 0.00044 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[5]]$e3e 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 15.1 0.00044 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[5]]$e3e 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 15.1 0.00044 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( linearHypothesis( fit3slsd[[ 1 ]]$e2, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[1]]$e2 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.16 0.69 162s > linearHypothesis( fit3slsd[[ 1 ]]$e2, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[1]]$e2 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.16 0.69 162s > 162s > print( linearHypothesis( fit3slsd[[ 1 ]]$e3, restrOnly2m, restrOnly2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[1]]$e3 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.16 0.69 162s > linearHypothesis( fit3slsd[[ 1 ]]$e3, restrictOnly2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[1]]$e3 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 34 1 0.16 0.69 162s > 162s > # testing both of the restrictions 162s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restr2m, restr2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[2]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 33 2 1 0.38 162s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[2]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 33 2 1 0.38 162s > 162s > print( linearHypothesis( fit3slsi[[ 3 ]]$e1, restr2m, restr2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[3]]$e1 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 33 2 5.59 0.0081 ** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > linearHypothesis( fit3slsi[[ 3 ]]$e1, restrict2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[3]]$e1 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 33 2 5.59 0.0081 ** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( linearHypothesis( fit3slsd[[ 4 ]]$e1e, restr2m, restr2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[4]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 33 2 0.64 0.53 162s > linearHypothesis( fit3slsd[[ 4 ]]$e1e, restrict2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[4]]$e1e 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 33 2 0.64 0.53 162s > 162s > print( linearHypothesis( fit3slsd[[ 5 ]]$e1w, restr2m, restr2q ) ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[5]]$e1w 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 33 2 0.45 0.64 162s > linearHypothesis( fit3slsd[[ 5 ]]$e1w, restrict2 ) 162s Linear hypothesis test (Theil's F test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[5]]$e1w 162s 162s Res.Df Df F Pr(>F) 162s 1 35 162s 2 33 2 0.45 0.64 162s > 162s > 162s > ## ************** Wald tests **************** 162s > # testing first restriction 162s > print( linearHypothesis( fit3sls[[ 1 ]]$e1, restrm, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[1]]$e1 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 1.11 0.29 162s > linearHypothesis( fit3sls[[ 1 ]]$e1, restrict, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[1]]$e1 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 1.11 0.29 162s > 162s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restrm, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[2]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 1.23 0.27 162s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[2]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 1.23 0.27 162s > 162s > print( linearHypothesis( fit3sls[[ 3 ]]$e1c, restrm, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[3]]$e1c 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 1.73 0.19 162s > linearHypothesis( fit3sls[[ 3 ]]$e1c, restrict, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[3]]$e1c 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 1.73 0.19 162s > 162s > print( linearHypothesis( fit3slsi[[ 4 ]]$e1, restrm, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[4]]$e1 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 4.81 0.028 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > linearHypothesis( fit3slsi[[ 4 ]]$e1, restrict, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[4]]$e1 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 4.81 0.028 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( linearHypothesis( fit3slsi[[ 2 ]]$e1we, restrm, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[2]]$e1we 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 5.72 0.017 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > linearHypothesis( fit3slsi[[ 2 ]]$e1we, restrict, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[2]]$e1we 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 5.72 0.017 * 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrm, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[5]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.15 0.7 162s > linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrict, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[5]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.15 0.7 162s > 162s > # testing second restriction 162s > # first restriction not imposed 162s > print( linearHypothesis( fit3sls[[ 5 ]]$e1c, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[5]]$e1c 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.12 0.73 162s > linearHypothesis( fit3sls[[ 5 ]]$e1c, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[5]]$e1c 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.12 0.73 162s > 162s > print( linearHypothesis( fit3sls[[ 3 ]]$e1wc, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[3]]$e1wc 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.12 0.73 162s > linearHypothesis( fit3sls[[ 3 ]]$e1wc, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[3]]$e1wc 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.12 0.73 162s > 162s > print( linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[1]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.16 0.69 162s > linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[1]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.16 0.69 162s > 162s > print( linearHypothesis( fit3slsd[[ 2 ]]$e1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[2]]$e1 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.17 0.68 162s > linearHypothesis( fit3slsd[[ 2 ]]$e1, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[2]]$e1 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 34 162s 2 33 1 0.17 0.68 162s > 162s > # first restriction imposed 162s > print( linearHypothesis( fit3sls[[ 4 ]]$e2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[4]]$e2 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.55 0.46 162s > linearHypothesis( fit3sls[[ 4 ]]$e2, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[4]]$e2 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.55 0.46 162s > 162s > print( linearHypothesis( fit3sls[[ 4 ]]$e3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[4]]$e3 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.55 0.46 162s > linearHypothesis( fit3sls[[ 4 ]]$e3, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[4]]$e3 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.55 0.46 162s > 162s > print( linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[5]]$e2e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 17.8 2.4e-05 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[5]]$e2e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 17.8 2.4e-05 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[5]]$e3e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 17.8 2.4e-05 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[5]]$e3e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 17.8 2.4e-05 *** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( linearHypothesis( fit3slsd[[ 1 ]]$e2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[1]]$e2 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.13 0.72 162s > linearHypothesis( fit3slsd[[ 1 ]]$e2, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[1]]$e2 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.13 0.72 162s > 162s > print( linearHypothesis( fit3slsd[[ 1 ]]$e3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[1]]$e3 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.13 0.72 162s > linearHypothesis( fit3slsd[[ 1 ]]$e3, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[1]]$e3 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.13 0.72 162s > 162s > print( linearHypothesis( fit3slsd[[ 2 ]]$e2we, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[2]]$e2we 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 1.52 0.22 162s > linearHypothesis( fit3slsd[[ 2 ]]$e2we, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[2]]$e2we 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 1.52 0.22 162s > 162s > print( linearHypothesis( fit3slsd[[ 3 ]]$e3w, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[3]]$e3w 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.23 0.63 162s > linearHypothesis( fit3slsd[[ 3 ]]$e3w, restrictOnly2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[3]]$e3w 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 34 1 0.23 0.63 162s > 162s > # testing both of the restrictions 162s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restr2m, restr2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[2]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 33 2 1.62 0.44 162s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[2]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 33 2 1.62 0.44 162s > 162s > print( linearHypothesis( fit3sls[[ 5 ]]$e1wc, restr2m, restr2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[5]]$e1wc 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 33 2 2.43 0.3 162s > linearHypothesis( fit3sls[[ 5 ]]$e1wc, restrict2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3sls[[5]]$e1wc 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 33 2 2.43 0.3 162s > 162s > print( linearHypothesis( fit3slsi[[ 3 ]]$e1, restr2m, restr2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[3]]$e1 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 33 2 11.3 0.0035 ** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > linearHypothesis( fit3slsi[[ 3 ]]$e1, restrict2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsi[[3]]$e1 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 33 2 11.3 0.0035 ** 162s --- 162s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 162s > 162s > print( linearHypothesis( fit3slsd[[ 4 ]]$e1e, restr2m, restr2q, test = "Chisq" ) ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[4]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 33 2 1.55 0.46 162s > linearHypothesis( fit3slsd[[ 4 ]]$e1e, restrict2, test = "Chisq" ) 162s Linear hypothesis test (Chi^2 statistic of a Wald test) 162s 162s Hypothesis: 162s demand_income - supply_trend = 0 162s - demand_price + supply_price = 0.5 162s 162s Model 1: restricted model 162s Model 2: fit3slsd[[4]]$e1e 162s 162s Res.Df Df Chisq Pr(>Chisq) 162s 1 35 162s 2 33 2 1.55 0.46 162s > 162s > 162s > ## *********** model frame ************* 162s > print( mf <- model.frame( fit3sls[[ 3 ]]$e1c ) ) 162s consump price income farmPrice trend 162s 1 98.5 100.3 87.4 98.0 1 162s 2 99.2 104.3 97.6 99.1 2 162s 3 102.2 103.4 96.7 99.1 3 162s 4 101.5 104.5 98.2 98.1 4 162s 5 104.2 98.0 99.8 110.8 5 162s 6 103.2 99.5 100.5 108.2 6 162s 7 104.0 101.1 103.2 105.6 7 162s 8 99.9 104.8 107.8 109.8 8 162s 9 100.3 96.4 96.6 108.7 9 162s 10 102.8 91.2 88.9 100.6 10 162s 11 95.4 93.1 75.1 81.0 11 162s 12 92.4 98.8 76.9 68.6 12 162s 13 94.5 102.9 84.6 70.9 13 162s 14 98.8 98.8 90.6 81.4 14 162s 15 105.8 95.1 103.1 102.3 15 162s 16 100.2 98.5 105.1 105.0 16 162s 17 103.5 86.5 96.4 110.5 17 162s 18 99.9 104.0 104.4 92.5 18 162s 19 105.2 105.8 110.7 89.3 19 162s 20 106.2 113.5 127.1 93.0 20 162s > print( mf1 <- model.frame( fit3sls[[ 3 ]]$e1c$eq[[ 1 ]] ) ) 162s consump price income 162s 1 98.5 100.3 87.4 162s 2 99.2 104.3 97.6 162s 3 102.2 103.4 96.7 162s 4 101.5 104.5 98.2 162s 5 104.2 98.0 99.8 162s 6 103.2 99.5 100.5 162s 7 104.0 101.1 103.2 162s 8 99.9 104.8 107.8 162s 9 100.3 96.4 96.6 162s 10 102.8 91.2 88.9 162s 11 95.4 93.1 75.1 162s 12 92.4 98.8 76.9 162s 13 94.5 102.9 84.6 162s 14 98.8 98.8 90.6 162s 15 105.8 95.1 103.1 162s 16 100.2 98.5 105.1 162s 17 103.5 86.5 96.4 162s 18 99.9 104.0 104.4 162s 19 105.2 105.8 110.7 162s 20 106.2 113.5 127.1 162s > print( attributes( mf1 )$terms ) 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s > print( mf2 <- model.frame( fit3sls[[ 3 ]]$e1c$eq[[ 2 ]] ) ) 162s consump price farmPrice trend 162s 1 98.5 100.3 98.0 1 162s 2 99.2 104.3 99.1 2 162s 3 102.2 103.4 99.1 3 162s 4 101.5 104.5 98.1 4 162s 5 104.2 98.0 110.8 5 162s 6 103.2 99.5 108.2 6 162s 7 104.0 101.1 105.6 7 162s 8 99.9 104.8 109.8 8 162s 9 100.3 96.4 108.7 9 162s 10 102.8 91.2 100.6 10 162s 11 95.4 93.1 81.0 11 162s 12 92.4 98.8 68.6 12 162s 13 94.5 102.9 70.9 13 162s 14 98.8 98.8 81.4 14 162s 15 105.8 95.1 102.3 15 162s 16 100.2 98.5 105.0 16 162s 17 103.5 86.5 110.5 17 162s 18 99.9 104.0 92.5 18 162s 19 105.2 105.8 89.3 19 162s 20 106.2 113.5 93.0 20 162s > print( attributes( mf2 )$terms ) 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s > 162s > print( all.equal( mf, model.frame( fit3sls[[ 3 ]]$e1wc ) ) ) 162s [1] TRUE 162s > print( all.equal( mf2, model.frame( fit3sls[[ 3 ]]$e1wc$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > print( all.equal( mf, model.frame( fit3sls[[ 4 ]]$e2e ) ) ) 162s [1] TRUE 162s > print( all.equal( mf2, model.frame( fit3sls[[ 4 ]]$e2e$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > print( all.equal( mf, model.frame( fit3sls[[ 5 ]]$e3 ) ) ) 162s [1] TRUE 162s > print( all.equal( mf1, model.frame( fit3sls[[ 5 ]]$e3$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > 162s > print( all.equal( mf, model.frame( fit3sls[[ 1 ]]$e4e ) ) ) 162s [1] TRUE 162s > print( all.equal( mf2, model.frame( fit3sls[[ 1 ]]$e4e$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > print( all.equal( mf, model.frame( fit3sls[[ 2 ]]$e5 ) ) ) 162s [1] TRUE 162s > print( all.equal( mf1, model.frame( fit3sls[[ 3 ]]$e5$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > 162s > print( all.equal( mf, model.frame( fit3slsi[[ 4 ]]$e3e ) ) ) 162s [1] TRUE 162s > print( all.equal( mf1, model.frame( fit3slsi[[ 4 ]]$e3e$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > 162s > print( all.equal( mf, model.frame( fit3slsd[[ 5 ]]$e4 ) ) ) 162s [1] TRUE 162s > print( all.equal( mf2, model.frame( fit3slsd[[ 5 ]]$e4$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > fit3sls[[ 3 ]]$e1c$eq[[ 1 ]]$modelInst 162s income farmPrice trend 162s 1 87.4 98.0 1 162s 2 97.6 99.1 2 162s 3 96.7 99.1 3 162s 4 98.2 98.1 4 162s 5 99.8 110.8 5 162s 6 100.5 108.2 6 162s 7 103.2 105.6 7 162s 8 107.8 109.8 8 162s 9 96.6 108.7 9 162s 10 88.9 100.6 10 162s 11 75.1 81.0 11 162s 12 76.9 68.6 12 162s 13 84.6 70.9 13 162s 14 90.6 81.4 14 162s 15 103.1 102.3 15 162s 16 105.1 105.0 16 162s 17 96.4 110.5 17 162s 18 104.4 92.5 18 162s 19 110.7 89.3 19 162s 20 127.1 93.0 20 162s > fit3sls[[ 3 ]]$e1c$eq[[ 2 ]]$modelInst 162s income farmPrice trend 162s 1 87.4 98.0 1 162s 2 97.6 99.1 2 162s 3 96.7 99.1 3 162s 4 98.2 98.1 4 162s 5 99.8 110.8 5 162s 6 100.5 108.2 6 162s 7 103.2 105.6 7 162s 8 107.8 109.8 8 162s 9 96.6 108.7 9 162s 10 88.9 100.6 10 162s 11 75.1 81.0 11 162s 12 76.9 68.6 12 162s 13 84.6 70.9 13 162s 14 90.6 81.4 14 162s 15 103.1 102.3 15 162s 16 105.1 105.0 16 162s 17 96.4 110.5 17 162s 18 104.4 92.5 18 162s 19 110.7 89.3 19 162s 20 127.1 93.0 20 162s > 162s > fit3sls[[ 1 ]]$e3$eq[[ 1 ]]$modelInst 162s income farmPrice trend 162s 1 87.4 98.0 1 162s 2 97.6 99.1 2 162s 3 96.7 99.1 3 162s 4 98.2 98.1 4 162s 5 99.8 110.8 5 162s 6 100.5 108.2 6 162s 7 103.2 105.6 7 162s 8 107.8 109.8 8 162s 9 96.6 108.7 9 162s 10 88.9 100.6 10 162s 11 75.1 81.0 11 162s 12 76.9 68.6 12 162s 13 84.6 70.9 13 162s 14 90.6 81.4 14 162s 15 103.1 102.3 15 162s 16 105.1 105.0 16 162s 17 96.4 110.5 17 162s 18 104.4 92.5 18 162s 19 110.7 89.3 19 162s 20 127.1 93.0 20 162s > fit3sls[[ 1 ]]$e3$eq[[ 2 ]]$modelInst 162s income farmPrice trend 162s 1 87.4 98.0 1 162s 2 97.6 99.1 2 162s 3 96.7 99.1 3 162s 4 98.2 98.1 4 162s 5 99.8 110.8 5 162s 6 100.5 108.2 6 162s 7 103.2 105.6 7 162s 8 107.8 109.8 8 162s 9 96.6 108.7 9 162s 10 88.9 100.6 10 162s 11 75.1 81.0 11 162s 12 76.9 68.6 12 162s 13 84.6 70.9 13 162s 14 90.6 81.4 14 162s 15 103.1 102.3 15 162s 16 105.1 105.0 16 162s 17 96.4 110.5 17 162s 18 104.4 92.5 18 162s 19 110.7 89.3 19 162s 20 127.1 93.0 20 162s > 162s > fit3slsd[[ 5 ]]$e4$eq[[ 1 ]]$modelInst 162s income farmPrice 162s 1 87.4 98.0 162s 2 97.6 99.1 162s 3 96.7 99.1 162s 4 98.2 98.1 162s 5 99.8 110.8 162s 6 100.5 108.2 162s 7 103.2 105.6 162s 8 107.8 109.8 162s 9 96.6 108.7 162s 10 88.9 100.6 162s 11 75.1 81.0 162s 12 76.9 68.6 162s 13 84.6 70.9 162s 14 90.6 81.4 162s 15 103.1 102.3 162s 16 105.1 105.0 162s 17 96.4 110.5 162s 18 104.4 92.5 162s 19 110.7 89.3 162s 20 127.1 93.0 162s > fit3slsd[[ 5 ]]$e4$eq[[ 2 ]]$modelInst 162s income farmPrice trend 162s 1 87.4 98.0 1 162s 2 97.6 99.1 2 162s 3 96.7 99.1 3 162s 4 98.2 98.1 4 162s 5 99.8 110.8 5 162s 6 100.5 108.2 6 162s 7 103.2 105.6 7 162s 8 107.8 109.8 8 162s 9 96.6 108.7 9 162s 10 88.9 100.6 10 162s 11 75.1 81.0 11 162s 12 76.9 68.6 12 162s 13 84.6 70.9 13 162s 14 90.6 81.4 14 162s 15 103.1 102.3 15 162s 16 105.1 105.0 16 162s 17 96.4 110.5 17 162s 18 104.4 92.5 18 162s 19 110.7 89.3 19 162s 20 127.1 93.0 20 162s > 162s > 162s > ## **************** model matrix ************************ 162s > # with x (returnModelMatrix) = TRUE 162s > print( !is.null( fit3sls[[ 4 ]]$e1c$eq[[ 1 ]]$x ) ) 162s [1] TRUE 162s > print( mm <- model.matrix( fit3sls[[ 4 ]]$e1c ) ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s demand_1 1 100.3 87.4 0 162s demand_2 1 104.3 97.6 0 162s demand_3 1 103.4 96.7 0 162s demand_4 1 104.5 98.2 0 162s demand_5 1 98.0 99.8 0 162s demand_6 1 99.5 100.5 0 162s demand_7 1 101.1 103.2 0 162s demand_8 1 104.8 107.8 0 162s demand_9 1 96.4 96.6 0 162s demand_10 1 91.2 88.9 0 162s demand_11 1 93.1 75.1 0 162s demand_12 1 98.8 76.9 0 162s demand_13 1 102.9 84.6 0 162s demand_14 1 98.8 90.6 0 162s demand_15 1 95.1 103.1 0 162s demand_16 1 98.5 105.1 0 162s demand_17 1 86.5 96.4 0 162s demand_18 1 104.0 104.4 0 162s demand_19 1 105.8 110.7 0 162s demand_20 1 113.5 127.1 0 162s supply_1 0 0.0 0.0 1 162s supply_2 0 0.0 0.0 1 162s supply_3 0 0.0 0.0 1 162s supply_4 0 0.0 0.0 1 162s supply_5 0 0.0 0.0 1 162s supply_6 0 0.0 0.0 1 162s supply_7 0 0.0 0.0 1 162s supply_8 0 0.0 0.0 1 162s supply_9 0 0.0 0.0 1 162s supply_10 0 0.0 0.0 1 162s supply_11 0 0.0 0.0 1 162s supply_12 0 0.0 0.0 1 162s supply_13 0 0.0 0.0 1 162s supply_14 0 0.0 0.0 1 162s supply_15 0 0.0 0.0 1 162s supply_16 0 0.0 0.0 1 162s supply_17 0 0.0 0.0 1 162s supply_18 0 0.0 0.0 1 162s supply_19 0 0.0 0.0 1 162s supply_20 0 0.0 0.0 1 162s supply_price supply_farmPrice supply_trend 162s demand_1 0.0 0.0 0 162s demand_2 0.0 0.0 0 162s demand_3 0.0 0.0 0 162s demand_4 0.0 0.0 0 162s demand_5 0.0 0.0 0 162s demand_6 0.0 0.0 0 162s demand_7 0.0 0.0 0 162s demand_8 0.0 0.0 0 162s demand_9 0.0 0.0 0 162s demand_10 0.0 0.0 0 162s demand_11 0.0 0.0 0 162s demand_12 0.0 0.0 0 162s demand_13 0.0 0.0 0 162s demand_14 0.0 0.0 0 162s demand_15 0.0 0.0 0 162s demand_16 0.0 0.0 0 162s demand_17 0.0 0.0 0 162s demand_18 0.0 0.0 0 162s demand_19 0.0 0.0 0 162s demand_20 0.0 0.0 0 162s supply_1 100.3 98.0 1 162s supply_2 104.3 99.1 2 162s supply_3 103.4 99.1 3 162s supply_4 104.5 98.1 4 162s supply_5 98.0 110.8 5 162s supply_6 99.5 108.2 6 162s supply_7 101.1 105.6 7 162s supply_8 104.8 109.8 8 162s supply_9 96.4 108.7 9 162s supply_10 91.2 100.6 10 162s supply_11 93.1 81.0 11 162s supply_12 98.8 68.6 12 162s supply_13 102.9 70.9 13 162s supply_14 98.8 81.4 14 162s supply_15 95.1 102.3 15 162s supply_16 98.5 105.0 16 162s supply_17 86.5 110.5 17 162s supply_18 104.0 92.5 18 162s supply_19 105.8 89.3 19 162s supply_20 113.5 93.0 20 162s > print( mm1 <- model.matrix( fit3sls[[ 4 ]]$e1c$eq[[ 1 ]] ) ) 162s (Intercept) price income 162s 1 1 100.3 87.4 162s 2 1 104.3 97.6 162s 3 1 103.4 96.7 162s 4 1 104.5 98.2 162s 5 1 98.0 99.8 162s 6 1 99.5 100.5 162s 7 1 101.1 103.2 162s 8 1 104.8 107.8 162s 9 1 96.4 96.6 162s 10 1 91.2 88.9 162s 11 1 93.1 75.1 162s 12 1 98.8 76.9 162s 13 1 102.9 84.6 162s 14 1 98.8 90.6 162s 15 1 95.1 103.1 162s 16 1 98.5 105.1 162s 17 1 86.5 96.4 162s 18 1 104.0 104.4 162s 19 1 105.8 110.7 162s 20 1 113.5 127.1 162s attr(,"assign") 162s [1] 0 1 2 162s > print( mm2 <- model.matrix( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]] ) ) 162s (Intercept) price farmPrice trend 162s 1 1 100.3 98.0 1 162s 2 1 104.3 99.1 2 162s 3 1 103.4 99.1 3 162s 4 1 104.5 98.1 4 162s 5 1 98.0 110.8 5 162s 6 1 99.5 108.2 6 162s 7 1 101.1 105.6 7 162s 8 1 104.8 109.8 8 162s 9 1 96.4 108.7 9 162s 10 1 91.2 100.6 10 162s 11 1 93.1 81.0 11 162s 12 1 98.8 68.6 12 162s 13 1 102.9 70.9 13 162s 14 1 98.8 81.4 14 162s 15 1 95.1 102.3 15 162s 16 1 98.5 105.0 16 162s 17 1 86.5 110.5 17 162s 18 1 104.0 92.5 18 162s 19 1 105.8 89.3 19 162s 20 1 113.5 93.0 20 162s attr(,"assign") 162s [1] 0 1 2 3 162s > 162s > # with x (returnModelMatrix) = FALSE 162s > print( all.equal( mm, model.matrix( fit3sls[[ 4 ]]$e1wc ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3sls[[ 4 ]]$e1wc$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3sls[[ 4 ]]$e1wc$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > print( !is.null( fit3sls[[ 4 ]]$e1wc$eq[[ 1 ]]$x ) ) 162s [1] FALSE 162s > 162s > # with x (returnModelMatrix) = TRUE 162s > print( !is.null( fit3sls[[ 5 ]]$e2$eq[[ 1 ]]$x ) ) 162s [1] TRUE 162s > print( all.equal( mm, model.matrix( fit3sls[[ 5 ]]$e2 ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3sls[[ 5 ]]$e2$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3sls[[ 5 ]]$e2$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > # with x (returnModelMatrix) = FALSE 162s > print( all.equal( mm, model.matrix( fit3sls[[ 5 ]]$e2e ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3sls[[ 5 ]]$e2e$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3sls[[ 5 ]]$e2e$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > print( !is.null( fit3sls[[ 5 ]]$e1wc$e2e[[ 1 ]]$x ) ) 162s [1] FALSE 162s > 162s > # with x (returnModelMatrix) = TRUE 162s > print( !is.null( fit3sls[[ 1 ]]$e3e$eq[[ 1 ]]$x ) ) 162s [1] TRUE 162s > print( all.equal( mm, model.matrix( fit3sls[[ 1 ]]$e3e ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3sls[[ 1 ]]$e3e$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3sls[[ 1 ]]$e3e$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > # with x (returnModelMatrix) = FALSE 162s > print( all.equal( mm, model.matrix( fit3sls[[ 1 ]]$e3 ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3sls[[ 1 ]]$e3$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3sls[[ 1 ]]$e3$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > print( !is.null( fit3sls[[ 1 ]]$e3$eq[[ 1 ]]$x ) ) 162s [1] FALSE 162s > 162s > # with x (returnModelMatrix) = TRUE 162s > print( !is.null( fit3slsi[[ 2 ]]$e4$eq[[ 1 ]]$x ) ) 162s [1] TRUE 162s > print( all.equal( mm, model.matrix( fit3slsi[[ 2 ]]$e4 ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3slsi[[ 2 ]]$e4$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3slsi[[ 2 ]]$e4$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > # with x (returnModelMatrix) = FALSE 162s > print( all.equal( mm, model.matrix( fit3slsi[[ 2 ]]$e4we ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3slsi[[ 2 ]]$e4we$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3slsi[[ 2 ]]$e4we$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > print( !is.null( fit3slsi[[ 2 ]]$e1wc$e4we[[ 1 ]]$x ) ) 162s [1] FALSE 162s > 162s > # with x (returnModelMatrix) = TRUE 162s > print( !is.null( fit3slsi[[ 5 ]]$e5w$eq[[ 1 ]]$x ) ) 162s [1] TRUE 162s > print( all.equal( mm, model.matrix( fit3slsi[[ 5 ]]$e5w ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3slsi[[ 5 ]]$e5w$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3slsi[[ 5 ]]$e5w$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > # with x (returnModelMatrix) = FALSE 162s > print( all.equal( mm, model.matrix( fit3slsi[[ 5 ]]$e5 ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3slsi[[ 5 ]]$e5$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3slsi[[ 5 ]]$e5$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > print( !is.null( fit3slsi[[ 5 ]]$e5$eq[[ 1 ]]$x ) ) 162s [1] FALSE 162s > 162s > # with x (returnModelMatrix) = TRUE 162s > print( !is.null( fit3slsd[[ 3 ]]$e5e$eq[[ 1 ]]$x ) ) 162s [1] TRUE 162s > print( all.equal( mm, model.matrix( fit3slsd[[ 3 ]]$e5e ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3slsd[[ 3 ]]$e5e$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3slsd[[ 3 ]]$e5e$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > # with x (returnModelMatrix) = FALSE 162s > print( all.equal( mm, model.matrix( fit3slsd[[ 3 ]]$e5we ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3slsd[[ 3 ]]$e5we$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3slsd[[ 3 ]]$e5we$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > print( !is.null( fit3sls[[ 3 ]]$e5we$eq[[ 1 ]]$x ) ) 162s [1] FALSE 162s > 162s > # with x (returnModelMatrix) = TRUE 162s > print( !is.null( fit3slsd[[ 2 ]]$e3w$eq[[ 1 ]]$x ) ) 162s [1] TRUE 162s > print( all.equal( mm, model.matrix( fit3slsd[[ 2 ]]$e3w ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3slsd[[ 2 ]]$e3w$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3slsd[[ 2 ]]$e3w$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > 162s > # with x (returnModelMatrix) = FALSE 162s > print( all.equal( mm, model.matrix( fit3slsd[[ 2 ]]$e3 ) ) ) 162s [1] TRUE 162s > print( all.equal( mm1, model.matrix( fit3slsd[[ 2 ]]$e3$eq[[ 1 ]] ) ) ) 162s [1] TRUE 162s > print( all.equal( mm2, model.matrix( fit3slsd[[ 2 ]]$e3$eq[[ 2 ]] ) ) ) 162s [1] TRUE 162s > print( !is.null( fit3slsd[[ 2 ]]$e3$eq[[ 1 ]]$x ) ) 162s [1] FALSE 162s > 162s > # matrices of instrumental variables 162s > model.matrix( fit3sls[[ 1 ]]$e1c, which = "z" ) 162s demand_(Intercept) demand_income demand_farmPrice demand_trend 162s demand_1 1 87.4 98.0 1 162s demand_2 1 97.6 99.1 2 162s demand_3 1 96.7 99.1 3 162s demand_4 1 98.2 98.1 4 162s demand_5 1 99.8 110.8 5 162s demand_6 1 100.5 108.2 6 162s demand_7 1 103.2 105.6 7 162s demand_8 1 107.8 109.8 8 162s demand_9 1 96.6 108.7 9 162s demand_10 1 88.9 100.6 10 162s demand_11 1 75.1 81.0 11 162s demand_12 1 76.9 68.6 12 162s demand_13 1 84.6 70.9 13 162s demand_14 1 90.6 81.4 14 162s demand_15 1 103.1 102.3 15 162s demand_16 1 105.1 105.0 16 162s demand_17 1 96.4 110.5 17 162s demand_18 1 104.4 92.5 18 162s demand_19 1 110.7 89.3 19 162s demand_20 1 127.1 93.0 20 162s supply_1 0 0.0 0.0 0 162s supply_2 0 0.0 0.0 0 162s supply_3 0 0.0 0.0 0 162s supply_4 0 0.0 0.0 0 162s supply_5 0 0.0 0.0 0 162s supply_6 0 0.0 0.0 0 162s supply_7 0 0.0 0.0 0 162s supply_8 0 0.0 0.0 0 162s supply_9 0 0.0 0.0 0 162s supply_10 0 0.0 0.0 0 162s supply_11 0 0.0 0.0 0 162s supply_12 0 0.0 0.0 0 162s supply_13 0 0.0 0.0 0 162s supply_14 0 0.0 0.0 0 162s supply_15 0 0.0 0.0 0 162s supply_16 0 0.0 0.0 0 162s supply_17 0 0.0 0.0 0 162s supply_18 0 0.0 0.0 0 162s supply_19 0 0.0 0.0 0 162s supply_20 0 0.0 0.0 0 162s supply_(Intercept) supply_income supply_farmPrice supply_trend 162s demand_1 0 0.0 0.0 0 162s demand_2 0 0.0 0.0 0 162s demand_3 0 0.0 0.0 0 162s demand_4 0 0.0 0.0 0 162s demand_5 0 0.0 0.0 0 162s demand_6 0 0.0 0.0 0 162s demand_7 0 0.0 0.0 0 162s demand_8 0 0.0 0.0 0 162s demand_9 0 0.0 0.0 0 162s demand_10 0 0.0 0.0 0 162s demand_11 0 0.0 0.0 0 162s demand_12 0 0.0 0.0 0 162s demand_13 0 0.0 0.0 0 162s demand_14 0 0.0 0.0 0 162s demand_15 0 0.0 0.0 0 162s demand_16 0 0.0 0.0 0 162s demand_17 0 0.0 0.0 0 162s demand_18 0 0.0 0.0 0 162s demand_19 0 0.0 0.0 0 162s demand_20 0 0.0 0.0 0 162s supply_1 1 87.4 98.0 1 162s supply_2 1 97.6 99.1 2 162s supply_3 1 96.7 99.1 3 162s supply_4 1 98.2 98.1 4 162s supply_5 1 99.8 110.8 5 162s supply_6 1 100.5 108.2 6 162s supply_7 1 103.2 105.6 7 162s supply_8 1 107.8 109.8 8 162s supply_9 1 96.6 108.7 9 162s supply_10 1 88.9 100.6 10 162s supply_11 1 75.1 81.0 11 162s supply_12 1 76.9 68.6 12 162s supply_13 1 84.6 70.9 13 162s supply_14 1 90.6 81.4 14 162s supply_15 1 103.1 102.3 15 162s supply_16 1 105.1 105.0 16 162s supply_17 1 96.4 110.5 17 162s supply_18 1 104.4 92.5 18 162s supply_19 1 110.7 89.3 19 162s supply_20 1 127.1 93.0 20 162s > model.matrix( fit3sls[[ 3 ]]$e1c$eq[[ 1 ]], which = "z" ) 162s (Intercept) income farmPrice trend 162s 1 1 87.4 98.0 1 162s 2 1 97.6 99.1 2 162s 3 1 96.7 99.1 3 162s 4 1 98.2 98.1 4 162s 5 1 99.8 110.8 5 162s 6 1 100.5 108.2 6 162s 7 1 103.2 105.6 7 162s 8 1 107.8 109.8 8 162s 9 1 96.6 108.7 9 162s 10 1 88.9 100.6 10 162s 11 1 75.1 81.0 11 162s 12 1 76.9 68.6 12 162s 13 1 84.6 70.9 13 162s 14 1 90.6 81.4 14 162s 15 1 103.1 102.3 15 162s 16 1 105.1 105.0 16 162s 17 1 96.4 110.5 17 162s 18 1 104.4 92.5 18 162s 19 1 110.7 89.3 19 162s 20 1 127.1 93.0 20 162s attr(,"assign") 162s [1] 0 1 2 3 162s > model.matrix( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]], which = "z" ) 162s (Intercept) income farmPrice trend 162s 1 1 87.4 98.0 1 162s 2 1 97.6 99.1 2 162s 3 1 96.7 99.1 3 162s 4 1 98.2 98.1 4 162s 5 1 99.8 110.8 5 162s 6 1 100.5 108.2 6 162s 7 1 103.2 105.6 7 162s 8 1 107.8 109.8 8 162s 9 1 96.6 108.7 9 162s 10 1 88.9 100.6 10 162s 11 1 75.1 81.0 11 162s 12 1 76.9 68.6 12 162s 13 1 84.6 70.9 13 162s 14 1 90.6 81.4 14 162s 15 1 103.1 102.3 15 162s 16 1 105.1 105.0 16 162s 17 1 96.4 110.5 17 162s 18 1 104.4 92.5 18 162s 19 1 110.7 89.3 19 162s 20 1 127.1 93.0 20 162s attr(,"assign") 162s [1] 0 1 2 3 162s > 162s > # matrices of fitted regressors 162s > model.matrix( fit3slsd[[ 1 ]]$e3w, which = "xHat" ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s demand_1 1 95.2 87.4 0 162s demand_2 1 99.3 97.6 0 162s demand_3 1 99.0 96.7 0 162s demand_4 1 99.9 98.2 0 162s demand_5 1 97.0 99.8 0 162s demand_6 1 98.0 100.5 0 162s demand_7 1 99.9 103.2 0 162s demand_8 1 100.7 107.8 0 162s demand_9 1 96.2 96.6 0 162s demand_10 1 95.1 88.9 0 162s demand_11 1 94.7 75.1 0 162s demand_12 1 99.0 76.9 0 162s demand_13 1 101.7 84.6 0 162s demand_14 1 101.3 90.6 0 162s demand_15 1 100.8 103.1 0 162s demand_16 1 100.9 105.1 0 162s demand_17 1 95.6 96.4 0 162s demand_18 1 104.2 104.4 0 162s demand_19 1 107.8 110.7 0 162s demand_20 1 113.9 127.1 0 162s supply_1 0 0.0 0.0 1 162s supply_2 0 0.0 0.0 1 162s supply_3 0 0.0 0.0 1 162s supply_4 0 0.0 0.0 1 162s supply_5 0 0.0 0.0 1 162s supply_6 0 0.0 0.0 1 162s supply_7 0 0.0 0.0 1 162s supply_8 0 0.0 0.0 1 162s supply_9 0 0.0 0.0 1 162s supply_10 0 0.0 0.0 1 162s supply_11 0 0.0 0.0 1 162s supply_12 0 0.0 0.0 1 162s supply_13 0 0.0 0.0 1 162s supply_14 0 0.0 0.0 1 162s supply_15 0 0.0 0.0 1 162s supply_16 0 0.0 0.0 1 162s supply_17 0 0.0 0.0 1 162s supply_18 0 0.0 0.0 1 162s supply_19 0 0.0 0.0 1 162s supply_20 0 0.0 0.0 1 162s supply_price supply_farmPrice supply_trend 162s demand_1 0.0 0.0 0 162s demand_2 0.0 0.0 0 162s demand_3 0.0 0.0 0 162s demand_4 0.0 0.0 0 162s demand_5 0.0 0.0 0 162s demand_6 0.0 0.0 0 162s demand_7 0.0 0.0 0 162s demand_8 0.0 0.0 0 162s demand_9 0.0 0.0 0 162s demand_10 0.0 0.0 0 162s demand_11 0.0 0.0 0 162s demand_12 0.0 0.0 0 162s demand_13 0.0 0.0 0 162s demand_14 0.0 0.0 0 162s demand_15 0.0 0.0 0 162s demand_16 0.0 0.0 0 162s demand_17 0.0 0.0 0 162s demand_18 0.0 0.0 0 162s demand_19 0.0 0.0 0 162s demand_20 0.0 0.0 0 162s supply_1 99.6 98.0 1 162s supply_2 105.1 99.1 2 162s supply_3 103.8 99.1 3 162s supply_4 104.5 98.1 4 162s supply_5 98.7 110.8 5 162s supply_6 99.6 108.2 6 162s supply_7 102.0 105.6 7 162s supply_8 102.2 109.8 8 162s supply_9 94.6 108.7 9 162s supply_10 92.7 100.6 10 162s supply_11 92.4 81.0 11 162s supply_12 98.9 68.6 12 162s supply_13 102.2 70.9 13 162s supply_14 100.3 81.4 14 162s supply_15 97.6 102.3 15 162s supply_16 96.9 105.0 16 162s supply_17 87.7 110.5 17 162s supply_18 101.1 92.5 18 162s supply_19 106.1 89.3 19 162s supply_20 114.4 93.0 20 162s > model.matrix( fit3slsd[[ 3 ]]$e3w$eq[[ 1 ]], which = "xHat" ) 162s (Intercept) price income 162s 1 1 95.2 87.4 162s 2 1 99.3 97.6 162s 3 1 99.0 96.7 162s 4 1 99.9 98.2 162s 5 1 97.0 99.8 162s 6 1 98.0 100.5 162s 7 1 99.9 103.2 162s 8 1 100.7 107.8 162s 9 1 96.2 96.6 162s 10 1 95.1 88.9 162s 11 1 94.7 75.1 162s 12 1 99.0 76.9 162s 13 1 101.7 84.6 162s 14 1 101.3 90.6 162s 15 1 100.8 103.1 162s 16 1 100.9 105.1 162s 17 1 95.6 96.4 162s 18 1 104.2 104.4 162s 19 1 107.8 110.7 162s 20 1 113.9 127.1 162s > model.matrix( fit3slsd[[ 4 ]]$e3w$eq[[ 2 ]], which = "xHat" ) 162s (Intercept) price farmPrice trend 162s 1 1 99.6 98.0 1 162s 2 1 105.1 99.1 2 162s 3 1 103.8 99.1 3 162s 4 1 104.5 98.1 4 162s 5 1 98.7 110.8 5 162s 6 1 99.6 108.2 6 162s 7 1 102.0 105.6 7 162s 8 1 102.2 109.8 8 162s 9 1 94.6 108.7 9 162s 10 1 92.7 100.6 10 162s 11 1 92.4 81.0 11 162s 12 1 98.9 68.6 12 162s 13 1 102.2 70.9 13 162s 14 1 100.3 81.4 14 162s 15 1 97.6 102.3 15 162s 16 1 96.9 105.0 16 162s 17 1 87.7 110.5 17 162s 18 1 101.1 92.5 18 162s 19 1 106.1 89.3 19 162s 20 1 114.4 93.0 20 162s > 162s > 162s > ## **************** formulas ************************ 162s > formula( fit3sls[[ 2 ]]$e1c ) 162s $demand 162s consump ~ price + income 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s 162s > formula( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]] ) 162s consump ~ price + income 162s > 162s > formula( fit3sls[[ 3 ]]$e2e ) 162s $demand 162s consump ~ price + income 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s 162s > formula( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]] ) 162s consump ~ price + farmPrice + trend 162s > 162s > formula( fit3sls[[ 4 ]]$e3 ) 162s $demand 162s consump ~ price + income 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s 162s > formula( fit3sls[[ 4 ]]$e3$eq[[ 1 ]] ) 162s consump ~ price + income 162s > 162s > formula( fit3sls[[ 5 ]]$e4e ) 162s $demand 162s consump ~ price + income 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s 162s > formula( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]] ) 162s consump ~ price + farmPrice + trend 162s > 162s > formula( fit3sls[[ 1 ]]$e5 ) 162s $demand 162s consump ~ price + income 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s 162s > formula( fit3sls[[ 1 ]]$e5$eq[[ 1 ]] ) 162s consump ~ price + income 162s > 162s > formula( fit3slsi[[ 3 ]]$e3e ) 162s $demand 162s consump ~ price + income 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s 162s > formula( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]] ) 162s consump ~ price + income 162s > 162s > formula( fit3slsd[[ 4 ]]$e4 ) 162s $demand 162s consump ~ price + income 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s 162s > formula( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]] ) 162s consump ~ price + farmPrice + trend 162s > 162s > formula( fit3slsd[[ 2 ]]$e1w ) 162s $demand 162s consump ~ price + income 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s 162s > formula( fit3slsd[[ 2 ]]$e1w$eq[[ 1 ]] ) 162s consump ~ price + income 162s > 162s > 162s > ## **************** model terms ******************* 162s > terms( fit3sls[[ 2 ]]$e1c ) 162s $demand 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s 162s > terms( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]] ) 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s > 162s > terms( fit3sls[[ 3 ]]$e2e ) 162s $demand 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s 162s > terms( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]] ) 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s > 162s > terms( fit3sls[[ 4 ]]$e3 ) 162s $demand 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s 162s > terms( fit3sls[[ 4 ]]$e3$eq[[ 1 ]] ) 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s > 162s > terms( fit3sls[[ 5 ]]$e4e ) 162s $demand 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s 162s > terms( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]] ) 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s > 162s > terms( fit3sls[[ 1 ]]$e5 ) 162s $demand 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s 162s > terms( fit3sls[[ 1 ]]$e5$eq[[ 1 ]] ) 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s > 162s > terms( fit3sls[[ 2 ]]$e4wSym ) 162s $demand 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s 162s > terms( fit3sls[[ 2 ]]$e4wSym$eq[[ 1 ]] ) 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s > 162s > terms( fit3slsi[[ 3 ]]$e3e ) 162s $demand 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s 162s > terms( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]] ) 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s > 162s > terms( fit3slsd[[ 4 ]]$e4 ) 162s $demand 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s 162s > terms( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]] ) 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s > 162s > terms( fit3slsd[[ 5 ]]$e5we ) 162s $demand 162s consump ~ price + income 162s attr(,"variables") 162s list(consump, price, income) 162s attr(,"factors") 162s price income 162s consump 0 0 162s price 1 0 162s income 0 1 162s attr(,"term.labels") 162s [1] "price" "income" 162s attr(,"order") 162s [1] 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, income) 162s attr(,"dataClasses") 162s consump price income 162s "numeric" "numeric" "numeric" 162s 162s $supply 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s 162s > terms( fit3slsd[[ 5 ]]$e5we$eq[[ 2 ]] ) 162s consump ~ price + farmPrice + trend 162s attr(,"variables") 162s list(consump, price, farmPrice, trend) 162s attr(,"factors") 162s price farmPrice trend 162s consump 0 0 0 162s price 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "price" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 1 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(consump, price, farmPrice, trend) 162s attr(,"dataClasses") 162s consump price farmPrice trend 162s "numeric" "numeric" "numeric" "numeric" 162s > 162s > 162s > ## **************** terms of instruments ******************* 162s > fit3sls[[ 2 ]]$e1c$eq[[ 1 ]]$termsInst 162s ~income + farmPrice + trend 162s attr(,"variables") 162s list(income, farmPrice, trend) 162s attr(,"factors") 162s income farmPrice trend 162s income 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "income" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 0 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(income, farmPrice, trend) 162s attr(,"dataClasses") 162s income farmPrice trend 162s "numeric" "numeric" "numeric" 162s > 162s > fit3sls[[ 3 ]]$e2e$eq[[ 2 ]]$termsInst 162s ~income + farmPrice + trend 162s attr(,"variables") 162s list(income, farmPrice, trend) 162s attr(,"factors") 162s income farmPrice trend 162s income 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "income" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 0 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(income, farmPrice, trend) 162s attr(,"dataClasses") 162s income farmPrice trend 162s "numeric" "numeric" "numeric" 162s > 162s > fit3sls[[ 4 ]]$e3$eq[[ 1 ]]$termsInst 162s ~income + farmPrice + trend 162s attr(,"variables") 162s list(income, farmPrice, trend) 162s attr(,"factors") 162s income farmPrice trend 162s income 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "income" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 0 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(income, farmPrice, trend) 162s attr(,"dataClasses") 162s income farmPrice trend 162s "numeric" "numeric" "numeric" 162s > 162s > fit3sls[[ 5 ]]$e4e$eq[[ 2 ]]$termsInst 162s ~income + farmPrice + trend 162s attr(,"variables") 162s list(income, farmPrice, trend) 162s attr(,"factors") 162s income farmPrice trend 162s income 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "income" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 0 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(income, farmPrice, trend) 162s attr(,"dataClasses") 162s income farmPrice trend 162s "numeric" "numeric" "numeric" 162s > 162s > fit3sls[[ 1 ]]$e5$eq[[ 1 ]]$termsInst 162s ~income + farmPrice + trend 162s attr(,"variables") 162s list(income, farmPrice, trend) 162s attr(,"factors") 162s income farmPrice trend 162s income 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "income" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 0 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(income, farmPrice, trend) 162s attr(,"dataClasses") 162s income farmPrice trend 162s "numeric" "numeric" "numeric" 162s > 162s > fit3sls[[ 2 ]]$e4wSym$eq[[ 1 ]]$termsInst 162s ~income + farmPrice + trend 162s attr(,"variables") 162s list(income, farmPrice, trend) 162s attr(,"factors") 162s income farmPrice trend 162s income 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "income" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 0 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(income, farmPrice, trend) 162s attr(,"dataClasses") 162s income farmPrice trend 162s "numeric" "numeric" "numeric" 162s > 162s > fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]]$termsInst 162s ~income + farmPrice + trend 162s attr(,"variables") 162s list(income, farmPrice, trend) 162s attr(,"factors") 162s income farmPrice trend 162s income 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "income" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 0 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(income, farmPrice, trend) 162s attr(,"dataClasses") 162s income farmPrice trend 162s "numeric" "numeric" "numeric" 162s > 162s > fit3slsd[[ 4 ]]$e4$eq[[ 2 ]]$termsInst 162s ~income + farmPrice + trend 162s attr(,"variables") 162s list(income, farmPrice, trend) 162s attr(,"factors") 162s income farmPrice trend 162s income 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "income" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 0 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(income, farmPrice, trend) 162s attr(,"dataClasses") 162s income farmPrice trend 162s "numeric" "numeric" "numeric" 162s > 162s > fit3slsd[[ 5 ]]$e5we$eq[[ 2 ]]$termsInst 162s ~income + farmPrice + trend 162s attr(,"variables") 162s list(income, farmPrice, trend) 162s attr(,"factors") 162s income farmPrice trend 162s income 1 0 0 162s farmPrice 0 1 0 162s trend 0 0 1 162s attr(,"term.labels") 162s [1] "income" "farmPrice" "trend" 162s attr(,"order") 162s [1] 1 1 1 162s attr(,"intercept") 162s [1] 1 162s attr(,"response") 162s [1] 0 162s attr(,".Environment") 162s 162s attr(,"predvars") 162s list(income, farmPrice, trend) 162s attr(,"dataClasses") 162s income farmPrice trend 162s "numeric" "numeric" "numeric" 162s > 162s > 162s > ## **************** estfun ************************ 162s > library( "sandwich" ) 162s > 162s > estfun( fit3sls[[ 1 ]]$e1 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s demand_1 0.93243 92.895 81.494 -0.67273 162s demand_2 -0.67769 -71.238 -66.143 0.48894 162s demand_3 3.38220 351.019 327.058 -2.44019 162s demand_4 2.06995 216.373 203.269 -1.49343 162s demand_5 3.17940 313.652 317.304 -2.29388 162s demand_6 1.83161 182.517 184.077 -1.32147 162s demand_7 2.47947 252.837 255.881 -1.78889 162s demand_8 -5.09517 -520.901 -549.259 3.67607 162s demand_9 -2.17668 -205.928 -210.267 1.57043 162s demand_10 3.95122 366.354 351.263 -2.85073 162s demand_11 -0.37870 -34.993 -28.440 0.27322 162s demand_12 -3.13231 -309.838 -240.875 2.25990 162s demand_13 -2.46263 -251.590 -208.339 1.77674 162s demand_14 0.13711 13.748 12.422 -0.09892 162s demand_15 3.55301 346.849 366.315 -2.56343 162s demand_16 -5.27287 -510.898 -554.179 3.80428 162s demand_17 -0.02852 -2.502 -2.750 0.02058 162s demand_18 -3.97374 -401.582 -414.859 2.86698 162s demand_19 2.30169 244.124 254.797 -1.66062 162s demand_20 -0.61976 -70.898 -78.771 0.44714 162s supply_1 -0.79213 -78.918 -69.232 0.70287 162s supply_2 0.37122 39.022 36.231 -0.32939 162s supply_3 -2.54401 -264.028 -246.006 2.25734 162s supply_4 -1.58295 -165.467 -155.446 1.40458 162s supply_5 -2.40285 -237.044 -239.804 2.13208 162s supply_6 -1.41153 -140.656 -141.858 1.25247 162s supply_7 -1.86174 -189.846 -192.132 1.65195 162s supply_8 3.60208 368.256 388.304 -3.19618 162s supply_9 1.52187 143.979 147.013 -1.35038 162s supply_10 -2.85966 -265.145 -254.224 2.53741 162s supply_11 0.33741 31.177 25.339 -0.29938 162s supply_12 2.36613 234.051 181.956 -2.09950 162s supply_13 1.88385 192.460 159.374 -1.67157 162s supply_14 -0.00962 -0.965 -0.872 0.00854 162s supply_15 -2.52306 -246.304 -260.128 2.23875 162s supply_16 3.84942 372.977 404.574 -3.41564 162s supply_17 0.07279 6.384 7.017 -0.06459 162s supply_18 2.96969 300.114 310.035 -2.63504 162s supply_19 -1.54232 -163.584 -170.735 1.36853 162s supply_20 0.55542 63.538 70.594 -0.49283 162s supply_price supply_farmPrice supply_trend 162s demand_1 -67.022 -65.927 -0.673 162s demand_2 51.397 48.454 0.978 162s demand_3 -253.253 -241.823 -7.321 162s demand_4 -156.109 -146.505 -5.974 162s demand_5 -226.294 -254.162 -11.469 162s demand_6 -131.682 -142.983 -7.929 162s demand_7 -182.417 -188.907 -12.522 162s demand_8 375.820 403.632 29.409 162s demand_9 148.573 170.706 14.134 162s demand_10 -264.317 -286.783 -28.507 162s demand_11 25.247 22.131 3.005 162s demand_12 223.542 155.029 27.119 162s demand_13 181.517 125.971 23.098 162s demand_14 -9.919 -8.052 -1.385 162s demand_15 -250.245 -262.238 -38.451 162s demand_16 368.603 399.449 60.868 162s demand_17 1.805 2.274 0.350 162s demand_18 289.734 265.195 51.606 162s demand_19 -176.131 -148.294 -31.552 162s demand_20 51.151 41.584 8.943 162s supply_1 70.025 68.881 0.703 162s supply_2 -34.625 -32.642 -0.659 162s supply_3 234.276 223.702 6.772 162s supply_4 146.821 137.789 5.618 162s supply_5 210.332 236.235 10.660 162s supply_6 124.806 135.517 7.515 162s supply_7 168.453 174.446 11.564 162s supply_8 -326.759 -350.940 -25.569 162s supply_9 -127.755 -146.786 -12.153 162s supply_10 235.267 255.264 25.374 162s supply_11 -27.664 -24.250 -3.293 162s supply_12 -207.676 -144.026 -25.194 162s supply_13 -170.773 -118.514 -21.730 162s supply_14 0.856 0.695 0.120 162s supply_15 218.549 229.024 33.581 162s supply_16 -330.948 -358.642 -54.650 162s supply_17 -5.665 -7.137 -1.098 162s supply_18 -266.295 -243.742 -47.431 162s supply_19 145.150 122.209 26.002 162s supply_20 -56.378 -45.834 -9.857 162s > round( colSums( estfun( fit3sls[[ 1 ]]$e1 ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > 162s > estfun( fit3sls[[ 2 ]]$e1e ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s demand_1 1.0970 109.29 95.88 -0.8158 162s demand_2 -0.7973 -83.81 -77.82 0.5929 162s demand_3 3.9791 412.96 384.77 -2.9592 162s demand_4 2.4352 254.56 239.14 -1.8110 162s demand_5 3.7405 369.00 373.30 -2.7817 162s demand_6 2.1548 214.73 216.56 -1.6025 162s demand_7 2.9170 297.45 301.04 -2.1693 162s demand_8 -5.9943 -612.82 -646.19 4.4579 162s demand_9 -2.5608 -242.27 -247.37 1.9044 162s demand_10 4.6485 431.00 413.25 -3.4570 162s demand_11 -0.4455 -41.17 -33.46 0.3313 162s demand_12 -3.6851 -364.52 -283.38 2.7405 162s demand_13 -2.8972 -295.99 -245.10 2.1546 162s demand_14 0.1613 16.17 14.61 -0.1200 162s demand_15 4.1800 408.06 430.96 -3.1086 162s demand_16 -6.2034 -601.06 -651.98 4.6134 162s demand_17 -0.0336 -2.94 -3.24 0.0250 162s demand_18 -4.6750 -472.45 -488.07 3.4767 162s demand_19 2.7079 287.21 299.76 -2.0138 162s demand_20 -0.7291 -83.41 -92.67 0.5422 162s supply_1 -0.9222 -91.88 -80.60 0.8435 162s supply_2 0.4880 51.30 47.63 -0.4463 162s supply_3 -3.0517 -316.72 -295.10 2.7912 162s supply_4 -1.8908 -197.65 -185.68 1.7294 162s supply_5 -2.8789 -284.00 -287.31 2.6331 162s supply_6 -1.6828 -167.69 -169.12 1.5391 162s supply_7 -2.2343 -227.83 -230.58 2.0435 162s supply_8 4.3919 449.01 473.45 -4.0170 162s supply_9 1.8611 176.08 179.79 -1.7022 162s supply_10 -3.4650 -321.27 -308.04 3.1691 162s supply_11 0.3885 35.90 29.18 -0.3554 162s supply_12 2.8352 280.45 218.03 -2.5932 162s supply_13 2.2501 229.88 190.36 -2.0580 162s supply_14 -0.0404 -4.05 -3.66 0.0369 162s supply_15 -3.0726 -299.95 -316.79 2.8103 162s supply_16 4.6536 450.90 489.09 -4.2563 162s supply_17 0.0715 6.27 6.89 -0.0654 162s supply_18 3.5683 360.61 372.53 -3.2636 162s supply_19 -1.9084 -202.41 -211.25 1.7454 162s supply_20 0.6388 73.07 81.19 -0.5842 162s supply_price supply_farmPrice supply_trend 162s demand_1 -81.28 -79.95 -0.816 162s demand_2 62.33 58.76 1.186 162s demand_3 -307.11 -293.25 -8.877 162s demand_4 -189.31 -177.66 -7.244 162s demand_5 -274.42 -308.22 -13.909 162s demand_6 -159.69 -173.39 -9.615 162s demand_7 -221.21 -229.08 -15.185 162s demand_8 455.75 489.48 35.663 162s demand_9 180.17 207.01 17.140 162s demand_10 -320.53 -347.78 -34.570 162s demand_11 30.62 26.84 3.645 162s demand_12 271.08 188.00 32.886 162s demand_13 220.12 152.76 28.010 162s demand_14 -12.03 -9.76 -1.679 162s demand_15 -303.47 -318.01 -46.629 162s demand_16 447.00 484.40 73.814 162s demand_17 2.19 2.76 0.424 162s demand_18 351.35 321.60 62.581 162s demand_19 -213.59 -179.83 -38.262 162s demand_20 62.03 50.43 10.845 162s supply_1 84.04 82.66 0.843 162s supply_2 -46.92 -44.23 -0.893 162s supply_3 289.68 276.60 8.373 162s supply_4 180.78 169.66 6.918 162s supply_5 259.76 291.74 13.165 162s supply_6 153.37 166.53 9.235 162s supply_7 208.38 215.80 14.305 162s supply_8 -410.67 -441.06 -32.136 162s supply_9 -161.04 -185.03 -15.320 162s supply_10 293.84 318.82 31.691 162s supply_11 -32.84 -28.78 -3.909 162s supply_12 -256.51 -177.89 -31.118 162s supply_13 -210.25 -145.91 -26.754 162s supply_14 3.70 3.00 0.517 162s supply_15 274.34 287.49 42.154 162s supply_16 -412.40 -446.91 -68.101 162s supply_17 -5.73 -7.23 -1.112 162s supply_18 -329.82 -301.88 -58.745 162s supply_19 185.13 155.87 33.163 162s supply_20 -66.83 -54.33 -11.684 162s > round( colSums( estfun( fit3sls[[ 2 ]]$e1e ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > 162s > estfun( fit3sls[[ 3 ]]$e1c ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s demand_1 1.3280 132.31 116.07 -0.9904 162s demand_2 -0.9652 -101.46 -94.20 0.7198 162s demand_3 4.8171 499.94 465.81 -3.5924 162s demand_4 2.9481 308.17 289.50 -2.1986 162s demand_5 4.5282 446.72 451.92 -3.3770 162s demand_6 2.6087 259.95 262.17 -1.9455 162s demand_7 3.5314 360.10 364.44 -2.6336 162s demand_8 -7.2568 -741.89 -782.28 5.4119 162s demand_9 -3.1001 -293.29 -299.47 2.3120 162s demand_10 5.6275 521.78 500.28 -4.1968 162s demand_11 -0.5394 -49.84 -40.51 0.4022 162s demand_12 -4.4612 -441.28 -343.06 3.3270 162s demand_13 -3.5074 -358.33 -296.72 2.6157 162s demand_14 0.1953 19.58 17.69 -0.1456 162s demand_15 5.0603 494.00 521.72 -3.7739 162s demand_16 -7.5098 -727.64 -789.29 5.6006 162s demand_17 -0.0406 -3.56 -3.92 0.0303 162s demand_18 -5.6596 -571.95 -590.86 4.2207 162s demand_19 3.2782 347.69 362.89 -2.4448 162s demand_20 -0.8827 -100.98 -112.19 0.6583 162s supply_1 -1.2187 -121.42 -106.51 1.0461 162s supply_2 0.4947 52.00 48.29 -0.4247 162s supply_3 -3.7909 -393.44 -366.58 3.2542 162s supply_4 -2.3698 -247.71 -232.71 2.0343 162s supply_5 -3.5854 -353.70 -357.82 3.0777 162s supply_6 -2.1176 -211.02 -212.82 1.8178 162s supply_7 -2.7729 -282.76 -286.16 2.3803 162s supply_8 5.2704 538.82 568.15 -4.5242 162s supply_9 2.2191 209.94 214.37 -1.9049 162s supply_10 -4.2139 -390.71 -374.62 3.6173 162s supply_11 0.5250 48.51 39.42 -0.4506 162s supply_12 3.5301 349.19 271.47 -3.0303 162s supply_13 2.8205 288.15 238.61 -2.4212 162s supply_14 0.0251 2.52 2.28 -0.0216 162s supply_15 -3.6967 -360.87 -381.13 3.1733 162s supply_16 5.6869 551.02 597.70 -4.8817 162s supply_17 0.1301 11.41 12.54 -0.1117 162s supply_18 4.4171 446.39 461.15 -3.7917 162s supply_19 -2.2186 -235.31 -245.60 1.9044 162s supply_20 0.8653 98.99 109.98 -0.7428 162s supply_price supply_farmPrice supply_trend 162s demand_1 -98.67 -97.06 -0.990 162s demand_2 75.67 71.33 1.440 162s demand_3 -372.84 -356.01 -10.777 162s demand_4 -229.82 -215.68 -8.794 162s demand_5 -333.15 -374.17 -16.885 162s demand_6 -193.86 -210.50 -11.673 162s demand_7 -268.55 -278.11 -18.435 162s demand_8 553.28 594.22 43.295 162s demand_9 218.73 251.31 20.808 162s demand_10 -389.13 -422.20 -41.968 162s demand_11 37.17 32.58 4.425 162s demand_12 329.10 228.23 39.924 162s demand_13 267.23 185.45 34.004 162s demand_14 -14.60 -11.85 -2.039 162s demand_15 -368.41 -386.07 -56.608 162s demand_16 542.65 588.07 89.610 162s demand_17 2.66 3.35 0.515 162s demand_18 426.54 390.42 75.973 162s demand_19 -259.30 -218.32 -46.450 162s demand_20 75.30 61.22 13.166 162s supply_1 104.22 102.52 1.046 162s supply_2 -44.64 -42.09 -0.849 162s supply_3 337.73 322.49 9.763 162s supply_4 212.64 199.56 8.137 162s supply_5 303.62 341.01 15.389 162s supply_6 181.14 196.69 10.907 162s supply_7 242.72 251.36 16.662 162s supply_8 -462.53 -496.76 -36.194 162s supply_9 -180.22 -207.07 -17.144 162s supply_10 335.39 363.90 36.173 162s supply_11 -41.64 -36.50 -4.957 162s supply_12 -299.75 -207.88 -36.364 162s supply_13 -247.35 -171.66 -31.475 162s supply_14 -2.16 -1.75 -0.302 162s supply_15 309.78 324.63 47.599 162s supply_16 -473.00 -512.58 -78.108 162s supply_17 -9.80 -12.34 -1.899 162s supply_18 -383.19 -350.73 -68.251 162s supply_19 201.99 170.07 36.184 162s supply_20 -84.97 -69.08 -14.856 162s > round( colSums( estfun( fit3sls[[ 3 ]]$e1c ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > 162s > estfun( fit3sls[[ 4 ]]$e1wc ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s demand_1 1.3280 132.31 116.07 -0.9904 162s demand_2 -0.9652 -101.46 -94.20 0.7198 162s demand_3 4.8171 499.94 465.81 -3.5924 162s demand_4 2.9481 308.17 289.50 -2.1986 162s demand_5 4.5282 446.72 451.92 -3.3770 162s demand_6 2.6087 259.95 262.17 -1.9455 162s demand_7 3.5314 360.10 364.44 -2.6336 162s demand_8 -7.2568 -741.89 -782.28 5.4119 162s demand_9 -3.1001 -293.29 -299.47 2.3120 162s demand_10 5.6275 521.78 500.28 -4.1968 162s demand_11 -0.5394 -49.84 -40.51 0.4022 162s demand_12 -4.4612 -441.28 -343.06 3.3270 162s demand_13 -3.5074 -358.33 -296.72 2.6157 162s demand_14 0.1953 19.58 17.69 -0.1456 162s demand_15 5.0603 494.00 521.72 -3.7739 162s demand_16 -7.5098 -727.64 -789.29 5.6006 162s demand_17 -0.0406 -3.56 -3.92 0.0303 162s demand_18 -5.6596 -571.95 -590.86 4.2207 162s demand_19 3.2782 347.69 362.89 -2.4448 162s demand_20 -0.8827 -100.98 -112.19 0.6583 162s supply_1 -1.2187 -121.42 -106.51 1.0461 162s supply_2 0.4947 52.00 48.29 -0.4247 162s supply_3 -3.7909 -393.44 -366.58 3.2542 162s supply_4 -2.3698 -247.71 -232.71 2.0343 162s supply_5 -3.5854 -353.70 -357.82 3.0777 162s supply_6 -2.1176 -211.02 -212.82 1.8178 162s supply_7 -2.7729 -282.76 -286.16 2.3803 162s supply_8 5.2704 538.82 568.15 -4.5242 162s supply_9 2.2191 209.94 214.37 -1.9049 162s supply_10 -4.2139 -390.71 -374.62 3.6173 162s supply_11 0.5250 48.51 39.42 -0.4506 162s supply_12 3.5301 349.19 271.47 -3.0303 162s supply_13 2.8205 288.15 238.61 -2.4212 162s supply_14 0.0251 2.52 2.28 -0.0216 162s supply_15 -3.6967 -360.87 -381.13 3.1733 162s supply_16 5.6869 551.02 597.70 -4.8817 162s supply_17 0.1301 11.41 12.54 -0.1117 162s supply_18 4.4171 446.39 461.15 -3.7917 162s supply_19 -2.2186 -235.31 -245.60 1.9044 162s supply_20 0.8653 98.99 109.98 -0.7428 162s supply_price supply_farmPrice supply_trend 162s demand_1 -98.67 -97.06 -0.990 162s demand_2 75.67 71.33 1.440 162s demand_3 -372.84 -356.01 -10.777 162s demand_4 -229.82 -215.68 -8.794 162s demand_5 -333.15 -374.17 -16.885 162s demand_6 -193.86 -210.50 -11.673 162s demand_7 -268.55 -278.11 -18.435 162s demand_8 553.28 594.22 43.295 162s demand_9 218.73 251.31 20.808 162s demand_10 -389.13 -422.20 -41.968 162s demand_11 37.17 32.58 4.425 162s demand_12 329.10 228.23 39.924 162s demand_13 267.23 185.45 34.004 162s demand_14 -14.60 -11.85 -2.039 162s demand_15 -368.41 -386.07 -56.608 162s demand_16 542.65 588.07 89.610 162s demand_17 2.66 3.35 0.515 162s demand_18 426.54 390.42 75.973 162s demand_19 -259.30 -218.32 -46.450 162s demand_20 75.30 61.22 13.166 162s supply_1 104.22 102.52 1.046 162s supply_2 -44.64 -42.09 -0.849 162s supply_3 337.73 322.49 9.763 162s supply_4 212.64 199.56 8.137 162s supply_5 303.62 341.01 15.389 162s supply_6 181.14 196.69 10.907 162s supply_7 242.72 251.36 16.662 162s supply_8 -462.53 -496.76 -36.194 162s supply_9 -180.22 -207.07 -17.144 162s supply_10 335.39 363.90 36.173 162s supply_11 -41.64 -36.50 -4.957 162s supply_12 -299.75 -207.88 -36.364 162s supply_13 -247.35 -171.66 -31.475 162s supply_14 -2.16 -1.75 -0.302 162s supply_15 309.78 324.63 47.599 162s supply_16 -473.00 -512.58 -78.108 162s supply_17 -9.80 -12.34 -1.899 162s supply_18 -383.19 -350.73 -68.251 162s supply_19 201.99 170.07 36.184 162s supply_20 -84.97 -69.08 -14.856 162s > 162s > round( colSums( estfun( fit3sls[[ 5 ]]$e1wc ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > round( colSums( estfun( fit3sls[[ 5 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > 162s > round( colSums( estfun( fit3sls[[ 4 ]]$e1wc ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > round( colSums( estfun( fit3sls[[ 4 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > 162s > round( colSums( estfun( fit3sls[[ 3 ]]$e1wc ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > round( colSums( estfun( fit3sls[[ 3 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > 162s > round( colSums( estfun( fit3sls[[ 2 ]]$e1wc ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > round( colSums( estfun( fit3sls[[ 2 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > 162s > round( colSums( estfun( fit3sls[[ 1 ]]$e1wc ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > round( colSums( estfun( fit3sls[[ 1 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 162s demand_(Intercept) demand_price demand_income supply_(Intercept) 162s 0 0 0 0 162s supply_price supply_farmPrice supply_trend 162s 0 0 0 162s > 162s > estfun( fit3slsd[[ 5 ]]$e1w ) 163s Warning message: 163s In estfun.systemfit(fit3slsd[[5]]$e1w) : 163s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 163s Warning message: 163s In estfun.systemfit(fit3slsd[[5]]$e1w) : 163s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 163s Warning message: 163s In estfun.systemfit(fit3slsd[[4]]$e1w) : 163s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 163s Warning message: 163s In estfun.systemfit(fit3slsd[[4]]$e1w, residFit = FALSE) : 163s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s demand_1 -0.471 -44.9 -41.2 0.299 163s demand_2 -1.315 -130.6 -128.3 0.835 163s demand_3 0.736 72.8 71.2 -0.467 163s demand_4 0.203 20.3 19.9 -0.129 163s demand_5 0.825 80.0 82.4 -0.524 163s demand_6 0.290 28.4 29.1 -0.184 163s demand_7 0.657 65.6 67.8 -0.417 163s demand_8 -2.887 -290.8 -311.2 1.833 163s demand_9 -1.172 -112.7 -113.2 0.744 163s demand_10 1.981 188.4 176.1 -1.258 163s demand_11 0.308 29.2 23.1 -0.196 163s demand_12 -0.922 -91.4 -70.9 0.586 163s demand_13 -0.639 -65.0 -54.1 0.406 163s demand_14 0.597 60.5 54.0 -0.379 163s demand_15 2.100 211.7 216.5 -1.333 163s demand_16 -1.984 -200.3 -208.6 1.260 163s demand_17 0.785 75.0 75.7 -0.499 163s demand_18 -1.136 -118.3 -118.6 0.721 163s demand_19 1.814 195.6 200.8 -1.152 163s demand_20 0.232 26.4 29.5 -0.147 163s supply_1 -0.434 -41.3 -37.9 0.449 163s supply_2 -0.126 -12.6 -12.3 0.131 163s supply_3 -1.272 -125.8 -123.0 1.316 163s supply_4 -0.902 -90.1 -88.6 0.933 163s supply_5 -0.805 -78.1 -80.4 0.833 163s supply_6 -0.457 -44.8 -46.0 0.473 163s supply_7 -0.758 -75.8 -78.3 0.784 163s supply_8 1.582 159.3 170.5 -1.636 163s supply_9 1.004 96.6 97.0 -1.039 163s supply_10 -0.856 -81.5 -76.1 0.886 163s supply_11 0.191 18.1 14.3 -0.197 163s supply_12 0.607 60.1 46.7 -0.628 163s supply_13 0.335 34.0 28.3 -0.346 163s supply_14 -0.201 -20.3 -18.2 0.208 163s supply_15 -0.801 -80.8 -82.6 0.829 163s supply_16 1.930 194.8 202.9 -1.997 163s supply_17 0.811 77.5 78.2 -0.839 163s supply_18 1.241 129.3 129.5 -1.283 163s supply_19 -0.858 -92.5 -95.0 0.888 163s supply_20 -0.229 -26.1 -29.1 0.237 163s supply_price supply_farmPrice supply_trend 163s demand_1 29.8 29.3 0.299 163s demand_2 87.8 82.7 1.670 163s demand_3 -48.5 -46.3 -1.402 163s demand_4 -13.5 -12.7 -0.516 163s demand_5 -51.7 -58.1 -2.620 163s demand_6 -18.3 -19.9 -1.105 163s demand_7 -42.5 -44.0 -2.919 163s demand_8 187.4 201.3 14.667 163s demand_9 70.4 80.9 6.698 163s demand_10 -116.6 -126.5 -12.579 163s demand_11 -18.1 -15.8 -2.152 163s demand_12 57.9 40.2 7.029 163s demand_13 41.5 28.8 5.278 163s demand_14 -38.0 -30.8 -5.304 163s demand_15 -130.2 -136.4 -20.000 163s demand_16 122.1 132.3 20.164 163s demand_17 -43.7 -55.1 -8.477 163s demand_18 72.9 66.7 12.986 163s demand_19 -122.2 -102.9 -21.890 163s demand_20 -16.9 -13.7 -2.947 163s supply_1 44.7 44.0 0.449 163s supply_2 13.7 13.0 0.262 163s supply_3 136.5 130.4 3.947 163s supply_4 97.5 91.5 3.731 163s supply_5 82.2 92.3 4.165 163s supply_6 47.1 51.2 2.839 163s supply_7 80.0 82.8 5.491 163s supply_8 -167.3 -179.7 -13.089 163s supply_9 -98.3 -112.9 -9.349 163s supply_10 82.1 89.1 8.857 163s supply_11 -18.2 -16.0 -2.169 163s supply_12 -62.1 -43.1 -7.532 163s supply_13 -35.4 -24.5 -4.499 163s supply_14 20.8 16.9 2.907 163s supply_15 80.9 84.8 12.430 163s supply_16 -193.5 -209.7 -31.948 163s supply_17 -73.6 -92.7 -14.264 163s supply_18 -129.7 -118.7 -23.101 163s supply_19 94.1 79.3 16.863 163s supply_20 27.1 22.1 4.744 163s > estfun( fit3slsd[[ 5 ]]$e1w, residFit = FALSE ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s demand_1 0.89947 85.649 78.613 -0.57123 163s demand_2 0.00817 0.811 0.797 -0.00519 163s demand_3 1.94109 192.071 187.703 -1.23275 163s demand_4 1.44439 144.277 141.839 -0.91731 163s demand_5 1.10477 107.119 110.256 -0.70162 163s demand_6 0.67950 66.596 68.290 -0.43154 163s demand_7 0.96428 96.352 99.513 -0.61239 163s demand_8 -1.80100 -181.402 -194.148 1.14378 163s demand_9 -1.09741 -105.536 -106.009 0.69694 163s demand_10 0.93145 88.611 82.806 -0.59155 163s demand_11 -0.13250 -12.551 -9.951 0.08415 163s demand_12 -0.98743 -97.798 -75.933 0.62710 163s demand_13 -0.32371 -32.932 -27.386 0.20558 163s demand_14 -0.09978 -10.112 -9.040 0.06337 163s demand_15 0.56754 57.219 58.513 -0.36043 163s demand_16 -2.64753 -267.185 -278.255 1.68140 163s demand_17 -1.65258 -157.934 -159.308 1.04952 163s demand_18 -1.17988 -122.919 -123.179 0.74932 163s demand_19 1.26015 135.883 139.499 -0.80030 163s demand_20 0.12101 13.783 15.380 -0.07685 163s supply_1 -0.39424 -37.540 -34.456 0.40779 163s supply_2 -0.17503 -17.388 -17.083 0.18104 163s supply_3 -1.29167 -127.811 -124.905 1.33607 163s supply_4 -0.90312 -90.210 -88.686 0.93416 163s supply_5 -0.84242 -81.682 -84.074 0.87137 163s supply_6 -0.46834 -45.901 -47.069 0.48444 163s supply_7 -0.80988 -80.925 -83.580 0.83772 163s supply_8 1.72577 173.825 186.038 -1.78508 163s supply_9 1.10899 106.650 107.128 -1.14710 163s supply_10 -0.94120 -89.538 -83.673 0.97355 163s supply_11 0.22943 21.733 17.231 -0.23732 163s supply_12 0.60019 59.445 46.155 -0.62082 163s supply_13 0.37695 38.348 31.890 -0.38990 163s supply_14 -0.28729 -29.116 -26.029 0.29717 163s supply_15 -0.94355 -95.128 -97.280 0.97597 163s supply_16 2.01917 203.771 212.215 -2.08856 163s supply_17 0.74286 70.994 71.612 -0.76839 163s supply_18 1.40908 146.797 147.108 -1.45750 163s supply_19 -0.87479 -94.329 -96.840 0.90486 163s supply_20 -0.28090 -31.995 -35.702 0.29055 163s supply_price supply_farmPrice supply_trend 163s demand_1 -56.911 -55.981 -0.5712 163s demand_2 -0.545 -0.514 -0.0104 163s demand_3 -127.940 -122.166 -3.6983 163s demand_4 -95.886 -89.988 -3.6692 163s demand_5 -69.215 -77.739 -3.5081 163s demand_6 -43.002 -46.692 -2.5892 163s demand_7 -62.447 -64.669 -4.2868 163s demand_8 116.934 125.587 9.1502 163s demand_9 65.935 75.758 6.2725 163s demand_10 -54.848 -59.510 -5.9155 163s demand_11 7.776 6.816 0.9257 163s demand_12 62.030 43.019 7.5252 163s demand_13 21.003 14.576 2.6726 163s demand_14 6.354 5.158 0.8871 163s demand_15 -35.186 -36.872 -5.4065 163s demand_16 162.914 176.547 26.9023 163s demand_17 92.041 115.972 17.8418 163s demand_18 75.726 69.312 13.4878 163s demand_19 -84.882 -71.467 -15.2057 163s demand_20 -8.791 -7.147 -1.5370 163s supply_1 40.627 39.963 0.4078 163s supply_2 19.031 17.941 0.3621 163s supply_3 138.662 132.404 4.0082 163s supply_4 97.648 91.641 3.7366 163s supply_5 85.962 96.548 4.3569 163s supply_6 48.274 52.416 2.9066 163s supply_7 85.424 88.463 5.8640 163s supply_8 -182.496 -196.002 -14.2806 163s supply_9 -108.523 -124.690 -10.3239 163s supply_10 90.266 97.939 9.7355 163s supply_11 -21.929 -19.223 -2.6105 163s supply_12 -61.410 -42.588 -7.4498 163s supply_13 -39.834 -27.644 -5.0687 163s supply_14 29.799 24.189 4.1603 163s supply_15 95.276 99.842 14.6396 163s supply_16 -202.365 -219.299 -33.4170 163s supply_17 -67.387 -84.908 -13.0627 163s supply_18 -147.294 -134.819 -26.2351 163s supply_19 95.972 80.804 17.1923 163s supply_20 33.238 27.021 5.8111 163s > 163s > round( colSums( estfun( fit3slsd[[ 5 ]]$e1w ) ), digits = 7 ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0.0 0.0 0.0 0.0 163s supply_price supply_farmPrice supply_trend 163s 38.6 0.0 -52.4 163s > round( colSums( estfun( fit3slsd[[ 5 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0 0 0 0 163s supply_price supply_farmPrice supply_trend 163s 0 0 0 163s > 163s > round( colSums( estfun( fit3slsd[[ 4 ]]$e1w ) ), digits = 7 ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0.00 0.00 0.00 0.00 163s supply_price supply_farmPrice supply_trend 163s 9.67 0.00 -13.12 163s > round( colSums( estfun( fit3slsd[[ 4 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0.0 0.0 0.0 0.0 163s supply_price supply_farmPrice supply_trend 163s -28.9 0.0 39.3 163s > 163s > round( colSums( estfun( fit3slsd[[ 3 ]]$e1w ) ), digits = 7 ) 163s Warning message: 163s In estfun.systemfit(fit3slsd[[3]]$e1w) : 163s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0.00 0.00 0.00 0.00 163s supply_price supply_farmPrice supply_trend 163s 9.67 0.00 -13.12 163s > round( colSums( estfun( fit3slsd[[ 3 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 163s Warning message: 163s In estfun.systemfit(fit3slsd[[3]]$e1w, residFit = FALSE) : 163s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0.0 0.0 0.0 0.0 163s supply_price supply_farmPrice supply_trend 163s -28.9 0.0 39.3 163s > 163s > round( colSums( estfun( fit3slsd[[ 2 ]]$e1w ) ), digits = 7 ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0.0 0.0 0.0 0.0 163s supply_price supply_farmPrice supply_trend 163s 38.6 0.0 -52.4 163s Warning message: 163s In estfun.systemfit(fit3slsd[[2]]$e1w) : 163s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 163s > round( colSums( estfun( fit3slsd[[ 2 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0 0 0 0 163s supply_price supply_farmPrice supply_trend 163s 0 0 0 163s > 163s > round( colSums( estfun( fit3slsd[[ 1 ]]$e1w ) ), digits = 7 ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0 0 0 0 163s supply_price supply_farmPrice supply_trend 163s 0 0 0 163s > round( colSums( estfun( fit3slsd[[ 1 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 163s Warning message: 163s In estfun.systemfit(fit3slsd[[1]]$e1w, residFit = FALSE) : 163s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s 0.0 0.0 0.0 0.0 163s supply_price supply_farmPrice supply_trend 163s -38.6 0.0 52.4 163s > 163s > 163s > ## **************** bread ************************ 163s > bread( fit3sls[[ 1 ]]$e1 ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s [1,] 2509.59 -26.9369 1.9721 2525.8 163s [2,] -26.94 0.3724 -0.1057 -14.1 163s [3,] 1.97 -0.1057 0.0881 -11.3 163s [4,] 2525.80 -14.1479 -11.2987 5658.1 163s [5,] -27.01 0.2401 0.0307 -43.3 163s [6,] 1.64 -0.0877 0.0732 -11.8 163s [7,] 2.47 -0.1324 0.1104 -16.4 163s supply_price supply_farmPrice supply_trend 163s [1,] -27.0066 1.6369 2.4699 163s [2,] 0.2401 -0.0877 -0.1324 163s [3,] 0.0307 0.0732 0.1104 163s [4,] -43.3336 -11.7989 -16.3581 163s [5,] 0.3974 0.0325 0.0428 163s [6,] 0.0325 0.0774 0.1019 163s [7,] 0.0428 0.1019 0.2125 163s > 163s > bread( fit3sls[[ 2 ]]$e1e ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s [1,] 2133.15 -22.8963 1.6763 2082.83 163s [2,] -22.90 0.3165 -0.0898 -11.67 163s [3,] 1.68 -0.0898 0.0749 -9.32 163s [4,] 2082.83 -11.6667 -9.3172 4526.47 163s [5,] -22.27 0.1980 0.0253 -34.67 163s [6,] 1.35 -0.0723 0.0603 -9.44 163s [7,] 2.04 -0.1091 0.0910 -13.09 163s supply_price supply_farmPrice supply_trend 163s [1,] -22.2702 1.3498 2.0367 163s [2,] 0.1980 -0.0723 -0.1091 163s [3,] 0.0253 0.0603 0.0910 163s [4,] -34.6668 -9.4391 -13.0865 163s [5,] 0.3179 0.0260 0.0342 163s [6,] 0.0260 0.0619 0.0815 163s [7,] 0.0342 0.0815 0.1700 163s > 163s > bread( fit3sls[[ 3 ]]$e1c ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s [1,] 2509.59 -26.9369 1.9721 2610.8 163s [2,] -26.94 0.3724 -0.1057 -14.6 163s [3,] 1.97 -0.1057 0.0881 -11.7 163s [4,] 2610.83 -14.6243 -11.6791 5650.4 163s [5,] -27.92 0.2482 0.0317 -43.3 163s [6,] 1.69 -0.0907 0.0756 -11.7 163s [7,] 2.55 -0.1368 0.1141 -16.7 163s supply_price supply_farmPrice supply_trend 163s [1,] -27.9159 1.6920 2.5531 163s [2,] 0.2482 -0.0907 -0.1368 163s [3,] 0.0317 0.0756 0.1141 163s [4,] -43.3005 -11.7199 -16.6696 163s [5,] 0.3972 0.0321 0.0441 163s [6,] 0.0321 0.0766 0.1051 163s [7,] 0.0441 0.1051 0.1999 163s > 163s > bread( fit3sls[[ 4 ]]$e1wc ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s [1,] 2509.59 -26.9369 1.9721 2610.8 163s [2,] -26.94 0.3724 -0.1057 -14.6 163s [3,] 1.97 -0.1057 0.0881 -11.7 163s [4,] 2610.83 -14.6243 -11.6791 5650.4 163s [5,] -27.92 0.2482 0.0317 -43.3 163s [6,] 1.69 -0.0907 0.0756 -11.7 163s [7,] 2.55 -0.1368 0.1141 -16.7 163s supply_price supply_farmPrice supply_trend 163s [1,] -27.9159 1.6920 2.5531 163s [2,] 0.2482 -0.0907 -0.1368 163s [3,] 0.0317 0.0756 0.1141 163s [4,] -43.3005 -11.7199 -16.6696 163s [5,] 0.3972 0.0321 0.0441 163s [6,] 0.0321 0.0766 0.1051 163s [7,] 0.0441 0.1051 0.1999 163s > 163s > bread( fit3slsd[[ 5 ]]$e1w ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s [1,] 4967.14 -60.707 11.4076 1773.52 163s [2,] -60.71 0.839 -0.2382 -6.24 163s [3,] 11.41 -0.238 0.1273 -11.71 163s [4,] 1773.52 -6.236 -11.7103 5325.96 163s [5,] -21.83 0.185 0.0346 -37.94 163s [6,] 6.07 -0.141 0.0826 -13.55 163s [7,] -16.09 0.136 0.0255 -20.05 163s supply_price supply_farmPrice supply_trend 163s [1,] -21.8336 6.0740 -16.0922 163s [2,] 0.1845 -0.1413 0.1360 163s [3,] 0.0346 0.0826 0.0255 163s [4,] -37.9350 -13.5483 -20.0519 163s [5,] 0.3216 0.0453 0.1323 163s [6,] 0.0453 0.0885 0.0440 163s [7,] 0.1323 0.0440 0.2443 163s > 163s > bread( fit3slsd[[ 4 ]]$e1w ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s [1,] 4967.14 -60.707 11.4076 1773.52 163s [2,] -60.71 0.839 -0.2382 -6.24 163s [3,] 11.41 -0.238 0.1273 -11.71 163s [4,] 1773.52 -6.236 -11.7103 5325.96 163s [5,] -21.83 0.185 0.0346 -37.94 163s [6,] 6.07 -0.141 0.0826 -13.55 163s [7,] -16.09 0.136 0.0255 -20.05 163s supply_price supply_farmPrice supply_trend 163s [1,] -21.8336 6.0740 -16.0922 163s [2,] 0.1845 -0.1413 0.1360 163s [3,] 0.0346 0.0826 0.0255 163s [4,] -37.9350 -13.5483 -20.0519 163s [5,] 0.3216 0.0453 0.1323 163s [6,] 0.0453 0.0885 0.0440 163s [7,] 0.1323 0.0440 0.2443 163s > 163s > bread( fit3slsd[[ 3 ]]$e1w ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s [1,] 4967.14 -60.707 11.4076 1773.52 163s [2,] -60.71 0.839 -0.2382 -6.24 163s [3,] 11.41 -0.238 0.1273 -11.71 163s [4,] 1773.52 -6.236 -11.7103 5325.96 163s [5,] -21.83 0.185 0.0346 -37.94 163s [6,] 6.07 -0.141 0.0826 -13.55 163s [7,] -16.09 0.136 0.0255 -20.05 163s supply_price supply_farmPrice supply_trend 163s [1,] -21.8336 6.0740 -16.0922 163s [2,] 0.1845 -0.1413 0.1360 163s [3,] 0.0346 0.0826 0.0255 163s [4,] -37.9350 -13.5483 -20.0519 163s [5,] 0.3216 0.0453 0.1323 163s [6,] 0.0453 0.0885 0.0440 163s [7,] 0.1323 0.0440 0.2443 163s > 163s > bread( fit3slsd[[ 2 ]]$e1w ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s [1,] 4967.14 -60.707 11.4076 1773.52 163s [2,] -60.71 0.839 -0.2382 -6.24 163s [3,] 11.41 -0.238 0.1273 -11.71 163s [4,] 1773.52 -6.236 -11.7103 5325.96 163s [5,] -21.83 0.185 0.0346 -37.94 163s [6,] 6.07 -0.141 0.0826 -13.55 163s [7,] -16.09 0.136 0.0255 -20.05 163s supply_price supply_farmPrice supply_trend 163s [1,] -21.8336 6.0740 -16.0922 163s [2,] 0.1845 -0.1413 0.1360 163s [3,] 0.0346 0.0826 0.0255 163s [4,] -37.9350 -13.5483 -20.0519 163s [5,] 0.3216 0.0453 0.1323 163s [6,] 0.0453 0.0885 0.0440 163s [7,] 0.1323 0.0440 0.2443 163s > 163s > bread( fit3slsd[[ 1 ]]$e1w ) 163s demand_(Intercept) demand_price demand_income supply_(Intercept) 163s [1,] 4967.14 -60.707 11.4076 1773.52 163s [2,] -60.71 0.839 -0.2382 -6.24 163s [3,] 11.41 -0.238 0.1273 -11.71 163s [4,] 1773.52 -6.236 -11.7103 5325.96 163s [5,] -21.83 0.185 0.0346 -37.94 163s [6,] 6.07 -0.141 0.0826 -13.55 163s [7,] -16.09 0.136 0.0255 -20.05 163s supply_price supply_farmPrice supply_trend 163s [1,] -21.8336 6.0740 -16.0922 163s [2,] 0.1845 -0.1413 0.1360 163s [3,] 0.0346 0.0826 0.0255 163s [4,] -37.9350 -13.5483 -20.0519 163s [5,] 0.3216 0.0453 0.1323 163s [6,] 0.0453 0.0885 0.0440 163s [7,] 0.1323 0.0440 0.2443 163s > 163s BEGIN TEST test_hausman.R 163s 163s R version 4.3.2 (2023-10-31) -- "Eye Holes" 163s Copyright (C) 2023 The R Foundation for Statistical Computing 163s Platform: x86_64-pc-linux-gnu (64-bit) 163s 163s R is free software and comes with ABSOLUTELY NO WARRANTY. 163s You are welcome to redistribute it under certain conditions. 163s Type 'license()' or 'licence()' for distribution details. 163s 163s R is a collaborative project with many contributors. 163s Type 'contributors()' for more information and 163s 'citation()' on how to cite R or R packages in publications. 163s 163s Type 'demo()' for some demos, 'help()' for on-line help, or 163s 'help.start()' for an HTML browser interface to help. 163s Type 'q()' to quit R. 163s 163s > library( "systemfit" ) 163s Loading required package: Matrix 164s Loading required package: car 164s Loading required package: carData 164s Loading required package: lmtest 164s Loading required package: zoo 164s 164s Attaching package: ‘zoo’ 164s 164s The following objects are masked from ‘package:base’: 164s 164s as.Date, as.Date.numeric 164s 164s 164s Please cite the 'systemfit' package as: 164s 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/. 164s 164s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 164s https://r-forge.r-project.org/projects/systemfit/ 164s > options( digits = 5 ) 164s > 164s > data( "Kmenta" ) 164s > useMatrix <- FALSE 164s > 164s > eqDemand <- consump ~ price + income 164s > eqSupply <- consump ~ price + farmPrice + trend 164s > inst <- ~ income + farmPrice + trend 164s > eqSystem <- list( demand = eqDemand, supply = eqSupply ) 164s > restrm <- matrix(0,1,7) # restriction matrix "R" 164s > restrm[1,3] <- 1 164s > restrm[1,7] <- -1 164s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 164s > restr2m[1,3] <- 1 164s > restr2m[1,7] <- -1 164s > restr2m[2,2] <- -1 164s > restr2m[2,5] <- 1 164s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 164s > tc <- matrix(0,7,6) 164s > tc[1,1] <- 1 164s > tc[2,2] <- 1 164s > tc[3,3] <- 1 164s > tc[4,4] <- 1 164s > tc[5,5] <- 1 164s > tc[6,6] <- 1 164s > tc[7,3] <- 1 164s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 164s > restr3m[1,2] <- -1 164s > restr3m[1,5] <- 1 164s > restr3q <- c( 0.5 ) # restriction vector "q" 2 164s > 164s > 164s > ## ******************* unrestricted estimation ***************** 164s > ## ******************** default estimation ********************* 164s > fit2sls1 <- systemfit( eqSystem, "2SLS", data = Kmenta, inst = inst, 164s + useMatrix = useMatrix ) 164s > fit3sls1 <- systemfit( eqSystem, "3SLS", data = Kmenta, inst = inst, 164s + useMatrix = useMatrix ) 164s > print( hausman.systemfit( fit2sls1, fit3sls1 ) ) 164s 164s Hausman specification test for consistency of the 3SLS estimation 164s 164s data: Kmenta 164s Hausman = 2.54, df = 7, p-value = 0.92 164s 164s > 164s > ## ************** 2SLS estimation with singleEqSigma = FALSE ***************** 164s > fit2sls1s <- systemfit( eqSystem, "2SLS", data = Kmenta, inst = inst, 164s + singleEqSigma = FALSE, useMatrix = useMatrix ) 164s > print( hausman.systemfit( fit2sls1s, fit3sls1 ) ) 164s 164s Hausman specification test for consistency of the 3SLS estimation 164s 164s data: Kmenta 164s Hausman = 3.28, df = 7, p-value = 0.86 164s 164s > 164s > ## ******************* estimations with methodResidCov = 0 ***************** 164s > fit2sls1r <- systemfit( eqSystem, "2SLS", data = Kmenta, inst = inst, 164s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 164s > fit3sls1r <- systemfit( eqSystem, "3SLS", data = Kmenta, inst = inst, 164s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 164s > print( hausman.systemfit( fit2sls1r, fit3sls1r ) ) 164s 164s Hausman specification test for consistency of the 3SLS estimation 164s 164s data: Kmenta 164s Hausman = 2.98, df = 7, p-value = 0.89 164s 164s > 164s > 164s > ## ********************* estimation with restriction ******************** 164s > ## *********************** default estimation *********************** 164s > fit2sls2 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restrm, 164s + inst = inst, useMatrix = useMatrix ) 164s > fit3sls2 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restrm, 164s + inst = inst, useMatrix = useMatrix ) 164s > # print( hausman.systemfit( fit2sls2, fit3sls2 ) ) 164s > 164s > ## ************* 2SLS estimation with singleEqSigma = TRUE ***************** 164s > fit2sls2s <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restrm, 164s + inst = inst, singleEqSigma = TRUE, useMatrix = useMatrix ) 164s > # print( hausman.systemfit( fit2sls2s, fit3sls2 ) ) 164s > 164s > ## ********************* estimations with methodResidCov = 0 ************** 164s > fit2sls2r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restrm, 164s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 164s > fit3sls2r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restrm, 164s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 164s > # print( hausman.systemfit( fit2sls2r, fit3sls2r ) ) 164s > 164s > 164s > ## ****************** estimation with restriction via restrict.regMat ****************** 164s > ## ********************** default estimation ******************** 164s > fit2sls3 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.regMat = tc, 164s + inst = inst, useMatrix = useMatrix ) 164s > fit3sls3 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.regMat = tc, 164s + inst = inst, useMatrix = useMatrix ) 164s > print( hausman.systemfit( fit2sls3, fit3sls3 ) ) 164s 164s Hausman specification test for consistency of the 3SLS estimation 164s 164s data: Kmenta 164s Hausman = -0.281, df = 6, p-value = 1 164s 164s > 164s > ## ******************* estimations with methodResidCov = 0 ******* 164s > fit2sls3r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.regMat = tc, 164s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 164s > fit3sls3r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.regMat = tc, 164s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 164s > print( hausman.systemfit( fit2sls3r, fit3sls3r ) ) 164s 164s Hausman specification test for consistency of the 3SLS estimation 164s 164s data: Kmenta 164s Hausman = -0.0132, df = 6, p-value = 1 164s 164s > 164s > 164s > ## ***************** estimations with 2 restrictions ******************* 164s > ## *********************** default estimations ************** 164s > fit2sls4 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr2m, 164s + restrict.rhs = restr2q, inst = inst, useMatrix = useMatrix ) 164s > fit3sls4 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr2m, 164s + restrict.rhs = restr2q, inst = inst, useMatrix = useMatrix ) 164s > # print( hausman.systemfit( fit2sls4, fit3sls4 ) ) 164s > 164s > ## ***************** estimations with methodResidCov = 0 ************** 164s > fit2sls4r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr2m, 164s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 164s + useMatrix = useMatrix ) 164s > fit3sls4r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr2m, 164s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 164s + useMatrix = useMatrix ) 164s > # print( hausman.systemfit( fit2sls4r, fit3sls4r ) ) 164s > 164s > 164s > ## *********** estimations with 2 restrictions via R and restrict.regMat *************** 164s > ## ***************** default estimations ******************* 164s > fit2sls5 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr3m, 164s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 164s + useMatrix = useMatrix ) 164s > fit3sls5 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr3m, 164s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 164s + useMatrix = useMatrix ) 164s > # print( hausman.systemfit( fit2sls5, fit3sls5 ) ) 164s > 164s > ## ************* estimations with methodResidCov = 0 ********* 164s > fit2sls5r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr3m, 164s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 164s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 164s > fit3sls5r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr3m, 164s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 164s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 164s > # print( hausman.systemfit( fit2sls5r, fit3sls5r ) ) 164s > 164s BEGIN TEST test_ols.R 164s 164s R version 4.3.2 (2023-10-31) -- "Eye Holes" 164s Copyright (C) 2023 The R Foundation for Statistical Computing 164s Platform: x86_64-pc-linux-gnu (64-bit) 164s 164s R is free software and comes with ABSOLUTELY NO WARRANTY. 164s You are welcome to redistribute it under certain conditions. 164s Type 'license()' or 'licence()' for distribution details. 164s 164s R is a collaborative project with many contributors. 164s Type 'contributors()' for more information and 164s 'citation()' on how to cite R or R packages in publications. 164s 164s Type 'demo()' for some demos, 'help()' for on-line help, or 164s 'help.start()' for an HTML browser interface to help. 164s Type 'q()' to quit R. 164s 164s > library( systemfit ) 164s Loading required package: Matrix 165s Loading required package: car 165s Loading required package: carData 165s Loading required package: lmtest 165s Loading required package: zoo 165s 165s Attaching package: ‘zoo’ 165s 165s The following objects are masked from ‘package:base’: 165s 165s as.Date, as.Date.numeric 165s 165s 165s Please cite the 'systemfit' package as: 165s 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/. 165s 165s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 165s https://r-forge.r-project.org/projects/systemfit/ 165s > options( digits = 3 ) 165s > 165s > data( "Kmenta" ) 165s > useMatrix <- FALSE 165s > 165s > demand <- consump ~ price + income 165s > supply <- consump ~ price + farmPrice + trend 165s > system <- list( demand = demand, supply = supply ) 165s > restrm <- matrix(0,1,7) # restriction matrix "R" 165s > restrm[1,3] <- 1 165s > restrm[1,7] <- -1 165s > restrict <- "demand_income - supply_trend = 0" 165s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 165s > restr2m[1,3] <- 1 165s > restr2m[1,7] <- -1 165s > restr2m[2,2] <- -1 165s > restr2m[2,5] <- 1 165s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 165s > restrict2 <- c( "demand_income - supply_trend = 0", 165s + "- demand_price + supply_price = 0.5" ) 165s > tc <- matrix(0,7,6) 165s > tc[1,1] <- 1 165s > tc[2,2] <- 1 165s > tc[3,3] <- 1 165s > tc[4,4] <- 1 165s > tc[5,5] <- 1 165s > tc[6,6] <- 1 165s > tc[7,3] <- 1 165s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 165s > restr3m[1,2] <- -1 165s > restr3m[1,5] <- 1 165s > restr3q <- c( 0.5 ) # restriction vector "q" 2 165s > restrict3 <- "- C2 + C5 = 0.5" 165s > 165s > # It is not possible to estimate OLS with systemfit 165s > # exactly as EViews does, because EViews uses 165s > # methodResidCov == "geomean" for the coefficient covariance matrix and 165s > # methodResidCov == "noDfCor" for the residual covariance matrix, while 165s > # systemfit uses always the same formulas for both calculations. 165s > 165s > ## ******* single-equation OLS estimations ********************* 165s > lmDemand <- lm( demand, data = Kmenta ) 165s > lmSupply <- lm( supply, data = Kmenta ) 165s > 165s > ## *************** OLS estimation ************************ 165s > ## ********** OLS estimation (default) ******************** 165s > fitols1 <- systemfit( system, "OLS", data = Kmenta, useMatrix = useMatrix ) 165s > print( summary( fitols1 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 33 156 4.43 0.709 0.558 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 63.3 3.73 1.93 0.764 0.736 165s supply 20 16 92.6 5.78 2.40 0.655 0.590 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.73 4.14 165s supply 4.14 5.78 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.891 165s supply 0.891 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 165s price -0.3163 0.0907 -3.49 0.0028 ** 165s income 0.3346 0.0454 7.37 1.1e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.93 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 165s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 165s price 0.1604 0.0949 1.69 0.11039 165s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 165s trend 0.2483 0.0975 2.55 0.02157 * 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.405 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 165s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 165s 165s > nobs( fitols1 ) 165s [1] 40 165s > all.equal( coef( fitols1 ), c( coef( lmDemand ), coef( lmSupply ) ), 165s + check.attributes = FALSE ) 165s [1] TRUE 165s > all.equal( coef( summary( fitols1 ) ), 165s + rbind( coef( summary( lmDemand ) ), coef( summary( lmSupply ) ) ), 165s + check.attributes = FALSE ) 165s [1] TRUE 165s > all.equal( vcov( fitols1 ), 165s + as.matrix( bdiag( vcov( lmDemand ), vcov( lmSupply ) ) ), 165s + check.attributes = FALSE ) 165s [1] TRUE 165s > 165s > ## ********** OLS estimation (no singleEqSigma=F) ****************** 165s > fitols1s <- systemfit( system, "OLS", data = Kmenta, 165s + singleEqSigma = FALSE, useMatrix = useMatrix ) 165s > print( summary( fitols1s ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 33 156 4.43 0.709 0.558 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 63.3 3.73 1.93 0.764 0.736 165s supply 20 16 92.6 5.78 2.40 0.655 0.590 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.73 4.14 165s supply 4.14 5.78 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.891 165s supply 0.891 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.8954 8.4671 11.80 1.3e-09 *** 165s price -0.3163 0.1021 -3.10 0.0065 ** 165s income 0.3346 0.0511 6.54 5.0e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.93 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 165s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 58.2754 10.3587 5.63 3.8e-05 *** 165s price 0.1604 0.0857 1.87 0.080 . 165s farmPrice 0.2481 0.0417 5.94 2.1e-05 *** 165s trend 0.2483 0.0881 2.82 0.012 * 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.405 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 165s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 165s 165s > all.equal( coef( fitols1s ), c( coef( lmDemand ), coef( lmSupply ) ), 165s + check.attributes = FALSE ) 165s [1] TRUE 165s > 165s > ## **************** OLS (useDfSys=T) *********************** 165s > print( summary( fitols1, useDfSys = TRUE ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 33 156 4.43 0.709 0.558 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 63.3 3.73 1.93 0.764 0.736 165s supply 20 16 92.6 5.78 2.40 0.655 0.590 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.73 4.14 165s supply 4.14 5.78 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.891 165s supply 0.891 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.8954 7.5194 13.29 8.4e-15 *** 165s price -0.3163 0.0907 -3.49 0.0014 ** 165s income 0.3346 0.0454 7.37 1.8e-08 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.93 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 165s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 58.2754 11.4629 5.08 1.4e-05 *** 165s price 0.1604 0.0949 1.69 0.100 165s farmPrice 0.2481 0.0462 5.37 6.1e-06 *** 165s trend 0.2483 0.0975 2.55 0.016 * 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.405 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 165s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 165s 165s > 165s > ## **************** OLS (methodResidCov="noDfCor") *********************** 165s > fitols1r <- systemfit( system, "OLS", data = Kmenta, 165s + methodResidCov = "noDfCor", x = TRUE, 165s + useMatrix = useMatrix ) 165s > print( summary( fitols1r ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 33 156 3.02 0.709 0.537 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 63.3 3.73 1.93 0.764 0.736 165s supply 20 16 92.6 5.78 2.40 0.655 0.590 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.17 3.41 165s supply 3.41 4.63 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.891 165s supply 0.891 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.8954 6.9325 14.41 5.8e-11 *** 165s price -0.3163 0.0836 -3.78 0.0015 ** 165s income 0.3346 0.0419 7.99 3.7e-07 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.93 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 165s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 58.2754 10.2527 5.68 3.4e-05 *** 165s price 0.1604 0.0849 1.89 0.077 . 165s farmPrice 0.2481 0.0413 6.01 1.8e-05 *** 165s trend 0.2483 0.0872 2.85 0.012 * 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.405 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 165s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 165s 165s > all.equal( coef( fitols1r ), c( coef( lmDemand ), coef( lmSupply ) ), 165s + check.attributes = FALSE ) 165s [1] TRUE 165s > 165s > ## ******** OLS (methodResidCov="noDfCor", singleEqSigma=F) *********** 165s > fitols1rs <- systemfit( system, "OLS", data = Kmenta, 165s + methodResidCov = "noDfCor", singleEqSigma = FALSE, 165s + useMatrix = useMatrix ) 165s > print( summary( fitols1rs ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 33 156 3.02 0.709 0.537 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 63.3 3.73 1.93 0.764 0.736 165s supply 20 16 92.6 5.78 2.40 0.655 0.590 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.17 3.41 165s supply 3.41 4.63 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.891 165s supply 0.891 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.8954 7.6907 12.99 3.0e-10 *** 165s price -0.3163 0.0927 -3.41 0.0033 ** 165s income 0.3346 0.0465 7.20 1.5e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.93 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 165s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 58.2754 9.4088 6.19 1.3e-05 *** 165s price 0.1604 0.0779 2.06 0.0561 . 165s farmPrice 0.2481 0.0379 6.55 6.7e-06 *** 165s trend 0.2483 0.0800 3.10 0.0068 ** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.405 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 165s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 165s 165s > all.equal( coef( fitols1rs ), c( coef( lmDemand ), coef( lmSupply ) ), 165s + check.attributes = FALSE ) 165s [1] TRUE 165s > 165s > ## **************** OLS (methodResidCov="Theil" ) *********************** 165s > fitols1r <- systemfit( system, "OLS", data = Kmenta, 165s + methodResidCov = "Theil", x = TRUE, 165s + useMatrix = useMatrix ) 165s > print( summary( fitols1r ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 33 156 3.26 0.709 0.503 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 63.3 3.73 1.93 0.764 0.736 165s supply 20 16 92.6 5.78 2.40 0.655 0.590 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.73 4.28 165s supply 4.28 5.78 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.891 165s supply 0.891 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 165s price -0.3163 0.0907 -3.49 0.0028 ** 165s income 0.3346 0.0454 7.37 1.1e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.93 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 165s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 165s price 0.1604 0.0949 1.69 0.11039 165s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 165s trend 0.2483 0.0975 2.55 0.02157 * 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.405 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 165s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 165s 165s > all.equal( coef( fitols1r ), c( coef( lmDemand ), coef( lmSupply ) ), 165s + check.attributes = FALSE ) 165s [1] TRUE 165s > 165s > ## **************** OLS (methodResidCov="max") *********************** 165s > fitols1r <- systemfit( system, "OLS", data = Kmenta, 165s + methodResidCov = "max", x = TRUE, 165s + useMatrix = useMatrix ) 165s > print( summary( fitols1r ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 33 156 3.37 0.709 0.509 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 63.3 3.73 1.93 0.764 0.736 165s supply 20 16 92.6 5.78 2.40 0.655 0.590 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.73 4.26 165s supply 4.26 5.78 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.891 165s supply 0.891 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 165s price -0.3163 0.0907 -3.49 0.0028 ** 165s income 0.3346 0.0454 7.37 1.1e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.93 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 165s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 165s price 0.1604 0.0949 1.69 0.11039 165s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 165s trend 0.2483 0.0975 2.55 0.02157 * 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.405 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 165s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 165s 165s > 165s > ## ******** OLS (methodResidCov="max", singleEqSigma=F) *********** 165s > fitols1rs <- systemfit( system, "OLS", data = Kmenta, 165s + methodResidCov = "max", singleEqSigma = FALSE, 165s + useMatrix = useMatrix ) 165s > print( summary( fitols1rs ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 33 156 3.37 0.709 0.509 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 63.3 3.73 1.93 0.764 0.736 165s supply 20 16 92.6 5.78 2.40 0.655 0.590 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.73 4.26 165s supply 4.26 5.78 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.891 165s supply 0.891 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.8954 8.4671 11.80 1.3e-09 *** 165s price -0.3163 0.1021 -3.10 0.0065 ** 165s income 0.3346 0.0511 6.54 5.0e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.93 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 165s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 58.2754 10.3587 5.63 3.8e-05 *** 165s price 0.1604 0.0857 1.87 0.080 . 165s farmPrice 0.2481 0.0417 5.94 2.1e-05 *** 165s trend 0.2483 0.0881 2.82 0.012 * 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.405 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 165s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 165s 165s > 165s > 165s > ## ********* OLS with cross-equation restriction ************ 165s > ## ****** OLS with cross-equation restriction (default) ********* 165s > fitols2 <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.matrix = restrm, useMatrix = useMatrix ) 165s > print( summary( fitols2 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 2.5 0.703 0.608 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.78 4.47 165s supply 4.47 5.94 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 8.4225 11.82 1.4e-13 *** 165s price -0.2917 0.0975 -2.99 0.0051 ** 165s income 0.3129 0.0441 7.10 3.3e-08 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 10.0721 5.60 2.9e-06 *** 165s price 0.1639 0.0853 1.92 0.063 . 165s farmPrice 0.2571 0.0402 6.39 2.7e-07 *** 165s trend 0.3129 0.0441 7.10 3.3e-08 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > # the same with symbolically specified restrictions 165s > fitols2Sym <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.matrix = restrict, useMatrix = useMatrix ) 165s > all.equal( fitols2, fitols2Sym ) 165s [1] "Component “call”: target, current do not match when deparsed" 165s > 165s > ## ****** OLS with cross-equation restriction (singleEqSigma=T) ******* 165s > fitols2s <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.matrix = restrm, singleEqSigma = TRUE, 165s + useMatrix = useMatrix ) 165s > print( summary( fitols2s ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 2.5 0.703 0.608 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.78 4.47 165s supply 4.47 5.94 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 7.5640 13.16 6.7e-15 *** 165s price -0.2917 0.0887 -3.29 0.0023 ** 165s income 0.3129 0.0415 7.54 9.4e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 11.3165 4.98 1.8e-05 *** 165s price 0.1639 0.0960 1.71 0.097 . 165s farmPrice 0.2571 0.0451 5.69 2.1e-06 *** 165s trend 0.3129 0.0415 7.54 9.4e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > ## ****** OLS with cross-equation restriction (useDfSys=F) ******* 165s > print( summary( fitols2, useDfSys = FALSE ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 2.5 0.703 0.608 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.78 4.47 165s supply 4.47 5.94 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 8.4225 11.82 1.3e-09 *** 165s price -0.2917 0.0975 -2.99 0.0082 ** 165s income 0.3129 0.0441 7.10 1.8e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 10.0721 5.60 4.0e-05 *** 165s price 0.1639 0.0853 1.92 0.073 . 165s farmPrice 0.2571 0.0402 6.39 8.9e-06 *** 165s trend 0.3129 0.0441 7.10 2.5e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > ## ****** OLS with cross-equation restriction (methodResidCov="noDfCor") ******* 165s > fitols2r <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.matrix = restrm, methodResidCov = "noDfCor", 165s + useMatrix = useMatrix ) 165s > print( summary( fitols2r ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 1.7 0.703 0.577 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.21 3.68 165s supply 3.68 4.75 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 165s price -0.2917 0.0899 -3.25 0.0026 ** 165s income 0.3129 0.0406 7.70 5.9e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 165s price 0.1639 0.0786 2.08 0.045 * 165s farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 165s trend 0.3129 0.0406 7.70 5.9e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > ## ** OLS with cross-equation restriction (methodResidCov="noDfCor",singleEqSigma=T) *** 165s > fitols2rs <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.matrix = restrm, methodResidCov = "noDfCor", 165s + x = TRUE, useMatrix = useMatrix ) 165s > print( summary( fitols2rs ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 1.7 0.703 0.577 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.21 3.68 165s supply 3.68 4.75 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 165s price -0.2917 0.0899 -3.25 0.0026 ** 165s income 0.3129 0.0406 7.70 5.9e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 165s price 0.1639 0.0786 2.08 0.045 * 165s farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 165s trend 0.3129 0.0406 7.70 5.9e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > ## *** OLS with cross-equation restriction via restrict.regMat *** 165s > ## *** OLS with cross-equation restriction via restrict.regMat (default) *** 165s > fitols3 <- systemfit( system, "OLS", data = Kmenta, restrict.regMat = tc, 165s + x = TRUE, useMatrix = useMatrix ) 165s > print( summary( fitols3 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 2.5 0.703 0.608 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.78 4.47 165s supply 4.47 5.94 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 8.4225 11.82 1.4e-13 *** 165s price -0.2917 0.0975 -2.99 0.0051 ** 165s income 0.3129 0.0441 7.10 3.3e-08 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 10.0721 5.60 2.9e-06 *** 165s price 0.1639 0.0853 1.92 0.063 . 165s farmPrice 0.2571 0.0402 6.39 2.7e-07 *** 165s trend 0.3129 0.0441 7.10 3.3e-08 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > ## *** OLS with cross-equation restriction via restrict.regMat (singleEqSigma=T) *** 165s > fitols3s <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.regMat = tc, singleEqSigma = TRUE, useMatrix = useMatrix ) 165s > print( summary( fitols3s ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 2.5 0.703 0.608 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.78 4.47 165s supply 4.47 5.94 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 7.5640 13.16 6.7e-15 *** 165s price -0.2917 0.0887 -3.29 0.0023 ** 165s income 0.3129 0.0415 7.54 9.4e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 11.3165 4.98 1.8e-05 *** 165s price 0.1639 0.0960 1.71 0.097 . 165s farmPrice 0.2571 0.0451 5.69 2.1e-06 *** 165s trend 0.3129 0.0415 7.54 9.4e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > ## *** OLS with cross-equation restriction via restrict.regMat (useDfSys=F) *** 165s > print( summary( fitols3, useDfSys = FALSE ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 2.5 0.703 0.608 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.78 4.47 165s supply 4.47 5.94 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 8.4225 11.82 1.3e-09 *** 165s price -0.2917 0.0975 -2.99 0.0082 ** 165s income 0.3129 0.0441 7.10 1.8e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 10.0721 5.60 4.0e-05 *** 165s price 0.1639 0.0853 1.92 0.073 . 165s farmPrice 0.2571 0.0402 6.39 8.9e-06 *** 165s trend 0.3129 0.0441 7.10 2.5e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > ## *** OLS with cross-equation restriction via restrict.regMat (methodResidCov="noDfCor") *** 165s > fitols3r <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.regMat = tc, methodResidCov = "noDfCor", 165s + useMatrix = useMatrix ) 165s > print( summary( fitols3r ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 1.7 0.703 0.577 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.21 3.68 165s supply 3.68 4.75 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 165s price -0.2917 0.0899 -3.25 0.0026 ** 165s income 0.3129 0.0406 7.70 5.9e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 165s price 0.1639 0.0786 2.08 0.045 * 165s farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 165s trend 0.3129 0.0406 7.70 5.9e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > ## OLS with cross-equation restriction via restrict.regMat (methodResidCov="noDfCor",singleEqSigma=T) 165s > fitols3rs <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.regMat = tc, methodResidCov = "noDfCor", singleEqSigma = TRUE, 165s + useMatrix = useMatrix ) 165s > print( summary( fitols3rs ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 1.7 0.703 0.577 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.21 3.68 165s supply 3.68 4.75 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 6.9734 14.28 6.7e-16 *** 165s price -0.2917 0.0816 -3.57 0.0011 ** 165s income 0.3129 0.0381 8.22 1.4e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 10.1248 5.57 3.1e-06 *** 165s price 0.1639 0.0859 1.91 0.065 . 165s farmPrice 0.2571 0.0404 6.36 2.9e-07 *** 165s trend 0.3129 0.0381 8.22 1.4e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > ## ********* OLS with 2 cross-equation restrictions *********** 165s > ## ********* OLS with 2 cross-equation restrictions (default) *********** 165s > fitols4 <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 165s + restrict.rhs = restr2q, useMatrix = useMatrix ) 165s > print( summary( fitols4 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 2.69 0.702 0.605 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.76 4.46 165s supply 4.46 5.99 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.938 165s supply 0.938 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.4817 6.1599 16.47 < 2e-16 *** 165s price -0.3168 0.0629 -5.04 1.4e-05 *** 165s income 0.3189 0.0399 8.00 2.0e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.94 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.1494 7.5515 7.17 2.3e-08 *** 165s price 0.1832 0.0629 2.91 0.0062 ** 165s farmPrice 0.2595 0.0391 6.64 1.1e-07 *** 165s trend 0.3189 0.0399 8.00 2.0e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.447 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 165s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 165s 165s > # the same with symbolically specified restrictions 165s > fitols4Sym <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.matrix = restrict2, useMatrix = useMatrix ) 165s > all.equal( fitols4, fitols4Sym ) 165s [1] "Component “call”: target, current do not match when deparsed" 165s > 165s > ## ****** OLS with 2 cross-equation restrictions (singleEqSigma=T) ******* 165s > fitols4s <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 165s + restrict.rhs = restr2q, singleEqSigma = TRUE, x = TRUE, 165s + useMatrix = useMatrix ) 165s > print( summary( fitols4s ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 2.69 0.702 0.605 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.76 4.46 165s supply 4.46 5.99 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.938 165s supply 0.938 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.4817 6.0474 16.78 < 2e-16 *** 165s price -0.3168 0.0648 -4.89 2.3e-05 *** 165s income 0.3189 0.0385 8.29 9.1e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.94 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.1494 7.9687 6.80 7.0e-08 *** 165s price 0.1832 0.0648 2.83 0.0077 ** 165s farmPrice 0.2595 0.0446 5.82 1.3e-06 *** 165s trend 0.3189 0.0385 8.29 9.1e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.447 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 165s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 165s 165s > 165s > ## ****** OLS with 2 cross-equation restrictions (useDfSys=F) ******* 165s > print( summary( fitols4, useDfSys = FALSE ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 2.69 0.702 0.605 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.76 4.46 165s supply 4.46 5.99 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.938 165s supply 0.938 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.4817 6.1599 16.47 6.9e-12 *** 165s price -0.3168 0.0629 -5.04 1e-04 *** 165s income 0.3189 0.0399 8.00 3.6e-07 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.94 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.1494 7.5515 7.17 2.2e-06 *** 165s price 0.1832 0.0629 2.91 0.01 * 165s farmPrice 0.2595 0.0391 6.64 5.6e-06 *** 165s trend 0.3189 0.0399 8.00 5.5e-07 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.447 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 165s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 165s 165s > 165s > ## ****** OLS with 2 cross-equation restrictions (methodResidCov="noDfCor") ******* 165s > fitols4r <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 165s + restrict.rhs = restr2q, methodResidCov = "noDfCor", 165s + useMatrix = useMatrix ) 165s > print( summary( fitols4r ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 1.83 0.702 0.575 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.20 3.67 165s supply 3.67 4.79 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.938 165s supply 0.938 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.4817 5.7621 17.61 < 2e-16 *** 165s price -0.3168 0.0589 -5.38 5.0e-06 *** 165s income 0.3189 0.0373 8.55 4.3e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.94 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.1494 7.0638 7.67 5.4e-09 *** 165s price 0.1832 0.0589 3.11 0.0037 ** 165s farmPrice 0.2595 0.0365 7.10 2.8e-08 *** 165s trend 0.3189 0.0373 8.55 4.3e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.447 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 165s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 165s 165s > 165s > ## OLS with 2 cross-equation restrictions (methodResidCov="noDfCor", singleEqSigma=T) * 165s > fitols4rs <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 165s + restrict.rhs = restr2q, methodResidCov = "noDfCor", 165s + singleEqSigma = TRUE, useMatrix = useMatrix ) 165s > print( summary( fitols4rs ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 1.83 0.702 0.575 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.20 3.67 165s supply 3.67 4.79 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.938 165s supply 0.938 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.4817 5.5234 18.37 < 2e-16 *** 165s price -0.3168 0.0589 -5.38 5.0e-06 *** 165s income 0.3189 0.0352 9.05 1.1e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.94 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.1494 7.2089 7.51 8.5e-09 *** 165s price 0.1832 0.0589 3.11 0.0037 ** 165s farmPrice 0.2595 0.0399 6.51 1.7e-07 *** 165s trend 0.3189 0.0352 9.05 1.1e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.447 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 165s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 165s 165s > 165s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat **** 165s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat (default) **** 165s > fitols5 <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr3m, 165s + restrict.rhs = restr3q, restrict.regMat = tc, methodResidCov = "noDfCor", 165s + useMatrix = useMatrix ) 165s > print( summary( fitols5 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 1.83 0.702 0.575 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.20 3.67 165s supply 3.67 4.79 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.938 165s supply 0.938 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.4817 5.7621 17.61 < 2e-16 *** 165s price -0.3168 0.0589 -5.38 5.0e-06 *** 165s income 0.3189 0.0373 8.55 4.3e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.94 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.1494 7.0638 7.67 5.4e-09 *** 165s price 0.1832 0.0589 3.11 0.0037 ** 165s farmPrice 0.2595 0.0365 7.10 2.8e-08 *** 165s trend 0.3189 0.0373 8.55 4.3e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.447 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 165s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 165s 165s > # the same with symbolically specified restrictions 165s > fitols5Sym <- systemfit( system, "OLS", data = Kmenta, 165s + restrict.matrix = restrict3, restrict.regMat = tc, 165s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 165s > all.equal( fitols5, fitols5Sym ) 165s [1] "Component “call”: target, current do not match when deparsed" 165s > 165s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat (singleEqSigma=T) **** 165s > fitols5s <- systemfit( system, "OLS", data = Kmenta,restrict.matrix = restr3m, 165s + restrict.rhs = restr3q, restrict.regMat = tc, singleEqSigma = T, 165s + x = TRUE, useMatrix = useMatrix ) 165s > print( summary( fitols5s ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 2.69 0.702 0.605 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.76 4.46 165s supply 4.46 5.99 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.938 165s supply 0.938 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.4817 6.0474 16.78 < 2e-16 *** 165s price -0.3168 0.0648 -4.89 2.3e-05 *** 165s income 0.3189 0.0385 8.29 9.1e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.94 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.1494 7.9687 6.80 7.0e-08 *** 165s price 0.1832 0.0648 2.83 0.0077 ** 165s farmPrice 0.2595 0.0446 5.82 1.3e-06 *** 165s trend 0.3189 0.0385 8.29 9.1e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.447 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 165s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 165s 165s > 165s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat (useDfSys=F) **** 165s > fitols5o <- systemfit( system, "OLS", data = Kmenta,restrict.matrix = restr3m, 165s + restrict.rhs = restr3q, restrict.regMat = tc, useMatrix = useMatrix ) 165s > print( summary( fitols5o, useDfSys = FALSE ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 2.69 0.702 0.605 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.76 4.46 165s supply 4.46 5.99 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.938 165s supply 0.938 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.4817 6.1599 16.47 6.9e-12 *** 165s price -0.3168 0.0629 -5.04 1e-04 *** 165s income 0.3189 0.0399 8.00 3.6e-07 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.94 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.1494 7.5515 7.17 2.2e-06 *** 165s price 0.1832 0.0629 2.91 0.01 * 165s farmPrice 0.2595 0.0391 6.64 5.6e-06 *** 165s trend 0.3189 0.0399 8.00 5.5e-07 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.447 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 165s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 165s 165s > 165s > ## OLS with 2 cross-equation restr. via R and restrict.regMat (methodResidCov="noDfCor",singleEqSigma=T) 165s > fitols5rs <- systemfit( system, "OLS", data = Kmenta,restrict.matrix = restr3m, 165s + restrict.rhs = restr3q, restrict.regMat = tc, methodResidCov = "noDfCor", 165s + singleEqSigma = TRUE, useMatrix = useMatrix ) 165s > print( summary( fitols5rs ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 1.83 0.702 0.575 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.20 3.67 165s supply 3.67 4.79 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.938 165s supply 0.938 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.4817 5.5234 18.37 < 2e-16 *** 165s price -0.3168 0.0589 -5.38 5.0e-06 *** 165s income 0.3189 0.0352 9.05 1.1e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.94 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.1494 7.2089 7.51 8.5e-09 *** 165s price 0.1832 0.0589 3.11 0.0037 ** 165s farmPrice 0.2595 0.0399 6.51 1.7e-07 *** 165s trend 0.3189 0.0352 9.05 1.1e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.447 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 165s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 165s 165s > 165s > 165s > ## *********** estimations with a single regressor ************ 165s > fitolsS1 <- systemfit( 165s + list( consump ~ price - 1, consump ~ price + trend ), "OLS", 165s + data = Kmenta, useMatrix = useMatrix ) 165s > print( summary( fitolsS1 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 36 1121 484 -1.09 -1.05 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s eq1 20 19 861 45.3 6.73 -2.213 -2.213 165s eq2 20 17 259 15.3 3.91 0.032 -0.082 165s 165s The covariance matrix of the residuals 165s eq1 eq2 165s eq1 45.3 14.4 165s eq2 14.4 15.3 165s 165s The correlations of the residuals 165s eq1 eq2 165s eq1 1.000 0.549 165s eq2 0.549 1.000 165s 165s 165s OLS estimates for 'eq1' (equation 1) 165s Model Formula: consump ~ price - 1 165s 165s Estimate Std. Error t value Pr(>|t|) 165s price 1.006 0.015 66.9 <2e-16 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 6.733 on 19 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 19 165s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 165s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 165s 165s 165s OLS estimates for 'eq2' (equation 2) 165s Model Formula: consump ~ price + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 93.6767 15.2367 6.15 1.1e-05 *** 165s price 0.0622 0.1513 0.41 0.69 165s trend 0.0953 0.1515 0.63 0.54 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 3.907 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 259.497 MSE: 15.265 Root MSE: 3.907 165s Multiple R-Squared: 0.032 Adjusted R-Squared: -0.082 165s 165s > fitolsS2 <- systemfit( 165s + list( consump ~ price - 1, consump ~ trend - 1 ), "OLS", 165s + data = Kmenta, useMatrix = useMatrix ) 165s > print( summary( fitolsS2 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 38 47370 110957 -87.3 -5.28 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s eq1 20 19 861 45.3 6.73 -2.21 -2.21 165s eq2 20 19 46509 2447.8 49.48 -172.47 -172.47 165s 165s The covariance matrix of the residuals 165s eq1 eq2 165s eq1 45.34 -5.15 165s eq2 -5.15 2447.84 165s 165s The correlations of the residuals 165s eq1 eq2 165s eq1 1.0000 -0.0439 165s eq2 -0.0439 1.0000 165s 165s 165s OLS estimates for 'eq1' (equation 1) 165s Model Formula: consump ~ price - 1 165s 165s Estimate Std. Error t value Pr(>|t|) 165s price 1.006 0.015 66.9 <2e-16 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 6.733 on 19 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 19 165s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 165s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 165s 165s 165s OLS estimates for 'eq2' (equation 2) 165s Model Formula: consump ~ trend - 1 165s 165s Estimate Std. Error t value Pr(>|t|) 165s trend 7.405 0.924 8.02 1.6e-07 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 49.476 on 19 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 19 165s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 165s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 165s 165s > fitolsS3 <- systemfit( 165s + list( consump ~ trend - 1, price ~ trend - 1 ), "OLS", 165s + data = Kmenta, useMatrix = useMatrix ) 165s > print( summary( fitolsS3 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 38 93537 108970 -99 -0.977 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s eq1 20 19 46509 2448 49.5 -172.5 -172.5 165s eq2 20 19 47028 2475 49.8 -69.5 -69.5 165s 165s The covariance matrix of the residuals 165s eq1 eq2 165s eq1 2448 2439 165s eq2 2439 2475 165s 165s The correlations of the residuals 165s eq1 eq2 165s eq1 1.000 0.988 165s eq2 0.988 1.000 165s 165s 165s OLS estimates for 'eq1' (equation 1) 165s Model Formula: consump ~ trend - 1 165s 165s Estimate Std. Error t value Pr(>|t|) 165s trend 7.405 0.924 8.02 1.6e-07 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 49.476 on 19 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 19 165s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 165s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 165s 165s 165s OLS estimates for 'eq2' (equation 2) 165s Model Formula: price ~ trend - 1 165s 165s Estimate Std. Error t value Pr(>|t|) 165s trend 7.318 0.929 7.88 2.1e-07 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 49.751 on 19 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 19 165s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 165s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 165s 165s > fitolsS4 <- systemfit( 165s + list( consump ~ trend - 1, price ~ trend - 1 ), "OLS", 165s + data = Kmenta, restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), 165s + useMatrix = useMatrix ) 165s > print( summary( fitolsS4 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 39 93548 111736 -99 -1.03 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s eq1 20 19 46514 2448 49.5 -172.5 -172.5 165s eq2 20 19 47033 2475 49.8 -69.5 -69.5 165s 165s The covariance matrix of the residuals 165s eq1 eq2 165s eq1 2448 2439 165s eq2 2439 2475 165s 165s The correlations of the residuals 165s eq1 eq2 165s eq1 1.000 0.988 165s eq2 0.988 1.000 165s 165s 165s OLS estimates for 'eq1' (equation 1) 165s Model Formula: consump ~ trend - 1 165s 165s Estimate Std. Error t value Pr(>|t|) 165s trend 7.362 0.646 11.4 5.7e-14 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 49.478 on 19 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 19 165s SSR: 46514.283 MSE: 2448.12 Root MSE: 49.478 165s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 165s 165s 165s OLS estimates for 'eq2' (equation 2) 165s Model Formula: price ~ trend - 1 165s 165s Estimate Std. Error t value Pr(>|t|) 165s trend 7.362 0.646 11.4 5.7e-14 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 49.754 on 19 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 19 165s SSR: 47033.469 MSE: 2475.446 Root MSE: 49.754 165s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 165s 165s > fitolsS5 <- systemfit( 165s + list( consump ~ 1, farmPrice ~ 1 ), "OLS", 165s + data = Kmenta, useMatrix = useMatrix ) 165s > print( summary( fitolsS5 ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 38 3337 1224 0 0 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s eq1 20 19 268 14.1 3.76 0 0 165s eq2 20 19 3069 161.5 12.71 0 0 165s 165s The covariance matrix of the residuals 165s eq1 eq2 165s eq1 14.1 32.5 165s eq2 32.5 161.5 165s 165s The correlations of the residuals 165s eq1 eq2 165s eq1 1.000 0.681 165s eq2 0.681 1.000 165s 165s 165s OLS estimates for 'eq1' (equation 1) 165s Model Formula: consump ~ 1 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 100.90 0.84 120 <2e-16 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 3.756 on 19 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 19 165s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 165s Multiple R-Squared: 0 Adjusted R-Squared: 0 165s 165s 165s OLS estimates for 'eq2' (equation 2) 165s Model Formula: farmPrice ~ 1 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 96.62 2.84 34 <2e-16 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 12.709 on 19 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 19 165s SSR: 3068.757 MSE: 161.514 Root MSE: 12.709 165s Multiple R-Squared: 0 Adjusted R-Squared: 0 165s 165s > 165s > 165s > ## **************** shorter summaries ********************** 165s > print( summary( fitols1, useDfSys = TRUE, equations = FALSE ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 33 156 4.43 0.709 0.558 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 63.3 3.73 1.93 0.764 0.736 165s supply 20 16 92.6 5.78 2.40 0.655 0.590 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.73 4.14 165s supply 4.14 5.78 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.891 165s supply 0.891 1.000 165s 165s 165s Coefficients: 165s Estimate Std. Error t value Pr(>|t|) 165s demand_(Intercept) 99.8954 7.5194 13.29 8.4e-15 *** 165s demand_price -0.3163 0.0907 -3.49 0.0014 ** 165s demand_income 0.3346 0.0454 7.37 1.8e-08 *** 165s supply_(Intercept) 58.2754 11.4629 5.08 1.4e-05 *** 165s supply_price 0.1604 0.0949 1.69 0.1004 165s supply_farmPrice 0.2481 0.0462 5.37 6.1e-06 *** 165s supply_trend 0.2483 0.0975 2.55 0.0157 * 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s > 165s > print( summary( fitols2r ), residCov = FALSE, equations = FALSE ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 1.7 0.703 0.577 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s 165s Coefficients: 165s Estimate Std. Error t value Pr(>|t|) 165s demand_(Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 165s demand_price -0.2917 0.0899 -3.25 0.0026 ** 165s demand_income 0.3129 0.0406 7.70 5.9e-09 *** 165s supply_(Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 165s supply_price 0.1639 0.0786 2.08 0.0447 * 165s supply_farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 165s supply_trend 0.3129 0.0406 7.70 5.9e-09 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s > 165s > print( summary( fitols3s, useDfSys = FALSE ), residCov = TRUE ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 34 159 2.5 0.703 0.608 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.2 3.78 1.94 0.761 0.732 165s supply 20 16 95.1 5.94 2.44 0.645 0.579 165s 165s The covariance matrix of the residuals 165s demand supply 165s demand 3.78 4.47 165s supply 4.47 5.94 165s 165s The correlations of the residuals 165s demand supply 165s demand 1.000 0.943 165s supply 0.943 1.000 165s 165s 165s OLS estimates for 'demand' (equation 1) 165s Model Formula: consump ~ price + income 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.5563 7.5640 13.16 2.4e-10 *** 165s price -0.2917 0.0887 -3.29 0.0043 ** 165s income 0.3129 0.0415 7.54 8.1e-07 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 1.943 on 17 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 17 165s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 165s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 165s 165s 165s OLS estimates for 'supply' (equation 2) 165s Model Formula: consump ~ price + farmPrice + trend 165s 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.3795 11.3165 4.98 0.00014 *** 165s price 0.1639 0.0960 1.71 0.10724 165s farmPrice 0.2571 0.0451 5.69 3.3e-05 *** 165s trend 0.3129 0.0415 7.54 1.2e-06 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s 165s Residual standard error: 2.438 on 16 degrees of freedom 165s Number of observations: 20 Degrees of Freedom: 16 165s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 165s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 165s 165s > 165s > print( summary( fitols4rs, residCov = FALSE, equations = FALSE ) ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 1.83 0.702 0.575 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s 165s Coefficients: 165s Estimate Std. Error t value Pr(>|t|) 165s demand_(Intercept) 101.4817 5.5234 18.37 < 2e-16 *** 165s demand_price -0.3168 0.0589 -5.38 5.0e-06 *** 165s demand_income 0.3189 0.0352 9.05 1.1e-10 *** 165s supply_(Intercept) 54.1494 7.2089 7.51 8.5e-09 *** 165s supply_price 0.1832 0.0589 3.11 0.0037 ** 165s supply_farmPrice 0.2595 0.0399 6.51 1.7e-07 *** 165s supply_trend 0.3189 0.0352 9.05 1.1e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s > 165s > print( summary( fitols5, equations = FALSE ), residCov = FALSE ) 165s 165s systemfit results 165s method: OLS 165s 165s N DF SSR detRCov OLS-R2 McElroy-R2 165s system 40 35 160 1.83 0.702 0.575 165s 165s N DF SSR MSE RMSE R2 Adj R2 165s demand 20 17 64.0 3.77 1.94 0.761 0.733 165s supply 20 16 95.8 5.99 2.45 0.643 0.576 165s 165s 165s Coefficients: 165s Estimate Std. Error t value Pr(>|t|) 165s demand_(Intercept) 101.4817 5.7621 17.61 < 2e-16 *** 165s demand_price -0.3168 0.0589 -5.38 5.0e-06 *** 165s demand_income 0.3189 0.0373 8.55 4.3e-10 *** 165s supply_(Intercept) 54.1494 7.0638 7.67 5.4e-09 *** 165s supply_price 0.1832 0.0589 3.11 0.0037 ** 165s supply_farmPrice 0.2595 0.0365 7.10 2.8e-08 *** 165s supply_trend 0.3189 0.0373 8.55 4.3e-10 *** 165s --- 165s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 165s > 165s > 165s > ## ****************** residuals ************************** 165s > print( residuals( fitols1 ) ) 165s demand supply 165s 1 1.074 -0.444 165s 2 -0.390 -0.896 165s 3 2.625 1.965 165s 4 1.802 1.134 165s 5 1.946 1.514 165s 6 1.175 0.680 165s 7 1.530 1.569 165s 8 -2.933 -4.407 165s 9 -1.365 -2.599 165s 10 2.031 2.469 165s 11 -0.149 -0.598 165s 12 -1.954 -1.697 165s 13 -1.121 -1.064 165s 14 -0.220 0.970 165s 15 1.487 3.159 165s 16 -3.701 -3.866 165s 17 -1.273 -0.265 165s 18 -2.002 -2.449 165s 19 1.738 3.110 165s 20 -0.299 1.714 165s > print( residuals( fitols1$eq[[ 2 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 11 165s -0.444 -0.896 1.965 1.134 1.514 0.680 1.569 -4.407 -2.599 2.469 -0.598 165s 12 13 14 15 16 17 18 19 20 165s -1.697 -1.064 0.970 3.159 -3.866 -0.265 -2.449 3.110 1.714 165s > 165s > print( residuals( fitols2r ) ) 165s demand supply 165s 1 0.8465 0.156 165s 2 -0.4933 -0.384 165s 3 2.5225 2.415 165s 4 1.7066 1.525 165s 5 2.0445 1.750 165s 6 1.2529 0.870 165s 7 1.6277 1.711 165s 8 -2.8261 -4.380 165s 9 -1.2979 -2.597 165s 10 2.0592 2.497 165s 11 -0.4663 -0.466 165s 12 -2.3732 -1.540 165s 13 -1.4734 -1.006 165s 14 -0.3398 0.885 165s 15 1.7283 2.835 165s 16 -3.4975 -4.290 165s 17 -0.9651 -0.760 165s 18 -1.9512 -2.911 165s 19 1.8829 2.606 165s 20 0.0129 1.085 165s > print( residuals( fitols2r$eq[[ 1 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 165s 0.8465 -0.4933 2.5225 1.7066 2.0445 1.2529 1.6277 -2.8261 -1.2979 2.0592 165s 11 12 13 14 15 16 17 18 19 20 165s -0.4663 -2.3732 -1.4734 -0.3398 1.7283 -3.4975 -0.9651 -1.9512 1.8829 0.0129 165s > 165s > print( residuals( fitols3s ) ) 165s demand supply 165s 1 0.8465 0.156 165s 2 -0.4933 -0.384 165s 3 2.5225 2.415 165s 4 1.7066 1.525 165s 5 2.0445 1.750 165s 6 1.2529 0.870 165s 7 1.6277 1.711 165s 8 -2.8261 -4.380 165s 9 -1.2979 -2.597 165s 10 2.0592 2.497 165s 11 -0.4663 -0.466 165s 12 -2.3732 -1.540 165s 13 -1.4734 -1.006 165s 14 -0.3398 0.885 165s 15 1.7283 2.835 165s 16 -3.4975 -4.290 165s 17 -0.9651 -0.760 165s 18 -1.9512 -2.911 165s 19 1.8829 2.606 165s 20 0.0129 1.085 165s > print( residuals( fitols3s$eq[[ 2 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 11 165s 0.156 -0.384 2.415 1.525 1.750 0.870 1.711 -4.380 -2.597 2.497 -0.466 165s 12 13 14 15 16 17 18 19 20 165s -1.540 -1.006 0.885 2.835 -4.290 -0.760 -2.911 2.606 1.085 165s > 165s > print( residuals( fitols4rs ) ) 165s demand supply 165s 1 0.915 0.204 165s 2 -0.387 -0.421 165s 3 2.613 2.388 165s 4 1.815 1.474 165s 5 1.980 1.787 165s 6 1.221 0.879 165s 7 1.620 1.690 165s 8 -2.769 -4.489 165s 9 -1.382 -2.549 165s 10 1.890 2.660 165s 11 -0.506 -0.297 165s 12 -2.280 -1.456 165s 13 -1.323 -1.013 165s 14 -0.330 0.925 165s 15 1.572 2.889 165s 16 -3.582 -4.313 165s 17 -1.298 -0.573 165s 18 -1.892 -3.023 165s 19 1.948 2.462 165s 20 0.174 0.777 165s > print( residuals( fitols4rs$eq[[ 1 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 11 165s 0.915 -0.387 2.613 1.815 1.980 1.221 1.620 -2.769 -1.382 1.890 -0.506 165s 12 13 14 15 16 17 18 19 20 165s -2.280 -1.323 -0.330 1.572 -3.582 -1.298 -1.892 1.948 0.174 165s > 165s > print( residuals( fitols5 ) ) 165s demand supply 165s 1 0.915 0.204 165s 2 -0.387 -0.421 165s 3 2.613 2.388 165s 4 1.815 1.474 165s 5 1.980 1.787 165s 6 1.221 0.879 165s 7 1.620 1.690 165s 8 -2.769 -4.489 165s 9 -1.382 -2.549 165s 10 1.890 2.660 165s 11 -0.506 -0.297 165s 12 -2.280 -1.456 165s 13 -1.323 -1.013 165s 14 -0.330 0.925 165s 15 1.572 2.889 165s 16 -3.582 -4.313 165s 17 -1.298 -0.573 165s 18 -1.892 -3.023 165s 19 1.948 2.462 165s 20 0.174 0.777 165s > print( residuals( fitols5$eq[[ 2 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 11 165s 0.204 -0.421 2.388 1.474 1.787 0.879 1.690 -4.489 -2.549 2.660 -0.297 165s 12 13 14 15 16 17 18 19 20 165s -1.456 -1.013 0.925 2.889 -4.313 -0.573 -3.023 2.462 0.777 165s > 165s > 165s > ## *************** coefficients ********************* 165s > print( round( coef( fitols1rs ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income supply_(Intercept) 165s 99.895 -0.316 0.335 58.275 165s supply_price supply_farmPrice supply_trend 165s 0.160 0.248 0.248 165s > print( round( coef( fitols1rs$eq[[ 2 ]] ), digits = 6 ) ) 165s (Intercept) price farmPrice trend 165s 58.275 0.160 0.248 0.248 165s > 165s > print( round( coef( fitols2s ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income supply_(Intercept) 165s 99.556 -0.292 0.313 56.380 165s supply_price supply_farmPrice supply_trend 165s 0.164 0.257 0.313 165s > print( round( coef( fitols2s$eq[[ 1 ]] ), digits = 6 ) ) 165s (Intercept) price income 165s 99.556 -0.292 0.313 165s > 165s > print( round( coef( fitols3 ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income supply_(Intercept) 165s 99.556 -0.292 0.313 56.380 165s supply_price supply_farmPrice supply_trend 165s 0.164 0.257 0.313 165s > print( round( coef( fitols3, modified.regMat = TRUE ), digits = 6 ) ) 165s C1 C2 C3 C4 C5 C6 165s 99.556 -0.292 0.313 56.380 0.164 0.257 165s > print( round( coef( fitols3$eq[[ 2 ]] ), digits = 6 ) ) 165s (Intercept) price farmPrice trend 165s 56.380 0.164 0.257 0.313 165s > 165s > print( round( coef( fitols4r ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income supply_(Intercept) 165s 101.482 -0.317 0.319 54.149 165s supply_price supply_farmPrice supply_trend 165s 0.183 0.260 0.319 165s > print( round( coef( fitols4r$eq[[ 1 ]] ), digits = 6 ) ) 165s (Intercept) price income 165s 101.482 -0.317 0.319 165s > 165s > print( round( coef( fitols5 ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income supply_(Intercept) 165s 101.482 -0.317 0.319 54.149 165s supply_price supply_farmPrice supply_trend 165s 0.183 0.260 0.319 165s > print( round( coef( fitols5, modified.regMat = TRUE ), digits = 6 ) ) 165s C1 C2 C3 C4 C5 C6 165s 101.482 -0.317 0.319 54.149 0.183 0.260 165s > print( round( coef( fitols5$eq[[ 2 ]] ), digits = 6 ) ) 165s (Intercept) price farmPrice trend 165s 54.149 0.183 0.260 0.319 165s > 165s > 165s > ## *************** coefficients with stats ********************* 165s > print( round( coef( summary( fitols1rs, useDfSys = FALSE ) ), digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s demand_(Intercept) 99.895 8.4671 11.80 0.000000 165s demand_price -0.316 0.1021 -3.10 0.006536 165s demand_income 0.335 0.0511 6.54 0.000005 165s supply_(Intercept) 58.275 10.3587 5.63 0.000038 165s supply_price 0.160 0.0857 1.87 0.079851 165s supply_farmPrice 0.248 0.0417 5.94 0.000021 165s supply_trend 0.248 0.0881 2.82 0.012382 165s > print( round( coef( summary( fitols1rs$eq[[ 2 ]], useDfSys = FALSE ) ), 165s + digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 58.275 10.3587 5.63 0.000038 165s price 0.160 0.0857 1.87 0.079851 165s farmPrice 0.248 0.0417 5.94 0.000021 165s trend 0.248 0.0881 2.82 0.012382 165s > 165s > print( round( coef( summary( fitols2s ) ), digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s demand_(Intercept) 99.556 7.5640 13.16 0.000000 165s demand_price -0.292 0.0887 -3.29 0.002340 165s demand_income 0.313 0.0415 7.54 0.000000 165s supply_(Intercept) 56.380 11.3165 4.98 0.000018 165s supply_price 0.164 0.0960 1.71 0.097028 165s supply_farmPrice 0.257 0.0451 5.69 0.000002 165s supply_trend 0.313 0.0415 7.54 0.000000 165s > print( round( coef( summary( fitols2s$eq[[ 1 ]] ) ), digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 99.556 7.5640 13.16 0.00000 165s price -0.292 0.0887 -3.29 0.00234 165s income 0.313 0.0415 7.54 0.00000 165s > 165s > print( round( coef( summary( fitols3, useDfSys = FALSE ) ), digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s demand_(Intercept) 99.556 8.4225 11.82 0.000000 165s demand_price -0.292 0.0975 -2.99 0.008189 165s demand_income 0.313 0.0441 7.10 0.000002 165s supply_(Intercept) 56.380 10.0721 5.60 0.000040 165s supply_price 0.164 0.0853 1.92 0.072611 165s supply_farmPrice 0.257 0.0402 6.39 0.000009 165s supply_trend 0.313 0.0441 7.10 0.000003 165s > print( round( coef( summary( fitols3, useDfSys = FALSE ), modified.regMat = TRUE ), 165s + digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s C1 99.556 8.4225 11.82 NA 165s C2 -0.292 0.0975 -2.99 NA 165s C3 0.313 0.0441 7.10 NA 165s C4 56.380 10.0721 5.60 NA 165s C5 0.164 0.0853 1.92 NA 165s C6 0.257 0.0402 6.39 NA 165s > print( round( coef( summary( fitols3$eq[[ 2 ]], useDfSys = FALSE ) ), 165s + digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 56.380 10.0721 5.60 0.000040 165s price 0.164 0.0853 1.92 0.072611 165s farmPrice 0.257 0.0402 6.39 0.000009 165s trend 0.313 0.0441 7.10 0.000003 165s > 165s > print( round( coef( summary( fitols4r, useDfSys = FALSE ) ), digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s demand_(Intercept) 101.482 5.7621 17.61 0.0e+00 165s demand_price -0.317 0.0589 -5.38 5.0e-05 165s demand_income 0.319 0.0373 8.55 0.0e+00 165s supply_(Intercept) 54.149 7.0638 7.67 1.0e-06 165s supply_price 0.183 0.0589 3.11 6.7e-03 165s supply_farmPrice 0.260 0.0365 7.10 3.0e-06 165s supply_trend 0.319 0.0373 8.55 0.0e+00 165s > print( round( coef( summary( fitols4r$eq[[ 1 ]], useDfSys = FALSE ) ), 165s + digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 101.482 5.7621 17.61 0e+00 165s price -0.317 0.0589 -5.38 5e-05 165s income 0.319 0.0373 8.55 0e+00 165s > 165s > print( round( coef( summary( fitols5 ) ), digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s demand_(Intercept) 101.482 5.7621 17.61 0.000000 165s demand_price -0.317 0.0589 -5.38 0.000005 165s demand_income 0.319 0.0373 8.55 0.000000 165s supply_(Intercept) 54.149 7.0638 7.67 0.000000 165s supply_price 0.183 0.0589 3.11 0.003680 165s supply_farmPrice 0.260 0.0365 7.10 0.000000 165s supply_trend 0.319 0.0373 8.55 0.000000 165s > print( round( coef( summary( fitols5 ), modified.regMat = TRUE ), digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s C1 101.482 5.7621 17.61 0.000000 165s C2 -0.317 0.0589 -5.38 0.000005 165s C3 0.319 0.0373 8.55 0.000000 165s C4 54.149 7.0638 7.67 0.000000 165s C5 0.183 0.0589 3.11 0.003680 165s C6 0.260 0.0365 7.10 0.000000 165s > print( round( coef( summary( fitols5$eq[[ 2 ]] ) ), digits = 6 ) ) 165s Estimate Std. Error t value Pr(>|t|) 165s (Intercept) 54.149 7.0638 7.67 0.00000 165s price 0.183 0.0589 3.11 0.00368 165s farmPrice 0.260 0.0365 7.10 0.00000 165s trend 0.319 0.0373 8.55 0.00000 165s > 165s > 165s > ## *********** variance covariance matrix of the coefficients ******* 165s > print( round( vcov( fitols1rs ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income 165s demand_(Intercept) 71.6926 -0.75420 0.04078 165s demand_price -0.7542 0.01043 -0.00296 165s demand_income 0.0408 -0.00296 0.00262 165s supply_(Intercept) 0.0000 0.00000 0.00000 165s supply_price 0.0000 0.00000 0.00000 165s supply_farmPrice 0.0000 0.00000 0.00000 165s supply_trend 0.0000 0.00000 0.00000 165s supply_(Intercept) supply_price supply_farmPrice 165s demand_(Intercept) 0.000 0.000000 0.000000 165s demand_price 0.000 0.000000 0.000000 165s demand_income 0.000 0.000000 0.000000 165s supply_(Intercept) 107.303 -0.806417 -0.248549 165s supply_price -0.806 0.007352 0.000689 165s supply_farmPrice -0.249 0.000689 0.001742 165s supply_trend -0.228 0.000426 0.001074 165s supply_trend 165s demand_(Intercept) 0.000000 165s demand_price 0.000000 165s demand_income 0.000000 165s supply_(Intercept) -0.227988 165s supply_price 0.000426 165s supply_farmPrice 0.001074 165s supply_trend 0.007766 165s > print( round( vcov( fitols1rs$eq[[ 2 ]] ), digits = 6 ) ) 165s (Intercept) price farmPrice trend 165s (Intercept) 107.303 -0.806417 -0.248549 -0.227988 165s price -0.806 0.007352 0.000689 0.000426 165s farmPrice -0.249 0.000689 0.001742 0.001074 165s trend -0.228 0.000426 0.001074 0.007766 165s > 165s > print( round( vcov( fitols2s ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income 165s demand_(Intercept) 57.21413 -0.596328 0.026850 165s demand_price -0.59633 0.007862 -0.001948 165s demand_income 0.02685 -0.001948 0.001722 165s supply_(Intercept) -0.78825 0.057190 -0.050565 165s supply_price 0.00147 -0.000107 0.000095 165s supply_farmPrice 0.00371 -0.000269 0.000238 165s supply_trend 0.02685 -0.001948 0.001722 165s supply_(Intercept) supply_price supply_farmPrice 165s demand_(Intercept) -0.7883 0.001474 0.003714 165s demand_price 0.0572 -0.000107 -0.000269 165s demand_income -0.0506 0.000095 0.000238 165s supply_(Intercept) 128.0635 -1.001596 -0.280017 165s supply_price -1.0016 0.009225 0.000806 165s supply_farmPrice -0.2800 0.000806 0.002038 165s supply_trend -0.0506 0.000095 0.000238 165s supply_trend 165s demand_(Intercept) 0.026850 165s demand_price -0.001948 165s demand_income 0.001722 165s supply_(Intercept) -0.050565 165s supply_price 0.000095 165s supply_farmPrice 0.000238 165s supply_trend 0.001722 165s > print( round( vcov( fitols2s$eq[[ 1 ]] ), digits = 6 ) ) 165s (Intercept) price income 165s (Intercept) 57.2141 -0.59633 0.02685 165s price -0.5963 0.00786 -0.00195 165s income 0.0268 -0.00195 0.00172 165s > 165s > print( round( vcov( fitols3 ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income 165s demand_(Intercept) 70.93892 -0.736413 0.030252 165s demand_price -0.73641 0.009503 -0.002195 165s demand_income 0.03025 -0.002195 0.001941 165s supply_(Intercept) -0.88813 0.064436 -0.056972 165s supply_price 0.00166 -0.000120 0.000107 165s supply_farmPrice 0.00419 -0.000304 0.000268 165s supply_trend 0.03025 -0.002195 0.001941 165s supply_(Intercept) supply_price supply_farmPrice 165s demand_(Intercept) -0.8881 0.001661 0.004185 165s demand_price 0.0644 -0.000120 -0.000304 165s demand_income -0.0570 0.000107 0.000268 165s supply_(Intercept) 101.4478 -0.790443 -0.223090 165s supply_price -0.7904 0.007274 0.000640 165s supply_farmPrice -0.2231 0.000640 0.001617 165s supply_trend -0.0570 0.000107 0.000268 165s supply_trend 165s demand_(Intercept) 0.030252 165s demand_price -0.002195 165s demand_income 0.001941 165s supply_(Intercept) -0.056972 165s supply_price 0.000107 165s supply_farmPrice 0.000268 165s supply_trend 0.001941 165s > print( round( vcov( fitols3, modified.regMat = TRUE ), digits = 6 ) ) 165s C1 C2 C3 C4 C5 C6 165s C1 70.93892 -0.736413 0.030252 -0.8881 0.001661 0.004185 165s C2 -0.73641 0.009503 -0.002195 0.0644 -0.000120 -0.000304 165s C3 0.03025 -0.002195 0.001941 -0.0570 0.000107 0.000268 165s C4 -0.88813 0.064436 -0.056972 101.4478 -0.790443 -0.223090 165s C5 0.00166 -0.000120 0.000107 -0.7904 0.007274 0.000640 165s C6 0.00419 -0.000304 0.000268 -0.2231 0.000640 0.001617 165s > print( round( vcov( fitols3$eq[[ 2 ]] ), digits = 6 ) ) 165s (Intercept) price farmPrice trend 165s (Intercept) 101.448 -0.790443 -0.223090 -0.056972 165s price -0.790 0.007274 0.000640 0.000107 165s farmPrice -0.223 0.000640 0.001617 0.000268 165s trend -0.057 0.000107 0.000268 0.001941 165s > 165s > print( round( vcov( fitols4r ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income 165s demand_(Intercept) 33.2016 -0.272100 -0.059329 165s demand_price -0.2721 0.003464 -0.000762 165s demand_income -0.0593 -0.000762 0.001390 165s supply_(Intercept) 30.8652 -0.357363 0.050012 165s supply_price -0.2721 0.003464 -0.000762 165s supply_farmPrice -0.0313 0.000196 0.000120 165s supply_trend -0.0593 -0.000762 0.001390 165s supply_(Intercept) supply_price supply_farmPrice 165s demand_(Intercept) 30.865 -0.272100 -0.031328 165s demand_price -0.357 0.003464 0.000196 165s demand_income 0.050 -0.000762 0.000120 165s supply_(Intercept) 49.897 -0.357363 -0.149852 165s supply_price -0.357 0.003464 0.000196 165s supply_farmPrice -0.150 0.000196 0.001335 165s supply_trend 0.050 -0.000762 0.000120 165s supply_trend 165s demand_(Intercept) -0.059329 165s demand_price -0.000762 165s demand_income 0.001390 165s supply_(Intercept) 0.050012 165s supply_price -0.000762 165s supply_farmPrice 0.000120 165s supply_trend 0.001390 165s > print( round( vcov( fitols4r$eq[[ 1 ]] ), digits = 6 ) ) 165s (Intercept) price income 165s (Intercept) 33.2016 -0.272100 -0.059329 165s price -0.2721 0.003464 -0.000762 165s income -0.0593 -0.000762 0.001390 165s > 165s > print( round( vcov( fitols5 ), digits = 6 ) ) 165s demand_(Intercept) demand_price demand_income 165s demand_(Intercept) 33.2016 -0.272100 -0.059329 165s demand_price -0.2721 0.003464 -0.000762 165s demand_income -0.0593 -0.000762 0.001390 165s supply_(Intercept) 30.8652 -0.357363 0.050012 165s supply_price -0.2721 0.003464 -0.000762 165s supply_farmPrice -0.0313 0.000196 0.000120 165s supply_trend -0.0593 -0.000762 0.001390 165s supply_(Intercept) supply_price supply_farmPrice 165s demand_(Intercept) 30.865 -0.272100 -0.031328 165s demand_price -0.357 0.003464 0.000196 165s demand_income 0.050 -0.000762 0.000120 165s supply_(Intercept) 49.897 -0.357363 -0.149852 165s supply_price -0.357 0.003464 0.000196 165s supply_farmPrice -0.150 0.000196 0.001335 165s supply_trend 0.050 -0.000762 0.000120 165s supply_trend 165s demand_(Intercept) -0.059329 165s demand_price -0.000762 165s demand_income 0.001390 165s supply_(Intercept) 0.050012 165s supply_price -0.000762 165s supply_farmPrice 0.000120 165s supply_trend 0.001390 165s > print( round( vcov( fitols5, modified.regMat = TRUE ), digits = 6 ) ) 165s C1 C2 C3 C4 C5 C6 165s C1 33.2016 -0.272100 -0.059329 30.865 -0.272100 -0.031328 165s C2 -0.2721 0.003464 -0.000762 -0.357 0.003464 0.000196 165s C3 -0.0593 -0.000762 0.001390 0.050 -0.000762 0.000120 165s C4 30.8652 -0.357363 0.050012 49.897 -0.357363 -0.149852 165s C5 -0.2721 0.003464 -0.000762 -0.357 0.003464 0.000196 165s C6 -0.0313 0.000196 0.000120 -0.150 0.000196 0.001335 165s > print( round( vcov( fitols5$eq[[ 2 ]] ), digits = 6 ) ) 165s (Intercept) price farmPrice trend 165s (Intercept) 49.897 -0.357363 -0.149852 0.050012 165s price -0.357 0.003464 0.000196 -0.000762 165s farmPrice -0.150 0.000196 0.001335 0.000120 165s trend 0.050 -0.000762 0.000120 0.001390 165s > 165s > 165s > ## *********** confidence intervals of coefficients ************* 165s > print( confint( fitols1, useDfSys = TRUE ) ) 165s 2.5 % 97.5 % 165s demand_(Intercept) 84.597 115.194 165s demand_price -0.501 -0.132 165s demand_income 0.242 0.427 165s supply_(Intercept) 34.954 81.597 165s supply_price -0.033 0.353 165s supply_farmPrice 0.154 0.342 165s supply_trend 0.050 0.447 165s > print( confint( fitols1$eq[[ 2 ]], level = 0.9, useDfSys = TRUE ) ) 165s 5 % 95 % 165s (Intercept) 38.876 77.675 165s price 0.000 0.321 165s farmPrice 0.170 0.326 165s trend 0.083 0.413 165s > 165s > print( confint( fitols2r, level = 0.9 ) ) 165s 5 % 95 % 165s demand_(Intercept) 83.776 115.337 165s demand_price -0.474 -0.109 165s demand_income 0.230 0.395 165s supply_(Intercept) 37.508 75.251 165s supply_price 0.004 0.324 165s supply_farmPrice 0.182 0.332 165s supply_trend 0.230 0.395 165s > print( confint( fitols2r$eq[[ 1 ]], level = 0.99 ) ) 165s 0.5 % 99.5 % 165s (Intercept) 78.370 120.743 165s price -0.537 -0.046 165s income 0.202 0.424 165s > 165s > print( confint( fitols3s, level = 0.99 ) ) 165s 0.5 % 99.5 % 165s demand_(Intercept) 84.184 114.928 165s demand_price -0.472 -0.112 165s demand_income 0.229 0.397 165s supply_(Intercept) 33.382 79.377 165s supply_price -0.031 0.359 165s supply_farmPrice 0.165 0.349 165s supply_trend 0.229 0.397 165s > print( confint( fitols3s$eq[[ 2 ]], level = 0.5 ) ) 165s 25 % 75 % 165s (Intercept) 48.664 64.095 165s price 0.098 0.229 165s farmPrice 0.226 0.288 165s trend 0.285 0.341 165s > 165s > print( confint( fitols4rs, level = 0.5 ) ) 165s 25 % 75 % 165s demand_(Intercept) 90.269 112.695 165s demand_price -0.436 -0.197 165s demand_income 0.247 0.390 165s supply_(Intercept) 39.515 68.784 165s supply_price 0.064 0.303 165s supply_farmPrice 0.179 0.340 165s supply_trend 0.247 0.390 165s > print( confint( fitols4rs$eq[[ 1 ]], level = 0.25 ) ) 165s 37.5 % 62.5 % 165s (Intercept) 99.708 103.256 165s price -0.336 -0.298 165s income 0.308 0.330 165s > 165s > print( confint( fitols5, level = 0.25 ) ) 165s 37.5 % 62.5 % 165s demand_(Intercept) 89.784 113.179 165s demand_price -0.436 -0.197 165s demand_income 0.243 0.395 165s supply_(Intercept) 39.809 68.490 165s supply_price 0.064 0.303 165s supply_farmPrice 0.185 0.334 165s supply_trend 0.243 0.395 165s > print( confint( fitols5$eq[[ 2 ]], level = 0.999 ) ) 165s 0.1 % 100 % 165s (Intercept) 28.782 79.517 165s price -0.028 0.395 165s farmPrice 0.128 0.391 165s trend 0.185 0.453 165s > 165s > print( confint( fitols3, level = 0.999, useDfSys = FALSE ) ) 165s 0.1 % 100 % 165s demand_(Intercept) 81.786 117.326 165s demand_price -0.497 -0.086 165s demand_income 0.220 0.406 165s supply_(Intercept) 35.028 77.731 165s supply_price -0.017 0.345 165s supply_farmPrice 0.172 0.342 165s supply_trend 0.219 0.406 165s > print( confint( fitols3$eq[[ 1 ]], useDfSys = FALSE ) ) 165s 2.5 % 97.5 % 165s (Intercept) 81.786 117.326 165s price -0.497 -0.086 165s income 0.220 0.406 165s > 165s > 165s > ## *********** fitted values ************* 165s > print( fitted( fitols1 ) ) 165s demand supply 165s 1 97.4 98.9 165s 2 99.6 100.1 165s 3 99.5 100.2 165s 4 99.7 100.4 165s 5 102.3 102.7 165s 6 102.1 102.6 165s 7 102.5 102.4 165s 8 102.8 104.3 165s 9 101.7 102.9 165s 10 100.8 100.4 165s 11 95.6 96.0 165s 12 94.4 94.1 165s 13 95.7 95.6 165s 14 99.0 97.8 165s 15 104.3 102.6 165s 16 103.9 104.1 165s 17 104.8 103.8 165s 18 101.9 102.4 165s 19 103.5 102.1 165s 20 106.5 104.5 165s > print( fitted( fitols1$eq[[ 2 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 11 12 13 165s 98.9 100.1 100.2 100.4 102.7 102.6 102.4 104.3 102.9 100.4 96.0 94.1 95.6 165s 14 15 16 17 18 19 20 165s 97.8 102.6 104.1 103.8 102.4 102.1 104.5 165s > 165s > print( fitted( fitols2r ) ) 165s demand supply 165s 1 97.6 98.3 165s 2 99.7 99.6 165s 3 99.6 99.7 165s 4 99.8 100.0 165s 5 102.2 102.5 165s 6 102.0 102.4 165s 7 102.4 102.3 165s 8 102.7 104.3 165s 9 101.6 102.9 165s 10 100.8 100.3 165s 11 95.9 95.9 165s 12 94.8 94.0 165s 13 96.0 95.5 165s 14 99.1 97.9 165s 15 104.1 103.0 165s 16 103.7 104.5 165s 17 104.5 104.3 165s 18 101.9 102.8 165s 19 103.3 102.6 165s 20 106.2 105.1 165s > print( fitted( fitols2r$eq[[ 1 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 11 12 13 165s 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 165s 14 15 16 17 18 19 20 165s 99.1 104.1 103.7 104.5 101.9 103.3 106.2 165s > 165s > print( fitted( fitols3s ) ) 165s demand supply 165s 1 97.6 98.3 165s 2 99.7 99.6 165s 3 99.6 99.7 165s 4 99.8 100.0 165s 5 102.2 102.5 165s 6 102.0 102.4 165s 7 102.4 102.3 165s 8 102.7 104.3 165s 9 101.6 102.9 165s 10 100.8 100.3 165s 11 95.9 95.9 165s 12 94.8 94.0 165s 13 96.0 95.5 165s 14 99.1 97.9 165s 15 104.1 103.0 165s 16 103.7 104.5 165s 17 104.5 104.3 165s 18 101.9 102.8 165s 19 103.3 102.6 165s 20 106.2 105.1 165s > print( fitted( fitols3s$eq[[ 2 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 11 12 13 165s 98.3 99.6 99.7 100.0 102.5 102.4 102.3 104.3 102.9 100.3 95.9 94.0 95.5 165s 14 15 16 17 18 19 20 165s 97.9 103.0 104.5 104.3 102.8 102.6 105.1 165s > 165s > print( fitted( fitols4rs ) ) 165s demand supply 165s 1 97.6 98.3 165s 2 99.6 99.6 165s 3 99.5 99.8 165s 4 99.7 100.0 165s 5 102.3 102.5 165s 6 102.0 102.4 165s 7 102.4 102.3 165s 8 102.7 104.4 165s 9 101.7 102.9 165s 10 100.9 100.2 165s 11 95.9 95.7 165s 12 94.7 93.9 165s 13 95.9 95.5 165s 14 99.1 97.8 165s 15 104.2 102.9 165s 16 103.8 104.5 165s 17 104.8 104.1 165s 18 101.8 103.0 165s 19 103.3 102.8 165s 20 106.1 105.5 165s > print( fitted( fitols4rs$eq[[ 1 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 11 12 13 165s 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 165s 14 15 16 17 18 19 20 165s 99.1 104.2 103.8 104.8 101.8 103.3 106.1 165s > 165s > print( fitted( fitols5 ) ) 165s demand supply 165s 1 97.6 98.3 165s 2 99.6 99.6 165s 3 99.5 99.8 165s 4 99.7 100.0 165s 5 102.3 102.5 165s 6 102.0 102.4 165s 7 102.4 102.3 165s 8 102.7 104.4 165s 9 101.7 102.9 165s 10 100.9 100.2 165s 11 95.9 95.7 165s 12 94.7 93.9 165s 13 95.9 95.5 165s 14 99.1 97.8 165s 15 104.2 102.9 165s 16 103.8 104.5 165s 17 104.8 104.1 165s 18 101.8 103.0 165s 19 103.3 102.8 165s 20 106.1 105.5 165s > print( fitted( fitols5$eq[[ 2 ]] ) ) 165s 1 2 3 4 5 6 7 8 9 10 11 12 13 165s 98.3 99.6 99.8 100.0 102.5 102.4 102.3 104.4 102.9 100.2 95.7 93.9 95.5 165s 14 15 16 17 18 19 20 165s 97.8 102.9 104.5 104.1 103.0 102.8 105.5 165s > 165s > 165s > ## *********** predicted values ************* 165s > predictData <- Kmenta 165s > predictData$consump <- NULL 165s > predictData$price <- Kmenta$price * 0.9 165s > predictData$income <- Kmenta$income * 1.1 165s > 165s > print( predict( fitols1, se.fit = TRUE, interval = "prediction", 165s + useDfSys = TRUE ) ) 165s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 165s 1 97.4 0.643 93.3 101.5 98.9 1.056 165s 2 99.6 0.577 95.5 103.7 100.1 1.037 165s 3 99.5 0.545 95.5 103.6 100.2 0.939 165s 4 99.7 0.582 95.6 103.8 100.4 0.912 165s 5 102.3 0.502 98.2 106.4 102.7 0.895 165s 6 102.1 0.463 98.0 106.1 102.6 0.791 165s 7 102.5 0.484 98.4 106.5 102.4 0.719 165s 8 102.8 0.601 98.7 106.9 104.3 0.963 165s 9 101.7 0.527 97.6 105.8 102.9 0.788 165s 10 100.8 0.788 96.5 105.0 100.4 0.981 165s 11 95.6 0.946 91.2 100.0 96.0 1.185 165s 12 94.4 0.980 90.0 98.8 94.1 1.394 165s 13 95.7 0.880 91.3 100.0 95.6 1.244 165s 14 99.0 0.508 94.9 103.0 97.8 0.896 165s 15 104.3 0.758 100.1 108.5 102.6 0.874 165s 16 103.9 0.616 99.8 108.0 104.1 0.916 165s 17 104.8 1.273 100.1 109.5 103.8 1.605 165s 18 101.9 0.536 97.9 106.0 102.4 0.962 165s 19 103.5 0.680 99.3 107.6 102.1 1.098 165s 20 106.5 1.274 101.8 111.2 104.5 1.664 165s supply.lwr supply.upr 165s 1 93.6 104.3 165s 2 94.8 105.4 165s 3 94.9 105.5 165s 4 95.1 105.6 165s 5 97.5 107.9 165s 6 97.4 107.7 165s 7 97.3 107.5 165s 8 99.0 109.6 165s 9 97.8 108.1 165s 10 95.1 105.6 165s 11 90.6 101.5 165s 12 88.5 99.8 165s 13 90.1 101.1 165s 14 92.6 103.0 165s 15 97.4 107.8 166s 16 98.9 109.3 166s 17 97.9 109.7 166s 18 97.1 107.6 166s 19 96.7 107.5 166s 20 98.6 110.5 166s > print( predict( fitols1$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 166s + useDfSys = TRUE ) ) 166s fit se.fit lwr upr 166s 1 98.9 1.056 93.6 104.3 166s 2 100.1 1.037 94.8 105.4 166s 3 100.2 0.939 94.9 105.5 166s 4 100.4 0.912 95.1 105.6 166s 5 102.7 0.895 97.5 107.9 166s 6 102.6 0.791 97.4 107.7 166s 7 102.4 0.719 97.3 107.5 166s 8 104.3 0.963 99.0 109.6 166s 9 102.9 0.788 97.8 108.1 166s 10 100.4 0.981 95.1 105.6 166s 11 96.0 1.185 90.6 101.5 166s 12 94.1 1.394 88.5 99.8 166s 13 95.6 1.244 90.1 101.1 166s 14 97.8 0.896 92.6 103.0 166s 15 102.6 0.874 97.4 107.8 166s 16 104.1 0.916 98.9 109.3 166s 17 103.8 1.605 97.9 109.7 166s 18 102.4 0.962 97.1 107.6 166s 19 102.1 1.098 96.7 107.5 166s 20 104.5 1.664 98.6 110.5 166s > 166s > print( predict( fitols2r, se.pred = TRUE, interval = "confidence", 166s + level = 0.999, newdata = predictData ) ) 166s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 166s 1 103 2.17 99.9 107 96.7 2.62 166s 2 106 2.16 102.4 109 97.9 2.55 166s 3 106 2.17 102.2 109 98.1 2.55 166s 4 106 2.16 102.5 109 98.3 2.54 166s 5 108 2.43 102.9 113 100.9 2.67 166s 6 108 2.38 103.1 113 100.7 2.63 166s 7 109 2.37 103.7 113 100.6 2.59 166s 8 109 2.33 104.5 114 102.6 2.55 166s 9 107 2.44 102.2 113 101.4 2.69 166s 10 106 2.57 100.2 112 98.8 2.84 166s 11 101 2.36 96.1 106 94.4 2.89 166s 12 100 2.17 96.6 104 92.3 2.88 166s 13 102 2.08 99.0 104 93.9 2.75 166s 14 105 2.25 100.7 109 96.3 2.72 166s 15 110 2.63 103.7 116 101.4 2.72 166s 16 110 2.52 104.1 116 102.9 2.65 166s 17 110 2.96 102.0 118 102.9 3.03 166s 18 108 2.28 103.9 112 101.1 2.55 166s 19 110 2.36 105.1 115 100.9 2.55 166s 20 114 2.57 107.4 120 103.3 2.51 166s supply.lwr supply.upr 166s 1 93.2 100.2 166s 2 95.2 100.5 166s 3 95.3 100.8 166s 4 95.8 100.8 166s 5 97.0 104.8 166s 6 97.2 104.3 166s 7 97.5 103.7 166s 8 99.9 105.2 166s 9 97.3 105.5 166s 10 93.6 104.1 166s 11 88.8 100.0 166s 12 86.8 97.9 166s 13 89.3 98.5 166s 14 91.9 100.6 166s 15 97.0 105.8 166s 16 99.2 106.6 166s 17 96.4 109.4 166s 18 98.4 103.9 166s 19 98.2 103.5 166s 20 101.1 105.5 166s > print( predict( fitols2r$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 166s + level = 0.999, newdata = predictData ) ) 166s fit se.pred lwr upr 166s 1 103 2.17 99.9 107 166s 2 106 2.16 102.4 109 166s 3 106 2.17 102.2 109 166s 4 106 2.16 102.5 109 166s 5 108 2.43 102.9 113 166s 6 108 2.38 103.1 113 166s 7 109 2.37 103.7 113 166s 8 109 2.33 104.5 114 166s 9 107 2.44 102.2 113 166s 10 106 2.57 100.2 112 166s 11 101 2.36 96.1 106 166s 12 100 2.17 96.6 104 166s 13 102 2.08 99.0 104 166s 14 105 2.25 100.7 109 166s 15 110 2.63 103.7 116 166s 16 110 2.52 104.1 116 166s 17 110 2.96 102.0 118 166s 18 108 2.28 103.9 112 166s 19 110 2.36 105.1 115 166s 20 114 2.57 107.4 120 166s > 166s > print( predict( fitols3s, se.fit = TRUE, se.pred = TRUE, 166s + interval = "prediction", level = 0.5, newdata = predictData ) ) 166s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 166s 1 103 0.940 2.16 101.8 105 96.7 166s 2 106 0.944 2.16 104.3 107 97.9 166s 3 106 0.969 2.17 104.2 107 98.1 166s 4 106 0.949 2.16 104.4 107 98.3 166s 5 108 1.452 2.43 106.5 110 100.9 166s 6 108 1.372 2.38 106.4 110 100.7 166s 7 109 1.356 2.37 106.9 110 100.6 166s 8 109 1.296 2.34 107.6 111 102.6 166s 9 107 1.464 2.43 105.8 109 101.4 166s 10 106 1.652 2.55 104.5 108 98.8 166s 11 101 1.305 2.34 99.4 103 94.4 166s 12 100 0.941 2.16 98.6 102 92.3 166s 13 102 0.725 2.07 100.2 103 93.9 166s 14 105 1.124 2.24 103.3 106 96.3 166s 15 110 1.774 2.63 108.3 112 101.4 166s 16 110 1.606 2.52 108.2 112 102.9 166s 17 110 2.216 2.95 108.0 112 102.9 166s 18 108 1.208 2.29 106.6 110 101.1 166s 19 110 1.356 2.37 108.3 112 100.9 166s 20 114 1.718 2.59 111.7 115 103.3 166s supply.se.fit supply.se.pred supply.lwr supply.upr 166s 1 1.149 2.69 94.8 98.5 166s 2 0.873 2.59 96.1 99.6 166s 3 0.907 2.60 96.3 99.8 166s 4 0.831 2.58 96.5 100.0 166s 5 1.324 2.77 99.0 102.8 166s 6 1.188 2.71 98.9 102.6 166s 7 1.049 2.65 98.8 102.4 166s 8 0.911 2.60 100.8 104.3 166s 9 1.396 2.81 99.5 103.3 166s 10 1.782 3.02 96.8 100.9 166s 11 1.906 3.09 92.3 96.5 166s 12 1.875 3.08 90.2 94.4 166s 13 1.560 2.89 91.9 95.8 166s 14 1.475 2.85 94.3 98.2 166s 15 1.477 2.85 99.5 103.3 166s 16 1.245 2.74 101.0 104.8 166s 17 2.195 3.28 100.6 105.1 166s 18 0.909 2.60 99.4 102.9 166s 19 0.875 2.59 99.1 102.6 166s 20 0.704 2.54 101.6 105.0 166s > print( predict( fitols3s$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 166s + interval = "prediction", level = 0.5, newdata = predictData ) ) 166s fit se.fit se.pred lwr upr 166s 1 96.7 1.149 2.69 94.8 98.5 166s 2 97.9 0.873 2.59 96.1 99.6 166s 3 98.1 0.907 2.60 96.3 99.8 166s 4 98.3 0.831 2.58 96.5 100.0 166s 5 100.9 1.324 2.77 99.0 102.8 166s 6 100.7 1.188 2.71 98.9 102.6 166s 7 100.6 1.049 2.65 98.8 102.4 166s 8 102.6 0.911 2.60 100.8 104.3 166s 9 101.4 1.396 2.81 99.5 103.3 166s 10 98.8 1.782 3.02 96.8 100.9 166s 11 94.4 1.906 3.09 92.3 96.5 166s 12 92.3 1.875 3.08 90.2 94.4 166s 13 93.9 1.560 2.89 91.9 95.8 166s 14 96.3 1.475 2.85 94.3 98.2 166s 15 101.4 1.477 2.85 99.5 103.3 166s 16 102.9 1.245 2.74 101.0 104.8 166s 17 102.9 2.195 3.28 100.6 105.1 166s 18 101.1 0.909 2.60 99.4 102.9 166s 19 100.9 0.875 2.59 99.1 102.6 166s 20 103.3 0.704 2.54 101.6 105.0 166s > 166s > print( predict( fitols4rs, se.fit = TRUE, se.pred = TRUE, 166s + interval = "confidence", level = 0.99 ) ) 166s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 166s 1 97.6 0.541 2.01 96.1 99.0 98.3 166s 2 99.6 0.471 2.00 98.3 100.9 99.6 166s 3 99.5 0.454 1.99 98.3 100.8 99.8 166s 4 99.7 0.475 2.00 98.4 101.0 100.0 166s 5 102.3 0.434 1.99 101.1 103.4 102.5 166s 6 102.0 0.418 1.98 100.9 103.2 102.4 166s 7 102.4 0.440 1.99 101.2 103.6 102.3 166s 8 102.7 0.537 2.01 101.2 104.1 104.4 166s 9 101.7 0.447 1.99 100.5 102.9 102.9 166s 10 100.9 0.628 2.04 99.2 102.6 100.2 166s 11 95.9 0.833 2.11 93.7 98.2 95.7 166s 12 94.7 0.807 2.10 92.5 96.9 93.9 166s 13 95.9 0.677 2.06 94.0 97.7 95.5 166s 14 99.1 0.459 1.99 97.8 100.3 97.8 166s 15 104.2 0.572 2.02 102.7 105.8 102.9 166s 16 103.8 0.509 2.01 102.4 105.2 104.5 166s 17 104.8 0.877 2.13 102.4 107.2 104.1 166s 18 101.8 0.478 2.00 100.5 103.1 103.0 166s 19 103.3 0.604 2.03 101.6 104.9 102.8 166s 20 106.1 1.102 2.23 103.1 109.1 105.5 166s supply.se.fit supply.se.pred supply.lwr supply.upr 166s 1 0.598 2.52 96.7 99.9 166s 2 0.679 2.54 97.8 101.5 166s 3 0.634 2.53 98.0 101.5 166s 4 0.643 2.53 98.3 101.8 166s 5 0.753 2.56 100.4 104.5 166s 6 0.680 2.54 100.5 104.2 166s 7 0.625 2.53 100.6 104.0 166s 8 0.799 2.57 102.2 106.6 166s 9 0.700 2.55 101.0 104.8 166s 10 0.716 2.55 98.2 102.1 166s 11 0.916 2.61 93.2 98.2 166s 12 1.226 2.74 90.5 97.2 166s 13 1.130 2.70 92.5 98.6 166s 14 0.796 2.57 95.7 100.0 166s 15 0.656 2.53 101.1 104.7 166s 16 0.644 2.53 102.8 106.3 166s 17 1.150 2.70 101.0 107.2 166s 18 0.575 2.51 101.4 104.5 166s 19 0.649 2.53 101.0 104.5 166s 20 0.875 2.60 103.1 107.8 166s > print( predict( fitols4rs$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 166s + interval = "confidence", level = 0.99 ) ) 166s fit se.fit se.pred lwr upr 166s 1 97.6 0.541 2.01 96.1 99.0 166s 2 99.6 0.471 2.00 98.3 100.9 166s 3 99.5 0.454 1.99 98.3 100.8 166s 4 99.7 0.475 2.00 98.4 101.0 166s 5 102.3 0.434 1.99 101.1 103.4 166s 6 102.0 0.418 1.98 100.9 103.2 166s 7 102.4 0.440 1.99 101.2 103.6 166s 8 102.7 0.537 2.01 101.2 104.1 166s 9 101.7 0.447 1.99 100.5 102.9 166s 10 100.9 0.628 2.04 99.2 102.6 166s 11 95.9 0.833 2.11 93.7 98.2 166s 12 94.7 0.807 2.10 92.5 96.9 166s 13 95.9 0.677 2.06 94.0 97.7 166s 14 99.1 0.459 1.99 97.8 100.3 166s 15 104.2 0.572 2.02 102.7 105.8 166s 16 103.8 0.509 2.01 102.4 105.2 166s 17 104.8 0.877 2.13 102.4 107.2 166s 18 101.8 0.478 2.00 100.5 103.1 166s 19 103.3 0.604 2.03 101.6 104.9 166s 20 106.1 1.102 2.23 103.1 109.1 166s > 166s > print( predict( fitols5, se.fit = TRUE, interval = "prediction", 166s + level = 0.9, newdata = predictData ) ) 166s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 166s 1 104 0.714 100.0 107 96.4 0.712 166s 2 106 0.748 102.5 110 97.7 0.591 166s 3 106 0.753 102.4 109 97.9 0.602 166s 4 106 0.756 102.6 110 98.1 0.565 166s 5 109 1.055 104.8 112 100.7 0.900 166s 6 108 1.013 104.7 112 100.5 0.811 166s 7 109 1.029 105.2 113 100.5 0.722 166s 8 109 1.055 105.7 113 102.5 0.703 166s 9 108 1.042 104.1 112 101.1 0.952 166s 10 107 1.148 102.8 110 98.5 1.136 166s 11 101 1.026 97.6 105 94.0 1.245 166s 12 100 0.800 96.7 104 92.1 1.347 166s 13 102 0.606 98.4 105 93.7 1.170 166s 14 105 0.820 101.5 109 96.0 1.034 166s 15 111 1.272 106.6 114 101.2 1.031 166s 16 110 1.191 106.4 114 102.7 0.925 166s 17 111 1.513 106.5 115 102.5 1.529 166s 18 108 0.963 104.8 112 101.0 0.720 166s 19 110 1.129 106.4 114 100.8 0.717 166s 20 114 1.601 109.5 118 103.4 0.562 166s supply.lwr supply.upr 166s 1 92.1 100.7 166s 2 93.4 102.0 166s 3 93.6 102.1 166s 4 93.9 102.4 166s 5 96.3 105.1 166s 6 96.2 104.9 166s 7 96.1 104.8 166s 8 98.2 106.8 166s 9 96.7 105.6 166s 10 93.9 103.0 166s 11 89.4 98.7 166s 12 87.4 96.8 166s 13 89.1 98.2 166s 14 91.5 100.5 166s 15 96.7 105.7 166s 16 98.3 107.2 166s 17 97.6 107.4 166s 18 96.7 105.4 166s 19 96.5 105.1 166s 20 99.1 107.6 166s > print( predict( fitols5$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 166s + level = 0.9, newdata = predictData ) ) 166s fit se.fit lwr upr 166s 1 96.4 0.712 92.1 100.7 166s 2 97.7 0.591 93.4 102.0 166s 3 97.9 0.602 93.6 102.1 166s 4 98.1 0.565 93.9 102.4 166s 5 100.7 0.900 96.3 105.1 166s 6 100.5 0.811 96.2 104.9 166s 7 100.5 0.722 96.1 104.8 166s 8 102.5 0.703 98.2 106.8 166s 9 101.1 0.952 96.7 105.6 166s 10 98.5 1.136 93.9 103.0 166s 11 94.0 1.245 89.4 98.7 166s 12 92.1 1.347 87.4 96.8 166s 13 93.7 1.170 89.1 98.2 166s 14 96.0 1.034 91.5 100.5 166s 15 101.2 1.031 96.7 105.7 166s 16 102.7 0.925 98.3 107.2 166s 17 102.5 1.529 97.6 107.4 166s 18 101.0 0.720 96.7 105.4 166s 19 100.8 0.717 96.5 105.1 166s 20 103.4 0.562 99.1 107.6 166s > 166s > # predict just one observation 166s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 166s + trend = 25 ) 166s > 166s > print( predict( fitols1, newdata = smallData ) ) 166s demand.pred supply.pred 166s 1 109 115 166s > print( predict( fitols1$eq[[ 1 ]], newdata = smallData ) ) 166s fit 166s 1 109 166s > 166s > print( predict( fitols2r, se.fit = TRUE, level = 0.9, 166s + newdata = smallData ) ) 166s demand.pred demand.se.fit supply.pred supply.se.fit 166s 1 109 2.48 116 2.8 166s > print( predict( fitols2r$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 166s + newdata = smallData ) ) 166s fit se.pred 166s 1 109 3.15 166s > 166s > print( predict( fitols3s, interval = "prediction", level = 0.975, 166s + newdata = smallData ) ) 166s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 166s 1 109 101 116 116 107 126 166s > print( predict( fitols3s$eq[[ 1 ]], interval = "confidence", level = 0.8, 166s + newdata = smallData ) ) 166s fit lwr upr 166s 1 109 105 112 166s > 166s > print( predict( fitols4rs, se.fit = TRUE, interval = "confidence", 166s + level = 0.999, newdata = smallData ) ) 166s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 166s 1 108 2.02 101 115 117 2.02 166s supply.lwr supply.upr 166s 1 110 124 166s > print( predict( fitols4rs$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 166s + level = 0.75, newdata = smallData ) ) 166s fit se.pred lwr upr 166s 1 117 3.18 113 121 166s > 166s > print( predict( fitols5, se.fit = TRUE, interval = "prediction", 166s + newdata = smallData ) ) 166s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 166s 1 108 2.18 102 114 117 2.01 166s supply.lwr supply.upr 166s 1 111 124 166s > print( predict( fitols5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 166s + newdata = smallData ) ) 166s fit se.pred lwr upr 166s 1 108 2.92 104 113 166s > 166s > print( predict( fitols5rs, se.fit = TRUE, se.pred = TRUE, 166s + interval = "prediction", level = 0.5, newdata = smallData ) ) 166s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 166s 1 108 2.02 2.8 106 110 117 166s supply.se.fit supply.se.pred supply.lwr supply.upr 166s 1 2.02 3.18 115 119 166s > print( predict( fitols5rs$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 166s + interval = "confidence", level = 0.25, newdata = smallData ) ) 166s fit se.fit se.pred lwr upr 166s 1 108 2.02 2.8 107 109 166s > 166s > 166s > ## ************ correlation of predicted values *************** 166s > print( correlation.systemfit( fitols1, 1, 2 ) ) 166s [,1] 166s [1,] 0 166s [2,] 0 166s [3,] 0 166s [4,] 0 166s [5,] 0 166s [6,] 0 166s [7,] 0 166s [8,] 0 166s [9,] 0 166s [10,] 0 166s [11,] 0 166s [12,] 0 166s [13,] 0 166s [14,] 0 166s [15,] 0 166s [16,] 0 166s [17,] 0 166s [18,] 0 166s [19,] 0 166s [20,] 0 166s > 166s > print( correlation.systemfit( fitols2r, 2, 1 ) ) 166s [,1] 166s [1,] 0.443122 166s [2,] 0.160426 166s [3,] 0.161091 166s [4,] 0.118312 166s [5,] -0.077411 166s [6,] -0.059235 166s [7,] -0.057777 166s [8,] -0.006908 166s [9,] -0.000372 166s [10,] -0.001410 166s [11,] 0.055233 166s [12,] 0.074936 166s [13,] 0.028274 166s [14,] -0.032082 166s [15,] 0.196029 166s [16,] 0.279921 166s [17,] 0.115570 166s [18,] 0.080620 166s [19,] 0.171681 166s [20,] 0.150544 166s > 166s > print( correlation.systemfit( fitols3s, 1, 2 ) ) 166s [,1] 166s [1,] 0.405901 166s [2,] 0.145364 166s [3,] 0.145375 166s [4,] 0.105835 166s [5,] -0.067958 166s [6,] -0.052026 166s [7,] -0.050543 166s [8,] -0.006031 166s [9,] -0.000326 166s [10,] -0.001237 166s [11,] 0.047534 166s [12,] 0.063493 166s [13,] 0.024060 166s [14,] -0.027910 166s [15,] 0.171580 166s [16,] 0.248212 166s [17,] 0.101409 166s [18,] 0.073084 166s [19,] 0.153950 166s [20,] 0.132944 166s > 166s > print( correlation.systemfit( fitols4rs, 2, 1 ) ) 166s [,1] 166s [1,] 0.38162 166s [2,] 0.29173 166s [3,] 0.25421 166s [4,] 0.28598 166s [5,] -0.02775 166s [6,] -0.04974 166s [7,] -0.05850 166s [8,] 0.09388 166s [9,] 0.09469 166s [10,] 0.43814 166s [11,] 0.10559 166s [12,] 0.00876 166s [13,] 0.04090 166s [14,] -0.03984 166s [15,] 0.40767 166s [16,] 0.24571 166s [17,] 0.64160 166s [18,] 0.24037 166s [19,] 0.34075 166s [20,] 0.54270 166s > 166s > print( correlation.systemfit( fitols5, 1, 2 ) ) 166s [,1] 166s [1,] 0.4051 166s [2,] 0.2729 166s [3,] 0.2415 166s [4,] 0.2693 166s [5,] -0.0301 166s [6,] -0.0527 166s [7,] -0.0624 166s [8,] 0.0971 166s [9,] 0.0945 166s [10,] 0.4365 166s [11,] 0.1258 166s [12,] 0.0210 166s [13,] 0.0436 166s [14,] -0.0405 166s [15,] 0.4102 166s [16,] 0.2610 166s [17,] 0.6400 166s [18,] 0.2661 166s [19,] 0.3796 166s [20,] 0.5742 166s > 166s > 166s > ## ************ Log-Likelihood values *************** 166s > print( logLik( fitols1 ) ) 166s 'log Lik.' -67.8 (df=8) 166s > print( logLik( fitols1, residCovDiag = TRUE ) ) 166s 'log Lik.' -83.6 (df=8) 166s > all.equal( logLik( fitols1, residCovDiag = TRUE ), 166s + logLik( lmDemand ) + logLik( lmSupply ), 166s + check.attributes = FALSE ) 166s [1] TRUE 166s > 166s > print( logLik( fitols2r ) ) 166s 'log Lik.' -62 (df=7) 166s > print( logLik( fitols2r, residCovDiag = TRUE ) ) 166s 'log Lik.' -84 (df=7) 166s > 166s > print( logLik( fitols3s ) ) 166s 'log Lik.' -62 (df=7) 166s > print( logLik( fitols3s, residCovDiag = TRUE ) ) 166s 'log Lik.' -84 (df=7) 166s > 166s > print( logLik( fitols4rs ) ) 166s 'log Lik.' -62.8 (df=6) 166s > print( logLik( fitols4rs, residCovDiag = TRUE ) ) 166s 'log Lik.' -84.1 (df=6) 166s > 166s > print( logLik( fitols5 ) ) 166s 'log Lik.' -62.8 (df=6) 166s > print( logLik( fitols5, residCovDiag = TRUE ) ) 166s 'log Lik.' -84.1 (df=6) 166s > 166s > 166s > ## ************** F tests **************** 166s > # testing first restriction 166s > print( linearHypothesis( fitols1, restrm ) ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.14 0.71 166s > linearHypothesis( fitols1, restrict ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.14 0.71 166s > 166s > print( linearHypothesis( fitols1s, restrm ) ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1s 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.15 0.7 166s > linearHypothesis( fitols1s, restrict ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1s 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.15 0.7 166s > 166s > print( linearHypothesis( fitols1, restrm ) ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.14 0.71 166s > linearHypothesis( fitols1, restrict ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.14 0.71 166s > 166s > print( linearHypothesis( fitols1r, restrm ) ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1r 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.14 0.71 166s > linearHypothesis( fitols1r, restrict ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1r 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.14 0.71 166s > 166s > # testing second restriction 166s > restrOnly2m <- matrix(0,1,7) 166s > restrOnly2q <- 0.5 166s > restrOnly2m[1,2] <- -1 166s > restrOnly2m[1,5] <- 1 166s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 166s > # first restriction not imposed 166s > print( linearHypothesis( fitols1, restrOnly2m, restrOnly2q ) ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.01 0.94 166s > linearHypothesis( fitols1, restrictOnly2 ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df F Pr(>F) 166s 1 34 166s 2 33 1 0.01 0.94 166s > 166s > # first restriction imposed 166s > print( linearHypothesis( fitols2, restrOnly2m, restrOnly2q ) ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols2 166s 166s Res.Df Df F Pr(>F) 166s 1 35 166s 2 34 1 0.02 0.88 166s > linearHypothesis( fitols2, restrictOnly2 ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols2 166s 166s Res.Df Df F Pr(>F) 166s 1 35 166s 2 34 1 0.02 0.88 166s > 166s > print( linearHypothesis( fitols3, restrOnly2m, restrOnly2q ) ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols3 166s 166s Res.Df Df F Pr(>F) 166s 1 35 166s 2 34 1 0.02 0.88 166s > linearHypothesis( fitols3, restrictOnly2 ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols3 166s 166s Res.Df Df F Pr(>F) 166s 1 35 166s 2 34 1 0.02 0.88 166s > 166s > # testing both of the restrictions 166s > print( linearHypothesis( fitols1, restr2m, restr2q ) ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df F Pr(>F) 166s 1 35 166s 2 33 2 0.08 0.93 166s > linearHypothesis( fitols1, restrict2 ) 166s Linear hypothesis test (Theil's F test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df F Pr(>F) 166s 1 35 166s 2 33 2 0.08 0.93 166s > 166s > 166s > ## ************** Wald tests **************** 166s > # testing first restriction 166s > print( linearHypothesis( fitols1, restrm, test = "Chisq" ) ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.64 0.42 166s > linearHypothesis( fitols1, restrict, test = "Chisq" ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.64 0.42 166s > 166s > print( linearHypothesis( fitols1s, restrm, test = "Chisq" ) ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1s 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.72 0.4 166s > linearHypothesis( fitols1s, restrict, test = "Chisq" ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1s 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.72 0.4 166s > 166s > print( linearHypothesis( fitols1, restrm, test = "Chisq" ) ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.64 0.42 166s > linearHypothesis( fitols1, restrict, test = "Chisq" ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.64 0.42 166s > 166s > print( linearHypothesis( fitols1r, restrm, test = "Chisq" ) ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1r 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.64 0.42 166s > linearHypothesis( fitols1r, restrict, test = "Chisq" ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s 166s Model 1: restricted model 166s Model 2: fitols1r 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.64 0.42 166s > 166s > # testing second restriction 166s > # first restriction not imposed 166s > print( linearHypothesis( fitols1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.03 0.86 166s > linearHypothesis( fitols1, restrictOnly2, test = "Chisq" ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 34 166s 2 33 1 0.03 0.86 166s > # first restriction imposed 166s > print( linearHypothesis( fitols2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols2 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 35 166s 2 34 1 0.12 0.73 166s > linearHypothesis( fitols2, restrictOnly2, test = "Chisq" ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols2 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 35 166s 2 34 1 0.12 0.73 166s > 166s > print( linearHypothesis( fitols3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols3 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 35 166s 2 34 1 0.12 0.73 166s > linearHypothesis( fitols3, restrictOnly2, test = "Chisq" ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols3 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 35 166s 2 34 1 0.12 0.73 166s > 166s > # testing both of the restrictions 166s > print( linearHypothesis( fitols1, restr2m, restr2q, test = "Chisq" ) ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 35 166s 2 33 2 0.72 0.7 166s > linearHypothesis( fitols1, restrict2, test = "Chisq" ) 166s Linear hypothesis test (Chi^2 statistic of a Wald test) 166s 166s Hypothesis: 166s demand_income - supply_trend = 0 166s - demand_price + supply_price = 0.5 166s 166s Model 1: restricted model 166s Model 2: fitols1 166s 166s Res.Df Df Chisq Pr(>Chisq) 166s 1 35 166s 2 33 2 0.72 0.7 166s > 166s > 166s > ## ****************** model frame ************************** 166s > print( mf <- model.frame( fitols1 ) ) 166s consump price income farmPrice trend 166s 1 98.5 100.3 87.4 98.0 1 166s 2 99.2 104.3 97.6 99.1 2 166s 3 102.2 103.4 96.7 99.1 3 166s 4 101.5 104.5 98.2 98.1 4 166s 5 104.2 98.0 99.8 110.8 5 166s 6 103.2 99.5 100.5 108.2 6 166s 7 104.0 101.1 103.2 105.6 7 166s 8 99.9 104.8 107.8 109.8 8 166s 9 100.3 96.4 96.6 108.7 9 166s 10 102.8 91.2 88.9 100.6 10 166s 11 95.4 93.1 75.1 81.0 11 166s 12 92.4 98.8 76.9 68.6 12 166s 13 94.5 102.9 84.6 70.9 13 166s 14 98.8 98.8 90.6 81.4 14 166s 15 105.8 95.1 103.1 102.3 15 166s 16 100.2 98.5 105.1 105.0 16 166s 17 103.5 86.5 96.4 110.5 17 166s 18 99.9 104.0 104.4 92.5 18 166s 19 105.2 105.8 110.7 89.3 19 166s 20 106.2 113.5 127.1 93.0 20 166s > print( mf1 <- model.frame( fitols1$eq[[ 1 ]] ) ) 166s consump price income 166s 1 98.5 100.3 87.4 166s 2 99.2 104.3 97.6 166s 3 102.2 103.4 96.7 166s 4 101.5 104.5 98.2 166s 5 104.2 98.0 99.8 166s 6 103.2 99.5 100.5 166s 7 104.0 101.1 103.2 166s 8 99.9 104.8 107.8 166s 9 100.3 96.4 96.6 166s 10 102.8 91.2 88.9 166s 11 95.4 93.1 75.1 166s 12 92.4 98.8 76.9 166s 13 94.5 102.9 84.6 166s 14 98.8 98.8 90.6 166s 15 105.8 95.1 103.1 166s 16 100.2 98.5 105.1 166s 17 103.5 86.5 96.4 166s 18 99.9 104.0 104.4 166s 19 105.2 105.8 110.7 166s 20 106.2 113.5 127.1 166s > print( attributes( mf1 )$terms ) 166s consump ~ price + income 166s attr(,"variables") 166s list(consump, price, income) 166s attr(,"factors") 166s price income 166s consump 0 0 166s price 1 0 166s income 0 1 166s attr(,"term.labels") 166s [1] "price" "income" 166s attr(,"order") 166s [1] 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, income) 166s attr(,"dataClasses") 166s consump price income 166s "numeric" "numeric" "numeric" 166s > print( mf2 <- model.frame( fitols1$eq[[ 2 ]] ) ) 166s consump price farmPrice trend 166s 1 98.5 100.3 98.0 1 166s 2 99.2 104.3 99.1 2 166s 3 102.2 103.4 99.1 3 166s 4 101.5 104.5 98.1 4 166s 5 104.2 98.0 110.8 5 166s 6 103.2 99.5 108.2 6 166s 7 104.0 101.1 105.6 7 166s 8 99.9 104.8 109.8 8 166s 9 100.3 96.4 108.7 9 166s 10 102.8 91.2 100.6 10 166s 11 95.4 93.1 81.0 11 166s 12 92.4 98.8 68.6 12 166s 13 94.5 102.9 70.9 13 166s 14 98.8 98.8 81.4 14 166s 15 105.8 95.1 102.3 15 166s 16 100.2 98.5 105.0 16 166s 17 103.5 86.5 110.5 17 166s 18 99.9 104.0 92.5 18 166s 19 105.2 105.8 89.3 19 166s 20 106.2 113.5 93.0 20 166s > print( attributes( mf2 )$terms ) 166s consump ~ price + farmPrice + trend 166s attr(,"variables") 166s list(consump, price, farmPrice, trend) 166s attr(,"factors") 166s price farmPrice trend 166s consump 0 0 0 166s price 1 0 0 166s farmPrice 0 1 0 166s trend 0 0 1 166s attr(,"term.labels") 166s [1] "price" "farmPrice" "trend" 166s attr(,"order") 166s [1] 1 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, farmPrice, trend) 166s attr(,"dataClasses") 166s consump price farmPrice trend 166s "numeric" "numeric" "numeric" "numeric" 166s > 166s > print( all.equal( mf, model.frame( fitols2r ) ) ) 166s [1] TRUE 166s > print( all.equal( mf1, model.frame( fitols2r$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > 166s > print( all.equal( mf, model.frame( fitols3s ) ) ) 166s [1] TRUE 166s > print( all.equal( mf2, model.frame( fitols3s$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > 166s > print( all.equal( mf, model.frame( fitols4rs ) ) ) 166s [1] TRUE 166s > print( all.equal( mf1, model.frame( fitols4rs$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > 166s > print( all.equal( mf, model.frame( fitols5 ) ) ) 166s [1] TRUE 166s > print( all.equal( mf2, model.frame( fitols5$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > 166s > 166s > ## **************** model matrix ************************ 166s > # with x (returnModelMatrix) = TRUE 166s > print( !is.null( fitols1r$eq[[ 1 ]]$x ) ) 166s [1] TRUE 166s > print( mm <- model.matrix( fitols1r ) ) 166s demand_(Intercept) demand_price demand_income supply_(Intercept) 166s demand_1 1 100.3 87.4 0 166s demand_2 1 104.3 97.6 0 166s demand_3 1 103.4 96.7 0 166s demand_4 1 104.5 98.2 0 166s demand_5 1 98.0 99.8 0 166s demand_6 1 99.5 100.5 0 166s demand_7 1 101.1 103.2 0 166s demand_8 1 104.8 107.8 0 166s demand_9 1 96.4 96.6 0 166s demand_10 1 91.2 88.9 0 166s demand_11 1 93.1 75.1 0 166s demand_12 1 98.8 76.9 0 166s demand_13 1 102.9 84.6 0 166s demand_14 1 98.8 90.6 0 166s demand_15 1 95.1 103.1 0 166s demand_16 1 98.5 105.1 0 166s demand_17 1 86.5 96.4 0 166s demand_18 1 104.0 104.4 0 166s demand_19 1 105.8 110.7 0 166s demand_20 1 113.5 127.1 0 166s supply_1 0 0.0 0.0 1 166s supply_2 0 0.0 0.0 1 166s supply_3 0 0.0 0.0 1 166s supply_4 0 0.0 0.0 1 166s supply_5 0 0.0 0.0 1 166s supply_6 0 0.0 0.0 1 166s supply_7 0 0.0 0.0 1 166s supply_8 0 0.0 0.0 1 166s supply_9 0 0.0 0.0 1 166s supply_10 0 0.0 0.0 1 166s supply_11 0 0.0 0.0 1 166s supply_12 0 0.0 0.0 1 166s supply_13 0 0.0 0.0 1 166s supply_14 0 0.0 0.0 1 166s supply_15 0 0.0 0.0 1 166s supply_16 0 0.0 0.0 1 166s supply_17 0 0.0 0.0 1 166s supply_18 0 0.0 0.0 1 166s supply_19 0 0.0 0.0 1 166s supply_20 0 0.0 0.0 1 166s supply_price supply_farmPrice supply_trend 166s demand_1 0.0 0.0 0 166s demand_2 0.0 0.0 0 166s demand_3 0.0 0.0 0 166s demand_4 0.0 0.0 0 166s demand_5 0.0 0.0 0 166s demand_6 0.0 0.0 0 166s demand_7 0.0 0.0 0 166s demand_8 0.0 0.0 0 166s demand_9 0.0 0.0 0 166s demand_10 0.0 0.0 0 166s demand_11 0.0 0.0 0 166s demand_12 0.0 0.0 0 166s demand_13 0.0 0.0 0 166s demand_14 0.0 0.0 0 166s demand_15 0.0 0.0 0 166s demand_16 0.0 0.0 0 166s demand_17 0.0 0.0 0 166s demand_18 0.0 0.0 0 166s demand_19 0.0 0.0 0 166s demand_20 0.0 0.0 0 166s supply_1 100.3 98.0 1 166s supply_2 104.3 99.1 2 166s supply_3 103.4 99.1 3 166s supply_4 104.5 98.1 4 166s supply_5 98.0 110.8 5 166s supply_6 99.5 108.2 6 166s supply_7 101.1 105.6 7 166s supply_8 104.8 109.8 8 166s supply_9 96.4 108.7 9 166s supply_10 91.2 100.6 10 166s supply_11 93.1 81.0 11 166s supply_12 98.8 68.6 12 166s supply_13 102.9 70.9 13 166s supply_14 98.8 81.4 14 166s supply_15 95.1 102.3 15 166s supply_16 98.5 105.0 16 166s supply_17 86.5 110.5 17 166s supply_18 104.0 92.5 18 166s supply_19 105.8 89.3 19 166s supply_20 113.5 93.0 20 166s > print( mm1 <- model.matrix( fitols1r$eq[[ 1 ]] ) ) 166s (Intercept) price income 166s 1 1 100.3 87.4 166s 2 1 104.3 97.6 166s 3 1 103.4 96.7 166s 4 1 104.5 98.2 166s 5 1 98.0 99.8 166s 6 1 99.5 100.5 166s 7 1 101.1 103.2 166s 8 1 104.8 107.8 166s 9 1 96.4 96.6 166s 10 1 91.2 88.9 166s 11 1 93.1 75.1 166s 12 1 98.8 76.9 166s 13 1 102.9 84.6 166s 14 1 98.8 90.6 166s 15 1 95.1 103.1 166s 16 1 98.5 105.1 166s 17 1 86.5 96.4 166s 18 1 104.0 104.4 166s 19 1 105.8 110.7 166s 20 1 113.5 127.1 166s attr(,"assign") 166s [1] 0 1 2 166s > print( mm2 <- model.matrix( fitols1r$eq[[ 2 ]] ) ) 166s (Intercept) price farmPrice trend 166s 1 1 100.3 98.0 1 166s 2 1 104.3 99.1 2 166s 3 1 103.4 99.1 3 166s 4 1 104.5 98.1 4 166s 5 1 98.0 110.8 5 166s 6 1 99.5 108.2 6 166s 7 1 101.1 105.6 7 166s 8 1 104.8 109.8 8 166s 9 1 96.4 108.7 9 166s 10 1 91.2 100.6 10 166s 11 1 93.1 81.0 11 166s 12 1 98.8 68.6 12 166s 13 1 102.9 70.9 13 166s 14 1 98.8 81.4 14 166s 15 1 95.1 102.3 15 166s 16 1 98.5 105.0 16 166s 17 1 86.5 110.5 17 166s 18 1 104.0 92.5 18 166s 19 1 105.8 89.3 19 166s 20 1 113.5 93.0 20 166s attr(,"assign") 166s [1] 0 1 2 3 166s > 166s > # with x (returnModelMatrix) = FALSE 166s > print( all.equal( mm, model.matrix( fitols1rs ) ) ) 166s [1] TRUE 166s > print( all.equal( mm1, model.matrix( fitols1rs$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > print( all.equal( mm2, model.matrix( fitols1rs$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > print( !is.null( fitols1rs$eq[[ 1 ]]$x ) ) 166s [1] FALSE 166s > 166s > # with x (returnModelMatrix) = TRUE 166s > print( !is.null( fitols2rs$eq[[ 1 ]]$x ) ) 166s [1] TRUE 166s > print( all.equal( mm, model.matrix( fitols2rs ) ) ) 166s [1] TRUE 166s > print( all.equal( mm1, model.matrix( fitols2rs$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > print( all.equal( mm2, model.matrix( fitols2rs$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > 166s > # with x (returnModelMatrix) = FALSE 166s > print( all.equal( mm, model.matrix( fitols2 ) ) ) 166s [1] TRUE 166s > print( all.equal( mm1, model.matrix( fitols2$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > print( all.equal( mm2, model.matrix( fitols2$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > print( !is.null( fitols2$eq[[ 1 ]]$x ) ) 166s [1] FALSE 166s > 166s > # with x (returnModelMatrix) = TRUE 166s > print( !is.null( fitols3$eq[[ 1 ]]$x ) ) 166s [1] TRUE 166s > print( all.equal( mm, model.matrix( fitols3 ) ) ) 166s [1] TRUE 166s > print( all.equal( mm1, model.matrix( fitols3$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > print( all.equal( mm2, model.matrix( fitols3$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > 166s > # with x (returnModelMatrix) = FALSE 166s > print( all.equal( mm, model.matrix( fitols3r ) ) ) 166s [1] TRUE 166s > print( all.equal( mm1, model.matrix( fitols3r$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > print( all.equal( mm2, model.matrix( fitols3r$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > print( !is.null( fitols3r$eq[[ 1 ]]$x ) ) 166s [1] FALSE 166s > 166s > # with x (returnModelMatrix) = TRUE 166s > print( !is.null( fitols4s$eq[[ 1 ]]$x ) ) 166s [1] TRUE 166s > print( all.equal( mm, model.matrix( fitols4s ) ) ) 166s [1] TRUE 166s > print( all.equal( mm1, model.matrix( fitols4s$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > print( all.equal( mm2, model.matrix( fitols4s$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > 166s > # with x (returnModelMatrix) = FALSE 166s > print( all.equal( mm, model.matrix( fitols4Sym ) ) ) 166s [1] TRUE 166s > print( all.equal( mm1, model.matrix( fitols4Sym$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > print( all.equal( mm2, model.matrix( fitols4Sym$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > print( !is.null( fitols4Sym$eq[[ 1 ]]$x ) ) 166s [1] FALSE 166s > 166s > # with x (returnModelMatrix) = TRUE 166s > print( !is.null( fitols5s$eq[[ 1 ]]$x ) ) 166s [1] TRUE 166s > print( all.equal( mm, model.matrix( fitols5s ) ) ) 166s [1] TRUE 166s > print( all.equal( mm1, model.matrix( fitols5s$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > print( all.equal( mm2, model.matrix( fitols5s$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > 166s > # with x (returnModelMatrix) = FALSE 166s > print( all.equal( mm, model.matrix( fitols5 ) ) ) 166s [1] TRUE 166s > print( all.equal( mm1, model.matrix( fitols5$eq[[ 1 ]] ) ) ) 166s [1] TRUE 166s > print( all.equal( mm2, model.matrix( fitols5$eq[[ 2 ]] ) ) ) 166s [1] TRUE 166s > print( !is.null( fitols5$eq[[ 1 ]]$x ) ) 166s [1] FALSE 166s > 166s > try( model.matrix( fitols1, which = "z" ) ) 166s Error in model.matrix.systemfit.equation(object$eq[[i]], which = which) : 166s argument 'which' can only be set to "xHat" or "z" if instruments were used 166s > 166s > 166s > ## **************** formulas ************************ 166s > formula( fitols1 ) 166s $demand 166s consump ~ price + income 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s 166s > formula( fitols1$eq[[ 2 ]] ) 166s consump ~ price + farmPrice + trend 166s > 166s > formula( fitols2r ) 166s $demand 166s consump ~ price + income 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s 166s > formula( fitols2r$eq[[ 1 ]] ) 166s consump ~ price + income 166s > 166s > formula( fitols3s ) 166s $demand 166s consump ~ price + income 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s 166s > formula( fitols3s$eq[[ 2 ]] ) 166s consump ~ price + farmPrice + trend 166s > 166s > formula( fitols4rs ) 166s $demand 166s consump ~ price + income 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s 166s > formula( fitols4rs$eq[[ 1 ]] ) 166s consump ~ price + income 166s > 166s > formula( fitols5 ) 166s $demand 166s consump ~ price + income 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s 166s > formula( fitols5$eq[[ 2 ]] ) 166s consump ~ price + farmPrice + trend 166s > 166s > 166s > ## **************** model terms ******************* 166s > terms( fitols1 ) 166s $demand 166s consump ~ price + income 166s attr(,"variables") 166s list(consump, price, income) 166s attr(,"factors") 166s price income 166s consump 0 0 166s price 1 0 166s income 0 1 166s attr(,"term.labels") 166s [1] "price" "income" 166s attr(,"order") 166s [1] 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, income) 166s attr(,"dataClasses") 166s consump price income 166s "numeric" "numeric" "numeric" 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s attr(,"variables") 166s list(consump, price, farmPrice, trend) 166s attr(,"factors") 166s price farmPrice trend 166s consump 0 0 0 166s price 1 0 0 166s farmPrice 0 1 0 166s trend 0 0 1 166s attr(,"term.labels") 166s [1] "price" "farmPrice" "trend" 166s attr(,"order") 166s [1] 1 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, farmPrice, trend) 166s attr(,"dataClasses") 166s consump price farmPrice trend 166s "numeric" "numeric" "numeric" "numeric" 166s 166s > terms( fitols1$eq[[ 2 ]] ) 166s consump ~ price + farmPrice + trend 166s attr(,"variables") 166s list(consump, price, farmPrice, trend) 166s attr(,"factors") 166s price farmPrice trend 166s consump 0 0 0 166s price 1 0 0 166s farmPrice 0 1 0 166s trend 0 0 1 166s attr(,"term.labels") 166s [1] "price" "farmPrice" "trend" 166s attr(,"order") 166s [1] 1 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, farmPrice, trend) 166s attr(,"dataClasses") 166s consump price farmPrice trend 166s "numeric" "numeric" "numeric" "numeric" 166s > 166s > terms( fitols2r ) 166s $demand 166s consump ~ price + income 166s attr(,"variables") 166s list(consump, price, income) 166s attr(,"factors") 166s price income 166s consump 0 0 166s price 1 0 166s income 0 1 166s attr(,"term.labels") 166s [1] "price" "income" 166s attr(,"order") 166s [1] 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, income) 166s attr(,"dataClasses") 166s consump price income 166s "numeric" "numeric" "numeric" 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s attr(,"variables") 166s list(consump, price, farmPrice, trend) 166s attr(,"factors") 166s price farmPrice trend 166s consump 0 0 0 166s price 1 0 0 166s farmPrice 0 1 0 166s trend 0 0 1 166s attr(,"term.labels") 166s [1] "price" "farmPrice" "trend" 166s attr(,"order") 166s [1] 1 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, farmPrice, trend) 166s attr(,"dataClasses") 166s consump price farmPrice trend 166s "numeric" "numeric" "numeric" "numeric" 166s 166s > terms( fitols2r$eq[[ 1 ]] ) 166s consump ~ price + income 166s attr(,"variables") 166s list(consump, price, income) 166s attr(,"factors") 166s price income 166s consump 0 0 166s price 1 0 166s income 0 1 166s attr(,"term.labels") 166s [1] "price" "income" 166s attr(,"order") 166s [1] 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, income) 166s attr(,"dataClasses") 166s consump price income 166s "numeric" "numeric" "numeric" 166s > 166s > terms( fitols3s ) 166s $demand 166s consump ~ price + income 166s attr(,"variables") 166s list(consump, price, income) 166s attr(,"factors") 166s price income 166s consump 0 0 166s price 1 0 166s income 0 1 166s attr(,"term.labels") 166s [1] "price" "income" 166s attr(,"order") 166s [1] 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, income) 166s attr(,"dataClasses") 166s consump price income 166s "numeric" "numeric" "numeric" 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s attr(,"variables") 166s list(consump, price, farmPrice, trend) 166s attr(,"factors") 166s price farmPrice trend 166s consump 0 0 0 166s price 1 0 0 166s farmPrice 0 1 0 166s trend 0 0 1 166s attr(,"term.labels") 166s [1] "price" "farmPrice" "trend" 166s attr(,"order") 166s [1] 1 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, farmPrice, trend) 166s attr(,"dataClasses") 166s consump price farmPrice trend 166s "numeric" "numeric" "numeric" "numeric" 166s 166s > terms( fitols3s$eq[[ 2 ]] ) 166s consump ~ price + farmPrice + trend 166s attr(,"variables") 166s list(consump, price, farmPrice, trend) 166s attr(,"factors") 166s price farmPrice trend 166s consump 0 0 0 166s price 1 0 0 166s farmPrice 0 1 0 166s trend 0 0 1 166s attr(,"term.labels") 166s [1] "price" "farmPrice" "trend" 166s attr(,"order") 166s [1] 1 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, farmPrice, trend) 166s attr(,"dataClasses") 166s consump price farmPrice trend 166s "numeric" "numeric" "numeric" "numeric" 166s > 166s > terms( fitols4rs ) 166s $demand 166s consump ~ price + income 166s attr(,"variables") 166s list(consump, price, income) 166s attr(,"factors") 166s price income 166s consump 0 0 166s price 1 0 166s income 0 1 166s attr(,"term.labels") 166s [1] "price" "income" 166s attr(,"order") 166s [1] 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, income) 166s attr(,"dataClasses") 166s consump price income 166s "numeric" "numeric" "numeric" 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s attr(,"variables") 166s list(consump, price, farmPrice, trend) 166s attr(,"factors") 166s price farmPrice trend 166s consump 0 0 0 166s price 1 0 0 166s farmPrice 0 1 0 166s trend 0 0 1 166s attr(,"term.labels") 166s [1] "price" "farmPrice" "trend" 166s attr(,"order") 166s [1] 1 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, farmPrice, trend) 166s attr(,"dataClasses") 166s consump price farmPrice trend 166s "numeric" "numeric" "numeric" "numeric" 166s 166s > terms( fitols4rs$eq[[ 1 ]] ) 166s consump ~ price + income 166s attr(,"variables") 166s list(consump, price, income) 166s attr(,"factors") 166s price income 166s consump 0 0 166s price 1 0 166s income 0 1 166s attr(,"term.labels") 166s [1] "price" "income" 166s attr(,"order") 166s [1] 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, income) 166s attr(,"dataClasses") 166s consump price income 166s "numeric" "numeric" "numeric" 166s > 166s > terms( fitols5 ) 166s $demand 166s consump ~ price + income 166s attr(,"variables") 166s list(consump, price, income) 166s attr(,"factors") 166s price income 166s consump 0 0 166s price 1 0 166s income 0 1 166s attr(,"term.labels") 166s [1] "price" "income" 166s attr(,"order") 166s [1] 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, income) 166s attr(,"dataClasses") 166s consump price income 166s "numeric" "numeric" "numeric" 166s 166s $supply 166s consump ~ price + farmPrice + trend 166s attr(,"variables") 166s list(consump, price, farmPrice, trend) 166s attr(,"factors") 166s price farmPrice trend 166s consump 0 0 0 166s price 1 0 0 166s farmPrice 0 1 0 166s trend 0 0 1 166s attr(,"term.labels") 166s [1] "price" "farmPrice" "trend" 166s attr(,"order") 166s [1] 1 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, farmPrice, trend) 166s attr(,"dataClasses") 166s consump price farmPrice trend 166s "numeric" "numeric" "numeric" "numeric" 166s 166s > terms( fitols5$eq[[ 2 ]] ) 166s consump ~ price + farmPrice + trend 166s attr(,"variables") 166s list(consump, price, farmPrice, trend) 166s attr(,"factors") 166s price farmPrice trend 166s consump 0 0 0 166s price 1 0 0 166s farmPrice 0 1 0 166s trend 0 0 1 166s attr(,"term.labels") 166s [1] "price" "farmPrice" "trend" 166s attr(,"order") 166s [1] 1 1 1 166s attr(,"intercept") 166s [1] 1 166s attr(,"response") 166s [1] 1 166s attr(,".Environment") 166s 166s attr(,"predvars") 166s list(consump, price, farmPrice, trend) 166s attr(,"dataClasses") 166s consump price farmPrice trend 166s "numeric" "numeric" "numeric" "numeric" 166s > 166s > 166s > ## **************** estfun ************************ 166s > library( "sandwich" ) 166s > 166s > estfun( fitols1 ) 166s demand_(Intercept) demand_price demand_income supply_(Intercept) 166s demand_1 1.074 107.8 93.9 0.000 166s demand_2 -0.390 -40.7 -38.1 0.000 166s demand_3 2.625 271.5 253.8 0.000 166s demand_4 1.802 188.4 177.0 0.000 166s demand_5 1.946 190.7 194.2 0.000 166s demand_6 1.175 116.8 118.0 0.000 166s demand_7 1.530 154.7 157.9 0.000 166s demand_8 -2.933 -307.2 -316.1 0.000 166s demand_9 -1.365 -131.7 -131.9 0.000 166s demand_10 2.031 185.3 180.5 0.000 166s demand_11 -0.149 -13.9 -11.2 0.000 166s demand_12 -1.954 -193.1 -150.3 0.000 166s demand_13 -1.121 -115.4 -94.8 0.000 166s demand_14 -0.220 -21.7 -19.9 0.000 166s demand_15 1.487 141.4 153.3 0.000 166s demand_16 -3.701 -364.3 -388.9 0.000 166s demand_17 -1.273 -110.1 -122.7 0.000 166s demand_18 -2.002 -208.3 -209.0 0.000 166s demand_19 1.738 183.8 192.4 0.000 166s demand_20 -0.299 -33.9 -38.0 0.000 166s supply_1 0.000 0.0 0.0 -0.444 166s supply_2 0.000 0.0 0.0 -0.896 166s supply_3 0.000 0.0 0.0 1.965 166s supply_4 0.000 0.0 0.0 1.134 166s supply_5 0.000 0.0 0.0 1.514 166s supply_6 0.000 0.0 0.0 0.680 166s supply_7 0.000 0.0 0.0 1.569 166s supply_8 0.000 0.0 0.0 -4.407 166s supply_9 0.000 0.0 0.0 -2.599 166s supply_10 0.000 0.0 0.0 2.469 166s supply_11 0.000 0.0 0.0 -0.598 166s supply_12 0.000 0.0 0.0 -1.697 166s supply_13 0.000 0.0 0.0 -1.064 166s supply_14 0.000 0.0 0.0 0.970 166s supply_15 0.000 0.0 0.0 3.159 166s supply_16 0.000 0.0 0.0 -3.866 166s supply_17 0.000 0.0 0.0 -0.265 166s supply_18 0.000 0.0 0.0 -2.449 166s supply_19 0.000 0.0 0.0 3.110 166s supply_20 0.000 0.0 0.0 1.714 166s supply_price supply_farmPrice supply_trend 166s demand_1 0.0 0.0 0.000 166s demand_2 0.0 0.0 0.000 166s demand_3 0.0 0.0 0.000 166s demand_4 0.0 0.0 0.000 166s demand_5 0.0 0.0 0.000 166s demand_6 0.0 0.0 0.000 166s demand_7 0.0 0.0 0.000 166s demand_8 0.0 0.0 0.000 166s demand_9 0.0 0.0 0.000 166s demand_10 0.0 0.0 0.000 166s demand_11 0.0 0.0 0.000 166s demand_12 0.0 0.0 0.000 166s demand_13 0.0 0.0 0.000 166s demand_14 0.0 0.0 0.000 166s demand_15 0.0 0.0 0.000 166s demand_16 0.0 0.0 0.000 166s demand_17 0.0 0.0 0.000 166s demand_18 0.0 0.0 0.000 166s demand_19 0.0 0.0 0.000 166s demand_20 0.0 0.0 0.000 166s supply_1 -44.6 -43.5 -0.444 166s supply_2 -93.4 -88.7 -1.791 166s supply_3 203.3 194.7 5.895 166s supply_4 118.5 111.3 4.537 166s supply_5 148.4 167.7 7.569 166s supply_6 67.7 73.6 4.082 166s supply_7 158.6 165.7 10.983 166s supply_8 -461.7 -483.9 -35.259 166s supply_9 -250.7 -282.5 -23.391 166s supply_10 225.3 248.4 24.694 166s supply_11 -55.7 -48.5 -6.581 166s supply_12 -167.7 -116.4 -20.369 166s supply_13 -109.5 -75.4 -13.832 166s supply_14 95.8 79.0 13.582 166s supply_15 300.5 323.2 47.386 166s supply_16 -380.6 -405.9 -61.848 166s supply_17 -22.9 -29.2 -4.500 166s supply_18 -254.7 -226.5 -44.080 166s supply_19 328.9 277.7 59.084 166s supply_20 194.5 159.4 34.282 166s > round( colSums( estfun( fitols1 ) ), digits = 7 ) 166s demand_(Intercept) demand_price demand_income supply_(Intercept) 166s 0 0 0 0 166s supply_price supply_farmPrice supply_trend 166s 0 0 0 166s > 166s > estfun( fitols1s ) 166s demand_(Intercept) demand_price demand_income supply_(Intercept) 166s demand_1 1.074 107.8 93.9 0.000 166s demand_2 -0.390 -40.7 -38.1 0.000 166s demand_3 2.625 271.5 253.8 0.000 166s demand_4 1.802 188.4 177.0 0.000 166s demand_5 1.946 190.7 194.2 0.000 166s demand_6 1.175 116.8 118.0 0.000 166s demand_7 1.530 154.7 157.9 0.000 166s demand_8 -2.933 -307.2 -316.1 0.000 166s demand_9 -1.365 -131.7 -131.9 0.000 166s demand_10 2.031 185.3 180.5 0.000 166s demand_11 -0.149 -13.9 -11.2 0.000 166s demand_12 -1.954 -193.1 -150.3 0.000 166s demand_13 -1.121 -115.4 -94.8 0.000 166s demand_14 -0.220 -21.7 -19.9 0.000 166s demand_15 1.487 141.4 153.3 0.000 166s demand_16 -3.701 -364.3 -388.9 0.000 166s demand_17 -1.273 -110.1 -122.7 0.000 166s demand_18 -2.002 -208.3 -209.0 0.000 166s demand_19 1.738 183.8 192.4 0.000 166s demand_20 -0.299 -33.9 -38.0 0.000 166s supply_1 0.000 0.0 0.0 -0.444 166s supply_2 0.000 0.0 0.0 -0.896 166s supply_3 0.000 0.0 0.0 1.965 166s supply_4 0.000 0.0 0.0 1.134 166s supply_5 0.000 0.0 0.0 1.514 166s supply_6 0.000 0.0 0.0 0.680 166s supply_7 0.000 0.0 0.0 1.569 166s supply_8 0.000 0.0 0.0 -4.407 166s supply_9 0.000 0.0 0.0 -2.599 166s supply_10 0.000 0.0 0.0 2.469 166s supply_11 0.000 0.0 0.0 -0.598 166s supply_12 0.000 0.0 0.0 -1.697 166s supply_13 0.000 0.0 0.0 -1.064 166s supply_14 0.000 0.0 0.0 0.970 166s supply_15 0.000 0.0 0.0 3.159 166s supply_16 0.000 0.0 0.0 -3.866 166s supply_17 0.000 0.0 0.0 -0.265 166s supply_18 0.000 0.0 0.0 -2.449 166s supply_19 0.000 0.0 0.0 3.110 166s supply_20 0.000 0.0 0.0 1.714 166s supply_price supply_farmPrice supply_trend 166s demand_1 0.0 0.0 0.000 166s demand_2 0.0 0.0 0.000 166s demand_3 0.0 0.0 0.000 166s demand_4 0.0 0.0 0.000 166s demand_5 0.0 0.0 0.000 166s demand_6 0.0 0.0 0.000 166s demand_7 0.0 0.0 0.000 166s demand_8 0.0 0.0 0.000 166s demand_9 0.0 0.0 0.000 166s demand_10 0.0 0.0 0.000 166s demand_11 0.0 0.0 0.000 166s demand_12 0.0 0.0 0.000 166s demand_13 0.0 0.0 0.000 166s demand_14 0.0 0.0 0.000 166s demand_15 0.0 0.0 0.000 166s demand_16 0.0 0.0 0.000 166s demand_17 0.0 0.0 0.000 166s demand_18 0.0 0.0 0.000 166s demand_19 0.0 0.0 0.000 166s demand_20 0.0 0.0 0.000 166s supply_1 -44.6 -43.5 -0.444 166s supply_2 -93.4 -88.7 -1.791 166s supply_3 203.3 194.7 5.895 166s supply_4 118.5 111.3 4.537 166s supply_5 148.4 167.7 7.569 166s supply_6 67.7 73.6 4.082 166s supply_7 158.6 165.7 10.983 166s supply_8 -461.7 -483.9 -35.259 166s supply_9 -250.7 -282.5 -23.391 166s supply_10 225.3 248.4 24.694 166s supply_11 -55.7 -48.5 -6.581 166s supply_12 -167.7 -116.4 -20.369 166s supply_13 -109.5 -75.4 -13.832 166s supply_14 95.8 79.0 13.582 166s supply_15 300.5 323.2 47.386 166s supply_16 -380.6 -405.9 -61.848 166s supply_17 -22.9 -29.2 -4.500 166s supply_18 -254.7 -226.5 -44.080 166s supply_19 328.9 277.7 59.084 166s supply_20 194.5 159.4 34.282 166s > round( colSums( estfun( fitols1s ) ), digits = 7 ) 166s demand_(Intercept) demand_price demand_income supply_(Intercept) 166s 0 0 0 0 166s supply_price supply_farmPrice supply_trend 166s 0 0 0 166s > 166s > estfun( fitols1r ) 166s demand_(Intercept) demand_price demand_income supply_(Intercept) 166s demand_1 1.074 107.8 93.9 0.000 166s demand_2 -0.390 -40.7 -38.1 0.000 166s demand_3 2.625 271.5 253.8 0.000 166s demand_4 1.802 188.4 177.0 0.000 166s demand_5 1.946 190.7 194.2 0.000 166s demand_6 1.175 116.8 118.0 0.000 166s demand_7 1.530 154.7 157.9 0.000 166s demand_8 -2.933 -307.2 -316.1 0.000 166s demand_9 -1.365 -131.7 -131.9 0.000 166s demand_10 2.031 185.3 180.5 0.000 166s demand_11 -0.149 -13.9 -11.2 0.000 166s demand_12 -1.954 -193.1 -150.3 0.000 166s demand_13 -1.121 -115.4 -94.8 0.000 166s demand_14 -0.220 -21.7 -19.9 0.000 166s demand_15 1.487 141.4 153.3 0.000 166s demand_16 -3.701 -364.3 -388.9 0.000 166s demand_17 -1.273 -110.1 -122.7 0.000 166s demand_18 -2.002 -208.3 -209.0 0.000 166s demand_19 1.738 183.8 192.4 0.000 166s demand_20 -0.299 -33.9 -38.0 0.000 166s supply_1 0.000 0.0 0.0 -0.444 166s supply_2 0.000 0.0 0.0 -0.896 166s supply_3 0.000 0.0 0.0 1.965 166s supply_4 0.000 0.0 0.0 1.134 166s supply_5 0.000 0.0 0.0 1.514 166s supply_6 0.000 0.0 0.0 0.680 166s supply_7 0.000 0.0 0.0 1.569 166s supply_8 0.000 0.0 0.0 -4.407 166s supply_9 0.000 0.0 0.0 -2.599 166s supply_10 0.000 0.0 0.0 2.469 166s supply_11 0.000 0.0 0.0 -0.598 166s supply_12 0.000 0.0 0.0 -1.697 166s supply_13 0.000 0.0 0.0 -1.064 166s supply_14 0.000 0.0 0.0 0.970 166s supply_15 0.000 0.0 0.0 3.159 166s supply_16 0.000 0.0 0.0 -3.866 166s supply_17 0.000 0.0 0.0 -0.265 166s supply_18 0.000 0.0 0.0 -2.449 166s supply_19 0.000 0.0 0.0 3.110 166s supply_20 0.000 0.0 0.0 1.714 166s supply_price supply_farmPrice supply_trend 166s demand_1 0.0 0.0 0.000 166s demand_2 0.0 0.0 0.000 166s demand_3 0.0 0.0 0.000 166s demand_4 0.0 0.0 0.000 166s demand_5 0.0 0.0 0.000 166s demand_6 0.0 0.0 0.000 166s demand_7 0.0 0.0 0.000 166s demand_8 0.0 0.0 0.000 166s demand_9 0.0 0.0 0.000 166s demand_10 0.0 0.0 0.000 166s demand_11 0.0 0.0 0.000 166s demand_12 0.0 0.0 0.000 166s demand_13 0.0 0.0 0.000 166s demand_14 0.0 0.0 0.000 166s demand_15 0.0 0.0 0.000 166s demand_16 0.0 0.0 0.000 166s demand_17 0.0 0.0 0.000 166s demand_18 0.0 0.0 0.000 166s demand_19 0.0 0.0 0.000 166s demand_20 0.0 0.0 0.000 166s supply_1 -44.6 -43.5 -0.444 166s supply_2 -93.4 -88.7 -1.791 166s supply_3 203.3 194.7 5.895 166s supply_4 118.5 111.3 4.537 166s supply_5 148.4 167.7 7.569 166s supply_6 67.7 73.6 4.082 166s supply_7 158.6 165.7 10.983 166s supply_8 -461.7 -483.9 -35.259 166s supply_9 -250.7 -282.5 -23.391 166s supply_10 225.3 248.4 24.694 166s supply_11 -55.7 -48.5 -6.581 166s supply_12 -167.7 -116.4 -20.369 166s supply_13 -109.5 -75.4 -13.832 166s supply_14 95.8 79.0 13.582 166s supply_15 300.5 323.2 47.386 166s supply_16 -380.6 -405.9 -61.848 166s supply_17 -22.9 -29.2 -4.500 166s supply_18 -254.7 -226.5 -44.080 166s supply_19 328.9 277.7 59.084 166s supply_20 194.5 159.4 34.282 166s > round( colSums( estfun( fitols1r ) ), digits = 7 ) 166s demand_(Intercept) demand_price demand_income supply_(Intercept) 166s 0 0 0 0 166s supply_price supply_farmPrice supply_trend 166s 0 0 0 166s > 166s > try( estfun( fitols2 ) ) 166s Error in estfun.systemfit(fitols2) : 166s returning the estimation function for models with restrictions has not yet been implemented. 166s Error in estfun.systemfit(fitols2Sym) : 166s returning the estimation function for models with restrictions has not yet been implemented. 166s Error in estfun.systemfit(fitols3s) : 166s returning the estimation function for models with restrictions has not yet been implemented. 166s > 166s > try( estfun( fitols2Sym ) ) 166s > 166s > try( estfun( fitols3s ) ) 166s > 166s > try( estfun( fitols4r ) ) 166s Error in estfun.systemfit(fitols4r) : 166s returning the estimation function for models with restrictions has not yet been implemented. 166s Error in estfun.systemfit(fitols4Sym) : 166s returning the estimation function for models with restrictions has not yet been implemented. 166s > 166s > try( estfun( fitols4Sym ) ) 166s > 166s Error in estfun.systemfit(fitols5) : 166s returning the estimation function for models with restrictions has not yet been implemented. 166s Error in estfun.systemfit(fitols5Sym) : 166s returning the estimation function for models with restrictions has not yet been implemented. 166s > try( estfun( fitols5 ) ) 166s > 166s > try( estfun( fitols5Sym ) ) 166s > 166s > 166s > ## **************** bread ************************ 166s > bread( fitols1 ) 166s demand_(Intercept) demand_price demand_incomeError in bread.systemfit(fitols2) : 166s returning the 'bread' for models with restrictions has not yet been implemented. 166s 166s demand_(Intercept) 607.086 -6.3865 0.3453 166s demand_price -6.386 0.0883 -0.0251 166s demand_income 0.345 -0.0251 0.0222 166s supply_(Intercept) 0.000 0.0000 0.0000 166s supply_price 0.000 0.0000 0.0000 166s supply_farmPrice 0.000 0.0000 0.0000 166s supply_trend 0.000 0.0000 0.0000 166s supply_(Intercept) supply_price supply_farmPrice 166s demand_(Intercept) 0.00 0.00000 0.00000 166s demand_price 0.00 0.00000 0.00000 166s demand_income 0.00 0.00000 0.00000 166s supply_(Intercept) 908.63 -6.82866 -2.10469 166s supply_price -6.83 0.06226 0.00584 166s supply_farmPrice -2.10 0.00584 0.01475 166s supply_trend -1.93 0.00361 0.00910 166s supply_trend 166s demand_(Intercept) 0.00000 166s demand_price 0.00000 166s demand_income 0.00000 166s supply_(Intercept) -1.93058 166s supply_price 0.00361 166s supply_farmPrice 0.00910 166s supply_trend 0.06576 166s > 166s > bread( fitols1s ) 166s demand_(Intercept) demand_price demand_income 166s demand_(Intercept) 607.086 -6.3865 0.3453 166s demand_price -6.386 0.0883 -0.0251 166s demand_income 0.345 -0.0251 0.0222 166s supply_(Intercept) 0.000 0.0000 0.0000 166s supply_price 0.000 0.0000 0.0000 166s supply_farmPrice 0.000 0.0000 0.0000 166s supply_trend 0.000 0.0000 0.0000 166s supply_(Intercept) supply_price supply_farmPrice 166s demand_(Intercept) 0.00 0.00000 0.00000 166s demand_price 0.00 0.00000 0.00000 166s demand_income 0.00 0.00000 0.00000 166s supply_(Intercept) 908.63 -6.82866 -2.10469 166s supply_price -6.83 0.06226 0.00584 166s supply_farmPrice -2.10 0.00584 0.01475 166s supply_trend -1.93 0.00361 0.00910 166s supply_trend 166s demand_(Intercept) 0.00000 166s demand_price 0.00000 166s demand_income 0.00000 166s supply_(Intercept) -1.93058 166s supply_price 0.00361 166s supply_farmPrice 0.00910 166s supply_trend 0.06576 166s > 166s > bread( fitols1r ) 166s demand_(Intercept) demand_price demand_income 166s demand_(Intercept) 607.086 -6.3865 0.3453 166s demand_price -6.386 0.0883 -0.0251 166s demand_income 0.345 -0.0251 0.0222 166s supply_(Intercept) 0.000 0.0000 0.0000 166s supply_price 0.000 0.0000 0.0000 166s supply_farmPrice 0.000 0.0000 0.0000 166s supply_trend 0.000 0.0000 0.0000 166s supply_(Intercept) supply_price supply_farmPrice 166s demand_(Intercept) 0.00 0.00000 0.00000 166s demand_price 0.00 0.00000 0.00000 166s demand_income 0.00 0.00000 0.00000 166s supply_(Intercept) 908.63 -6.82866 -2.10469 166s supply_price -6.83 0.06226 0.00584 166s supply_farmPrice -2.10 0.00584 0.01475 166s supply_trend -1.93 0.00361 0.00910 166s supply_trend 166s demand_(Intercept) 0.00000 166s demand_price 0.00000 166s demand_income 0.00000 166s supply_(Intercept) -1.93058 166s supply_price 0.00361 166s supply_farmPrice 0.00910 166s supply_trend 0.06576 166s > 166s > try( bread( fitols2 ) ) 166s > 166s BEGIN TEST test_panel.R 166s 166s R version 4.3.2 (2023-10-31) -- "Eye Holes" 166s Copyright (C) 2023 The R Foundation for Statistical Computing 166s Platform: x86_64-pc-linux-gnu (64-bit) 166s 166s R is free software and comes with ABSOLUTELY NO WARRANTY. 166s You are welcome to redistribute it under certain conditions. 166s Type 'license()' or 'licence()' for distribution details. 166s 166s R is a collaborative project with many contributors. 166s Type 'contributors()' for more information and 166s 'citation()' on how to cite R or R packages in publications. 166s 166s Type 'demo()' for some demos, 'help()' for on-line help, or 166s 'help.start()' for an HTML browser interface to help. 166s Type 'q()' to quit R. 166s 166s Loading required package: Matrix 166s > library( systemfit ) 167s Loading required package: car 167s Loading required package: carData 167s Loading required package: lmtest 167s Loading required package: zoo 167s 167s Attaching package: ‘zoo’ 167s 167s The following objects are masked from ‘package:base’: 167s 167s as.Date, as.Date.numeric 167s 167s 167s Please cite the 'systemfit' package as: 167s 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/. 167s 167s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 167s https://r-forge.r-project.org/projects/systemfit/ 167s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 167s + library( plm ) 167s + options( digits = 3 ) 167s + useMatrix <- FALSE 167s + } 167s > 167s > ## Repeating the OLS and SUR estimations in Theil (1971, pp. 295, 300) 167s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 167s + data( "GrunfeldGreene" ) 167s + GrunfeldTheil <- subset( GrunfeldGreene, 167s + firm %in% c( "General Electric", "Westinghouse" ) ) 167s + GrunfeldTheil <- pdata.frame( GrunfeldTheil, c( "firm", "year" ) ) 167s + formulaGrunfeld <- invest ~ value + capital 167s + } 167s > 167s > # OLS 167s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 167s + theilOls <- systemfit( formulaGrunfeld, "OLS", 167s + data = GrunfeldTheil, useMatrix = useMatrix ) 167s + print( theilOls ) 167s + print( summary( theilOls ) ) 167s + print( summary( theilOls, useDfSys = TRUE, residCov = FALSE, 167s + equations = FALSE ) ) 167s + print( summary( theilOls, equations = FALSE ) ) 167s + print( coef( theilOls ) ) 167s + print( coef( summary(theilOls ) ) ) 167s + print( vcov( theilOls ) ) 167s + print( residuals( theilOls ) ) 167s + print( confint( theilOls ) ) 167s + print( fitted(theilOls ) ) 167s + print( logLik( theilOls ) ) 167s + print( logLik( theilOls, residCovDiag = TRUE ) ) 167s + print( nobs( theilOls ) ) 167s + print( model.frame( theilOls ) ) 167s + print( model.matrix( theilOls ) ) 167s + print( formula( theilOls ) ) 167s + print( formula( theilOls$eq[[ 1 ]] ) ) 167s + print( terms( theilOls ) ) 167s + print( terms( theilOls$eq[[ 1 ]] ) ) 167s + } 167s 167s systemfit results 167s method: OLS 167s 167s Coefficients: 167s General.Electric_(Intercept) General.Electric_value 167s -9.9563 0.0266 167s General.Electric_capital Westinghouse_(Intercept) 167s 0.1517 -0.5094 167s Westinghouse_value Westinghouse_capital 167s 0.0529 0.0924 167s 167s systemfit results 167s method: OLS 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 40 34 14990 38001 0.711 0.618 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s General.Electric 20 17 13217 777 27.9 0.705 0.671 167s Westinghouse 20 17 1773 104 10.2 0.744 0.714 167s 167s The covariance matrix of the residuals 167s General.Electric Westinghouse 167s General.Electric 777 208 167s Westinghouse 208 104 167s 167s The correlations of the residuals 167s General.Electric Westinghouse 167s General.Electric 1.000 0.729 167s Westinghouse 0.729 1.000 167s 167s 167s OLS estimates for 'General.Electric' (equation 1) 167s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -9.9563 31.3742 -0.32 0.75 167s value 0.0266 0.0156 1.71 0.11 167s capital 0.1517 0.0257 5.90 1.7e-05 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 27.883 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 167s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 167s 167s 167s OLS estimates for 'Westinghouse' (equation 2) 167s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -0.5094 8.0153 -0.06 0.9501 167s value 0.0529 0.0157 3.37 0.0037 ** 167s capital 0.0924 0.0561 1.65 0.1179 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 10.213 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 167s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 167s 167s 167s systemfit results 167s method: OLS 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 40 34 14990 38001 0.711 0.618 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s General.Electric 20 17 13217 777 27.9 0.705 0.671 167s Westinghouse 20 17 1773 104 10.2 0.744 0.714 167s 167s 167s Coefficients: 167s Estimate Std. Error t value Pr(>|t|) 167s General.Electric_(Intercept) -9.9563 31.3742 -0.32 0.7529 167s General.Electric_value 0.0266 0.0156 1.71 0.0972 . 167s General.Electric_capital 0.1517 0.0257 5.90 1.2e-06 *** 167s Westinghouse_(Intercept) -0.5094 8.0153 -0.06 0.9497 167s Westinghouse_value 0.0529 0.0157 3.37 0.0019 ** 167s Westinghouse_capital 0.0924 0.0561 1.65 0.1087 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s systemfit results 167s method: OLS 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 40 34 14990 38001 0.711 0.618 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s General.Electric 20 17 13217 777 27.9 0.705 0.671 167s Westinghouse 20 17 1773 104 10.2 0.744 0.714 167s 167s The covariance matrix of the residuals 167s General.Electric Westinghouse 167s General.Electric 777 208 167s Westinghouse 208 104 167s 167s The correlations of the residuals 167s General.Electric Westinghouse 167s General.Electric 1.000 0.729 167s Westinghouse 0.729 1.000 167s 167s 167s Coefficients: 167s Estimate Std. Error t value Pr(>|t|) 167s General.Electric_(Intercept) -9.9563 31.3742 -0.32 0.7548 167s General.Electric_value 0.0266 0.0156 1.71 0.1063 167s General.Electric_capital 0.1517 0.0257 5.90 1.7e-05 *** 167s Westinghouse_(Intercept) -0.5094 8.0153 -0.06 0.9501 167s Westinghouse_value 0.0529 0.0157 3.37 0.0037 ** 167s Westinghouse_capital 0.0924 0.0561 1.65 0.1179 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s General.Electric_(Intercept) General.Electric_value 167s -9.9563 0.0266 167s General.Electric_capital Westinghouse_(Intercept) 167s 0.1517 -0.5094 167s Westinghouse_value Westinghouse_capital 167s 0.0529 0.0924 167s Estimate Std. Error t value Pr(>|t|) 167s General.Electric_(Intercept) -9.9563 31.3742 -0.3173 7.55e-01 167s General.Electric_value 0.0266 0.0156 1.7057 1.06e-01 167s General.Electric_capital 0.1517 0.0257 5.9015 1.74e-05 167s Westinghouse_(Intercept) -0.5094 8.0153 -0.0636 9.50e-01 167s Westinghouse_value 0.0529 0.0157 3.3677 3.65e-03 167s Westinghouse_capital 0.0924 0.0561 1.6472 1.18e-01 167s General.Electric_(Intercept) 167s General.Electric_(Intercept) 984.344 167s General.Electric_value -0.451 167s General.Electric_capital -0.173 167s Westinghouse_(Intercept) 0.000 167s Westinghouse_value 0.000 167s Westinghouse_capital 0.000 167s General.Electric_value General.Electric_capital 167s General.Electric_(Intercept) -4.51e-01 -1.73e-01 167s General.Electric_value 2.42e-04 -4.73e-05 167s General.Electric_capital -4.73e-05 6.61e-04 167s Westinghouse_(Intercept) 0.00e+00 0.00e+00 167s Westinghouse_value 0.00e+00 0.00e+00 167s Westinghouse_capital 0.00e+00 0.00e+00 167s Westinghouse_(Intercept) Westinghouse_value 167s General.Electric_(Intercept) 0.000 0.000000 167s General.Electric_value 0.000 0.000000 167s General.Electric_capital 0.000 0.000000 167s Westinghouse_(Intercept) 64.245 -0.109545 167s Westinghouse_value -0.110 0.000247 167s Westinghouse_capital 0.169 -0.000653 167s Westinghouse_capital 167s General.Electric_(Intercept) 0.000000 167s General.Electric_value 0.000000 167s General.Electric_capital 0.000000 167s Westinghouse_(Intercept) 0.168911 167s Westinghouse_value -0.000653 167s Westinghouse_capital 0.003147 167s General.Electric Westinghouse 167s X1935 -2.860 3.144 167s X1936 -14.402 -0.958 167s X1937 -5.175 -3.684 167s X1938 -23.295 -7.915 167s X1939 -28.031 -10.322 167s X1940 -0.562 -6.613 167s X1941 40.750 17.265 167s X1942 16.036 8.547 167s X1943 -23.719 -2.916 167s X1944 -26.780 -3.257 167s X1945 1.768 -7.753 167s X1946 58.737 5.796 167s X1947 43.936 15.050 167s X1948 31.227 2.969 167s X1949 -23.552 -11.433 167s X1950 -37.511 -13.481 167s X1951 -4.983 4.619 167s X1952 1.893 13.138 167s X1953 5.087 11.308 167s X1954 -8.563 -13.505 167s 2.5 % 97.5 % 167s General.Electric_(Intercept) -76.150 56.238 167s General.Electric_value -0.006 0.059 167s General.Electric_capital 0.097 0.206 167s Westinghouse_(Intercept) -17.420 16.401 167s Westinghouse_value 0.020 0.086 167s Westinghouse_capital -0.026 0.211 167s General.Electric Westinghouse 167s X1935 36.0 9.79 167s X1936 59.4 26.86 167s X1937 82.4 38.73 167s X1938 67.9 30.81 167s X1939 76.1 29.16 167s X1940 75.0 35.18 167s X1941 72.3 31.25 167s X1942 75.9 34.79 167s X1943 85.0 39.94 167s X1944 83.6 41.07 167s X1945 91.8 47.02 167s X1946 101.2 47.66 167s X1947 103.3 40.51 167s X1948 115.1 46.59 167s X1949 121.9 43.47 167s X1950 131.0 45.72 167s X1951 140.2 49.76 167s X1952 155.4 58.64 167s X1953 174.4 78.77 167s X1954 198.2 82.11 167s 'log Lik.' -159 (df=7) 167s 'log Lik.' -167 (df=7) 167s [1] 40 167s General.Electric_invest General.Electric_value General.Electric_capital 167s X1935 33.1 1171 97.8 167s X1936 45.0 2016 104.4 167s X1937 77.2 2803 118.0 167s X1938 44.6 2040 156.2 167s X1939 48.1 2256 172.6 167s X1940 74.4 2132 186.6 167s X1941 113.0 1834 220.9 167s X1942 91.9 1588 287.8 167s X1943 61.3 1749 319.9 167s X1944 56.8 1687 321.3 167s X1945 93.6 2008 319.6 167s X1946 159.9 2208 346.0 167s X1947 147.2 1657 456.4 167s X1948 146.3 1604 543.4 167s X1949 98.3 1432 618.3 167s X1950 93.5 1610 647.4 167s X1951 135.2 1819 671.3 167s X1952 157.3 2080 726.1 167s X1953 179.5 2372 800.3 167s X1954 189.6 2760 888.9 167s Westinghouse_invest Westinghouse_value Westinghouse_capital 167s X1935 12.9 192 1.8 167s X1936 25.9 516 0.8 167s X1937 35.0 729 7.4 167s X1938 22.9 560 18.1 167s X1939 18.8 520 23.5 167s X1940 28.6 628 26.5 167s X1941 48.5 537 36.2 167s X1942 43.3 561 60.8 167s X1943 37.0 617 84.4 167s X1944 37.8 627 91.2 167s X1945 39.3 737 92.4 167s X1946 53.5 760 86.0 167s X1947 55.6 581 111.1 167s X1948 49.6 662 130.6 167s X1949 32.0 584 141.8 167s X1950 32.2 635 136.7 167s X1951 54.4 724 129.7 167s X1952 71.8 864 145.5 167s X1953 90.1 1194 174.8 167s X1954 68.6 1189 213.5 167s General.Electric_(Intercept) General.Electric_value 167s General.Electric_X1935 1 1171 167s General.Electric_X1936 1 2016 167s General.Electric_X1937 1 2803 167s General.Electric_X1938 1 2040 167s General.Electric_X1939 1 2256 167s General.Electric_X1940 1 2132 167s General.Electric_X1941 1 1834 167s General.Electric_X1942 1 1588 167s General.Electric_X1943 1 1749 167s General.Electric_X1944 1 1687 167s General.Electric_X1945 1 2008 167s General.Electric_X1946 1 2208 167s General.Electric_X1947 1 1657 167s General.Electric_X1948 1 1604 167s General.Electric_X1949 1 1432 167s General.Electric_X1950 1 1610 167s General.Electric_X1951 1 1819 167s General.Electric_X1952 1 2080 167s General.Electric_X1953 1 2372 167s General.Electric_X1954 1 2760 167s Westinghouse_X1935 0 0 167s Westinghouse_X1936 0 0 167s Westinghouse_X1937 0 0 167s Westinghouse_X1938 0 0 167s Westinghouse_X1939 0 0 167s Westinghouse_X1940 0 0 167s Westinghouse_X1941 0 0 167s Westinghouse_X1942 0 0 167s Westinghouse_X1943 0 0 167s Westinghouse_X1944 0 0 167s Westinghouse_X1945 0 0 167s Westinghouse_X1946 0 0 167s Westinghouse_X1947 0 0 167s Westinghouse_X1948 0 0 167s Westinghouse_X1949 0 0 167s Westinghouse_X1950 0 0 167s Westinghouse_X1951 0 0 167s Westinghouse_X1952 0 0 167s Westinghouse_X1953 0 0 167s Westinghouse_X1954 0 0 167s General.Electric_capital Westinghouse_(Intercept) 167s General.Electric_X1935 97.8 0 167s General.Electric_X1936 104.4 0 167s General.Electric_X1937 118.0 0 167s General.Electric_X1938 156.2 0 167s General.Electric_X1939 172.6 0 167s General.Electric_X1940 186.6 0 167s General.Electric_X1941 220.9 0 167s General.Electric_X1942 287.8 0 167s General.Electric_X1943 319.9 0 167s General.Electric_X1944 321.3 0 167s General.Electric_X1945 319.6 0 167s General.Electric_X1946 346.0 0 167s General.Electric_X1947 456.4 0 167s General.Electric_X1948 543.4 0 167s General.Electric_X1949 618.3 0 167s General.Electric_X1950 647.4 0 167s General.Electric_X1951 671.3 0 167s General.Electric_X1952 726.1 0 167s General.Electric_X1953 800.3 0 167s General.Electric_X1954 888.9 0 167s Westinghouse_X1935 0.0 1 167s Westinghouse_X1936 0.0 1 167s Westinghouse_X1937 0.0 1 167s Westinghouse_X1938 0.0 1 167s Westinghouse_X1939 0.0 1 167s Westinghouse_X1940 0.0 1 167s Westinghouse_X1941 0.0 1 167s Westinghouse_X1942 0.0 1 167s Westinghouse_X1943 0.0 1 167s Westinghouse_X1944 0.0 1 167s Westinghouse_X1945 0.0 1 167s Westinghouse_X1946 0.0 1 167s Westinghouse_X1947 0.0 1 167s Westinghouse_X1948 0.0 1 167s Westinghouse_X1949 0.0 1 167s Westinghouse_X1950 0.0 1 167s Westinghouse_X1951 0.0 1 167s Westinghouse_X1952 0.0 1 167s Westinghouse_X1953 0.0 1 167s Westinghouse_X1954 0.0 1 167s Westinghouse_value Westinghouse_capital 167s General.Electric_X1935 0 0.0 167s General.Electric_X1936 0 0.0 167s General.Electric_X1937 0 0.0 167s General.Electric_X1938 0 0.0 167s General.Electric_X1939 0 0.0 167s General.Electric_X1940 0 0.0 167s General.Electric_X1941 0 0.0 167s General.Electric_X1942 0 0.0 167s General.Electric_X1943 0 0.0 167s General.Electric_X1944 0 0.0 167s General.Electric_X1945 0 0.0 167s General.Electric_X1946 0 0.0 167s General.Electric_X1947 0 0.0 167s General.Electric_X1948 0 0.0 167s General.Electric_X1949 0 0.0 167s General.Electric_X1950 0 0.0 167s General.Electric_X1951 0 0.0 167s General.Electric_X1952 0 0.0 167s General.Electric_X1953 0 0.0 167s General.Electric_X1954 0 0.0 167s Westinghouse_X1935 192 1.8 167s Westinghouse_X1936 516 0.8 167s Westinghouse_X1937 729 7.4 167s Westinghouse_X1938 560 18.1 167s Westinghouse_X1939 520 23.5 167s Westinghouse_X1940 628 26.5 167s Westinghouse_X1941 537 36.2 167s Westinghouse_X1942 561 60.8 167s Westinghouse_X1943 617 84.4 167s Westinghouse_X1944 627 91.2 167s Westinghouse_X1945 737 92.4 167s Westinghouse_X1946 760 86.0 167s Westinghouse_X1947 581 111.1 167s Westinghouse_X1948 662 130.6 167s Westinghouse_X1949 584 141.8 167s Westinghouse_X1950 635 136.7 167s Westinghouse_X1951 724 129.7 167s Westinghouse_X1952 864 145.5 167s Westinghouse_X1953 1194 174.8 167s Westinghouse_X1954 1189 213.5 167s $General.Electric 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s 167s $Westinghouse 167s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s $General.Electric 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s attr(,"variables") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"factors") 167s General.Electric_value General.Electric_capital 167s General.Electric_invest 0 0 167s General.Electric_value 1 0 167s General.Electric_capital 0 1 167s attr(,"term.labels") 167s [1] "General.Electric_value" "General.Electric_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"dataClasses") 167s General.Electric_invest General.Electric_value General.Electric_capital 167s "numeric" "numeric" "numeric" 167s 167s $Westinghouse 167s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s attr(,"variables") 167s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 167s attr(,"factors") 167s Westinghouse_value Westinghouse_capital 167s Westinghouse_invest 0 0 167s Westinghouse_value 1 0 167s Westinghouse_capital 0 1 167s attr(,"term.labels") 167s [1] "Westinghouse_value" "Westinghouse_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 167s attr(,"dataClasses") 167s Westinghouse_invest Westinghouse_value Westinghouse_capital 167s "numeric" "numeric" "numeric" 167s 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s attr(,"variables") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"factors") 167s General.Electric_value General.Electric_capital 167s General.Electric_invest 0 0 167s General.Electric_value 1 0 167s General.Electric_capital 0 1 167s attr(,"term.labels") 167s [1] "General.Electric_value" "General.Electric_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"dataClasses") 167s General.Electric_invest General.Electric_value General.Electric_capital 167s "numeric" "numeric" "numeric" 167s > 167s > # SUR 167s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 167s + theilSur <- systemfit( formulaGrunfeld, "SUR", 167s + data = GrunfeldTheil, methodResidCov = "noDfCor", useMatrix = useMatrix ) 167s + print( theilSur ) 167s + print( summary( theilSur ) ) 167s + print( summary( theilSur, useDfSys = TRUE, equations = FALSE ) ) 167s + print( summary( theilSur, residCov = FALSE, equations = FALSE ) ) 167s + print( coef( theilSur ) ) 167s + print( coef( summary( theilSur ) ) ) 167s + print( vcov( theilSur ) ) 167s + print( residuals( theilSur ) ) 167s + print( confint( theilSur ) ) 167s + print( fitted( theilSur ) ) 167s + print( logLik( theilSur ) ) 167s + print( logLik( theilSur, residCovDiag = TRUE ) ) 167s + print( nobs( theilSur ) ) 167s + print( model.frame( theilSur ) ) 167s + print( model.matrix( theilSur ) ) 167s + print( formula( theilSur ) ) 167s + print( formula( theilSur$eq[[ 2 ]] ) ) 167s + print( terms( theilSur ) ) 167s + print( terms( theilSur$eq[[ 2 ]] ) ) 167s + } 167s 167s systemfit results 167s method: SUR 167s 167s Coefficients: 167s General.Electric_(Intercept) General.Electric_value 167s -27.7193 0.0383 167s General.Electric_capital Westinghouse_(Intercept) 167s 0.1390 -1.2520 167s Westinghouse_value Westinghouse_capital 167s 0.0576 0.0640 167s 167s systemfit results 167s method: SUR 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 40 34 15590 25750 0.699 0.615 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s General.Electric 20 17 13788 811 28.5 0.693 0.656 167s Westinghouse 20 17 1801 106 10.3 0.740 0.710 167s 167s The covariance matrix of the residuals used for estimation 167s General.Electric Westinghouse 167s General.Electric 661 176.4 167s Westinghouse 176 88.7 167s 167s The covariance matrix of the residuals 167s General.Electric Westinghouse 167s General.Electric 689 190.6 167s Westinghouse 191 90.1 167s 167s The correlations of the residuals 167s General.Electric Westinghouse 167s General.Electric 1.000 0.765 167s Westinghouse 0.765 1.000 167s 167s 167s SUR estimates for 'General.Electric' (equation 1) 167s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -27.7193 27.0328 -1.03 0.32 167s value 0.0383 0.0133 2.88 0.01 * 167s capital 0.1390 0.0230 6.04 1.3e-05 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 28.479 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 13788.376 MSE: 811.081 Root MSE: 28.479 167s Multiple R-Squared: 0.693 Adjusted R-Squared: 0.656 167s 167s 167s SUR estimates for 'Westinghouse' (equation 2) 167s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -1.2520 6.9563 -0.18 0.85930 167s value 0.0576 0.0134 4.30 0.00049 *** 167s capital 0.0640 0.0489 1.31 0.20818 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 10.294 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 1801.301 MSE: 105.959 Root MSE: 10.294 167s Multiple R-Squared: 0.74 Adjusted R-Squared: 0.71 167s 167s 167s systemfit results 167s method: SUR 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 40 34 15590 25750 0.699 0.615 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s General.Electric 20 17 13788 811 28.5 0.693 0.656 167s Westinghouse 20 17 1801 106 10.3 0.740 0.710 167s 167s The covariance matrix of the residuals used for estimation 167s General.Electric Westinghouse 167s General.Electric 661 176.4 167s Westinghouse 176 88.7 167s 167s The covariance matrix of the residuals 167s General.Electric Westinghouse 167s General.Electric 689 190.6 167s Westinghouse 191 90.1 167s 167s The correlations of the residuals 167s General.Electric Westinghouse 167s General.Electric 1.000 0.765 167s Westinghouse 0.765 1.000 167s 167s 167s Coefficients: 167s Estimate Std. Error t value Pr(>|t|) 167s General.Electric_(Intercept) -27.7193 27.0328 -1.03 0.31242 167s General.Electric_value 0.0383 0.0133 2.88 0.00679 ** 167s General.Electric_capital 0.1390 0.0230 6.04 7.7e-07 *** 167s Westinghouse_(Intercept) -1.2520 6.9563 -0.18 0.85824 167s Westinghouse_value 0.0576 0.0134 4.30 0.00014 *** 167s Westinghouse_capital 0.0640 0.0489 1.31 0.19954 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s systemfit results 167s method: SUR 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 40 34 15590 25750 0.699 0.615 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s General.Electric 20 17 13788 811 28.5 0.693 0.656 167s Westinghouse 20 17 1801 106 10.3 0.740 0.710 167s 167s 167s Coefficients: 167s Estimate Std. Error t value Pr(>|t|) 167s General.Electric_(Intercept) -27.7193 27.0328 -1.03 0.31955 167s General.Electric_value 0.0383 0.0133 2.88 0.01034 * 167s General.Electric_capital 0.1390 0.0230 6.04 1.3e-05 *** 167s Westinghouse_(Intercept) -1.2520 6.9563 -0.18 0.85930 167s Westinghouse_value 0.0576 0.0134 4.30 0.00049 *** 167s Westinghouse_capital 0.0640 0.0489 1.31 0.20818 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s General.Electric_(Intercept) General.Electric_value 167s -27.7193 0.0383 167s General.Electric_capital Westinghouse_(Intercept) 167s 0.1390 -1.2520 167s Westinghouse_value Westinghouse_capital 167s 0.0576 0.0640 167s Estimate Std. Error t value Pr(>|t|) 167s General.Electric_(Intercept) -27.7193 27.0328 -1.03 3.20e-01 167s General.Electric_value 0.0383 0.0133 2.88 1.03e-02 167s General.Electric_capital 0.1390 0.0230 6.04 1.34e-05 167s Westinghouse_(Intercept) -1.2520 6.9563 -0.18 8.59e-01 167s Westinghouse_value 0.0576 0.0134 4.30 4.88e-04 167s Westinghouse_capital 0.0640 0.0489 1.31 2.08e-01 167s General.Electric_(Intercept) 167s General.Electric_(Intercept) 730.774 167s General.Electric_value -0.329 167s General.Electric_capital -0.146 167s Westinghouse_(Intercept) 126.963 167s Westinghouse_value -0.226 167s Westinghouse_capital 0.393 167s General.Electric_value General.Electric_capital 167s General.Electric_(Intercept) -0.329266 -1.46e-01 167s General.Electric_value 0.000177 -3.40e-05 167s General.Electric_capital -0.000034 5.31e-04 167s Westinghouse_(Intercept) -0.052688 -3.96e-02 167s Westinghouse_value 0.000120 -1.69e-05 167s Westinghouse_capital -0.000325 5.95e-04 167s Westinghouse_(Intercept) Westinghouse_value 167s General.Electric_(Intercept) 126.9626 -2.26e-01 167s General.Electric_value -0.0527 1.20e-04 167s General.Electric_capital -0.0396 -1.69e-05 167s Westinghouse_(Intercept) 48.3908 -8.00e-02 167s Westinghouse_value -0.0800 1.80e-04 167s Westinghouse_capital 0.1136 -4.75e-04 167s Westinghouse_capital 167s General.Electric_(Intercept) 0.392515 167s General.Electric_value -0.000325 167s General.Electric_capital 0.000595 167s Westinghouse_(Intercept) 0.113618 167s Westinghouse_value -0.000475 167s Westinghouse_capital 0.002391 167s General.Electric Westinghouse 167s X1935 2.3756 3.03 167s X1936 -19.0218 -2.64 167s X1937 -18.8820 -6.18 167s X1938 -27.5395 -9.31 167s X1939 -34.6138 -11.37 167s X1940 -5.5099 -8.09 167s X1941 39.7415 16.49 167s X1942 18.7681 8.36 167s X1943 -22.4783 -2.70 167s X1944 -24.7900 -2.89 167s X1945 -0.0321 -7.87 167s X1946 54.9123 5.38 167s X1947 47.9946 16.20 167s X1948 37.0021 4.29 167s X1949 -14.7994 -9.42 167s X1950 -30.4914 -11.86 167s X1951 -0.1173 5.62 167s X1952 4.3913 13.93 167s X1953 5.0921 11.37 167s X1954 -12.0024 -12.32 167s 2.5 % 97.5 % 167s General.Electric_(Intercept) -84.754 29.315 167s General.Electric_value 0.010 0.066 167s General.Electric_capital 0.090 0.188 167s Westinghouse_(Intercept) -15.929 13.425 167s Westinghouse_value 0.029 0.086 167s Westinghouse_capital -0.039 0.167 167s General.Electric Westinghouse 167s X1935 30.7 9.9 167s X1936 64.0 28.5 167s X1937 96.1 41.2 167s X1938 72.1 32.2 167s X1939 82.7 30.2 167s X1940 79.9 36.7 167s X1941 73.3 32.0 167s X1942 73.1 35.0 167s X1943 83.8 39.7 167s X1944 81.6 40.7 167s X1945 93.6 47.1 167s X1946 105.0 48.1 167s X1947 99.2 39.4 167s X1948 109.3 45.3 167s X1949 113.1 41.5 167s X1950 124.0 44.1 167s X1951 135.3 48.8 167s X1952 152.9 57.9 167s X1953 174.4 78.7 167s X1954 201.6 80.9 167s 'log Lik.' -158 (df=9) 167s 'log Lik.' -167 (df=9) 167s [1] 40 167s General.Electric_invest General.Electric_value General.Electric_capital 167s X1935 33.1 1171 97.8 167s X1936 45.0 2016 104.4 167s X1937 77.2 2803 118.0 167s X1938 44.6 2040 156.2 167s X1939 48.1 2256 172.6 167s X1940 74.4 2132 186.6 167s X1941 113.0 1834 220.9 167s X1942 91.9 1588 287.8 167s X1943 61.3 1749 319.9 167s X1944 56.8 1687 321.3 167s X1945 93.6 2008 319.6 167s X1946 159.9 2208 346.0 167s X1947 147.2 1657 456.4 167s X1948 146.3 1604 543.4 167s X1949 98.3 1432 618.3 167s X1950 93.5 1610 647.4 167s X1951 135.2 1819 671.3 167s X1952 157.3 2080 726.1 167s X1953 179.5 2372 800.3 167s X1954 189.6 2760 888.9 167s Westinghouse_invest Westinghouse_value Westinghouse_capital 167s X1935 12.9 192 1.8 167s X1936 25.9 516 0.8 167s X1937 35.0 729 7.4 167s X1938 22.9 560 18.1 167s X1939 18.8 520 23.5 167s X1940 28.6 628 26.5 167s X1941 48.5 537 36.2 167s X1942 43.3 561 60.8 167s X1943 37.0 617 84.4 167s X1944 37.8 627 91.2 167s X1945 39.3 737 92.4 167s X1946 53.5 760 86.0 167s X1947 55.6 581 111.1 167s X1948 49.6 662 130.6 167s X1949 32.0 584 141.8 167s X1950 32.2 635 136.7 167s X1951 54.4 724 129.7 167s X1952 71.8 864 145.5 167s X1953 90.1 1194 174.8 167s X1954 68.6 1189 213.5 167s General.Electric_(Intercept) General.Electric_value 167s General.Electric_X1935 1 1171 167s General.Electric_X1936 1 2016 167s General.Electric_X1937 1 2803 167s General.Electric_X1938 1 2040 167s General.Electric_X1939 1 2256 167s General.Electric_X1940 1 2132 167s General.Electric_X1941 1 1834 167s General.Electric_X1942 1 1588 167s General.Electric_X1943 1 1749 167s General.Electric_X1944 1 1687 167s General.Electric_X1945 1 2008 167s General.Electric_X1946 1 2208 167s General.Electric_X1947 1 1657 167s General.Electric_X1948 1 1604 167s General.Electric_X1949 1 1432 167s General.Electric_X1950 1 1610 167s General.Electric_X1951 1 1819 167s General.Electric_X1952 1 2080 167s General.Electric_X1953 1 2372 167s General.Electric_X1954 1 2760 167s Westinghouse_X1935 0 0 167s Westinghouse_X1936 0 0 167s Westinghouse_X1937 0 0 167s Westinghouse_X1938 0 0 167s Westinghouse_X1939 0 0 167s Westinghouse_X1940 0 0 167s Westinghouse_X1941 0 0 167s Westinghouse_X1942 0 0 167s Westinghouse_X1943 0 0 167s Westinghouse_X1944 0 0 167s Westinghouse_X1945 0 0 167s Westinghouse_X1946 0 0 167s Westinghouse_X1947 0 0 167s Westinghouse_X1948 0 0 167s Westinghouse_X1949 0 0 167s Westinghouse_X1950 0 0 167s Westinghouse_X1951 0 0 167s Westinghouse_X1952 0 0 167s Westinghouse_X1953 0 0 167s Westinghouse_X1954 0 0 167s General.Electric_capital Westinghouse_(Intercept) 167s General.Electric_X1935 97.8 0 167s General.Electric_X1936 104.4 0 167s General.Electric_X1937 118.0 0 167s General.Electric_X1938 156.2 0 167s General.Electric_X1939 172.6 0 167s General.Electric_X1940 186.6 0 167s General.Electric_X1941 220.9 0 167s General.Electric_X1942 287.8 0 167s General.Electric_X1943 319.9 0 167s General.Electric_X1944 321.3 0 167s General.Electric_X1945 319.6 0 167s General.Electric_X1946 346.0 0 167s General.Electric_X1947 456.4 0 167s General.Electric_X1948 543.4 0 167s General.Electric_X1949 618.3 0 167s General.Electric_X1950 647.4 0 167s General.Electric_X1951 671.3 0 167s General.Electric_X1952 726.1 0 167s General.Electric_X1953 800.3 0 167s General.Electric_X1954 888.9 0 167s Westinghouse_X1935 0.0 1 167s Westinghouse_X1936 0.0 1 167s Westinghouse_X1937 0.0 1 167s Westinghouse_X1938 0.0 1 167s Westinghouse_X1939 0.0 1 167s Westinghouse_X1940 0.0 1 167s Westinghouse_X1941 0.0 1 167s Westinghouse_X1942 0.0 1 167s Westinghouse_X1943 0.0 1 167s Westinghouse_X1944 0.0 1 167s Westinghouse_X1945 0.0 1 167s Westinghouse_X1946 0.0 1 167s Westinghouse_X1947 0.0 1 167s Westinghouse_X1948 0.0 1 167s Westinghouse_X1949 0.0 1 167s Westinghouse_X1950 0.0 1 167s Westinghouse_X1951 0.0 1 167s Westinghouse_X1952 0.0 1 167s Westinghouse_X1953 0.0 1 167s Westinghouse_X1954 0.0 1 167s Westinghouse_value Westinghouse_capital 167s General.Electric_X1935 0 0.0 167s General.Electric_X1936 0 0.0 167s General.Electric_X1937 0 0.0 167s General.Electric_X1938 0 0.0 167s General.Electric_X1939 0 0.0 167s General.Electric_X1940 0 0.0 167s General.Electric_X1941 0 0.0 167s General.Electric_X1942 0 0.0 167s General.Electric_X1943 0 0.0 167s General.Electric_X1944 0 0.0 167s General.Electric_X1945 0 0.0 167s General.Electric_X1946 0 0.0 167s General.Electric_X1947 0 0.0 167s General.Electric_X1948 0 0.0 167s General.Electric_X1949 0 0.0 167s General.Electric_X1950 0 0.0 167s General.Electric_X1951 0 0.0 167s General.Electric_X1952 0 0.0 167s General.Electric_X1953 0 0.0 167s General.Electric_X1954 0 0.0 167s Westinghouse_X1935 192 1.8 167s Westinghouse_X1936 516 0.8 167s Westinghouse_X1937 729 7.4 167s Westinghouse_X1938 560 18.1 167s Westinghouse_X1939 520 23.5 167s Westinghouse_X1940 628 26.5 167s Westinghouse_X1941 537 36.2 167s Westinghouse_X1942 561 60.8 167s Westinghouse_X1943 617 84.4 167s Westinghouse_X1944 627 91.2 167s Westinghouse_X1945 737 92.4 167s Westinghouse_X1946 760 86.0 167s Westinghouse_X1947 581 111.1 167s Westinghouse_X1948 662 130.6 167s Westinghouse_X1949 584 141.8 167s Westinghouse_X1950 635 136.7 167s Westinghouse_X1951 724 129.7 167s Westinghouse_X1952 864 145.5 167s Westinghouse_X1953 1194 174.8 167s Westinghouse_X1954 1189 213.5 167s $General.Electric 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s 167s $Westinghouse 167s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s 167s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s $General.Electric 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s attr(,"variables") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"factors") 167s General.Electric_value General.Electric_capital 167s General.Electric_invest 0 0 167s General.Electric_value 1 0 167s General.Electric_capital 0 1 167s attr(,"term.labels") 167s [1] "General.Electric_value" "General.Electric_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"dataClasses") 167s General.Electric_invest General.Electric_value General.Electric_capital 167s "numeric" "numeric" "numeric" 167s 167s $Westinghouse 167s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s attr(,"variables") 167s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 167s attr(,"factors") 167s Westinghouse_value Westinghouse_capital 167s Westinghouse_invest 0 0 167s Westinghouse_value 1 0 167s Westinghouse_capital 0 1 167s attr(,"term.labels") 167s [1] "Westinghouse_value" "Westinghouse_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 167s attr(,"dataClasses") 167s Westinghouse_invest Westinghouse_value Westinghouse_capital 167s "numeric" "numeric" "numeric" 167s 167s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s attr(,"variables") 167s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 167s attr(,"factors") 167s Westinghouse_value Westinghouse_capital 167s Westinghouse_invest 0 0 167s Westinghouse_value 1 0 167s Westinghouse_capital 0 1 167s attr(,"term.labels") 167s [1] "Westinghouse_value" "Westinghouse_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 167s attr(,"dataClasses") 167s Westinghouse_invest Westinghouse_value Westinghouse_capital 167s "numeric" "numeric" "numeric" 167s > 167s > ## Repeating the OLS and SUR estimations in Greene (2003, pp. 351) 167s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 167s + GrunfeldGreene <- pdata.frame( GrunfeldGreene, c( "firm", "year" ) ) 167s + formulaGrunfeld <- invest ~ value + capital 167s + } 167s > 167s > # OLS 167s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 167s + greeneOls <- systemfit( formulaGrunfeld, "OLS", 167s + data = GrunfeldGreene, useMatrix = useMatrix ) 167s + print( greeneOls ) 167s + print( summary( greeneOls ) ) 167s + print( summary( greeneOls, useDfSys = TRUE, equations = FALSE ) ) 167s + print( summary( greeneOls, residCov = FALSE ) ) 167s + print( sapply( greeneOls$eq, function(x){return(summary(x)$ssr/20)} ) ) # sigma^2 167s + print( coef( greeneOls ) ) 167s + print( coef( summary( greeneOls ) ) ) 167s + print( vcov( greeneOls ) ) 167s + print( residuals( greeneOls ) ) 167s + print( confint(greeneOls ) ) 167s + print( fitted( greeneOls ) ) 167s + print( logLik( greeneOls ) ) 167s + print( logLik( greeneOls, residCovDiag = TRUE ) ) 167s + print( nobs( greeneOls ) ) 167s + print( model.frame( greeneOls ) ) 167s + print( model.matrix( greeneOls ) ) 167s + print( formula( greeneOls ) ) 167s + print( formula( greeneOls$eq[[ 2 ]] ) ) 167s + print( terms( greeneOls ) ) 167s + print( terms( greeneOls$eq[[ 2 ]] ) ) 167s + } 167s 167s systemfit results 167s method: OLS 167s 167s Coefficients: 167s Chrysler_(Intercept) Chrysler_value 167s -6.1900 0.0779 167s Chrysler_capital General.Electric_(Intercept) 167s 0.3157 -9.9563 167s General.Electric_value General.Electric_capital 167s 0.0266 0.1517 167s General.Motors_(Intercept) General.Motors_value 167s -149.7825 0.1193 167s General.Motors_capital US.Steel_(Intercept) 167s 0.3714 -30.3685 167s US.Steel_value US.Steel_capital 167s 0.1566 0.4239 167s Westinghouse_(Intercept) Westinghouse_value 167s -0.5094 0.0529 167s Westinghouse_capital 167s 0.0924 167s 167s systemfit results 167s method: OLS 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 100 85 339121 2.09e+14 0.848 0.862 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s Chrysler 20 17 2997 176 13.3 0.914 0.903 167s General.Electric 20 17 13217 777 27.9 0.705 0.671 167s General.Motors 20 17 143206 8424 91.8 0.921 0.912 167s US.Steel 20 17 177928 10466 102.3 0.440 0.374 167s Westinghouse 20 17 1773 104 10.2 0.744 0.714 167s 167s The covariance matrix of the residuals 167s Chrysler General.Electric General.Motors US.Steel Westinghouse 167s Chrysler 176.3 -25.1 -333 492 15.7 167s General.Electric -25.1 777.4 715 1065 207.6 167s General.Motors -332.7 714.7 8424 -2614 148.4 167s US.Steel 491.9 1064.6 -2614 10466 642.6 167s Westinghouse 15.7 207.6 148 643 104.3 167s 167s The correlations of the residuals 167s Chrysler General.Electric General.Motors US.Steel Westinghouse 167s Chrysler 1.0000 -0.0679 -0.273 0.362 0.115 167s General.Electric -0.0679 1.0000 0.279 0.373 0.729 167s General.Motors -0.2730 0.2793 1.000 -0.278 0.158 167s US.Steel 0.3621 0.3732 -0.278 1.000 0.615 167s Westinghouse 0.1154 0.7290 0.158 0.615 1.000 167s 167s 167s OLS estimates for 'Chrysler' (equation 1) 167s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -6.1900 13.5065 -0.46 0.6525 167s value 0.0779 0.0200 3.90 0.0011 ** 167s capital 0.3157 0.0288 10.96 4e-09 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 13.279 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 2997.444 MSE: 176.32 Root MSE: 13.279 167s Multiple R-Squared: 0.914 Adjusted R-Squared: 0.903 167s 167s 167s OLS estimates for 'General.Electric' (equation 2) 167s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -9.9563 31.3742 -0.32 0.75 167s value 0.0266 0.0156 1.71 0.11 167s capital 0.1517 0.0257 5.90 1.7e-05 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 27.883 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 167s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 167s 167s 167s OLS estimates for 'General.Motors' (equation 3) 167s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -149.7825 105.8421 -1.42 0.17508 167s value 0.1193 0.0258 4.62 0.00025 *** 167s capital 0.3714 0.0371 10.02 1.5e-08 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 91.782 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 143205.877 MSE: 8423.875 Root MSE: 91.782 167s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.912 167s 167s 167s OLS estimates for 'US.Steel' (equation 4) 167s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -30.3685 157.0477 -0.19 0.849 167s value 0.1566 0.0789 1.98 0.064 . 167s capital 0.4239 0.1552 2.73 0.014 * 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 102.305 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 177928.314 MSE: 10466.371 Root MSE: 102.305 167s Multiple R-Squared: 0.44 Adjusted R-Squared: 0.374 167s 167s 167s OLS estimates for 'Westinghouse' (equation 5) 167s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -0.5094 8.0153 -0.06 0.9501 167s value 0.0529 0.0157 3.37 0.0037 ** 167s capital 0.0924 0.0561 1.65 0.1179 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 10.213 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 167s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 167s 167s 167s systemfit results 167s method: OLS 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 100 85 339121 2.09e+14 0.848 0.862 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s Chrysler 20 17 2997 176 13.3 0.914 0.903 167s General.Electric 20 17 13217 777 27.9 0.705 0.671 167s General.Motors 20 17 143206 8424 91.8 0.921 0.912 167s US.Steel 20 17 177928 10466 102.3 0.440 0.374 167s Westinghouse 20 17 1773 104 10.2 0.744 0.714 167s 167s The covariance matrix of the residuals 167s Chrysler General.Electric General.Motors US.Steel Westinghouse 167s Chrysler 176.3 -25.1 -333 492 15.7 167s General.Electric -25.1 777.4 715 1065 207.6 167s General.Motors -332.7 714.7 8424 -2614 148.4 167s US.Steel 491.9 1064.6 -2614 10466 642.6 167s Westinghouse 15.7 207.6 148 643 104.3 167s 167s The correlations of the residuals 167s Chrysler General.Electric General.Motors US.Steel Westinghouse 167s Chrysler 1.0000 -0.0679 -0.273 0.362 0.115 167s General.Electric -0.0679 1.0000 0.279 0.373 0.729 167s General.Motors -0.2730 0.2793 1.000 -0.278 0.158 167s US.Steel 0.3621 0.3732 -0.278 1.000 0.615 167s Westinghouse 0.1154 0.7290 0.158 0.615 1.000 167s 167s 167s Coefficients: 167s Estimate Std. Error t value Pr(>|t|) 167s Chrysler_(Intercept) -6.1900 13.5065 -0.46 0.64791 167s Chrysler_value 0.0779 0.0200 3.90 0.00019 *** 167s Chrysler_capital 0.3157 0.0288 10.96 < 2e-16 *** 167s General.Electric_(Intercept) -9.9563 31.3742 -0.32 0.75176 167s General.Electric_value 0.0266 0.0156 1.71 0.09171 . 167s General.Electric_capital 0.1517 0.0257 5.90 7.2e-08 *** 167s General.Motors_(Intercept) -149.7825 105.8421 -1.42 0.16068 167s General.Motors_value 0.1193 0.0258 4.62 1.4e-05 *** 167s General.Motors_capital 0.3714 0.0371 10.02 4.4e-16 *** 167s US.Steel_(Intercept) -30.3685 157.0477 -0.19 0.84713 167s US.Steel_value 0.1566 0.0789 1.98 0.05039 . 167s US.Steel_capital 0.4239 0.1552 2.73 0.00768 ** 167s Westinghouse_(Intercept) -0.5094 8.0153 -0.06 0.94948 167s Westinghouse_value 0.0529 0.0157 3.37 0.00114 ** 167s Westinghouse_capital 0.0924 0.0561 1.65 0.10321 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s systemfit results 167s method: OLS 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 100 85 339121 2.09e+14 0.848 0.862 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s Chrysler 20 17 2997 176 13.3 0.914 0.903 167s General.Electric 20 17 13217 777 27.9 0.705 0.671 167s General.Motors 20 17 143206 8424 91.8 0.921 0.912 167s US.Steel 20 17 177928 10466 102.3 0.440 0.374 167s Westinghouse 20 17 1773 104 10.2 0.744 0.714 167s 167s 167s OLS estimates for 'Chrysler' (equation 1) 167s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -6.1900 13.5065 -0.46 0.6525 167s value 0.0779 0.0200 3.90 0.0011 ** 167s capital 0.3157 0.0288 10.96 4e-09 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 13.279 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 2997.444 MSE: 176.32 Root MSE: 13.279 167s Multiple R-Squared: 0.914 Adjusted R-Squared: 0.903 167s 167s 167s OLS estimates for 'General.Electric' (equation 2) 167s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -9.9563 31.3742 -0.32 0.75 167s value 0.0266 0.0156 1.71 0.11 167s capital 0.1517 0.0257 5.90 1.7e-05 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 27.883 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 167s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 167s 167s 167s OLS estimates for 'General.Motors' (equation 3) 167s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -149.7825 105.8421 -1.42 0.17508 167s value 0.1193 0.0258 4.62 0.00025 *** 167s capital 0.3714 0.0371 10.02 1.5e-08 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 91.782 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 143205.877 MSE: 8423.875 Root MSE: 91.782 167s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.912 167s 167s 167s OLS estimates for 'US.Steel' (equation 4) 167s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -30.3685 157.0477 -0.19 0.849 167s value 0.1566 0.0789 1.98 0.064 . 167s capital 0.4239 0.1552 2.73 0.014 * 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 102.305 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 177928.314 MSE: 10466.371 Root MSE: 102.305 167s Multiple R-Squared: 0.44 Adjusted R-Squared: 0.374 167s 167s 167s OLS estimates for 'Westinghouse' (equation 5) 167s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -0.5094 8.0153 -0.06 0.9501 167s value 0.0529 0.0157 3.37 0.0037 ** 167s capital 0.0924 0.0561 1.65 0.1179 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 10.213 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 167s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 167s 167s [1] 149.9 660.8 7160.3 8896.4 88.7 167s Chrysler_(Intercept) Chrysler_value 167s -6.1900 0.0779 167s Chrysler_capital General.Electric_(Intercept) 167s 0.3157 -9.9563 167s General.Electric_value General.Electric_capital 167s 0.0266 0.1517 167s General.Motors_(Intercept) General.Motors_value 167s -149.7825 0.1193 167s General.Motors_capital US.Steel_(Intercept) 167s 0.3714 -30.3685 167s US.Steel_value US.Steel_capital 167s 0.1566 0.4239 167s Westinghouse_(Intercept) Westinghouse_value 167s -0.5094 0.0529 167s Westinghouse_capital 167s 0.0924 167s Estimate Std. Error t value Pr(>|t|) 167s Chrysler_(Intercept) -6.1900 13.5065 -0.4583 6.53e-01 167s Chrysler_value 0.0779 0.0200 3.9026 1.15e-03 167s Chrysler_capital 0.3157 0.0288 10.9574 3.99e-09 167s General.Electric_(Intercept) -9.9563 31.3742 -0.3173 7.55e-01 167s General.Electric_value 0.0266 0.0156 1.7057 1.06e-01 167s General.Electric_capital 0.1517 0.0257 5.9015 1.74e-05 167s General.Motors_(Intercept) -149.7825 105.8421 -1.4151 1.75e-01 167s General.Motors_value 0.1193 0.0258 4.6172 2.46e-04 167s General.Motors_capital 0.3714 0.0371 10.0193 1.51e-08 167s US.Steel_(Intercept) -30.3685 157.0477 -0.1934 8.49e-01 167s US.Steel_value 0.1566 0.0789 1.9848 6.35e-02 167s US.Steel_capital 0.4239 0.1552 2.7308 1.42e-02 167s Westinghouse_(Intercept) -0.5094 8.0153 -0.0636 9.50e-01 167s Westinghouse_value 0.0529 0.0157 3.3677 3.65e-03 167s Westinghouse_capital 0.0924 0.0561 1.6472 1.18e-01 167s Chrysler_(Intercept) Chrysler_value 167s Chrysler_(Intercept) 182.4250 -0.254690 167s Chrysler_value -0.2547 0.000399 167s Chrysler_capital 0.0243 -0.000180 167s General.Electric_(Intercept) 0.0000 0.000000 167s General.Electric_value 0.0000 0.000000 167s General.Electric_capital 0.0000 0.000000 167s General.Motors_(Intercept) 0.0000 0.000000 167s General.Motors_value 0.0000 0.000000 167s General.Motors_capital 0.0000 0.000000 167s US.Steel_(Intercept) 0.0000 0.000000 167s US.Steel_value 0.0000 0.000000 167s US.Steel_capital 0.0000 0.000000 167s Westinghouse_(Intercept) 0.0000 0.000000 167s Westinghouse_value 0.0000 0.000000 167s Westinghouse_capital 0.0000 0.000000 167s Chrysler_capital General.Electric_(Intercept) 167s Chrysler_(Intercept) 0.02429 0.000 167s Chrysler_value -0.00018 0.000 167s Chrysler_capital 0.00083 0.000 167s General.Electric_(Intercept) 0.00000 984.344 167s General.Electric_value 0.00000 -0.451 167s General.Electric_capital 0.00000 -0.173 167s General.Motors_(Intercept) 0.00000 0.000 167s General.Motors_value 0.00000 0.000 167s General.Motors_capital 0.00000 0.000 167s US.Steel_(Intercept) 0.00000 0.000 167s US.Steel_value 0.00000 0.000 167s US.Steel_capital 0.00000 0.000 167s Westinghouse_(Intercept) 0.00000 0.000 167s Westinghouse_value 0.00000 0.000 167s Westinghouse_capital 0.00000 0.000 167s General.Electric_value General.Electric_capital 167s Chrysler_(Intercept) 0.00e+00 0.00e+00 167s Chrysler_value 0.00e+00 0.00e+00 167s Chrysler_capital 0.00e+00 0.00e+00 167s General.Electric_(Intercept) -4.51e-01 -1.73e-01 167s General.Electric_value 2.42e-04 -4.73e-05 167s General.Electric_capital -4.73e-05 6.61e-04 167s General.Motors_(Intercept) 0.00e+00 0.00e+00 167s General.Motors_value 0.00e+00 0.00e+00 167s General.Motors_capital 0.00e+00 0.00e+00 167s US.Steel_(Intercept) 0.00e+00 0.00e+00 167s US.Steel_value 0.00e+00 0.00e+00 167s US.Steel_capital 0.00e+00 0.00e+00 167s Westinghouse_(Intercept) 0.00e+00 0.00e+00 167s Westinghouse_value 0.00e+00 0.00e+00 167s Westinghouse_capital 0.00e+00 0.00e+00 167s General.Motors_(Intercept) General.Motors_value 167s Chrysler_(Intercept) 0.000 0.000000 167s Chrysler_value 0.000 0.000000 167s Chrysler_capital 0.000 0.000000 167s General.Electric_(Intercept) 0.000 0.000000 167s General.Electric_value 0.000 0.000000 167s General.Electric_capital 0.000 0.000000 167s General.Motors_(Intercept) 11202.555 -2.623398 167s General.Motors_value -2.623 0.000667 167s General.Motors_capital 0.907 -0.000415 167s US.Steel_(Intercept) 0.000 0.000000 167s US.Steel_value 0.000 0.000000 167s US.Steel_capital 0.000 0.000000 167s Westinghouse_(Intercept) 0.000 0.000000 167s Westinghouse_value 0.000 0.000000 167s Westinghouse_capital 0.000 0.000000 167s General.Motors_capital US.Steel_(Intercept) 167s Chrysler_(Intercept) 0.000000 0.00 167s Chrysler_value 0.000000 0.00 167s Chrysler_capital 0.000000 0.00 167s General.Electric_(Intercept) 0.000000 0.00 167s General.Electric_value 0.000000 0.00 167s General.Electric_capital 0.000000 0.00 167s General.Motors_(Intercept) 0.906860 0.00 167s General.Motors_value -0.000415 0.00 167s General.Motors_capital 0.001374 0.00 167s US.Steel_(Intercept) 0.000000 24663.98 167s US.Steel_value 0.000000 -11.71 167s US.Steel_capital 0.000000 -3.52 167s Westinghouse_(Intercept) 0.000000 0.00 167s Westinghouse_value 0.000000 0.00 167s Westinghouse_capital 0.000000 0.00 167s US.Steel_value US.Steel_capital 167s Chrysler_(Intercept) 0.00000 0.00000 167s Chrysler_value 0.00000 0.00000 167s Chrysler_capital 0.00000 0.00000 167s General.Electric_(Intercept) 0.00000 0.00000 167s General.Electric_value 0.00000 0.00000 167s General.Electric_capital 0.00000 0.00000 167s General.Motors_(Intercept) 0.00000 0.00000 167s General.Motors_value 0.00000 0.00000 167s General.Motors_capital 0.00000 0.00000 167s US.Steel_(Intercept) -11.70740 -3.52078 167s US.Steel_value 0.00622 -0.00188 167s US.Steel_capital -0.00188 0.02409 167s Westinghouse_(Intercept) 0.00000 0.00000 167s Westinghouse_value 0.00000 0.00000 167s Westinghouse_capital 0.00000 0.00000 167s Westinghouse_(Intercept) Westinghouse_value 167s Chrysler_(Intercept) 0.000 0.000000 167s Chrysler_value 0.000 0.000000 167s Chrysler_capital 0.000 0.000000 167s General.Electric_(Intercept) 0.000 0.000000 167s General.Electric_value 0.000 0.000000 167s General.Electric_capital 0.000 0.000000 167s General.Motors_(Intercept) 0.000 0.000000 167s General.Motors_value 0.000 0.000000 167s General.Motors_capital 0.000 0.000000 167s US.Steel_(Intercept) 0.000 0.000000 167s US.Steel_value 0.000 0.000000 167s US.Steel_capital 0.000 0.000000 167s Westinghouse_(Intercept) 64.245 -0.109545 167s Westinghouse_value -0.110 0.000247 167s Westinghouse_capital 0.169 -0.000653 167s Westinghouse_capital 167s Chrysler_(Intercept) 0.000000 167s Chrysler_value 0.000000 167s Chrysler_capital 0.000000 167s General.Electric_(Intercept) 0.000000 167s General.Electric_value 0.000000 167s General.Electric_capital 0.000000 167s General.Motors_(Intercept) 0.000000 167s General.Motors_value 0.000000 167s General.Motors_capital 0.000000 167s US.Steel_(Intercept) 0.000000 167s US.Steel_value 0.000000 167s US.Steel_capital 0.000000 167s Westinghouse_(Intercept) 0.168911 167s Westinghouse_value -0.000653 167s Westinghouse_capital 0.003147 167s Chrysler General.Electric General.Motors US.Steel Westinghouse 167s X1935 10.622 -2.860 99.14 4.15 3.144 167s X1936 10.425 -14.402 -34.01 81.32 -0.958 167s X1937 -7.404 -5.175 -140.48 31.18 -3.684 167s X1938 7.302 -23.295 -3.28 -99.75 -7.915 167s X1939 -14.682 -28.031 -109.45 -178.23 -10.322 167s X1940 -2.315 -0.562 -19.91 -160.69 -6.613 167s X1941 0.631 40.750 24.12 19.65 17.265 167s X1942 -1.581 16.036 98.02 9.82 8.547 167s X1943 -13.459 -23.719 67.76 -46.76 -2.916 167s X1944 -7.780 -26.780 100.03 -83.74 -3.257 167s X1945 11.757 1.768 35.12 -91.24 -7.753 167s X1946 -16.133 58.737 103.90 28.34 5.796 167s X1947 -6.823 43.936 15.18 57.32 15.050 167s X1948 6.615 31.227 -51.86 140.23 2.969 167s X1949 -7.379 -23.552 -115.39 25.65 -11.433 167s X1950 1.268 -37.511 -63.51 34.88 -13.481 167s X1951 39.502 -4.983 -119.40 115.10 4.619 167s X1952 2.774 1.893 -77.82 149.19 13.138 167s X1953 -6.215 5.087 49.50 89.00 11.308 167s X1954 -7.124 -8.563 142.33 -125.42 -13.505 167s 2.5 % 97.5 % 167s Chrysler_(Intercept) -34.686 22.306 167s Chrysler_value 0.036 0.120 167s Chrysler_capital 0.255 0.377 167s General.Electric_(Intercept) -76.150 56.238 167s General.Electric_value -0.006 0.059 167s General.Electric_capital 0.097 0.206 167s General.Motors_(Intercept) -373.090 73.525 167s General.Motors_value 0.065 0.174 167s General.Motors_capital 0.293 0.450 167s US.Steel_(Intercept) -361.710 300.973 167s US.Steel_value -0.010 0.323 167s US.Steel_capital 0.096 0.751 167s Westinghouse_(Intercept) -17.420 16.401 167s Westinghouse_value 0.020 0.086 167s Westinghouse_capital -0.026 0.211 167s Chrysler General.Electric General.Motors US.Steel Westinghouse 167s X1935 29.7 36.0 218 206 9.79 167s X1936 62.3 59.4 426 274 26.86 167s X1937 73.7 82.4 551 439 38.73 167s X1938 44.3 67.9 261 362 30.81 167s X1939 67.1 76.1 440 409 29.16 167s X1940 71.7 75.0 481 422 35.18 167s X1941 67.7 72.3 488 453 31.25 167s X1942 48.4 75.9 350 436 34.79 167s X1943 60.9 85.0 432 408 39.94 167s X1944 67.3 83.6 447 372 41.07 167s X1945 77.0 91.8 526 350 47.02 167s X1946 90.3 101.2 584 392 47.66 167s X1947 69.5 103.3 554 363 40.51 167s X1948 82.7 115.1 581 354 46.59 167s X1949 86.4 121.9 670 379 43.47 167s X1950 99.4 131.0 706 384 45.72 167s X1951 121.1 140.2 875 473 49.76 167s X1952 142.2 155.4 969 496 58.64 167s X1953 181.1 174.4 1255 552 78.77 167s X1954 179.6 198.2 1344 585 82.11 167s 'log Lik.' -464 (df=16) 167s 'log Lik.' -481 (df=16) 167s [1] 100 167s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 167s X1935 40.3 418 10.5 33.1 167s X1936 72.8 838 10.2 45.0 167s X1937 66.3 884 34.7 77.2 167s X1938 51.6 438 51.8 44.6 167s X1939 52.4 680 64.3 48.1 167s X1940 69.4 728 67.1 74.4 167s X1941 68.3 644 75.2 113.0 167s X1942 46.8 411 71.4 91.9 167s X1943 47.4 588 67.1 61.3 167s X1944 59.6 698 60.5 56.8 167s X1945 88.8 846 54.6 93.6 167s X1946 74.1 894 84.8 159.9 167s X1947 62.7 579 96.8 147.2 167s X1948 89.4 695 110.2 146.3 167s X1949 79.0 590 147.4 98.3 167s X1950 100.7 694 163.2 93.5 167s X1951 160.6 809 203.5 135.2 167s X1952 145.0 727 290.6 157.3 167s X1953 174.9 1002 346.1 179.5 167s X1954 172.5 703 414.9 189.6 167s General.Electric_value General.Electric_capital General.Motors_invest 167s X1935 1171 97.8 318 167s X1936 2016 104.4 392 167s X1937 2803 118.0 411 167s X1938 2040 156.2 258 167s X1939 2256 172.6 331 167s X1940 2132 186.6 461 167s X1941 1834 220.9 512 167s X1942 1588 287.8 448 167s X1943 1749 319.9 500 167s X1944 1687 321.3 548 167s X1945 2008 319.6 561 167s X1946 2208 346.0 688 167s X1947 1657 456.4 569 167s X1948 1604 543.4 529 167s X1949 1432 618.3 555 167s X1950 1610 647.4 643 167s X1951 1819 671.3 756 167s X1952 2080 726.1 891 167s X1953 2372 800.3 1304 167s X1954 2760 888.9 1487 167s General.Motors_value General.Motors_capital US.Steel_invest 167s X1935 3078 2.8 210 167s X1936 4662 52.6 355 167s X1937 5387 156.9 470 167s X1938 2792 209.2 262 167s X1939 4313 203.4 230 167s X1940 4644 207.2 262 167s X1941 4551 255.2 473 167s X1942 3244 303.7 446 167s X1943 4054 264.1 362 167s X1944 4379 201.6 288 167s X1945 4841 265.0 259 167s X1946 4901 402.2 420 167s X1947 3526 761.5 420 167s X1948 3255 922.4 494 167s X1949 3700 1020.1 405 167s X1950 3756 1099.0 419 167s X1951 4833 1207.7 588 167s X1952 4925 1430.5 645 167s X1953 6242 1777.3 641 167s X1954 5594 2226.3 459 167s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 167s X1935 1362 53.8 12.9 192 167s X1936 1807 50.5 25.9 516 167s X1937 2676 118.1 35.0 729 167s X1938 1802 260.2 22.9 560 167s X1939 1957 312.7 18.8 520 167s X1940 2203 254.2 28.6 628 167s X1941 2380 261.4 48.5 537 167s X1942 2169 298.7 43.3 561 167s X1943 1985 301.8 37.0 617 167s X1944 1814 279.1 37.8 627 167s X1945 1850 213.8 39.3 737 167s X1946 2068 232.6 53.5 760 167s X1947 1797 264.8 55.6 581 167s X1948 1626 306.9 49.6 662 167s X1949 1667 351.1 32.0 584 167s X1950 1677 357.8 32.2 635 167s X1951 2290 342.1 54.4 724 167s X1952 2159 444.2 71.8 864 167s X1953 2031 623.6 90.1 1194 167s X1954 2116 669.7 68.6 1189 167s Westinghouse_capital 167s X1935 1.8 167s X1936 0.8 167s X1937 7.4 167s X1938 18.1 167s X1939 23.5 167s X1940 26.5 167s X1941 36.2 167s X1942 60.8 167s X1943 84.4 167s X1944 91.2 167s X1945 92.4 167s X1946 86.0 167s X1947 111.1 167s X1948 130.6 167s X1949 141.8 167s X1950 136.7 167s X1951 129.7 167s X1952 145.5 167s X1953 174.8 167s X1954 213.5 167s Chrysler_(Intercept) Chrysler_value Chrysler_capital 167s Chrysler_X1935 1 418 10.5 167s Chrysler_X1936 1 838 10.2 167s Chrysler_X1937 1 884 34.7 167s Chrysler_X1938 1 438 51.8 167s Chrysler_X1939 1 680 64.3 167s Chrysler_X1940 1 728 67.1 167s Chrysler_X1941 1 644 75.2 167s Chrysler_X1942 1 411 71.4 167s Chrysler_X1943 1 588 67.1 167s Chrysler_X1944 1 698 60.5 167s Chrysler_X1945 1 846 54.6 167s Chrysler_X1946 1 894 84.8 167s Chrysler_X1947 1 579 96.8 167s Chrysler_X1948 1 695 110.2 167s Chrysler_X1949 1 590 147.4 167s Chrysler_X1950 1 694 163.2 167s Chrysler_X1951 1 809 203.5 167s Chrysler_X1952 1 727 290.6 167s Chrysler_X1953 1 1002 346.1 167s Chrysler_X1954 1 703 414.9 167s General.Electric_X1935 0 0 0.0 167s General.Electric_X1936 0 0 0.0 167s General.Electric_X1937 0 0 0.0 167s General.Electric_X1938 0 0 0.0 167s General.Electric_X1939 0 0 0.0 167s General.Electric_X1940 0 0 0.0 167s General.Electric_X1941 0 0 0.0 167s General.Electric_X1942 0 0 0.0 167s General.Electric_X1943 0 0 0.0 167s General.Electric_X1944 0 0 0.0 167s General.Electric_X1945 0 0 0.0 167s General.Electric_X1946 0 0 0.0 167s General.Electric_X1947 0 0 0.0 167s General.Electric_X1948 0 0 0.0 167s General.Electric_X1949 0 0 0.0 167s General.Electric_X1950 0 0 0.0 167s General.Electric_X1951 0 0 0.0 167s General.Electric_X1952 0 0 0.0 167s General.Electric_X1953 0 0 0.0 167s General.Electric_X1954 0 0 0.0 167s General.Motors_X1935 0 0 0.0 167s General.Motors_X1936 0 0 0.0 167s General.Motors_X1937 0 0 0.0 167s General.Motors_X1938 0 0 0.0 167s General.Motors_X1939 0 0 0.0 167s General.Motors_X1940 0 0 0.0 167s General.Motors_X1941 0 0 0.0 167s General.Motors_X1942 0 0 0.0 167s General.Motors_X1943 0 0 0.0 167s General.Motors_X1944 0 0 0.0 167s General.Motors_X1945 0 0 0.0 167s General.Motors_X1946 0 0 0.0 167s General.Motors_X1947 0 0 0.0 167s General.Motors_X1948 0 0 0.0 167s General.Motors_X1949 0 0 0.0 167s General.Motors_X1950 0 0 0.0 167s General.Motors_X1951 0 0 0.0 167s General.Motors_X1952 0 0 0.0 167s General.Motors_X1953 0 0 0.0 167s General.Motors_X1954 0 0 0.0 167s US.Steel_X1935 0 0 0.0 167s US.Steel_X1936 0 0 0.0 167s US.Steel_X1937 0 0 0.0 167s US.Steel_X1938 0 0 0.0 167s US.Steel_X1939 0 0 0.0 167s US.Steel_X1940 0 0 0.0 167s US.Steel_X1941 0 0 0.0 167s US.Steel_X1942 0 0 0.0 167s US.Steel_X1943 0 0 0.0 167s US.Steel_X1944 0 0 0.0 167s US.Steel_X1945 0 0 0.0 167s US.Steel_X1946 0 0 0.0 167s US.Steel_X1947 0 0 0.0 167s US.Steel_X1948 0 0 0.0 167s US.Steel_X1949 0 0 0.0 167s US.Steel_X1950 0 0 0.0 167s US.Steel_X1951 0 0 0.0 167s US.Steel_X1952 0 0 0.0 167s US.Steel_X1953 0 0 0.0 167s US.Steel_X1954 0 0 0.0 167s Westinghouse_X1935 0 0 0.0 167s Westinghouse_X1936 0 0 0.0 167s Westinghouse_X1937 0 0 0.0 167s Westinghouse_X1938 0 0 0.0 167s Westinghouse_X1939 0 0 0.0 167s Westinghouse_X1940 0 0 0.0 167s Westinghouse_X1941 0 0 0.0 167s Westinghouse_X1942 0 0 0.0 167s Westinghouse_X1943 0 0 0.0 167s Westinghouse_X1944 0 0 0.0 167s Westinghouse_X1945 0 0 0.0 167s Westinghouse_X1946 0 0 0.0 167s Westinghouse_X1947 0 0 0.0 167s Westinghouse_X1948 0 0 0.0 167s Westinghouse_X1949 0 0 0.0 167s Westinghouse_X1950 0 0 0.0 167s Westinghouse_X1951 0 0 0.0 167s Westinghouse_X1952 0 0 0.0 167s Westinghouse_X1953 0 0 0.0 167s Westinghouse_X1954 0 0 0.0 167s General.Electric_(Intercept) General.Electric_value 167s Chrysler_X1935 0 0 167s Chrysler_X1936 0 0 167s Chrysler_X1937 0 0 167s Chrysler_X1938 0 0 167s Chrysler_X1939 0 0 167s Chrysler_X1940 0 0 167s Chrysler_X1941 0 0 167s Chrysler_X1942 0 0 167s Chrysler_X1943 0 0 167s Chrysler_X1944 0 0 167s Chrysler_X1945 0 0 167s Chrysler_X1946 0 0 167s Chrysler_X1947 0 0 167s Chrysler_X1948 0 0 167s Chrysler_X1949 0 0 167s Chrysler_X1950 0 0 167s Chrysler_X1951 0 0 167s Chrysler_X1952 0 0 167s Chrysler_X1953 0 0 167s Chrysler_X1954 0 0 167s General.Electric_X1935 1 1171 167s General.Electric_X1936 1 2016 167s General.Electric_X1937 1 2803 167s General.Electric_X1938 1 2040 167s General.Electric_X1939 1 2256 167s General.Electric_X1940 1 2132 167s General.Electric_X1941 1 1834 167s General.Electric_X1942 1 1588 167s General.Electric_X1943 1 1749 167s General.Electric_X1944 1 1687 167s General.Electric_X1945 1 2008 167s General.Electric_X1946 1 2208 167s General.Electric_X1947 1 1657 167s General.Electric_X1948 1 1604 167s General.Electric_X1949 1 1432 167s General.Electric_X1950 1 1610 167s General.Electric_X1951 1 1819 167s General.Electric_X1952 1 2080 167s General.Electric_X1953 1 2372 167s General.Electric_X1954 1 2760 167s General.Motors_X1935 0 0 167s General.Motors_X1936 0 0 167s General.Motors_X1937 0 0 167s General.Motors_X1938 0 0 167s General.Motors_X1939 0 0 167s General.Motors_X1940 0 0 167s General.Motors_X1941 0 0 167s General.Motors_X1942 0 0 167s General.Motors_X1943 0 0 167s General.Motors_X1944 0 0 167s General.Motors_X1945 0 0 167s General.Motors_X1946 0 0 167s General.Motors_X1947 0 0 167s General.Motors_X1948 0 0 167s General.Motors_X1949 0 0 167s General.Motors_X1950 0 0 167s General.Motors_X1951 0 0 167s General.Motors_X1952 0 0 167s General.Motors_X1953 0 0 167s General.Motors_X1954 0 0 167s US.Steel_X1935 0 0 167s US.Steel_X1936 0 0 167s US.Steel_X1937 0 0 167s US.Steel_X1938 0 0 167s US.Steel_X1939 0 0 167s US.Steel_X1940 0 0 167s US.Steel_X1941 0 0 167s US.Steel_X1942 0 0 167s US.Steel_X1943 0 0 167s US.Steel_X1944 0 0 167s US.Steel_X1945 0 0 167s US.Steel_X1946 0 0 167s US.Steel_X1947 0 0 167s US.Steel_X1948 0 0 167s US.Steel_X1949 0 0 167s US.Steel_X1950 0 0 167s US.Steel_X1951 0 0 167s US.Steel_X1952 0 0 167s US.Steel_X1953 0 0 167s US.Steel_X1954 0 0 167s Westinghouse_X1935 0 0 167s Westinghouse_X1936 0 0 167s Westinghouse_X1937 0 0 167s Westinghouse_X1938 0 0 167s Westinghouse_X1939 0 0 167s Westinghouse_X1940 0 0 167s Westinghouse_X1941 0 0 167s Westinghouse_X1942 0 0 167s Westinghouse_X1943 0 0 167s Westinghouse_X1944 0 0 167s Westinghouse_X1945 0 0 167s Westinghouse_X1946 0 0 167s Westinghouse_X1947 0 0 167s Westinghouse_X1948 0 0 167s Westinghouse_X1949 0 0 167s Westinghouse_X1950 0 0 167s Westinghouse_X1951 0 0 167s Westinghouse_X1952 0 0 167s Westinghouse_X1953 0 0 167s Westinghouse_X1954 0 0 167s General.Electric_capital General.Motors_(Intercept) 167s Chrysler_X1935 0.0 0 167s Chrysler_X1936 0.0 0 167s Chrysler_X1937 0.0 0 167s Chrysler_X1938 0.0 0 167s Chrysler_X1939 0.0 0 167s Chrysler_X1940 0.0 0 167s Chrysler_X1941 0.0 0 167s Chrysler_X1942 0.0 0 167s Chrysler_X1943 0.0 0 167s Chrysler_X1944 0.0 0 167s Chrysler_X1945 0.0 0 167s Chrysler_X1946 0.0 0 167s Chrysler_X1947 0.0 0 167s Chrysler_X1948 0.0 0 167s Chrysler_X1949 0.0 0 167s Chrysler_X1950 0.0 0 167s Chrysler_X1951 0.0 0 167s Chrysler_X1952 0.0 0 167s Chrysler_X1953 0.0 0 167s Chrysler_X1954 0.0 0 167s General.Electric_X1935 97.8 0 167s General.Electric_X1936 104.4 0 167s General.Electric_X1937 118.0 0 167s General.Electric_X1938 156.2 0 167s General.Electric_X1939 172.6 0 167s General.Electric_X1940 186.6 0 167s General.Electric_X1941 220.9 0 167s General.Electric_X1942 287.8 0 167s General.Electric_X1943 319.9 0 167s General.Electric_X1944 321.3 0 167s General.Electric_X1945 319.6 0 167s General.Electric_X1946 346.0 0 167s General.Electric_X1947 456.4 0 167s General.Electric_X1948 543.4 0 167s General.Electric_X1949 618.3 0 167s General.Electric_X1950 647.4 0 167s General.Electric_X1951 671.3 0 167s General.Electric_X1952 726.1 0 167s General.Electric_X1953 800.3 0 167s General.Electric_X1954 888.9 0 167s General.Motors_X1935 0.0 1 167s General.Motors_X1936 0.0 1 167s General.Motors_X1937 0.0 1 167s General.Motors_X1938 0.0 1 167s General.Motors_X1939 0.0 1 167s General.Motors_X1940 0.0 1 167s General.Motors_X1941 0.0 1 167s General.Motors_X1942 0.0 1 167s General.Motors_X1943 0.0 1 167s General.Motors_X1944 0.0 1 167s General.Motors_X1945 0.0 1 167s General.Motors_X1946 0.0 1 167s General.Motors_X1947 0.0 1 167s General.Motors_X1948 0.0 1 167s General.Motors_X1949 0.0 1 167s General.Motors_X1950 0.0 1 167s General.Motors_X1951 0.0 1 167s General.Motors_X1952 0.0 1 167s General.Motors_X1953 0.0 1 167s General.Motors_X1954 0.0 1 167s US.Steel_X1935 0.0 0 167s US.Steel_X1936 0.0 0 167s US.Steel_X1937 0.0 0 167s US.Steel_X1938 0.0 0 167s US.Steel_X1939 0.0 0 167s US.Steel_X1940 0.0 0 167s US.Steel_X1941 0.0 0 167s US.Steel_X1942 0.0 0 167s US.Steel_X1943 0.0 0 167s US.Steel_X1944 0.0 0 167s US.Steel_X1945 0.0 0 167s US.Steel_X1946 0.0 0 167s US.Steel_X1947 0.0 0 167s US.Steel_X1948 0.0 0 167s US.Steel_X1949 0.0 0 167s US.Steel_X1950 0.0 0 167s US.Steel_X1951 0.0 0 167s US.Steel_X1952 0.0 0 167s US.Steel_X1953 0.0 0 167s US.Steel_X1954 0.0 0 167s Westinghouse_X1935 0.0 0 167s Westinghouse_X1936 0.0 0 167s Westinghouse_X1937 0.0 0 167s Westinghouse_X1938 0.0 0 167s Westinghouse_X1939 0.0 0 167s Westinghouse_X1940 0.0 0 167s Westinghouse_X1941 0.0 0 167s Westinghouse_X1942 0.0 0 167s Westinghouse_X1943 0.0 0 167s Westinghouse_X1944 0.0 0 167s Westinghouse_X1945 0.0 0 167s Westinghouse_X1946 0.0 0 167s Westinghouse_X1947 0.0 0 167s Westinghouse_X1948 0.0 0 167s Westinghouse_X1949 0.0 0 167s Westinghouse_X1950 0.0 0 167s Westinghouse_X1951 0.0 0 167s Westinghouse_X1952 0.0 0 167s Westinghouse_X1953 0.0 0 167s Westinghouse_X1954 0.0 0 167s General.Motors_value General.Motors_capital 167s Chrysler_X1935 0 0.0 167s Chrysler_X1936 0 0.0 167s Chrysler_X1937 0 0.0 167s Chrysler_X1938 0 0.0 167s Chrysler_X1939 0 0.0 167s Chrysler_X1940 0 0.0 167s Chrysler_X1941 0 0.0 167s Chrysler_X1942 0 0.0 167s Chrysler_X1943 0 0.0 167s Chrysler_X1944 0 0.0 167s Chrysler_X1945 0 0.0 167s Chrysler_X1946 0 0.0 167s Chrysler_X1947 0 0.0 167s Chrysler_X1948 0 0.0 167s Chrysler_X1949 0 0.0 167s Chrysler_X1950 0 0.0 167s Chrysler_X1951 0 0.0 167s Chrysler_X1952 0 0.0 167s Chrysler_X1953 0 0.0 167s Chrysler_X1954 0 0.0 167s General.Electric_X1935 0 0.0 167s General.Electric_X1936 0 0.0 167s General.Electric_X1937 0 0.0 167s General.Electric_X1938 0 0.0 167s General.Electric_X1939 0 0.0 167s General.Electric_X1940 0 0.0 167s General.Electric_X1941 0 0.0 167s General.Electric_X1942 0 0.0 167s General.Electric_X1943 0 0.0 167s General.Electric_X1944 0 0.0 167s General.Electric_X1945 0 0.0 167s General.Electric_X1946 0 0.0 167s General.Electric_X1947 0 0.0 167s General.Electric_X1948 0 0.0 167s General.Electric_X1949 0 0.0 167s General.Electric_X1950 0 0.0 167s General.Electric_X1951 0 0.0 167s General.Electric_X1952 0 0.0 167s General.Electric_X1953 0 0.0 167s General.Electric_X1954 0 0.0 167s General.Motors_X1935 3078 2.8 167s General.Motors_X1936 4662 52.6 167s General.Motors_X1937 5387 156.9 167s General.Motors_X1938 2792 209.2 167s General.Motors_X1939 4313 203.4 167s General.Motors_X1940 4644 207.2 167s General.Motors_X1941 4551 255.2 167s General.Motors_X1942 3244 303.7 167s General.Motors_X1943 4054 264.1 167s General.Motors_X1944 4379 201.6 167s General.Motors_X1945 4841 265.0 167s General.Motors_X1946 4901 402.2 167s General.Motors_X1947 3526 761.5 167s General.Motors_X1948 3255 922.4 167s General.Motors_X1949 3700 1020.1 167s General.Motors_X1950 3756 1099.0 167s General.Motors_X1951 4833 1207.7 167s General.Motors_X1952 4925 1430.5 167s General.Motors_X1953 6242 1777.3 167s General.Motors_X1954 5594 2226.3 167s US.Steel_X1935 0 0.0 167s US.Steel_X1936 0 0.0 167s US.Steel_X1937 0 0.0 167s US.Steel_X1938 0 0.0 167s US.Steel_X1939 0 0.0 167s US.Steel_X1940 0 0.0 167s US.Steel_X1941 0 0.0 167s US.Steel_X1942 0 0.0 167s US.Steel_X1943 0 0.0 167s US.Steel_X1944 0 0.0 167s US.Steel_X1945 0 0.0 167s US.Steel_X1946 0 0.0 167s US.Steel_X1947 0 0.0 167s US.Steel_X1948 0 0.0 167s US.Steel_X1949 0 0.0 167s US.Steel_X1950 0 0.0 167s US.Steel_X1951 0 0.0 167s US.Steel_X1952 0 0.0 167s US.Steel_X1953 0 0.0 167s US.Steel_X1954 0 0.0 167s Westinghouse_X1935 0 0.0 167s Westinghouse_X1936 0 0.0 167s Westinghouse_X1937 0 0.0 167s Westinghouse_X1938 0 0.0 167s Westinghouse_X1939 0 0.0 167s Westinghouse_X1940 0 0.0 167s Westinghouse_X1941 0 0.0 167s Westinghouse_X1942 0 0.0 167s Westinghouse_X1943 0 0.0 167s Westinghouse_X1944 0 0.0 167s Westinghouse_X1945 0 0.0 167s Westinghouse_X1946 0 0.0 167s Westinghouse_X1947 0 0.0 167s Westinghouse_X1948 0 0.0 167s Westinghouse_X1949 0 0.0 167s Westinghouse_X1950 0 0.0 167s Westinghouse_X1951 0 0.0 167s Westinghouse_X1952 0 0.0 167s Westinghouse_X1953 0 0.0 167s Westinghouse_X1954 0 0.0 167s US.Steel_(Intercept) US.Steel_value US.Steel_capital 167s Chrysler_X1935 0 0 0.0 167s Chrysler_X1936 0 0 0.0 167s Chrysler_X1937 0 0 0.0 167s Chrysler_X1938 0 0 0.0 167s Chrysler_X1939 0 0 0.0 167s Chrysler_X1940 0 0 0.0 167s Chrysler_X1941 0 0 0.0 167s Chrysler_X1942 0 0 0.0 167s Chrysler_X1943 0 0 0.0 167s Chrysler_X1944 0 0 0.0 167s Chrysler_X1945 0 0 0.0 167s Chrysler_X1946 0 0 0.0 167s Chrysler_X1947 0 0 0.0 167s Chrysler_X1948 0 0 0.0 167s Chrysler_X1949 0 0 0.0 167s Chrysler_X1950 0 0 0.0 167s Chrysler_X1951 0 0 0.0 167s Chrysler_X1952 0 0 0.0 167s Chrysler_X1953 0 0 0.0 167s Chrysler_X1954 0 0 0.0 167s General.Electric_X1935 0 0 0.0 167s General.Electric_X1936 0 0 0.0 167s General.Electric_X1937 0 0 0.0 167s General.Electric_X1938 0 0 0.0 167s General.Electric_X1939 0 0 0.0 167s General.Electric_X1940 0 0 0.0 167s General.Electric_X1941 0 0 0.0 167s General.Electric_X1942 0 0 0.0 167s General.Electric_X1943 0 0 0.0 167s General.Electric_X1944 0 0 0.0 167s General.Electric_X1945 0 0 0.0 167s General.Electric_X1946 0 0 0.0 167s General.Electric_X1947 0 0 0.0 167s General.Electric_X1948 0 0 0.0 167s General.Electric_X1949 0 0 0.0 167s General.Electric_X1950 0 0 0.0 167s General.Electric_X1951 0 0 0.0 167s General.Electric_X1952 0 0 0.0 167s General.Electric_X1953 0 0 0.0 167s General.Electric_X1954 0 0 0.0 167s General.Motors_X1935 0 0 0.0 167s General.Motors_X1936 0 0 0.0 167s General.Motors_X1937 0 0 0.0 167s General.Motors_X1938 0 0 0.0 167s General.Motors_X1939 0 0 0.0 167s General.Motors_X1940 0 0 0.0 167s General.Motors_X1941 0 0 0.0 167s General.Motors_X1942 0 0 0.0 167s General.Motors_X1943 0 0 0.0 167s General.Motors_X1944 0 0 0.0 167s General.Motors_X1945 0 0 0.0 167s General.Motors_X1946 0 0 0.0 167s General.Motors_X1947 0 0 0.0 167s General.Motors_X1948 0 0 0.0 167s General.Motors_X1949 0 0 0.0 167s General.Motors_X1950 0 0 0.0 167s General.Motors_X1951 0 0 0.0 167s General.Motors_X1952 0 0 0.0 167s General.Motors_X1953 0 0 0.0 167s General.Motors_X1954 0 0 0.0 167s US.Steel_X1935 1 1362 53.8 167s US.Steel_X1936 1 1807 50.5 167s US.Steel_X1937 1 2676 118.1 167s US.Steel_X1938 1 1802 260.2 167s US.Steel_X1939 1 1957 312.7 167s US.Steel_X1940 1 2203 254.2 167s US.Steel_X1941 1 2380 261.4 167s US.Steel_X1942 1 2169 298.7 167s US.Steel_X1943 1 1985 301.8 167s US.Steel_X1944 1 1814 279.1 167s US.Steel_X1945 1 1850 213.8 167s US.Steel_X1946 1 2068 232.6 167s US.Steel_X1947 1 1797 264.8 167s US.Steel_X1948 1 1626 306.9 167s US.Steel_X1949 1 1667 351.1 167s US.Steel_X1950 1 1677 357.8 167s US.Steel_X1951 1 2290 342.1 167s US.Steel_X1952 1 2159 444.2 167s US.Steel_X1953 1 2031 623.6 167s US.Steel_X1954 1 2116 669.7 167s Westinghouse_X1935 0 0 0.0 167s Westinghouse_X1936 0 0 0.0 167s Westinghouse_X1937 0 0 0.0 167s Westinghouse_X1938 0 0 0.0 167s Westinghouse_X1939 0 0 0.0 167s Westinghouse_X1940 0 0 0.0 167s Westinghouse_X1941 0 0 0.0 167s Westinghouse_X1942 0 0 0.0 167s Westinghouse_X1943 0 0 0.0 167s Westinghouse_X1944 0 0 0.0 167s Westinghouse_X1945 0 0 0.0 167s Westinghouse_X1946 0 0 0.0 167s Westinghouse_X1947 0 0 0.0 167s Westinghouse_X1948 0 0 0.0 167s Westinghouse_X1949 0 0 0.0 167s Westinghouse_X1950 0 0 0.0 167s Westinghouse_X1951 0 0 0.0 167s Westinghouse_X1952 0 0 0.0 167s Westinghouse_X1953 0 0 0.0 167s Westinghouse_X1954 0 0 0.0 167s Westinghouse_(Intercept) Westinghouse_value 167s Chrysler_X1935 0 0 167s Chrysler_X1936 0 0 167s Chrysler_X1937 0 0 167s Chrysler_X1938 0 0 167s Chrysler_X1939 0 0 167s Chrysler_X1940 0 0 167s Chrysler_X1941 0 0 167s Chrysler_X1942 0 0 167s Chrysler_X1943 0 0 167s Chrysler_X1944 0 0 167s Chrysler_X1945 0 0 167s Chrysler_X1946 0 0 167s Chrysler_X1947 0 0 167s Chrysler_X1948 0 0 167s Chrysler_X1949 0 0 167s Chrysler_X1950 0 0 167s Chrysler_X1951 0 0 167s Chrysler_X1952 0 0 167s Chrysler_X1953 0 0 167s Chrysler_X1954 0 0 167s General.Electric_X1935 0 0 167s General.Electric_X1936 0 0 167s General.Electric_X1937 0 0 167s General.Electric_X1938 0 0 167s General.Electric_X1939 0 0 167s General.Electric_X1940 0 0 167s General.Electric_X1941 0 0 167s General.Electric_X1942 0 0 167s General.Electric_X1943 0 0 167s General.Electric_X1944 0 0 167s General.Electric_X1945 0 0 167s General.Electric_X1946 0 0 167s General.Electric_X1947 0 0 167s General.Electric_X1948 0 0 167s General.Electric_X1949 0 0 167s General.Electric_X1950 0 0 167s General.Electric_X1951 0 0 167s General.Electric_X1952 0 0 167s General.Electric_X1953 0 0 167s General.Electric_X1954 0 0 167s General.Motors_X1935 0 0 167s General.Motors_X1936 0 0 167s General.Motors_X1937 0 0 167s General.Motors_X1938 0 0 167s General.Motors_X1939 0 0 167s General.Motors_X1940 0 0 167s General.Motors_X1941 0 0 167s General.Motors_X1942 0 0 167s General.Motors_X1943 0 0 167s General.Motors_X1944 0 0 167s General.Motors_X1945 0 0 167s General.Motors_X1946 0 0 167s General.Motors_X1947 0 0 167s General.Motors_X1948 0 0 167s General.Motors_X1949 0 0 167s General.Motors_X1950 0 0 167s General.Motors_X1951 0 0 167s General.Motors_X1952 0 0 167s General.Motors_X1953 0 0 167s General.Motors_X1954 0 0 167s US.Steel_X1935 0 0 167s US.Steel_X1936 0 0 167s US.Steel_X1937 0 0 167s US.Steel_X1938 0 0 167s US.Steel_X1939 0 0 167s US.Steel_X1940 0 0 167s US.Steel_X1941 0 0 167s US.Steel_X1942 0 0 167s US.Steel_X1943 0 0 167s US.Steel_X1944 0 0 167s US.Steel_X1945 0 0 167s US.Steel_X1946 0 0 167s US.Steel_X1947 0 0 167s US.Steel_X1948 0 0 167s US.Steel_X1949 0 0 167s US.Steel_X1950 0 0 167s US.Steel_X1951 0 0 167s US.Steel_X1952 0 0 167s US.Steel_X1953 0 0 167s US.Steel_X1954 0 0 167s Westinghouse_X1935 1 192 167s Westinghouse_X1936 1 516 167s Westinghouse_X1937 1 729 167s Westinghouse_X1938 1 560 167s Westinghouse_X1939 1 520 167s Westinghouse_X1940 1 628 167s Westinghouse_X1941 1 537 167s Westinghouse_X1942 1 561 167s Westinghouse_X1943 1 617 167s Westinghouse_X1944 1 627 167s Westinghouse_X1945 1 737 167s Westinghouse_X1946 1 760 167s Westinghouse_X1947 1 581 167s Westinghouse_X1948 1 662 167s Westinghouse_X1949 1 584 167s Westinghouse_X1950 1 635 167s Westinghouse_X1951 1 724 167s Westinghouse_X1952 1 864 167s Westinghouse_X1953 1 1194 167s Westinghouse_X1954 1 1189 167s Westinghouse_capital 167s Chrysler_X1935 0.0 167s Chrysler_X1936 0.0 167s Chrysler_X1937 0.0 167s Chrysler_X1938 0.0 167s Chrysler_X1939 0.0 167s Chrysler_X1940 0.0 167s Chrysler_X1941 0.0 167s Chrysler_X1942 0.0 167s Chrysler_X1943 0.0 167s Chrysler_X1944 0.0 167s Chrysler_X1945 0.0 167s Chrysler_X1946 0.0 167s Chrysler_X1947 0.0 167s Chrysler_X1948 0.0 167s Chrysler_X1949 0.0 167s Chrysler_X1950 0.0 167s Chrysler_X1951 0.0 167s Chrysler_X1952 0.0 167s Chrysler_X1953 0.0 167s Chrysler_X1954 0.0 167s General.Electric_X1935 0.0 167s General.Electric_X1936 0.0 167s General.Electric_X1937 0.0 167s General.Electric_X1938 0.0 167s General.Electric_X1939 0.0 167s General.Electric_X1940 0.0 167s General.Electric_X1941 0.0 167s General.Electric_X1942 0.0 167s General.Electric_X1943 0.0 167s General.Electric_X1944 0.0 167s General.Electric_X1945 0.0 167s General.Electric_X1946 0.0 167s General.Electric_X1947 0.0 167s General.Electric_X1948 0.0 167s General.Electric_X1949 0.0 167s General.Electric_X1950 0.0 167s General.Electric_X1951 0.0 167s General.Electric_X1952 0.0 167s General.Electric_X1953 0.0 167s General.Electric_X1954 0.0 167s General.Motors_X1935 0.0 167s General.Motors_X1936 0.0 167s General.Motors_X1937 0.0 167s General.Motors_X1938 0.0 167s General.Motors_X1939 0.0 167s General.Motors_X1940 0.0 167s General.Motors_X1941 0.0 167s General.Motors_X1942 0.0 167s General.Motors_X1943 0.0 167s General.Motors_X1944 0.0 167s General.Motors_X1945 0.0 167s General.Motors_X1946 0.0 167s General.Motors_X1947 0.0 167s General.Motors_X1948 0.0 167s General.Motors_X1949 0.0 167s General.Motors_X1950 0.0 167s General.Motors_X1951 0.0 167s General.Motors_X1952 0.0 167s General.Motors_X1953 0.0 167s General.Motors_X1954 0.0 167s US.Steel_X1935 0.0 167s US.Steel_X1936 0.0 167s US.Steel_X1937 0.0 167s US.Steel_X1938 0.0 167s US.Steel_X1939 0.0 167s US.Steel_X1940 0.0 167s US.Steel_X1941 0.0 167s US.Steel_X1942 0.0 167s US.Steel_X1943 0.0 167s US.Steel_X1944 0.0 167s US.Steel_X1945 0.0 167s US.Steel_X1946 0.0 167s US.Steel_X1947 0.0 167s US.Steel_X1948 0.0 167s US.Steel_X1949 0.0 167s US.Steel_X1950 0.0 167s US.Steel_X1951 0.0 167s US.Steel_X1952 0.0 167s US.Steel_X1953 0.0 167s US.Steel_X1954 0.0 167s Westinghouse_X1935 1.8 167s Westinghouse_X1936 0.8 167s Westinghouse_X1937 7.4 167s Westinghouse_X1938 18.1 167s Westinghouse_X1939 23.5 167s Westinghouse_X1940 26.5 167s Westinghouse_X1941 36.2 167s Westinghouse_X1942 60.8 167s Westinghouse_X1943 84.4 167s Westinghouse_X1944 91.2 167s Westinghouse_X1945 92.4 167s Westinghouse_X1946 86.0 167s Westinghouse_X1947 111.1 167s Westinghouse_X1948 130.6 167s Westinghouse_X1949 141.8 167s Westinghouse_X1950 136.7 167s Westinghouse_X1951 129.7 167s Westinghouse_X1952 145.5 167s Westinghouse_X1953 174.8 167s Westinghouse_X1954 213.5 167s $Chrysler 167s Chrysler_invest ~ Chrysler_value + Chrysler_capital 167s 167s 167s $General.Electric 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s 167s $General.Motors 167s General.Motors_invest ~ General.Motors_value + General.Motors_capital 167s 167s 167s $US.Steel 167s US.Steel_invest ~ US.Steel_value + US.Steel_capital 167s 167s 167s $Westinghouse 167s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s $Chrysler 167s Chrysler_invest ~ Chrysler_value + Chrysler_capital 167s attr(,"variables") 167s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 167s attr(,"factors") 167s Chrysler_value Chrysler_capital 167s Chrysler_invest 0 0 167s Chrysler_value 1 0 167s Chrysler_capital 0 1 167s attr(,"term.labels") 167s [1] "Chrysler_value" "Chrysler_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 167s attr(,"dataClasses") 167s Chrysler_invest Chrysler_value Chrysler_capital 167s "numeric" "numeric" "numeric" 167s 167s $General.Electric 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s attr(,"variables") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"factors") 167s General.Electric_value General.Electric_capital 167s General.Electric_invest 0 0 167s General.Electric_value 1 0 167s General.Electric_capital 0 1 167s attr(,"term.labels") 167s [1] "General.Electric_value" "General.Electric_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"dataClasses") 167s General.Electric_invest General.Electric_value General.Electric_capital 167s "numeric" "numeric" "numeric" 167s 167s $General.Motors 167s General.Motors_invest ~ General.Motors_value + General.Motors_capital 167s attr(,"variables") 167s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 167s attr(,"factors") 167s General.Motors_value General.Motors_capital 167s General.Motors_invest 0 0 167s General.Motors_value 1 0 167s General.Motors_capital 0 1 167s attr(,"term.labels") 167s [1] "General.Motors_value" "General.Motors_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 167s attr(,"dataClasses") 167s General.Motors_invest General.Motors_value General.Motors_capital 167s "numeric" "numeric" "numeric" 167s 167s $US.Steel 167s US.Steel_invest ~ US.Steel_value + US.Steel_capital 167s attr(,"variables") 167s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 167s attr(,"factors") 167s US.Steel_value US.Steel_capital 167s US.Steel_invest 0 0 167s US.Steel_value 1 0 167s US.Steel_capital 0 1 167s attr(,"term.labels") 167s [1] "US.Steel_value" "US.Steel_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 167s attr(,"dataClasses") 167s US.Steel_invest US.Steel_value US.Steel_capital 167s "numeric" "numeric" "numeric" 167s 167s $Westinghouse 167s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s attr(,"variables") 167s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 167s attr(,"factors") 167s Westinghouse_value Westinghouse_capital 167s Westinghouse_invest 0 0 167s Westinghouse_value 1 0 167s Westinghouse_capital 0 1 167s attr(,"term.labels") 167s [1] "Westinghouse_value" "Westinghouse_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 167s attr(,"dataClasses") 167s Westinghouse_invest Westinghouse_value Westinghouse_capital 167s "numeric" "numeric" "numeric" 167s 167s General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s attr(,"variables") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"factors") 167s General.Electric_value General.Electric_capital 167s General.Electric_invest 0 0 167s General.Electric_value 1 0 167s General.Electric_capital 0 1 167s attr(,"term.labels") 167s [1] "General.Electric_value" "General.Electric_capital" 167s attr(,"order") 167s [1] 1 1 167s attr(,"intercept") 167s [1] 1 167s attr(,"response") 167s [1] 1 167s attr(,".Environment") 167s 167s attr(,"predvars") 167s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 167s attr(,"dataClasses") 167s General.Electric_invest General.Electric_value General.Electric_capital 167s "numeric" "numeric" "numeric" 167s > 167s > # OLS Pooled 167s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 167s + greeneOlsPooled <- systemfit( formulaGrunfeld, "OLS", 167s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix ) 167s + print( greeneOlsPooled ) 167s + print( summary( greeneOlsPooled ) ) 167s + print( summary( greeneOlsPooled, useDfSys = FALSE, residCov = FALSE ) ) 167s + print( summary( greeneOlsPooled, residCov = FALSE, equations = FALSE ) ) 167s + print( sum( sapply( greeneOlsPooled$eq, function(x){return(summary(x)$ssr)}) )/97 ) # sigma^2 167s + print( coef( greeneOlsPooled ) ) 167s + print( coef( greeneOlsPooled, modified.regMat = TRUE ) ) 167s + print( coef( summary( greeneOlsPooled ) ) ) 167s + print( coef( summary( greeneOlsPooled ), modified.regMat = TRUE ) ) 167s + print( vcov( greeneOlsPooled ) ) 167s + print( vcov( greeneOlsPooled, modified.regMat = TRUE ) ) 167s + print( residuals( greeneOlsPooled ) ) 167s + print( confint( greeneOlsPooled ) ) 167s + print( fitted( greeneOlsPooled ) ) 167s + print( logLik( greeneOlsPooled ) ) 167s + print( logLik( greeneOlsPooled, residCovDiag = TRUE ) ) 167s + print( nobs( greeneOlsPooled ) ) 167s + print( model.frame( greeneOlsPooled ) ) 167s + print( model.matrix( greeneOlsPooled ) ) 167s + print( formula( greeneOlsPooled ) ) 167s + print( formula( greeneOlsPooled$eq[[ 1 ]] ) ) 167s + print( terms( greeneOlsPooled ) ) 167s + print( terms( greeneOlsPooled$eq[[ 1 ]] ) ) 167s + } 167s 167s systemfit results 167s method: OLS 167s 167s Coefficients: 167s Chrysler_(Intercept) Chrysler_value 167s -48.030 0.105 167s Chrysler_capital General.Electric_(Intercept) 167s 0.305 -48.030 167s General.Electric_value General.Electric_capital 167s 0.105 0.305 167s General.Motors_(Intercept) General.Motors_value 167s -48.030 0.105 167s General.Motors_capital US.Steel_(Intercept) 167s 0.305 -48.030 167s US.Steel_value US.Steel_capital 167s 0.105 0.305 167s Westinghouse_(Intercept) Westinghouse_value 167s -48.030 0.105 167s Westinghouse_capital 167s 0.305 167s 167s systemfit results 167s method: OLS 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 100 97 1570884 4.2e+17 0.294 0.812 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s Chrysler 20 17 15117 889 29.8 0.564 0.513 167s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 167s General.Motors 20 17 188218 11072 105.2 0.897 0.884 167s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 167s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 167s 167s The covariance matrix of the residuals 167s Chrysler General.Electric General.Motors US.Steel Westinghouse 167s Chrysler 889.2 -4898 -198 4748 -94.6 167s General.Electric -4898.1 40339 -2254 -32821 2658.0 167s General.Motors -197.7 -2254 11072 304 -1328.6 167s US.Steel 4748.1 -32821 304 39359 -1377.3 167s Westinghouse -94.6 2658 -1329 -1377 745.2 167s 167s The correlations of the residuals 167s Chrysler General.Electric General.Motors US.Steel Westinghouse 167s Chrysler 1.000 0.144 -0.1852 0.2218 0.186 167s General.Electric 0.144 1.000 -0.2592 -0.1216 0.881 167s General.Motors -0.185 -0.259 1.0000 -0.0155 -0.469 167s US.Steel 0.222 -0.122 -0.0155 1.0000 -0.119 167s Westinghouse 0.186 0.881 -0.4689 -0.1186 1.000 167s 167s 167s OLS estimates for 'Chrysler' (equation 1) 167s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.028 * 167s value 0.1051 0.0114 9.24 6.0e-15 *** 167s capital 0.3054 0.0435 7.02 3.1e-10 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 29.82 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 15117.016 MSE: 889.236 Root MSE: 29.82 167s Multiple R-Squared: 0.564 Adjusted R-Squared: 0.513 167s 167s 167s OLS estimates for 'General.Electric' (equation 2) 167s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.028 * 167s value 0.1051 0.0114 9.24 6.0e-15 *** 167s capital 0.3054 0.0435 7.02 3.1e-10 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 200.847 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 685769.815 MSE: 40339.401 Root MSE: 200.847 167s Multiple R-Squared: -14.291 Adjusted R-Squared: -16.09 167s 167s 167s OLS estimates for 'General.Motors' (equation 3) 167s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.028 * 167s value 0.1051 0.0114 9.24 6.0e-15 *** 167s capital 0.3054 0.0435 7.02 3.1e-10 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 105.222 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 188218.158 MSE: 11071.656 Root MSE: 105.222 167s Multiple R-Squared: 0.897 Adjusted R-Squared: 0.884 167s 167s 167s OLS estimates for 'US.Steel' (equation 4) 167s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.028 * 167s value 0.1051 0.0114 9.24 6.0e-15 *** 167s capital 0.3054 0.0435 7.02 3.1e-10 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 198.392 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 669110.225 MSE: 39359.425 Root MSE: 198.392 167s Multiple R-Squared: -1.105 Adjusted R-Squared: -1.352 167s 167s 167s OLS estimates for 'Westinghouse' (equation 5) 167s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.028 * 167s value 0.1051 0.0114 9.24 6.0e-15 *** 167s capital 0.3054 0.0435 7.02 3.1e-10 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 27.298 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 12668.473 MSE: 745.204 Root MSE: 27.298 167s Multiple R-Squared: -0.826 Adjusted R-Squared: -1.041 167s 167s 167s systemfit results 167s method: OLS 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 100 97 1570884 4.2e+17 0.294 0.812 167s 167s N DF SSR MSE RMSE R2 Adj R2 167s Chrysler 20 17 15117 889 29.8 0.564 0.513 167s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 167s General.Motors 20 17 188218 11072 105.2 0.897 0.884 167s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 167s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 167s 167s 167s OLS estimates for 'Chrysler' (equation 1) 167s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.039 * 167s value 0.1051 0.0114 9.24 4.9e-08 *** 167s capital 0.3054 0.0435 7.02 2.1e-06 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 29.82 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 15117.016 MSE: 889.236 Root MSE: 29.82 167s Multiple R-Squared: 0.564 Adjusted R-Squared: 0.513 167s 167s 167s OLS estimates for 'General.Electric' (equation 2) 167s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.039 * 167s value 0.1051 0.0114 9.24 4.9e-08 *** 167s capital 0.3054 0.0435 7.02 2.1e-06 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 200.847 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 685769.815 MSE: 40339.401 Root MSE: 200.847 167s Multiple R-Squared: -14.291 Adjusted R-Squared: -16.09 167s 167s 167s OLS estimates for 'General.Motors' (equation 3) 167s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.039 * 167s value 0.1051 0.0114 9.24 4.9e-08 *** 167s capital 0.3054 0.0435 7.02 2.1e-06 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 105.222 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 188218.158 MSE: 11071.656 Root MSE: 105.222 167s Multiple R-Squared: 0.897 Adjusted R-Squared: 0.884 167s 167s 167s OLS estimates for 'US.Steel' (equation 4) 167s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.039 * 167s value 0.1051 0.0114 9.24 4.9e-08 *** 167s capital 0.3054 0.0435 7.02 2.1e-06 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 198.392 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 669110.225 MSE: 39359.425 Root MSE: 198.392 167s Multiple R-Squared: -1.105 Adjusted R-Squared: -1.352 167s 167s 167s OLS estimates for 'Westinghouse' (equation 5) 167s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 167s 167s 167s Estimate Std. Error t value Pr(>|t|) 167s (Intercept) -48.0297 21.4802 -2.24 0.039 * 167s value 0.1051 0.0114 9.24 4.9e-08 *** 167s capital 0.3054 0.0435 7.02 2.1e-06 *** 167s --- 167s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 167s 167s Residual standard error: 27.298 on 17 degrees of freedom 167s Number of observations: 20 Degrees of Freedom: 17 167s SSR: 12668.473 MSE: 745.204 Root MSE: 27.298 167s Multiple R-Squared: -0.826 Adjusted R-Squared: -1.041 167s 167s 167s systemfit results 167s method: OLS 167s 167s N DF SSR detRCov OLS-R2 McElroy-R2 167s system 100 97 1570884 4.2e+17 0.294 0.812 167s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 15117 889 29.8 0.564 0.513 168s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 168s General.Motors 20 17 188218 11072 105.2 0.897 0.884 168s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 168s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 168s 168s 168s Coefficients: 168s Estimate Std. Error t value Pr(>|t|) 168s Chrysler_(Intercept) -48.0297 21.4802 -2.24 0.028 * 168s Chrysler_value 0.1051 0.0114 9.24 6.0e-15 *** 168s Chrysler_capital 0.3054 0.0435 7.02 3.1e-10 *** 168s General.Electric_(Intercept) -48.0297 21.4802 -2.24 0.028 * 168s General.Electric_value 0.1051 0.0114 9.24 6.0e-15 *** 168s General.Electric_capital 0.3054 0.0435 7.02 3.1e-10 *** 168s General.Motors_(Intercept) -48.0297 21.4802 -2.24 0.028 * 168s General.Motors_value 0.1051 0.0114 9.24 6.0e-15 *** 168s General.Motors_capital 0.3054 0.0435 7.02 3.1e-10 *** 168s US.Steel_(Intercept) -48.0297 21.4802 -2.24 0.028 * 168s US.Steel_value 0.1051 0.0114 9.24 6.0e-15 *** 168s US.Steel_capital 0.3054 0.0435 7.02 3.1e-10 *** 168s Westinghouse_(Intercept) -48.0297 21.4802 -2.24 0.028 * 168s Westinghouse_value 0.1051 0.0114 9.24 6.0e-15 *** 168s Westinghouse_capital 0.3054 0.0435 7.02 3.1e-10 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s [1] 16195 168s Chrysler_(Intercept) Chrysler_value 168s -48.030 0.105 168s Chrysler_capital General.Electric_(Intercept) 168s 0.305 -48.030 168s General.Electric_value General.Electric_capital 168s 0.105 0.305 168s General.Motors_(Intercept) General.Motors_value 168s -48.030 0.105 168s General.Motors_capital US.Steel_(Intercept) 168s 0.305 -48.030 168s US.Steel_value US.Steel_capital 168s 0.105 0.305 168s Westinghouse_(Intercept) Westinghouse_value 168s -48.030 0.105 168s Westinghouse_capital 168s 0.305 168s C1 C2 C3 168s -48.030 0.105 0.305 168s Estimate Std. Error t value Pr(>|t|) 168s Chrysler_(Intercept) -48.030 21.4802 -2.24 2.76e-02 168s Chrysler_value 0.105 0.0114 9.24 6.00e-15 168s Chrysler_capital 0.305 0.0435 7.02 3.06e-10 168s General.Electric_(Intercept) -48.030 21.4802 -2.24 2.76e-02 168s General.Electric_value 0.105 0.0114 9.24 6.00e-15 168s General.Electric_capital 0.305 0.0435 7.02 3.06e-10 168s General.Motors_(Intercept) -48.030 21.4802 -2.24 2.76e-02 168s General.Motors_value 0.105 0.0114 9.24 6.00e-15 168s General.Motors_capital 0.305 0.0435 7.02 3.06e-10 168s US.Steel_(Intercept) -48.030 21.4802 -2.24 2.76e-02 168s US.Steel_value 0.105 0.0114 9.24 6.00e-15 168s US.Steel_capital 0.305 0.0435 7.02 3.06e-10 168s Westinghouse_(Intercept) -48.030 21.4802 -2.24 2.76e-02 168s Westinghouse_value 0.105 0.0114 9.24 6.00e-15 168s Westinghouse_capital 0.305 0.0435 7.02 3.06e-10 168s Estimate Std. Error t value Pr(>|t|) 168s C1 -48.030 21.4802 -2.24 2.76e-02 168s C2 0.105 0.0114 9.24 6.00e-15 168s C3 0.305 0.0435 7.02 3.06e-10 168s Chrysler_(Intercept) Chrysler_value 168s Chrysler_(Intercept) 461.39750 -0.154668 168s Chrysler_value -0.15467 0.000129 168s Chrysler_capital -0.00689 -0.000303 168s General.Electric_(Intercept) 461.39750 -0.154668 168s General.Electric_value -0.15467 0.000129 168s General.Electric_capital -0.00689 -0.000303 168s General.Motors_(Intercept) 461.39750 -0.154668 168s General.Motors_value -0.15467 0.000129 168s General.Motors_capital -0.00689 -0.000303 168s US.Steel_(Intercept) 461.39750 -0.154668 168s US.Steel_value -0.15467 0.000129 168s US.Steel_capital -0.00689 -0.000303 168s Westinghouse_(Intercept) 461.39750 -0.154668 168s Westinghouse_value -0.15467 0.000129 168s Westinghouse_capital -0.00689 -0.000303 168s Chrysler_capital General.Electric_(Intercept) 168s Chrysler_(Intercept) -0.006891 461.39750 168s Chrysler_value -0.000303 -0.15467 168s Chrysler_capital 0.001893 -0.00689 168s General.Electric_(Intercept) -0.006891 461.39750 168s General.Electric_value -0.000303 -0.15467 168s General.Electric_capital 0.001893 -0.00689 168s General.Motors_(Intercept) -0.006891 461.39750 168s General.Motors_value -0.000303 -0.15467 168s General.Motors_capital 0.001893 -0.00689 168s US.Steel_(Intercept) -0.006891 461.39750 168s US.Steel_value -0.000303 -0.15467 168s US.Steel_capital 0.001893 -0.00689 168s Westinghouse_(Intercept) -0.006891 461.39750 168s Westinghouse_value -0.000303 -0.15467 168s Westinghouse_capital 0.001893 -0.00689 168s General.Electric_value General.Electric_capital 168s Chrysler_(Intercept) -0.154668 -0.006891 168s Chrysler_value 0.000129 -0.000303 168s Chrysler_capital -0.000303 0.001893 168s General.Electric_(Intercept) -0.154668 -0.006891 168s General.Electric_value 0.000129 -0.000303 168s General.Electric_capital -0.000303 0.001893 168s General.Motors_(Intercept) -0.154668 -0.006891 168s General.Motors_value 0.000129 -0.000303 168s General.Motors_capital -0.000303 0.001893 168s US.Steel_(Intercept) -0.154668 -0.006891 168s US.Steel_value 0.000129 -0.000303 168s US.Steel_capital -0.000303 0.001893 168s Westinghouse_(Intercept) -0.154668 -0.006891 168s Westinghouse_value 0.000129 -0.000303 168s Westinghouse_capital -0.000303 0.001893 168s General.Motors_(Intercept) General.Motors_value 168s Chrysler_(Intercept) 461.39750 -0.154668 168s Chrysler_value -0.15467 0.000129 168s Chrysler_capital -0.00689 -0.000303 168s General.Electric_(Intercept) 461.39750 -0.154668 168s General.Electric_value -0.15467 0.000129 168s General.Electric_capital -0.00689 -0.000303 168s General.Motors_(Intercept) 461.39750 -0.154668 168s General.Motors_value -0.15467 0.000129 168s General.Motors_capital -0.00689 -0.000303 168s US.Steel_(Intercept) 461.39750 -0.154668 168s US.Steel_value -0.15467 0.000129 168s US.Steel_capital -0.00689 -0.000303 168s Westinghouse_(Intercept) 461.39750 -0.154668 168s Westinghouse_value -0.15467 0.000129 168s Westinghouse_capital -0.00689 -0.000303 168s General.Motors_capital US.Steel_(Intercept) 168s Chrysler_(Intercept) -0.006891 461.39750 168s Chrysler_value -0.000303 -0.15467 168s Chrysler_capital 0.001893 -0.00689 168s General.Electric_(Intercept) -0.006891 461.39750 168s General.Electric_value -0.000303 -0.15467 168s General.Electric_capital 0.001893 -0.00689 168s General.Motors_(Intercept) -0.006891 461.39750 168s General.Motors_value -0.000303 -0.15467 168s General.Motors_capital 0.001893 -0.00689 168s US.Steel_(Intercept) -0.006891 461.39750 168s US.Steel_value -0.000303 -0.15467 168s US.Steel_capital 0.001893 -0.00689 168s Westinghouse_(Intercept) -0.006891 461.39750 168s Westinghouse_value -0.000303 -0.15467 168s Westinghouse_capital 0.001893 -0.00689 168s US.Steel_value US.Steel_capital 168s Chrysler_(Intercept) -0.154668 -0.006891 168s Chrysler_value 0.000129 -0.000303 168s Chrysler_capital -0.000303 0.001893 168s General.Electric_(Intercept) -0.154668 -0.006891 168s General.Electric_value 0.000129 -0.000303 168s General.Electric_capital -0.000303 0.001893 168s General.Motors_(Intercept) -0.154668 -0.006891 168s General.Motors_value 0.000129 -0.000303 168s General.Motors_capital -0.000303 0.001893 168s US.Steel_(Intercept) -0.154668 -0.006891 168s US.Steel_value 0.000129 -0.000303 168s US.Steel_capital -0.000303 0.001893 168s Westinghouse_(Intercept) -0.154668 -0.006891 168s Westinghouse_value 0.000129 -0.000303 168s Westinghouse_capital -0.000303 0.001893 168s Westinghouse_(Intercept) Westinghouse_value 168s Chrysler_(Intercept) 461.39750 -0.154668 168s Chrysler_value -0.15467 0.000129 168s Chrysler_capital -0.00689 -0.000303 168s General.Electric_(Intercept) 461.39750 -0.154668 168s General.Electric_value -0.15467 0.000129 168s General.Electric_capital -0.00689 -0.000303 168s General.Motors_(Intercept) 461.39750 -0.154668 168s General.Motors_value -0.15467 0.000129 168s General.Motors_capital -0.00689 -0.000303 168s US.Steel_(Intercept) 461.39750 -0.154668 168s US.Steel_value -0.15467 0.000129 168s US.Steel_capital -0.00689 -0.000303 168s Westinghouse_(Intercept) 461.39750 -0.154668 168s Westinghouse_value -0.15467 0.000129 168s Westinghouse_capital -0.00689 -0.000303 168s Westinghouse_capital 168s Chrysler_(Intercept) -0.006891 168s Chrysler_value -0.000303 168s Chrysler_capital 0.001893 168s General.Electric_(Intercept) -0.006891 168s General.Electric_value -0.000303 168s General.Electric_capital 0.001893 168s General.Motors_(Intercept) -0.006891 168s General.Motors_value -0.000303 168s General.Motors_capital 0.001893 168s US.Steel_(Intercept) -0.006891 168s US.Steel_value -0.000303 168s US.Steel_capital 0.001893 168s Westinghouse_(Intercept) -0.006891 168s Westinghouse_value -0.000303 168s Westinghouse_capital 0.001893 168s C1 C2 C3 168s C1 461.39750 -0.154668 -0.006891 168s C2 -0.15467 0.000129 -0.000303 168s C3 -0.00689 -0.000303 0.001893 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s X1935 41.24 -71.7 41.27 98.333 40.29 168s X1936 29.63 -150.7 -66.11 198.009 19.46 168s X1937 10.81 -205.4 -155.39 200.626 4.21 168s X1938 37.79 -169.4 -51.57 41.520 6.50 168s X1939 9.38 -193.7 -136.54 -22.742 5.06 168s X1940 20.47 -158.6 -42.05 0.513 2.46 168s X1941 25.78 -99.2 3.84 190.851 29.04 168s X1942 29.85 -114.8 62.38 174.529 13.83 168s X1943 13.11 -172.2 41.00 108.865 -5.58 168s X1944 15.73 -170.6 73.77 60.388 -7.87 168s X1945 31.19 -166.9 19.60 47.014 -18.39 168s X1946 2.33 -129.8 98.30 180.017 -4.69 168s X1947 20.31 -118.2 13.81 198.862 8.57 168s X1948 30.75 -140.2 -46.46 277.965 -11.89 168s X1949 19.97 -192.9 -97.21 170.739 -24.58 168s X1950 25.98 -225.4 -39.33 181.300 -28.22 168s X1951 61.49 -213.0 -72.74 291.171 -13.26 168s X1952 27.89 -234.9 -15.13 330.665 -15.43 168s X1953 12.03 -266.1 153.79 285.144 -40.69 168s X1954 19.93 -323.8 267.09 80.518 -73.50 168s 2.5 % 97.5 % 168s Chrysler_(Intercept) -90.662 -5.398 168s Chrysler_value 0.083 0.128 168s Chrysler_capital 0.219 0.392 168s General.Electric_(Intercept) -90.662 -5.398 168s General.Electric_value 0.083 0.128 168s General.Electric_capital 0.219 0.392 168s General.Motors_(Intercept) -90.662 -5.398 168s General.Motors_value 0.083 0.128 168s General.Motors_capital 0.219 0.392 168s US.Steel_(Intercept) -90.662 -5.398 168s US.Steel_value 0.083 0.128 168s US.Steel_capital 0.219 0.392 168s Westinghouse_(Intercept) -90.662 -5.398 168s Westinghouse_value 0.083 0.128 168s Westinghouse_capital 0.219 0.392 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s X1935 -0.95 105 276 112 -27.36 168s X1936 43.13 196 458 157 6.44 168s X1937 55.45 283 566 269 30.84 168s X1938 13.81 214 309 221 16.39 168s X1939 43.03 242 467 253 13.78 168s X1940 48.94 233 503 261 26.11 168s X1941 42.57 212 508 282 19.47 168s X1942 16.95 207 386 271 29.51 168s X1943 34.29 233 459 253 42.60 168s X1944 43.84 227 474 228 45.68 168s X1945 57.59 261 542 212 57.66 168s X1946 71.79 290 590 240 58.15 168s X1947 42.37 265 555 222 46.99 168s X1948 58.61 287 576 217 61.45 168s X1949 59.01 291 652 234 56.62 168s X1950 74.68 319 682 238 60.46 168s X1951 99.13 348 829 297 67.64 168s X1952 117.11 392 906 315 87.21 168s X1953 162.90 446 1151 356 130.77 168s X1954 152.56 513 1220 379 142.10 168s 'log Lik.' -540 (df=4) 168s 'log Lik.' -573 (df=4) 168s [1] 100 168s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 168s X1935 40.3 418 10.5 33.1 168s X1936 72.8 838 10.2 45.0 168s X1937 66.3 884 34.7 77.2 168s X1938 51.6 438 51.8 44.6 168s X1939 52.4 680 64.3 48.1 168s X1940 69.4 728 67.1 74.4 168s X1941 68.3 644 75.2 113.0 168s X1942 46.8 411 71.4 91.9 168s X1943 47.4 588 67.1 61.3 168s X1944 59.6 698 60.5 56.8 168s X1945 88.8 846 54.6 93.6 168s X1946 74.1 894 84.8 159.9 168s X1947 62.7 579 96.8 147.2 168s X1948 89.4 695 110.2 146.3 168s X1949 79.0 590 147.4 98.3 168s X1950 100.7 694 163.2 93.5 168s X1951 160.6 809 203.5 135.2 168s X1952 145.0 727 290.6 157.3 168s X1953 174.9 1002 346.1 179.5 168s X1954 172.5 703 414.9 189.6 168s General.Electric_value General.Electric_capital General.Motors_invest 168s X1935 1171 97.8 318 168s X1936 2016 104.4 392 168s X1937 2803 118.0 411 168s X1938 2040 156.2 258 168s X1939 2256 172.6 331 168s X1940 2132 186.6 461 168s X1941 1834 220.9 512 168s X1942 1588 287.8 448 168s X1943 1749 319.9 500 168s X1944 1687 321.3 548 168s X1945 2008 319.6 561 168s X1946 2208 346.0 688 168s X1947 1657 456.4 569 168s X1948 1604 543.4 529 168s X1949 1432 618.3 555 168s X1950 1610 647.4 643 168s X1951 1819 671.3 756 168s X1952 2080 726.1 891 168s X1953 2372 800.3 1304 168s X1954 2760 888.9 1487 168s General.Motors_value General.Motors_capital US.Steel_invest 168s X1935 3078 2.8 210 168s X1936 4662 52.6 355 168s X1937 5387 156.9 470 168s X1938 2792 209.2 262 168s X1939 4313 203.4 230 168s X1940 4644 207.2 262 168s X1941 4551 255.2 473 168s X1942 3244 303.7 446 168s X1943 4054 264.1 362 168s X1944 4379 201.6 288 168s X1945 4841 265.0 259 168s X1946 4901 402.2 420 168s X1947 3526 761.5 420 168s X1948 3255 922.4 494 168s X1949 3700 1020.1 405 168s X1950 3756 1099.0 419 168s X1951 4833 1207.7 588 168s X1952 4925 1430.5 645 168s X1953 6242 1777.3 641 168s X1954 5594 2226.3 459 168s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 168s X1935 1362 53.8 12.9 192 168s X1936 1807 50.5 25.9 516 168s X1937 2676 118.1 35.0 729 168s X1938 1802 260.2 22.9 560 168s X1939 1957 312.7 18.8 520 168s X1940 2203 254.2 28.6 628 168s X1941 2380 261.4 48.5 537 168s X1942 2169 298.7 43.3 561 168s X1943 1985 301.8 37.0 617 168s X1944 1814 279.1 37.8 627 168s X1945 1850 213.8 39.3 737 168s X1946 2068 232.6 53.5 760 168s X1947 1797 264.8 55.6 581 168s X1948 1626 306.9 49.6 662 168s X1949 1667 351.1 32.0 584 168s X1950 1677 357.8 32.2 635 168s X1951 2290 342.1 54.4 724 168s X1952 2159 444.2 71.8 864 168s X1953 2031 623.6 90.1 1194 168s X1954 2116 669.7 68.6 1189 168s Westinghouse_capital 168s X1935 1.8 168s X1936 0.8 168s X1937 7.4 168s X1938 18.1 168s X1939 23.5 168s X1940 26.5 168s X1941 36.2 168s X1942 60.8 168s X1943 84.4 168s X1944 91.2 168s X1945 92.4 168s X1946 86.0 168s X1947 111.1 168s X1948 130.6 168s X1949 141.8 168s X1950 136.7 168s X1951 129.7 168s X1952 145.5 168s X1953 174.8 168s X1954 213.5 168s Chrysler_(Intercept) Chrysler_value Chrysler_capital 168s Chrysler_X1935 1 418 10.5 168s Chrysler_X1936 1 838 10.2 168s Chrysler_X1937 1 884 34.7 168s Chrysler_X1938 1 438 51.8 168s Chrysler_X1939 1 680 64.3 168s Chrysler_X1940 1 728 67.1 168s Chrysler_X1941 1 644 75.2 168s Chrysler_X1942 1 411 71.4 168s Chrysler_X1943 1 588 67.1 168s Chrysler_X1944 1 698 60.5 168s Chrysler_X1945 1 846 54.6 168s Chrysler_X1946 1 894 84.8 168s Chrysler_X1947 1 579 96.8 168s Chrysler_X1948 1 695 110.2 168s Chrysler_X1949 1 590 147.4 168s Chrysler_X1950 1 694 163.2 168s Chrysler_X1951 1 809 203.5 168s Chrysler_X1952 1 727 290.6 168s Chrysler_X1953 1 1002 346.1 168s Chrysler_X1954 1 703 414.9 168s General.Electric_X1935 0 0 0.0 168s General.Electric_X1936 0 0 0.0 168s General.Electric_X1937 0 0 0.0 168s General.Electric_X1938 0 0 0.0 168s General.Electric_X1939 0 0 0.0 168s General.Electric_X1940 0 0 0.0 168s General.Electric_X1941 0 0 0.0 168s General.Electric_X1942 0 0 0.0 168s General.Electric_X1943 0 0 0.0 168s General.Electric_X1944 0 0 0.0 168s General.Electric_X1945 0 0 0.0 168s General.Electric_X1946 0 0 0.0 168s General.Electric_X1947 0 0 0.0 168s General.Electric_X1948 0 0 0.0 168s General.Electric_X1949 0 0 0.0 168s General.Electric_X1950 0 0 0.0 168s General.Electric_X1951 0 0 0.0 168s General.Electric_X1952 0 0 0.0 168s General.Electric_X1953 0 0 0.0 168s General.Electric_X1954 0 0 0.0 168s General.Motors_X1935 0 0 0.0 168s General.Motors_X1936 0 0 0.0 168s General.Motors_X1937 0 0 0.0 168s General.Motors_X1938 0 0 0.0 168s General.Motors_X1939 0 0 0.0 168s General.Motors_X1940 0 0 0.0 168s General.Motors_X1941 0 0 0.0 168s General.Motors_X1942 0 0 0.0 168s General.Motors_X1943 0 0 0.0 168s General.Motors_X1944 0 0 0.0 168s General.Motors_X1945 0 0 0.0 168s General.Motors_X1946 0 0 0.0 168s General.Motors_X1947 0 0 0.0 168s General.Motors_X1948 0 0 0.0 168s General.Motors_X1949 0 0 0.0 168s General.Motors_X1950 0 0 0.0 168s General.Motors_X1951 0 0 0.0 168s General.Motors_X1952 0 0 0.0 168s General.Motors_X1953 0 0 0.0 168s General.Motors_X1954 0 0 0.0 168s US.Steel_X1935 0 0 0.0 168s US.Steel_X1936 0 0 0.0 168s US.Steel_X1937 0 0 0.0 168s US.Steel_X1938 0 0 0.0 168s US.Steel_X1939 0 0 0.0 168s US.Steel_X1940 0 0 0.0 168s US.Steel_X1941 0 0 0.0 168s US.Steel_X1942 0 0 0.0 168s US.Steel_X1943 0 0 0.0 168s US.Steel_X1944 0 0 0.0 168s US.Steel_X1945 0 0 0.0 168s US.Steel_X1946 0 0 0.0 168s US.Steel_X1947 0 0 0.0 168s US.Steel_X1948 0 0 0.0 168s US.Steel_X1949 0 0 0.0 168s US.Steel_X1950 0 0 0.0 168s US.Steel_X1951 0 0 0.0 168s US.Steel_X1952 0 0 0.0 168s US.Steel_X1953 0 0 0.0 168s US.Steel_X1954 0 0 0.0 168s Westinghouse_X1935 0 0 0.0 168s Westinghouse_X1936 0 0 0.0 168s Westinghouse_X1937 0 0 0.0 168s Westinghouse_X1938 0 0 0.0 168s Westinghouse_X1939 0 0 0.0 168s Westinghouse_X1940 0 0 0.0 168s Westinghouse_X1941 0 0 0.0 168s Westinghouse_X1942 0 0 0.0 168s Westinghouse_X1943 0 0 0.0 168s Westinghouse_X1944 0 0 0.0 168s Westinghouse_X1945 0 0 0.0 168s Westinghouse_X1946 0 0 0.0 168s Westinghouse_X1947 0 0 0.0 168s Westinghouse_X1948 0 0 0.0 168s Westinghouse_X1949 0 0 0.0 168s Westinghouse_X1950 0 0 0.0 168s Westinghouse_X1951 0 0 0.0 168s Westinghouse_X1952 0 0 0.0 168s Westinghouse_X1953 0 0 0.0 168s Westinghouse_X1954 0 0 0.0 168s General.Electric_(Intercept) General.Electric_value 168s Chrysler_X1935 0 0 168s Chrysler_X1936 0 0 168s Chrysler_X1937 0 0 168s Chrysler_X1938 0 0 168s Chrysler_X1939 0 0 168s Chrysler_X1940 0 0 168s Chrysler_X1941 0 0 168s Chrysler_X1942 0 0 168s Chrysler_X1943 0 0 168s Chrysler_X1944 0 0 168s Chrysler_X1945 0 0 168s Chrysler_X1946 0 0 168s Chrysler_X1947 0 0 168s Chrysler_X1948 0 0 168s Chrysler_X1949 0 0 168s Chrysler_X1950 0 0 168s Chrysler_X1951 0 0 168s Chrysler_X1952 0 0 168s Chrysler_X1953 0 0 168s Chrysler_X1954 0 0 168s General.Electric_X1935 1 1171 168s General.Electric_X1936 1 2016 168s General.Electric_X1937 1 2803 168s General.Electric_X1938 1 2040 168s General.Electric_X1939 1 2256 168s General.Electric_X1940 1 2132 168s General.Electric_X1941 1 1834 168s General.Electric_X1942 1 1588 168s General.Electric_X1943 1 1749 168s General.Electric_X1944 1 1687 168s General.Electric_X1945 1 2008 168s General.Electric_X1946 1 2208 168s General.Electric_X1947 1 1657 168s General.Electric_X1948 1 1604 168s General.Electric_X1949 1 1432 168s General.Electric_X1950 1 1610 168s General.Electric_X1951 1 1819 168s General.Electric_X1952 1 2080 168s General.Electric_X1953 1 2372 168s General.Electric_X1954 1 2760 168s General.Motors_X1935 0 0 168s General.Motors_X1936 0 0 168s General.Motors_X1937 0 0 168s General.Motors_X1938 0 0 168s General.Motors_X1939 0 0 168s General.Motors_X1940 0 0 168s General.Motors_X1941 0 0 168s General.Motors_X1942 0 0 168s General.Motors_X1943 0 0 168s General.Motors_X1944 0 0 168s General.Motors_X1945 0 0 168s General.Motors_X1946 0 0 168s General.Motors_X1947 0 0 168s General.Motors_X1948 0 0 168s General.Motors_X1949 0 0 168s General.Motors_X1950 0 0 168s General.Motors_X1951 0 0 168s General.Motors_X1952 0 0 168s General.Motors_X1953 0 0 168s General.Motors_X1954 0 0 168s US.Steel_X1935 0 0 168s US.Steel_X1936 0 0 168s US.Steel_X1937 0 0 168s US.Steel_X1938 0 0 168s US.Steel_X1939 0 0 168s US.Steel_X1940 0 0 168s US.Steel_X1941 0 0 168s US.Steel_X1942 0 0 168s US.Steel_X1943 0 0 168s US.Steel_X1944 0 0 168s US.Steel_X1945 0 0 168s US.Steel_X1946 0 0 168s US.Steel_X1947 0 0 168s US.Steel_X1948 0 0 168s US.Steel_X1949 0 0 168s US.Steel_X1950 0 0 168s US.Steel_X1951 0 0 168s US.Steel_X1952 0 0 168s US.Steel_X1953 0 0 168s US.Steel_X1954 0 0 168s Westinghouse_X1935 0 0 168s Westinghouse_X1936 0 0 168s Westinghouse_X1937 0 0 168s Westinghouse_X1938 0 0 168s Westinghouse_X1939 0 0 168s Westinghouse_X1940 0 0 168s Westinghouse_X1941 0 0 168s Westinghouse_X1942 0 0 168s Westinghouse_X1943 0 0 168s Westinghouse_X1944 0 0 168s Westinghouse_X1945 0 0 168s Westinghouse_X1946 0 0 168s Westinghouse_X1947 0 0 168s Westinghouse_X1948 0 0 168s Westinghouse_X1949 0 0 168s Westinghouse_X1950 0 0 168s Westinghouse_X1951 0 0 168s Westinghouse_X1952 0 0 168s Westinghouse_X1953 0 0 168s Westinghouse_X1954 0 0 168s General.Electric_capital General.Motors_(Intercept) 168s Chrysler_X1935 0.0 0 168s Chrysler_X1936 0.0 0 168s Chrysler_X1937 0.0 0 168s Chrysler_X1938 0.0 0 168s Chrysler_X1939 0.0 0 168s Chrysler_X1940 0.0 0 168s Chrysler_X1941 0.0 0 168s Chrysler_X1942 0.0 0 168s Chrysler_X1943 0.0 0 168s Chrysler_X1944 0.0 0 168s Chrysler_X1945 0.0 0 168s Chrysler_X1946 0.0 0 168s Chrysler_X1947 0.0 0 168s Chrysler_X1948 0.0 0 168s Chrysler_X1949 0.0 0 168s Chrysler_X1950 0.0 0 168s Chrysler_X1951 0.0 0 168s Chrysler_X1952 0.0 0 168s Chrysler_X1953 0.0 0 168s Chrysler_X1954 0.0 0 168s General.Electric_X1935 97.8 0 168s General.Electric_X1936 104.4 0 168s General.Electric_X1937 118.0 0 168s General.Electric_X1938 156.2 0 168s General.Electric_X1939 172.6 0 168s General.Electric_X1940 186.6 0 168s General.Electric_X1941 220.9 0 168s General.Electric_X1942 287.8 0 168s General.Electric_X1943 319.9 0 168s General.Electric_X1944 321.3 0 168s General.Electric_X1945 319.6 0 168s General.Electric_X1946 346.0 0 168s General.Electric_X1947 456.4 0 168s General.Electric_X1948 543.4 0 168s General.Electric_X1949 618.3 0 168s General.Electric_X1950 647.4 0 168s General.Electric_X1951 671.3 0 168s General.Electric_X1952 726.1 0 168s General.Electric_X1953 800.3 0 168s General.Electric_X1954 888.9 0 168s General.Motors_X1935 0.0 1 168s General.Motors_X1936 0.0 1 168s General.Motors_X1937 0.0 1 168s General.Motors_X1938 0.0 1 168s General.Motors_X1939 0.0 1 168s General.Motors_X1940 0.0 1 168s General.Motors_X1941 0.0 1 168s General.Motors_X1942 0.0 1 168s General.Motors_X1943 0.0 1 168s General.Motors_X1944 0.0 1 168s General.Motors_X1945 0.0 1 168s General.Motors_X1946 0.0 1 168s General.Motors_X1947 0.0 1 168s General.Motors_X1948 0.0 1 168s General.Motors_X1949 0.0 1 168s General.Motors_X1950 0.0 1 168s General.Motors_X1951 0.0 1 168s General.Motors_X1952 0.0 1 168s General.Motors_X1953 0.0 1 168s General.Motors_X1954 0.0 1 168s US.Steel_X1935 0.0 0 168s US.Steel_X1936 0.0 0 168s US.Steel_X1937 0.0 0 168s US.Steel_X1938 0.0 0 168s US.Steel_X1939 0.0 0 168s US.Steel_X1940 0.0 0 168s US.Steel_X1941 0.0 0 168s US.Steel_X1942 0.0 0 168s US.Steel_X1943 0.0 0 168s US.Steel_X1944 0.0 0 168s US.Steel_X1945 0.0 0 168s US.Steel_X1946 0.0 0 168s US.Steel_X1947 0.0 0 168s US.Steel_X1948 0.0 0 168s US.Steel_X1949 0.0 0 168s US.Steel_X1950 0.0 0 168s US.Steel_X1951 0.0 0 168s US.Steel_X1952 0.0 0 168s US.Steel_X1953 0.0 0 168s US.Steel_X1954 0.0 0 168s Westinghouse_X1935 0.0 0 168s Westinghouse_X1936 0.0 0 168s Westinghouse_X1937 0.0 0 168s Westinghouse_X1938 0.0 0 168s Westinghouse_X1939 0.0 0 168s Westinghouse_X1940 0.0 0 168s Westinghouse_X1941 0.0 0 168s Westinghouse_X1942 0.0 0 168s Westinghouse_X1943 0.0 0 168s Westinghouse_X1944 0.0 0 168s Westinghouse_X1945 0.0 0 168s Westinghouse_X1946 0.0 0 168s Westinghouse_X1947 0.0 0 168s Westinghouse_X1948 0.0 0 168s Westinghouse_X1949 0.0 0 168s Westinghouse_X1950 0.0 0 168s Westinghouse_X1951 0.0 0 168s Westinghouse_X1952 0.0 0 168s Westinghouse_X1953 0.0 0 168s Westinghouse_X1954 0.0 0 168s General.Motors_value General.Motors_capital 168s Chrysler_X1935 0 0.0 168s Chrysler_X1936 0 0.0 168s Chrysler_X1937 0 0.0 168s Chrysler_X1938 0 0.0 168s Chrysler_X1939 0 0.0 168s Chrysler_X1940 0 0.0 168s Chrysler_X1941 0 0.0 168s Chrysler_X1942 0 0.0 168s Chrysler_X1943 0 0.0 168s Chrysler_X1944 0 0.0 168s Chrysler_X1945 0 0.0 168s Chrysler_X1946 0 0.0 168s Chrysler_X1947 0 0.0 168s Chrysler_X1948 0 0.0 168s Chrysler_X1949 0 0.0 168s Chrysler_X1950 0 0.0 168s Chrysler_X1951 0 0.0 168s Chrysler_X1952 0 0.0 168s Chrysler_X1953 0 0.0 168s Chrysler_X1954 0 0.0 168s General.Electric_X1935 0 0.0 168s General.Electric_X1936 0 0.0 168s General.Electric_X1937 0 0.0 168s General.Electric_X1938 0 0.0 168s General.Electric_X1939 0 0.0 168s General.Electric_X1940 0 0.0 168s General.Electric_X1941 0 0.0 168s General.Electric_X1942 0 0.0 168s General.Electric_X1943 0 0.0 168s General.Electric_X1944 0 0.0 168s General.Electric_X1945 0 0.0 168s General.Electric_X1946 0 0.0 168s General.Electric_X1947 0 0.0 168s General.Electric_X1948 0 0.0 168s General.Electric_X1949 0 0.0 168s General.Electric_X1950 0 0.0 168s General.Electric_X1951 0 0.0 168s General.Electric_X1952 0 0.0 168s General.Electric_X1953 0 0.0 168s General.Electric_X1954 0 0.0 168s General.Motors_X1935 3078 2.8 168s General.Motors_X1936 4662 52.6 168s General.Motors_X1937 5387 156.9 168s General.Motors_X1938 2792 209.2 168s General.Motors_X1939 4313 203.4 168s General.Motors_X1940 4644 207.2 168s General.Motors_X1941 4551 255.2 168s General.Motors_X1942 3244 303.7 168s General.Motors_X1943 4054 264.1 168s General.Motors_X1944 4379 201.6 168s General.Motors_X1945 4841 265.0 168s General.Motors_X1946 4901 402.2 168s General.Motors_X1947 3526 761.5 168s General.Motors_X1948 3255 922.4 168s General.Motors_X1949 3700 1020.1 168s General.Motors_X1950 3756 1099.0 168s General.Motors_X1951 4833 1207.7 168s General.Motors_X1952 4925 1430.5 168s General.Motors_X1953 6242 1777.3 168s General.Motors_X1954 5594 2226.3 168s US.Steel_X1935 0 0.0 168s US.Steel_X1936 0 0.0 168s US.Steel_X1937 0 0.0 168s US.Steel_X1938 0 0.0 168s US.Steel_X1939 0 0.0 168s US.Steel_X1940 0 0.0 168s US.Steel_X1941 0 0.0 168s US.Steel_X1942 0 0.0 168s US.Steel_X1943 0 0.0 168s US.Steel_X1944 0 0.0 168s US.Steel_X1945 0 0.0 168s US.Steel_X1946 0 0.0 168s US.Steel_X1947 0 0.0 168s US.Steel_X1948 0 0.0 168s US.Steel_X1949 0 0.0 168s US.Steel_X1950 0 0.0 168s US.Steel_X1951 0 0.0 168s US.Steel_X1952 0 0.0 168s US.Steel_X1953 0 0.0 168s US.Steel_X1954 0 0.0 168s Westinghouse_X1935 0 0.0 168s Westinghouse_X1936 0 0.0 168s Westinghouse_X1937 0 0.0 168s Westinghouse_X1938 0 0.0 168s Westinghouse_X1939 0 0.0 168s Westinghouse_X1940 0 0.0 168s Westinghouse_X1941 0 0.0 168s Westinghouse_X1942 0 0.0 168s Westinghouse_X1943 0 0.0 168s Westinghouse_X1944 0 0.0 168s Westinghouse_X1945 0 0.0 168s Westinghouse_X1946 0 0.0 168s Westinghouse_X1947 0 0.0 168s Westinghouse_X1948 0 0.0 168s Westinghouse_X1949 0 0.0 168s Westinghouse_X1950 0 0.0 168s Westinghouse_X1951 0 0.0 168s Westinghouse_X1952 0 0.0 168s Westinghouse_X1953 0 0.0 168s Westinghouse_X1954 0 0.0 168s US.Steel_(Intercept) US.Steel_value US.Steel_capital 168s Chrysler_X1935 0 0 0.0 168s Chrysler_X1936 0 0 0.0 168s Chrysler_X1937 0 0 0.0 168s Chrysler_X1938 0 0 0.0 168s Chrysler_X1939 0 0 0.0 168s Chrysler_X1940 0 0 0.0 168s Chrysler_X1941 0 0 0.0 168s Chrysler_X1942 0 0 0.0 168s Chrysler_X1943 0 0 0.0 168s Chrysler_X1944 0 0 0.0 168s Chrysler_X1945 0 0 0.0 168s Chrysler_X1946 0 0 0.0 168s Chrysler_X1947 0 0 0.0 168s Chrysler_X1948 0 0 0.0 168s Chrysler_X1949 0 0 0.0 168s Chrysler_X1950 0 0 0.0 168s Chrysler_X1951 0 0 0.0 168s Chrysler_X1952 0 0 0.0 168s Chrysler_X1953 0 0 0.0 168s Chrysler_X1954 0 0 0.0 168s General.Electric_X1935 0 0 0.0 168s General.Electric_X1936 0 0 0.0 168s General.Electric_X1937 0 0 0.0 168s General.Electric_X1938 0 0 0.0 168s General.Electric_X1939 0 0 0.0 168s General.Electric_X1940 0 0 0.0 168s General.Electric_X1941 0 0 0.0 168s General.Electric_X1942 0 0 0.0 168s General.Electric_X1943 0 0 0.0 168s General.Electric_X1944 0 0 0.0 168s General.Electric_X1945 0 0 0.0 168s General.Electric_X1946 0 0 0.0 168s General.Electric_X1947 0 0 0.0 168s General.Electric_X1948 0 0 0.0 168s General.Electric_X1949 0 0 0.0 168s General.Electric_X1950 0 0 0.0 168s General.Electric_X1951 0 0 0.0 168s General.Electric_X1952 0 0 0.0 168s General.Electric_X1953 0 0 0.0 168s General.Electric_X1954 0 0 0.0 168s General.Motors_X1935 0 0 0.0 168s General.Motors_X1936 0 0 0.0 168s General.Motors_X1937 0 0 0.0 168s General.Motors_X1938 0 0 0.0 168s General.Motors_X1939 0 0 0.0 168s General.Motors_X1940 0 0 0.0 168s General.Motors_X1941 0 0 0.0 168s General.Motors_X1942 0 0 0.0 168s General.Motors_X1943 0 0 0.0 168s General.Motors_X1944 0 0 0.0 168s General.Motors_X1945 0 0 0.0 168s General.Motors_X1946 0 0 0.0 168s General.Motors_X1947 0 0 0.0 168s General.Motors_X1948 0 0 0.0 168s General.Motors_X1949 0 0 0.0 168s General.Motors_X1950 0 0 0.0 168s General.Motors_X1951 0 0 0.0 168s General.Motors_X1952 0 0 0.0 168s General.Motors_X1953 0 0 0.0 168s General.Motors_X1954 0 0 0.0 168s US.Steel_X1935 1 1362 53.8 168s US.Steel_X1936 1 1807 50.5 168s US.Steel_X1937 1 2676 118.1 168s US.Steel_X1938 1 1802 260.2 168s US.Steel_X1939 1 1957 312.7 168s US.Steel_X1940 1 2203 254.2 168s US.Steel_X1941 1 2380 261.4 168s US.Steel_X1942 1 2169 298.7 168s US.Steel_X1943 1 1985 301.8 168s US.Steel_X1944 1 1814 279.1 168s US.Steel_X1945 1 1850 213.8 168s US.Steel_X1946 1 2068 232.6 168s US.Steel_X1947 1 1797 264.8 168s US.Steel_X1948 1 1626 306.9 168s US.Steel_X1949 1 1667 351.1 168s US.Steel_X1950 1 1677 357.8 168s US.Steel_X1951 1 2290 342.1 168s US.Steel_X1952 1 2159 444.2 168s US.Steel_X1953 1 2031 623.6 168s US.Steel_X1954 1 2116 669.7 168s Westinghouse_X1935 0 0 0.0 168s Westinghouse_X1936 0 0 0.0 168s Westinghouse_X1937 0 0 0.0 168s Westinghouse_X1938 0 0 0.0 168s Westinghouse_X1939 0 0 0.0 168s Westinghouse_X1940 0 0 0.0 168s Westinghouse_X1941 0 0 0.0 168s Westinghouse_X1942 0 0 0.0 168s Westinghouse_X1943 0 0 0.0 168s Westinghouse_X1944 0 0 0.0 168s Westinghouse_X1945 0 0 0.0 168s Westinghouse_X1946 0 0 0.0 168s Westinghouse_X1947 0 0 0.0 168s Westinghouse_X1948 0 0 0.0 168s Westinghouse_X1949 0 0 0.0 168s Westinghouse_X1950 0 0 0.0 168s Westinghouse_X1951 0 0 0.0 168s Westinghouse_X1952 0 0 0.0 168s Westinghouse_X1953 0 0 0.0 168s Westinghouse_X1954 0 0 0.0 168s Westinghouse_(Intercept) Westinghouse_value 168s Chrysler_X1935 0 0 168s Chrysler_X1936 0 0 168s Chrysler_X1937 0 0 168s Chrysler_X1938 0 0 168s Chrysler_X1939 0 0 168s Chrysler_X1940 0 0 168s Chrysler_X1941 0 0 168s Chrysler_X1942 0 0 168s Chrysler_X1943 0 0 168s Chrysler_X1944 0 0 168s Chrysler_X1945 0 0 168s Chrysler_X1946 0 0 168s Chrysler_X1947 0 0 168s Chrysler_X1948 0 0 168s Chrysler_X1949 0 0 168s Chrysler_X1950 0 0 168s Chrysler_X1951 0 0 168s Chrysler_X1952 0 0 168s Chrysler_X1953 0 0 168s Chrysler_X1954 0 0 168s General.Electric_X1935 0 0 168s General.Electric_X1936 0 0 168s General.Electric_X1937 0 0 168s General.Electric_X1938 0 0 168s General.Electric_X1939 0 0 168s General.Electric_X1940 0 0 168s General.Electric_X1941 0 0 168s General.Electric_X1942 0 0 168s General.Electric_X1943 0 0 168s General.Electric_X1944 0 0 168s General.Electric_X1945 0 0 168s General.Electric_X1946 0 0 168s General.Electric_X1947 0 0 168s General.Electric_X1948 0 0 168s General.Electric_X1949 0 0 168s General.Electric_X1950 0 0 168s General.Electric_X1951 0 0 168s General.Electric_X1952 0 0 168s General.Electric_X1953 0 0 168s General.Electric_X1954 0 0 168s General.Motors_X1935 0 0 168s General.Motors_X1936 0 0 168s General.Motors_X1937 0 0 168s General.Motors_X1938 0 0 168s General.Motors_X1939 0 0 168s General.Motors_X1940 0 0 168s General.Motors_X1941 0 0 168s General.Motors_X1942 0 0 168s General.Motors_X1943 0 0 168s General.Motors_X1944 0 0 168s General.Motors_X1945 0 0 168s General.Motors_X1946 0 0 168s General.Motors_X1947 0 0 168s General.Motors_X1948 0 0 168s General.Motors_X1949 0 0 168s General.Motors_X1950 0 0 168s General.Motors_X1951 0 0 168s General.Motors_X1952 0 0 168s General.Motors_X1953 0 0 168s General.Motors_X1954 0 0 168s US.Steel_X1935 0 0 168s US.Steel_X1936 0 0 168s US.Steel_X1937 0 0 168s US.Steel_X1938 0 0 168s US.Steel_X1939 0 0 168s US.Steel_X1940 0 0 168s US.Steel_X1941 0 0 168s US.Steel_X1942 0 0 168s US.Steel_X1943 0 0 168s US.Steel_X1944 0 0 168s US.Steel_X1945 0 0 168s US.Steel_X1946 0 0 168s US.Steel_X1947 0 0 168s US.Steel_X1948 0 0 168s US.Steel_X1949 0 0 168s US.Steel_X1950 0 0 168s US.Steel_X1951 0 0 168s US.Steel_X1952 0 0 168s US.Steel_X1953 0 0 168s US.Steel_X1954 0 0 168s Westinghouse_X1935 1 192 168s Westinghouse_X1936 1 516 168s Westinghouse_X1937 1 729 168s Westinghouse_X1938 1 560 168s Westinghouse_X1939 1 520 168s Westinghouse_X1940 1 628 168s Westinghouse_X1941 1 537 168s Westinghouse_X1942 1 561 168s Westinghouse_X1943 1 617 168s Westinghouse_X1944 1 627 168s Westinghouse_X1945 1 737 168s Westinghouse_X1946 1 760 168s Westinghouse_X1947 1 581 168s Westinghouse_X1948 1 662 168s Westinghouse_X1949 1 584 168s Westinghouse_X1950 1 635 168s Westinghouse_X1951 1 724 168s Westinghouse_X1952 1 864 168s Westinghouse_X1953 1 1194 168s Westinghouse_X1954 1 1189 168s Westinghouse_capital 168s Chrysler_X1935 0.0 168s Chrysler_X1936 0.0 168s Chrysler_X1937 0.0 168s Chrysler_X1938 0.0 168s Chrysler_X1939 0.0 168s Chrysler_X1940 0.0 168s Chrysler_X1941 0.0 168s Chrysler_X1942 0.0 168s Chrysler_X1943 0.0 168s Chrysler_X1944 0.0 168s Chrysler_X1945 0.0 168s Chrysler_X1946 0.0 168s Chrysler_X1947 0.0 168s Chrysler_X1948 0.0 168s Chrysler_X1949 0.0 168s Chrysler_X1950 0.0 168s Chrysler_X1951 0.0 168s Chrysler_X1952 0.0 168s Chrysler_X1953 0.0 168s Chrysler_X1954 0.0 168s General.Electric_X1935 0.0 168s General.Electric_X1936 0.0 168s General.Electric_X1937 0.0 168s General.Electric_X1938 0.0 168s General.Electric_X1939 0.0 168s General.Electric_X1940 0.0 168s General.Electric_X1941 0.0 168s General.Electric_X1942 0.0 168s General.Electric_X1943 0.0 168s General.Electric_X1944 0.0 168s General.Electric_X1945 0.0 168s General.Electric_X1946 0.0 168s General.Electric_X1947 0.0 168s General.Electric_X1948 0.0 168s General.Electric_X1949 0.0 168s General.Electric_X1950 0.0 168s General.Electric_X1951 0.0 168s General.Electric_X1952 0.0 168s General.Electric_X1953 0.0 168s General.Electric_X1954 0.0 168s General.Motors_X1935 0.0 168s General.Motors_X1936 0.0 168s General.Motors_X1937 0.0 168s General.Motors_X1938 0.0 168s General.Motors_X1939 0.0 168s General.Motors_X1940 0.0 168s General.Motors_X1941 0.0 168s General.Motors_X1942 0.0 168s General.Motors_X1943 0.0 168s General.Motors_X1944 0.0 168s General.Motors_X1945 0.0 168s General.Motors_X1946 0.0 168s General.Motors_X1947 0.0 168s General.Motors_X1948 0.0 168s General.Motors_X1949 0.0 168s General.Motors_X1950 0.0 168s General.Motors_X1951 0.0 168s General.Motors_X1952 0.0 168s General.Motors_X1953 0.0 168s General.Motors_X1954 0.0 168s US.Steel_X1935 0.0 168s US.Steel_X1936 0.0 168s US.Steel_X1937 0.0 168s US.Steel_X1938 0.0 168s US.Steel_X1939 0.0 168s US.Steel_X1940 0.0 168s US.Steel_X1941 0.0 168s US.Steel_X1942 0.0 168s US.Steel_X1943 0.0 168s US.Steel_X1944 0.0 168s US.Steel_X1945 0.0 168s US.Steel_X1946 0.0 168s US.Steel_X1947 0.0 168s US.Steel_X1948 0.0 168s US.Steel_X1949 0.0 168s US.Steel_X1950 0.0 168s US.Steel_X1951 0.0 168s US.Steel_X1952 0.0 168s US.Steel_X1953 0.0 168s US.Steel_X1954 0.0 168s Westinghouse_X1935 1.8 168s Westinghouse_X1936 0.8 168s Westinghouse_X1937 7.4 168s Westinghouse_X1938 18.1 168s Westinghouse_X1939 23.5 168s Westinghouse_X1940 26.5 168s Westinghouse_X1941 36.2 168s Westinghouse_X1942 60.8 168s Westinghouse_X1943 84.4 168s Westinghouse_X1944 91.2 168s Westinghouse_X1945 92.4 168s Westinghouse_X1946 86.0 168s Westinghouse_X1947 111.1 168s Westinghouse_X1948 130.6 168s Westinghouse_X1949 141.8 168s Westinghouse_X1950 136.7 168s Westinghouse_X1951 129.7 168s Westinghouse_X1952 145.5 168s Westinghouse_X1953 174.8 168s Westinghouse_X1954 213.5 168s $Chrysler 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s 168s $General.Electric 168s General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s 168s $General.Motors 168s General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s 168s $US.Steel 168s US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s 168s $Westinghouse 168s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s $Chrysler 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s attr(,"variables") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"factors") 168s Chrysler_value Chrysler_capital 168s Chrysler_invest 0 0 168s Chrysler_value 1 0 168s Chrysler_capital 0 1 168s attr(,"term.labels") 168s [1] "Chrysler_value" "Chrysler_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"dataClasses") 168s Chrysler_invest Chrysler_value Chrysler_capital 168s "numeric" "numeric" "numeric" 168s 168s $General.Electric 168s General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s attr(,"variables") 168s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 168s attr(,"factors") 168s General.Electric_value General.Electric_capital 168s General.Electric_invest 0 0 168s General.Electric_value 1 0 168s General.Electric_capital 0 1 168s attr(,"term.labels") 168s [1] "General.Electric_value" "General.Electric_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 168s attr(,"dataClasses") 168s General.Electric_invest General.Electric_value General.Electric_capital 168s "numeric" "numeric" "numeric" 168s 168s $General.Motors 168s General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s attr(,"variables") 168s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 168s attr(,"factors") 168s General.Motors_value General.Motors_capital 168s General.Motors_invest 0 0 168s General.Motors_value 1 0 168s General.Motors_capital 0 1 168s attr(,"term.labels") 168s [1] "General.Motors_value" "General.Motors_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 168s attr(,"dataClasses") 168s General.Motors_invest General.Motors_value General.Motors_capital 168s "numeric" "numeric" "numeric" 168s 168s $US.Steel 168s US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s attr(,"variables") 168s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 168s attr(,"factors") 168s US.Steel_value US.Steel_capital 168s US.Steel_invest 0 0 168s US.Steel_value 1 0 168s US.Steel_capital 0 1 168s attr(,"term.labels") 168s [1] "US.Steel_value" "US.Steel_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 168s attr(,"dataClasses") 168s US.Steel_invest US.Steel_value US.Steel_capital 168s "numeric" "numeric" "numeric" 168s 168s $Westinghouse 168s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s attr(,"variables") 168s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 168s attr(,"factors") 168s Westinghouse_value Westinghouse_capital 168s Westinghouse_invest 0 0 168s Westinghouse_value 1 0 168s Westinghouse_capital 0 1 168s attr(,"term.labels") 168s [1] "Westinghouse_value" "Westinghouse_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 168s attr(,"dataClasses") 168s Westinghouse_invest Westinghouse_value Westinghouse_capital 168s "numeric" "numeric" "numeric" 168s 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s attr(,"variables") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"factors") 168s Chrysler_value Chrysler_capital 168s Chrysler_invest 0 0 168s Chrysler_value 1 0 168s Chrysler_capital 0 1 168s attr(,"term.labels") 168s [1] "Chrysler_value" "Chrysler_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"dataClasses") 168s Chrysler_invest Chrysler_value Chrysler_capital 168s "numeric" "numeric" "numeric" 168s > 168s > # SUR 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greeneSur <- systemfit( formulaGrunfeld, "SUR", 168s + data = GrunfeldGreene, methodResidCov = "noDfCor", useMatrix = useMatrix ) 168s + print( greeneSur ) 168s + print( summary( greeneSur ) ) 168s + print( summary( greeneSur, useDfSys = TRUE, residCov = FALSE ) ) 168s + print( summary( greeneSur, equations = FALSE ) ) 168s + print( coef( greeneSur ) ) 168s + print( coef( summary( greeneSur ) ) ) 168s + print( vcov( greeneSur ) ) 168s + print( residuals( greeneSur ) ) 168s + print( confint( greeneSur ) ) 168s + print( fitted( greeneSur ) ) 168s + print( logLik( greeneSur ) ) 168s + print( logLik( greeneSur, residCovDiag = TRUE ) ) 168s + print( nobs( greeneSur ) ) 168s + print( model.frame( greeneSur ) ) 168s + print( model.matrix( greeneSur ) ) 168s + print( formula( greeneSur ) ) 168s + print( formula( greeneSur$eq[[ 1 ]] ) ) 168s + print( terms( greeneSur ) ) 168s + print( terms( greeneSur$eq[[ 1 ]] ) ) 168s + } 168s 168s systemfit results 168s method: SUR 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_value 168s 0.5043 0.0695 168s Chrysler_capital General.Electric_(Intercept) 168s 0.3085 -22.4389 168s General.Electric_value General.Electric_capital 168s 0.0373 0.1308 168s General.Motors_(Intercept) General.Motors_value 168s -162.3641 0.1205 168s General.Motors_capital US.Steel_(Intercept) 168s 0.3827 85.4233 168s US.Steel_value US.Steel_capital 168s 0.1015 0.4000 168s Westinghouse_(Intercept) Westinghouse_value 168s 1.0889 0.0570 168s Westinghouse_capital 168s 0.0415 168s 168s systemfit results 168s method: SUR 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 85 347048 6.18e+13 0.844 0.869 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 3057 180 13.4 0.912 0.901 168s General.Electric 20 17 14009 824 28.7 0.688 0.651 168s General.Motors 20 17 144321 8489 92.1 0.921 0.911 168s US.Steel 20 17 183763 10810 104.0 0.422 0.354 168s Westinghouse 20 17 1898 112 10.6 0.726 0.694 168s 168s The covariance matrix of the residuals used for estimation 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 149.9 -21.4 -283 418 13.3 168s General.Electric -21.4 660.8 608 905 176.4 168s General.Motors -282.8 607.5 7160 -2222 126.2 168s US.Steel 418.1 905.0 -2222 8896 546.2 168s Westinghouse 13.3 176.4 126 546 88.7 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 152.85 2.05 -314 455 16.7 168s General.Electric 2.05 700.46 605 1224 200.3 168s General.Motors -313.70 605.34 7216 -2687 129.9 168s US.Steel 455.09 1224.41 -2687 9188 652.7 168s Westinghouse 16.66 200.32 130 653 94.9 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.00000 0.00626 -0.299 0.384 0.138 168s General.Electric 0.00626 1.00000 0.269 0.483 0.777 168s General.Motors -0.29870 0.26925 1.000 -0.330 0.157 168s US.Steel 0.38402 0.48264 -0.330 1.000 0.699 168s Westinghouse 0.13832 0.77690 0.157 0.699 1.000 168s 168s 168s SUR estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 0.5043 11.5128 0.04 0.96557 168s value 0.0695 0.0169 4.12 0.00072 *** 168s capital 0.3085 0.0259 11.93 1.1e-09 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 13.41 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 3056.985 MSE: 179.823 Root MSE: 13.41 168s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.901 168s 168s 168s SUR estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -22.4389 25.5186 -0.88 0.3915 168s value 0.0373 0.0123 3.04 0.0074 ** 168s capital 0.1308 0.0220 5.93 1.6e-05 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 28.707 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 14009.115 MSE: 824.066 Root MSE: 28.707 168s Multiple R-Squared: 0.688 Adjusted R-Squared: 0.651 168s 168s 168s SUR estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -162.3641 89.4592 -1.81 0.087 . 168s value 0.1205 0.0216 5.57 3.4e-05 *** 168s capital 0.3827 0.0328 11.68 1.5e-09 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 92.138 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 144320.876 MSE: 8489.463 Root MSE: 92.138 168s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.911 168s 168s 168s SUR estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 85.4233 111.8774 0.76 0.4556 168s value 0.1015 0.0548 1.85 0.0814 . 168s capital 0.4000 0.1278 3.13 0.0061 ** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 103.969 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 183763.011 MSE: 10809.589 Root MSE: 103.969 168s Multiple R-Squared: 0.422 Adjusted R-Squared: 0.354 168s 168s 168s SUR estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 1.0889 6.2588 0.17 0.86394 168s value 0.0570 0.0114 5.02 0.00011 *** 168s capital 0.0415 0.0412 1.01 0.32787 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 10.567 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 1898.249 MSE: 111.662 Root MSE: 10.567 168s Multiple R-Squared: 0.726 Adjusted R-Squared: 0.694 168s 168s 168s systemfit results 168s method: SUR 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 85 347048 6.18e+13 0.844 0.869 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 3057 180 13.4 0.912 0.901 168s General.Electric 20 17 14009 824 28.7 0.688 0.651 168s General.Motors 20 17 144321 8489 92.1 0.921 0.911 168s US.Steel 20 17 183763 10810 104.0 0.422 0.354 168s Westinghouse 20 17 1898 112 10.6 0.726 0.694 168s 168s 168s SUR estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 0.5043 11.5128 0.04 0.97 168s value 0.0695 0.0169 4.12 8.9e-05 *** 168s capital 0.3085 0.0259 11.93 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 13.41 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 3056.985 MSE: 179.823 Root MSE: 13.41 168s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.901 168s 168s 168s SUR estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -22.4389 25.5186 -0.88 0.3817 168s value 0.0373 0.0123 3.04 0.0031 ** 168s capital 0.1308 0.0220 5.93 6.3e-08 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 28.707 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 14009.115 MSE: 824.066 Root MSE: 28.707 168s Multiple R-Squared: 0.688 Adjusted R-Squared: 0.651 168s 168s 168s SUR estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -162.3641 89.4592 -1.81 0.073 . 168s value 0.1205 0.0216 5.57 2.9e-07 *** 168s capital 0.3827 0.0328 11.68 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 92.138 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 144320.876 MSE: 8489.463 Root MSE: 92.138 168s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.911 168s 168s 168s SUR estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 85.4233 111.8774 0.76 0.4473 168s value 0.1015 0.0548 1.85 0.0674 . 168s capital 0.4000 0.1278 3.13 0.0024 ** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 103.969 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 183763.011 MSE: 10809.589 Root MSE: 103.969 168s Multiple R-Squared: 0.422 Adjusted R-Squared: 0.354 168s 168s 168s SUR estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 1.0889 6.2588 0.17 0.86 168s value 0.0570 0.0114 5.02 2.8e-06 *** 168s capital 0.0415 0.0412 1.01 0.32 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 10.567 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 1898.249 MSE: 111.662 Root MSE: 10.567 168s Multiple R-Squared: 0.726 Adjusted R-Squared: 0.694 168s 168s 168s systemfit results 168s method: SUR 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 85 347048 6.18e+13 0.844 0.869 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 3057 180 13.4 0.912 0.901 168s General.Electric 20 17 14009 824 28.7 0.688 0.651 168s General.Motors 20 17 144321 8489 92.1 0.921 0.911 168s US.Steel 20 17 183763 10810 104.0 0.422 0.354 168s Westinghouse 20 17 1898 112 10.6 0.726 0.694 168s 168s The covariance matrix of the residuals used for estimation 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 149.9 -21.4 -283 418 13.3 168s General.Electric -21.4 660.8 608 905 176.4 168s General.Motors -282.8 607.5 7160 -2222 126.2 168s US.Steel 418.1 905.0 -2222 8896 546.2 168s Westinghouse 13.3 176.4 126 546 88.7 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 152.85 2.05 -314 455 16.7 168s General.Electric 2.05 700.46 605 1224 200.3 168s General.Motors -313.70 605.34 7216 -2687 129.9 168s US.Steel 455.09 1224.41 -2687 9188 652.7 168s Westinghouse 16.66 200.32 130 653 94.9 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.00000 0.00626 -0.299 0.384 0.138 168s General.Electric 0.00626 1.00000 0.269 0.483 0.777 168s General.Motors -0.29870 0.26925 1.000 -0.330 0.157 168s US.Steel 0.38402 0.48264 -0.330 1.000 0.699 168s Westinghouse 0.13832 0.77690 0.157 0.699 1.000 168s 168s 168s Coefficients: 168s Estimate Std. Error t value Pr(>|t|) 168s Chrysler_(Intercept) 0.5043 11.5128 0.04 0.96557 168s Chrysler_value 0.0695 0.0169 4.12 0.00072 *** 168s Chrysler_capital 0.3085 0.0259 11.93 1.1e-09 *** 168s General.Electric_(Intercept) -22.4389 25.5186 -0.88 0.39149 168s General.Electric_value 0.0373 0.0123 3.04 0.00738 ** 168s General.Electric_capital 0.1308 0.0220 5.93 1.6e-05 *** 168s General.Motors_(Intercept) -162.3641 89.4592 -1.81 0.08722 . 168s General.Motors_value 0.1205 0.0216 5.57 3.4e-05 *** 168s General.Motors_capital 0.3827 0.0328 11.68 1.5e-09 *** 168s US.Steel_(Intercept) 85.4233 111.8774 0.76 0.45561 168s US.Steel_value 0.1015 0.0548 1.85 0.08142 . 168s US.Steel_capital 0.4000 0.1278 3.13 0.00610 ** 168s Westinghouse_(Intercept) 1.0889 6.2588 0.17 0.86394 168s Westinghouse_value 0.0570 0.0114 5.02 0.00011 *** 168s Westinghouse_capital 0.0415 0.0412 1.01 0.32787 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s Chrysler_(Intercept) Chrysler_value 168s 0.5043 0.0695 168s Chrysler_capital General.Electric_(Intercept) 168s 0.3085 -22.4389 168s General.Electric_value General.Electric_capital 168s 0.0373 0.1308 168s General.Motors_(Intercept) General.Motors_value 168s -162.3641 0.1205 168s General.Motors_capital US.Steel_(Intercept) 168s 0.3827 85.4233 168s US.Steel_value US.Steel_capital 168s 0.1015 0.4000 168s Westinghouse_(Intercept) Westinghouse_value 168s 1.0889 0.0570 168s Westinghouse_capital 168s 0.0415 168s Estimate Std. Error t value Pr(>|t|) 168s Chrysler_(Intercept) 0.5043 11.5128 0.0438 9.66e-01 168s Chrysler_value 0.0695 0.0169 4.1157 7.22e-04 168s Chrysler_capital 0.3085 0.0259 11.9297 1.10e-09 168s General.Electric_(Intercept) -22.4389 25.5186 -0.8793 3.91e-01 168s General.Electric_value 0.0373 0.0123 3.0409 7.38e-03 168s General.Electric_capital 0.1308 0.0220 5.9313 1.64e-05 168s General.Motors_(Intercept) -162.3641 89.4592 -1.8150 8.72e-02 168s General.Motors_value 0.1205 0.0216 5.5709 3.38e-05 168s General.Motors_capital 0.3827 0.0328 11.6805 1.52e-09 168s US.Steel_(Intercept) 85.4233 111.8774 0.7635 4.56e-01 168s US.Steel_value 0.1015 0.0548 1.8523 8.14e-02 168s US.Steel_capital 0.4000 0.1278 3.1300 6.10e-03 168s Westinghouse_(Intercept) 1.0889 6.2588 0.1740 8.64e-01 168s Westinghouse_value 0.0570 0.0114 5.0174 1.06e-04 168s Westinghouse_capital 0.0415 0.0412 1.0074 3.28e-01 168s Chrysler_(Intercept) Chrysler_value 168s Chrysler_(Intercept) 1.33e+02 -1.82e-01 168s Chrysler_value -1.82e-01 2.86e-04 168s Chrysler_capital 9.57e-03 -1.31e-04 168s General.Electric_(Intercept) -2.94e+01 3.74e-02 168s General.Electric_value 1.28e-02 -1.86e-05 168s General.Electric_capital 8.80e-03 -2.96e-06 168s General.Motors_(Intercept) -1.56e+02 1.91e-01 168s General.Motors_value 3.28e-02 -4.91e-05 168s General.Motors_capital -8.18e-04 3.42e-05 168s US.Steel_(Intercept) 1.80e+02 -1.87e-01 168s US.Steel_value -7.46e-02 1.13e-04 168s US.Steel_capital -4.03e-02 -1.22e-04 168s Westinghouse_(Intercept) -3.04e-01 3.03e-03 168s Westinghouse_value 1.14e-03 -3.70e-06 168s Westinghouse_capital 2.42e-03 -6.41e-06 168s Chrysler_capital General.Electric_(Intercept) 168s Chrysler_(Intercept) 9.57e-03 -29.3642 168s Chrysler_value -1.31e-04 0.0374 168s Chrysler_capital 6.69e-04 0.0198 168s General.Electric_(Intercept) 1.98e-02 651.1982 168s General.Electric_value 1.28e-06 -0.2851 168s General.Electric_capital -5.56e-05 -0.1615 168s General.Motors_(Intercept) 7.79e-02 571.3402 168s General.Motors_value 1.03e-05 -0.1196 168s General.Motors_capital -1.89e-04 -0.0352 168s US.Steel_(Intercept) -2.45e-01 644.2920 168s US.Steel_value -3.26e-05 -0.2201 168s US.Steel_capital 1.03e-03 -0.5505 168s Westinghouse_(Intercept) -9.35e-03 102.8679 168s Westinghouse_value 1.18e-05 -0.1700 168s Westinghouse_capital 1.67e-05 0.2338 168s General.Electric_value General.Electric_capital 168s Chrysler_(Intercept) 1.28e-02 8.80e-03 168s Chrysler_value -1.86e-05 -2.96e-06 168s Chrysler_capital 1.28e-06 -5.56e-05 168s General.Electric_(Intercept) -2.85e-01 -1.61e-01 168s General.Electric_value 1.50e-04 -1.70e-05 168s General.Electric_capital -1.70e-05 4.86e-04 168s General.Motors_(Intercept) -2.61e-01 -8.74e-02 168s General.Motors_value 6.35e-05 -9.49e-06 168s General.Motors_capital -2.27e-05 1.98e-04 168s US.Steel_(Intercept) -3.04e-01 -2.30e-02 168s US.Steel_value 1.35e-04 -1.07e-04 168s US.Steel_capital 1.23e-04 7.77e-04 168s Westinghouse_(Intercept) -4.02e-02 -4.02e-02 168s Westinghouse_value 8.74e-05 1.04e-06 168s Westinghouse_capital -2.16e-04 4.61e-04 168s General.Motors_(Intercept) General.Motors_value 168s Chrysler_(Intercept) -1.56e+02 3.28e-02 168s Chrysler_value 1.91e-01 -4.91e-05 168s Chrysler_capital 7.79e-02 1.03e-05 168s General.Electric_(Intercept) 5.71e+02 -1.20e-01 168s General.Electric_value -2.61e-01 6.35e-05 168s General.Electric_capital -8.74e-02 -9.49e-06 168s General.Motors_(Intercept) 8.00e+03 -1.84e+00 168s General.Motors_value -1.84e+00 4.68e-04 168s General.Motors_capital 5.32e-01 -2.83e-04 168s US.Steel_(Intercept) -1.75e+03 3.73e-01 168s US.Steel_value 8.02e-01 -2.06e-04 168s US.Steel_capital 2.01e-01 1.09e-04 168s Westinghouse_(Intercept) 1.10e+02 -2.33e-02 168s Westinghouse_value -2.06e-01 5.10e-05 168s Westinghouse_capital 3.98e-01 -1.28e-04 168s General.Motors_capital US.Steel_(Intercept) 168s Chrysler_(Intercept) -8.18e-04 1.80e+02 168s Chrysler_value 3.42e-05 -1.87e-01 168s Chrysler_capital -1.89e-04 -2.45e-01 168s General.Electric_(Intercept) -3.52e-02 6.44e+02 168s General.Electric_value -2.27e-05 -3.04e-01 168s General.Electric_capital 1.98e-04 -2.30e-02 168s General.Motors_(Intercept) 5.32e-01 -1.75e+03 168s General.Motors_value -2.83e-04 3.73e-01 168s General.Motors_capital 1.07e-03 3.74e-02 168s US.Steel_(Intercept) 3.74e-02 1.25e+04 168s US.Steel_value 1.39e-04 -5.65e+00 168s US.Steel_capital -1.04e-03 -3.12e+00 168s Westinghouse_(Intercept) -4.87e-03 2.74e+02 168s Westinghouse_value -2.38e-05 -5.09e-01 168s Westinghouse_capital 2.43e-04 1.10e+00 168s US.Steel_value US.Steel_capital 168s Chrysler_(Intercept) -7.46e-02 -0.040281 168s Chrysler_value 1.13e-04 -0.000122 168s Chrysler_capital -3.26e-05 0.001031 168s General.Electric_(Intercept) -2.20e-01 -0.550482 168s General.Electric_value 1.35e-04 0.000123 168s General.Electric_capital -1.07e-04 0.000777 168s General.Motors_(Intercept) 8.02e-01 0.200945 168s General.Motors_value -2.06e-04 0.000109 168s General.Motors_capital 1.39e-04 -0.001036 168s US.Steel_(Intercept) -5.65e+00 -3.119830 168s US.Steel_value 3.00e-03 -0.000901 168s US.Steel_capital -9.01e-04 0.016331 168s Westinghouse_(Intercept) -8.35e-02 -0.275101 168s Westinghouse_value 2.23e-04 0.000229 168s Westinghouse_capital -7.74e-04 0.001422 168s Westinghouse_(Intercept) Westinghouse_value 168s Chrysler_(Intercept) -0.30387 1.14e-03 168s Chrysler_value 0.00303 -3.70e-06 168s Chrysler_capital -0.00935 1.18e-05 168s General.Electric_(Intercept) 102.86790 -1.70e-01 168s General.Electric_value -0.04016 8.74e-05 168s General.Electric_capital -0.04021 1.04e-06 168s General.Motors_(Intercept) 110.26166 -2.06e-01 168s General.Motors_value -0.02326 5.10e-05 168s General.Motors_capital -0.00487 -2.38e-05 168s US.Steel_(Intercept) 274.40848 -5.09e-01 168s US.Steel_value -0.08348 2.23e-04 168s US.Steel_capital -0.27510 2.29e-04 168s Westinghouse_(Intercept) 39.17263 -5.99e-02 168s Westinghouse_value -0.05992 1.29e-04 168s Westinghouse_capital 0.06376 -3.12e-04 168s Westinghouse_capital 168s Chrysler_(Intercept) 2.42e-03 168s Chrysler_value -6.41e-06 168s Chrysler_capital 1.67e-05 168s General.Electric_(Intercept) 2.34e-01 168s General.Electric_value -2.16e-04 168s General.Electric_capital 4.61e-04 168s General.Motors_(Intercept) 3.98e-01 168s General.Motors_value -1.28e-04 168s General.Motors_capital 2.43e-04 168s US.Steel_(Intercept) 1.10e+00 168s US.Steel_value -7.74e-04 168s US.Steel_capital 1.42e-03 168s Westinghouse_(Intercept) 6.38e-02 168s Westinghouse_value -3.12e-04 168s Westinghouse_capital 1.70e-03 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s X1935 7.511 -0.905 107.95 -35.3 0.849 168s X1936 10.843 -21.387 -27.67 66.3 -4.639 168s X1937 -6.422 -20.333 -136.20 65.7 -7.906 168s X1938 4.659 -29.453 3.55 -110.1 -10.898 168s X1939 -15.204 -36.171 -104.40 -178.7 -12.863 168s X1940 -2.413 -7.078 -15.30 -149.0 -9.449 168s X1941 -0.116 38.153 28.30 41.3 15.299 168s X1942 -4.311 17.481 103.23 20.6 7.734 168s X1943 -14.728 -23.336 72.44 -46.0 -2.758 168s X1944 -8.172 -25.700 105.03 -92.9 -2.792 168s X1945 12.566 -0.629 38.84 -100.0 -7.681 168s X1946 -14.709 54.737 106.00 32.0 5.446 168s X1947 -7.958 48.169 14.88 46.8 16.715 168s X1948 6.548 37.841 -53.65 121.3 5.293 168s X1949 -8.057 -13.518 -118.82 10.1 -8.216 168s X1950 1.571 -28.788 -67.90 20.0 -10.735 168s X1951 41.064 1.996 -126.32 133.6 6.645 168s X1952 4.273 7.222 -87.37 163.0 15.390 168s X1953 -2.011 8.833 34.43 100.0 13.695 168s X1954 -4.934 -7.135 122.97 -108.7 -9.129 168s 2.5 % 97.5 % 168s Chrysler_(Intercept) -23.786 24.794 168s Chrysler_value 0.034 0.105 168s Chrysler_capital 0.254 0.363 168s General.Electric_(Intercept) -76.278 31.401 168s General.Electric_value 0.011 0.063 168s General.Electric_capital 0.084 0.177 168s General.Motors_(Intercept) -351.107 26.378 168s General.Motors_value 0.075 0.166 168s General.Motors_capital 0.314 0.452 168s US.Steel_(Intercept) -150.617 321.464 168s US.Steel_value -0.014 0.217 168s US.Steel_capital 0.130 0.670 168s Westinghouse_(Intercept) -12.116 14.294 168s Westinghouse_value 0.033 0.081 168s Westinghouse_capital -0.045 0.128 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s X1935 32.8 34.0 210 245 12.1 168s X1936 61.9 66.4 419 289 30.5 168s X1937 72.7 97.5 547 404 43.0 168s X1938 46.9 74.1 254 372 33.8 168s X1939 67.6 84.3 435 409 31.7 168s X1940 71.8 81.5 476 411 38.0 168s X1941 68.5 74.8 484 432 33.2 168s X1942 51.1 74.4 345 425 35.6 168s X1943 62.1 84.6 427 408 39.8 168s X1944 67.7 82.5 442 381 40.6 168s X1945 76.2 94.2 522 359 47.0 168s X1946 88.8 105.2 582 388 48.0 168s X1947 70.6 99.0 554 374 38.8 168s X1948 82.8 108.5 583 373 44.3 168s X1949 87.0 111.8 674 395 40.3 168s X1950 99.1 122.3 711 399 43.0 168s X1951 119.6 133.2 882 455 47.7 168s X1952 140.7 150.1 979 482 56.4 168s X1953 176.9 170.7 1270 541 76.4 168s X1954 177.4 196.7 1364 568 77.7 168s 'log Lik.' -459 (df=30) 168s 'log Lik.' -483 (df=30) 168s [1] 100 168s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 168s X1935 40.3 418 10.5 33.1 168s X1936 72.8 838 10.2 45.0 168s X1937 66.3 884 34.7 77.2 168s X1938 51.6 438 51.8 44.6 168s X1939 52.4 680 64.3 48.1 168s X1940 69.4 728 67.1 74.4 168s X1941 68.3 644 75.2 113.0 168s X1942 46.8 411 71.4 91.9 168s X1943 47.4 588 67.1 61.3 168s X1944 59.6 698 60.5 56.8 168s X1945 88.8 846 54.6 93.6 168s X1946 74.1 894 84.8 159.9 168s X1947 62.7 579 96.8 147.2 168s X1948 89.4 695 110.2 146.3 168s X1949 79.0 590 147.4 98.3 168s X1950 100.7 694 163.2 93.5 168s X1951 160.6 809 203.5 135.2 168s X1952 145.0 727 290.6 157.3 168s X1953 174.9 1002 346.1 179.5 168s X1954 172.5 703 414.9 189.6 168s General.Electric_value General.Electric_capital General.Motors_invest 168s X1935 1171 97.8 318 168s X1936 2016 104.4 392 168s X1937 2803 118.0 411 168s X1938 2040 156.2 258 168s X1939 2256 172.6 331 168s X1940 2132 186.6 461 168s X1941 1834 220.9 512 168s X1942 1588 287.8 448 168s X1943 1749 319.9 500 168s X1944 1687 321.3 548 168s X1945 2008 319.6 561 168s X1946 2208 346.0 688 168s X1947 1657 456.4 569 168s X1948 1604 543.4 529 168s X1949 1432 618.3 555 168s X1950 1610 647.4 643 168s X1951 1819 671.3 756 168s X1952 2080 726.1 891 168s X1953 2372 800.3 1304 168s X1954 2760 888.9 1487 168s General.Motors_value General.Motors_capital US.Steel_invest 168s X1935 3078 2.8 210 168s X1936 4662 52.6 355 168s X1937 5387 156.9 470 168s X1938 2792 209.2 262 168s X1939 4313 203.4 230 168s X1940 4644 207.2 262 168s X1941 4551 255.2 473 168s X1942 3244 303.7 446 168s X1943 4054 264.1 362 168s X1944 4379 201.6 288 168s X1945 4841 265.0 259 168s X1946 4901 402.2 420 168s X1947 3526 761.5 420 168s X1948 3255 922.4 494 168s X1949 3700 1020.1 405 168s X1950 3756 1099.0 419 168s X1951 4833 1207.7 588 168s X1952 4925 1430.5 645 168s X1953 6242 1777.3 641 168s X1954 5594 2226.3 459 168s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 168s X1935 1362 53.8 12.9 192 168s X1936 1807 50.5 25.9 516 168s X1937 2676 118.1 35.0 729 168s X1938 1802 260.2 22.9 560 168s X1939 1957 312.7 18.8 520 168s X1940 2203 254.2 28.6 628 168s X1941 2380 261.4 48.5 537 168s X1942 2169 298.7 43.3 561 168s X1943 1985 301.8 37.0 617 168s X1944 1814 279.1 37.8 627 168s X1945 1850 213.8 39.3 737 168s X1946 2068 232.6 53.5 760 168s X1947 1797 264.8 55.6 581 168s X1948 1626 306.9 49.6 662 168s X1949 1667 351.1 32.0 584 168s X1950 1677 357.8 32.2 635 168s X1951 2290 342.1 54.4 724 168s X1952 2159 444.2 71.8 864 168s X1953 2031 623.6 90.1 1194 168s X1954 2116 669.7 68.6 1189 168s Westinghouse_capital 168s X1935 1.8 168s X1936 0.8 168s X1937 7.4 168s X1938 18.1 168s X1939 23.5 168s X1940 26.5 168s X1941 36.2 168s X1942 60.8 168s X1943 84.4 168s X1944 91.2 168s X1945 92.4 168s X1946 86.0 168s X1947 111.1 168s X1948 130.6 168s X1949 141.8 168s X1950 136.7 168s X1951 129.7 168s X1952 145.5 168s X1953 174.8 168s X1954 213.5 168s Chrysler_(Intercept) Chrysler_value Chrysler_capital 168s Chrysler_X1935 1 418 10.5 168s Chrysler_X1936 1 838 10.2 168s Chrysler_X1937 1 884 34.7 168s Chrysler_X1938 1 438 51.8 168s Chrysler_X1939 1 680 64.3 168s Chrysler_X1940 1 728 67.1 168s Chrysler_X1941 1 644 75.2 168s Chrysler_X1942 1 411 71.4 168s Chrysler_X1943 1 588 67.1 168s Chrysler_X1944 1 698 60.5 168s Chrysler_X1945 1 846 54.6 168s Chrysler_X1946 1 894 84.8 168s Chrysler_X1947 1 579 96.8 168s Chrysler_X1948 1 695 110.2 168s Chrysler_X1949 1 590 147.4 168s Chrysler_X1950 1 694 163.2 168s Chrysler_X1951 1 809 203.5 168s Chrysler_X1952 1 727 290.6 168s Chrysler_X1953 1 1002 346.1 168s Chrysler_X1954 1 703 414.9 168s General.Electric_X1935 0 0 0.0 168s General.Electric_X1936 0 0 0.0 168s General.Electric_X1937 0 0 0.0 168s General.Electric_X1938 0 0 0.0 168s General.Electric_X1939 0 0 0.0 168s General.Electric_X1940 0 0 0.0 168s General.Electric_X1941 0 0 0.0 168s General.Electric_X1942 0 0 0.0 168s General.Electric_X1943 0 0 0.0 168s General.Electric_X1944 0 0 0.0 168s General.Electric_X1945 0 0 0.0 168s General.Electric_X1946 0 0 0.0 168s General.Electric_X1947 0 0 0.0 168s General.Electric_X1948 0 0 0.0 168s General.Electric_X1949 0 0 0.0 168s General.Electric_X1950 0 0 0.0 168s General.Electric_X1951 0 0 0.0 168s General.Electric_X1952 0 0 0.0 168s General.Electric_X1953 0 0 0.0 168s General.Electric_X1954 0 0 0.0 168s General.Motors_X1935 0 0 0.0 168s General.Motors_X1936 0 0 0.0 168s General.Motors_X1937 0 0 0.0 168s General.Motors_X1938 0 0 0.0 168s General.Motors_X1939 0 0 0.0 168s General.Motors_X1940 0 0 0.0 168s General.Motors_X1941 0 0 0.0 168s General.Motors_X1942 0 0 0.0 168s General.Motors_X1943 0 0 0.0 168s General.Motors_X1944 0 0 0.0 168s General.Motors_X1945 0 0 0.0 168s General.Motors_X1946 0 0 0.0 168s General.Motors_X1947 0 0 0.0 168s General.Motors_X1948 0 0 0.0 168s General.Motors_X1949 0 0 0.0 168s General.Motors_X1950 0 0 0.0 168s General.Motors_X1951 0 0 0.0 168s General.Motors_X1952 0 0 0.0 168s General.Motors_X1953 0 0 0.0 168s General.Motors_X1954 0 0 0.0 168s US.Steel_X1935 0 0 0.0 168s US.Steel_X1936 0 0 0.0 168s US.Steel_X1937 0 0 0.0 168s US.Steel_X1938 0 0 0.0 168s US.Steel_X1939 0 0 0.0 168s US.Steel_X1940 0 0 0.0 168s US.Steel_X1941 0 0 0.0 168s US.Steel_X1942 0 0 0.0 168s US.Steel_X1943 0 0 0.0 168s US.Steel_X1944 0 0 0.0 168s US.Steel_X1945 0 0 0.0 168s US.Steel_X1946 0 0 0.0 168s US.Steel_X1947 0 0 0.0 168s US.Steel_X1948 0 0 0.0 168s US.Steel_X1949 0 0 0.0 168s US.Steel_X1950 0 0 0.0 168s US.Steel_X1951 0 0 0.0 168s US.Steel_X1952 0 0 0.0 168s US.Steel_X1953 0 0 0.0 168s US.Steel_X1954 0 0 0.0 168s Westinghouse_X1935 0 0 0.0 168s Westinghouse_X1936 0 0 0.0 168s Westinghouse_X1937 0 0 0.0 168s Westinghouse_X1938 0 0 0.0 168s Westinghouse_X1939 0 0 0.0 168s Westinghouse_X1940 0 0 0.0 168s Westinghouse_X1941 0 0 0.0 168s Westinghouse_X1942 0 0 0.0 168s Westinghouse_X1943 0 0 0.0 168s Westinghouse_X1944 0 0 0.0 168s Westinghouse_X1945 0 0 0.0 168s Westinghouse_X1946 0 0 0.0 168s Westinghouse_X1947 0 0 0.0 168s Westinghouse_X1948 0 0 0.0 168s Westinghouse_X1949 0 0 0.0 168s Westinghouse_X1950 0 0 0.0 168s Westinghouse_X1951 0 0 0.0 168s Westinghouse_X1952 0 0 0.0 168s Westinghouse_X1953 0 0 0.0 168s Westinghouse_X1954 0 0 0.0 168s General.Electric_(Intercept) General.Electric_value 168s Chrysler_X1935 0 0 168s Chrysler_X1936 0 0 168s Chrysler_X1937 0 0 168s Chrysler_X1938 0 0 168s Chrysler_X1939 0 0 168s Chrysler_X1940 0 0 168s Chrysler_X1941 0 0 168s Chrysler_X1942 0 0 168s Chrysler_X1943 0 0 168s Chrysler_X1944 0 0 168s Chrysler_X1945 0 0 168s Chrysler_X1946 0 0 168s Chrysler_X1947 0 0 168s Chrysler_X1948 0 0 168s Chrysler_X1949 0 0 168s Chrysler_X1950 0 0 168s Chrysler_X1951 0 0 168s Chrysler_X1952 0 0 168s Chrysler_X1953 0 0 168s Chrysler_X1954 0 0 168s General.Electric_X1935 1 1171 168s General.Electric_X1936 1 2016 168s General.Electric_X1937 1 2803 168s General.Electric_X1938 1 2040 168s General.Electric_X1939 1 2256 168s General.Electric_X1940 1 2132 168s General.Electric_X1941 1 1834 168s General.Electric_X1942 1 1588 168s General.Electric_X1943 1 1749 168s General.Electric_X1944 1 1687 168s General.Electric_X1945 1 2008 168s General.Electric_X1946 1 2208 168s General.Electric_X1947 1 1657 168s General.Electric_X1948 1 1604 168s General.Electric_X1949 1 1432 168s General.Electric_X1950 1 1610 168s General.Electric_X1951 1 1819 168s General.Electric_X1952 1 2080 168s General.Electric_X1953 1 2372 168s General.Electric_X1954 1 2760 168s General.Motors_X1935 0 0 168s General.Motors_X1936 0 0 168s General.Motors_X1937 0 0 168s General.Motors_X1938 0 0 168s General.Motors_X1939 0 0 168s General.Motors_X1940 0 0 168s General.Motors_X1941 0 0 168s General.Motors_X1942 0 0 168s General.Motors_X1943 0 0 168s General.Motors_X1944 0 0 168s General.Motors_X1945 0 0 168s General.Motors_X1946 0 0 168s General.Motors_X1947 0 0 168s General.Motors_X1948 0 0 168s General.Motors_X1949 0 0 168s General.Motors_X1950 0 0 168s General.Motors_X1951 0 0 168s General.Motors_X1952 0 0 168s General.Motors_X1953 0 0 168s General.Motors_X1954 0 0 168s US.Steel_X1935 0 0 168s US.Steel_X1936 0 0 168s US.Steel_X1937 0 0 168s US.Steel_X1938 0 0 168s US.Steel_X1939 0 0 168s US.Steel_X1940 0 0 168s US.Steel_X1941 0 0 168s US.Steel_X1942 0 0 168s US.Steel_X1943 0 0 168s US.Steel_X1944 0 0 168s US.Steel_X1945 0 0 168s US.Steel_X1946 0 0 168s US.Steel_X1947 0 0 168s US.Steel_X1948 0 0 168s US.Steel_X1949 0 0 168s US.Steel_X1950 0 0 168s US.Steel_X1951 0 0 168s US.Steel_X1952 0 0 168s US.Steel_X1953 0 0 168s US.Steel_X1954 0 0 168s Westinghouse_X1935 0 0 168s Westinghouse_X1936 0 0 168s Westinghouse_X1937 0 0 168s Westinghouse_X1938 0 0 168s Westinghouse_X1939 0 0 168s Westinghouse_X1940 0 0 168s Westinghouse_X1941 0 0 168s Westinghouse_X1942 0 0 168s Westinghouse_X1943 0 0 168s Westinghouse_X1944 0 0 168s Westinghouse_X1945 0 0 168s Westinghouse_X1946 0 0 168s Westinghouse_X1947 0 0 168s Westinghouse_X1948 0 0 168s Westinghouse_X1949 0 0 168s Westinghouse_X1950 0 0 168s Westinghouse_X1951 0 0 168s Westinghouse_X1952 0 0 168s Westinghouse_X1953 0 0 168s Westinghouse_X1954 0 0 168s General.Electric_capital General.Motors_(Intercept) 168s Chrysler_X1935 0.0 0 168s Chrysler_X1936 0.0 0 168s Chrysler_X1937 0.0 0 168s Chrysler_X1938 0.0 0 168s Chrysler_X1939 0.0 0 168s Chrysler_X1940 0.0 0 168s Chrysler_X1941 0.0 0 168s Chrysler_X1942 0.0 0 168s Chrysler_X1943 0.0 0 168s Chrysler_X1944 0.0 0 168s Chrysler_X1945 0.0 0 168s Chrysler_X1946 0.0 0 168s Chrysler_X1947 0.0 0 168s Chrysler_X1948 0.0 0 168s Chrysler_X1949 0.0 0 168s Chrysler_X1950 0.0 0 168s Chrysler_X1951 0.0 0 168s Chrysler_X1952 0.0 0 168s Chrysler_X1953 0.0 0 168s Chrysler_X1954 0.0 0 168s General.Electric_X1935 97.8 0 168s General.Electric_X1936 104.4 0 168s General.Electric_X1937 118.0 0 168s General.Electric_X1938 156.2 0 168s General.Electric_X1939 172.6 0 168s General.Electric_X1940 186.6 0 168s General.Electric_X1941 220.9 0 168s General.Electric_X1942 287.8 0 168s General.Electric_X1943 319.9 0 168s General.Electric_X1944 321.3 0 168s General.Electric_X1945 319.6 0 168s General.Electric_X1946 346.0 0 168s General.Electric_X1947 456.4 0 168s General.Electric_X1948 543.4 0 168s General.Electric_X1949 618.3 0 168s General.Electric_X1950 647.4 0 168s General.Electric_X1951 671.3 0 168s General.Electric_X1952 726.1 0 168s General.Electric_X1953 800.3 0 168s General.Electric_X1954 888.9 0 168s General.Motors_X1935 0.0 1 168s General.Motors_X1936 0.0 1 168s General.Motors_X1937 0.0 1 168s General.Motors_X1938 0.0 1 168s General.Motors_X1939 0.0 1 168s General.Motors_X1940 0.0 1 168s General.Motors_X1941 0.0 1 168s General.Motors_X1942 0.0 1 168s General.Motors_X1943 0.0 1 168s General.Motors_X1944 0.0 1 168s General.Motors_X1945 0.0 1 168s General.Motors_X1946 0.0 1 168s General.Motors_X1947 0.0 1 168s General.Motors_X1948 0.0 1 168s General.Motors_X1949 0.0 1 168s General.Motors_X1950 0.0 1 168s General.Motors_X1951 0.0 1 168s General.Motors_X1952 0.0 1 168s General.Motors_X1953 0.0 1 168s General.Motors_X1954 0.0 1 168s US.Steel_X1935 0.0 0 168s US.Steel_X1936 0.0 0 168s US.Steel_X1937 0.0 0 168s US.Steel_X1938 0.0 0 168s US.Steel_X1939 0.0 0 168s US.Steel_X1940 0.0 0 168s US.Steel_X1941 0.0 0 168s US.Steel_X1942 0.0 0 168s US.Steel_X1943 0.0 0 168s US.Steel_X1944 0.0 0 168s US.Steel_X1945 0.0 0 168s US.Steel_X1946 0.0 0 168s US.Steel_X1947 0.0 0 168s US.Steel_X1948 0.0 0 168s US.Steel_X1949 0.0 0 168s US.Steel_X1950 0.0 0 168s US.Steel_X1951 0.0 0 168s US.Steel_X1952 0.0 0 168s US.Steel_X1953 0.0 0 168s US.Steel_X1954 0.0 0 168s Westinghouse_X1935 0.0 0 168s Westinghouse_X1936 0.0 0 168s Westinghouse_X1937 0.0 0 168s Westinghouse_X1938 0.0 0 168s Westinghouse_X1939 0.0 0 168s Westinghouse_X1940 0.0 0 168s Westinghouse_X1941 0.0 0 168s Westinghouse_X1942 0.0 0 168s Westinghouse_X1943 0.0 0 168s Westinghouse_X1944 0.0 0 168s Westinghouse_X1945 0.0 0 168s Westinghouse_X1946 0.0 0 168s Westinghouse_X1947 0.0 0 168s Westinghouse_X1948 0.0 0 168s Westinghouse_X1949 0.0 0 168s Westinghouse_X1950 0.0 0 168s Westinghouse_X1951 0.0 0 168s Westinghouse_X1952 0.0 0 168s Westinghouse_X1953 0.0 0 168s Westinghouse_X1954 0.0 0 168s General.Motors_value General.Motors_capital 168s Chrysler_X1935 0 0.0 168s Chrysler_X1936 0 0.0 168s Chrysler_X1937 0 0.0 168s Chrysler_X1938 0 0.0 168s Chrysler_X1939 0 0.0 168s Chrysler_X1940 0 0.0 168s Chrysler_X1941 0 0.0 168s Chrysler_X1942 0 0.0 168s Chrysler_X1943 0 0.0 168s Chrysler_X1944 0 0.0 168s Chrysler_X1945 0 0.0 168s Chrysler_X1946 0 0.0 168s Chrysler_X1947 0 0.0 168s Chrysler_X1948 0 0.0 168s Chrysler_X1949 0 0.0 168s Chrysler_X1950 0 0.0 168s Chrysler_X1951 0 0.0 168s Chrysler_X1952 0 0.0 168s Chrysler_X1953 0 0.0 168s Chrysler_X1954 0 0.0 168s General.Electric_X1935 0 0.0 168s General.Electric_X1936 0 0.0 168s General.Electric_X1937 0 0.0 168s General.Electric_X1938 0 0.0 168s General.Electric_X1939 0 0.0 168s General.Electric_X1940 0 0.0 168s General.Electric_X1941 0 0.0 168s General.Electric_X1942 0 0.0 168s General.Electric_X1943 0 0.0 168s General.Electric_X1944 0 0.0 168s General.Electric_X1945 0 0.0 168s General.Electric_X1946 0 0.0 168s General.Electric_X1947 0 0.0 168s General.Electric_X1948 0 0.0 168s General.Electric_X1949 0 0.0 168s General.Electric_X1950 0 0.0 168s General.Electric_X1951 0 0.0 168s General.Electric_X1952 0 0.0 168s General.Electric_X1953 0 0.0 168s General.Electric_X1954 0 0.0 168s General.Motors_X1935 3078 2.8 168s General.Motors_X1936 4662 52.6 168s General.Motors_X1937 5387 156.9 168s General.Motors_X1938 2792 209.2 168s General.Motors_X1939 4313 203.4 168s General.Motors_X1940 4644 207.2 168s General.Motors_X1941 4551 255.2 168s General.Motors_X1942 3244 303.7 168s General.Motors_X1943 4054 264.1 168s General.Motors_X1944 4379 201.6 168s General.Motors_X1945 4841 265.0 168s General.Motors_X1946 4901 402.2 168s General.Motors_X1947 3526 761.5 168s General.Motors_X1948 3255 922.4 168s General.Motors_X1949 3700 1020.1 168s General.Motors_X1950 3756 1099.0 168s General.Motors_X1951 4833 1207.7 168s General.Motors_X1952 4925 1430.5 168s General.Motors_X1953 6242 1777.3 168s General.Motors_X1954 5594 2226.3 168s US.Steel_X1935 0 0.0 168s US.Steel_X1936 0 0.0 168s US.Steel_X1937 0 0.0 168s US.Steel_X1938 0 0.0 168s US.Steel_X1939 0 0.0 168s US.Steel_X1940 0 0.0 168s US.Steel_X1941 0 0.0 168s US.Steel_X1942 0 0.0 168s US.Steel_X1943 0 0.0 168s US.Steel_X1944 0 0.0 168s US.Steel_X1945 0 0.0 168s US.Steel_X1946 0 0.0 168s US.Steel_X1947 0 0.0 168s US.Steel_X1948 0 0.0 168s US.Steel_X1949 0 0.0 168s US.Steel_X1950 0 0.0 168s US.Steel_X1951 0 0.0 168s US.Steel_X1952 0 0.0 168s US.Steel_X1953 0 0.0 168s US.Steel_X1954 0 0.0 168s Westinghouse_X1935 0 0.0 168s Westinghouse_X1936 0 0.0 168s Westinghouse_X1937 0 0.0 168s Westinghouse_X1938 0 0.0 168s Westinghouse_X1939 0 0.0 168s Westinghouse_X1940 0 0.0 168s Westinghouse_X1941 0 0.0 168s Westinghouse_X1942 0 0.0 168s Westinghouse_X1943 0 0.0 168s Westinghouse_X1944 0 0.0 168s Westinghouse_X1945 0 0.0 168s Westinghouse_X1946 0 0.0 168s Westinghouse_X1947 0 0.0 168s Westinghouse_X1948 0 0.0 168s Westinghouse_X1949 0 0.0 168s Westinghouse_X1950 0 0.0 168s Westinghouse_X1951 0 0.0 168s Westinghouse_X1952 0 0.0 168s Westinghouse_X1953 0 0.0 168s Westinghouse_X1954 0 0.0 168s US.Steel_(Intercept) US.Steel_value US.Steel_capital 168s Chrysler_X1935 0 0 0.0 168s Chrysler_X1936 0 0 0.0 168s Chrysler_X1937 0 0 0.0 168s Chrysler_X1938 0 0 0.0 168s Chrysler_X1939 0 0 0.0 168s Chrysler_X1940 0 0 0.0 168s Chrysler_X1941 0 0 0.0 168s Chrysler_X1942 0 0 0.0 168s Chrysler_X1943 0 0 0.0 168s Chrysler_X1944 0 0 0.0 168s Chrysler_X1945 0 0 0.0 168s Chrysler_X1946 0 0 0.0 168s Chrysler_X1947 0 0 0.0 168s Chrysler_X1948 0 0 0.0 168s Chrysler_X1949 0 0 0.0 168s Chrysler_X1950 0 0 0.0 168s Chrysler_X1951 0 0 0.0 168s Chrysler_X1952 0 0 0.0 168s Chrysler_X1953 0 0 0.0 168s Chrysler_X1954 0 0 0.0 168s General.Electric_X1935 0 0 0.0 168s General.Electric_X1936 0 0 0.0 168s General.Electric_X1937 0 0 0.0 168s General.Electric_X1938 0 0 0.0 168s General.Electric_X1939 0 0 0.0 168s General.Electric_X1940 0 0 0.0 168s General.Electric_X1941 0 0 0.0 168s General.Electric_X1942 0 0 0.0 168s General.Electric_X1943 0 0 0.0 168s General.Electric_X1944 0 0 0.0 168s General.Electric_X1945 0 0 0.0 168s General.Electric_X1946 0 0 0.0 168s General.Electric_X1947 0 0 0.0 168s General.Electric_X1948 0 0 0.0 168s General.Electric_X1949 0 0 0.0 168s General.Electric_X1950 0 0 0.0 168s General.Electric_X1951 0 0 0.0 168s General.Electric_X1952 0 0 0.0 168s General.Electric_X1953 0 0 0.0 168s General.Electric_X1954 0 0 0.0 168s General.Motors_X1935 0 0 0.0 168s General.Motors_X1936 0 0 0.0 168s General.Motors_X1937 0 0 0.0 168s General.Motors_X1938 0 0 0.0 168s General.Motors_X1939 0 0 0.0 168s General.Motors_X1940 0 0 0.0 168s General.Motors_X1941 0 0 0.0 168s General.Motors_X1942 0 0 0.0 168s General.Motors_X1943 0 0 0.0 168s General.Motors_X1944 0 0 0.0 168s General.Motors_X1945 0 0 0.0 168s General.Motors_X1946 0 0 0.0 168s General.Motors_X1947 0 0 0.0 168s General.Motors_X1948 0 0 0.0 168s General.Motors_X1949 0 0 0.0 168s General.Motors_X1950 0 0 0.0 168s General.Motors_X1951 0 0 0.0 168s General.Motors_X1952 0 0 0.0 168s General.Motors_X1953 0 0 0.0 168s General.Motors_X1954 0 0 0.0 168s US.Steel_X1935 1 1362 53.8 168s US.Steel_X1936 1 1807 50.5 168s US.Steel_X1937 1 2676 118.1 168s US.Steel_X1938 1 1802 260.2 168s US.Steel_X1939 1 1957 312.7 168s US.Steel_X1940 1 2203 254.2 168s US.Steel_X1941 1 2380 261.4 168s US.Steel_X1942 1 2169 298.7 168s US.Steel_X1943 1 1985 301.8 168s US.Steel_X1944 1 1814 279.1 168s US.Steel_X1945 1 1850 213.8 168s US.Steel_X1946 1 2068 232.6 168s US.Steel_X1947 1 1797 264.8 168s US.Steel_X1948 1 1626 306.9 168s US.Steel_X1949 1 1667 351.1 168s US.Steel_X1950 1 1677 357.8 168s US.Steel_X1951 1 2290 342.1 168s US.Steel_X1952 1 2159 444.2 168s US.Steel_X1953 1 2031 623.6 168s US.Steel_X1954 1 2116 669.7 168s Westinghouse_X1935 0 0 0.0 168s Westinghouse_X1936 0 0 0.0 168s Westinghouse_X1937 0 0 0.0 168s Westinghouse_X1938 0 0 0.0 168s Westinghouse_X1939 0 0 0.0 168s Westinghouse_X1940 0 0 0.0 168s Westinghouse_X1941 0 0 0.0 168s Westinghouse_X1942 0 0 0.0 168s Westinghouse_X1943 0 0 0.0 168s Westinghouse_X1944 0 0 0.0 168s Westinghouse_X1945 0 0 0.0 168s Westinghouse_X1946 0 0 0.0 168s Westinghouse_X1947 0 0 0.0 168s Westinghouse_X1948 0 0 0.0 168s Westinghouse_X1949 0 0 0.0 168s Westinghouse_X1950 0 0 0.0 168s Westinghouse_X1951 0 0 0.0 168s Westinghouse_X1952 0 0 0.0 168s Westinghouse_X1953 0 0 0.0 168s Westinghouse_X1954 0 0 0.0 168s Westinghouse_(Intercept) Westinghouse_value 168s Chrysler_X1935 0 0 168s Chrysler_X1936 0 0 168s Chrysler_X1937 0 0 168s Chrysler_X1938 0 0 168s Chrysler_X1939 0 0 168s Chrysler_X1940 0 0 168s Chrysler_X1941 0 0 168s Chrysler_X1942 0 0 168s Chrysler_X1943 0 0 168s Chrysler_X1944 0 0 168s Chrysler_X1945 0 0 168s Chrysler_X1946 0 0 168s Chrysler_X1947 0 0 168s Chrysler_X1948 0 0 168s Chrysler_X1949 0 0 168s Chrysler_X1950 0 0 168s Chrysler_X1951 0 0 168s Chrysler_X1952 0 0 168s Chrysler_X1953 0 0 168s Chrysler_X1954 0 0 168s General.Electric_X1935 0 0 168s General.Electric_X1936 0 0 168s General.Electric_X1937 0 0 168s General.Electric_X1938 0 0 168s General.Electric_X1939 0 0 168s General.Electric_X1940 0 0 168s General.Electric_X1941 0 0 168s General.Electric_X1942 0 0 168s General.Electric_X1943 0 0 168s General.Electric_X1944 0 0 168s General.Electric_X1945 0 0 168s General.Electric_X1946 0 0 168s General.Electric_X1947 0 0 168s General.Electric_X1948 0 0 168s General.Electric_X1949 0 0 168s General.Electric_X1950 0 0 168s General.Electric_X1951 0 0 168s General.Electric_X1952 0 0 168s General.Electric_X1953 0 0 168s General.Electric_X1954 0 0 168s General.Motors_X1935 0 0 168s General.Motors_X1936 0 0 168s General.Motors_X1937 0 0 168s General.Motors_X1938 0 0 168s General.Motors_X1939 0 0 168s General.Motors_X1940 0 0 168s General.Motors_X1941 0 0 168s General.Motors_X1942 0 0 168s General.Motors_X1943 0 0 168s General.Motors_X1944 0 0 168s General.Motors_X1945 0 0 168s General.Motors_X1946 0 0 168s General.Motors_X1947 0 0 168s General.Motors_X1948 0 0 168s General.Motors_X1949 0 0 168s General.Motors_X1950 0 0 168s General.Motors_X1951 0 0 168s General.Motors_X1952 0 0 168s General.Motors_X1953 0 0 168s General.Motors_X1954 0 0 168s US.Steel_X1935 0 0 168s US.Steel_X1936 0 0 168s US.Steel_X1937 0 0 168s US.Steel_X1938 0 0 168s US.Steel_X1939 0 0 168s US.Steel_X1940 0 0 168s US.Steel_X1941 0 0 168s US.Steel_X1942 0 0 168s US.Steel_X1943 0 0 168s US.Steel_X1944 0 0 168s US.Steel_X1945 0 0 168s US.Steel_X1946 0 0 168s US.Steel_X1947 0 0 168s US.Steel_X1948 0 0 168s US.Steel_X1949 0 0 168s US.Steel_X1950 0 0 168s US.Steel_X1951 0 0 168s US.Steel_X1952 0 0 168s US.Steel_X1953 0 0 168s US.Steel_X1954 0 0 168s Westinghouse_X1935 1 192 168s Westinghouse_X1936 1 516 168s Westinghouse_X1937 1 729 168s Westinghouse_X1938 1 560 168s Westinghouse_X1939 1 520 168s Westinghouse_X1940 1 628 168s Westinghouse_X1941 1 537 168s Westinghouse_X1942 1 561 168s Westinghouse_X1943 1 617 168s Westinghouse_X1944 1 627 168s Westinghouse_X1945 1 737 168s Westinghouse_X1946 1 760 168s Westinghouse_X1947 1 581 168s Westinghouse_X1948 1 662 168s Westinghouse_X1949 1 584 168s Westinghouse_X1950 1 635 168s Westinghouse_X1951 1 724 168s Westinghouse_X1952 1 864 168s Westinghouse_X1953 1 1194 168s Westinghouse_X1954 1 1189 168s Westinghouse_capital 168s Chrysler_X1935 0.0 168s Chrysler_X1936 0.0 168s Chrysler_X1937 0.0 168s Chrysler_X1938 0.0 168s Chrysler_X1939 0.0 168s Chrysler_X1940 0.0 168s Chrysler_X1941 0.0 168s Chrysler_X1942 0.0 168s Chrysler_X1943 0.0 168s Chrysler_X1944 0.0 168s Chrysler_X1945 0.0 168s Chrysler_X1946 0.0 168s Chrysler_X1947 0.0 168s Chrysler_X1948 0.0 168s Chrysler_X1949 0.0 168s Chrysler_X1950 0.0 168s Chrysler_X1951 0.0 168s Chrysler_X1952 0.0 168s Chrysler_X1953 0.0 168s Chrysler_X1954 0.0 168s General.Electric_X1935 0.0 168s General.Electric_X1936 0.0 168s General.Electric_X1937 0.0 168s General.Electric_X1938 0.0 168s General.Electric_X1939 0.0 168s General.Electric_X1940 0.0 168s General.Electric_X1941 0.0 168s General.Electric_X1942 0.0 168s General.Electric_X1943 0.0 168s General.Electric_X1944 0.0 168s General.Electric_X1945 0.0 168s General.Electric_X1946 0.0 168s General.Electric_X1947 0.0 168s General.Electric_X1948 0.0 168s General.Electric_X1949 0.0 168s General.Electric_X1950 0.0 168s General.Electric_X1951 0.0 168s General.Electric_X1952 0.0 168s General.Electric_X1953 0.0 168s General.Electric_X1954 0.0 168s General.Motors_X1935 0.0 168s General.Motors_X1936 0.0 168s General.Motors_X1937 0.0 168s General.Motors_X1938 0.0 168s General.Motors_X1939 0.0 168s General.Motors_X1940 0.0 168s General.Motors_X1941 0.0 168s General.Motors_X1942 0.0 168s General.Motors_X1943 0.0 168s General.Motors_X1944 0.0 168s General.Motors_X1945 0.0 168s General.Motors_X1946 0.0 168s General.Motors_X1947 0.0 168s General.Motors_X1948 0.0 168s General.Motors_X1949 0.0 168s General.Motors_X1950 0.0 168s General.Motors_X1951 0.0 168s General.Motors_X1952 0.0 168s General.Motors_X1953 0.0 168s General.Motors_X1954 0.0 168s US.Steel_X1935 0.0 168s US.Steel_X1936 0.0 168s US.Steel_X1937 0.0 168s US.Steel_X1938 0.0 168s US.Steel_X1939 0.0 168s US.Steel_X1940 0.0 168s US.Steel_X1941 0.0 168s US.Steel_X1942 0.0 168s US.Steel_X1943 0.0 168s US.Steel_X1944 0.0 168s US.Steel_X1945 0.0 168s US.Steel_X1946 0.0 168s US.Steel_X1947 0.0 168s US.Steel_X1948 0.0 168s US.Steel_X1949 0.0 168s US.Steel_X1950 0.0 168s US.Steel_X1951 0.0 168s US.Steel_X1952 0.0 168s US.Steel_X1953 0.0 168s US.Steel_X1954 0.0 168s Westinghouse_X1935 1.8 168s Westinghouse_X1936 0.8 168s Westinghouse_X1937 7.4 168s Westinghouse_X1938 18.1 168s Westinghouse_X1939 23.5 168s Westinghouse_X1940 26.5 168s Westinghouse_X1941 36.2 168s Westinghouse_X1942 60.8 168s Westinghouse_X1943 84.4 168s Westinghouse_X1944 91.2 168s Westinghouse_X1945 92.4 168s Westinghouse_X1946 86.0 168s Westinghouse_X1947 111.1 168s Westinghouse_X1948 130.6 168s Westinghouse_X1949 141.8 168s Westinghouse_X1950 136.7 168s Westinghouse_X1951 129.7 168s Westinghouse_X1952 145.5 168s Westinghouse_X1953 174.8 168s Westinghouse_X1954 213.5 168s $Chrysler 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s 168s $General.Electric 168s General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s 168s $General.Motors 168s General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s 168s $US.Steel 168s US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s 168s $Westinghouse 168s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s $Chrysler 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s attr(,"variables") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"factors") 168s Chrysler_value Chrysler_capital 168s Chrysler_invest 0 0 168s Chrysler_value 1 0 168s Chrysler_capital 0 1 168s attr(,"term.labels") 168s [1] "Chrysler_value" "Chrysler_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"dataClasses") 168s Chrysler_invest Chrysler_value Chrysler_capital 168s "numeric" "numeric" "numeric" 168s 168s $General.Electric 168s General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s attr(,"variables") 168s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 168s attr(,"factors") 168s General.Electric_value General.Electric_capital 168s General.Electric_invest 0 0 168s General.Electric_value 1 0 168s General.Electric_capital 0 1 168s attr(,"term.labels") 168s [1] "General.Electric_value" "General.Electric_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 168s attr(,"dataClasses") 168s General.Electric_invest General.Electric_value General.Electric_capital 168s "numeric" "numeric" "numeric" 168s 168s $General.Motors 168s General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s attr(,"variables") 168s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 168s attr(,"factors") 168s General.Motors_value General.Motors_capital 168s General.Motors_invest 0 0 168s General.Motors_value 1 0 168s General.Motors_capital 0 1 168s attr(,"term.labels") 168s [1] "General.Motors_value" "General.Motors_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 168s attr(,"dataClasses") 168s General.Motors_invest General.Motors_value General.Motors_capital 168s "numeric" "numeric" "numeric" 168s 168s $US.Steel 168s US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s attr(,"variables") 168s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 168s attr(,"factors") 168s US.Steel_value US.Steel_capital 168s US.Steel_invest 0 0 168s US.Steel_value 1 0 168s US.Steel_capital 0 1 168s attr(,"term.labels") 168s [1] "US.Steel_value" "US.Steel_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 168s attr(,"dataClasses") 168s US.Steel_invest US.Steel_value US.Steel_capital 168s "numeric" "numeric" "numeric" 168s 168s $Westinghouse 168s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s attr(,"variables") 168s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 168s attr(,"factors") 168s Westinghouse_value Westinghouse_capital 168s Westinghouse_invest 0 0 168s Westinghouse_value 1 0 168s Westinghouse_capital 0 1 168s attr(,"term.labels") 168s [1] "Westinghouse_value" "Westinghouse_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 168s attr(,"dataClasses") 168s Westinghouse_invest Westinghouse_value Westinghouse_capital 168s "numeric" "numeric" "numeric" 168s 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s attr(,"variables") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"factors") 168s Chrysler_value Chrysler_capital 168s Chrysler_invest 0 0 168s Chrysler_value 1 0 168s Chrysler_capital 0 1 168s attr(,"term.labels") 168s [1] "Chrysler_value" "Chrysler_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"dataClasses") 168s Chrysler_invest Chrysler_value Chrysler_capital 168s "numeric" "numeric" "numeric" 168s > 168s > # SUR Pooled 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greeneSurPooled <- systemfit( formulaGrunfeld, "SUR", 168s + data = GrunfeldGreene, pooled = TRUE, methodResidCov = "noDfCor", 168s + residCovWeighted = TRUE, useMatrix = useMatrix ) 168s + print( greeneSurPooled ) 168s + print( summary( greeneSurPooled ) ) 168s + print( summary( greeneSurPooled, useDfSys = FALSE, equations = FALSE ) ) 168s + print( summary( greeneSurPooled, residCov = FALSE, equations = FALSE ) ) 168s + print( coef( greeneSurPooled ) ) 168s + print( coef( greeneSurPooled, modified.regMat = TRUE ) ) 168s + print( coef( summary( greeneSurPooled ) ) ) 168s + print( coef( summary( greeneSurPooled ), modified.regMat = TRUE ) ) 168s + print( vcov( greeneSurPooled ) ) 168s + print( vcov( greeneSurPooled, modified.regMat = TRUE ) ) 168s + print( residuals( greeneSurPooled ) ) 168s + print( confint( greeneSurPooled ) ) 168s + print( fitted( greeneSurPooled ) ) 168s + print( logLik( greeneSurPooled ) ) 168s + print( logLik( greeneSurPooled, residCovDiag = TRUE ) ) 168s + print( nobs( greeneSurPooled ) ) 168s + print( model.frame( greeneSurPooled ) ) 168s + print( model.matrix( greeneSurPooled ) ) 168s + print( formula( greeneSurPooled ) ) 168s + print( formula( greeneSurPooled$eq[[ 1 ]] ) ) 168s + print( terms( greeneSurPooled ) ) 168s + print( terms( greeneSurPooled$eq[[ 1 ]] ) ) 168s + } 168s 168s systemfit results 168s method: SUR 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_value 168s -28.2467 0.0891 168s Chrysler_capital General.Electric_(Intercept) 168s 0.3340 -28.2467 168s General.Electric_value General.Electric_capital 168s 0.0891 0.3340 168s General.Motors_(Intercept) General.Motors_value 168s -28.2467 0.0891 168s General.Motors_capital US.Steel_(Intercept) 168s 0.3340 -28.2467 168s US.Steel_value US.Steel_capital 168s 0.0891 0.3340 168s Westinghouse_(Intercept) Westinghouse_value 168s -28.2467 0.0891 168s Westinghouse_capital 168s 0.3340 168s 168s systemfit results 168s method: SUR 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 97 1604301 9.95e+16 0.279 0.844 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 6112 360 19.0 0.824 0.803 168s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 168s General.Motors 20 17 201010 11824 108.7 0.890 0.877 168s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 168s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 168s 168s The covariance matrix of the residuals used for estimation 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 409 -2594 -197 2594 -102 168s General.Electric -2594 36563 -3480 -28623 3797 168s General.Motors -197 -3480 8612 996 -971 168s US.Steel 2594 -28623 996 32903 -2272 168s Westinghouse -102 3797 -971 -2272 778 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 305.61 -1967 -4.81 2159 -124 168s General.Electric -1966.65 34557 -7160.67 -28722 4274 168s General.Motors -4.81 -7161 10050.52 4440 -1401 168s US.Steel 2158.60 -28722 4439.99 34469 -2894 168s Westinghouse -123.92 4274 -1400.75 -2894 833 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.000 0.220 -0.3447 0.2008 0.2907 168s General.Electric 0.220 1.000 -0.2233 -0.1587 0.8973 168s General.Motors -0.345 -0.223 1.0000 -0.0924 -0.3760 168s US.Steel 0.201 -0.159 -0.0924 1.0000 -0.0757 168s Westinghouse 0.291 0.897 -0.3760 -0.0757 1.0000 168s 168s 168s SUR estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 18.962 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 6112.2 MSE: 359.541 Root MSE: 18.962 168s Multiple R-Squared: 0.824 Adjusted R-Squared: 0.803 168s 168s 168s SUR estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 201.63 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 691132.056 MSE: 40654.827 Root MSE: 201.63 168s Multiple R-Squared: -14.41 Adjusted R-Squared: -16.223 168s 168s 168s SUR estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 108.739 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 201010.497 MSE: 11824.147 Root MSE: 108.739 168s Multiple R-Squared: 0.89 Adjusted R-Squared: 0.877 168s 168s 168s SUR estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 201.375 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 689379.52 MSE: 40551.736 Root MSE: 201.375 168s Multiple R-Squared: -1.168 Adjusted R-Squared: -1.424 168s 168s 168s SUR estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 31.312 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 16667.149 MSE: 980.421 Root MSE: 31.312 168s Multiple R-Squared: -1.402 Adjusted R-Squared: -1.685 168s 168s 168s systemfit results 168s method: SUR 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 97 1604301 9.95e+16 0.279 0.844 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 6112 360 19.0 0.824 0.803 168s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 168s General.Motors 20 17 201010 11824 108.7 0.890 0.877 168s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 168s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 168s 168s The covariance matrix of the residuals used for estimation 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 409 -2594 -197 2594 -102 168s General.Electric -2594 36563 -3480 -28623 3797 168s General.Motors -197 -3480 8612 996 -971 168s US.Steel 2594 -28623 996 32903 -2272 168s Westinghouse -102 3797 -971 -2272 778 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 305.61 -1967 -4.81 2159 -124 168s General.Electric -1966.65 34557 -7160.67 -28722 4274 168s General.Motors -4.81 -7161 10050.52 4440 -1401 168s US.Steel 2158.60 -28722 4439.99 34469 -2894 168s Westinghouse -123.92 4274 -1400.75 -2894 833 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.000 0.220 -0.3447 0.2008 0.2907 168s General.Electric 0.220 1.000 -0.2233 -0.1587 0.8973 168s General.Motors -0.345 -0.223 1.0000 -0.0924 -0.3760 168s US.Steel 0.201 -0.159 -0.0924 1.0000 -0.0757 168s Westinghouse 0.291 0.897 -0.3760 -0.0757 1.0000 168s 168s 168s Coefficients: 168s Estimate Std. Error t value Pr(>|t|) 168s Chrysler_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 168s Chrysler_value 0.08910 0.00507 17.57 2.5e-12 *** 168s Chrysler_capital 0.33402 0.01671 19.99 3.0e-13 *** 168s General.Electric_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 168s General.Electric_value 0.08910 0.00507 17.57 2.5e-12 *** 168s General.Electric_capital 0.33402 0.01671 19.99 3.0e-13 *** 168s General.Motors_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 168s General.Motors_value 0.08910 0.00507 17.57 2.5e-12 *** 168s General.Motors_capital 0.33402 0.01671 19.99 3.0e-13 *** 168s US.Steel_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 168s US.Steel_value 0.08910 0.00507 17.57 2.5e-12 *** 168s US.Steel_capital 0.33402 0.01671 19.99 3.0e-13 *** 168s Westinghouse_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 168s Westinghouse_value 0.08910 0.00507 17.57 2.5e-12 *** 168s Westinghouse_capital 0.33402 0.01671 19.99 3.0e-13 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s systemfit results 168s method: SUR 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 97 1604301 9.95e+16 0.279 0.844 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 6112 360 19.0 0.824 0.803 168s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 168s General.Motors 20 17 201010 11824 108.7 0.890 0.877 168s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 168s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 168s 168s 168s Coefficients: 168s Estimate Std. Error t value Pr(>|t|) 168s Chrysler_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s Chrysler_value 0.08910 0.00507 17.57 < 2e-16 *** 168s Chrysler_capital 0.33402 0.01671 19.99 < 2e-16 *** 168s General.Electric_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s General.Electric_value 0.08910 0.00507 17.57 < 2e-16 *** 168s General.Electric_capital 0.33402 0.01671 19.99 < 2e-16 *** 168s General.Motors_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s General.Motors_value 0.08910 0.00507 17.57 < 2e-16 *** 168s General.Motors_capital 0.33402 0.01671 19.99 < 2e-16 *** 168s US.Steel_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s US.Steel_value 0.08910 0.00507 17.57 < 2e-16 *** 168s US.Steel_capital 0.33402 0.01671 19.99 < 2e-16 *** 168s Westinghouse_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s Westinghouse_value 0.08910 0.00507 17.57 < 2e-16 *** 168s Westinghouse_capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s Chrysler_(Intercept) Chrysler_value 168s -28.2467 0.0891 168s Chrysler_capital General.Electric_(Intercept) 168s 0.3340 -28.2467 168s General.Electric_value General.Electric_capital 168s 0.0891 0.3340 168s General.Motors_(Intercept) General.Motors_value 168s -28.2467 0.0891 168s General.Motors_capital US.Steel_(Intercept) 168s 0.3340 -28.2467 168s US.Steel_value US.Steel_capital 168s 0.0891 0.3340 168s Westinghouse_(Intercept) Westinghouse_value 168s -28.2467 0.0891 168s Westinghouse_capital 168s 0.3340 168s C1 C2 C3 168s -28.2467 0.0891 0.3340 168s Estimate Std. Error t value Pr(>|t|) 168s Chrysler_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 168s Chrysler_value 0.0891 0.00507 17.57 0.00e+00 168s Chrysler_capital 0.3340 0.01671 19.99 0.00e+00 168s General.Electric_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 168s General.Electric_value 0.0891 0.00507 17.57 0.00e+00 168s General.Electric_capital 0.3340 0.01671 19.99 0.00e+00 168s General.Motors_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 168s General.Motors_value 0.0891 0.00507 17.57 0.00e+00 168s General.Motors_capital 0.3340 0.01671 19.99 0.00e+00 168s US.Steel_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 168s US.Steel_value 0.0891 0.00507 17.57 0.00e+00 168s US.Steel_capital 0.3340 0.01671 19.99 0.00e+00 168s Westinghouse_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 168s Westinghouse_value 0.0891 0.00507 17.57 0.00e+00 168s Westinghouse_capital 0.3340 0.01671 19.99 0.00e+00 168s Estimate Std. Error t value Pr(>|t|) 168s C1 -28.2467 4.88824 -5.78 9.12e-08 168s C2 0.0891 0.00507 17.57 0.00e+00 168s C3 0.3340 0.01671 19.99 0.00e+00 168s Chrysler_(Intercept) Chrysler_value 168s Chrysler_(Intercept) 23.89487 -1.73e-02 168s Chrysler_value -0.01729 2.57e-05 168s Chrysler_capital 0.00114 -4.74e-05 168s General.Electric_(Intercept) 23.89487 -1.73e-02 168s General.Electric_value -0.01729 2.57e-05 168s General.Electric_capital 0.00114 -4.74e-05 168s General.Motors_(Intercept) 23.89487 -1.73e-02 168s General.Motors_value -0.01729 2.57e-05 168s General.Motors_capital 0.00114 -4.74e-05 168s US.Steel_(Intercept) 23.89487 -1.73e-02 168s US.Steel_value -0.01729 2.57e-05 168s US.Steel_capital 0.00114 -4.74e-05 168s Westinghouse_(Intercept) 23.89487 -1.73e-02 168s Westinghouse_value -0.01729 2.57e-05 168s Westinghouse_capital 0.00114 -4.74e-05 168s Chrysler_capital General.Electric_(Intercept) 168s Chrysler_(Intercept) 1.14e-03 23.89487 168s Chrysler_value -4.74e-05 -0.01729 168s Chrysler_capital 2.79e-04 0.00114 168s General.Electric_(Intercept) 1.14e-03 23.89487 168s General.Electric_value -4.74e-05 -0.01729 168s General.Electric_capital 2.79e-04 0.00114 168s General.Motors_(Intercept) 1.14e-03 23.89487 168s General.Motors_value -4.74e-05 -0.01729 168s General.Motors_capital 2.79e-04 0.00114 168s US.Steel_(Intercept) 1.14e-03 23.89487 168s US.Steel_value -4.74e-05 -0.01729 168s US.Steel_capital 2.79e-04 0.00114 168s Westinghouse_(Intercept) 1.14e-03 23.89487 168s Westinghouse_value -4.74e-05 -0.01729 168s Westinghouse_capital 2.79e-04 0.00114 168s General.Electric_value General.Electric_capital 168s Chrysler_(Intercept) -1.73e-02 1.14e-03 168s Chrysler_value 2.57e-05 -4.74e-05 168s Chrysler_capital -4.74e-05 2.79e-04 168s General.Electric_(Intercept) -1.73e-02 1.14e-03 168s General.Electric_value 2.57e-05 -4.74e-05 168s General.Electric_capital -4.74e-05 2.79e-04 168s General.Motors_(Intercept) -1.73e-02 1.14e-03 168s General.Motors_value 2.57e-05 -4.74e-05 168s General.Motors_capital -4.74e-05 2.79e-04 168s US.Steel_(Intercept) -1.73e-02 1.14e-03 168s US.Steel_value 2.57e-05 -4.74e-05 168s US.Steel_capital -4.74e-05 2.79e-04 168s Westinghouse_(Intercept) -1.73e-02 1.14e-03 168s Westinghouse_value 2.57e-05 -4.74e-05 168s Westinghouse_capital -4.74e-05 2.79e-04 168s General.Motors_(Intercept) General.Motors_value 168s Chrysler_(Intercept) 23.89487 -1.73e-02 168s Chrysler_value -0.01729 2.57e-05 168s Chrysler_capital 0.00114 -4.74e-05 168s General.Electric_(Intercept) 23.89487 -1.73e-02 168s General.Electric_value -0.01729 2.57e-05 168s General.Electric_capital 0.00114 -4.74e-05 168s General.Motors_(Intercept) 23.89487 -1.73e-02 168s General.Motors_value -0.01729 2.57e-05 168s General.Motors_capital 0.00114 -4.74e-05 168s US.Steel_(Intercept) 23.89487 -1.73e-02 168s US.Steel_value -0.01729 2.57e-05 168s US.Steel_capital 0.00114 -4.74e-05 168s Westinghouse_(Intercept) 23.89487 -1.73e-02 168s Westinghouse_value -0.01729 2.57e-05 168s Westinghouse_capital 0.00114 -4.74e-05 168s General.Motors_capital US.Steel_(Intercept) 168s Chrysler_(Intercept) 1.14e-03 23.89487 168s Chrysler_value -4.74e-05 -0.01729 168s Chrysler_capital 2.79e-04 0.00114 168s General.Electric_(Intercept) 1.14e-03 23.89487 168s General.Electric_value -4.74e-05 -0.01729 168s General.Electric_capital 2.79e-04 0.00114 168s General.Motors_(Intercept) 1.14e-03 23.89487 168s General.Motors_value -4.74e-05 -0.01729 168s General.Motors_capital 2.79e-04 0.00114 168s US.Steel_(Intercept) 1.14e-03 23.89487 168s US.Steel_value -4.74e-05 -0.01729 168s US.Steel_capital 2.79e-04 0.00114 168s Westinghouse_(Intercept) 1.14e-03 23.89487 168s Westinghouse_value -4.74e-05 -0.01729 168s Westinghouse_capital 2.79e-04 0.00114 168s US.Steel_value US.Steel_capital 168s Chrysler_(Intercept) -1.73e-02 1.14e-03 168s Chrysler_value 2.57e-05 -4.74e-05 168s Chrysler_capital -4.74e-05 2.79e-04 168s General.Electric_(Intercept) -1.73e-02 1.14e-03 168s General.Electric_value 2.57e-05 -4.74e-05 168s General.Electric_capital -4.74e-05 2.79e-04 168s General.Motors_(Intercept) -1.73e-02 1.14e-03 168s General.Motors_value 2.57e-05 -4.74e-05 168s General.Motors_capital -4.74e-05 2.79e-04 168s US.Steel_(Intercept) -1.73e-02 1.14e-03 168s US.Steel_value 2.57e-05 -4.74e-05 168s US.Steel_capital -4.74e-05 2.79e-04 168s Westinghouse_(Intercept) -1.73e-02 1.14e-03 168s Westinghouse_value 2.57e-05 -4.74e-05 168s Westinghouse_capital -4.74e-05 2.79e-04 168s Westinghouse_(Intercept) Westinghouse_value 168s Chrysler_(Intercept) 23.89487 -1.73e-02 168s Chrysler_value -0.01729 2.57e-05 168s Chrysler_capital 0.00114 -4.74e-05 168s General.Electric_(Intercept) 23.89487 -1.73e-02 168s General.Electric_value -0.01729 2.57e-05 168s General.Electric_capital 0.00114 -4.74e-05 168s General.Motors_(Intercept) 23.89487 -1.73e-02 168s General.Motors_value -0.01729 2.57e-05 168s General.Motors_capital 0.00114 -4.74e-05 168s US.Steel_(Intercept) 23.89487 -1.73e-02 168s US.Steel_value -0.01729 2.57e-05 168s US.Steel_capital 0.00114 -4.74e-05 168s Westinghouse_(Intercept) 23.89487 -1.73e-02 168s Westinghouse_value -0.01729 2.57e-05 168s Westinghouse_capital 0.00114 -4.74e-05 168s Westinghouse_capital 168s Chrysler_(Intercept) 1.14e-03 168s Chrysler_value -4.74e-05 168s Chrysler_capital 2.79e-04 168s General.Electric_(Intercept) 1.14e-03 168s General.Electric_value -4.74e-05 168s General.Electric_capital 2.79e-04 168s General.Motors_(Intercept) 1.14e-03 168s General.Motors_value -4.74e-05 168s General.Motors_capital 2.79e-04 168s US.Steel_(Intercept) 1.14e-03 168s US.Steel_value -4.74e-05 168s US.Steel_capital 2.79e-04 168s Westinghouse_(Intercept) 1.14e-03 168s Westinghouse_value -4.74e-05 168s Westinghouse_capital 2.79e-04 168s C1 C2 C3 168s C1 23.89487 -1.73e-02 1.14e-03 168s C2 -0.01729 2.57e-05 -4.74e-05 168s C3 0.00114 -4.74e-05 2.79e-04 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s X1935 27.830 -75.6 70.61 98.79 23.51 168s X1936 22.951 -141.2 -12.88 205.66 7.90 168s X1937 4.160 -183.7 -93.56 220.24 -4.13 168s X1938 23.527 -161.1 -32.72 43.09 -4.84 168s X1939 -1.382 -182.3 -93.20 -20.20 -7.09 168s X1940 10.397 -149.7 6.46 8.66 -8.03 168s X1941 14.133 -96.0 49.49 201.63 16.81 168s X1942 14.586 -117.5 85.75 180.85 1.28 168s X1943 0.807 -173.2 78.44 112.17 -17.92 168s X1944 5.381 -172.6 118.21 61.60 -20.25 168s X1945 23.374 -163.8 69.60 50.68 -29.03 168s X1946 -5.596 -124.2 145.33 186.62 -14.78 168s X1947 7.005 -124.6 28.58 200.21 -5.11 168s X1948 18.909 -149.9 -40.65 275.38 -24.83 168s X1949 5.397 -207.5 -87.07 167.54 -39.09 168s X1950 12.604 -238.0 -30.56 178.08 -41.77 168s X1951 48.812 -222.9 -49.87 298.18 -25.19 168s X1952 11.406 -242.3 2.83 332.67 -25.56 168s X1953 -1.660 -270.9 182.86 279.96 -46.40 168s X1954 -0.502 -325.0 272.93 75.36 -80.40 168s 2.5 % 97.5 % 168s Chrysler_(Intercept) -37.948 -18.545 168s Chrysler_value 0.079 0.099 168s Chrysler_capital 0.301 0.367 168s General.Electric_(Intercept) -37.948 -18.545 168s General.Electric_value 0.079 0.099 168s General.Electric_capital 0.301 0.367 168s General.Motors_(Intercept) -37.948 -18.545 168s General.Motors_value 0.079 0.099 168s General.Motors_capital 0.301 0.367 168s US.Steel_(Intercept) -37.948 -18.545 168s US.Steel_value 0.079 0.099 168s US.Steel_capital 0.301 0.367 168s Westinghouse_(Intercept) -37.948 -18.545 168s Westinghouse_value 0.079 0.099 168s Westinghouse_capital 0.301 0.367 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s X1935 12.5 109 247 111 -10.6 168s X1936 49.8 186 405 150 18.0 168s X1937 62.1 261 504 250 39.2 168s X1938 28.1 206 290 219 27.7 168s X1939 53.8 230 424 251 25.9 168s X1940 59.0 224 455 253 36.6 168s X1941 54.2 209 463 271 31.7 168s X1942 32.2 209 362 265 42.1 168s X1943 46.6 234 421 249 54.9 168s X1944 54.2 229 429 227 58.1 168s X1945 65.4 257 492 208 68.3 168s X1946 79.7 284 543 234 68.2 168s X1947 55.7 272 540 220 60.7 168s X1948 70.5 296 570 219 74.4 168s X1949 73.6 306 642 238 71.1 168s X1950 88.1 331 673 241 74.0 168s X1951 111.8 358 806 290 79.6 168s X1952 133.6 400 888 313 97.3 168s X1953 176.6 450 1122 361 136.5 168s X1954 173.0 515 1214 384 149.0 168s 'log Lik.' -533 (df=18) 168s 'log Lik.' -568 (df=18) 168s [1] 100 168s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 168s X1935 40.3 418 10.5 33.1 168s X1936 72.8 838 10.2 45.0 168s X1937 66.3 884 34.7 77.2 168s X1938 51.6 438 51.8 44.6 168s X1939 52.4 680 64.3 48.1 168s X1940 69.4 728 67.1 74.4 168s X1941 68.3 644 75.2 113.0 168s X1942 46.8 411 71.4 91.9 168s X1943 47.4 588 67.1 61.3 168s X1944 59.6 698 60.5 56.8 168s X1945 88.8 846 54.6 93.6 168s X1946 74.1 894 84.8 159.9 168s X1947 62.7 579 96.8 147.2 168s X1948 89.4 695 110.2 146.3 168s X1949 79.0 590 147.4 98.3 168s X1950 100.7 694 163.2 93.5 168s X1951 160.6 809 203.5 135.2 168s X1952 145.0 727 290.6 157.3 168s X1953 174.9 1002 346.1 179.5 168s X1954 172.5 703 414.9 189.6 168s General.Electric_value General.Electric_capital General.Motors_invest 168s X1935 1171 97.8 318 168s X1936 2016 104.4 392 168s X1937 2803 118.0 411 168s X1938 2040 156.2 258 168s X1939 2256 172.6 331 168s X1940 2132 186.6 461 168s X1941 1834 220.9 512 168s X1942 1588 287.8 448 168s X1943 1749 319.9 500 168s X1944 1687 321.3 548 168s X1945 2008 319.6 561 168s X1946 2208 346.0 688 168s X1947 1657 456.4 569 168s X1948 1604 543.4 529 168s X1949 1432 618.3 555 168s X1950 1610 647.4 643 168s X1951 1819 671.3 756 168s X1952 2080 726.1 891 168s X1953 2372 800.3 1304 168s X1954 2760 888.9 1487 168s General.Motors_value General.Motors_capital US.Steel_invest 168s X1935 3078 2.8 210 168s X1936 4662 52.6 355 168s X1937 5387 156.9 470 168s X1938 2792 209.2 262 168s X1939 4313 203.4 230 168s X1940 4644 207.2 262 168s X1941 4551 255.2 473 168s X1942 3244 303.7 446 168s X1943 4054 264.1 362 168s X1944 4379 201.6 288 168s X1945 4841 265.0 259 168s X1946 4901 402.2 420 168s X1947 3526 761.5 420 168s X1948 3255 922.4 494 168s X1949 3700 1020.1 405 168s X1950 3756 1099.0 419 168s X1951 4833 1207.7 588 168s X1952 4925 1430.5 645 168s X1953 6242 1777.3 641 168s X1954 5594 2226.3 459 168s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 168s X1935 1362 53.8 12.9 192 168s X1936 1807 50.5 25.9 516 168s X1937 2676 118.1 35.0 729 168s X1938 1802 260.2 22.9 560 168s X1939 1957 312.7 18.8 520 168s X1940 2203 254.2 28.6 628 168s X1941 2380 261.4 48.5 537 168s X1942 2169 298.7 43.3 561 168s X1943 1985 301.8 37.0 617 168s X1944 1814 279.1 37.8 627 168s X1945 1850 213.8 39.3 737 168s X1946 2068 232.6 53.5 760 168s X1947 1797 264.8 55.6 581 168s X1948 1626 306.9 49.6 662 168s X1949 1667 351.1 32.0 584 168s X1950 1677 357.8 32.2 635 168s X1951 2290 342.1 54.4 724 168s X1952 2159 444.2 71.8 864 168s X1953 2031 623.6 90.1 1194 168s X1954 2116 669.7 68.6 1189 168s Westinghouse_capital 168s X1935 1.8 168s X1936 0.8 168s X1937 7.4 168s X1938 18.1 168s X1939 23.5 168s X1940 26.5 168s X1941 36.2 168s X1942 60.8 168s X1943 84.4 168s X1944 91.2 168s X1945 92.4 168s X1946 86.0 168s X1947 111.1 168s X1948 130.6 168s X1949 141.8 168s X1950 136.7 168s X1951 129.7 168s X1952 145.5 168s X1953 174.8 168s X1954 213.5 168s Chrysler_(Intercept) Chrysler_value Chrysler_capital 168s Chrysler_X1935 1 418 10.5 168s Chrysler_X1936 1 838 10.2 168s Chrysler_X1937 1 884 34.7 168s Chrysler_X1938 1 438 51.8 168s Chrysler_X1939 1 680 64.3 168s Chrysler_X1940 1 728 67.1 168s Chrysler_X1941 1 644 75.2 168s Chrysler_X1942 1 411 71.4 168s Chrysler_X1943 1 588 67.1 168s Chrysler_X1944 1 698 60.5 168s Chrysler_X1945 1 846 54.6 168s Chrysler_X1946 1 894 84.8 168s Chrysler_X1947 1 579 96.8 168s Chrysler_X1948 1 695 110.2 168s Chrysler_X1949 1 590 147.4 168s Chrysler_X1950 1 694 163.2 168s Chrysler_X1951 1 809 203.5 168s Chrysler_X1952 1 727 290.6 168s Chrysler_X1953 1 1002 346.1 168s Chrysler_X1954 1 703 414.9 168s General.Electric_X1935 0 0 0.0 168s General.Electric_X1936 0 0 0.0 168s General.Electric_X1937 0 0 0.0 168s General.Electric_X1938 0 0 0.0 168s General.Electric_X1939 0 0 0.0 168s General.Electric_X1940 0 0 0.0 168s General.Electric_X1941 0 0 0.0 168s General.Electric_X1942 0 0 0.0 168s General.Electric_X1943 0 0 0.0 168s General.Electric_X1944 0 0 0.0 168s General.Electric_X1945 0 0 0.0 168s General.Electric_X1946 0 0 0.0 168s General.Electric_X1947 0 0 0.0 168s General.Electric_X1948 0 0 0.0 168s General.Electric_X1949 0 0 0.0 168s General.Electric_X1950 0 0 0.0 168s General.Electric_X1951 0 0 0.0 168s General.Electric_X1952 0 0 0.0 168s General.Electric_X1953 0 0 0.0 168s General.Electric_X1954 0 0 0.0 168s General.Motors_X1935 0 0 0.0 168s General.Motors_X1936 0 0 0.0 168s General.Motors_X1937 0 0 0.0 168s General.Motors_X1938 0 0 0.0 168s General.Motors_X1939 0 0 0.0 168s General.Motors_X1940 0 0 0.0 168s General.Motors_X1941 0 0 0.0 168s General.Motors_X1942 0 0 0.0 168s General.Motors_X1943 0 0 0.0 168s General.Motors_X1944 0 0 0.0 168s General.Motors_X1945 0 0 0.0 168s General.Motors_X1946 0 0 0.0 168s General.Motors_X1947 0 0 0.0 168s General.Motors_X1948 0 0 0.0 168s General.Motors_X1949 0 0 0.0 168s General.Motors_X1950 0 0 0.0 168s General.Motors_X1951 0 0 0.0 168s General.Motors_X1952 0 0 0.0 168s General.Motors_X1953 0 0 0.0 168s General.Motors_X1954 0 0 0.0 168s US.Steel_X1935 0 0 0.0 168s US.Steel_X1936 0 0 0.0 168s US.Steel_X1937 0 0 0.0 168s US.Steel_X1938 0 0 0.0 168s US.Steel_X1939 0 0 0.0 168s US.Steel_X1940 0 0 0.0 168s US.Steel_X1941 0 0 0.0 168s US.Steel_X1942 0 0 0.0 168s US.Steel_X1943 0 0 0.0 168s US.Steel_X1944 0 0 0.0 168s US.Steel_X1945 0 0 0.0 168s US.Steel_X1946 0 0 0.0 168s US.Steel_X1947 0 0 0.0 168s US.Steel_X1948 0 0 0.0 168s US.Steel_X1949 0 0 0.0 168s US.Steel_X1950 0 0 0.0 168s US.Steel_X1951 0 0 0.0 168s US.Steel_X1952 0 0 0.0 168s US.Steel_X1953 0 0 0.0 168s US.Steel_X1954 0 0 0.0 168s Westinghouse_X1935 0 0 0.0 168s Westinghouse_X1936 0 0 0.0 168s Westinghouse_X1937 0 0 0.0 168s Westinghouse_X1938 0 0 0.0 168s Westinghouse_X1939 0 0 0.0 168s Westinghouse_X1940 0 0 0.0 168s Westinghouse_X1941 0 0 0.0 168s Westinghouse_X1942 0 0 0.0 168s Westinghouse_X1943 0 0 0.0 168s Westinghouse_X1944 0 0 0.0 168s Westinghouse_X1945 0 0 0.0 168s Westinghouse_X1946 0 0 0.0 168s Westinghouse_X1947 0 0 0.0 168s Westinghouse_X1948 0 0 0.0 168s Westinghouse_X1949 0 0 0.0 168s Westinghouse_X1950 0 0 0.0 168s Westinghouse_X1951 0 0 0.0 168s Westinghouse_X1952 0 0 0.0 168s Westinghouse_X1953 0 0 0.0 168s Westinghouse_X1954 0 0 0.0 168s General.Electric_(Intercept) General.Electric_value 168s Chrysler_X1935 0 0 168s Chrysler_X1936 0 0 168s Chrysler_X1937 0 0 168s Chrysler_X1938 0 0 168s Chrysler_X1939 0 0 168s Chrysler_X1940 0 0 168s Chrysler_X1941 0 0 168s Chrysler_X1942 0 0 168s Chrysler_X1943 0 0 168s Chrysler_X1944 0 0 168s Chrysler_X1945 0 0 168s Chrysler_X1946 0 0 168s Chrysler_X1947 0 0 168s Chrysler_X1948 0 0 168s Chrysler_X1949 0 0 168s Chrysler_X1950 0 0 168s Chrysler_X1951 0 0 168s Chrysler_X1952 0 0 168s Chrysler_X1953 0 0 168s Chrysler_X1954 0 0 168s General.Electric_X1935 1 1171 168s General.Electric_X1936 1 2016 168s General.Electric_X1937 1 2803 168s General.Electric_X1938 1 2040 168s General.Electric_X1939 1 2256 168s General.Electric_X1940 1 2132 168s General.Electric_X1941 1 1834 168s General.Electric_X1942 1 1588 168s General.Electric_X1943 1 1749 168s General.Electric_X1944 1 1687 168s General.Electric_X1945 1 2008 168s General.Electric_X1946 1 2208 168s General.Electric_X1947 1 1657 168s General.Electric_X1948 1 1604 168s General.Electric_X1949 1 1432 168s General.Electric_X1950 1 1610 168s General.Electric_X1951 1 1819 168s General.Electric_X1952 1 2080 168s General.Electric_X1953 1 2372 168s General.Electric_X1954 1 2760 168s General.Motors_X1935 0 0 168s General.Motors_X1936 0 0 168s General.Motors_X1937 0 0 168s General.Motors_X1938 0 0 168s General.Motors_X1939 0 0 168s General.Motors_X1940 0 0 168s General.Motors_X1941 0 0 168s General.Motors_X1942 0 0 168s General.Motors_X1943 0 0 168s General.Motors_X1944 0 0 168s General.Motors_X1945 0 0 168s General.Motors_X1946 0 0 168s General.Motors_X1947 0 0 168s General.Motors_X1948 0 0 168s General.Motors_X1949 0 0 168s General.Motors_X1950 0 0 168s General.Motors_X1951 0 0 168s General.Motors_X1952 0 0 168s General.Motors_X1953 0 0 168s General.Motors_X1954 0 0 168s US.Steel_X1935 0 0 168s US.Steel_X1936 0 0 168s US.Steel_X1937 0 0 168s US.Steel_X1938 0 0 168s US.Steel_X1939 0 0 168s US.Steel_X1940 0 0 168s US.Steel_X1941 0 0 168s US.Steel_X1942 0 0 168s US.Steel_X1943 0 0 168s US.Steel_X1944 0 0 168s US.Steel_X1945 0 0 168s US.Steel_X1946 0 0 168s US.Steel_X1947 0 0 168s US.Steel_X1948 0 0 168s US.Steel_X1949 0 0 168s US.Steel_X1950 0 0 168s US.Steel_X1951 0 0 168s US.Steel_X1952 0 0 168s US.Steel_X1953 0 0 168s US.Steel_X1954 0 0 168s Westinghouse_X1935 0 0 168s Westinghouse_X1936 0 0 168s Westinghouse_X1937 0 0 168s Westinghouse_X1938 0 0 168s Westinghouse_X1939 0 0 168s Westinghouse_X1940 0 0 168s Westinghouse_X1941 0 0 168s Westinghouse_X1942 0 0 168s Westinghouse_X1943 0 0 168s Westinghouse_X1944 0 0 168s Westinghouse_X1945 0 0 168s Westinghouse_X1946 0 0 168s Westinghouse_X1947 0 0 168s Westinghouse_X1948 0 0 168s Westinghouse_X1949 0 0 168s Westinghouse_X1950 0 0 168s Westinghouse_X1951 0 0 168s Westinghouse_X1952 0 0 168s Westinghouse_X1953 0 0 168s Westinghouse_X1954 0 0 168s General.Electric_capital General.Motors_(Intercept) 168s Chrysler_X1935 0.0 0 168s Chrysler_X1936 0.0 0 168s Chrysler_X1937 0.0 0 168s Chrysler_X1938 0.0 0 168s Chrysler_X1939 0.0 0 168s Chrysler_X1940 0.0 0 168s Chrysler_X1941 0.0 0 168s Chrysler_X1942 0.0 0 168s Chrysler_X1943 0.0 0 168s Chrysler_X1944 0.0 0 168s Chrysler_X1945 0.0 0 168s Chrysler_X1946 0.0 0 168s Chrysler_X1947 0.0 0 168s Chrysler_X1948 0.0 0 168s Chrysler_X1949 0.0 0 168s Chrysler_X1950 0.0 0 168s Chrysler_X1951 0.0 0 168s Chrysler_X1952 0.0 0 168s Chrysler_X1953 0.0 0 168s Chrysler_X1954 0.0 0 168s General.Electric_X1935 97.8 0 168s General.Electric_X1936 104.4 0 168s General.Electric_X1937 118.0 0 168s General.Electric_X1938 156.2 0 168s General.Electric_X1939 172.6 0 168s General.Electric_X1940 186.6 0 168s General.Electric_X1941 220.9 0 168s General.Electric_X1942 287.8 0 168s General.Electric_X1943 319.9 0 168s General.Electric_X1944 321.3 0 168s General.Electric_X1945 319.6 0 168s General.Electric_X1946 346.0 0 168s General.Electric_X1947 456.4 0 168s General.Electric_X1948 543.4 0 168s General.Electric_X1949 618.3 0 168s General.Electric_X1950 647.4 0 168s General.Electric_X1951 671.3 0 168s General.Electric_X1952 726.1 0 168s General.Electric_X1953 800.3 0 168s General.Electric_X1954 888.9 0 168s General.Motors_X1935 0.0 1 168s General.Motors_X1936 0.0 1 168s General.Motors_X1937 0.0 1 168s General.Motors_X1938 0.0 1 168s General.Motors_X1939 0.0 1 168s General.Motors_X1940 0.0 1 168s General.Motors_X1941 0.0 1 168s General.Motors_X1942 0.0 1 168s General.Motors_X1943 0.0 1 168s General.Motors_X1944 0.0 1 168s General.Motors_X1945 0.0 1 168s General.Motors_X1946 0.0 1 168s General.Motors_X1947 0.0 1 168s General.Motors_X1948 0.0 1 168s General.Motors_X1949 0.0 1 168s General.Motors_X1950 0.0 1 168s General.Motors_X1951 0.0 1 168s General.Motors_X1952 0.0 1 168s General.Motors_X1953 0.0 1 168s General.Motors_X1954 0.0 1 168s US.Steel_X1935 0.0 0 168s US.Steel_X1936 0.0 0 168s US.Steel_X1937 0.0 0 168s US.Steel_X1938 0.0 0 168s US.Steel_X1939 0.0 0 168s US.Steel_X1940 0.0 0 168s US.Steel_X1941 0.0 0 168s US.Steel_X1942 0.0 0 168s US.Steel_X1943 0.0 0 168s US.Steel_X1944 0.0 0 168s US.Steel_X1945 0.0 0 168s US.Steel_X1946 0.0 0 168s US.Steel_X1947 0.0 0 168s US.Steel_X1948 0.0 0 168s US.Steel_X1949 0.0 0 168s US.Steel_X1950 0.0 0 168s US.Steel_X1951 0.0 0 168s US.Steel_X1952 0.0 0 168s US.Steel_X1953 0.0 0 168s US.Steel_X1954 0.0 0 168s Westinghouse_X1935 0.0 0 168s Westinghouse_X1936 0.0 0 168s Westinghouse_X1937 0.0 0 168s Westinghouse_X1938 0.0 0 168s Westinghouse_X1939 0.0 0 168s Westinghouse_X1940 0.0 0 168s Westinghouse_X1941 0.0 0 168s Westinghouse_X1942 0.0 0 168s Westinghouse_X1943 0.0 0 168s Westinghouse_X1944 0.0 0 168s Westinghouse_X1945 0.0 0 168s Westinghouse_X1946 0.0 0 168s Westinghouse_X1947 0.0 0 168s Westinghouse_X1948 0.0 0 168s Westinghouse_X1949 0.0 0 168s Westinghouse_X1950 0.0 0 168s Westinghouse_X1951 0.0 0 168s Westinghouse_X1952 0.0 0 168s Westinghouse_X1953 0.0 0 168s Westinghouse_X1954 0.0 0 168s General.Motors_value General.Motors_capital 168s Chrysler_X1935 0 0.0 168s Chrysler_X1936 0 0.0 168s Chrysler_X1937 0 0.0 168s Chrysler_X1938 0 0.0 168s Chrysler_X1939 0 0.0 168s Chrysler_X1940 0 0.0 168s Chrysler_X1941 0 0.0 168s Chrysler_X1942 0 0.0 168s Chrysler_X1943 0 0.0 168s Chrysler_X1944 0 0.0 168s Chrysler_X1945 0 0.0 168s Chrysler_X1946 0 0.0 168s Chrysler_X1947 0 0.0 168s Chrysler_X1948 0 0.0 168s Chrysler_X1949 0 0.0 168s Chrysler_X1950 0 0.0 168s Chrysler_X1951 0 0.0 168s Chrysler_X1952 0 0.0 168s Chrysler_X1953 0 0.0 168s Chrysler_X1954 0 0.0 168s General.Electric_X1935 0 0.0 168s General.Electric_X1936 0 0.0 168s General.Electric_X1937 0 0.0 168s General.Electric_X1938 0 0.0 168s General.Electric_X1939 0 0.0 168s General.Electric_X1940 0 0.0 168s General.Electric_X1941 0 0.0 168s General.Electric_X1942 0 0.0 168s General.Electric_X1943 0 0.0 168s General.Electric_X1944 0 0.0 168s General.Electric_X1945 0 0.0 168s General.Electric_X1946 0 0.0 168s General.Electric_X1947 0 0.0 168s General.Electric_X1948 0 0.0 168s General.Electric_X1949 0 0.0 168s General.Electric_X1950 0 0.0 168s General.Electric_X1951 0 0.0 168s General.Electric_X1952 0 0.0 168s General.Electric_X1953 0 0.0 168s General.Electric_X1954 0 0.0 168s General.Motors_X1935 3078 2.8 168s General.Motors_X1936 4662 52.6 168s General.Motors_X1937 5387 156.9 168s General.Motors_X1938 2792 209.2 168s General.Motors_X1939 4313 203.4 168s General.Motors_X1940 4644 207.2 168s General.Motors_X1941 4551 255.2 168s General.Motors_X1942 3244 303.7 168s General.Motors_X1943 4054 264.1 168s General.Motors_X1944 4379 201.6 168s General.Motors_X1945 4841 265.0 168s General.Motors_X1946 4901 402.2 168s General.Motors_X1947 3526 761.5 168s General.Motors_X1948 3255 922.4 168s General.Motors_X1949 3700 1020.1 168s General.Motors_X1950 3756 1099.0 168s General.Motors_X1951 4833 1207.7 168s General.Motors_X1952 4925 1430.5 168s General.Motors_X1953 6242 1777.3 168s General.Motors_X1954 5594 2226.3 168s US.Steel_X1935 0 0.0 168s US.Steel_X1936 0 0.0 168s US.Steel_X1937 0 0.0 168s US.Steel_X1938 0 0.0 168s US.Steel_X1939 0 0.0 168s US.Steel_X1940 0 0.0 168s US.Steel_X1941 0 0.0 168s US.Steel_X1942 0 0.0 168s US.Steel_X1943 0 0.0 168s US.Steel_X1944 0 0.0 168s US.Steel_X1945 0 0.0 168s US.Steel_X1946 0 0.0 168s US.Steel_X1947 0 0.0 168s US.Steel_X1948 0 0.0 168s US.Steel_X1949 0 0.0 168s US.Steel_X1950 0 0.0 168s US.Steel_X1951 0 0.0 168s US.Steel_X1952 0 0.0 168s US.Steel_X1953 0 0.0 168s US.Steel_X1954 0 0.0 168s Westinghouse_X1935 0 0.0 168s Westinghouse_X1936 0 0.0 168s Westinghouse_X1937 0 0.0 168s Westinghouse_X1938 0 0.0 168s Westinghouse_X1939 0 0.0 168s Westinghouse_X1940 0 0.0 168s Westinghouse_X1941 0 0.0 168s Westinghouse_X1942 0 0.0 168s Westinghouse_X1943 0 0.0 168s Westinghouse_X1944 0 0.0 168s Westinghouse_X1945 0 0.0 168s Westinghouse_X1946 0 0.0 168s Westinghouse_X1947 0 0.0 168s Westinghouse_X1948 0 0.0 168s Westinghouse_X1949 0 0.0 168s Westinghouse_X1950 0 0.0 168s Westinghouse_X1951 0 0.0 168s Westinghouse_X1952 0 0.0 168s Westinghouse_X1953 0 0.0 168s Westinghouse_X1954 0 0.0 168s US.Steel_(Intercept) US.Steel_value US.Steel_capital 168s Chrysler_X1935 0 0 0.0 168s Chrysler_X1936 0 0 0.0 168s Chrysler_X1937 0 0 0.0 168s Chrysler_X1938 0 0 0.0 168s Chrysler_X1939 0 0 0.0 168s Chrysler_X1940 0 0 0.0 168s Chrysler_X1941 0 0 0.0 168s Chrysler_X1942 0 0 0.0 168s Chrysler_X1943 0 0 0.0 168s Chrysler_X1944 0 0 0.0 168s Chrysler_X1945 0 0 0.0 168s Chrysler_X1946 0 0 0.0 168s Chrysler_X1947 0 0 0.0 168s Chrysler_X1948 0 0 0.0 168s Chrysler_X1949 0 0 0.0 168s Chrysler_X1950 0 0 0.0 168s Chrysler_X1951 0 0 0.0 168s Chrysler_X1952 0 0 0.0 168s Chrysler_X1953 0 0 0.0 168s Chrysler_X1954 0 0 0.0 168s General.Electric_X1935 0 0 0.0 168s General.Electric_X1936 0 0 0.0 168s General.Electric_X1937 0 0 0.0 168s General.Electric_X1938 0 0 0.0 168s General.Electric_X1939 0 0 0.0 168s General.Electric_X1940 0 0 0.0 168s General.Electric_X1941 0 0 0.0 168s General.Electric_X1942 0 0 0.0 168s General.Electric_X1943 0 0 0.0 168s General.Electric_X1944 0 0 0.0 168s General.Electric_X1945 0 0 0.0 168s General.Electric_X1946 0 0 0.0 168s General.Electric_X1947 0 0 0.0 168s General.Electric_X1948 0 0 0.0 168s General.Electric_X1949 0 0 0.0 168s General.Electric_X1950 0 0 0.0 168s General.Electric_X1951 0 0 0.0 168s General.Electric_X1952 0 0 0.0 168s General.Electric_X1953 0 0 0.0 168s General.Electric_X1954 0 0 0.0 168s General.Motors_X1935 0 0 0.0 168s General.Motors_X1936 0 0 0.0 168s General.Motors_X1937 0 0 0.0 168s General.Motors_X1938 0 0 0.0 168s General.Motors_X1939 0 0 0.0 168s General.Motors_X1940 0 0 0.0 168s General.Motors_X1941 0 0 0.0 168s General.Motors_X1942 0 0 0.0 168s General.Motors_X1943 0 0 0.0 168s General.Motors_X1944 0 0 0.0 168s General.Motors_X1945 0 0 0.0 168s General.Motors_X1946 0 0 0.0 168s General.Motors_X1947 0 0 0.0 168s General.Motors_X1948 0 0 0.0 168s General.Motors_X1949 0 0 0.0 168s General.Motors_X1950 0 0 0.0 168s General.Motors_X1951 0 0 0.0 168s General.Motors_X1952 0 0 0.0 168s General.Motors_X1953 0 0 0.0 168s General.Motors_X1954 0 0 0.0 168s US.Steel_X1935 1 1362 53.8 168s US.Steel_X1936 1 1807 50.5 168s US.Steel_X1937 1 2676 118.1 168s US.Steel_X1938 1 1802 260.2 168s US.Steel_X1939 1 1957 312.7 168s US.Steel_X1940 1 2203 254.2 168s US.Steel_X1941 1 2380 261.4 168s US.Steel_X1942 1 2169 298.7 168s US.Steel_X1943 1 1985 301.8 168s US.Steel_X1944 1 1814 279.1 168s US.Steel_X1945 1 1850 213.8 168s US.Steel_X1946 1 2068 232.6 168s US.Steel_X1947 1 1797 264.8 168s US.Steel_X1948 1 1626 306.9 168s US.Steel_X1949 1 1667 351.1 168s US.Steel_X1950 1 1677 357.8 168s US.Steel_X1951 1 2290 342.1 168s US.Steel_X1952 1 2159 444.2 168s US.Steel_X1953 1 2031 623.6 168s US.Steel_X1954 1 2116 669.7 168s Westinghouse_X1935 0 0 0.0 168s Westinghouse_X1936 0 0 0.0 168s Westinghouse_X1937 0 0 0.0 168s Westinghouse_X1938 0 0 0.0 168s Westinghouse_X1939 0 0 0.0 168s Westinghouse_X1940 0 0 0.0 168s Westinghouse_X1941 0 0 0.0 168s Westinghouse_X1942 0 0 0.0 168s Westinghouse_X1943 0 0 0.0 168s Westinghouse_X1944 0 0 0.0 168s Westinghouse_X1945 0 0 0.0 168s Westinghouse_X1946 0 0 0.0 168s Westinghouse_X1947 0 0 0.0 168s Westinghouse_X1948 0 0 0.0 168s Westinghouse_X1949 0 0 0.0 168s Westinghouse_X1950 0 0 0.0 168s Westinghouse_X1951 0 0 0.0 168s Westinghouse_X1952 0 0 0.0 168s Westinghouse_X1953 0 0 0.0 168s Westinghouse_X1954 0 0 0.0 168s Westinghouse_(Intercept) Westinghouse_value 168s Chrysler_X1935 0 0 168s Chrysler_X1936 0 0 168s Chrysler_X1937 0 0 168s Chrysler_X1938 0 0 168s Chrysler_X1939 0 0 168s Chrysler_X1940 0 0 168s Chrysler_X1941 0 0 168s Chrysler_X1942 0 0 168s Chrysler_X1943 0 0 168s Chrysler_X1944 0 0 168s Chrysler_X1945 0 0 168s Chrysler_X1946 0 0 168s Chrysler_X1947 0 0 168s Chrysler_X1948 0 0 168s Chrysler_X1949 0 0 168s Chrysler_X1950 0 0 168s Chrysler_X1951 0 0 168s Chrysler_X1952 0 0 168s Chrysler_X1953 0 0 168s Chrysler_X1954 0 0 168s General.Electric_X1935 0 0 168s General.Electric_X1936 0 0 168s General.Electric_X1937 0 0 168s General.Electric_X1938 0 0 168s General.Electric_X1939 0 0 168s General.Electric_X1940 0 0 168s General.Electric_X1941 0 0 168s General.Electric_X1942 0 0 168s General.Electric_X1943 0 0 168s General.Electric_X1944 0 0 168s General.Electric_X1945 0 0 168s General.Electric_X1946 0 0 168s General.Electric_X1947 0 0 168s General.Electric_X1948 0 0 168s General.Electric_X1949 0 0 168s General.Electric_X1950 0 0 168s General.Electric_X1951 0 0 168s General.Electric_X1952 0 0 168s General.Electric_X1953 0 0 168s General.Electric_X1954 0 0 168s General.Motors_X1935 0 0 168s General.Motors_X1936 0 0 168s General.Motors_X1937 0 0 168s General.Motors_X1938 0 0 168s General.Motors_X1939 0 0 168s General.Motors_X1940 0 0 168s General.Motors_X1941 0 0 168s General.Motors_X1942 0 0 168s General.Motors_X1943 0 0 168s General.Motors_X1944 0 0 168s General.Motors_X1945 0 0 168s General.Motors_X1946 0 0 168s General.Motors_X1947 0 0 168s General.Motors_X1948 0 0 168s General.Motors_X1949 0 0 168s General.Motors_X1950 0 0 168s General.Motors_X1951 0 0 168s General.Motors_X1952 0 0 168s General.Motors_X1953 0 0 168s General.Motors_X1954 0 0 168s US.Steel_X1935 0 0 168s US.Steel_X1936 0 0 168s US.Steel_X1937 0 0 168s US.Steel_X1938 0 0 168s US.Steel_X1939 0 0 168s US.Steel_X1940 0 0 168s US.Steel_X1941 0 0 168s US.Steel_X1942 0 0 168s US.Steel_X1943 0 0 168s US.Steel_X1944 0 0 168s US.Steel_X1945 0 0 168s US.Steel_X1946 0 0 168s US.Steel_X1947 0 0 168s US.Steel_X1948 0 0 168s US.Steel_X1949 0 0 168s US.Steel_X1950 0 0 168s US.Steel_X1951 0 0 168s US.Steel_X1952 0 0 168s US.Steel_X1953 0 0 168s US.Steel_X1954 0 0 168s Westinghouse_X1935 1 192 168s Westinghouse_X1936 1 516 168s Westinghouse_X1937 1 729 168s Westinghouse_X1938 1 560 168s Westinghouse_X1939 1 520 168s Westinghouse_X1940 1 628 168s Westinghouse_X1941 1 537 168s Westinghouse_X1942 1 561 168s Westinghouse_X1943 1 617 168s Westinghouse_X1944 1 627 168s Westinghouse_X1945 1 737 168s Westinghouse_X1946 1 760 168s Westinghouse_X1947 1 581 168s Westinghouse_X1948 1 662 168s Westinghouse_X1949 1 584 168s Westinghouse_X1950 1 635 168s Westinghouse_X1951 1 724 168s Westinghouse_X1952 1 864 168s Westinghouse_X1953 1 1194 168s Westinghouse_X1954 1 1189 168s Westinghouse_capital 168s Chrysler_X1935 0.0 168s Chrysler_X1936 0.0 168s Chrysler_X1937 0.0 168s Chrysler_X1938 0.0 168s Chrysler_X1939 0.0 168s Chrysler_X1940 0.0 168s Chrysler_X1941 0.0 168s Chrysler_X1942 0.0 168s Chrysler_X1943 0.0 168s Chrysler_X1944 0.0 168s Chrysler_X1945 0.0 168s Chrysler_X1946 0.0 168s Chrysler_X1947 0.0 168s Chrysler_X1948 0.0 168s Chrysler_X1949 0.0 168s Chrysler_X1950 0.0 168s Chrysler_X1951 0.0 168s Chrysler_X1952 0.0 168s Chrysler_X1953 0.0 168s Chrysler_X1954 0.0 168s General.Electric_X1935 0.0 168s General.Electric_X1936 0.0 168s General.Electric_X1937 0.0 168s General.Electric_X1938 0.0 168s General.Electric_X1939 0.0 168s General.Electric_X1940 0.0 168s General.Electric_X1941 0.0 168s General.Electric_X1942 0.0 168s General.Electric_X1943 0.0 168s General.Electric_X1944 0.0 168s General.Electric_X1945 0.0 168s General.Electric_X1946 0.0 168s General.Electric_X1947 0.0 168s General.Electric_X1948 0.0 168s General.Electric_X1949 0.0 168s General.Electric_X1950 0.0 168s General.Electric_X1951 0.0 168s General.Electric_X1952 0.0 168s General.Electric_X1953 0.0 168s General.Electric_X1954 0.0 168s General.Motors_X1935 0.0 168s General.Motors_X1936 0.0 168s General.Motors_X1937 0.0 168s General.Motors_X1938 0.0 168s General.Motors_X1939 0.0 168s General.Motors_X1940 0.0 168s General.Motors_X1941 0.0 168s General.Motors_X1942 0.0 168s General.Motors_X1943 0.0 168s General.Motors_X1944 0.0 168s General.Motors_X1945 0.0 168s General.Motors_X1946 0.0 168s General.Motors_X1947 0.0 168s General.Motors_X1948 0.0 168s General.Motors_X1949 0.0 168s General.Motors_X1950 0.0 168s General.Motors_X1951 0.0 168s General.Motors_X1952 0.0 168s General.Motors_X1953 0.0 168s General.Motors_X1954 0.0 168s US.Steel_X1935 0.0 168s US.Steel_X1936 0.0 168s US.Steel_X1937 0.0 168s US.Steel_X1938 0.0 168s US.Steel_X1939 0.0 168s US.Steel_X1940 0.0 168s US.Steel_X1941 0.0 168s US.Steel_X1942 0.0 168s US.Steel_X1943 0.0 168s US.Steel_X1944 0.0 168s US.Steel_X1945 0.0 168s US.Steel_X1946 0.0 168s US.Steel_X1947 0.0 168s US.Steel_X1948 0.0 168s US.Steel_X1949 0.0 168s US.Steel_X1950 0.0 168s US.Steel_X1951 0.0 168s US.Steel_X1952 0.0 168s US.Steel_X1953 0.0 168s US.Steel_X1954 0.0 168s Westinghouse_X1935 1.8 168s Westinghouse_X1936 0.8 168s Westinghouse_X1937 7.4 168s Westinghouse_X1938 18.1 168s Westinghouse_X1939 23.5 168s Westinghouse_X1940 26.5 168s Westinghouse_X1941 36.2 168s Westinghouse_X1942 60.8 168s Westinghouse_X1943 84.4 168s Westinghouse_X1944 91.2 168s Westinghouse_X1945 92.4 168s Westinghouse_X1946 86.0 168s Westinghouse_X1947 111.1 168s Westinghouse_X1948 130.6 168s Westinghouse_X1949 141.8 168s Westinghouse_X1950 136.7 168s Westinghouse_X1951 129.7 168s Westinghouse_X1952 145.5 168s Westinghouse_X1953 174.8 168s Westinghouse_X1954 213.5 168s $Chrysler 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s 168s $General.Electric 168s General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s 168s $General.Motors 168s General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s 168s $US.Steel 168s US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s 168s $Westinghouse 168s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s $Chrysler 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s attr(,"variables") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"factors") 168s Chrysler_value Chrysler_capital 168s Chrysler_invest 0 0 168s Chrysler_value 1 0 168s Chrysler_capital 0 1 168s attr(,"term.labels") 168s [1] "Chrysler_value" "Chrysler_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"dataClasses") 168s Chrysler_invest Chrysler_value Chrysler_capital 168s "numeric" "numeric" "numeric" 168s 168s $General.Electric 168s General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s attr(,"variables") 168s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 168s attr(,"factors") 168s General.Electric_value General.Electric_capital 168s General.Electric_invest 0 0 168s General.Electric_value 1 0 168s General.Electric_capital 0 1 168s attr(,"term.labels") 168s [1] "General.Electric_value" "General.Electric_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 168s attr(,"dataClasses") 168s General.Electric_invest General.Electric_value General.Electric_capital 168s "numeric" "numeric" "numeric" 168s 168s $General.Motors 168s General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s attr(,"variables") 168s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 168s attr(,"factors") 168s General.Motors_value General.Motors_capital 168s General.Motors_invest 0 0 168s General.Motors_value 1 0 168s General.Motors_capital 0 1 168s attr(,"term.labels") 168s [1] "General.Motors_value" "General.Motors_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 168s attr(,"dataClasses") 168s General.Motors_invest General.Motors_value General.Motors_capital 168s "numeric" "numeric" "numeric" 168s 168s $US.Steel 168s US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s attr(,"variables") 168s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 168s attr(,"factors") 168s US.Steel_value US.Steel_capital 168s US.Steel_invest 0 0 168s US.Steel_value 1 0 168s US.Steel_capital 0 1 168s attr(,"term.labels") 168s [1] "US.Steel_value" "US.Steel_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 168s attr(,"dataClasses") 168s US.Steel_invest US.Steel_value US.Steel_capital 168s "numeric" "numeric" "numeric" 168s 168s $Westinghouse 168s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s attr(,"variables") 168s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 168s attr(,"factors") 168s Westinghouse_value Westinghouse_capital 168s Westinghouse_invest 0 0 168s Westinghouse_value 1 0 168s Westinghouse_capital 0 1 168s attr(,"term.labels") 168s [1] "Westinghouse_value" "Westinghouse_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 168s attr(,"dataClasses") 168s Westinghouse_invest Westinghouse_value Westinghouse_capital 168s "numeric" "numeric" "numeric" 168s 168s Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s attr(,"variables") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"factors") 168s Chrysler_value Chrysler_capital 168s Chrysler_invest 0 0 168s Chrysler_value 1 0 168s Chrysler_capital 0 1 168s attr(,"term.labels") 168s [1] "Chrysler_value" "Chrysler_capital" 168s attr(,"order") 168s [1] 1 1 168s attr(,"intercept") 168s [1] 1 168s attr(,"response") 168s [1] 1 168s attr(,".Environment") 168s 168s attr(,"predvars") 168s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 168s attr(,"dataClasses") 168s Chrysler_invest Chrysler_value Chrysler_capital 168s "numeric" "numeric" "numeric" 168s > 168s > 168s > ######### IV estimation ####################### 168s > ### 2SLS ### 168s > # instruments = explanatory variables -> 2SLS estimates = OLS estimates 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greene2sls <- systemfit( formulaGrunfeld, inst = ~ value + capital, "2SLS", 168s + data = GrunfeldGreene, useMatrix = useMatrix ) 168s + print( greene2sls ) 168s + print( summary( greene2sls ) ) 168s + print( all.equal( coef( summary( greene2sls ) ), coef( summary( greeneOls ) ) ) ) 168s + print( all.equal( greene2sls[ -c(1,2,6) ], greeneOls[ -c(1,2,6) ] ) ) 168s + for( i in 1:length( greene2sls$eq ) ) { 168s + print( all.equal( greene2sls$eq[[i]][ -c(3,15:17) ], 168s + greeneOls$eq[[i]][-3] ) ) 168s + } 168s + } 168s 168s systemfit results 168s method: 2SLS 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_value 168s -6.1900 0.0779 168s Chrysler_capital General.Electric_(Intercept) 168s 0.3157 -9.9563 168s General.Electric_value General.Electric_capital 168s 0.0266 0.1517 168s General.Motors_(Intercept) General.Motors_value 168s -149.7825 0.1193 168s General.Motors_capital US.Steel_(Intercept) 168s 0.3714 -30.3685 168s US.Steel_value US.Steel_capital 168s 0.1566 0.4239 168s Westinghouse_(Intercept) Westinghouse_value 168s -0.5094 0.0529 168s Westinghouse_capital 168s 0.0924 168s 168s systemfit results 168s method: 2SLS 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 85 339121 2.09e+14 0.848 0.862 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 2997 176 13.3 0.914 0.903 168s General.Electric 20 17 13217 777 27.9 0.705 0.671 168s General.Motors 20 17 143206 8424 91.8 0.921 0.912 168s US.Steel 20 17 177928 10466 102.3 0.440 0.374 168s Westinghouse 20 17 1773 104 10.2 0.744 0.714 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 176.3 -25.1 -333 492 15.7 168s General.Electric -25.1 777.4 715 1065 207.6 168s General.Motors -332.7 714.7 8424 -2614 148.4 168s US.Steel 491.9 1064.6 -2614 10466 642.6 168s Westinghouse 15.7 207.6 148 643 104.3 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.0000 -0.0679 -0.273 0.362 0.115 168s General.Electric -0.0679 1.0000 0.279 0.373 0.729 168s General.Motors -0.2730 0.2793 1.000 -0.278 0.158 168s US.Steel 0.3621 0.3732 -0.278 1.000 0.615 168s Westinghouse 0.1154 0.7290 0.158 0.615 1.000 168s 168s 168s 2SLS estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s Instruments: ~Chrysler_value + Chrysler_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -6.1900 13.5065 -0.46 0.6525 168s value 0.0779 0.0200 3.90 0.0011 ** 168s capital 0.3157 0.0288 10.96 4e-09 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 13.279 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 2997.444 MSE: 176.32 Root MSE: 13.279 168s Multiple R-Squared: 0.914 Adjusted R-Squared: 0.903 168s 168s 168s 2SLS estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s Instruments: ~General.Electric_value + General.Electric_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -9.9563 31.3742 -0.32 0.75 168s value 0.0266 0.0156 1.71 0.11 168s capital 0.1517 0.0257 5.90 1.7e-05 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 27.883 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 168s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 168s 168s 168s 2SLS estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s Instruments: ~General.Motors_value + General.Motors_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -149.7825 105.8421 -1.42 0.17508 168s value 0.1193 0.0258 4.62 0.00025 *** 168s capital 0.3714 0.0371 10.02 1.5e-08 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 91.782 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 143205.877 MSE: 8423.875 Root MSE: 91.782 168s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.912 168s 168s 168s 2SLS estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s Instruments: ~US.Steel_value + US.Steel_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -30.3685 157.0477 -0.19 0.849 168s value 0.1566 0.0789 1.98 0.064 . 168s capital 0.4239 0.1552 2.73 0.014 * 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 102.305 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 177928.314 MSE: 10466.371 Root MSE: 102.305 168s Multiple R-Squared: 0.44 Adjusted R-Squared: 0.374 168s 168s 168s 2SLS estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s Instruments: ~Westinghouse_value + Westinghouse_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -0.5094 8.0153 -0.06 0.9501 168s value 0.0529 0.0157 3.37 0.0037 ** 168s capital 0.0924 0.0561 1.65 0.1179 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 10.213 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 168s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 168s 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s > # 'real' IV/2SLS estimation 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greene2slsR <- systemfit( invest ~ capital, inst = ~ value, "2SLS", 168s + data = GrunfeldGreene, useMatrix = useMatrix ) 168s + print( greene2slsR ) 168s + print( summary( greene2slsR ) ) 168s + } 168s 168s systemfit results 168s method: 2SLS 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_capital 168s 4.314 0.675 168s General.Electric_(Intercept) General.Electric_capital 168s -106.788 0.522 168s General.Motors_(Intercept) General.Motors_capital 168s 110.940 0.767 168s US.Steel_(Intercept) US.Steel_capital 168s -323.878 2.432 168s Westinghouse_(Intercept) Westinghouse_capital 168s 13.163 0.347 168s 168s systemfit results 168s method: 2SLS 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 90 3239824 2.75e+17 -0.456 0.476 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 18 30374 1687 41.1 0.124 0.076 168s General.Electric 20 18 174998 9722 98.6 -2.902 -3.119 168s General.Motors 20 18 1100181 61121 247.2 0.396 0.362 168s US.Steel 20 18 1930347 107242 327.5 -5.072 -5.409 168s Westinghouse 20 18 3924 218 14.8 0.434 0.403 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1687 3089 6820 11741 179 168s General.Electric 3089 9722 20780 23319 886 168s General.Motors 6820 20780 61121 44203 1908 168s US.Steel 11741 23319 44203 107242 1977 168s Westinghouse 179 886 1908 1977 218 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.000 0.763 0.672 0.873 0.295 168s General.Electric 0.763 1.000 0.852 0.722 0.608 168s General.Motors 0.672 0.852 1.000 0.546 0.523 168s US.Steel 0.873 0.722 0.546 1.000 0.409 168s Westinghouse 0.295 0.608 0.523 0.409 1.000 168s 168s 168s 2SLS estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_capital 168s 168s Instruments: ~Chrysler_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 4.314 34.033 0.13 0.901 168s capital 0.675 0.270 2.50 0.022 * 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 41.078 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 30373.531 MSE: 1687.418 Root MSE: 41.078 168s Multiple R-Squared: 0.124 Adjusted R-Squared: 0.076 168s 168s 168s 2SLS estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_capital 168s 168s Instruments: ~General.Electric_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -106.788 306.251 -0.35 0.73 168s capital 0.522 0.763 0.68 0.50 168s 168s Residual standard error: 98.601 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 174998.166 MSE: 9722.12 Root MSE: 98.601 168s Multiple R-Squared: -2.902 Adjusted R-Squared: -3.119 168s 168s 168s 2SLS estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_capital 168s 168s Instruments: ~General.Motors_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 110.940 145.626 0.76 0.4560 168s capital 0.767 0.208 3.69 0.0017 ** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 247.227 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 1100180.666 MSE: 61121.148 Root MSE: 247.227 168s Multiple R-Squared: 0.396 Adjusted R-Squared: 0.362 168s 168s 168s 2SLS estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_capital 168s 168s Instruments: ~US.Steel_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -323.88 962.57 -0.34 0.74 168s capital 2.43 3.20 0.76 0.46 168s 168s Residual standard error: 327.478 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 1930347.395 MSE: 107241.522 Root MSE: 327.478 168s Multiple R-Squared: -5.072 Adjusted R-Squared: -5.409 168s 168s 168s 2SLS estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_capital 168s 168s Instruments: ~Westinghouse_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 13.1626 7.0965 1.85 0.08008 . 168s capital 0.3471 0.0734 4.73 0.00017 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 14.765 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 3923.899 MSE: 217.994 Root MSE: 14.765 168s Multiple R-Squared: 0.434 Adjusted R-Squared: 0.403 168s 168s > 168s > ### 2SLS, pooled ### 168s > # instruments = explanatory variables -> 2SLS estimates = OLS estimates 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greene2slsPooled <- systemfit( formulaGrunfeld, inst = ~ value + capital, "2SLS", 168s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix ) 168s + print( greene2slsPooled ) 168s + print( summary( greene2slsPooled ) ) 168s + print( all.equal( coef( summary( greene2slsPooled ) ), 168s + coef( summary( greeneOlsPooled ) ) ) ) 168s + print( all.equal( greene2slsPooled[ -c(1,2,6) ], greeneOlsPooled[ -c(1,2,6) ] ) ) 168s + for( i in 1:length( greene2slsPooled$eq ) ) { 168s + print( all.equal( greene2slsPooled$eq[[i]][ -c(3,15:17) ], 168s + greeneOlsPooled$eq[[i]][-3] ) ) 168s + } 168s + } 168s 168s systemfit results 168s method: 2SLS 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_value 168s -48.030 0.105 168s Chrysler_capital General.Electric_(Intercept) 168s 0.305 -48.030 168s General.Electric_value General.Electric_capital 168s 0.105 0.305 168s General.Motors_(Intercept) General.Motors_value 168s -48.030 0.105 168s General.Motors_capital US.Steel_(Intercept) 168s 0.305 -48.030 168s US.Steel_value US.Steel_capital 168s 0.105 0.305 168s Westinghouse_(Intercept) Westinghouse_value 168s -48.030 0.105 168s Westinghouse_capital 168s 0.305 168s 168s systemfit results 168s method: 2SLS 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 97 1570884 4.2e+17 0.294 0.812 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 15117 889 29.8 0.564 0.513 168s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 168s General.Motors 20 17 188218 11072 105.2 0.897 0.884 168s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 168s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 889.2 -4898 -198 4748 -94.6 168s General.Electric -4898.1 40339 -2254 -32821 2658.0 168s General.Motors -197.7 -2254 11072 304 -1328.6 168s US.Steel 4748.1 -32821 304 39359 -1377.3 168s Westinghouse -94.6 2658 -1329 -1377 745.2 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.000 0.144 -0.1852 0.2218 0.186 168s General.Electric 0.144 1.000 -0.2592 -0.1216 0.881 168s General.Motors -0.185 -0.259 1.0000 -0.0155 -0.469 168s US.Steel 0.222 -0.122 -0.0155 1.0000 -0.119 168s Westinghouse 0.186 0.881 -0.4689 -0.1186 1.000 168s 168s 168s 2SLS estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s Instruments: ~Chrysler_value + Chrysler_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -48.0297 21.4802 -2.24 0.028 * 168s value 0.1051 0.0114 9.24 6.0e-15 *** 168s capital 0.3054 0.0435 7.02 3.1e-10 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 29.82 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 15117.016 MSE: 889.236 Root MSE: 29.82 168s Multiple R-Squared: 0.564 Adjusted R-Squared: 0.513 168s 168s 168s 2SLS estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s Instruments: ~General.Electric_value + General.Electric_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -48.0297 21.4802 -2.24 0.028 * 168s value 0.1051 0.0114 9.24 6.0e-15 *** 168s capital 0.3054 0.0435 7.02 3.1e-10 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 200.847 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 685769.815 MSE: 40339.401 Root MSE: 200.847 168s Multiple R-Squared: -14.291 Adjusted R-Squared: -16.09 168s 168s 168s 2SLS estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s Instruments: ~General.Motors_value + General.Motors_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -48.0297 21.4802 -2.24 0.028 * 168s value 0.1051 0.0114 9.24 6.0e-15 *** 168s capital 0.3054 0.0435 7.02 3.1e-10 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 105.222 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 188218.158 MSE: 11071.656 Root MSE: 105.222 168s Multiple R-Squared: 0.897 Adjusted R-Squared: 0.884 168s 168s 168s 2SLS estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s Instruments: ~US.Steel_value + US.Steel_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -48.0297 21.4802 -2.24 0.028 * 168s value 0.1051 0.0114 9.24 6.0e-15 *** 168s capital 0.3054 0.0435 7.02 3.1e-10 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 198.392 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 669110.225 MSE: 39359.425 Root MSE: 198.392 168s Multiple R-Squared: -1.105 Adjusted R-Squared: -1.352 168s 168s 168s 2SLS estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s Instruments: ~Westinghouse_value + Westinghouse_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -48.0297 21.4802 -2.24 0.028 * 168s value 0.1051 0.0114 9.24 6.0e-15 *** 168s capital 0.3054 0.0435 7.02 3.1e-10 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 27.298 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 12668.473 MSE: 745.204 Root MSE: 27.298 168s Multiple R-Squared: -0.826 Adjusted R-Squared: -1.041 168s 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s > # 'real' IV/2SLS estimation 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greene2slsRPooled <- systemfit( invest ~ capital, inst = ~ value, "2SLS", 168s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix ) 168s + print( greene2slsRPooled ) 168s + print( summary( greene2slsRPooled ) ) 168s + } 168s 168s systemfit results 168s method: 2SLS 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_capital 168s -15.105 0.849 168s General.Electric_(Intercept) General.Electric_capital 168s -15.105 0.849 168s General.Motors_(Intercept) General.Motors_capital 168s -15.105 0.849 168s US.Steel_(Intercept) US.Steel_capital 168s -15.105 0.849 168s Westinghouse_(Intercept) Westinghouse_capital 168s -15.105 0.849 168s 168s systemfit results 168s method: 2SLS 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 98 4164182 2.53e+19 -0.871 -0.832 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 18 64130 3563 59.7 -0.849 -0.952 168s General.Electric 20 18 1575287 87516 295.8 -34.125 -36.076 168s General.Motors 20 18 1655592 91977 303.3 0.091 0.040 168s US.Steel 20 18 833908 46328 215.2 -1.623 -1.769 168s Westinghouse 20 18 35264 1959 44.3 -4.082 -4.365 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 3563 9506 13222 2659 1862 168s General.Electric 9506 87516 29381 -35898 10615 168s General.Motors 13222 29381 91977 17584 8562 168s US.Steel 2659 -35898 17584 46328 -762 168s Westinghouse 1862 10615 8562 -762 1959 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.000 0.843 0.763 0.397 0.742 168s General.Electric 0.843 1.000 0.893 0.226 0.933 168s General.Motors 0.763 0.893 1.000 0.114 0.801 168s US.Steel 0.397 0.226 0.114 1.000 0.375 168s Westinghouse 0.742 0.933 0.801 0.375 1.000 168s 168s 168s 2SLS estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_capital 168s 168s Instruments: ~Chrysler_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -15.1045 33.8915 -0.45 0.66 168s capital 0.8489 0.0865 9.82 4.4e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 59.689 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 64130.003 MSE: 3562.778 Root MSE: 59.689 168s Multiple R-Squared: -0.849 Adjusted R-Squared: -0.952 168s 168s 168s 2SLS estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_capital 168s 168s Instruments: ~General.Electric_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -15.1045 33.8915 -0.45 0.66 168s capital 0.8489 0.0865 9.82 4.4e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 295.831 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 1575287.29 MSE: 87515.961 Root MSE: 295.831 168s Multiple R-Squared: -34.125 Adjusted R-Squared: -36.076 168s 168s 168s 2SLS estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_capital 168s 168s Instruments: ~General.Motors_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -15.1045 33.8915 -0.45 0.66 168s capital 0.8489 0.0865 9.82 4.4e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 303.278 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 1655591.854 MSE: 91977.325 Root MSE: 303.278 168s Multiple R-Squared: 0.091 Adjusted R-Squared: 0.04 168s 168s 168s 2SLS estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_capital 168s 168s Instruments: ~US.Steel_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -15.1045 33.8915 -0.45 0.66 168s capital 0.8489 0.0865 9.82 4.4e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 215.24 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 833908.389 MSE: 46328.244 Root MSE: 215.24 168s Multiple R-Squared: -1.623 Adjusted R-Squared: -1.769 168s 168s 168s 2SLS estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_capital 168s 168s Instruments: ~Westinghouse_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -15.1045 33.8915 -0.45 0.66 168s capital 0.8489 0.0865 9.82 4.4e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 44.262 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 35264.462 MSE: 1959.137 Root MSE: 44.262 168s Multiple R-Squared: -4.082 Adjusted R-Squared: -4.365 168s 168s > 168s > ### 3SLS ### 168s > # instruments = explanatory variables -> 3SLS estimates = SUR estimates 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greene3sls <- systemfit( formulaGrunfeld, inst = ~ value + capital, "3SLS", 168s + data = GrunfeldGreene, useMatrix = useMatrix, methodResidCov = "noDfCor" ) 168s + print( greene3sls ) 168s + print( summary( greene3sls ) ) 168s + print( all.equal( coef( summary( greene3sls ) ), coef( summary( greeneSur ) ) ) ) 168s + print( all.equal( greene3sls[ -c(1,2,7) ], greeneSur[ -c(1,2,7) ] ) ) 168s + for( i in 1:length( greene3sls$eq ) ) { 168s + print( all.equal( greene3sls$eq[[i]][ -c(3,15:17) ], 168s + greeneSur$eq[[i]][-3] ) ) 168s + } 168s + } 168s 168s systemfit results 168s method: 3SLS 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_value 168s 0.5043 0.0695 168s Chrysler_capital General.Electric_(Intercept) 168s 0.3085 -22.4389 168s General.Electric_value General.Electric_capital 168s 0.0373 0.1308 168s General.Motors_(Intercept) General.Motors_value 168s -162.3641 0.1205 168s General.Motors_capital US.Steel_(Intercept) 168s 0.3827 85.4233 168s US.Steel_value US.Steel_capital 168s 0.1015 0.4000 168s Westinghouse_(Intercept) Westinghouse_value 168s 1.0889 0.0570 168s Westinghouse_capital 168s 0.0415 168s 168s systemfit results 168s method: 3SLS 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 85 347048 6.18e+13 0.844 0.869 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 3057 180 13.4 0.912 0.901 168s General.Electric 20 17 14009 824 28.7 0.688 0.651 168s General.Motors 20 17 144321 8489 92.1 0.921 0.911 168s US.Steel 20 17 183763 10810 104.0 0.422 0.354 168s Westinghouse 20 17 1898 112 10.6 0.726 0.694 168s 168s The covariance matrix of the residuals used for estimation 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 149.9 -21.4 -283 418 13.3 168s General.Electric -21.4 660.8 608 905 176.4 168s General.Motors -282.8 607.5 7160 -2222 126.2 168s US.Steel 418.1 905.0 -2222 8896 546.2 168s Westinghouse 13.3 176.4 126 546 88.7 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 152.85 2.05 -314 455 16.7 168s General.Electric 2.05 700.46 605 1224 200.3 168s General.Motors -313.70 605.34 7216 -2687 129.9 168s US.Steel 455.09 1224.41 -2687 9188 652.7 168s Westinghouse 16.66 200.32 130 653 94.9 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.00000 0.00626 -0.299 0.384 0.138 168s General.Electric 0.00626 1.00000 0.269 0.483 0.777 168s General.Motors -0.29870 0.26925 1.000 -0.330 0.157 168s US.Steel 0.38402 0.48264 -0.330 1.000 0.699 168s Westinghouse 0.13832 0.77690 0.157 0.699 1.000 168s 168s 168s 3SLS estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s Instruments: ~Chrysler_value + Chrysler_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 0.5043 11.5128 0.04 0.96557 168s value 0.0695 0.0169 4.12 0.00072 *** 168s capital 0.3085 0.0259 11.93 1.1e-09 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 13.41 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 3056.985 MSE: 179.823 Root MSE: 13.41 168s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.901 168s 168s 168s 3SLS estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s Instruments: ~General.Electric_value + General.Electric_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -22.4389 25.5186 -0.88 0.3915 168s value 0.0373 0.0123 3.04 0.0074 ** 168s capital 0.1308 0.0220 5.93 1.6e-05 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 28.707 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 14009.115 MSE: 824.066 Root MSE: 28.707 168s Multiple R-Squared: 0.688 Adjusted R-Squared: 0.651 168s 168s 168s 3SLS estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s Instruments: ~General.Motors_value + General.Motors_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -162.3641 89.4592 -1.81 0.087 . 168s value 0.1205 0.0216 5.57 3.4e-05 *** 168s capital 0.3827 0.0328 11.68 1.5e-09 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 92.138 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 144320.876 MSE: 8489.463 Root MSE: 92.138 168s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.911 168s 168s 168s 3SLS estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s Instruments: ~US.Steel_value + US.Steel_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 85.4233 111.8774 0.76 0.4556 168s value 0.1015 0.0548 1.85 0.0814 . 168s capital 0.4000 0.1278 3.13 0.0061 ** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 103.969 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 183763.011 MSE: 10809.589 Root MSE: 103.969 168s Multiple R-Squared: 0.422 Adjusted R-Squared: 0.354 168s 168s 168s 3SLS estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s Instruments: ~Westinghouse_value + Westinghouse_capital 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 1.0889 6.2588 0.17 0.86394 168s value 0.0570 0.0114 5.02 0.00011 *** 168s capital 0.0415 0.0412 1.01 0.32787 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 10.567 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 1898.249 MSE: 111.662 Root MSE: 10.567 168s Multiple R-Squared: 0.726 Adjusted R-Squared: 0.694 168s 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s > # 'real' IV/3SLS estimation 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greene3slsR <- systemfit( invest ~ capital, inst = ~ value, "3SLS", 168s + data = GrunfeldGreene, useMatrix = useMatrix ) 168s + print( greene3slsR ) 168s + print( summary( greene3slsR ) ) 168s + } 168s 168s systemfit results 168s method: 3SLS 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_capital 168s 23.499 0.517 168s General.Electric_(Intercept) General.Electric_capital 168s -108.596 0.527 168s General.Motors_(Intercept) General.Motors_capital 168s 199.856 0.629 168s US.Steel_(Intercept) US.Steel_capital 168s 181.691 0.746 168s Westinghouse_(Intercept) Westinghouse_capital 168s 11.668 0.365 168s 168s systemfit results 168s method: 3SLS 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 90 1026043 4.46e+16 0.539 0.539 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 18 12139 674 26.0 0.650 0.631 168s General.Electric 20 18 178965 9942 99.7 -2.990 -3.212 168s General.Motors 20 18 577860 32103 179.2 0.683 0.665 168s US.Steel 20 18 252838 14047 118.5 0.205 0.160 168s Westinghouse 20 18 4241 236 15.3 0.389 0.355 168s 168s The covariance matrix of the residuals used for estimation 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1687 3089 6820 11741 179 168s General.Electric 3089 9722 20780 23319 886 168s General.Motors 6820 20780 61121 44203 1908 168s US.Steel 11741 23319 44203 107242 1977 168s Westinghouse 179 886 1908 1977 218 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 674 1587 1944 1371 137 168s General.Electric 1587 9942 13003 2009 996 168s General.Motors 1944 13003 32103 -908 1571 168s US.Steel 1371 2009 -908 14047 888 168s Westinghouse 137 996 1571 888 236 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.000 0.613 0.4178 0.4454 0.343 168s General.Electric 0.613 1.000 0.7278 0.1700 0.651 168s General.Motors 0.418 0.728 1.0000 -0.0428 0.571 168s US.Steel 0.445 0.170 -0.0428 1.0000 0.488 168s Westinghouse 0.343 0.651 0.5713 0.4880 1.000 168s 168s 168s 3SLS estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_capital 168s 168s Instruments: ~Chrysler_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 23.499 17.165 1.37 0.18784 168s capital 0.517 0.120 4.32 0.00041 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 25.969 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 12138.974 MSE: 674.387 Root MSE: 25.969 168s Multiple R-Squared: 0.65 Adjusted R-Squared: 0.631 168s 168s 168s 3SLS estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_capital 168s 168s Instruments: ~General.Electric_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -108.596 152.939 -0.71 0.49 168s capital 0.527 0.378 1.39 0.18 168s 168s Residual standard error: 99.712 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 178964.956 MSE: 9942.498 Root MSE: 99.712 168s Multiple R-Squared: -2.99 Adjusted R-Squared: -3.212 168s 168s 168s 3SLS estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_capital 168s 168s Instruments: ~General.Motors_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 199.856 98.953 2.02 0.059 . 168s capital 0.629 0.127 4.97 9.8e-05 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 179.174 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 577859.714 MSE: 32103.317 Root MSE: 179.174 168s Multiple R-Squared: 0.683 Adjusted R-Squared: 0.665 168s 168s 168s 3SLS estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_capital 168s 168s Instruments: ~US.Steel_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 181.691 448.797 0.40 0.69 168s capital 0.746 1.477 0.51 0.62 168s 168s Residual standard error: 118.518 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 252838.286 MSE: 14046.571 Root MSE: 118.518 168s Multiple R-Squared: 0.205 Adjusted R-Squared: 0.16 168s 168s 168s 3SLS estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_capital 168s 168s Instruments: ~Westinghouse_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 11.6685 5.9043 1.98 0.064 . 168s capital 0.3646 0.0572 6.38 5.2e-06 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 15.349 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 4240.92 MSE: 235.607 Root MSE: 15.349 168s Multiple R-Squared: 0.389 Adjusted R-Squared: 0.355 168s 168s > 168s > ### 3SLS, Pooled ### 168s > # instruments = explanatory variables -> 3SLS estimates = SUR estimates 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greene3slsPooled <- systemfit( formulaGrunfeld, inst = ~ capital + value, "3SLS", 168s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix, 168s + residCovWeighted = TRUE, methodResidCov = "noDfCor" ) 168s + print( greene3slsPooled ) 168s + print( summary( greene3slsPooled ) ) 168s + print( all.equal( coef( summary( greene3slsPooled ) ), 168s + coef( summary( greeneSurPooled ) ) ) ) 168s + print( all.equal( greene3slsPooled[ -c(1,2,7) ], greeneSurPooled[ -c(1,2,7) ] ) ) 168s + for( i in 1:length( greene3slsPooled$eq ) ) { 168s + print( all.equal( greene3slsPooled$eq[[i]][ -c(3,15:17) ], 168s + greeneSurPooled$eq[[i]][-3] ) ) 168s + } 168s + } 168s 168s systemfit results 168s method: 3SLS 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_value 168s -28.2467 0.0891 168s Chrysler_capital General.Electric_(Intercept) 168s 0.3340 -28.2467 168s General.Electric_value General.Electric_capital 168s 0.0891 0.3340 168s General.Motors_(Intercept) General.Motors_value 168s -28.2467 0.0891 168s General.Motors_capital US.Steel_(Intercept) 168s 0.3340 -28.2467 168s US.Steel_value US.Steel_capital 168s 0.0891 0.3340 168s Westinghouse_(Intercept) Westinghouse_value 168s -28.2467 0.0891 168s Westinghouse_capital 168s 0.3340 168s 168s systemfit results 168s method: 3SLS 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 97 1604301 9.95e+16 0.279 0.844 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 17 6112 360 19.0 0.824 0.803 168s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 168s General.Motors 20 17 201010 11824 108.7 0.890 0.877 168s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 168s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 168s 168s The covariance matrix of the residuals used for estimation 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 409 -2594 -197 2594 -102 168s General.Electric -2594 36563 -3480 -28623 3797 168s General.Motors -197 -3480 8612 996 -971 168s US.Steel 2594 -28623 996 32903 -2272 168s Westinghouse -102 3797 -971 -2272 778 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 305.61 -1967 -4.81 2159 -124 168s General.Electric -1966.65 34557 -7160.67 -28722 4274 168s General.Motors -4.81 -7161 10050.52 4440 -1401 168s US.Steel 2158.60 -28722 4439.99 34469 -2894 168s Westinghouse -123.92 4274 -1400.75 -2894 833 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.000 0.220 -0.3447 0.2008 0.2907 168s General.Electric 0.220 1.000 -0.2233 -0.1587 0.8973 168s General.Motors -0.345 -0.223 1.0000 -0.0924 -0.3760 168s US.Steel 0.201 -0.159 -0.0924 1.0000 -0.0757 168s Westinghouse 0.291 0.897 -0.3760 -0.0757 1.0000 168s 168s 168s 3SLS estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 168s 168s Instruments: ~Chrysler_capital + Chrysler_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 18.962 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 6112.2 MSE: 359.541 Root MSE: 18.962 168s Multiple R-Squared: 0.824 Adjusted R-Squared: 0.803 168s 168s 168s 3SLS estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 168s 168s Instruments: ~General.Electric_capital + General.Electric_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 201.63 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 691132.056 MSE: 40654.827 Root MSE: 201.63 168s Multiple R-Squared: -14.41 Adjusted R-Squared: -16.223 168s 168s 168s 3SLS estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 168s 168s Instruments: ~General.Motors_capital + General.Motors_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 108.739 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 201010.497 MSE: 11824.147 Root MSE: 108.739 168s Multiple R-Squared: 0.89 Adjusted R-Squared: 0.877 168s 168s 168s 3SLS estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 168s 168s Instruments: ~US.Steel_capital + US.Steel_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 201.375 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 689379.52 MSE: 40551.736 Root MSE: 201.375 168s Multiple R-Squared: -1.168 Adjusted R-Squared: -1.424 168s 168s 168s 3SLS estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 168s 168s Instruments: ~Westinghouse_capital + Westinghouse_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 168s value 0.08910 0.00507 17.57 < 2e-16 *** 168s capital 0.33402 0.01671 19.99 < 2e-16 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 31.312 on 17 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 17 168s SSR: 16667.149 MSE: 980.421 Root MSE: 31.312 168s Multiple R-Squared: -1.402 Adjusted R-Squared: -1.685 168s 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s [1] TRUE 168s > # 'real' IV/3SLS estimation 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + greene3slsRPooled <- systemfit( invest ~ capital, inst = ~ value, "3SLS", 168s + data = GrunfeldGreene, useMatrix = useMatrix ) 168s + print( greene3slsRPooled ) 168s + print( summary( greene3slsRPooled ) ) 168s + } 168s 168s systemfit results 168s method: 3SLS 168s 168s Coefficients: 168s Chrysler_(Intercept) Chrysler_capital 168s 23.499 0.517 168s General.Electric_(Intercept) General.Electric_capital 168s -108.596 0.527 168s General.Motors_(Intercept) General.Motors_capital 168s 199.856 0.629 168s US.Steel_(Intercept) US.Steel_capital 168s 181.691 0.746 168s Westinghouse_(Intercept) Westinghouse_capital 168s 11.668 0.365 168s 168s systemfit results 168s method: 3SLS 168s 168s N DF SSR detRCov OLS-R2 McElroy-R2 168s system 100 90 1026043 4.46e+16 0.539 0.539 168s 168s N DF SSR MSE RMSE R2 Adj R2 168s Chrysler 20 18 12139 674 26.0 0.650 0.631 168s General.Electric 20 18 178965 9942 99.7 -2.990 -3.212 168s General.Motors 20 18 577860 32103 179.2 0.683 0.665 168s US.Steel 20 18 252838 14047 118.5 0.205 0.160 168s Westinghouse 20 18 4241 236 15.3 0.389 0.355 168s 168s The covariance matrix of the residuals used for estimation 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1687 3089 6820 11741 179 168s General.Electric 3089 9722 20780 23319 886 168s General.Motors 6820 20780 61121 44203 1908 168s US.Steel 11741 23319 44203 107242 1977 168s Westinghouse 179 886 1908 1977 218 168s 168s The covariance matrix of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 674 1587 1944 1371 137 168s General.Electric 1587 9942 13003 2009 996 168s General.Motors 1944 13003 32103 -908 1571 168s US.Steel 1371 2009 -908 14047 888 168s Westinghouse 137 996 1571 888 236 168s 168s The correlations of the residuals 168s Chrysler General.Electric General.Motors US.Steel Westinghouse 168s Chrysler 1.000 0.613 0.4178 0.4454 0.343 168s General.Electric 0.613 1.000 0.7278 0.1700 0.651 168s General.Motors 0.418 0.728 1.0000 -0.0428 0.571 168s US.Steel 0.445 0.170 -0.0428 1.0000 0.488 168s Westinghouse 0.343 0.651 0.5713 0.4880 1.000 168s 168s 168s 3SLS estimates for 'Chrysler' (equation 1) 168s Model Formula: Chrysler_invest ~ Chrysler_capital 168s 168s Instruments: ~Chrysler_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 23.499 17.165 1.37 0.18784 168s capital 0.517 0.120 4.32 0.00041 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 25.969 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 12138.974 MSE: 674.387 Root MSE: 25.969 168s Multiple R-Squared: 0.65 Adjusted R-Squared: 0.631 168s 168s 168s 3SLS estimates for 'General.Electric' (equation 2) 168s Model Formula: General.Electric_invest ~ General.Electric_capital 168s 168s Instruments: ~General.Electric_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) -108.596 152.939 -0.71 0.49 168s capital 0.527 0.378 1.39 0.18 168s 168s Residual standard error: 99.712 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 178964.956 MSE: 9942.498 Root MSE: 99.712 168s Multiple R-Squared: -2.99 Adjusted R-Squared: -3.212 168s 168s 168s 3SLS estimates for 'General.Motors' (equation 3) 168s Model Formula: General.Motors_invest ~ General.Motors_capital 168s 168s Instruments: ~General.Motors_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 199.856 98.953 2.02 0.059 . 168s capital 0.629 0.127 4.97 9.8e-05 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 179.174 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 577859.714 MSE: 32103.317 Root MSE: 179.174 168s Multiple R-Squared: 0.683 Adjusted R-Squared: 0.665 168s 168s 168s 3SLS estimates for 'US.Steel' (equation 4) 168s Model Formula: US.Steel_invest ~ US.Steel_capital 168s 168s Instruments: ~US.Steel_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 181.691 448.797 0.40 0.69 168s capital 0.746 1.477 0.51 0.62 168s 168s Residual standard error: 118.518 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 252838.286 MSE: 14046.571 Root MSE: 118.518 168s Multiple R-Squared: 0.205 Adjusted R-Squared: 0.16 168s 168s 168s 3SLS estimates for 'Westinghouse' (equation 5) 168s Model Formula: Westinghouse_invest ~ Westinghouse_capital 168s 168s Instruments: ~Westinghouse_value 168s 168s 168s Estimate Std. Error t value Pr(>|t|) 168s (Intercept) 11.6685 5.9043 1.98 0.064 . 168s capital 0.3646 0.0572 6.38 5.2e-06 *** 168s --- 168s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 168s 168s Residual standard error: 15.349 on 18 degrees of freedom 168s Number of observations: 20 Degrees of Freedom: 18 168s SSR: 4240.92 MSE: 235.607 Root MSE: 15.349 168s Multiple R-Squared: 0.389 Adjusted R-Squared: 0.355 168s 168s > 168s > 168s > ## **************** estfun ************************ 168s > library( "sandwich" ) 168s > 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + print( estfun( theilOls ) ) 168s + print( round( colSums( estfun( theilOls ) ), digits = 7 ) ) 168s + 168s + print( estfun( theilSur ) ) 168s + print( round( colSums( estfun( theilSur ) ), digits = 7 ) ) 168s + 168s + print( estfun( greeneOls ) ) 168s + print( round( colSums( estfun( greeneOls ) ), digits = 7 ) ) 168s + 168s + print( try( estfun( greeneOlsPooled ) ) ) 168s + 168s + print( estfun( greeneSur ) ) 168s + print( round( colSums( estfun( greeneSur ) ), digits = 7 ) ) 168s + 168s + print( try( estfun( greeneSurPooled ) ) ) 168s + } 168s General.Electric_(Intercept) General.Electric_value 168s General.Electric_X1935 -2.860 -3348 168s General.Electric_X1936 -14.402 -29032 168s General.Electric_X1937 -5.175 -14506 168s General.Electric_X1938 -23.295 -47514 168s General.Electric_X1939 -28.031 -63243 168s General.Electric_X1940 -0.562 -1199 168s General.Electric_X1941 40.750 74739 168s General.Electric_X1942 16.036 25464 168s General.Electric_X1943 -23.719 -41494 168s General.Electric_X1944 -26.780 -45183 168s General.Electric_X1945 1.768 3550 168s General.Electric_X1946 58.737 129709 168s General.Electric_X1947 43.936 72789 168s General.Electric_X1948 31.227 50101 168s General.Electric_X1949 -23.552 -33722 168s General.Electric_X1950 -37.511 -60411 168s General.Electric_X1951 -4.983 -9066 168s General.Electric_X1952 1.893 3937 168s General.Electric_X1953 5.087 12064 168s General.Electric_X1954 -8.563 -23633 168s Westinghouse_X1935 0.000 0 168s Westinghouse_X1936 0.000 0 168s Westinghouse_X1937 0.000 0 168s Westinghouse_X1938 0.000 0 168s Westinghouse_X1939 0.000 0 168s Westinghouse_X1940 0.000 0 168s Westinghouse_X1941 0.000 0 168s Westinghouse_X1942 0.000 0 168s Westinghouse_X1943 0.000 0 168s Westinghouse_X1944 0.000 0 168s Westinghouse_X1945 0.000 0 168s Westinghouse_X1946 0.000 0 168s Westinghouse_X1947 0.000 0 168s Westinghouse_X1948 0.000 0 168s Westinghouse_X1949 0.000 0 168s Westinghouse_X1950 0.000 0 168s Westinghouse_X1951 0.000 0 168s Westinghouse_X1952 0.000 0 168s Westinghouse_X1953 0.000 0 168s Westinghouse_X1954 0.000 0 168s General.Electric_capital Westinghouse_(Intercept) 168s General.Electric_X1935 -280 0.000 168s General.Electric_X1936 -1504 0.000 168s General.Electric_X1937 -611 0.000 168s General.Electric_X1938 -3639 0.000 168s General.Electric_X1939 -4838 0.000 168s General.Electric_X1940 -105 0.000 168s General.Electric_X1941 9002 0.000 168s General.Electric_X1942 4615 0.000 168s General.Electric_X1943 -7588 0.000 168s General.Electric_X1944 -8604 0.000 168s General.Electric_X1945 565 0.000 168s General.Electric_X1946 20323 0.000 168s General.Electric_X1947 20052 0.000 168s General.Electric_X1948 16969 0.000 168s General.Electric_X1949 -14562 0.000 168s General.Electric_X1950 -24285 0.000 168s General.Electric_X1951 -3345 0.000 168s General.Electric_X1952 1374 0.000 168s General.Electric_X1953 4071 0.000 168s General.Electric_X1954 -7612 0.000 168s Westinghouse_X1935 0 3.144 168s Westinghouse_X1936 0 -0.958 168s Westinghouse_X1937 0 -3.684 168s Westinghouse_X1938 0 -7.915 168s Westinghouse_X1939 0 -10.322 168s Westinghouse_X1940 0 -6.613 168s Westinghouse_X1941 0 17.265 168s Westinghouse_X1942 0 8.547 168s Westinghouse_X1943 0 -2.916 168s Westinghouse_X1944 0 -3.257 168s Westinghouse_X1945 0 -7.753 168s Westinghouse_X1946 0 5.796 168s Westinghouse_X1947 0 15.050 168s Westinghouse_X1948 0 2.969 168s Westinghouse_X1949 0 -11.433 168s Westinghouse_X1950 0 -13.481 168s Westinghouse_X1951 0 4.619 168s Westinghouse_X1952 0 13.138 168s Westinghouse_X1953 0 11.308 168s Westinghouse_X1954 0 -13.505 168s Westinghouse_value Westinghouse_capital 168s General.Electric_X1935 0 0.000 168s General.Electric_X1936 0 0.000 168s General.Electric_X1937 0 0.000 168s General.Electric_X1938 0 0.000 168s General.Electric_X1939 0 0.000 168s General.Electric_X1940 0 0.000 168s General.Electric_X1941 0 0.000 168s General.Electric_X1942 0 0.000 168s General.Electric_X1943 0 0.000 168s General.Electric_X1944 0 0.000 168s General.Electric_X1945 0 0.000 168s General.Electric_X1946 0 0.000 168s General.Electric_X1947 0 0.000 168s General.Electric_X1948 0 0.000 168s General.Electric_X1949 0 0.000 168s General.Electric_X1950 0 0.000 168s General.Electric_X1951 0 0.000 168s General.Electric_X1952 0 0.000 168s General.Electric_X1953 0 0.000 168s General.Electric_X1954 0 0.000 168s Westinghouse_X1935 602 5.659 168s Westinghouse_X1936 -494 -0.766 168s Westinghouse_X1937 -2686 -27.263 168s Westinghouse_X1938 -4436 -143.262 168s Westinghouse_X1939 -5366 -242.563 168s Westinghouse_X1940 -4156 -175.254 168s Westinghouse_X1941 9273 624.987 168s Westinghouse_X1942 4797 519.651 168s Westinghouse_X1943 -1800 -246.108 168s Westinghouse_X1944 -2041 -297.023 168s Westinghouse_X1945 -5715 -716.333 168s Westinghouse_X1946 4408 498.495 168s Westinghouse_X1947 8750 1672.098 168s Westinghouse_X1948 1967 387.794 168s Westinghouse_X1949 -6675 -1621.262 168s Westinghouse_X1950 -8563 -1842.843 168s Westinghouse_X1951 3344 599.149 168s Westinghouse_X1952 11353 1911.642 168s Westinghouse_X1953 13496 1976.568 168s Westinghouse_X1954 -16056 -2883.365 168s General.Electric_(Intercept) General.Electric_value 168s 0 0 168s General.Electric_capital Westinghouse_(Intercept) 168s 0 0 168s Westinghouse_value Westinghouse_capital 168s 0 0 168s General.Electric_(Intercept) General.Electric_value 168s General.Electric_X1935 0.007671 8.980 168s General.Electric_X1936 -0.061426 -123.822 168s General.Electric_X1937 -0.060974 -170.929 168s General.Electric_X1938 -0.088931 -181.393 168s General.Electric_X1939 -0.111776 -252.189 168s General.Electric_X1940 -0.017793 -37.937 168s General.Electric_X1941 0.128334 235.378 168s General.Electric_X1942 0.060606 96.243 168s General.Electric_X1943 -0.072587 -126.985 168s General.Electric_X1944 -0.080053 -135.065 168s General.Electric_X1945 -0.000104 -0.208 168s General.Electric_X1946 0.177325 391.586 168s General.Electric_X1947 0.154986 256.765 168s General.Electric_X1948 0.119488 191.707 168s General.Electric_X1949 -0.047791 -68.427 168s General.Electric_X1950 -0.098464 -158.576 168s General.Electric_X1951 -0.000379 -0.689 168s General.Electric_X1952 0.014181 29.492 168s General.Electric_X1953 0.016444 38.998 168s General.Electric_X1954 -0.038758 -106.969 168s Westinghouse_X1935 -0.019477 -22.800 168s Westinghouse_X1936 0.016942 34.151 168s Westinghouse_X1937 0.039739 111.402 168s Westinghouse_X1938 0.059843 122.062 168s Westinghouse_X1939 0.073091 164.909 168s Westinghouse_X1940 0.052015 110.907 168s Westinghouse_X1941 -0.105994 -194.404 168s Westinghouse_X1942 -0.053728 -85.321 168s Westinghouse_X1943 0.017332 30.320 168s Westinghouse_X1944 0.018569 31.330 168s Westinghouse_X1945 0.050605 101.599 168s Westinghouse_X1946 -0.034591 -76.387 168s Westinghouse_X1947 -0.104099 -172.460 168s Westinghouse_X1948 -0.027559 -44.215 168s Westinghouse_X1949 0.060567 86.720 168s Westinghouse_X1950 0.076221 122.754 168s Westinghouse_X1951 -0.036128 -65.731 168s Westinghouse_X1952 -0.089492 -186.117 168s Westinghouse_X1953 -0.073054 -173.256 168s Westinghouse_X1954 0.079198 218.578 168s General.Electric_capital Westinghouse_(Intercept) 168s General.Electric_X1935 0.7503 -0.015267 168s General.Electric_X1936 -6.4128 0.122246 168s General.Electric_X1937 -7.1950 0.121347 168s General.Electric_X1938 -13.8911 0.176986 168s General.Electric_X1939 -19.2925 0.222450 168s General.Electric_X1940 -3.3201 0.035410 168s General.Electric_X1941 28.3490 -0.255403 168s General.Electric_X1942 17.4425 -0.120615 168s General.Electric_X1943 -23.2207 0.144459 168s General.Electric_X1944 -25.7209 0.159316 168s General.Electric_X1945 -0.0331 0.000206 168s General.Electric_X1946 61.3543 -0.352901 168s General.Electric_X1947 70.7355 -0.308443 168s General.Electric_X1948 64.9300 -0.237798 168s General.Electric_X1949 -29.5489 0.095110 168s General.Electric_X1950 -63.7453 0.195956 168s General.Electric_X1951 -0.2543 0.000754 168s General.Electric_X1952 10.2966 -0.028221 168s General.Electric_X1953 13.1598 -0.032725 168s General.Electric_X1954 -34.4523 0.077135 168s Westinghouse_X1935 -1.9049 0.072945 168s Westinghouse_X1936 1.7687 -0.063449 168s Westinghouse_X1937 4.6893 -0.148830 168s Westinghouse_X1938 9.3475 -0.224122 168s Westinghouse_X1939 12.6156 -0.273739 168s Westinghouse_X1940 9.7061 -0.194806 168s Westinghouse_X1941 -23.4141 0.396965 168s Westinghouse_X1942 -15.4630 0.201221 168s Westinghouse_X1943 5.5444 -0.064910 168s Westinghouse_X1944 5.9663 -0.069544 168s Westinghouse_X1945 16.1733 -0.189523 168s Westinghouse_X1946 -11.9684 0.129548 168s Westinghouse_X1947 -47.5107 0.389866 168s Westinghouse_X1948 -14.9755 0.103212 168s Westinghouse_X1949 37.4485 -0.226832 168s Westinghouse_X1950 49.3457 -0.285461 168s Westinghouse_X1951 -24.2526 0.135304 168s Westinghouse_X1952 -64.9804 0.335163 168s Westinghouse_X1953 -58.4654 0.273600 168s Westinghouse_X1954 70.3989 -0.296608 168s Westinghouse_value Westinghouse_capital 168s General.Electric_X1935 -2.924 -0.0275 168s General.Electric_X1936 63.079 0.0978 168s General.Electric_X1937 88.462 0.8980 168s General.Electric_X1938 99.183 3.2034 168s General.Electric_X1939 115.652 5.2276 168s General.Electric_X1940 22.255 0.9384 168s General.Electric_X1941 -137.177 -9.2456 168s General.Electric_X1942 -67.689 -7.3334 168s General.Electric_X1943 89.160 12.1924 168s General.Electric_X1944 99.843 14.5296 168s General.Electric_X1945 0.152 0.0190 168s General.Electric_X1946 -268.381 -30.3494 168s General.Electric_X1947 -179.329 -34.2680 168s General.Electric_X1948 -157.494 -31.0565 168s General.Electric_X1949 55.525 13.4866 168s General.Electric_X1950 124.471 26.7872 168s General.Electric_X1951 0.546 0.0978 168s General.Electric_X1952 -24.386 -4.1062 168s General.Electric_X1953 -39.057 -5.7203 168s General.Electric_X1954 91.705 16.4682 168s Westinghouse_X1935 13.969 0.1313 168s Westinghouse_X1936 -32.740 -0.0508 168s Westinghouse_X1937 -108.497 -1.1013 168s Westinghouse_X1938 -125.598 -4.0566 168s Westinghouse_X1939 -142.317 -6.4329 168s Westinghouse_X1940 -122.436 -5.1624 168s Westinghouse_X1941 213.210 14.3701 168s Westinghouse_X1942 112.925 12.2342 168s Westinghouse_X1943 -40.063 -5.4784 168s Westinghouse_X1944 -43.583 -6.3424 168s Westinghouse_X1945 -139.717 -17.5120 168s Westinghouse_X1946 98.521 11.1411 168s Westinghouse_X1947 226.668 43.3141 168s Westinghouse_X1948 68.357 13.4795 168s Westinghouse_X1949 -132.425 -32.1648 168s Westinghouse_X1950 -181.325 -39.0225 168s Westinghouse_X1951 97.933 17.5490 168s Westinghouse_X1952 289.614 48.7662 168s Westinghouse_X1953 326.541 47.8252 168s Westinghouse_X1954 -352.637 -63.3258 168s General.Electric_(Intercept) General.Electric_value 168s 0 0 168s General.Electric_capital Westinghouse_(Intercept) 168s 0 0 168s Westinghouse_value Westinghouse_capital 168s 0 0 168s Chrysler_(Intercept) Chrysler_value Chrysler_capital 168s Chrysler_X1935 10.622 4435 111.5 168s Chrysler_X1936 10.425 8734 106.3 168s Chrysler_X1937 -7.404 -6544 -256.9 168s Chrysler_X1938 7.302 3198 378.3 168s Chrysler_X1939 -14.682 -9979 -944.0 168s Chrysler_X1940 -2.315 -1685 -155.3 168s Chrysler_X1941 0.631 406 47.4 168s Chrysler_X1942 -1.581 -650 -112.9 168s Chrysler_X1943 -13.459 -7919 -903.1 168s Chrysler_X1944 -7.780 -5433 -470.7 168s Chrysler_X1945 11.757 9951 641.9 168s Chrysler_X1946 -16.133 -14419 -1368.1 168s Chrysler_X1947 -6.823 -3951 -660.5 168s Chrysler_X1948 6.615 4595 729.0 168s Chrysler_X1949 -7.379 -4356 -1087.7 168s Chrysler_X1950 1.268 879 206.9 168s Chrysler_X1951 39.502 31957 8038.6 168s Chrysler_X1952 2.774 2017 806.2 168s Chrysler_X1953 -6.215 -6224 -2151.0 168s Chrysler_X1954 -7.124 -5010 -2955.9 168s General.Electric_X1935 0.000 0 0.0 168s General.Electric_X1936 0.000 0 0.0 168s General.Electric_X1937 0.000 0 0.0 168s General.Electric_X1938 0.000 0 0.0 168s General.Electric_X1939 0.000 0 0.0 168s General.Electric_X1940 0.000 0 0.0 168s General.Electric_X1941 0.000 0 0.0 168s General.Electric_X1942 0.000 0 0.0 168s General.Electric_X1943 0.000 0 0.0 168s General.Electric_X1944 0.000 0 0.0 168s General.Electric_X1945 0.000 0 0.0 168s General.Electric_X1946 0.000 0 0.0 168s General.Electric_X1947 0.000 0 0.0 168s General.Electric_X1948 0.000 0 0.0 168s General.Electric_X1949 0.000 0 0.0 168s General.Electric_X1950 0.000 0 0.0 168s General.Electric_X1951 0.000 0 0.0 168s General.Electric_X1952 0.000 0 0.0 168s General.Electric_X1953 0.000 0 0.0 168s General.Electric_X1954 0.000 0 0.0 168s General.Motors_X1935 0.000 0 0.0 168s General.Motors_X1936 0.000 0 0.0 168s General.Motors_X1937 0.000 0 0.0 168s General.Motors_X1938 0.000 0 0.0 168s General.Motors_X1939 0.000 0 0.0 168s General.Motors_X1940 0.000 0 0.0 168s General.Motors_X1941 0.000 0 0.0 168s General.Motors_X1942 0.000 0 0.0 168s General.Motors_X1943 0.000 0 0.0 168s General.Motors_X1944 0.000 0 0.0 168s General.Motors_X1945 0.000 0 0.0 168s General.Motors_X1946 0.000 0 0.0 168s General.Motors_X1947 0.000 0 0.0 168s General.Motors_X1948 0.000 0 0.0 168s General.Motors_X1949 0.000 0 0.0 168s General.Motors_X1950 0.000 0 0.0 168s General.Motors_X1951 0.000 0 0.0 168s General.Motors_X1952 0.000 0 0.0 168s General.Motors_X1953 0.000 0 0.0 168s General.Motors_X1954 0.000 0 0.0 168s US.Steel_X1935 0.000 0 0.0 168s US.Steel_X1936 0.000 0 0.0 168s US.Steel_X1937 0.000 0 0.0 168s US.Steel_X1938 0.000 0 0.0 168s US.Steel_X1939 0.000 0 0.0 168s US.Steel_X1940 0.000 0 0.0 168s US.Steel_X1941 0.000 0 0.0 168s US.Steel_X1942 0.000 0 0.0 168s US.Steel_X1943 0.000 0 0.0 168s US.Steel_X1944 0.000 0 0.0 168s US.Steel_X1945 0.000 0 0.0 168s US.Steel_X1946 0.000 0 0.0 168s US.Steel_X1947 0.000 0 0.0 168s US.Steel_X1948 0.000 0 0.0 168s US.Steel_X1949 0.000 0 0.0 168s US.Steel_X1950 0.000 0 0.0 168s US.Steel_X1951 0.000 0 0.0 168s US.Steel_X1952 0.000 0 0.0 168s US.Steel_X1953 0.000 0 0.0 168s US.Steel_X1954 0.000 0 0.0 168s Westinghouse_X1935 0.000 0 0.0 168s Westinghouse_X1936 0.000 0 0.0 168s Westinghouse_X1937 0.000 0 0.0 168s Westinghouse_X1938 0.000 0 0.0 168s Westinghouse_X1939 0.000 0 0.0 168s Westinghouse_X1940 0.000 0 0.0 168s Westinghouse_X1941 0.000 0 0.0 168s Westinghouse_X1942 0.000 0 0.0 168s Westinghouse_X1943 0.000 0 0.0 168s Westinghouse_X1944 0.000 0 0.0 168s Westinghouse_X1945 0.000 0 0.0 168s Westinghouse_X1946 0.000 0 0.0 168s Westinghouse_X1947 0.000 0 0.0 168s Westinghouse_X1948 0.000 0 0.0 168s Westinghouse_X1949 0.000 0 0.0 168s Westinghouse_X1950 0.000 0 0.0 168s Westinghouse_X1951 0.000 0 0.0 168s Westinghouse_X1952 0.000 0 0.0 168s Westinghouse_X1953 0.000 0 0.0 168s Westinghouse_X1954 0.000 0 0.0 168s General.Electric_(Intercept) General.Electric_value 168s Chrysler_X1935 0.000 0 168s Chrysler_X1936 0.000 0 168s Chrysler_X1937 0.000 0 168s Chrysler_X1938 0.000 0 168s Chrysler_X1939 0.000 0 168s Chrysler_X1940 0.000 0 168s Chrysler_X1941 0.000 0 168s Chrysler_X1942 0.000 0 168s Chrysler_X1943 0.000 0 168s Chrysler_X1944 0.000 0 168s Chrysler_X1945 0.000 0 168s Chrysler_X1946 0.000 0 168s Chrysler_X1947 0.000 0 168s Chrysler_X1948 0.000 0 168s Chrysler_X1949 0.000 0 168s Chrysler_X1950 0.000 0 168s Chrysler_X1951 0.000 0 168s Chrysler_X1952 0.000 0 168s Chrysler_X1953 0.000 0 168s Chrysler_X1954 0.000 0 168s General.Electric_X1935 -2.860 -3348 168s General.Electric_X1936 -14.402 -29032 168s General.Electric_X1937 -5.175 -14506 168s General.Electric_X1938 -23.295 -47514 168s General.Electric_X1939 -28.031 -63243 168s General.Electric_X1940 -0.562 -1199 168s General.Electric_X1941 40.750 74739 168s General.Electric_X1942 16.036 25464 168s General.Electric_X1943 -23.719 -41494 168s General.Electric_X1944 -26.780 -45183 168s General.Electric_X1945 1.768 3550 168s General.Electric_X1946 58.737 129709 168s General.Electric_X1947 43.936 72789 168s General.Electric_X1948 31.227 50101 168s General.Electric_X1949 -23.552 -33722 168s General.Electric_X1950 -37.511 -60411 168s General.Electric_X1951 -4.983 -9066 168s General.Electric_X1952 1.893 3937 168s General.Electric_X1953 5.087 12064 168s General.Electric_X1954 -8.563 -23633 168s General.Motors_X1935 0.000 0 168s General.Motors_X1936 0.000 0 168s General.Motors_X1937 0.000 0 168s General.Motors_X1938 0.000 0 168s General.Motors_X1939 0.000 0 168s General.Motors_X1940 0.000 0 168s General.Motors_X1941 0.000 0 168s General.Motors_X1942 0.000 0 168s General.Motors_X1943 0.000 0 168s General.Motors_X1944 0.000 0 168s General.Motors_X1945 0.000 0 168s General.Motors_X1946 0.000 0 168s General.Motors_X1947 0.000 0 168s General.Motors_X1948 0.000 0 168s General.Motors_X1949 0.000 0 168s General.Motors_X1950 0.000 0 168s General.Motors_X1951 0.000 0 168s General.Motors_X1952 0.000 0 168s General.Motors_X1953 0.000 0 168s General.Motors_X1954 0.000 0 168s US.Steel_X1935 0.000 0 168s US.Steel_X1936 0.000 0 168s US.Steel_X1937 0.000 0 168s US.Steel_X1938 0.000 0 168s US.Steel_X1939 0.000 0 168s US.Steel_X1940 0.000 0 168s US.Steel_X1941 0.000 0 168s US.Steel_X1942 0.000 0 168s US.Steel_X1943 0.000 0 168s US.Steel_X1944 0.000 0 168s US.Steel_X1945 0.000 0 168s US.Steel_X1946 0.000 0 168s US.Steel_X1947 0.000 0 168s US.Steel_X1948 0.000 0 168s US.Steel_X1949 0.000 0 168s US.Steel_X1950 0.000 0 168s US.Steel_X1951 0.000 0 168s US.Steel_X1952 0.000 0 168s US.Steel_X1953 0.000 0 168s US.Steel_X1954 0.000 0 168s Westinghouse_X1935 0.000 0 168s Westinghouse_X1936 0.000 0 168s Westinghouse_X1937 0.000 0 168s Westinghouse_X1938 0.000 0 168s Westinghouse_X1939 0.000 0 168s Westinghouse_X1940 0.000 0 168s Westinghouse_X1941 0.000 0 168s Westinghouse_X1942 0.000 0 168s Westinghouse_X1943 0.000 0 168s Westinghouse_X1944 0.000 0 168s Westinghouse_X1945 0.000 0 168s Westinghouse_X1946 0.000 0 168s Westinghouse_X1947 0.000 0 168s Westinghouse_X1948 0.000 0 168s Westinghouse_X1949 0.000 0 168s Westinghouse_X1950 0.000 0 168s Westinghouse_X1951 0.000 0 168s Westinghouse_X1952 0.000 0 168s Westinghouse_X1953 0.000 0 168s Westinghouse_X1954 0.000 0 168s General.Electric_capital General.Motors_(Intercept) 168s Chrysler_X1935 0 0.00 168s Chrysler_X1936 0 0.00 168s Chrysler_X1937 0 0.00 168s Chrysler_X1938 0 0.00 168s Chrysler_X1939 0 0.00 168s Chrysler_X1940 0 0.00 168s Chrysler_X1941 0 0.00 168s Chrysler_X1942 0 0.00 168s Chrysler_X1943 0 0.00 168s Chrysler_X1944 0 0.00 168s Chrysler_X1945 0 0.00 168s Chrysler_X1946 0 0.00 168s Chrysler_X1947 0 0.00 168s Chrysler_X1948 0 0.00 168s Chrysler_X1949 0 0.00 168s Chrysler_X1950 0 0.00 168s Chrysler_X1951 0 0.00 168s Chrysler_X1952 0 0.00 168s Chrysler_X1953 0 0.00 168s Chrysler_X1954 0 0.00 168s General.Electric_X1935 -280 0.00 168s General.Electric_X1936 -1504 0.00 168s General.Electric_X1937 -611 0.00 168s General.Electric_X1938 -3639 0.00 168s General.Electric_X1939 -4838 0.00 168s General.Electric_X1940 -105 0.00 168s General.Electric_X1941 9002 0.00 168s General.Electric_X1942 4615 0.00 168s General.Electric_X1943 -7588 0.00 168s General.Electric_X1944 -8604 0.00 168s General.Electric_X1945 565 0.00 168s General.Electric_X1946 20323 0.00 168s General.Electric_X1947 20052 0.00 168s General.Electric_X1948 16969 0.00 168s General.Electric_X1949 -14562 0.00 168s General.Electric_X1950 -24285 0.00 168s General.Electric_X1951 -3345 0.00 168s General.Electric_X1952 1374 0.00 168s General.Electric_X1953 4071 0.00 168s General.Electric_X1954 -7612 0.00 168s General.Motors_X1935 0 99.14 168s General.Motors_X1936 0 -34.01 168s General.Motors_X1937 0 -140.48 168s General.Motors_X1938 0 -3.28 168s General.Motors_X1939 0 -109.45 168s General.Motors_X1940 0 -19.91 168s General.Motors_X1941 0 24.12 168s General.Motors_X1942 0 98.02 168s General.Motors_X1943 0 67.76 168s General.Motors_X1944 0 100.03 168s General.Motors_X1945 0 35.12 168s General.Motors_X1946 0 103.90 168s General.Motors_X1947 0 15.18 168s General.Motors_X1948 0 -51.86 168s General.Motors_X1949 0 -115.39 168s General.Motors_X1950 0 -63.51 168s General.Motors_X1951 0 -119.40 168s General.Motors_X1952 0 -77.82 168s General.Motors_X1953 0 49.50 168s General.Motors_X1954 0 142.33 168s US.Steel_X1935 0 0.00 168s US.Steel_X1936 0 0.00 168s US.Steel_X1937 0 0.00 168s US.Steel_X1938 0 0.00 168s US.Steel_X1939 0 0.00 168s US.Steel_X1940 0 0.00 168s US.Steel_X1941 0 0.00 168s US.Steel_X1942 0 0.00 168s US.Steel_X1943 0 0.00 168s US.Steel_X1944 0 0.00 168s US.Steel_X1945 0 0.00 168s US.Steel_X1946 0 0.00 168s US.Steel_X1947 0 0.00 168s US.Steel_X1948 0 0.00 168s US.Steel_X1949 0 0.00 168s US.Steel_X1950 0 0.00 168s US.Steel_X1951 0 0.00 168s US.Steel_X1952 0 0.00 168s US.Steel_X1953 0 0.00 168s US.Steel_X1954 0 0.00 168s Westinghouse_X1935 0 0.00 168s Westinghouse_X1936 0 0.00 168s Westinghouse_X1937 0 0.00 168s Westinghouse_X1938 0 0.00 168s Westinghouse_X1939 0 0.00 168s Westinghouse_X1940 0 0.00 168s Westinghouse_X1941 0 0.00 168s Westinghouse_X1942 0 0.00 168s Westinghouse_X1943 0 0.00 168s Westinghouse_X1944 0 0.00 168s Westinghouse_X1945 0 0.00 168s Westinghouse_X1946 0 0.00 168s Westinghouse_X1947 0 0.00 168s Westinghouse_X1948 0 0.00 168s Westinghouse_X1949 0 0.00 168s Westinghouse_X1950 0 0.00 168s Westinghouse_X1951 0 0.00 168s Westinghouse_X1952 0 0.00 168s Westinghouse_X1953 0 0.00 168s Westinghouse_X1954 0 0.00 168s General.Motors_value General.Motors_capital 168s Chrysler_X1935 0 0 168s Chrysler_X1936 0 0 168s Chrysler_X1937 0 0 168s Chrysler_X1938 0 0 168s Chrysler_X1939 0 0 168s Chrysler_X1940 0 0 168s Chrysler_X1941 0 0 168s Chrysler_X1942 0 0 168s Chrysler_X1943 0 0 168s Chrysler_X1944 0 0 168s Chrysler_X1945 0 0 168s Chrysler_X1946 0 0 168s Chrysler_X1947 0 0 168s Chrysler_X1948 0 0 168s Chrysler_X1949 0 0 168s Chrysler_X1950 0 0 168s Chrysler_X1951 0 0 168s Chrysler_X1952 0 0 168s Chrysler_X1953 0 0 168s Chrysler_X1954 0 0 168s General.Electric_X1935 0 0 168s General.Electric_X1936 0 0 168s General.Electric_X1937 0 0 168s General.Electric_X1938 0 0 168s General.Electric_X1939 0 0 168s General.Electric_X1940 0 0 168s General.Electric_X1941 0 0 168s General.Electric_X1942 0 0 168s General.Electric_X1943 0 0 168s General.Electric_X1944 0 0 168s General.Electric_X1945 0 0 168s General.Electric_X1946 0 0 168s General.Electric_X1947 0 0 168s General.Electric_X1948 0 0 168s General.Electric_X1949 0 0 168s General.Electric_X1950 0 0 168s General.Electric_X1951 0 0 168s General.Electric_X1952 0 0 168s General.Electric_X1953 0 0 168s General.Electric_X1954 0 0 168s General.Motors_X1935 305191 278 168s General.Motors_X1936 -158530 -1789 168s General.Motors_X1937 -756753 -22041 168s General.Motors_X1938 -9158 -686 168s General.Motors_X1939 -472086 -22262 168s General.Motors_X1940 -92456 -4125 168s General.Motors_X1941 109770 6155 168s General.Motors_X1942 317973 29767 168s General.Motors_X1943 274659 17894 168s General.Motors_X1944 438073 20167 168s General.Motors_X1945 170027 9308 168s General.Motors_X1946 509223 41790 168s General.Motors_X1947 53544 11562 168s General.Motors_X1948 -168794 -47837 168s General.Motors_X1949 -426971 -117711 168s General.Motors_X1950 -238505 -69794 168s General.Motors_X1951 -577039 -144194 168s General.Motors_X1952 -383234 -111315 168s General.Motors_X1953 308954 87974 168s General.Motors_X1954 796113 316860 168s US.Steel_X1935 0 0 168s US.Steel_X1936 0 0 168s US.Steel_X1937 0 0 168s US.Steel_X1938 0 0 168s US.Steel_X1939 0 0 168s US.Steel_X1940 0 0 168s US.Steel_X1941 0 0 168s US.Steel_X1942 0 0 168s US.Steel_X1943 0 0 168s US.Steel_X1944 0 0 168s US.Steel_X1945 0 0 168s US.Steel_X1946 0 0 168s US.Steel_X1947 0 0 168s US.Steel_X1948 0 0 168s US.Steel_X1949 0 0 168s US.Steel_X1950 0 0 168s US.Steel_X1951 0 0 168s US.Steel_X1952 0 0 168s US.Steel_X1953 0 0 168s US.Steel_X1954 0 0 168s Westinghouse_X1935 0 0 168s Westinghouse_X1936 0 0 168s Westinghouse_X1937 0 0 168s Westinghouse_X1938 0 0 168s Westinghouse_X1939 0 0 168s Westinghouse_X1940 0 0 168s Westinghouse_X1941 0 0 168s Westinghouse_X1942 0 0 168s Westinghouse_X1943 0 0 168s Westinghouse_X1944 0 0 168s Westinghouse_X1945 0 0 168s Westinghouse_X1946 0 0 168s Westinghouse_X1947 0 0 168s Westinghouse_X1948 0 0 168s Westinghouse_X1949 0 0 168s Westinghouse_X1950 0 0 168s Westinghouse_X1951 0 0 168s Westinghouse_X1952 0 0 168s Westinghouse_X1953 0 0 168s Westinghouse_X1954 0 0 168s US.Steel_(Intercept) US.Steel_value US.Steel_capital 168s Chrysler_X1935 0.00 0 0 168s Chrysler_X1936 0.00 0 0 168s Chrysler_X1937 0.00 0 0 168s Chrysler_X1938 0.00 0 0 168s Chrysler_X1939 0.00 0 0 168s Chrysler_X1940 0.00 0 0 168s Chrysler_X1941 0.00 0 0 168s Chrysler_X1942 0.00 0 0 168s Chrysler_X1943 0.00 0 0 168s Chrysler_X1944 0.00 0 0 168s Chrysler_X1945 0.00 0 0 168s Chrysler_X1946 0.00 0 0 168s Chrysler_X1947 0.00 0 0 168s Chrysler_X1948 0.00 0 0 168s Chrysler_X1949 0.00 0 0 168s Chrysler_X1950 0.00 0 0 168s Chrysler_X1951 0.00 0 0 168s Chrysler_X1952 0.00 0 0 168s Chrysler_X1953 0.00 0 0 168s Chrysler_X1954 0.00 0 0 168s General.Electric_X1935 0.00 0 0 168s General.Electric_X1936 0.00 0 0 168s General.Electric_X1937 0.00 0 0 168s General.Electric_X1938 0.00 0 0 168s General.Electric_X1939 0.00 0 0 168s General.Electric_X1940 0.00 0 0 168s General.Electric_X1941 0.00 0 0 168s General.Electric_X1942 0.00 0 0 168s General.Electric_X1943 0.00 0 0 168s General.Electric_X1944 0.00 0 0 168s General.Electric_X1945 0.00 0 0 168s General.Electric_X1946 0.00 0 0 168s General.Electric_X1947 0.00 0 0 168s General.Electric_X1948 0.00 0 0 168s General.Electric_X1949 0.00 0 0 168s General.Electric_X1950 0.00 0 0 168s General.Electric_X1951 0.00 0 0 168s General.Electric_X1952 0.00 0 0 168s General.Electric_X1953 0.00 0 0 168s General.Electric_X1954 0.00 0 0 168s General.Motors_X1935 0.00 0 0 168s General.Motors_X1936 0.00 0 0 168s General.Motors_X1937 0.00 0 0 168s General.Motors_X1938 0.00 0 0 168s General.Motors_X1939 0.00 0 0 168s General.Motors_X1940 0.00 0 0 168s General.Motors_X1941 0.00 0 0 168s General.Motors_X1942 0.00 0 0 168s General.Motors_X1943 0.00 0 0 168s General.Motors_X1944 0.00 0 0 168s General.Motors_X1945 0.00 0 0 168s General.Motors_X1946 0.00 0 0 168s General.Motors_X1947 0.00 0 0 168s General.Motors_X1948 0.00 0 0 168s General.Motors_X1949 0.00 0 0 168s General.Motors_X1950 0.00 0 0 168s General.Motors_X1951 0.00 0 0 168s General.Motors_X1952 0.00 0 0 168s General.Motors_X1953 0.00 0 0 168s General.Motors_X1954 0.00 0 0 168s US.Steel_X1935 4.15 5657 223 168s US.Steel_X1936 81.32 146961 4107 168s US.Steel_X1937 31.18 83446 3682 168s US.Steel_X1938 -99.75 -179733 -25954 168s US.Steel_X1939 -178.23 -348850 -55733 168s US.Steel_X1940 -160.69 -353980 -40847 168s US.Steel_X1941 19.65 46784 5137 168s US.Steel_X1942 9.82 21296 2933 168s US.Steel_X1943 -46.76 -92829 -14113 168s US.Steel_X1944 -83.74 -151889 -23371 168s US.Steel_X1945 -91.24 -168815 -19507 168s US.Steel_X1946 28.34 58590 6591 168s US.Steel_X1947 57.32 102983 15178 168s US.Steel_X1948 140.23 227988 43037 168s US.Steel_X1949 25.65 42751 9004 168s US.Steel_X1950 34.88 58503 12479 168s US.Steel_X1951 115.10 263510 39374 168s US.Steel_X1952 149.19 322157 66269 168s US.Steel_X1953 89.00 180793 55503 168s US.Steel_X1954 -125.42 -265326 -83994 168s Westinghouse_X1935 0.00 0 0 168s Westinghouse_X1936 0.00 0 0 168s Westinghouse_X1937 0.00 0 0 168s Westinghouse_X1938 0.00 0 0 168s Westinghouse_X1939 0.00 0 0 168s Westinghouse_X1940 0.00 0 0 168s Westinghouse_X1941 0.00 0 0 168s Westinghouse_X1942 0.00 0 0 168s Westinghouse_X1943 0.00 0 0 168s Westinghouse_X1944 0.00 0 0 168s Westinghouse_X1945 0.00 0 0 168s Westinghouse_X1946 0.00 0 0 168s Westinghouse_X1947 0.00 0 0 168s Westinghouse_X1948 0.00 0 0 168s Westinghouse_X1949 0.00 0 0 168s Westinghouse_X1950 0.00 0 0 168s Westinghouse_X1951 0.00 0 0 168s Westinghouse_X1952 0.00 0 0 168s Westinghouse_X1953 0.00 0 0 168s Westinghouse_X1954 0.00 0 0 168s Westinghouse_(Intercept) Westinghouse_value 168s Chrysler_X1935 0.000 0 168s Chrysler_X1936 0.000 0 168s Chrysler_X1937 0.000 0 168s Chrysler_X1938 0.000 0 168s Chrysler_X1939 0.000 0 168s Chrysler_X1940 0.000 0 168s Chrysler_X1941 0.000 0 168s Chrysler_X1942 0.000 0 168s Chrysler_X1943 0.000 0 168s Chrysler_X1944 0.000 0 168s Chrysler_X1945 0.000 0 168s Chrysler_X1946 0.000 0 168s Chrysler_X1947 0.000 0 168s Chrysler_X1948 0.000 0 168s Chrysler_X1949 0.000 0 168s Chrysler_X1950 0.000 0 168s Chrysler_X1951 0.000 0 168s Chrysler_X1952 0.000 0 168s Chrysler_X1953 0.000 0 168s Chrysler_X1954 0.000 0 168s General.Electric_X1935 0.000 0 168s General.Electric_X1936 0.000 0 168s General.Electric_X1937 0.000 0 168s General.Electric_X1938 0.000 0 168s General.Electric_X1939 0.000 0 168s General.Electric_X1940 0.000 0 168s General.Electric_X1941 0.000 0 168s General.Electric_X1942 0.000 0 168s General.Electric_X1943 0.000 0 168s General.Electric_X1944 0.000 0 168s General.Electric_X1945 0.000 0 168s General.Electric_X1946 0.000 0 168s General.Electric_X1947 0.000 0 168s General.Electric_X1948 0.000 0 168s General.Electric_X1949 0.000 0 168s General.Electric_X1950 0.000 0 168s General.Electric_X1951 0.000 0 168s General.Electric_X1952 0.000 0 168s General.Electric_X1953 0.000 0 168s General.Electric_X1954 0.000 0 168s General.Motors_X1935 0.000 0 168s General.Motors_X1936 0.000 0 168s General.Motors_X1937 0.000 0 168s General.Motors_X1938 0.000 0 168s General.Motors_X1939 0.000 0 168s General.Motors_X1940 0.000 0 168s General.Motors_X1941 0.000 0 168s General.Motors_X1942 0.000 0 168s General.Motors_X1943 0.000 0 168s General.Motors_X1944 0.000 0 168s General.Motors_X1945 0.000 0 168s General.Motors_X1946 0.000 0 168s General.Motors_X1947 0.000 0 168s General.Motors_X1948 0.000 0 168s General.Motors_X1949 0.000 0 168s General.Motors_X1950 0.000 0 168s General.Motors_X1951 0.000 0 168s General.Motors_X1952 0.000 0 168s General.Motors_X1953 0.000 0 168s General.Motors_X1954 0.000 0 168s US.Steel_X1935 0.000 0 168s US.Steel_X1936 0.000 0 168s US.Steel_X1937 0.000 0 168s US.Steel_X1938 0.000 0 168s US.Steel_X1939 0.000 0 168s US.Steel_X1940 0.000 0 168s US.Steel_X1941 0.000 0 168s US.Steel_X1942 0.000 0 168s US.Steel_X1943 0.000 0 168s US.Steel_X1944 0.000 0 168s US.Steel_X1945 0.000 0 168s US.Steel_X1946 0.000 0 168s US.Steel_X1947 0.000 0 168s US.Steel_X1948 0.000 0 168s US.Steel_X1949 0.000 0 168s US.Steel_X1950 0.000 0 168s US.Steel_X1951 0.000 0 168s US.Steel_X1952 0.000 0 168s US.Steel_X1953 0.000 0 168s US.Steel_X1954 0.000 0 168s Westinghouse_X1935 3.144 602 168s Westinghouse_X1936 -0.958 -494 168s Westinghouse_X1937 -3.684 -2686 168s Westinghouse_X1938 -7.915 -4436 168s Westinghouse_X1939 -10.322 -5366 168s Westinghouse_X1940 -6.613 -4156 168s Westinghouse_X1941 17.265 9273 168s Westinghouse_X1942 8.547 4797 168s Westinghouse_X1943 -2.916 -1800 168s Westinghouse_X1944 -3.257 -2041 168s Westinghouse_X1945 -7.753 -5715 168s Westinghouse_X1946 5.796 4408 168s Westinghouse_X1947 15.050 8750 168s Westinghouse_X1948 2.969 1967 168s Westinghouse_X1949 -11.433 -6675 168s Westinghouse_X1950 -13.481 -8563 168s Westinghouse_X1951 4.619 3344 168s Westinghouse_X1952 13.138 11353 168s Westinghouse_X1953 11.308 13496 168s Westinghouse_X1954 -13.505 -16056 168s Westinghouse_capital 168s Chrysler_X1935 0.000 168s Chrysler_X1936 0.000 168s Chrysler_X1937 0.000 168s Chrysler_X1938 0.000 168s Chrysler_X1939 0.000 168s Chrysler_X1940 0.000 168s Chrysler_X1941 0.000 168s Chrysler_X1942 0.000 168s Chrysler_X1943 0.000 168s Chrysler_X1944 0.000 168s Chrysler_X1945 0.000 168s Chrysler_X1946 0.000 168s Chrysler_X1947 0.000 168s Chrysler_X1948 0.000 168s Chrysler_X1949 0.000 168s Chrysler_X1950 0.000 168s Chrysler_X1951 0.000 168s Chrysler_X1952 0.000 168s Chrysler_X1953 0.000 168s Chrysler_X1954 0.000 168s General.Electric_X1935 0.000 168s General.Electric_X1936 0.000 168s General.Electric_X1937 0.000 168s General.Electric_X1938 0.000 168s General.Electric_X1939 0.000 168s General.Electric_X1940 0.000 168s General.Electric_X1941 0.000 168s General.Electric_X1942 0.000 168s General.Electric_X1943 0.000 168s General.Electric_X1944 0.000 168s General.Electric_X1945 0.000 168s General.Electric_X1946 0.000 168s General.Electric_X1947 0.000 168s General.Electric_X1948 0.000 168s General.Electric_X1949 0.000 168s General.Electric_X1950 0.000 168s General.Electric_X1951 0.000 168s General.Electric_X1952 0.000 168s General.Electric_X1953 0.000 168s General.Electric_X1954 0.000 168s General.Motors_X1935 0.000 168s General.Motors_X1936 0.000 168s General.Motors_X1937 0.000 168s General.Motors_X1938 0.000 168s General.Motors_X1939 0.000 168s General.Motors_X1940 0.000 168s General.Motors_X1941 0.000 168s General.Motors_X1942 0.000 168s General.Motors_X1943 0.000 168s General.Motors_X1944 0.000 168s General.Motors_X1945 0.000 168s General.Motors_X1946 0.000 168s General.Motors_X1947 0.000 168s General.Motors_X1948 0.000 168s General.Motors_X1949 0.000 168s General.Motors_X1950 0.000 168s General.Motors_X1951 0.000 168s General.Motors_X1952 0.000 168s General.Motors_X1953 0.000 168s General.Motors_X1954 0.000 168s US.Steel_X1935 0.000 168s US.Steel_X1936 0.000 168s US.Steel_X1937 0.000 168s US.Steel_X1938 0.000 168s US.Steel_X1939 0.000 168s US.Steel_X1940 0.000 168s US.Steel_X1941 0.000 168s US.Steel_X1942 0.000 168s US.Steel_X1943 0.000 168s US.Steel_X1944 0.000 168s US.Steel_X1945 0.000 168s US.Steel_X1946 0.000 168s US.Steel_X1947 0.000 168s US.Steel_X1948 0.000 168s US.Steel_X1949 0.000 168s US.Steel_X1950 0.000 168s US.Steel_X1951 0.000 168s US.Steel_X1952 0.000 168s US.Steel_X1953 0.000 168s US.Steel_X1954 0.000 168s Westinghouse_X1935 5.659 168s Westinghouse_X1936 -0.766 168s Westinghouse_X1937 -27.263 168s Westinghouse_X1938 -143.262 168s Westinghouse_X1939 -242.563 168s Westinghouse_X1940 -175.254 168s Westinghouse_X1941 624.987 168s Westinghouse_X1942 519.651 168s Westinghouse_X1943 -246.108 168s Westinghouse_X1944 -297.023 168s Westinghouse_X1945 -716.333 168s Westinghouse_X1946 498.495 168s Westinghouse_X1947 1672.098 168s Westinghouse_X1948 387.794 168s Westinghouse_X1949 -1621.262 168s Westinghouse_X1950 -1842.843 168s Westinghouse_X1951 599.149 168s Westinghouse_X1952 1911.642 168s Westinghouse_X1953 1976.568 168s Westinghouse_X1954 -2883.365 168s Chrysler_(Intercept) Chrysler_value 168s 0 0 168s Chrysler_capital General.Electric_(Intercept) 168s 0 0 168s General.Electric_value General.Electric_capital 168s 0 0 168s General.Motors_(Intercept) General.Motors_value 168s 0 0 168s General.Motors_capital US.Steel_(Intercept) 168s 0 0 168s US.Steel_value US.Steel_capital 168s 0 0 168s Westinghouse_(Intercept) Westinghouse_value 168s 0 0 168s Westinghouse_capital 168s 0 168s [1] "Error in estfun.systemfit(greeneOlsPooled) : \n returning the estimation function for models with restrictions has not yet been implemented.\n" 168s attr(,"class") 168s [1] "try-error" 168s attr(,"condition") 168s 168s Error in estfun.systemfit(greeneOlsPooled) : 168s returning the estimation function for models with restrictions has not yet been implemented. 168s Chrysler_(Intercept) Chrysler_value Chrysler_capital 168s Chrysler_X1935 0.061827 25.813 0.64918 168s Chrysler_X1936 0.089260 74.782 0.91045 168s Chrysler_X1937 -0.052866 -46.729 -1.83447 168s Chrysler_X1938 0.038353 16.795 1.98668 168s Chrysler_X1939 -0.125156 -85.069 -8.04755 168s Chrysler_X1940 -0.019863 -14.456 -1.33281 168s Chrysler_X1941 -0.000958 -0.617 -0.07206 168s Chrysler_X1942 -0.035485 -14.581 -2.53362 168s Chrysler_X1943 -0.121241 -71.338 -8.13529 168s Chrysler_X1944 -0.067270 -46.981 -4.06984 168s Chrysler_X1945 0.103440 87.551 5.64781 168s Chrysler_X1946 -0.121081 -108.222 -10.26763 168s Chrysler_X1947 -0.065512 -37.931 -6.34155 168s Chrysler_X1948 0.053900 37.439 5.93977 168s Chrysler_X1949 -0.066320 -39.149 -9.77563 168s Chrysler_X1950 0.012935 8.971 2.11101 168s Chrysler_X1951 0.338038 273.472 68.79064 168s Chrysler_X1952 0.035175 25.572 10.22178 168s Chrysler_X1953 -0.016558 -16.583 -5.73086 168s Chrysler_X1954 -0.040615 -28.561 -16.85128 168s General.Electric_X1935 -0.000794 -0.332 -0.00834 168s General.Electric_X1936 -0.018766 -15.722 -0.19142 168s General.Electric_X1937 -0.017841 -15.770 -0.61909 168s General.Electric_X1938 -0.025844 -11.317 -1.33872 168s General.Electric_X1939 -0.031739 -21.573 -2.04083 168s General.Electric_X1940 -0.006211 -4.520 -0.41674 168s General.Electric_X1941 0.033478 21.546 2.51754 168s General.Electric_X1942 0.015339 6.303 1.09520 168s General.Electric_X1943 -0.020477 -12.049 -1.37400 168s General.Electric_X1944 -0.022551 -15.749 -1.36432 168s General.Electric_X1945 -0.000552 -0.467 -0.03015 168s General.Electric_X1946 0.048030 42.930 4.07298 168s General.Electric_X1947 0.042267 24.472 4.09142 168s General.Electric_X1948 0.033204 23.064 3.65913 168s General.Electric_X1949 -0.011862 -7.002 -1.74842 168s General.Electric_X1950 -0.025261 -17.518 -4.12252 168s General.Electric_X1951 0.001752 1.417 0.35646 168s General.Electric_X1952 0.006337 4.607 1.84166 168s General.Electric_X1953 0.007751 7.762 2.68249 168s General.Electric_X1954 -0.006261 -4.402 -2.59748 168s General.Motors_X1935 0.015266 6.374 0.16030 168s General.Motors_X1936 -0.003913 -3.278 -0.03991 168s General.Motors_X1937 -0.019260 -17.024 -0.66833 168s General.Motors_X1938 0.000502 0.220 0.02603 168s General.Motors_X1939 -0.014763 -10.035 -0.94928 168s General.Motors_X1940 -0.002163 -1.575 -0.14517 168s General.Motors_X1941 0.004002 2.576 0.30095 168s General.Motors_X1942 0.014599 5.999 1.04234 168s General.Motors_X1943 0.010244 6.027 0.68736 168s General.Motors_X1944 0.014852 10.373 0.89857 168s General.Motors_X1945 0.005493 4.649 0.29991 168s General.Motors_X1946 0.014990 13.398 1.27114 168s General.Motors_X1947 0.002105 1.219 0.20375 168s General.Motors_X1948 -0.007587 -5.270 -0.83607 168s General.Motors_X1949 -0.016803 -9.919 -2.47682 168s General.Motors_X1950 -0.009602 -6.659 -1.56700 168s General.Motors_X1951 -0.017864 -14.452 -3.63526 168s General.Motors_X1952 -0.012355 -8.982 -3.59050 168s General.Motors_X1953 0.004869 4.876 1.68503 168s General.Motors_X1954 0.017389 12.228 7.21481 168s US.Steel_X1935 0.013928 5.815 0.14625 168s US.Steel_X1936 -0.026161 -21.918 -0.26684 168s US.Steel_X1937 -0.025907 -22.899 -0.89897 168s US.Steel_X1938 0.043429 19.017 2.24961 168s US.Steel_X1939 0.070526 47.937 4.53484 168s US.Steel_X1940 0.058816 42.806 3.94653 168s US.Steel_X1941 -0.016278 -10.476 -1.22408 168s US.Steel_X1942 -0.008142 -3.346 -0.58136 168s US.Steel_X1943 0.018146 10.677 1.21761 168s US.Steel_X1944 0.036672 25.612 2.21866 168s US.Steel_X1945 0.039460 33.399 2.15450 168s US.Steel_X1946 -0.012632 -11.291 -1.07122 168s US.Steel_X1947 -0.018481 -10.700 -1.78894 168s US.Steel_X1948 -0.047880 -33.258 -5.27643 168s US.Steel_X1949 -0.003976 -2.347 -0.58605 168s US.Steel_X1950 -0.007908 -5.484 -1.29060 168s US.Steel_X1951 -0.052722 -42.652 -10.72894 168s US.Steel_X1952 -0.064309 -46.753 -18.68822 168s US.Steel_X1953 -0.039465 -39.524 -13.65875 168s US.Steel_X1954 0.042884 30.156 17.79265 168s Westinghouse_X1935 -0.000639 -0.267 -0.00671 168s Westinghouse_X1936 0.003489 2.923 0.03559 168s Westinghouse_X1937 0.005946 5.256 0.20632 168s Westinghouse_X1938 0.008196 3.589 0.42458 168s Westinghouse_X1939 0.009675 6.576 0.62207 168s Westinghouse_X1940 0.007107 5.172 0.47686 168s Westinghouse_X1941 -0.011506 -7.406 -0.86528 168s Westinghouse_X1942 -0.005817 -2.390 -0.41532 168s Westinghouse_X1943 0.002074 1.221 0.13919 168s Westinghouse_X1944 0.002100 1.466 0.12704 168s Westinghouse_X1945 0.005777 4.890 0.31543 168s Westinghouse_X1946 -0.004096 -3.661 -0.34734 168s Westinghouse_X1947 -0.012571 -7.279 -1.21688 168s Westinghouse_X1948 -0.003981 -2.765 -0.43871 168s Westinghouse_X1949 0.006180 3.648 0.91087 168s Westinghouse_X1950 0.008074 5.599 1.31765 168s Westinghouse_X1951 -0.004997 -4.043 -1.01696 168s Westinghouse_X1952 -0.011575 -8.415 -3.36372 168s Westinghouse_X1953 -0.010300 -10.316 -3.56494 168s Westinghouse_X1954 0.006866 4.828 2.84858 168s General.Electric_(Intercept) General.Electric_value 168s Chrysler_X1935 0.006590 7.715 168s Chrysler_X1936 0.009515 19.180 168s Chrysler_X1937 -0.005635 -15.797 168s Chrysler_X1938 0.004088 8.339 168s Chrysler_X1939 -0.013341 -30.100 168s Chrysler_X1940 -0.002117 -4.514 168s Chrysler_X1941 -0.000102 -0.187 168s Chrysler_X1942 -0.003782 -6.007 168s Chrysler_X1943 -0.012924 -22.609 168s Chrysler_X1944 -0.007171 -12.098 168s Chrysler_X1945 0.011026 22.137 168s Chrysler_X1946 -0.012907 -28.501 168s Chrysler_X1947 -0.006983 -11.569 168s Chrysler_X1948 0.005745 9.218 168s Chrysler_X1949 -0.007069 -10.122 168s Chrysler_X1950 0.001379 2.221 168s Chrysler_X1951 0.036033 65.558 168s Chrysler_X1952 0.003749 7.798 168s Chrysler_X1953 -0.001765 -4.186 168s Chrysler_X1954 -0.004329 -11.949 168s General.Electric_X1935 -0.003192 -3.736 168s General.Electric_X1936 -0.075425 -152.042 168s General.Electric_X1937 -0.071707 -201.016 168s General.Electric_X1938 -0.103871 -211.866 168s General.Electric_X1939 -0.127565 -287.812 168s General.Electric_X1940 -0.024962 -53.224 168s General.Electric_X1941 0.134553 246.784 168s General.Electric_X1942 0.061649 97.899 168s General.Electric_X1943 -0.082300 -143.975 168s General.Electric_X1944 -0.090635 -152.920 168s General.Electric_X1945 -0.002219 -4.456 168s General.Electric_X1946 0.193042 426.295 168s General.Electric_X1947 0.169877 281.435 168s General.Electric_X1948 0.133454 214.114 168s General.Electric_X1949 -0.047674 -68.260 168s General.Electric_X1950 -0.101526 -163.508 168s General.Electric_X1951 0.007040 12.809 168s General.Electric_X1952 0.025471 52.972 168s General.Electric_X1953 0.031151 73.878 168s General.Electric_X1954 -0.025162 -69.445 168s General.Motors_X1935 -0.016212 -18.978 168s General.Motors_X1936 0.004155 8.376 168s General.Motors_X1937 0.020453 57.337 168s General.Motors_X1938 -0.000534 -1.088 168s General.Motors_X1939 0.015678 35.372 168s General.Motors_X1940 0.002297 4.899 168s General.Motors_X1941 -0.004250 -7.795 168s General.Motors_X1942 -0.015503 -24.619 168s General.Motors_X1943 -0.010878 -19.031 168s General.Motors_X1944 -0.015772 -26.611 168s General.Motors_X1945 -0.005833 -11.711 168s General.Motors_X1946 -0.015918 -35.152 168s General.Motors_X1947 -0.002235 -3.703 168s General.Motors_X1948 0.008057 12.926 168s General.Motors_X1949 0.017844 25.549 168s General.Motors_X1950 0.010196 16.421 168s General.Motors_X1951 0.018970 34.514 168s General.Motors_X1952 0.013121 27.287 168s General.Motors_X1953 -0.005170 -12.262 168s General.Motors_X1954 -0.018466 -50.965 168s US.Steel_X1935 0.000660 0.772 168s US.Steel_X1936 -0.001239 -2.497 168s US.Steel_X1937 -0.001227 -3.439 168s US.Steel_X1938 0.002057 4.195 168s US.Steel_X1939 0.003340 7.535 168s US.Steel_X1940 0.002785 5.939 168s US.Steel_X1941 -0.000771 -1.414 168s US.Steel_X1942 -0.000386 -0.612 168s US.Steel_X1943 0.000859 1.503 168s US.Steel_X1944 0.001737 2.930 168s US.Steel_X1945 0.001869 3.752 168s US.Steel_X1946 -0.000598 -1.321 168s US.Steel_X1947 -0.000875 -1.450 168s US.Steel_X1948 -0.002267 -3.638 168s US.Steel_X1949 -0.000188 -0.270 168s US.Steel_X1950 -0.000374 -0.603 168s US.Steel_X1951 -0.002497 -4.542 168s US.Steel_X1952 -0.003045 -6.333 168s US.Steel_X1953 -0.001869 -4.432 168s US.Steel_X1954 0.002031 5.605 168s Westinghouse_X1935 -0.005793 -6.781 168s Westinghouse_X1936 0.031644 63.787 168s Westinghouse_X1937 0.053929 151.178 168s Westinghouse_X1938 0.074341 151.634 168s Westinghouse_X1939 0.087747 197.975 168s Westinghouse_X1940 0.064457 137.434 168s Westinghouse_X1941 -0.104362 -191.410 168s Westinghouse_X1942 -0.052757 -83.779 168s Westinghouse_X1943 0.018814 32.913 168s Westinghouse_X1944 0.019045 32.133 168s Westinghouse_X1945 0.052397 105.198 168s Westinghouse_X1946 -0.037151 -82.040 168s Westinghouse_X1947 -0.114019 -188.895 168s Westinghouse_X1948 -0.036108 -57.931 168s Westinghouse_X1949 0.056048 80.250 168s Westinghouse_X1950 0.073229 117.935 168s Westinghouse_X1951 -0.045325 -82.465 168s Westinghouse_X1952 -0.104985 -218.337 168s Westinghouse_X1953 -0.093423 -221.562 168s Westinghouse_X1954 0.062271 171.863 168s General.Electric_capital General.Motors_(Intercept) 168s Chrysler_X1935 0.6445 1.06e-03 168s Chrysler_X1936 0.9933 1.53e-03 168s Chrysler_X1937 -0.6650 -9.08e-04 168s Chrysler_X1938 0.6386 6.59e-04 168s Chrysler_X1939 -2.3026 -2.15e-03 168s Chrysler_X1940 -0.3951 -3.41e-04 168s Chrysler_X1941 -0.0226 -1.65e-05 168s Chrysler_X1942 -1.0886 -6.10e-04 168s Chrysler_X1943 -4.1343 -2.08e-03 168s Chrysler_X1944 -2.3039 -1.16e-03 168s Chrysler_X1945 3.5239 1.78e-03 168s Chrysler_X1946 -4.4657 -2.08e-03 168s Chrysler_X1947 -3.1871 -1.13e-03 168s Chrysler_X1948 3.1221 9.26e-04 168s Chrysler_X1949 -4.3710 -1.14e-03 168s Chrysler_X1950 0.8926 2.22e-04 168s Chrysler_X1951 24.1889 5.81e-03 168s Chrysler_X1952 2.7225 6.04e-04 168s Chrysler_X1953 -1.4126 -2.84e-04 168s Chrysler_X1954 -3.8484 -6.98e-04 168s General.Electric_X1935 -0.3121 1.36e-04 168s General.Electric_X1936 -7.8744 3.21e-03 168s General.Electric_X1937 -8.4614 3.05e-03 168s General.Electric_X1938 -16.2246 4.42e-03 168s General.Electric_X1939 -22.0177 5.43e-03 168s General.Electric_X1940 -4.6579 1.06e-03 168s General.Electric_X1941 29.7228 -5.73e-03 168s General.Electric_X1942 17.7427 -2.63e-03 168s General.Electric_X1943 -26.3277 3.50e-03 168s General.Electric_X1944 -29.1212 3.86e-03 168s General.Electric_X1945 -0.7094 9.45e-05 168s General.Electric_X1946 66.7926 -8.22e-03 168s General.Electric_X1947 77.5319 -7.23e-03 168s General.Electric_X1948 72.5190 -5.68e-03 168s General.Electric_X1949 -29.4770 2.03e-03 168s General.Electric_X1950 -65.7280 4.32e-03 168s General.Electric_X1951 4.7261 -3.00e-04 168s General.Electric_X1952 18.4946 -1.08e-03 168s General.Electric_X1953 24.9302 -1.33e-03 168s General.Electric_X1954 -22.3665 1.07e-03 168s General.Motors_X1935 -1.5855 2.13e-02 168s General.Motors_X1936 0.4338 -5.46e-03 168s General.Motors_X1937 2.4135 -2.69e-02 168s General.Motors_X1938 -0.0833 7.00e-04 168s General.Motors_X1939 2.7060 -2.06e-02 168s General.Motors_X1940 0.4287 -3.02e-03 168s General.Motors_X1941 -0.9388 5.58e-03 168s General.Motors_X1942 -4.4617 2.04e-02 168s General.Motors_X1943 -3.4800 1.43e-02 168s General.Motors_X1944 -5.0677 2.07e-02 168s General.Motors_X1945 -1.8642 7.66e-03 168s General.Motors_X1946 -5.5077 2.09e-02 168s General.Motors_X1947 -1.0202 2.93e-03 168s General.Motors_X1948 4.3781 -1.06e-02 168s General.Motors_X1949 11.0331 -2.34e-02 168s General.Motors_X1950 6.6012 -1.34e-02 168s General.Motors_X1951 12.7347 -2.49e-02 168s General.Motors_X1952 9.5270 -1.72e-02 168s General.Motors_X1953 -4.1377 6.79e-03 168s General.Motors_X1954 -16.4148 2.42e-02 168s US.Steel_X1935 0.0645 -3.30e-03 168s US.Steel_X1936 -0.1293 6.19e-03 168s US.Steel_X1937 -0.1448 6.13e-03 168s US.Steel_X1938 0.3212 -1.03e-02 168s US.Steel_X1939 0.5764 -1.67e-02 168s US.Steel_X1940 0.5197 -1.39e-02 168s US.Steel_X1941 -0.1703 3.85e-03 168s US.Steel_X1942 -0.1110 1.93e-03 168s US.Steel_X1943 0.2749 -4.29e-03 168s US.Steel_X1944 0.5580 -8.68e-03 168s US.Steel_X1945 0.5972 -9.34e-03 168s US.Steel_X1946 -0.2070 2.99e-03 168s US.Steel_X1947 -0.3994 4.37e-03 168s US.Steel_X1948 -1.2321 1.13e-02 168s US.Steel_X1949 -0.1164 9.41e-04 168s US.Steel_X1950 -0.2424 1.87e-03 168s US.Steel_X1951 -1.6760 1.25e-02 168s US.Steel_X1952 -2.2112 1.52e-02 168s US.Steel_X1953 -1.4956 9.34e-03 168s US.Steel_X1954 1.8051 -1.01e-02 168s Westinghouse_X1935 -0.5665 -4.91e-04 168s Westinghouse_X1936 3.3036 2.68e-03 168s Westinghouse_X1937 6.3636 4.57e-03 168s Westinghouse_X1938 11.6121 6.30e-03 168s Westinghouse_X1939 15.1452 7.44e-03 168s Westinghouse_X1940 12.0276 5.46e-03 168s Westinghouse_X1941 -23.0535 -8.84e-03 168s Westinghouse_X1942 -15.1836 -4.47e-03 168s Westinghouse_X1943 6.0186 1.59e-03 168s Westinghouse_X1944 6.1191 1.61e-03 168s Westinghouse_X1945 16.7462 4.44e-03 168s Westinghouse_X1946 -12.8541 -3.15e-03 168s Westinghouse_X1947 -52.0382 -9.66e-03 168s Westinghouse_X1948 -19.6209 -3.06e-03 168s Westinghouse_X1949 34.6547 4.75e-03 168s Westinghouse_X1950 47.4084 6.21e-03 168s Westinghouse_X1951 -30.4270 -3.84e-03 168s Westinghouse_X1952 -76.2296 -8.90e-03 168s Westinghouse_X1953 -74.7663 -7.92e-03 168s Westinghouse_X1954 55.3529 5.28e-03 168s General.Motors_value General.Motors_capital 168s Chrysler_X1935 3.2697 2.97e-03 168s Chrysler_X1936 7.1482 8.07e-02 168s Chrysler_X1937 -4.8925 -1.42e-01 168s Chrysler_X1938 1.8397 1.38e-01 168s Chrysler_X1939 -9.2736 -4.37e-01 168s Chrysler_X1940 -1.5846 -7.07e-02 168s Chrysler_X1941 -0.0749 -4.20e-03 168s Chrysler_X1942 -1.9776 -1.85e-01 168s Chrysler_X1943 -8.4430 -5.50e-01 168s Chrysler_X1944 -5.0608 -2.33e-01 168s Chrysler_X1945 8.6022 4.71e-01 168s Chrysler_X1946 -10.1940 -8.37e-01 168s Chrysler_X1947 -3.9688 -8.57e-01 168s Chrysler_X1948 3.0137 8.54e-01 168s Chrysler_X1949 -4.2157 -1.16e+00 168s Chrysler_X1950 0.8345 2.44e-01 168s Chrysler_X1951 28.0658 7.01e+00 168s Chrysler_X1952 2.9759 8.64e-01 168s Chrysler_X1953 -1.7755 -5.06e-01 168s Chrysler_X1954 -3.9028 -1.55e+00 168s General.Electric_X1935 0.4184 3.81e-04 168s General.Electric_X1936 14.9723 1.69e-01 168s General.Electric_X1937 16.4491 4.79e-01 168s General.Electric_X1938 12.3500 9.25e-01 168s General.Electric_X1939 23.4292 1.10e+00 168s General.Electric_X1940 4.9361 2.20e-01 168s General.Electric_X1941 -26.0763 -1.46e+00 168s General.Electric_X1942 -8.5163 -7.97e-01 168s General.Electric_X1943 14.2062 9.26e-01 168s General.Electric_X1944 16.9016 7.78e-01 168s General.Electric_X1945 0.4575 2.50e-02 168s General.Electric_X1946 -40.2860 -3.31e+00 168s General.Electric_X1947 -25.5097 -5.51e+00 168s General.Electric_X1948 -18.4956 -5.24e+00 168s General.Electric_X1949 7.5116 2.07e+00 168s General.Electric_X1950 16.2362 4.75e+00 168s General.Electric_X1951 -1.4489 -3.62e-01 168s General.Electric_X1952 -5.3416 -1.55e+00 168s General.Electric_X1953 -8.2795 -2.36e+00 168s General.Electric_X1954 5.9933 2.39e+00 168s General.Motors_X1935 65.5183 5.96e-02 168s General.Motors_X1936 -25.4300 -2.87e-01 168s General.Motors_X1937 -144.6452 -4.21e+00 168s General.Motors_X1938 1.9558 1.47e-01 168s General.Motors_X1939 -88.7707 -4.19e+00 168s General.Motors_X1940 -14.0060 -6.25e-01 168s General.Motors_X1941 25.3914 1.42e+00 168s General.Motors_X1942 66.0227 6.18e+00 168s General.Motors_X1943 57.8898 3.77e+00 168s General.Motors_X1944 90.6754 4.17e+00 168s General.Motors_X1945 37.0686 2.03e+00 168s General.Motors_X1946 102.4144 8.40e+00 168s General.Motors_X1947 10.3479 2.23e+00 168s General.Motors_X1948 -34.4239 -9.76e+00 168s General.Motors_X1949 -86.6782 -2.39e+01 168s General.Motors_X1950 -50.2708 -1.47e+01 168s General.Motors_X1951 -120.3581 -3.01e+01 168s General.Motors_X1952 -84.8289 -2.46e+01 168s General.Motors_X1953 42.3640 1.21e+01 168s General.Motors_X1954 135.6002 5.40e+01 168s US.Steel_X1935 -10.1444 -9.23e-03 168s US.Steel_X1936 28.8526 3.26e-01 168s US.Steel_X1937 33.0183 9.62e-01 168s US.Steel_X1938 -28.6886 -2.15e+00 168s US.Steel_X1939 -71.9676 -3.39e+00 168s US.Steel_X1940 -64.6193 -2.88e+00 168s US.Steel_X1941 17.5269 9.83e-01 168s US.Steel_X1942 6.2492 5.85e-01 168s US.Steel_X1943 -17.4030 -1.13e+00 168s US.Steel_X1944 -37.9949 -1.75e+00 168s US.Steel_X1945 -45.1924 -2.47e+00 168s US.Steel_X1946 14.6469 1.20e+00 168s US.Steel_X1947 15.4188 3.33e+00 168s US.Steel_X1948 36.8685 1.04e+01 168s US.Steel_X1949 3.4806 9.60e-01 168s US.Steel_X1950 7.0265 2.06e+00 168s US.Steel_X1951 60.2830 1.51e+01 168s US.Steel_X1952 74.9299 2.18e+01 168s US.Steel_X1953 58.2771 1.66e+01 168s US.Steel_X1954 -56.7511 -2.26e+01 168s Westinghouse_X1935 -1.5111 -1.37e-03 168s Westinghouse_X1936 12.4999 1.41e-01 168s Westinghouse_X1937 24.6178 7.17e-01 168s Westinghouse_X1938 17.5894 1.32e+00 168s Westinghouse_X1939 32.0707 1.51e+00 168s Westinghouse_X1940 25.3645 1.13e+00 168s Westinghouse_X1941 -40.2479 -2.26e+00 168s Westinghouse_X1942 -14.5028 -1.36e+00 168s Westinghouse_X1943 6.4627 4.21e-01 168s Westinghouse_X1944 7.0674 3.25e-01 168s Westinghouse_X1945 21.4937 1.18e+00 168s Westinghouse_X1946 -15.4283 -1.27e+00 168s Westinghouse_X1947 -34.0718 -7.36e+00 168s Westinghouse_X1948 -9.9583 -2.82e+00 168s Westinghouse_X1949 17.5737 4.84e+00 168s Westinghouse_X1950 23.3044 6.82e+00 168s Westinghouse_X1951 -18.5624 -4.64e+00 168s Westinghouse_X1952 -43.8127 -1.27e+01 168s Westinghouse_X1953 -49.4119 -1.41e+01 168s Westinghouse_X1954 29.5158 1.17e+01 168s US.Steel_(Intercept) US.Steel_value US.Steel_capital 168s Chrysler_X1935 -2.96e-03 -4.0379 -0.15945 168s Chrysler_X1936 -4.28e-03 -7.7323 -0.21608 168s Chrysler_X1937 2.53e-03 6.7824 0.29930 168s Chrysler_X1938 -1.84e-03 -3.3128 -0.47838 168s Chrysler_X1939 6.00e-03 11.7430 1.87608 168s Chrysler_X1940 9.52e-04 2.0975 0.24204 168s Chrysler_X1941 4.59e-05 0.1094 0.01201 168s Chrysler_X1942 1.70e-03 3.6889 0.50810 168s Chrysler_X1943 5.81e-03 11.5373 1.75404 168s Chrysler_X1944 3.22e-03 5.8493 0.90002 168s Chrysler_X1945 -4.96e-03 -9.1744 -1.06014 168s Chrysler_X1946 5.80e-03 12.0014 1.35006 168s Chrysler_X1947 3.14e-03 5.6424 0.83159 168s Chrysler_X1948 -2.58e-03 -4.2007 -0.79297 168s Chrysler_X1949 3.18e-03 5.2997 1.11622 168s Chrysler_X1950 -6.20e-04 -1.0401 -0.22186 168s Chrysler_X1951 -1.62e-02 -37.1002 -5.54355 168s Chrysler_X1952 -1.69e-03 -3.6411 -0.74900 168s Chrysler_X1953 7.94e-04 1.6124 0.49499 168s Chrysler_X1954 1.95e-03 4.1188 1.30389 168s General.Electric_X1935 1.69e-05 0.0230 0.00091 168s General.Electric_X1936 4.00e-04 0.7222 0.02018 168s General.Electric_X1937 3.80e-04 1.0168 0.04487 168s General.Electric_X1938 5.50e-04 0.9917 0.14321 168s General.Electric_X1939 6.76e-04 1.3230 0.21136 168s General.Electric_X1940 1.32e-04 0.2914 0.03362 168s General.Electric_X1941 -7.13e-04 -1.6972 -0.18636 168s General.Electric_X1942 -3.27e-04 -0.7084 -0.09757 168s General.Electric_X1943 4.36e-04 0.8656 0.13161 168s General.Electric_X1944 4.80e-04 0.8711 0.13403 168s General.Electric_X1945 1.18e-05 0.0218 0.00251 168s General.Electric_X1946 -1.02e-03 -2.1149 -0.23791 168s General.Electric_X1947 -9.00e-04 -1.6172 -0.23835 168s General.Electric_X1948 -7.07e-04 -1.1496 -0.21701 168s General.Electric_X1949 2.53e-04 0.4211 0.08869 168s General.Electric_X1950 5.38e-04 0.9023 0.19248 168s General.Electric_X1951 -3.73e-05 -0.0854 -0.01276 168s General.Electric_X1952 -1.35e-04 -0.2914 -0.05995 168s General.Electric_X1953 -1.65e-04 -0.3353 -0.10293 168s General.Electric_X1954 1.33e-04 0.2820 0.08929 168s General.Motors_X1935 1.01e-02 13.7309 0.54222 168s General.Motors_X1936 -2.58e-03 -4.6683 -0.13046 168s General.Motors_X1937 -1.27e-02 -34.0295 -1.50166 168s General.Motors_X1938 3.32e-04 0.5977 0.08631 168s General.Motors_X1939 -9.75e-03 -19.0765 -3.04769 168s General.Motors_X1940 -1.43e-03 -3.1463 -0.36306 168s General.Motors_X1941 2.64e-03 6.2893 0.69062 168s General.Motors_X1942 9.64e-03 20.9002 2.87877 168s General.Motors_X1943 6.76e-03 13.4247 2.04099 168s General.Motors_X1944 9.81e-03 17.7857 2.73663 168s General.Motors_X1945 3.63e-03 6.7092 0.77528 168s General.Motors_X1946 9.90e-03 20.4619 2.30180 168s General.Motors_X1947 1.39e-03 2.4966 0.36796 168s General.Motors_X1948 -5.01e-03 -8.1431 -1.53716 168s General.Motors_X1949 -1.11e-02 -18.4924 -3.89482 168s General.Motors_X1950 -6.34e-03 -10.6327 -2.26803 168s General.Motors_X1951 -1.18e-02 -27.0005 -4.03445 168s General.Motors_X1952 -8.16e-03 -17.6138 -3.62324 168s General.Motors_X1953 3.21e-03 6.5289 2.00435 168s General.Motors_X1954 1.15e-02 24.2859 7.68815 168s US.Steel_X1935 -8.99e-03 -12.2508 -0.48377 168s US.Steel_X1936 1.69e-02 30.5206 0.85291 168s US.Steel_X1937 1.67e-02 44.7615 1.97524 168s US.Steel_X1938 -2.80e-02 -50.5201 -7.29526 168s US.Steel_X1939 -4.55e-02 -89.1179 -14.23756 168s US.Steel_X1940 -3.80e-02 -83.6458 -9.65217 168s US.Steel_X1941 1.05e-02 25.0160 2.74698 168s US.Steel_X1942 5.26e-03 11.3993 1.57013 168s US.Steel_X1943 -1.17e-02 -23.2554 -3.53559 168s US.Steel_X1944 -2.37e-02 -42.9442 -6.60771 168s US.Steel_X1945 -2.55e-02 -47.1333 -5.44650 168s US.Steel_X1946 8.16e-03 16.8627 1.89692 168s US.Steel_X1947 1.19e-02 21.4365 3.15933 168s US.Steel_X1948 3.09e-02 50.2553 9.48663 168s US.Steel_X1949 2.57e-03 4.2789 0.90121 168s US.Steel_X1950 5.11e-03 8.5638 1.82670 168s US.Steel_X1951 3.40e-02 77.9272 11.64398 168s US.Steel_X1952 4.15e-02 89.6523 18.44196 168s US.Steel_X1953 2.55e-02 51.7535 15.88809 168s US.Steel_X1954 -2.77e-02 -58.5688 -18.54102 168s Westinghouse_X1935 -1.36e-03 -1.8578 -0.07336 168s Westinghouse_X1936 7.45e-03 13.4613 0.37618 168s Westinghouse_X1937 1.27e-02 33.9762 1.49930 168s Westinghouse_X1938 1.75e-02 31.5341 4.55362 168s Westinghouse_X1939 2.07e-02 40.4306 6.45923 168s Westinghouse_X1940 1.52e-02 33.4258 3.85712 168s Westinghouse_X1941 -2.46e-02 -58.4830 -6.42196 168s Westinghouse_X1942 -1.24e-02 -26.9329 -3.70970 168s Westinghouse_X1943 4.43e-03 8.7920 1.33667 168s Westinghouse_X1944 4.48e-03 8.1323 1.25129 168s Westinghouse_X1945 1.23e-02 22.8217 2.63717 168s Westinghouse_X1946 -8.75e-03 -18.0831 -2.03421 168s Westinghouse_X1947 -2.68e-02 -48.2250 -7.10746 168s Westinghouse_X1948 -8.50e-03 -13.8193 -2.60865 168s Westinghouse_X1949 1.32e-02 21.9947 4.63248 168s Westinghouse_X1950 1.72e-02 28.9161 6.16798 168s Westinghouse_X1951 -1.07e-02 -24.4289 -3.65019 168s Westinghouse_X1952 -2.47e-02 -53.3679 -10.97807 168s Westinghouse_X1953 -2.20e-02 -44.6732 -13.71448 168s Westinghouse_X1954 1.47e-02 31.0114 9.81721 168s Westinghouse_(Intercept) Westinghouse_value 168s Chrysler_X1935 -5.65e-03 -1.082 168s Chrysler_X1936 -8.16e-03 -4.208 168s Chrysler_X1937 4.83e-03 3.521 168s Chrysler_X1938 -3.50e-03 -1.964 168s Chrysler_X1939 1.14e-02 5.945 168s Chrysler_X1940 1.81e-03 1.141 168s Chrysler_X1941 8.76e-05 0.047 168s Chrysler_X1942 3.24e-03 1.819 168s Chrysler_X1943 1.11e-02 6.837 168s Chrysler_X1944 6.15e-03 3.852 168s Chrysler_X1945 -9.45e-03 -6.967 168s Chrysler_X1946 1.11e-02 8.413 168s Chrysler_X1947 5.99e-03 3.480 168s Chrysler_X1948 -4.92e-03 -3.262 168s Chrysler_X1949 6.06e-03 3.537 168s Chrysler_X1950 -1.18e-03 -0.751 168s Chrysler_X1951 -3.09e-02 -22.354 168s Chrysler_X1952 -3.21e-03 -2.777 168s Chrysler_X1953 1.51e-03 1.806 168s Chrysler_X1954 3.71e-03 4.412 168s General.Electric_X1935 6.17e-03 1.182 168s General.Electric_X1936 1.46e-01 75.280 168s General.Electric_X1937 1.39e-01 101.111 168s General.Electric_X1938 2.01e-01 112.591 168s General.Electric_X1939 2.47e-01 128.281 168s General.Electric_X1940 4.83e-02 30.346 168s General.Electric_X1941 -2.60e-01 -139.785 168s General.Electric_X1942 -1.19e-01 -66.920 168s General.Electric_X1943 1.59e-01 98.251 168s General.Electric_X1944 1.75e-01 109.867 168s General.Electric_X1945 4.29e-03 3.165 168s General.Electric_X1946 -3.73e-01 -283.963 168s General.Electric_X1947 -3.29e-01 -191.038 168s General.Electric_X1948 -2.58e-01 -170.961 168s General.Electric_X1949 9.22e-02 53.834 168s General.Electric_X1950 1.96e-01 124.738 168s General.Electric_X1951 -1.36e-02 -9.856 168s General.Electric_X1952 -4.93e-02 -42.572 168s General.Electric_X1953 -6.03e-02 -71.913 168s General.Electric_X1954 4.87e-02 57.863 168s General.Motors_X1935 -6.24e-02 -11.950 168s General.Motors_X1936 1.60e-02 8.253 168s General.Motors_X1937 7.87e-02 57.392 168s General.Motors_X1938 -2.05e-03 -1.151 168s General.Motors_X1939 6.03e-02 31.373 168s General.Motors_X1940 8.84e-03 5.558 168s General.Motors_X1941 -1.64e-02 -8.786 168s General.Motors_X1942 -5.97e-02 -33.488 168s General.Motors_X1943 -4.19e-02 -25.843 168s General.Motors_X1944 -6.07e-02 -38.047 168s General.Motors_X1945 -2.25e-02 -16.552 168s General.Motors_X1946 -6.13e-02 -46.597 168s General.Motors_X1947 -8.60e-03 -5.002 168s General.Motors_X1948 3.10e-02 20.539 168s General.Motors_X1949 6.87e-02 40.098 168s General.Motors_X1950 3.92e-02 24.930 168s General.Motors_X1951 7.30e-02 52.851 168s General.Motors_X1952 5.05e-02 43.640 168s General.Motors_X1953 -1.99e-02 -23.751 168s General.Motors_X1954 -7.11e-02 -84.506 168s US.Steel_X1935 5.67e-02 10.854 168s US.Steel_X1936 -1.06e-01 -54.933 168s US.Steel_X1937 -1.05e-01 -76.855 168s US.Steel_X1938 1.77e-01 99.039 168s US.Steel_X1939 2.87e-01 149.211 168s US.Steel_X1940 2.39e-01 150.428 168s US.Steel_X1941 -6.62e-02 -35.578 168s US.Steel_X1942 -3.31e-02 -18.595 168s US.Steel_X1943 7.38e-02 45.577 168s US.Steel_X1944 1.49e-01 93.525 168s US.Steel_X1945 1.61e-01 118.378 168s US.Steel_X1946 -5.14e-02 -39.094 168s US.Steel_X1947 -7.52e-02 -43.725 168s US.Steel_X1948 -1.95e-01 -129.046 168s US.Steel_X1949 -1.62e-02 -9.446 168s US.Steel_X1950 -3.22e-02 -20.441 168s US.Steel_X1951 -2.15e-01 -155.289 168s US.Steel_X1952 -2.62e-01 -226.135 168s US.Steel_X1953 -1.61e-01 -191.674 168s US.Steel_X1954 1.75e-01 207.479 168s Westinghouse_X1935 3.03e-02 5.802 168s Westinghouse_X1936 -1.66e-01 -85.410 168s Westinghouse_X1937 -2.82e-01 -205.647 168s Westinghouse_X1938 -3.89e-01 -217.923 168s Westinghouse_X1939 -4.59e-01 -238.632 168s Westinghouse_X1940 -3.37e-01 -211.909 168s Westinghouse_X1941 5.46e-01 293.206 168s Westinghouse_X1942 2.76e-01 154.873 168s Westinghouse_X1943 -9.84e-02 -60.742 168s Westinghouse_X1944 -9.96e-02 -62.433 168s Westinghouse_X1945 -2.74e-01 -202.055 168s Westinghouse_X1946 1.94e-01 147.788 168s Westinghouse_X1947 5.96e-01 346.758 168s Westinghouse_X1948 1.89e-01 125.092 168s Westinghouse_X1949 -2.93e-01 -171.160 168s Westinghouse_X1950 -3.83e-01 -243.315 168s Westinghouse_X1951 2.37e-01 171.608 168s Westinghouse_X1952 5.49e-01 474.533 168s Westinghouse_X1953 4.89e-01 583.245 168s Westinghouse_X1954 -3.26e-01 -387.265 168s Westinghouse_capital 168s Chrysler_X1935 -0.01017 168s Chrysler_X1936 -0.00652 168s Chrysler_X1937 0.03574 168s Chrysler_X1938 -0.06342 168s Chrysler_X1939 0.26872 168s Chrysler_X1940 0.04809 168s Chrysler_X1941 0.00317 168s Chrysler_X1942 0.19712 168s Chrysler_X1943 0.93491 168s Chrysler_X1944 0.56053 168s Chrysler_X1945 -0.87325 168s Chrysler_X1946 0.95137 168s Chrysler_X1947 0.66499 168s Chrysler_X1948 -0.64315 168s Chrysler_X1949 0.85922 168s Chrysler_X1950 -0.16155 168s Chrysler_X1951 -4.00575 168s Chrysler_X1952 -0.46760 168s Chrysler_X1953 0.26445 168s Chrysler_X1954 0.79226 168s General.Electric_X1935 0.01111 168s General.Electric_X1936 0.11671 168s General.Electric_X1937 1.02637 168s General.Electric_X1938 3.63650 168s General.Electric_X1939 5.79842 168s General.Electric_X1940 1.27948 168s General.Electric_X1941 -9.42136 168s General.Electric_X1942 -7.25009 168s General.Electric_X1943 13.43544 168s General.Electric_X1944 15.98834 168s General.Electric_X1945 0.39668 168s General.Electric_X1946 -32.11157 168s General.Electric_X1947 -36.50562 168s General.Electric_X1948 -33.71211 168s General.Electric_X1949 13.07588 168s General.Electric_X1950 26.84462 168s General.Electric_X1951 -1.76618 168s General.Electric_X1952 -7.16842 168s General.Electric_X1953 -10.53235 168s General.Electric_X1954 10.39092 168s General.Motors_X1935 -0.11232 168s General.Motors_X1936 0.01280 168s General.Motors_X1937 0.58258 168s General.Motors_X1938 -0.03717 168s General.Motors_X1939 1.41811 168s General.Motors_X1940 0.23434 168s General.Motors_X1941 -0.59216 168s General.Motors_X1942 -3.62807 168s General.Motors_X1943 -3.53399 168s General.Motors_X1944 -5.53672 168s General.Motors_X1945 -2.07456 168s General.Motors_X1946 -5.26934 168s General.Motors_X1947 -0.95586 168s General.Motors_X1948 4.05009 168s General.Motors_X1949 9.73943 168s General.Motors_X1950 5.36510 168s General.Motors_X1951 9.47046 168s General.Motors_X1952 7.34822 168s General.Motors_X1953 -3.47863 168s General.Motors_X1954 -15.17538 168s US.Steel_X1935 0.10202 168s US.Steel_X1936 -0.08517 168s US.Steel_X1937 -0.78015 168s US.Steel_X1938 3.19880 168s US.Steel_X1939 6.74450 168s US.Steel_X1940 6.34264 168s US.Steel_X1941 -2.39791 168s US.Steel_X1942 -2.01455 168s US.Steel_X1943 6.23245 168s US.Steel_X1944 13.61008 168s US.Steel_X1945 14.83734 168s US.Steel_X1946 -4.42093 168s US.Steel_X1947 -8.35538 168s US.Steel_X1948 -25.44676 168s US.Steel_X1949 -2.29427 168s US.Steel_X1950 -4.39917 168s US.Steel_X1951 -27.82678 168s US.Steel_X1952 -38.07729 168s US.Steel_X1953 -28.07253 168s US.Steel_X1954 37.25854 168s Westinghouse_X1935 0.05454 168s Westinghouse_X1936 -0.13242 168s Westinghouse_X1937 -2.08750 168s Westinghouse_X1938 -7.03855 168s Westinghouse_X1939 -10.78640 168s Westinghouse_X1940 -8.93489 168s Westinghouse_X1941 19.76178 168s Westinghouse_X1942 16.77886 168s Westinghouse_X1943 -8.30621 168s Westinghouse_X1944 -9.08553 168s Westinghouse_X1945 -25.32546 168s Westinghouse_X1946 16.71244 168s Westinghouse_X1947 66.26222 168s Westinghouse_X1948 24.66709 168s Westinghouse_X1949 -41.57334 168s Westinghouse_X1950 -52.36326 168s Westinghouse_X1951 30.75091 168s Westinghouse_X1952 79.90351 168s Westinghouse_X1953 85.42211 168s Westinghouse_X1954 -69.54427 168s Error in estfun.systemfit(greeneSurPooled) : 168s returning the estimation function for models with restrictions has not yet been implemented. 168s Chrysler_(Intercept) Chrysler_value 168s 0 0 168s Chrysler_capital General.Electric_(Intercept) 168s 0 0 168s General.Electric_value General.Electric_capital 168s 0 0 168s General.Motors_(Intercept) General.Motors_value 168s 0 0 168s General.Motors_capital US.Steel_(Intercept) 168s 0 0 168s US.Steel_value US.Steel_capital 168s 0 0 168s Westinghouse_(Intercept) Westinghouse_value 168s 0 0 168s Westinghouse_capital 168s 0 168s [1] "Error in estfun.systemfit(greeneSurPooled) : \n returning the estimation function for models with restrictions has not yet been implemented.\n" 168s attr(,"class") 168s [1] "try-error" 168s attr(,"condition") 168s 168s > 168s > ## **************** bread ************************ 168s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 168s + print( bread( theilOls ) ) 168s + 168s + print( bread( theilSur ) ) 168s + 168s + print( bread( greeneOls ) ) 168s + 168s + print( try( bread( greeneOlsPooled ) ) ) 168s + 168s + print( bread( greeneSur ) ) 168s + 168s + print( try( bread( greeneSurPooled ) ) ) 168s + } 168s General.Electric_(Intercept) 168s General.Electric_(Intercept) 50.64496 168s General.Electric_value -0.02323 168s General.Electric_capital -0.00888 168s Westinghouse_(Intercept) 0.00000 168s Westinghouse_value 0.00000 168s Westinghouse_capital 0.00000 168s General.Electric_value General.Electric_capital 168s General.Electric_(Intercept) -2.32e-02 -8.88e-03 168s General.Electric_value 1.25e-05 -2.43e-06 168s General.Electric_capital -2.43e-06 3.40e-05 168s Westinghouse_(Intercept) 0.00e+00 0.00e+00 168s Westinghouse_value 0.00e+00 0.00e+00 168s Westinghouse_capital 0.00e+00 0.00e+00 168s Westinghouse_(Intercept) Westinghouse_value 168s General.Electric_(Intercept) 0.0000 0.00e+00 168s General.Electric_value 0.0000 0.00e+00 168s General.Electric_capital 0.0000 0.00e+00 168s Westinghouse_(Intercept) 24.6366 -4.20e-02 168s Westinghouse_value -0.0420 9.46e-05 168s Westinghouse_capital 0.0648 -2.51e-04 168s Westinghouse_capital 168s General.Electric_(Intercept) 0.000000 168s General.Electric_value 0.000000 168s General.Electric_capital 0.000000 168s Westinghouse_(Intercept) 0.064774 168s Westinghouse_value -0.000251 168s Westinghouse_capital 0.001207 168s General.Electric_(Intercept) General.Electric_value 168s [1,] 29230.95 -13.17064 168s [2,] -13.17 0.00707 168s [3,] -5.85 -0.00136 168s [4,] 5078.50 -2.10754 168s [5,] -9.05 0.00480 168s [6,] 15.70 -0.01299 168s General.Electric_capital Westinghouse_(Intercept) Westinghouse_value 168s [1,] -5.849668 5078.50 -9.047719 168s [2,] -0.001362 -2.11 0.004800 168s [3,] 0.021226 -1.58 -0.000675 168s [4,] -1.584851 1935.63 -3.200900 168s [5,] -0.000675 -3.20 0.007194 168s [6,] 0.023793 4.54 -0.018984 168s Westinghouse_capital 168s [1,] 15.7006 168s [2,] -0.0130 168s [3,] 0.0238 168s [4,] 4.5447 168s [5,] -0.0190 168s [6,] 0.0957 168s Chrysler_(Intercept) Chrysler_value 168s Chrysler_(Intercept) 103.4623 -0.144448 168s Chrysler_value -0.1444 0.000226 168s Chrysler_capital 0.0138 -0.000102 168s General.Electric_(Intercept) 0.0000 0.000000 168s General.Electric_value 0.0000 0.000000 168s General.Electric_capital 0.0000 0.000000 168s General.Motors_(Intercept) 0.0000 0.000000 168s General.Motors_value 0.0000 0.000000 168s General.Motors_capital 0.0000 0.000000 168s US.Steel_(Intercept) 0.0000 0.000000 168s US.Steel_value 0.0000 0.000000 168s US.Steel_capital 0.0000 0.000000 168s Westinghouse_(Intercept) 0.0000 0.000000 168s Westinghouse_value 0.0000 0.000000 168s Westinghouse_capital 0.0000 0.000000 168s Chrysler_capital General.Electric_(Intercept) 168s Chrysler_(Intercept) 0.013776 0.0000 168s Chrysler_value -0.000102 0.0000 168s Chrysler_capital 0.000471 0.0000 168s General.Electric_(Intercept) 0.000000 126.6124 168s General.Electric_value 0.000000 -0.0581 168s General.Electric_capital 0.000000 -0.0222 168s General.Motors_(Intercept) 0.000000 0.0000 168s General.Motors_value 0.000000 0.0000 168s General.Motors_capital 0.000000 0.0000 168s US.Steel_(Intercept) 0.000000 0.0000 168s US.Steel_value 0.000000 0.0000 168s US.Steel_capital 0.000000 0.0000 168s Westinghouse_(Intercept) 0.000000 0.0000 168s Westinghouse_value 0.000000 0.0000 168s Westinghouse_capital 0.000000 0.0000 168s General.Electric_value General.Electric_capital 168s Chrysler_(Intercept) 0.00e+00 0.00e+00 168s Chrysler_value 0.00e+00 0.00e+00 168s Chrysler_capital 0.00e+00 0.00e+00 168s General.Electric_(Intercept) -5.81e-02 -2.22e-02 168s General.Electric_value 3.12e-05 -6.09e-06 168s General.Electric_capital -6.09e-06 8.50e-05 168s General.Motors_(Intercept) 0.00e+00 0.00e+00 168s General.Motors_value 0.00e+00 0.00e+00 168s General.Motors_capital 0.00e+00 0.00e+00 168s US.Steel_(Intercept) 0.00e+00 0.00e+00 168s US.Steel_value 0.00e+00 0.00e+00 168s US.Steel_capital 0.00e+00 0.00e+00 168s Westinghouse_(Intercept) 0.00e+00 0.00e+00 168s Westinghouse_value 0.00e+00 0.00e+00 168s Westinghouse_capital 0.00e+00 0.00e+00 168s General.Motors_(Intercept) General.Motors_value 168s Chrysler_(Intercept) 0.0000 0.00e+00 168s Chrysler_value 0.0000 0.00e+00 168s Chrysler_capital 0.0000 0.00e+00 168s General.Electric_(Intercept) 0.0000 0.00e+00 168s General.Electric_value 0.0000 0.00e+00 168s General.Electric_capital 0.0000 0.00e+00 168s General.Motors_(Intercept) 132.9858 -3.11e-02 168s General.Motors_value -0.0311 7.92e-06 168s General.Motors_capital 0.0108 -4.93e-06 168s US.Steel_(Intercept) 0.0000 0.00e+00 168s US.Steel_value 0.0000 0.00e+00 168s US.Steel_capital 0.0000 0.00e+00 168s Westinghouse_(Intercept) 0.0000 0.00e+00 168s Westinghouse_value 0.0000 0.00e+00 168s Westinghouse_capital 0.0000 0.00e+00 168s General.Motors_capital US.Steel_(Intercept) 168s Chrysler_(Intercept) 0.00e+00 0.0000 168s Chrysler_value 0.00e+00 0.0000 168s Chrysler_capital 0.00e+00 0.0000 168s General.Electric_(Intercept) 0.00e+00 0.0000 168s General.Electric_value 0.00e+00 0.0000 168s General.Electric_capital 0.00e+00 0.0000 168s General.Motors_(Intercept) 1.08e-02 0.0000 168s General.Motors_value -4.93e-06 0.0000 168s General.Motors_capital 1.63e-05 0.0000 168s US.Steel_(Intercept) 0.00e+00 235.6498 168s US.Steel_value 0.00e+00 -0.1119 168s US.Steel_capital 0.00e+00 -0.0336 168s Westinghouse_(Intercept) 0.00e+00 0.0000 168s Westinghouse_value 0.00e+00 0.0000 168s Westinghouse_capital 0.00e+00 0.0000 168s US.Steel_value US.Steel_capital 168s Chrysler_(Intercept) 0.00e+00 0.00e+00 168s Chrysler_value 0.00e+00 0.00e+00 168s Chrysler_capital 0.00e+00 0.00e+00 168s General.Electric_(Intercept) 0.00e+00 0.00e+00 168s General.Electric_value 0.00e+00 0.00e+00 168s General.Electric_capital 0.00e+00 0.00e+00 168s General.Motors_(Intercept) 0.00e+00 0.00e+00 168s General.Motors_value 0.00e+00 0.00e+00 168s General.Motors_capital 0.00e+00 0.00e+00 168s US.Steel_(Intercept) -1.12e-01 -3.36e-02 168s US.Steel_value 5.95e-05 -1.79e-05 168s US.Steel_capital -1.79e-05 2.30e-04 168s Westinghouse_(Intercept) 0.00e+00 0.00e+00 168s Westinghouse_value 0.00e+00 0.00e+00 168s Westinghouse_capital 0.00e+00 0.00e+00 168s Westinghouse_(Intercept) Westinghouse_value 168s Chrysler_(Intercept) 0.000 0.000000 168s Chrysler_value 0.000 0.000000 168s Chrysler_capital 0.000 0.000000 168s General.Electric_(Intercept) 0.000 0.000000 168s General.Electric_value 0.000 0.000000 168s General.Electric_capital 0.000 0.000000 168s General.Motors_(Intercept) 0.000 0.000000 168s General.Motors_value 0.000 0.000000 168s General.Motors_capital 0.000 0.000000 168s US.Steel_(Intercept) 0.000 0.000000 168s US.Steel_value 0.000 0.000000 168s US.Steel_capital 0.000 0.000000 168s Westinghouse_(Intercept) 61.592 -0.105021 168s Westinghouse_value -0.105 0.000237 168s Westinghouse_capital 0.162 -0.000626 168s Westinghouse_capital 168s Chrysler_(Intercept) 0.000000 168s Chrysler_value 0.000000 168s Chrysler_capital 0.000000 168s General.Electric_(Intercept) 0.000000 168s General.Electric_value 0.000000 168s General.Electric_capital 0.000000 168s General.Motors_(Intercept) 0.000000 168s General.Motors_value 0.000000 168s General.Motors_capital 0.000000 168s US.Steel_(Intercept) 0.000000 168s US.Steel_value 0.000000 168s US.Steel_capital 0.000000 168s Westinghouse_(Intercept) 0.161935 168s Westinghouse_value -0.000626 168s Westinghouse_capital 0.003017 168s Error in bread.systemfit(greeneOlsPooled) : 168s returning the 'bread' for models with restrictions has not yet been implemented. 168s [1] "Error in bread.systemfit(greeneOlsPooled) : \n returning the 'bread' for models with restrictions has not yet been implemented.\n" 168s attr(,"class") 168s [1] "try-error" 168s attr(,"condition") 168s 168s Chrysler_(Intercept) Chrysler_value Chrysler_capital 168s [1,] 1.33e+04 -1.82e+01 9.57e-01 168s [2,] -1.82e+01 2.86e-02 -1.31e-02 168s [3,] 9.57e-01 -1.31e-02 6.69e-02 168s [4,] -2.94e+03 3.74e+00 1.98e+00 168s [5,] 1.28e+00 -1.86e-03 1.28e-04 168s [6,]Error in bread.systemfit(greeneSurPooled) : 168s returning the 'bread' for models with restrictions has not yet been implemented. 168s 8.80e-01 -2.96e-04 -5.56e-03 168s [7,] -1.56e+04 1.91e+01 7.79e+00 168s [8,] 3.28e+00 -4.91e-03 1.03e-03 168s [9,] -8.18e-02 3.42e-03 -1.89e-02 168s [10,] 1.80e+04 -1.87e+01 -2.45e+01 168s [11,] -7.46e+00 1.13e-02 -3.26e-03 168s [12,] -4.03e+00 -1.22e-02 1.03e-01 168s [13,] -3.04e+01 3.03e-01 -9.35e-01 168s [14,] 1.14e-01 -3.70e-04 1.18e-03 168s [15,] 2.42e-01 -6.41e-04 1.67e-03 168s General.Electric_(Intercept) General.Electric_value 168s [1,] -2936.42 1.28e+00 168s [2,] 3.74 -1.86e-03 168s [3,] 1.98 1.28e-04 168s [4,] 65119.82 -2.85e+01 168s [5,] -28.51 1.50e-02 168s [6,] -16.15 -1.70e-03 168s [7,] 57134.02 -2.61e+01 168s [8,] -11.96 6.35e-03 168s [9,] -3.52 -2.27e-03 168s [10,] 64429.20 -3.04e+01 168s [11,] -22.01 1.35e-02 168s [12,] -55.05 1.23e-02 168s [13,] 10286.79 -4.02e+00 168s [14,] -17.00 8.74e-03 168s [15,] 23.38 -2.16e-02 168s General.Electric_capital General.Motors_(Intercept) General.Motors_value 168s [1,] 8.80e-01 -1.56e+04 3.28e+00 168s [2,] -2.96e-04 1.91e+01 -4.91e-03 168s [3,] -5.56e-03 7.79e+00 1.03e-03 168s [4,] -1.61e+01 5.71e+04 -1.20e+01 168s [5,] -1.70e-03 -2.61e+01 6.35e-03 168s [6,] 4.86e-02 -8.74e+00 -9.49e-04 168s [7,] -8.74e+00 8.00e+05 -1.84e+02 168s [8,] -9.49e-04 -1.84e+02 4.68e-02 168s [9,] 1.98e-02 5.32e+01 -2.83e-02 168s [10,] -2.30e+00 -1.75e+05 3.73e+01 168s [11,] -1.07e-02 8.02e+01 -2.06e-02 168s [12,] 7.77e-02 2.01e+01 1.09e-02 168s [13,] -4.02e+00 1.10e+04 -2.33e+00 168s [14,] 1.04e-04 -2.06e+01 5.10e-03 168s [15,] 4.61e-02 3.98e+01 -1.28e-02 168s General.Motors_capital US.Steel_(Intercept) US.Steel_value 168s [1,] -0.08183 1.80e+04 -7.46e+00 168s [2,] 0.00342 -1.87e+01 1.13e-02 168s [3,] -0.01889 -2.45e+01 -3.26e-03 168s [4,] -3.51957 6.44e+04 -2.20e+01 168s [5,] -0.00227 -3.04e+01 1.35e-02 168s [6,] 0.01982 -2.30e+00 -1.07e-02 168s [7,] 53.22544 -1.75e+05 8.02e+01 168s [8,] -0.02835 3.73e+01 -2.06e-02 168s [9,] 0.10737 3.74e+00 1.39e-02 168s [10,] 3.74276 1.25e+06 -5.65e+02 168s [11,] 0.01386 -5.65e+02 3.00e-01 168s [12,] -0.10360 -3.12e+02 -9.01e-02 168s [13,] -0.48733 2.74e+04 -8.35e+00 168s [14,] -0.00238 -5.09e+01 2.23e-02 168s [15,] 0.02432 1.10e+02 -7.74e-02 168s US.Steel_capital Westinghouse_(Intercept) Westinghouse_value 168s [1,] -4.0281 -30.387 1.14e-01 168s [2,] -0.0122 0.303 -3.70e-04 168s [3,] 0.1031 -0.935 1.18e-03 168s [4,] -55.0482 10286.790 -1.70e+01 168s [5,] 0.0123 -4.016 8.74e-03 168s [6,] 0.0777 -4.021 1.04e-04 168s [7,] 20.0945 11026.166 -2.06e+01 168s [8,] 0.0109 -2.326 5.10e-03 168s [9,] -0.1036 -0.487 -2.38e-03 168s [10,] -311.9830 27440.848 -5.09e+01 168s [11,] -0.0901 -8.348 2.23e-02 168s [12,] 1.6331 -27.510 2.29e-02 168s [13,] -27.5101 3917.263 -5.99e+00 168s [14,] 0.0229 -5.992 1.29e-02 168s [15,] 0.1422 6.376 -3.12e-02 168s Westinghouse_capital 168s [1,] 2.42e-01 168s [2,] -6.41e-04 168s [3,] 1.67e-03 168s [4,] 2.34e+01 168s [5,] -2.16e-02 168s [6,] 4.61e-02 168s [7,] 3.98e+01 168s [8,] -1.28e-02 168s [9,] 2.43e-02 168s [10,] 1.10e+02 168s [11,] -7.74e-02 168s [12,] 1.42e-01 168s [13,] 6.38e+00 168s [14,] -3.12e-02 168s [15,] 1.70e-01 168s [1] "Error in bread.systemfit(greeneSurPooled) : \n returning the 'bread' for models with restrictions has not yet been implemented.\n" 168s attr(,"class") 168s [1] "try-error" 168s attr(,"condition") 168s 168s > 168s BEGIN TEST test_sur.R 168s 168s R version 4.3.2 (2023-10-31) -- "Eye Holes" 168s Copyright (C) 2023 The R Foundation for Statistical Computing 168s Platform: x86_64-pc-linux-gnu (64-bit) 168s 168s R is free software and comes with ABSOLUTELY NO WARRANTY. 168s You are welcome to redistribute it under certain conditions. 168s Type 'license()' or 'licence()' for distribution details. 168s 168s R is a collaborative project with many contributors. 168s Type 'contributors()' for more information and 168s 'citation()' on how to cite R or R packages in publications. 168s 168s Type 'demo()' for some demos, 'help()' for on-line help, or 168s 'help.start()' for an HTML browser interface to help. 168s Type 'q()' to quit R. 168s 168s > library( systemfit ) 168s Loading required package: Matrix 169s Loading required package: car 169s Loading required package: carData 169s Loading required package: lmtest 169s Loading required package: zoo 169s 169s Attaching package: ‘zoo’ 169s 169s The following objects are masked from ‘package:base’: 169s 169s as.Date, as.Date.numeric 169s 169s 169s Please cite the 'systemfit' package as: 169s 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/. 169s 169s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 169s https://r-forge.r-project.org/projects/systemfit/ 169s > options( digits = 3 ) 169s > 169s > data( "Kmenta" ) 169s > useMatrix <- FALSE 169s > 169s > demand <- consump ~ price + income 169s > supply <- consump ~ price + farmPrice + trend 169s > system <- list( demand = demand, supply = supply ) 169s > restrm <- matrix(0,1,7) # restriction matrix "R" 169s > restrm[1,3] <- 1 169s > restrm[1,7] <- -1 169s > restrict <- "demand_income - supply_trend = 0" 169s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 169s > restr2m[1,3] <- 1 169s > restr2m[1,7] <- -1 169s > restr2m[2,2] <- -1 169s > restr2m[2,5] <- 1 169s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 169s > restrict2 <- c( "demand_income - supply_trend = 0", 169s + "- demand_price + supply_price = 0.5" ) 169s > restrict2i <- c( "demand_income - supply_trend = 0", 169s + "- demand_price + supply_income = 0.5" ) 169s > tc <- matrix(0,7,6) 169s > tc[1,1] <- 1 169s > tc[2,2] <- 1 169s > tc[3,3] <- 1 169s > tc[4,4] <- 1 169s > tc[5,5] <- 1 169s > tc[6,6] <- 1 169s > tc[7,3] <- 1 169s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 169s > restr3m[1,2] <- -1 169s > restr3m[1,5] <- 1 169s > restr3q <- c( 0.5 ) # restriction vector "q" 2 169s > restrict3 <- "- C2 + C5 = 0.5" 169s > 169s > # the standard equations do not converge and lead to a singular weighting matrix 169s > # both in R and in EViews, since both equations have the same endogenous variable 169s > supply2 <- price ~ income + farmPrice + trend 169s > system2 <- list( demand = demand, supply = supply2 ) 169s > 169s > 169s > ## *************** SUR estimation ************************ 169s > fitsur1 <- systemfit( system, "SUR", data = Kmenta, useMatrix = useMatrix ) 169s > print( summary( fitsur1 ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 170 0.879 0.683 0.789 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 65.7 3.86 1.97 0.755 0.726 169s supply 20 16 104.1 6.50 2.55 0.612 0.539 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.73 4.14 169s supply 4.14 5.78 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.86 4.92 169s supply 4.92 6.50 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.982 169s supply 0.982 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 99.3329 7.5145 13.22 2.3e-10 *** 169s price -0.2755 0.0885 -3.11 0.0063 ** 169s income 0.2986 0.0419 7.12 1.7e-06 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.966 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 65.683 MSE: 3.864 Root MSE: 1.966 169s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 61.9662 11.0808 5.59 4.0e-05 *** 169s price 0.1469 0.0944 1.56 0.13941 169s farmPrice 0.2140 0.0399 5.37 6.3e-05 *** 169s trend 0.3393 0.0679 5.00 0.00013 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.55 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 104.058 MSE: 6.504 Root MSE: 2.55 169s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 169s 169s > nobs( fitsur1 ) 169s [1] 40 169s > 169s > ## ********************* SUR (EViews-like) ***************** 169s > fitsur1e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 169s + useMatrix = useMatrix ) 169s > print( summary( fitsur1e, useDfSys = TRUE ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 170 0.598 0.683 0.748 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.2 3.89 1.97 0.753 0.724 169s supply 20 16 103.5 6.47 2.54 0.614 0.541 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.17 3.41 169s supply 3.41 4.63 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.31 4.07 169s supply 4.07 5.18 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.982 169s supply 0.982 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 99.2757 6.9280 14.33 8.9e-16 *** 169s price -0.2713 0.0816 -3.33 0.0022 ** 169s income 0.2949 0.0387 7.63 8.9e-09 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.973 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 66.186 MSE: 3.893 Root MSE: 1.973 169s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 62.2942 9.9110 6.29 4.2e-07 *** 169s price 0.1461 0.0845 1.73 0.093 . 169s farmPrice 0.2121 0.0357 5.95 1.1e-06 *** 169s trend 0.3322 0.0607 5.47 4.6e-06 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.544 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 103.55 MSE: 6.472 Root MSE: 2.544 169s Multiple R-Squared: 0.614 Adjusted R-Squared: 0.541 169s 169s > nobs( fitsur1e ) 169s [1] 40 169s > 169s > ## ********************* SUR (methodResidCov="Theil") ***************** 169s > fitsur1r2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 169s + useMatrix = useMatrix ) 169s > print( summary( fitsur1r2 ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 172 -0.896 0.679 1.01 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.8 3.93 1.98 0.751 0.722 169s supply 20 16 105.3 6.58 2.57 0.607 0.534 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.73 4.28 169s supply 4.28 5.78 169s 169s warning: this covariance matrix is NOT positive semidefinit! 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.93 5.17 169s supply 5.17 6.58 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.984 169s supply 0.984 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 99.2120 7.5127 13.21 2.3e-10 *** 169s price -0.2667 0.0877 -3.04 0.0074 ** 169s income 0.2908 0.0406 7.16 1.6e-06 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.982 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 66.802 MSE: 3.93 Root MSE: 1.982 169s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 63.0768 10.9735 5.75 3.0e-05 *** 169s price 0.1439 0.0943 1.52 0.15 169s farmPrice 0.2064 0.0384 5.37 6.2e-05 *** 169s trend 0.3325 0.0640 5.19 8.9e-05 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.566 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 105.322 MSE: 6.583 Root MSE: 2.566 169s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.534 169s 169s > 169s > ## *************** SUR (methodResidCov="Theil", useDfSys = TRUE ) *************** 169s > fitsur1e2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 169s + x = TRUE, useMatrix = useMatrix ) 169s > print( summary( fitsur1e2, useDfSys = TRUE ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 172 -0.896 0.679 1.01 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.8 3.93 1.98 0.751 0.722 169s supply 20 16 105.3 6.58 2.57 0.607 0.534 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.73 4.28 169s supply 4.28 5.78 169s 169s warning: this covariance matrix is NOT positive semidefinit! 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.93 5.17 169s supply 5.17 6.58 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.984 169s supply 0.984 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 99.2120 7.5127 13.21 1.0e-14 *** 169s price -0.2667 0.0877 -3.04 0.0046 ** 169s income 0.2908 0.0406 7.16 3.3e-08 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.982 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 66.802 MSE: 3.93 Root MSE: 1.982 169s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 63.0768 10.9735 5.75 2.0e-06 *** 169s price 0.1439 0.0943 1.52 0.14 169s farmPrice 0.2064 0.0384 5.37 6.1e-06 *** 169s trend 0.3325 0.0640 5.19 1.0e-05 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.566 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 105.322 MSE: 6.583 Root MSE: 2.566 169s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.534 169s 169s > 169s > ## ********************* SUR (methodResidCov="max") ***************** 169s > fitsur1r3 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "max", 169s + useMatrix = useMatrix ) 169s > print( summary( fitsur1r3 ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 172 -0.735 0.68 0.957 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.7 3.92 1.98 0.751 0.722 169s supply 20 16 105.2 6.57 2.56 0.608 0.534 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.73 4.26 169s supply 4.26 5.78 169s 169s warning: this covariance matrix is NOT positive semidefinit! 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.92 5.15 169s supply 5.15 6.57 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.984 169s supply 0.984 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 99.2250 7.5129 13.21 2.3e-10 *** 169s price -0.2677 0.0878 -3.05 0.0073 ** 169s income 0.2916 0.0408 7.15 1.6e-06 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.98 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 66.671 MSE: 3.922 Root MSE: 1.98 169s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 62.9575 10.9850 5.73 3.1e-05 *** 169s price 0.1442 0.0944 1.53 0.15 169s farmPrice 0.2072 0.0386 5.37 6.2e-05 *** 169s trend 0.3333 0.0644 5.18 9.2e-05 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.564 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 105.187 MSE: 6.574 Root MSE: 2.564 169s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 169s 169s > 169s > ## *************** WSUR estimation ************************ 169s > fitsur1w <- systemfit( system, "SUR", data = Kmenta, residCovWeighted = TRUE, 169s + useMatrix = useMatrix ) 169s > summary( fitsur1w ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 170 0.879 0.683 0.789 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 65.7 3.86 1.97 0.755 0.726 169s supply 20 16 104.1 6.50 2.55 0.612 0.539 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.73 4.14 169s supply 4.14 5.78 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.86 4.92 169s supply 4.92 6.50 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.982 169s supply 0.982 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 99.3329 7.5145 13.22 2.3e-10 *** 169s price -0.2755 0.0885 -3.11 0.0063 ** 169s income 0.2986 0.0419 7.12 1.7e-06 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.966 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 65.683 MSE: 3.864 Root MSE: 1.966 169s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 61.9662 11.0808 5.59 4.0e-05 *** 169s price 0.1469 0.0944 1.56 0.13941 169s farmPrice 0.2140 0.0399 5.37 6.3e-05 *** 169s trend 0.3393 0.0679 5.00 0.00013 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.55 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 104.058 MSE: 6.504 Root MSE: 2.55 169s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 169s 169s > nobs( fitsur1w ) 169s [1] 40 169s > 169s > ## *************** WSUR (methodResidCov="Theil", useDfSys = TRUE ) *************** 169s > fitsur1we2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 169s + residCovWeighted = TRUE, useMatrix = useMatrix ) 169s > summary( fitsur1we2, useDfSys = TRUE ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 172 -0.896 0.679 1.01 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.8 3.93 1.98 0.751 0.722 169s supply 20 16 105.3 6.58 2.57 0.607 0.534 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.73 4.28 169s supply 4.28 5.78 169s 169s warning: this covariance matrix is NOT positive semidefinit! 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.93 5.17 169s supply 5.17 6.58 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.984 169s supply 0.984 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 99.2120 7.5127 13.21 1.0e-14 *** 169s price -0.2667 0.0877 -3.04 0.0046 ** 169s income 0.2908 0.0406 7.16 3.3e-08 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.982 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 66.802 MSE: 3.93 Root MSE: 1.982 169s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 63.0768 10.9735 5.75 2.0e-06 *** 169s price 0.1439 0.0943 1.52 0.14 169s farmPrice 0.2064 0.0384 5.37 6.1e-06 *** 169s trend 0.3325 0.0640 5.19 1.0e-05 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.566 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 105.322 MSE: 6.583 Root MSE: 2.566 169s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.534 169s 169s > 169s > 169s > ## *************** SUR with cross-equation restriction ************** 169s > fitsur2 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restrm, 169s + useMatrix = useMatrix ) 169s > print( summary( fitsur2 ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 34 179 0.933 0.665 0.753 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 71.6 4.21 2.05 0.733 0.702 169s supply 20 16 107.8 6.74 2.60 0.598 0.523 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.78 4.47 169s supply 4.47 5.94 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 4.21 5.24 169s supply 5.24 6.74 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.983 169s supply 0.983 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 98.8408 7.5581 13.08 8.0e-15 *** 169s price -0.2398 0.0860 -2.79 0.0086 ** 169s income 0.2670 0.0368 7.25 2.2e-08 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.052 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 71.597 MSE: 4.212 Root MSE: 2.052 169s Multiple R-Squared: 0.733 Adjusted R-Squared: 0.702 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 67.4283 10.6647 6.32 3.3e-07 *** 169s price 0.1332 0.0953 1.40 0.17 169s farmPrice 0.1795 0.0337 5.33 6.3e-06 *** 169s trend 0.2670 0.0368 7.25 2.2e-08 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.596 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 107.806 MSE: 6.738 Root MSE: 2.596 169s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 169s 169s > nobs( fitsur2 ) 169s [1] 40 169s > # the same with symbolically specified restrictions 169s > fitsur2Sym <- systemfit( system, "SUR", data = Kmenta, 169s + restrict.matrix = restrict, useMatrix = useMatrix ) 169s > all.equal( fitsur2, fitsur2Sym ) 169s [1] "Component “call”: target, current do not match when deparsed" 169s > nobs( fitsur2Sym ) 169s [1] 40 169s > 169s > ## *************** SUR with cross-equation restriction (EViews-like) ** 169s > fitsur2e <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restrm, 169s + methodResidCov = "noDfCor", x = TRUE, 169s + useMatrix = useMatrix ) 169s > print( summary( fitsur2e ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 34 180 0.62 0.663 0.707 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 72.6 4.27 2.07 0.729 0.697 169s supply 20 16 107.9 6.75 2.60 0.597 0.522 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.21 3.68 169s supply 3.68 4.75 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.63 4.35 169s supply 4.35 5.40 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.984 169s supply 0.984 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 98.7799 6.9687 14.17 8.9e-16 *** 169s price -0.2354 0.0795 -2.96 0.0056 ** 169s income 0.2631 0.0344 7.66 6.7e-09 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.066 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 72.577 MSE: 4.269 Root MSE: 2.066 169s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 67.6039 9.5712 7.06 3.7e-08 *** 169s price 0.1328 0.0853 1.56 0.13 169s farmPrice 0.1785 0.0305 5.85 1.3e-06 *** 169s trend 0.2631 0.0344 7.66 6.7e-09 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.597 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 107.917 MSE: 6.745 Root MSE: 2.597 169s Multiple R-Squared: 0.597 Adjusted R-Squared: 0.522 169s 169s > 169s > ## *************** WSUR with cross-equation restriction (EViews-like) ** 169s > fitsur2we <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restrm, 169s + methodResidCov = "noDfCor", residCovWeighted = TRUE, 169s + x = TRUE, useMatrix = useMatrix ) 169s > summary( fitsur2we ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 34 182 0.609 0.661 0.711 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 73 4.29 2.07 0.728 0.696 169s supply 20 16 109 6.79 2.61 0.595 0.519 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.19 3.69 169s supply 3.69 4.78 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.65 4.38 169s supply 4.38 5.43 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.985 169s supply 0.985 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 98.7542 6.9468 14.22 6.7e-16 *** 169s price -0.2335 0.0790 -2.96 0.0056 ** 169s income 0.2614 0.0338 7.74 5.3e-09 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.072 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 73.009 MSE: 4.295 Root MSE: 2.072 169s Multiple R-Squared: 0.728 Adjusted R-Squared: 0.696 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 67.8882 9.5640 7.10 3.4e-08 *** 169s price 0.1320 0.0855 1.55 0.13 169s farmPrice 0.1765 0.0301 5.86 1.3e-06 *** 169s trend 0.2614 0.0338 7.74 5.3e-09 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.606 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 108.634 MSE: 6.79 Root MSE: 2.606 169s Multiple R-Squared: 0.595 Adjusted R-Squared: 0.519 169s 169s > 169s > 169s > ## *************** SUR with restriction via restrict.regMat ******************* 169s > fitsur3 <- systemfit( system, "SUR", data = Kmenta, restrict.regMat = tc, 169s + useMatrix = useMatrix ) 169s > print( summary( fitsur3 ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 34 179 0.933 0.665 0.753 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 71.6 4.21 2.05 0.733 0.702 169s supply 20 16 107.8 6.74 2.60 0.598 0.523 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.78 4.47 169s supply 4.47 5.94 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 4.21 5.24 169s supply 5.24 6.74 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.983 169s supply 0.983 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 98.8408 7.5581 13.08 8.0e-15 *** 169s price -0.2398 0.0860 -2.79 0.0086 ** 169s income 0.2670 0.0368 7.25 2.2e-08 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.052 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 71.597 MSE: 4.212 Root MSE: 2.052 169s Multiple R-Squared: 0.733 Adjusted R-Squared: 0.702 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 67.4283 10.6647 6.32 3.3e-07 *** 169s price 0.1332 0.0953 1.40 0.17 169s farmPrice 0.1795 0.0337 5.33 6.3e-06 *** 169s trend 0.2670 0.0368 7.25 2.2e-08 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.596 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 107.806 MSE: 6.738 Root MSE: 2.596 169s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 169s 169s > nobs( fitsur3 ) 169s [1] 40 169s > 169s > ## *************** SUR with restriction via restrict.regMat (EViews-like) ************** 169s > fitsur3e <- systemfit( system, "SUR", data = Kmenta, restrict.regMat = tc, 169s + methodResidCov = "noDfCor", x = TRUE, 169s + useMatrix = useMatrix ) 169s > print( summary( fitsur3e ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 34 180 0.62 0.663 0.707 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 72.6 4.27 2.07 0.729 0.697 169s supply 20 16 107.9 6.75 2.60 0.597 0.522 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.21 3.68 169s supply 3.68 4.75 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.63 4.35 169s supply 4.35 5.40 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.984 169s supply 0.984 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 98.7799 6.9687 14.17 8.9e-16 *** 169s price -0.2354 0.0795 -2.96 0.0056 ** 169s income 0.2631 0.0344 7.66 6.7e-09 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.066 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 72.577 MSE: 4.269 Root MSE: 2.066 169s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 67.6039 9.5712 7.06 3.7e-08 *** 169s price 0.1328 0.0853 1.56 0.13 169s farmPrice 0.1785 0.0305 5.85 1.3e-06 *** 169s trend 0.2631 0.0344 7.66 6.7e-09 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.597 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 107.917 MSE: 6.745 Root MSE: 2.597 169s Multiple R-Squared: 0.597 Adjusted R-Squared: 0.522 169s 169s > 169s > ## *************** WSUR with restriction via restrict.regMat ******************* 169s > fitsur3w <- systemfit( system, "SUR", data = Kmenta, restrict.regMat = tc, 169s + residCovWeighted = TRUE, x = TRUE, useMatrix = useMatrix ) 169s > summary( fitsur3w ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 34 181 0.919 0.663 0.757 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 72 4.24 2.06 0.731 0.700 169s supply 20 16 109 6.79 2.60 0.595 0.519 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.75 4.48 169s supply 4.48 5.98 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 4.24 5.28 169s supply 5.28 6.79 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.984 169s supply 0.984 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 98.8139 7.5317 13.12 7.3e-15 *** 169s price -0.2378 0.0854 -2.79 0.0087 ** 169s income 0.2653 0.0361 7.34 1.7e-08 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.058 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 72.023 MSE: 4.237 Root MSE: 2.058 169s Multiple R-Squared: 0.731 Adjusted R-Squared: 0.7 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 67.7366 10.6556 6.36 3.0e-07 *** 169s price 0.1324 0.0955 1.39 0.17 169s farmPrice 0.1774 0.0332 5.35 6.1e-06 *** 169s trend 0.2653 0.0361 7.34 1.7e-08 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.605 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 108.579 MSE: 6.786 Root MSE: 2.605 169s Multiple R-Squared: 0.595 Adjusted R-Squared: 0.519 169s 169s > 169s > 169s > ## *************** SUR with 2 restrictions *************************** 169s > fitsur4 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr2m, 169s + restrict.rhs = restr2q, useMatrix = useMatrix ) 169s > print( summary( fitsur4 ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 35 165 1.76 0.691 0.69 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 64 3.76 1.94 0.761 0.733 169s supply 20 16 101 6.34 2.52 0.622 0.551 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.76 4.46 169s supply 4.46 5.99 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.76 4.70 169s supply 4.70 6.34 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.962 169s supply 0.962 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 96.8275 7.4665 12.97 6.2e-15 *** 169s price -0.2798 0.0840 -3.33 0.002 ** 169s income 0.3286 0.0206 15.93 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.94 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 63.987 MSE: 3.764 Root MSE: 1.94 169s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 52.9386 7.6655 6.91 5.1e-08 *** 169s price 0.2202 0.0840 2.62 0.013 * 169s farmPrice 0.2327 0.0212 10.97 7.2e-13 *** 169s trend 0.3286 0.0206 15.93 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.518 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 101.473 MSE: 6.342 Root MSE: 2.518 169s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 169s 169s > nobs( fitsur4 ) 169s [1] 40 169s > # the same with symbolically specified restrictions 169s > fitsur4Sym <- systemfit( system, "SUR", data = Kmenta, 169s + restrict.matrix = restrict2, useMatrix = useMatrix ) 169s > all.equal( fitsur4, fitsur4Sym ) 169s [1] "Component “call”: target, current do not match when deparsed" 169s > 169s > ## *************** SUR with 2 restrictions (EViews-like) ************** 169s > fitsur4e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 169s + restrict.matrix = restr2m, restrict.rhs = restr2q, useMatrix = useMatrix ) 169s > print( summary( fitsur4e ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 35 165 1.2 0.693 0.653 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 63.8 3.75 1.94 0.762 0.734 169s supply 20 16 100.8 6.30 2.51 0.624 0.553 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.20 3.67 169s supply 3.67 4.79 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.19 3.86 169s supply 3.86 5.04 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.962 169s supply 0.962 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 97.2678 6.9200 14.06 4.4e-16 *** 169s price -0.2851 0.0767 -3.72 7e-04 *** 169s income 0.3296 0.0184 17.86 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.937 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 63.811 MSE: 3.754 Root MSE: 1.937 169s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 53.3040 7.1045 7.5 8.7e-09 *** 169s price 0.2149 0.0767 2.8 0.0082 ** 169s farmPrice 0.2343 0.0187 12.6 1.6e-14 *** 169s trend 0.3296 0.0184 17.9 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.51 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 100.835 MSE: 6.302 Root MSE: 2.51 169s Multiple R-Squared: 0.624 Adjusted R-Squared: 0.553 169s 169s > 169s > ## *************** SUR with 2 restrictions (methodResidCov = "Theil") ************** 169s > fitsur4r2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 169s + restrict.matrix = restr2m, restrict.rhs = restr2q, useMatrix = useMatrix ) 169s > print( summary( fitsur4r2 ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 35 175 0.034 0.673 0.708 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 67 3.94 1.99 0.750 0.721 169s supply 20 16 108 6.76 2.60 0.596 0.521 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.76 4.61 169s supply 4.61 5.99 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.94 5.16 169s supply 5.16 6.76 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.967 169s supply 0.967 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 92.5266 7.2896 12.69 1.2e-14 *** 169s price -0.2304 0.0827 -2.79 0.0086 ** 169s income 0.3221 0.0166 19.37 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.986 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 67.048 MSE: 3.944 Root MSE: 1.986 169s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 48.7011 7.4034 6.58 1.3e-07 *** 169s price 0.2696 0.0827 3.26 0.0025 ** 169s farmPrice 0.2261 0.0166 13.62 1.6e-15 *** 169s trend 0.3221 0.0166 19.37 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.601 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 108.217 MSE: 6.764 Root MSE: 2.601 169s Multiple R-Squared: 0.596 Adjusted R-Squared: 0.521 169s 169s > 169s > ## *************** SUR with 2 restrictions (methodResidCov = "max") ************** 169s > fitsur4r3 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "max", 169s + restrict.matrix = restr2m, restrict.rhs = restr2q, 169s + x = TRUE, useMatrix = useMatrix ) 169s > print( summary( fitsur4r3 ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 35 173 0.217 0.677 0.702 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.4 3.91 1.98 0.752 0.723 169s supply 20 16 106.9 6.68 2.58 0.601 0.526 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.76 4.59 169s supply 4.59 5.99 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.91 5.09 169s supply 5.09 6.68 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.966 169s supply 0.966 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 93.1978 7.3168 12.74 1.1e-14 *** 169s price -0.2381 0.0829 -2.87 0.0069 ** 169s income 0.3231 0.0170 18.96 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.976 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 66.405 MSE: 3.906 Root MSE: 1.976 169s Multiple R-Squared: 0.752 Adjusted R-Squared: 0.723 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 49.3676 7.4381 6.64 1.1e-07 *** 169s price 0.2619 0.0829 3.16 0.0033 ** 169s farmPrice 0.2271 0.0171 13.29 3.1e-15 *** 169s trend 0.3231 0.0170 18.96 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.585 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 106.924 MSE: 6.683 Root MSE: 2.585 169s Multiple R-Squared: 0.601 Adjusted R-Squared: 0.526 169s 169s > 169s > ## *************** WSUR with 2 restrictions (EViews-like) ************** 169s > fitsur4we <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 169s + restrict.matrix = restr2m, restrict.rhs = restr2q, residCovWeighted = TRUE, 169s + useMatrix = useMatrix ) 169s > summary( fitsur4we ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 35 165 1.2 0.692 0.654 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 63.9 3.76 1.94 0.762 0.733 169s supply 20 16 101.2 6.33 2.52 0.623 0.552 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.18 3.69 169s supply 3.69 4.81 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.20 3.87 169s supply 3.87 5.06 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.962 169s supply 0.962 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 96.9414 6.8894 14.07 4.4e-16 *** 169s price -0.2814 0.0766 -3.67 8e-04 *** 169s income 0.3291 0.0181 18.18 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.939 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 63.936 MSE: 3.761 Root MSE: 1.939 169s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.733 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 52.9963 7.0652 7.50 8.7e-09 *** 169s price 0.2186 0.0766 2.85 0.0072 ** 169s farmPrice 0.2337 0.0183 12.76 1.0e-14 *** 169s trend 0.3291 0.0181 18.18 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.515 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 101.201 MSE: 6.325 Root MSE: 2.515 169s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 169s 169s > 169s > 169s > ## *************** SUR with 2 restrictions via R and restrict.regMat **************** 169s > fitsur5 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr3m, 169s + restrict.rhs = restr3q, restrict.regMat = tc, 169s + x = TRUE, useMatrix = useMatrix ) 169s > print( summary( fitsur5 ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 35 165 1.76 0.691 0.69 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 64 3.76 1.94 0.761 0.733 169s supply 20 16 101 6.34 2.52 0.622 0.551 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.76 4.46 169s supply 4.46 5.99 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.76 4.70 169s supply 4.70 6.34 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.962 169s supply 0.962 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 96.8275 7.4665 12.97 6.2e-15 *** 169s price -0.2798 0.0840 -3.33 0.002 ** 169s income 0.3286 0.0206 15.93 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.94 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 63.987 MSE: 3.764 Root MSE: 1.94 169s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 52.9386 7.6655 6.91 5.1e-08 *** 169s price 0.2202 0.0840 2.62 0.013 * 169s farmPrice 0.2327 0.0212 10.97 7.2e-13 *** 169s trend 0.3286 0.0206 15.93 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.518 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 101.473 MSE: 6.342 Root MSE: 2.518 169s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 169s 169s > nobs( fitsur5 ) 169s [1] 40 169s > # the same with symbolically specified restrictions 169s > fitsur5Sym <- systemfit( system, "SUR", data = Kmenta, 169s + restrict.matrix = restrict3, restrict.regMat = tc, 169s + x = TRUE, useMatrix = useMatrix ) 169s > all.equal( fitsur5, fitsur5Sym ) 169s [1] "Component “call”: target, current do not match when deparsed" 169s > 169s > ## *************** SUR with 2 restrictions via R and restrict.regMat (EViews-like) ************** 169s > fitsur5e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 169s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 169s + useMatrix = useMatrix ) 169s > print( summary( fitsur5e ) ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 35 165 1.2 0.693 0.653 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 63.8 3.75 1.94 0.762 0.734 169s supply 20 16 100.8 6.30 2.51 0.624 0.553 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.20 3.67 169s supply 3.67 4.79 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.19 3.86 169s supply 3.86 5.04 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.962 169s supply 0.962 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 97.2678 6.9200 14.06 4.4e-16 *** 169s price -0.2851 0.0767 -3.72 7e-04 *** 169s income 0.3296 0.0184 17.86 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.937 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 63.811 MSE: 3.754 Root MSE: 1.937 169s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 53.3040 7.1045 7.5 8.7e-09 *** 169s price 0.2149 0.0767 2.8 0.0082 ** 169s farmPrice 0.2343 0.0187 12.6 1.6e-14 *** 169s trend 0.3296 0.0184 17.9 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.51 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 100.835 MSE: 6.302 Root MSE: 2.51 169s Multiple R-Squared: 0.624 Adjusted R-Squared: 0.553 169s 169s > 169s > ## ************ WSUR with 2 restrictions via R and restrict.regMat ************ 169s > fitsur5w <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr3m, 169s + restrict.rhs = restr3q, restrict.regMat = tc, residCovWeighted = TRUE, 169s + useMatrix = useMatrix ) 169s > summary( fitsur5w ) 169s 169s systemfit results 169s method: SUR 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 35 166 1.75 0.69 0.691 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 64.2 3.77 1.94 0.761 0.733 169s supply 20 16 102.0 6.37 2.52 0.620 0.548 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.74 4.47 169s supply 4.47 6.02 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.77 4.72 169s supply 4.72 6.37 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 0.963 169s supply 0.963 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 96.4421 7.4234 12.99 6e-15 *** 169s price -0.2753 0.0838 -3.29 0.0023 ** 169s income 0.3280 0.0202 16.21 <2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.943 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 64.16 MSE: 3.774 Root MSE: 1.943 169s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: consump ~ price + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 52.5761 7.6099 6.91 5.0e-08 *** 169s price 0.2247 0.0838 2.68 0.011 * 169s farmPrice 0.2318 0.0208 11.14 4.7e-13 *** 169s trend 0.3280 0.0202 16.21 < 2e-16 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 2.524 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 101.967 MSE: 6.373 Root MSE: 2.524 169s Multiple R-Squared: 0.62 Adjusted R-Squared: 0.548 169s 169s > 169s > 169s > ## ************** iterated SUR **************************** 169s > fitsuri1 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 169s + useMatrix = useMatrix ) 169s > print( summary( fitsuri1 ) ) 169s 169s systemfit results 169s method: iterated SUR 169s 169s convergence achieved after 6 iterations 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 108 4.42 0.885 0.958 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.3 3.90 1.98 0.753 0.724 169s supply 20 16 41.4 2.59 1.61 0.938 0.926 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.90 -2.38 169s supply -2.38 2.59 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.90 -2.38 169s supply -2.38 2.59 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 -0.749 169s supply -0.749 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 94.0537 7.4051 12.70 4.2e-10 *** 169s price -0.2355 0.0882 -2.67 0.016 * 169s income 0.3117 0.0457 6.81 3.0e-06 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.975 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 66.286 MSE: 3.899 Root MSE: 1.975 169s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: price ~ income + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 89.2982 3.3822 26.4 1.3e-14 *** 169s income 0.6655 0.0423 15.7 3.7e-11 *** 169s farmPrice -0.4742 0.0372 -12.7 8.7e-10 *** 169s trend -0.7966 0.0656 -12.2 1.7e-09 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.609 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 41.411 MSE: 2.588 Root MSE: 1.609 169s Multiple R-Squared: 0.938 Adjusted R-Squared: 0.926 169s 169s > nobs( fitsuri1 ) 169s [1] 40 169s > 169s > ## ************** iterated SUR (EViews-like) ***************** 169s > fitsuri1e <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "noDfCor", 169s + maxit = 100, useMatrix = useMatrix ) 169s > print( summary( fitsuri1e, useDfSys = TRUE ) ) 169s 169s systemfit results 169s method: iterated SUR 169s 169s convergence achieved after 7 iterations 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 108 3.01 0.885 0.959 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.7 3.93 1.98 0.751 0.722 169s supply 20 16 41.2 2.57 1.60 0.938 0.927 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.34 -1.97 169s supply -1.97 2.06 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.34 -1.97 169s supply -1.97 2.06 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.00 -0.75 169s supply -0.75 1.00 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 93.6193 6.8499 13.67 4.0e-15 *** 169s price -0.2295 0.0816 -2.81 0.0082 ** 169s income 0.3100 0.0423 7.33 2.1e-08 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.981 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 66.742 MSE: 3.926 Root MSE: 1.981 169s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: price ~ income + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 89.2690 3.0165 29.6 < 2e-16 *** 169s income 0.6641 0.0377 17.6 < 2e-16 *** 169s farmPrice -0.4730 0.0332 -14.2 1.3e-15 *** 169s trend -0.7919 0.0585 -13.6 4.9e-15 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.604 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 41.176 MSE: 2.573 Root MSE: 1.604 169s Multiple R-Squared: 0.938 Adjusted R-Squared: 0.927 169s 169s > 169s > ## ************** iterated SUR (methodResidCov = "Theil") **************************** 169s > fitsuri1r2 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 169s + methodResidCov = "Theil", useMatrix = useMatrix ) 169s > print( summary( fitsuri1r2 ) ) 169s 169s systemfit results 169s method: iterated SUR 169s 169s convergence achieved after 7 iterations 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 109 4 0.884 0.961 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.9 3.94 1.98 0.750 0.721 169s supply 20 16 41.8 2.61 1.62 0.937 0.926 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.94 -2.51 169s supply -2.51 2.61 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.94 -2.51 169s supply -2.51 2.61 169s 169s The correlations of the residuals 169s demand supply 169s demand 1.000 -0.754 169s supply -0.754 1.000 169s 169s 169s SUR estimates for 'demand' (equation 1) 169s Model Formula: consump ~ price + income 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 93.4405 7.3821 12.66 4.4e-10 *** 169s price -0.2271 0.0877 -2.59 0.019 * 169s income 0.3093 0.0458 6.75 3.4e-06 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.984 on 17 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 17 169s SSR: 66.939 MSE: 3.938 Root MSE: 1.984 169s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 169s 169s 169s SUR estimates for 'supply' (equation 2) 169s Model Formula: price ~ income + farmPrice + trend 169s 169s Estimate Std. Error t value Pr(>|t|) 169s (Intercept) 89.1602 3.3868 26.3 1.3e-14 *** 169s income 0.6635 0.0423 15.7 3.9e-11 *** 169s farmPrice -0.4710 0.0369 -12.8 8.5e-10 *** 169s trend -0.7952 0.0643 -12.4 1.3e-09 *** 169s --- 169s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 169s 169s Residual standard error: 1.616 on 16 degrees of freedom 169s Number of observations: 20 Degrees of Freedom: 16 169s SSR: 41.764 MSE: 2.61 Root MSE: 1.616 169s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 169s 169s > 169s > ## ************** iterated SUR (methodResidCov="Theil", useDfSys=TRUE) ***************** 169s > fitsuri1e2 <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "Theil", 169s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 169s > print( summary( fitsuri1e2, useDfSys = TRUE ) ) 169s 169s systemfit results 169s method: iterated SUR 169s 169s convergence achieved after 7 iterations 169s 169s N DF SSR detRCov OLS-R2 McElroy-R2 169s system 40 33 109 4 0.884 0.961 169s 169s N DF SSR MSE RMSE R2 Adj R2 169s demand 20 17 66.9 3.94 1.98 0.750 0.721 169s supply 20 16 41.8 2.61 1.62 0.937 0.926 169s 169s The covariance matrix of the residuals used for estimation 169s demand supply 169s demand 3.94 -2.51 169s supply -2.51 2.61 169s 169s The covariance matrix of the residuals 169s demand supply 169s demand 3.94 -2.51 169s supply -2.51 2.61 169s 169s The correlations of the residuals 170s demand supply 170s demand 1.000 -0.754 170s supply -0.754 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 93.4405 7.3821 12.66 3.3e-14 *** 170s price -0.2271 0.0877 -2.59 0.014 * 170s income 0.3093 0.0458 6.75 1.1e-07 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.984 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 66.939 MSE: 3.938 Root MSE: 1.984 170s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 89.1602 3.3868 26.3 < 2e-16 *** 170s income 0.6635 0.0423 15.7 < 2e-16 *** 170s farmPrice -0.4710 0.0369 -12.8 2.7e-14 *** 170s trend -0.7952 0.0643 -12.4 6.0e-14 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.616 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 41.764 MSE: 2.61 Root MSE: 1.616 170s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 170s 170s > 170s > ## ************** iterated SUR (methodResidCov = "max") **************************** 170s > fitsuri1r3 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 170s + methodResidCov = "max", useMatrix = useMatrix ) 170s > print( summary( fitsuri1r3 ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 7 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 33 109 4.06 0.884 0.96 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 66.8 3.93 1.98 0.751 0.721 170s supply 20 16 41.7 2.61 1.61 0.937 0.926 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.93 -2.49 170s supply -2.49 2.61 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.93 -2.49 170s supply -2.49 2.61 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 -0.754 170s supply -0.754 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 93.5427 7.3858 12.67 4.4e-10 *** 170s price -0.2285 0.0877 -2.60 0.019 * 170s income 0.3097 0.0458 6.76 3.3e-06 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.983 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 66.826 MSE: 3.931 Root MSE: 1.983 170s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 89.1830 3.3861 26.3 1.3e-14 *** 170s income 0.6639 0.0423 15.7 3.8e-11 *** 170s farmPrice -0.4715 0.0370 -12.8 8.5e-10 *** 170s trend -0.7955 0.0645 -12.3 1.4e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.615 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 41.708 MSE: 2.607 Root MSE: 1.615 170s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 170s 170s > 170s > ## ************** iterated WSUR (methodResidCov = "max") **************************** 170s > fitsuri1wr3 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 170s + methodResidCov = "max", residCovWeighted = TRUE, useMatrix = useMatrix ) 170s > summary( fitsuri1wr3 ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 7 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 33 109 4.06 0.884 0.96 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 66.8 3.93 1.98 0.751 0.721 170s supply 20 16 41.7 2.61 1.61 0.937 0.926 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.93 -2.49 170s supply -2.49 2.61 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.93 -2.49 170s supply -2.49 2.61 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 -0.754 170s supply -0.754 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 93.5427 7.3858 12.67 4.4e-10 *** 170s price -0.2285 0.0877 -2.60 0.019 * 170s income 0.3097 0.0458 6.76 3.3e-06 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.983 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 66.826 MSE: 3.931 Root MSE: 1.983 170s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 89.1830 3.3861 26.3 1.3e-14 *** 170s income 0.6639 0.0423 15.7 3.8e-11 *** 170s farmPrice -0.4715 0.0370 -12.8 8.5e-10 *** 170s trend -0.7955 0.0645 -12.3 1.4e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.615 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 41.708 MSE: 2.607 Root MSE: 1.615 170s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 170s 170s > 170s > 170s > ## *********** iterated SUR with restriction ******************* 170s > fitsuri2 <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restrm, 170s + maxit = 100, useMatrix = useMatrix ) 170s > print( summary( fitsuri2 ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 21 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 587 110 0.372 0.669 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67 3.94 1.99 0.75 0.721 170s supply 20 16 520 32.52 5.70 0.22 0.074 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.94 4.24 170s supply 4.24 32.52 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.94 4.24 170s supply 4.24 32.52 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.375 170s supply 0.375 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 107.3678 7.4986 14.32 4.4e-16 *** 170s price -0.3945 0.0912 -4.33 0.00013 *** 170s income 0.3382 0.0466 7.25 2.1e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.986 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.024 MSE: 3.943 Root MSE: 1.986 170s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 170s income 0.3125 0.1233 2.53 0.016 * 170s farmPrice -0.1972 0.1157 -1.70 0.097 . 170s trend 0.3382 0.0466 7.25 2.1e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.703 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 520.329 MSE: 32.521 Root MSE: 5.703 170s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 170s 170s > 170s > ## *********** iterated SUR with restriction (EViews-like) *************** 170s > fitsuri2e <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restrm, 170s + methodResidCov = "noDfCor", maxit = 100, x = TRUE, 170s + useMatrix = useMatrix ) 170s > print( summary( fitsuri2e ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 22 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 588 74.9 0.372 0.664 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67.5 3.97 1.99 0.748 0.719 170s supply 20 16 520.2 32.51 5.70 0.220 0.074 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.37 3.58 170s supply 3.58 26.01 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.37 3.58 170s supply 3.58 26.01 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.382 170s supply 0.382 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 107.8051 6.9270 15.56 < 2e-16 *** 170s price -0.3986 0.0843 -4.73 3.8e-05 *** 170s income 0.3379 0.0431 7.84 4.0e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.992 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.47 MSE: 3.969 Root MSE: 1.992 170s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 85.1071 10.8287 7.86 3.8e-09 *** 170s income 0.3106 0.1101 2.82 0.0079 ** 170s farmPrice -0.1960 0.1034 -1.89 0.0667 . 170s trend 0.3379 0.0431 7.84 4.0e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.702 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 520.205 MSE: 32.513 Root MSE: 5.702 170s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 170s 170s > 170s > ## *********** iterated WSUR with restriction ******************* 170s > fitsuri2w <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restrm, 170s + maxit = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 170s > summary( fitsuri2w ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 18 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 587 110 0.372 0.669 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67 3.94 1.99 0.75 0.721 170s supply 20 16 520 32.52 5.70 0.22 0.074 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.94 4.24 170s supply 4.24 32.52 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.94 4.24 170s supply 4.24 32.52 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.375 170s supply 0.375 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 107.3672 7.4986 14.32 4.4e-16 *** 170s price -0.3945 0.0912 -4.33 0.00013 *** 170s income 0.3382 0.0466 7.25 2.1e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.986 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.023 MSE: 3.943 Root MSE: 1.986 170s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 170s income 0.3125 0.1233 2.53 0.016 * 170s farmPrice -0.1972 0.1157 -1.70 0.097 . 170s trend 0.3382 0.0466 7.25 2.1e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.703 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 520.327 MSE: 32.52 Root MSE: 5.703 170s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 170s 170s > 170s > 170s > ## *********** iterated SUR with restriction via restrict.regMat ******************** 170s > fitsuri3 <- systemfit( system2, "SUR", data = Kmenta, restrict.regMat = tc, 170s + maxit = 100, useMatrix = useMatrix ) 170s > print( summary( fitsuri3 ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 21 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 587 110 0.372 0.669 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67 3.94 1.99 0.75 0.721 170s supply 20 16 520 32.52 5.70 0.22 0.074 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.94 4.24 170s supply 4.24 32.52 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.94 4.24 170s supply 4.24 32.52 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.375 170s supply 0.375 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 107.3678 7.4986 14.32 4.4e-16 *** 170s price -0.3945 0.0912 -4.33 0.00013 *** 170s income 0.3382 0.0466 7.25 2.1e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.986 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.024 MSE: 3.943 Root MSE: 1.986 170s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 170s income 0.3125 0.1233 2.53 0.016 * 170s farmPrice -0.1972 0.1157 -1.70 0.097 . 170s trend 0.3382 0.0466 7.25 2.1e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.703 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 520.329 MSE: 32.521 Root MSE: 5.703 170s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 170s 170s > 170s > ## *********** iterated SUR with restriction via restrict.regMat (EViews-like) *************** 170s > fitsuri3e <- systemfit( system2, "SUR", data = Kmenta, restrict.regMat = tc, 170s + methodResidCov = "noDfCor", maxit = 100, x = TRUE, 170s + useMatrix = useMatrix ) 170s > print( summary( fitsuri3e ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 22 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 588 74.9 0.372 0.664 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67.5 3.97 1.99 0.748 0.719 170s supply 20 16 520.2 32.51 5.70 0.220 0.074 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.37 3.58 170s supply 3.58 26.01 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.37 3.58 170s supply 3.58 26.01 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.382 170s supply 0.382 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 107.8051 6.9270 15.56 < 2e-16 *** 170s price -0.3986 0.0843 -4.73 3.8e-05 *** 170s income 0.3379 0.0431 7.84 4.0e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.992 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.47 MSE: 3.969 Root MSE: 1.992 170s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 85.1071 10.8287 7.86 3.8e-09 *** 170s income 0.3106 0.1101 2.82 0.0079 ** 170s farmPrice -0.1960 0.1034 -1.89 0.0667 . 170s trend 0.3379 0.0431 7.84 4.0e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.702 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 520.205 MSE: 32.513 Root MSE: 5.702 170s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 170s 170s > 170s > ## *********** iterated WSUR with restriction via restrict.regMat (EViews-like) *************** 170s > fitsuri3we <- systemfit( system2, "SUR", data = Kmenta, restrict.regMat = tc, 170s + methodResidCov = "noDfCor", maxit = 100, residCovWeighted = TRUE, 170s + useMatrix = useMatrix ) 170s > summary( fitsuri3we ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 20 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 588 74.9 0.372 0.664 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67.5 3.97 1.99 0.748 0.719 170s supply 20 16 520.2 32.51 5.70 0.220 0.074 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.37 3.58 170s supply 3.58 26.01 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.37 3.58 170s supply 3.58 26.01 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.382 170s supply 0.382 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 107.8055 6.9270 15.56 < 2e-16 *** 170s price -0.3986 0.0843 -4.73 3.8e-05 *** 170s income 0.3379 0.0431 7.84 4.0e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.992 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.471 MSE: 3.969 Root MSE: 1.992 170s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 85.1071 10.8288 7.86 3.8e-09 *** 170s income 0.3106 0.1101 2.82 0.008 ** 170s farmPrice -0.1960 0.1034 -1.89 0.067 . 170s trend 0.3379 0.0431 7.84 4.0e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.702 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 520.206 MSE: 32.513 Root MSE: 5.702 170s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 170s 170s > 170s > 170s > ## *************** iterated SUR with 2 restrictions *************************** 170s > fitsurio4 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr2m, 170s + restrict.rhs = restr2q, maxit = 100, useMatrix = useMatrix ) 170s > print( summary( fitsurio4 ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 10 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 176 1.74 0.671 0.705 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67.2 3.95 1.99 0.749 0.720 170s supply 20 16 109.2 6.83 2.61 0.593 0.516 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.95 5.02 170s supply 5.02 6.83 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.95 5.02 170s supply 5.02 6.83 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.967 170s supply 0.967 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 170s price -0.2276 0.0850 -2.68 0.011 * 170s income 0.3203 0.0185 17.32 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.988 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.206 MSE: 3.953 Root MSE: 1.988 170s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.72 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: consump ~ price + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 48.7295 7.4587 6.53 1.5e-07 *** 170s price 0.2724 0.0850 3.20 0.0029 ** 170s farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 170s trend 0.3203 0.0185 17.32 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.613 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 109.234 MSE: 6.827 Root MSE: 2.613 170s Multiple R-Squared: 0.593 Adjusted R-Squared: 0.516 170s 170s > fitsuri4 <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restr2m, 170s + restrict.rhs = restr2q, maxit = 100, useMatrix = useMatrix ) 170s > print( summary( fitsuri4 ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 19 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 575 121 0.385 0.637 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 65.5 3.85 1.96 0.756 0.727 170s supply 20 16 509.3 31.83 5.64 0.237 0.094 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.85 1.23 170s supply 1.23 31.83 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.85 1.23 170s supply 1.23 31.83 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.111 170s supply 0.111 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 98.0356 6.7437 14.54 2.2e-16 *** 170s price -0.2646 0.0777 -3.40 0.0017 ** 170s income 0.3007 0.0436 6.89 5.3e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.963 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 65.532 MSE: 3.855 Root MSE: 1.963 170s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 90.0046 10.4367 8.62 3.5e-10 *** 170s income 0.2354 0.0777 3.03 0.0046 ** 170s farmPrice -0.1667 0.1108 -1.50 0.1416 170s trend 0.3007 0.0436 6.89 5.3e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.642 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 509.345 MSE: 31.834 Root MSE: 5.642 170s Multiple R-Squared: 0.237 Adjusted R-Squared: 0.094 170s 170s > 170s > ## *************** iterated SUR with 2 restrictions (EViews-like) ************** 170s > fitsurio4e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 170s + restrict.matrix = restr2m, restrict.rhs = restr2q, maxit = 100, 170s + useMatrix = useMatrix ) 170s > print( summary( fitsurio4e ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 9 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 173 1.18 0.677 0.665 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 66.3 3.90 1.97 0.753 0.724 170s supply 20 16 106.7 6.67 2.58 0.602 0.527 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.31 4.06 170s supply 4.06 5.34 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.31 4.06 170s supply 4.06 5.34 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.966 170s supply 0.966 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 93.3596 6.8576 13.61 1.6e-15 *** 170s price -0.2398 0.0779 -3.08 0.0041 ** 170s income 0.3232 0.0163 19.81 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.974 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 66.265 MSE: 3.898 Root MSE: 1.974 170s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: consump ~ price + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 49.5456 6.9727 7.11 2.8e-08 *** 170s price 0.2602 0.0779 3.34 0.002 ** 170s farmPrice 0.2270 0.0164 13.81 8.9e-16 *** 170s trend 0.3232 0.0163 19.81 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.583 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 106.722 MSE: 6.67 Root MSE: 2.583 170s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.527 170s 170s > fitsuri4e <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "noDfCor", 170s + restrict.matrix = restr2m, restrict.rhs = restr2q, maxit = 100, 170s + useMatrix = useMatrix ) 170s > print( summary( fitsuri4e ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 20 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 570 82.4 0.391 0.629 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 66 3.88 1.97 0.754 0.725 170s supply 20 16 504 31.50 5.61 0.245 0.103 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.300 0.876 170s supply 0.876 25.203 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.300 0.876 170s supply 0.876 25.203 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.0000 0.0961 170s supply 0.0961 1.0000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 97.6297 6.1560 15.86 < 2e-16 *** 170s price -0.2576 0.0709 -3.63 0.00089 *** 170s income 0.2976 0.0403 7.38 1.2e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.97 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 65.995 MSE: 3.882 Root MSE: 1.97 170s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 89.5437 9.3372 9.59 2.5e-11 *** 170s income 0.2424 0.0709 3.42 0.0016 ** 170s farmPrice -0.1687 0.0988 -1.71 0.0967 . 170s trend 0.2976 0.0403 7.38 1.2e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.613 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 504.066 MSE: 31.504 Root MSE: 5.613 170s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.103 170s 170s > 170s > ## *************** iterated WSUR with 2 restrictions *************************** 170s > fitsurio4w <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr2m, 170s + restrict.rhs = restr2q, maxit = 100, residCovWeighted = TRUE, 170s + useMatrix = useMatrix ) 170s > summary( fitsurio4w ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 10 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 176 1.74 0.671 0.705 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67.2 3.95 1.99 0.749 0.720 170s supply 20 16 109.2 6.83 2.61 0.593 0.516 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.95 5.02 170s supply 5.02 6.83 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.95 5.02 170s supply 5.02 6.83 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.967 170s supply 0.967 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 170s price -0.2276 0.0850 -2.68 0.011 * 170s income 0.3203 0.0185 17.32 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.988 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.206 MSE: 3.953 Root MSE: 1.988 170s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.72 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: consump ~ price + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 48.7294 7.4587 6.53 1.5e-07 *** 170s price 0.2724 0.0850 3.20 0.0029 ** 170s farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 170s trend 0.3203 0.0185 17.32 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.613 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 109.234 MSE: 6.827 Root MSE: 2.613 170s Multiple R-Squared: 0.593 Adjusted R-Squared: 0.516 170s 170s > fitsuri4w <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restr2m, 170s + restrict.rhs = restr2q, maxit = 100, residCovWeighted = TRUE, 170s + useMatrix = useMatrix ) 170s > summary( fitsuri4w ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 18 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 575 121 0.385 0.637 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 65.5 3.85 1.96 0.756 0.727 170s supply 20 16 509.3 31.83 5.64 0.237 0.094 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.85 1.23 170s supply 1.23 31.83 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.85 1.23 170s supply 1.23 31.83 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.111 170s supply 0.111 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 98.0361 6.7437 14.54 2.2e-16 *** 170s price -0.2646 0.0777 -3.40 0.0017 ** 170s income 0.3007 0.0436 6.89 5.3e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.963 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 65.531 MSE: 3.855 Root MSE: 1.963 170s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 90.0052 10.4368 8.62 3.5e-10 *** 170s income 0.2354 0.0777 3.03 0.0046 ** 170s farmPrice -0.1667 0.1108 -1.50 0.1416 170s trend 0.3007 0.0436 6.89 5.3e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.642 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 509.349 MSE: 31.834 Root MSE: 5.642 170s Multiple R-Squared: 0.237 Adjusted R-Squared: 0.094 170s 170s > 170s > 170s > ## *************** iterated SUR with 2 restrictions via R and restrict.regMat **************** 170s > fitsurio5 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr3m, 170s + restrict.rhs = restr3q, restrict.regMat = tc, maxit = 100, 170s + useMatrix = useMatrix ) 170s > print( summary( fitsurio5 ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 10 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 176 1.74 0.671 0.705 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67.2 3.95 1.99 0.749 0.720 170s supply 20 16 109.2 6.83 2.61 0.593 0.516 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.95 5.02 170s supply 5.02 6.83 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.95 5.02 170s supply 5.02 6.83 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.967 170s supply 0.967 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 170s price -0.2276 0.0850 -2.68 0.011 * 170s income 0.3203 0.0185 17.32 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.988 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.206 MSE: 3.953 Root MSE: 1.988 170s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.72 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: consump ~ price + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 48.7295 7.4587 6.53 1.5e-07 *** 170s price 0.2724 0.0850 3.20 0.0029 ** 170s farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 170s trend 0.3203 0.0185 17.32 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.613 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 109.234 MSE: 6.827 Root MSE: 2.613 170s Multiple R-Squared: 0.593 Adjusted R-Squared: 0.516 170s 170s > fitsuri5 <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restr3m, 170s + restrict.rhs = restr3q, restrict.regMat = tc, maxit = 100, 170s + useMatrix = useMatrix ) 170s > print( summary( fitsuri5 ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 19 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 575 121 0.385 0.637 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 65.5 3.85 1.96 0.756 0.727 170s supply 20 16 509.3 31.83 5.64 0.237 0.094 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.85 1.23 170s supply 1.23 31.83 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.85 1.23 170s supply 1.23 31.83 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.111 170s supply 0.111 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 98.0356 6.7437 14.54 2.2e-16 *** 170s price -0.2646 0.0777 -3.40 0.0017 ** 170s income 0.3007 0.0436 6.89 5.3e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.963 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 65.532 MSE: 3.855 Root MSE: 1.963 170s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 90.0046 10.4367 8.62 3.5e-10 *** 170s income 0.2354 0.0777 3.03 0.0046 ** 170s farmPrice -0.1667 0.1108 -1.50 0.1416 170s trend 0.3007 0.0436 6.89 5.3e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.642 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 509.345 MSE: 31.834 Root MSE: 5.642 170s Multiple R-Squared: 0.237 Adjusted R-Squared: 0.094 170s 170s > 170s > ## ********* iterated SUR with 2 restrictions via R and restrict.regMat (EViews-like) ********** 170s > fitsurio5e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 170s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 170s + maxit = 100, useMatrix = useMatrix ) 170s > print( summary( fitsurio5e ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 9 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 173 1.18 0.677 0.665 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 66.3 3.90 1.97 0.753 0.724 170s supply 20 16 106.7 6.67 2.58 0.602 0.527 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.31 4.06 170s supply 4.06 5.34 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.31 4.06 170s supply 4.06 5.34 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.966 170s supply 0.966 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 93.3596 6.8576 13.61 1.6e-15 *** 170s price -0.2398 0.0779 -3.08 0.0041 ** 170s income 0.3232 0.0163 19.81 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.974 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 66.265 MSE: 3.898 Root MSE: 1.974 170s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: consump ~ price + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 49.5456 6.9727 7.11 2.8e-08 *** 170s price 0.2602 0.0779 3.34 0.002 ** 170s farmPrice 0.2270 0.0164 13.81 8.9e-16 *** 170s trend 0.3232 0.0163 19.81 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.583 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 106.722 MSE: 6.67 Root MSE: 2.583 170s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.527 170s 170s > fitsuri5e <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "noDfCor", 170s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 170s + maxit = 100, useMatrix = useMatrix ) 170s > print( summary( fitsuri5e ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 20 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 570 82.4 0.391 0.629 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 66 3.88 1.97 0.754 0.725 170s supply 20 16 504 31.50 5.61 0.245 0.103 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.300 0.876 170s supply 0.876 25.203 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.300 0.876 170s supply 0.876 25.203 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.0000 0.0961 170s supply 0.0961 1.0000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 97.6297 6.1560 15.86 < 2e-16 *** 170s price -0.2576 0.0709 -3.63 0.00089 *** 170s income 0.2976 0.0403 7.38 1.2e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.97 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 65.995 MSE: 3.882 Root MSE: 1.97 170s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 89.5437 9.3372 9.59 2.5e-11 *** 170s income 0.2424 0.0709 3.42 0.0016 ** 170s farmPrice -0.1687 0.0988 -1.71 0.0967 . 170s trend 0.2976 0.0403 7.38 1.2e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.613 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 504.066 MSE: 31.504 Root MSE: 5.613 170s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.103 170s 170s > nobs( fitsuri5e ) 170s [1] 40 170s > 170s > ## ********* iterated SUR with 2 restrictions via R and restrict.regMat (methodResidCov="Theil") ********** 170s > fitsurio5r2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 170s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 170s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 170s > print( summary( fitsurio5r2 ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s warning: convergence not achieved after 100 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 253 -1.67 0.527 0.927 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 95.8 5.63 2.37 0.643 0.601 170s supply 20 16 157.7 9.86 3.14 0.412 0.301 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 4.26 5.29 170s supply 5.29 6.69 170s 170s warning: this covariance matrix is NOT positive semidefinit! 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 5.63 7.56 170s supply 7.56 9.86 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.982 170s supply 0.982 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 78.0342 7.1638 10.89 8.6e-13 *** 170s price -0.0647 0.0815 -0.79 0.43 170s income 0.3007 0.0131 23.01 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.373 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 95.76 MSE: 5.633 Root MSE: 2.373 170s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.601 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: consump ~ price + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 34.1958 7.2257 4.73 3.6e-05 *** 170s price 0.4353 0.0815 5.34 5.7e-06 *** 170s farmPrice 0.2070 0.0124 16.68 < 2e-16 *** 170s trend 0.3007 0.0131 23.01 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 3.14 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 157.737 MSE: 9.859 Root MSE: 3.14 170s Multiple R-Squared: 0.412 Adjusted R-Squared: 0.301 170s 170s > fitsuri5r2 <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "Theil", 170s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 170s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 170s > print( summary( fitsuri5r2 ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 21 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 576 121 0.384 0.637 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 65.4 3.85 1.96 0.756 0.727 170s supply 20 16 510.8 31.92 5.65 0.235 0.091 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.85 1.34 170s supply 1.34 31.92 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.85 1.34 170s supply 1.34 31.92 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.117 170s supply 0.117 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 98.2200 6.7593 14.53 2.2e-16 *** 170s price -0.2669 0.0778 -3.43 0.0016 ** 170s income 0.3011 0.0435 6.92 4.9e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.962 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 65.447 MSE: 3.85 Root MSE: 1.962 170s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 90.2167 10.4342 8.65 3.3e-10 *** 170s income 0.2331 0.0778 3.00 0.005 ** 170s farmPrice -0.1666 0.1111 -1.50 0.143 170s trend 0.3011 0.0435 6.92 4.9e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.65 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 510.75 MSE: 31.922 Root MSE: 5.65 170s Multiple R-Squared: 0.235 Adjusted R-Squared: 0.091 170s 170s > 170s > ## ********* iterated SUR with 2 restrictions via R and restrict.regMat (methodResidCov="max") ********** 170s > # fitsuri5e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "max", 170s > # restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 170s > # maxit = 100, useMatrix = useMatrix ) 170s > # print( summary( fitsuri5e ) ) 170s > # print( round( vcov( fitsuri5e ), digits = 6 ) ) 170s > # disabled, because the estimation does not converge 170s > 170s > ## ********* iterated WSUR with 2 restrictions via R and restrict.regMat (methodResidCov="Theil") ********** 170s > fitsurio5wr2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 170s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 170s + maxit = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 170s > summary( fitsurio5wr2 ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s warning: convergence not achieved after 100 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 253 -1.67 0.527 0.927 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 95.8 5.63 2.37 0.643 0.601 170s supply 20 16 157.7 9.86 3.14 0.412 0.301 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 4.26 5.29 170s supply 5.29 6.69 170s 170s warning: this covariance matrix is NOT positive semidefinit! 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 5.63 7.56 170s supply 7.56 9.86 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.982 170s supply 0.982 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 78.0342 7.1638 10.89 8.6e-13 *** 170s price -0.0647 0.0815 -0.79 0.43 170s income 0.3007 0.0131 23.01 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.373 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 95.76 MSE: 5.633 Root MSE: 2.373 170s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.601 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: consump ~ price + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 34.1958 7.2257 4.73 3.6e-05 *** 170s price 0.4353 0.0815 5.34 5.7e-06 *** 170s farmPrice 0.2070 0.0124 16.68 < 2e-16 *** 170s trend 0.3007 0.0131 23.01 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 3.14 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 157.737 MSE: 9.859 Root MSE: 3.14 170s Multiple R-Squared: 0.412 Adjusted R-Squared: 0.301 170s 170s > fitsuri5wr2 <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "Theil", 170s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 170s + maxit = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 170s > summary( fitsuri5wr2 ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 19 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 576 121 0.384 0.637 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 65.4 3.85 1.96 0.756 0.727 170s supply 20 16 510.8 31.92 5.65 0.235 0.091 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.85 1.34 170s supply 1.34 31.92 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.85 1.34 170s supply 1.34 31.92 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.117 170s supply 0.117 1.000 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 98.2200 6.7593 14.53 2.2e-16 *** 170s price -0.2669 0.0778 -3.43 0.0016 ** 170s income 0.3011 0.0435 6.92 4.9e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.962 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 65.447 MSE: 3.85 Root MSE: 1.962 170s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 90.2168 10.4342 8.65 3.3e-10 *** 170s income 0.2331 0.0778 3.00 0.005 ** 170s farmPrice -0.1666 0.1111 -1.50 0.143 170s trend 0.3011 0.0435 6.92 4.9e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.65 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 510.75 MSE: 31.922 Root MSE: 5.65 170s Multiple R-Squared: 0.235 Adjusted R-Squared: 0.091 170s 170s > 170s > 170s > ## *********** estimations with a single regressor ************ 170s > fitsurS1 <- systemfit( 170s + list( price ~ consump - 1, farmPrice ~ consump + trend ), "SUR", 170s + data = Kmenta, useMatrix = useMatrix ) 170s > print( summary( fitsurS1 ) ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 36 2060 2543 0.449 0.465 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s eq1 20 19 848 44.6 6.68 -0.271 -0.271 170s eq2 20 17 1211 71.3 8.44 0.605 0.559 170s 170s The covariance matrix of the residuals used for estimation 170s eq1 eq2 170s eq1 44.6 -20.5 170s eq2 -20.5 68.9 170s 170s The covariance matrix of the residuals 170s eq1 eq2 170s eq1 44.6 -25.3 170s eq2 -25.3 71.3 170s 170s The correlations of the residuals 170s eq1 eq2 170s eq1 1.000 -0.448 170s eq2 -0.448 1.000 170s 170s 170s SUR estimates for 'eq1' (equation 1) 170s Model Formula: price ~ consump - 1 170s 170s Estimate Std. Error t value Pr(>|t|) 170s consump 0.9902 0.0148 66.9 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 6.682 on 19 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 19 170s SSR: 848.208 MSE: 44.643 Root MSE: 6.682 170s Multiple R-Squared: -0.271 Adjusted R-Squared: -0.271 170s 170s 170s SUR estimates for 'eq2' (equation 2) 170s Model Formula: farmPrice ~ consump + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) -108.487 47.754 -2.27 0.03638 * 170s consump 2.123 0.477 4.45 0.00035 *** 170s trend -0.862 0.303 -2.85 0.01111 * 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 8.441 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 1211.393 MSE: 71.258 Root MSE: 8.441 170s Multiple R-Squared: 0.605 Adjusted R-Squared: 0.559 170s 170s > nobs( fitsurS1 ) 170s [1] 40 170s > fitsurS2 <- systemfit( 170s + list( consump ~ price - 1, consump ~ trend - 1 ), "SUR", 170s + data = Kmenta, useMatrix = useMatrix ) 170s > print( summary( fitsurS2 ) ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 38 47370 110949 -87.3 -5.28 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s eq1 20 19 861 45.3 6.73 -2.21 -2.21 170s eq2 20 19 46509 2447.8 49.48 -172.47 -172.47 170s 170s The covariance matrix of the residuals used for estimation 170s eq1 eq2 170s eq1 45.34 -5.15 170s eq2 -5.15 2447.84 170s 170s The covariance matrix of the residuals 170s eq1 eq2 170s eq1 45.34 -6.37 170s eq2 -6.37 2447.84 170s 170s The correlations of the residuals 170s eq1 eq2 170s eq1 1.0000 -0.0439 170s eq2 -0.0439 1.0000 170s 170s 170s SUR estimates for 'eq1' (equation 1) 170s Model Formula: consump ~ price - 1 170s 170s Estimate Std. Error t value Pr(>|t|) 170s price 1.006 0.015 67 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 6.734 on 19 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 19 170s SSR: 861.496 MSE: 45.342 Root MSE: 6.734 170s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 170s 170s 170s SUR estimates for 'eq2' (equation 2) 170s Model Formula: consump ~ trend - 1 170s 170s Estimate Std. Error t value Pr(>|t|) 170s trend 7.410 0.924 8.02 1.6e-07 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 49.476 on 19 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 19 170s SSR: 46508.986 MSE: 2447.841 Root MSE: 49.476 170s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 170s 170s > nobs( fitsurS2 ) 170s [1] 40 170s > fitsurS3 <- systemfit( 170s + list( consump ~ trend - 1, price ~ trend - 1 ), "SUR", 170s + data = Kmenta, useMatrix = useMatrix ) 170s > nobs( fitsurS3 ) 170s [1] 40 170s > print( summary( fitsurS3 ) ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 38 93537 108970 -99 -0.977 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s eq1 20 19 46509 2448 49.5 -172.5 -172.5 170s eq2 20 19 47028 2475 49.8 -69.5 -69.5 170s 170s The covariance matrix of the residuals used for estimation 170s eq1 eq2 170s eq1 2448 2439 170s eq2 2439 2475 170s 170s The covariance matrix of the residuals 170s eq1 eq2 170s eq1 2448 2439 170s eq2 2439 2475 170s 170s The correlations of the residuals 170s eq1 eq2 170s eq1 1.000 0.988 170s eq2 0.988 1.000 170s 170s 170s SUR estimates for 'eq1' (equation 1) 170s Model Formula: consump ~ trend - 1 170s 170s Estimate Std. Error t value Pr(>|t|) 170s trend 7.405 0.924 8.02 1.6e-07 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 49.476 on 19 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 19 170s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 170s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 170s 170s 170s SUR estimates for 'eq2' (equation 2) 170s Model Formula: price ~ trend - 1 170s 170s Estimate Std. Error t value Pr(>|t|) 170s trend 7.318 0.929 7.88 2.1e-07 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 49.751 on 19 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 19 170s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 170s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 170s 170s > fitsurS4 <- systemfit( 170s + list( consump ~ trend - 1, price ~ trend - 1 ), "SUR", 170s + data = Kmenta, restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), 170s + useMatrix = useMatrix ) 170s > print( summary( fitsurS4 ) ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 39 93552 111731 -99 -1.03 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s eq1 20 19 46510 2448 49.5 -172.5 -172.5 170s eq2 20 19 47042 2476 49.8 -69.5 -69.5 170s 170s The covariance matrix of the residuals used for estimation 170s eq1 eq2 170s eq1 2448 2439 170s eq2 2439 2475 170s 170s The covariance matrix of the residuals 170s eq1 eq2 170s eq1 2448 2439 170s eq2 2439 2476 170s 170s The correlations of the residuals 170s eq1 eq2 170s eq1 1.000 0.988 170s eq2 0.988 1.000 170s 170s 170s SUR estimates for 'eq1' (equation 1) 170s Model Formula: consump ~ trend - 1 170s 170s Estimate Std. Error t value Pr(>|t|) 170s trend 7.388 0.923 8 9.4e-10 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 49.476 on 19 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 19 170s SSR: 46509.787 MSE: 2447.884 Root MSE: 49.476 170s Multiple R-Squared: -172.47 Adjusted R-Squared: -172.47 170s 170s 170s SUR estimates for 'eq2' (equation 2) 170s Model Formula: price ~ trend - 1 170s 170s Estimate Std. Error t value Pr(>|t|) 170s trend 7.388 0.923 8 9.4e-10 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 49.758 on 19 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 19 170s SSR: 47041.803 MSE: 2475.884 Root MSE: 49.758 170s Multiple R-Squared: -69.501 Adjusted R-Squared: -69.501 170s 170s > nobs( fitsurS4 ) 170s [1] 40 170s > fitsurS5 <- systemfit( 170s + list( consump ~ 1, price ~ 1 ), "SUR", 170s + data = Kmenta, useMatrix = useMatrix ) 170s > print( summary( fitsurS5 ) ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 38 935 491 0 0 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s eq1 20 19 268 14.1 3.76 0 0 170s eq2 20 19 667 35.1 5.93 0 0 170s 170s The covariance matrix of the residuals used for estimation 170s eq1 eq2 170s eq1 14.11 2.18 170s eq2 2.18 35.12 170s 170s The covariance matrix of the residuals 170s eq1 eq2 170s eq1 14.11 2.18 170s eq2 2.18 35.12 170s 170s The correlations of the residuals 170s eq1 eq2 170s eq1 1.0000 0.0981 170s eq2 0.0981 1.0000 170s 170s 170s SUR estimates for 'eq1' (equation 1) 170s Model Formula: consump ~ 1 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 100.90 0.84 120 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 3.756 on 19 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 19 170s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 170s Multiple R-Squared: 0 Adjusted R-Squared: 0 170s 170s 170s SUR estimates for 'eq2' (equation 2) 170s Model Formula: price ~ 1 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 100.02 1.33 75.5 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.926 on 19 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 19 170s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 170s Multiple R-Squared: 0 Adjusted R-Squared: 0 170s 170s > nobs( fitsurS5 ) 170s [1] 40 170s > 170s > 170s > ## **************** shorter summaries ********************** 170s > print( summary( fitsur1e2, useDfSys = TRUE, equations = FALSE ) ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 33 172 -0.896 0.679 1.01 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 66.8 3.93 1.98 0.751 0.722 170s supply 20 16 105.3 6.58 2.57 0.607 0.534 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.73 4.28 170s supply 4.28 5.78 170s 170s warning: this covariance matrix is NOT positive semidefinit! 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.93 5.17 170s supply 5.17 6.58 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.984 170s supply 0.984 1.000 170s 170s 170s Coefficients: 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 99.2120 7.5127 13.21 1.0e-14 *** 170s demand_price -0.2667 0.0877 -3.04 0.0046 ** 170s demand_income 0.2908 0.0406 7.16 3.3e-08 *** 170s supply_(Intercept) 63.0768 10.9735 5.75 2.0e-06 *** 170s supply_price 0.1439 0.0943 1.52 0.1368 170s supply_farmPrice 0.2064 0.0384 5.37 6.1e-06 *** 170s supply_trend 0.3325 0.0640 5.19 1.0e-05 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > 170s > print( summary( fitsur2e, useDfSys = FALSE, residCov = FALSE ) ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 180 0.62 0.663 0.707 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 72.6 4.27 2.07 0.729 0.697 170s supply 20 16 107.9 6.75 2.60 0.597 0.522 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 98.7799 6.9687 14.17 7.6e-11 *** 170s price -0.2354 0.0795 -2.96 0.0088 ** 170s income 0.2631 0.0344 7.66 6.6e-07 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.066 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 72.577 MSE: 4.269 Root MSE: 2.066 170s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: consump ~ price + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 67.6039 9.5712 7.06 2.7e-06 *** 170s price 0.1328 0.0853 1.56 0.14 170s farmPrice 0.1785 0.0305 5.85 2.5e-05 *** 170s trend 0.2631 0.0344 7.66 9.7e-07 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.597 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 107.917 MSE: 6.745 Root MSE: 2.597 170s Multiple R-Squared: 0.597 Adjusted R-Squared: 0.522 170s 170s > 170s > print( summary( fitsur3 ), equations = FALSE ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 179 0.933 0.665 0.753 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 71.6 4.21 2.05 0.733 0.702 170s supply 20 16 107.8 6.74 2.60 0.598 0.523 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.78 4.47 170s supply 4.47 5.94 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 4.21 5.24 170s supply 5.24 6.74 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.983 170s supply 0.983 1.000 170s 170s 170s Coefficients: 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 98.8408 7.5581 13.08 8.0e-15 *** 170s demand_price -0.2398 0.0860 -2.79 0.0086 ** 170s demand_income 0.2670 0.0368 7.25 2.2e-08 *** 170s supply_(Intercept) 67.4283 10.6647 6.32 3.3e-07 *** 170s supply_price 0.1332 0.0953 1.40 0.1713 170s supply_farmPrice 0.1795 0.0337 5.33 6.3e-06 *** 170s supply_trend 0.2670 0.0368 7.25 2.2e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > 170s > print( summary( fitsur4r3 ), residCov = FALSE, equations = FALSE ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 173 0.217 0.677 0.702 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 66.4 3.91 1.98 0.752 0.723 170s supply 20 16 106.9 6.68 2.58 0.601 0.526 170s 170s 170s Coefficients: 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 93.1978 7.3168 12.74 1.1e-14 *** 170s demand_price -0.2381 0.0829 -2.87 0.0069 ** 170s demand_income 0.3231 0.0170 18.96 < 2e-16 *** 170s supply_(Intercept) 49.3676 7.4381 6.64 1.1e-07 *** 170s supply_price 0.2619 0.0829 3.16 0.0033 ** 170s supply_farmPrice 0.2271 0.0171 13.29 3.1e-15 *** 170s supply_trend 0.3231 0.0170 18.96 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > 170s > print( summary( fitsur5, residCov = FALSE ), equations = FALSE ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 165 1.76 0.691 0.69 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 64 3.76 1.94 0.761 0.733 170s supply 20 16 101 6.34 2.52 0.622 0.551 170s 170s 170s Coefficients: 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 96.8275 7.4665 12.97 6.2e-15 *** 170s demand_price -0.2798 0.0840 -3.33 0.002 ** 170s demand_income 0.3286 0.0206 15.93 < 2e-16 *** 170s supply_(Intercept) 52.9386 7.6655 6.91 5.1e-08 *** 170s supply_price 0.2202 0.0840 2.62 0.013 * 170s supply_farmPrice 0.2327 0.0212 10.97 7.2e-13 *** 170s supply_trend 0.3286 0.0206 15.93 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > 170s > print( summary( fitsur5w, equations = FALSE, residCov = FALSE ), 170s + equations = TRUE ) 170s 170s systemfit results 170s method: SUR 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 166 1.75 0.69 0.691 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 64.2 3.77 1.94 0.761 0.733 170s supply 20 16 102.0 6.37 2.52 0.620 0.548 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 96.4421 7.4234 12.99 6e-15 *** 170s price -0.2753 0.0838 -3.29 0.0023 ** 170s income 0.3280 0.0202 16.21 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.943 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 64.16 MSE: 3.774 Root MSE: 1.943 170s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: consump ~ price + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 52.5761 7.6099 6.91 5.0e-08 *** 170s price 0.2247 0.0838 2.68 0.011 * 170s farmPrice 0.2318 0.0208 11.14 4.7e-13 *** 170s trend 0.3280 0.0202 16.21 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 2.524 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 101.967 MSE: 6.373 Root MSE: 2.524 170s Multiple R-Squared: 0.62 Adjusted R-Squared: 0.548 170s 170s > 170s > print( summary( fitsuri1r3, useDfSys = FALSE ), residCov = FALSE ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 7 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 33 109 4.06 0.884 0.96 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 66.8 3.93 1.98 0.751 0.721 170s supply 20 16 41.7 2.61 1.61 0.937 0.926 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 93.5427 7.3858 12.67 4.4e-10 *** 170s price -0.2285 0.0877 -2.60 0.019 * 170s income 0.3097 0.0458 6.76 3.3e-06 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.983 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 66.826 MSE: 3.931 Root MSE: 1.983 170s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 89.1830 3.3861 26.3 1.3e-14 *** 170s income 0.6639 0.0423 15.7 3.8e-11 *** 170s farmPrice -0.4715 0.0370 -12.8 8.5e-10 *** 170s trend -0.7955 0.0645 -12.3 1.4e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.615 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 41.708 MSE: 2.607 Root MSE: 1.615 170s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 170s 170s > 170s > print( summary( fitsuri2 ), residCov = FALSE ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 21 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 587 110 0.372 0.669 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67 3.94 1.99 0.75 0.721 170s supply 20 16 520 32.52 5.70 0.22 0.074 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 107.3678 7.4986 14.32 4.4e-16 *** 170s price -0.3945 0.0912 -4.33 0.00013 *** 170s income 0.3382 0.0466 7.25 2.1e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.986 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 67.024 MSE: 3.943 Root MSE: 1.986 170s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 170s income 0.3125 0.1233 2.53 0.016 * 170s farmPrice -0.1972 0.1157 -1.70 0.097 . 170s trend 0.3382 0.0466 7.25 2.1e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.703 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 520.329 MSE: 32.521 Root MSE: 5.703 170s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 170s 170s > 170s > print( summary( fitsuri3e, residCov = FALSE, equations = FALSE ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 22 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 34 588 74.9 0.372 0.664 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67.5 3.97 1.99 0.748 0.719 170s supply 20 16 520.2 32.51 5.70 0.220 0.074 170s 170s 170s Coefficients: 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 107.8051 6.9270 15.56 < 2e-16 *** 170s demand_price -0.3986 0.0843 -4.73 3.8e-05 *** 170s demand_income 0.3379 0.0431 7.84 4.0e-09 *** 170s supply_(Intercept) 85.1071 10.8287 7.86 3.8e-09 *** 170s supply_income 0.3106 0.1101 2.82 0.0079 ** 170s supply_farmPrice -0.1960 0.1034 -1.89 0.0667 . 170s supply_trend 0.3379 0.0431 7.84 4.0e-09 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > 170s > print( summary( fitsurio4, residCov = FALSE ), equations = FALSE ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 10 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 176 1.74 0.671 0.705 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 67.2 3.95 1.99 0.749 0.720 170s supply 20 16 109.2 6.83 2.61 0.593 0.516 170s 170s 170s Coefficients: 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 170s demand_price -0.2276 0.0850 -2.68 0.0112 * 170s demand_income 0.3203 0.0185 17.32 < 2e-16 *** 170s supply_(Intercept) 48.7295 7.4587 6.53 1.5e-07 *** 170s supply_price 0.2724 0.0850 3.20 0.0029 ** 170s supply_farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 170s supply_trend 0.3203 0.0185 17.32 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( summary( fitsuri4, equations = FALSE ), residCov = FALSE ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 19 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 575 121 0.385 0.637 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 65.5 3.85 1.96 0.756 0.727 170s supply 20 16 509.3 31.83 5.64 0.237 0.094 170s 170s 170s Coefficients: 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 98.0356 6.7437 14.54 2.2e-16 *** 170s demand_price -0.2646 0.0777 -3.40 0.0017 ** 170s demand_income 0.3007 0.0436 6.89 5.3e-08 *** 170s supply_(Intercept) 90.0046 10.4367 8.62 3.5e-10 *** 170s supply_income 0.2354 0.0777 3.03 0.0046 ** 170s supply_farmPrice -0.1667 0.1108 -1.50 0.1416 170s supply_trend 0.3007 0.0436 6.89 5.3e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > 170s > print( summary( fitsuri4w, useDfSys = FALSE, equations = FALSE ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 18 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 575 121 0.385 0.637 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 65.5 3.85 1.96 0.756 0.727 170s supply 20 16 509.3 31.83 5.64 0.237 0.094 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 3.85 1.23 170s supply 1.23 31.83 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 3.85 1.23 170s supply 1.23 31.83 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.111 170s supply 0.111 1.000 170s 170s 170s Coefficients: 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 98.0361 6.7437 14.54 5.1e-11 *** 170s demand_price -0.2646 0.0777 -3.40 0.0034 ** 170s demand_income 0.3007 0.0436 6.89 2.6e-06 *** 170s supply_(Intercept) 90.0052 10.4368 8.62 2.1e-07 *** 170s supply_income 0.2354 0.0777 3.03 0.0080 ** 170s supply_farmPrice -0.1667 0.1108 -1.50 0.1521 170s supply_trend 0.3007 0.0436 6.89 3.6e-06 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > 170s > print( summary( fitsurio5r2, equations = FALSE ) ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s warning: convergence not achieved after 100 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 253 -1.67 0.527 0.927 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 95.8 5.63 2.37 0.643 0.601 170s supply 20 16 157.7 9.86 3.14 0.412 0.301 170s 170s The covariance matrix of the residuals used for estimation 170s demand supply 170s demand 4.26 5.29 170s supply 5.29 6.69 170s 170s warning: this covariance matrix is NOT positive semidefinit! 170s 170s The covariance matrix of the residuals 170s demand supply 170s demand 5.63 7.56 170s supply 7.56 9.86 170s 170s The correlations of the residuals 170s demand supply 170s demand 1.000 0.982 170s supply 0.982 1.000 170s 170s 170s Coefficients: 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 78.0342 7.1638 10.89 8.6e-13 *** 170s demand_price -0.0647 0.0815 -0.79 0.43 170s demand_income 0.3007 0.0131 23.01 < 2e-16 *** 170s supply_(Intercept) 34.1958 7.2257 4.73 3.6e-05 *** 170s supply_price 0.4353 0.0815 5.34 5.7e-06 *** 170s supply_farmPrice 0.2070 0.0124 16.68 < 2e-16 *** 170s supply_trend 0.3007 0.0131 23.01 < 2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( summary( fitsuri5r2 ), residCov = FALSE ) 170s 170s systemfit results 170s method: iterated SUR 170s 170s convergence achieved after 21 iterations 170s 170s N DF SSR detRCov OLS-R2 McElroy-R2 170s system 40 35 576 121 0.384 0.637 170s 170s N DF SSR MSE RMSE R2 Adj R2 170s demand 20 17 65.4 3.85 1.96 0.756 0.727 170s supply 20 16 510.8 31.92 5.65 0.235 0.091 170s 170s 170s SUR estimates for 'demand' (equation 1) 170s Model Formula: consump ~ price + income 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 98.2200 6.7593 14.53 2.2e-16 *** 170s price -0.2669 0.0778 -3.43 0.0016 ** 170s income 0.3011 0.0435 6.92 4.9e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 1.962 on 17 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 17 170s SSR: 65.447 MSE: 3.85 Root MSE: 1.962 170s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 170s 170s 170s SUR estimates for 'supply' (equation 2) 170s Model Formula: price ~ income + farmPrice + trend 170s 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 90.2167 10.4342 8.65 3.3e-10 *** 170s income 0.2331 0.0778 3.00 0.005 ** 170s farmPrice -0.1666 0.1111 -1.50 0.143 170s trend 0.3011 0.0435 6.92 4.9e-08 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s 170s Residual standard error: 5.65 on 16 degrees of freedom 170s Number of observations: 20 Degrees of Freedom: 16 170s SSR: 510.75 MSE: 31.922 Root MSE: 5.65 170s Multiple R-Squared: 0.235 Adjusted R-Squared: 0.091 170s 170s > 170s > 170s > ## ****************** residuals ************************** 170s > print( residuals( fitsur1e2 ) ) 170s demand supply 170s 1 0.615 0.41825 170s 2 -0.598 -0.00625 170s 3 2.419 2.75649 170s 4 1.609 1.81727 170s 5 2.145 2.53566 170s 6 1.332 1.53338 170s 7 1.727 2.25581 170s 8 -2.718 -3.56834 170s 9 -1.229 -2.02733 170s 10 2.088 2.53245 170s 11 -0.789 -1.40733 170s 12 -2.799 -3.01416 170s 13 -1.831 -2.30119 170s 14 -0.461 0.01871 170s 15 1.974 2.93624 170s 16 -3.291 -4.00484 170s 17 -0.652 -0.45580 170s 18 -1.899 -3.18683 170s 19 2.030 2.18284 170s 20 0.329 0.98497 170s > print( residuals( fitsur1e2$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 170s 0.41825 -0.00625 2.75649 1.81727 2.53566 1.53338 2.25581 -3.56834 170s 9 10 11 12 13 14 15 16 170s -2.02733 2.53245 -1.40733 -3.01416 -2.30119 0.01871 2.93624 -4.00484 170s 17 18 19 20 170s -0.45580 -3.18683 2.18284 0.98497 170s > 170s > print( residuals( fitsur1w ) ) 170s demand supply 170s 1 0.696 0.4713 170s 2 -0.561 0.0197 170s 3 2.455 2.7782 170s 4 1.643 1.8366 170s 5 2.110 2.4709 170s 6 1.304 1.4773 170s 7 1.692 2.2079 170s 8 -2.756 -3.6663 170s 9 -1.253 -2.0985 170s 10 2.078 2.5321 170s 11 -0.675 -1.2705 170s 12 -2.649 -2.8068 170s 13 -1.706 -2.1305 170s 14 -0.419 0.1150 170s 15 1.887 2.8772 170s 16 -3.364 -4.1013 170s 17 -0.762 -0.5650 170s 18 -1.918 -3.2183 170s 19 1.978 2.1637 170s 20 0.218 0.9075 170s > print( residuals( fitsur1w$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 170s 0.4713 0.0197 2.7782 1.8366 2.4709 1.4773 2.2079 -3.6663 -2.0985 2.5321 170s 11 12 13 14 15 16 17 18 19 20 170s -1.2705 -2.8068 -2.1305 0.1150 2.8772 -4.1013 -0.5650 -3.2183 2.1637 0.9075 170s > 170s > print( residuals( fitsur2e ) ) 170s demand supply 170s 1 0.325 -0.200 170s 2 -0.729 -0.481 170s 3 2.288 2.342 170s 4 1.487 1.457 170s 5 2.271 2.527 170s 6 1.432 1.537 170s 7 1.851 2.275 170s 8 -2.582 -3.322 170s 9 -1.143 -1.834 170s 10 2.124 2.512 170s 11 -1.193 -1.885 170s 12 -3.332 -3.705 170s 13 -2.280 -2.813 170s 14 -0.614 -0.177 170s 15 2.281 3.353 170s 16 -3.032 -3.407 170s 17 -0.260 0.233 170s 18 -1.834 -2.737 170s 19 2.215 2.632 170s 20 0.726 1.692 170s > print( residuals( fitsur2e$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 170s 0.325 -0.729 2.288 1.487 2.271 1.432 1.851 -2.582 -1.143 2.124 -1.193 170s 12 13 14 15 16 17 18 19 20 170s -3.332 -2.280 -0.614 2.281 -3.032 -0.260 -1.834 2.215 0.726 170s > 170s > print( residuals( fitsur3 ) ) 170s demand supply 170s 1 0.366 -0.164 170s 2 -0.711 -0.452 170s 3 2.307 2.368 170s 4 1.504 1.479 170s 5 2.253 2.535 170s 6 1.418 1.544 170s 7 1.833 2.279 170s 8 -2.601 -3.327 170s 9 -1.155 -1.839 170s 10 2.119 2.513 170s 11 -1.136 -1.869 170s 12 -3.257 -3.682 170s 13 -2.217 -2.798 170s 14 -0.593 -0.175 170s 15 2.238 3.332 170s 16 -3.069 -3.436 170s 17 -0.315 0.199 170s 18 -1.844 -2.764 170s 19 2.189 2.604 170s 20 0.671 1.654 170s > print( residuals( fitsur3$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 170s -0.164 -0.452 2.368 1.479 2.535 1.544 2.279 -3.327 -1.839 2.513 -1.869 170s 12 13 14 15 16 17 18 19 20 170s -3.682 -2.798 -0.175 3.332 -3.436 0.199 -2.764 2.604 1.654 170s > 170s > print( residuals( fitsur4r3 ) ) 170s demand supply 170s 1 0.934 0.265 170s 2 -0.721 -0.638 170s 3 2.348 2.232 170s 4 1.459 1.196 170s 5 2.129 2.428 170s 6 1.253 1.318 170s 7 1.514 1.913 170s 8 -3.185 -4.425 170s 9 -1.097 -1.870 170s 10 2.619 3.483 170s 11 0.135 -0.260 170s 12 -2.097 -2.275 170s 13 -1.496 -2.085 170s 14 -0.201 0.516 170s 15 1.934 3.439 170s 16 -3.491 -3.942 170s 17 -0.229 0.913 170s 18 -2.236 -3.503 170s 19 1.440 1.736 170s 20 -1.012 -0.441 170s > print( residuals( fitsur4r3$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 170s 0.934 -0.721 2.348 1.459 2.129 1.253 1.514 -3.185 -1.097 2.619 0.135 170s 12 13 14 15 16 17 18 19 20 170s -2.097 -1.496 -0.201 1.934 -3.491 -0.229 -2.236 1.440 -1.012 170s > 170s > print( residuals( fitsur5 ) ) 170s demand supply 170s 1 1.0025 0.3219 170s 2 -0.5449 -0.4286 170s 3 2.4949 2.4014 170s 4 1.6426 1.4106 170s 5 2.0329 2.2956 170s 6 1.2129 1.2545 170s 7 1.5260 1.9262 170s 8 -3.0444 -4.2868 170s 9 -1.2406 -2.0779 170s 10 2.3001 3.0973 170s 11 -0.0303 -0.4650 170s 12 -2.0337 -2.1783 170s 13 -1.3041 -1.8356 170s 14 -0.2155 0.5292 170s 15 1.6991 3.1787 170s 16 -3.5980 -4.0840 170s 17 -0.7860 0.2371 170s 18 -2.1070 -3.3544 170s 19 1.6070 1.9694 170s 20 -0.6134 0.0885 170s > print( residuals( fitsur5$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 170s 0.3219 -0.4286 2.4014 1.4106 2.2956 1.2545 1.9262 -4.2868 -2.0779 3.0973 170s 11 12 13 14 15 16 17 18 19 20 170s -0.4650 -2.1783 -1.8356 0.5292 3.1787 -4.0840 0.2371 -3.3544 1.9694 0.0885 170s > 170s > print( residuals( fitsuri1r3 ) ) 170s demand supply 170s 1 0.7952 0.123 170s 2 -0.7614 -1.393 170s 3 2.3039 -0.829 170s 4 1.4250 -0.430 170s 5 2.1792 -1.213 170s 6 1.2979 -0.653 170s 7 1.5795 -1.266 170s 8 -3.0935 2.153 170s 9 -1.0750 1.548 170s 10 2.5876 -1.582 170s 11 -0.0991 0.990 170s 12 -2.3616 0.460 170s 13 -1.6970 1.335 170s 14 -0.2819 -1.054 170s 15 2.0557 -2.339 170s 16 -3.3745 1.734 170s 17 -0.1140 -1.054 170s 18 -2.1822 3.461 170s 19 1.5612 0.318 170s 20 -0.7450 -0.308 170s > print( residuals( fitsuri1r3$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 170s 0.7952 -0.7614 2.3039 1.4250 2.1792 1.2979 1.5795 -3.0935 -1.0750 2.5876 170s 11 12 13 14 15 16 17 18 19 20 170s -0.0991 -2.3616 -1.6970 -0.2819 2.0557 -3.3745 -0.1140 -2.1822 1.5612 -0.7450 170s > 170s > print( residuals( fitsuri2 ) ) 170s demand supply 170s 1 1.1341 6.955 170s 2 -0.0587 7.587 170s 3 2.8946 6.701 170s 4 2.1508 6.768 170s 5 1.7798 1.930 170s 6 1.1200 2.315 170s 7 1.5920 2.230 170s 8 -2.5983 4.980 170s 9 -1.6414 -0.392 170s 10 1.3742 -5.140 170s 11 -0.6115 -3.174 170s 12 -1.9764 -0.804 170s 13 -0.8493 1.012 170s 14 -0.2942 -3.282 170s 15 1.0840 -7.042 170s 16 -3.8500 -4.140 170s 17 -2.3259 -12.628 170s 18 -1.7141 -1.498 170s 19 2.1409 -2.683 170s 20 0.6494 0.305 170s > print( residuals( fitsuri2$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 170s 6.955 7.587 6.701 6.768 1.930 2.315 2.230 4.980 -0.392 -5.140 170s 11 12 13 14 15 16 17 18 19 20 170s -3.174 -0.804 1.012 -3.282 -7.042 -4.140 -12.628 -1.498 -2.683 0.305 170s > 170s > print( residuals( fitsuri3e ) ) 170s demand supply 170s 1 1.1327 6.932 170s 2 -0.0412 7.582 170s 3 2.9085 6.695 170s 4 2.1695 6.766 170s 5 1.7721 1.915 170s 6 1.1185 2.305 170s 7 1.5978 2.229 170s 8 -2.5761 4.982 170s 9 -1.6564 -0.410 170s 10 1.3358 -5.161 170s 11 -0.6458 -3.196 170s 12 -1.9868 -0.807 170s 13 -0.8408 1.021 170s 14 -0.3012 -3.275 170s 15 1.0652 -7.037 170s 16 -3.8545 -4.135 170s 17 -2.3819 -12.646 170s 18 -1.6959 -1.478 170s 19 2.1679 -2.647 170s 20 0.7125 0.366 170s > print( residuals( fitsuri3e$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 170s 1.1327 -0.0412 2.9085 2.1695 1.7721 1.1185 1.5978 -2.5761 -1.6564 1.3358 170s 11 12 13 14 15 16 17 18 19 20 170s -0.6458 -1.9868 -0.8408 -0.3012 1.0652 -3.8545 -2.3819 -1.6959 2.1679 0.7125 170s > 170s > print( residuals( fitsurio4 ) ) 170s demand supply 170s 1 0.9019 0.240 170s 2 -0.7658 -0.697 170s 3 2.3097 2.184 170s 4 1.4141 1.136 170s 5 2.1571 2.490 170s 6 1.2670 1.356 170s 7 1.5188 1.928 170s 8 -3.2060 -4.430 170s 9 -1.0620 -1.789 170s 10 2.6864 3.589 170s 11 0.1438 -0.248 170s 12 -2.1427 -2.369 170s 13 -1.5629 -2.210 170s 14 -0.2076 0.479 170s 15 2.0012 3.526 170s 16 -3.4530 -3.876 170s 17 -0.0902 1.129 170s 18 -2.2581 -3.539 170s 19 1.4172 1.671 170s 20 -1.0688 -0.569 170s > print( residuals( fitsurio4$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 170s 0.240 -0.697 2.184 1.136 2.490 1.356 1.928 -4.430 -1.789 3.589 -0.248 170s 12 13 14 15 16 17 18 19 20 170s -2.369 -2.210 0.479 3.526 -3.876 1.129 -3.539 1.671 -0.569 170s > print( residuals( fitsuri4 ) ) 170s demand supply 170s 1 0.7146 5.775 170s 2 -0.6076 7.198 170s 3 2.4197 6.280 170s 4 1.5931 6.531 170s 5 2.1268 1.465 170s 6 1.3043 2.021 170s 7 1.6685 2.261 170s 8 -2.8295 5.275 170s 9 -1.2125 -0.890 170s 10 2.1921 -5.945 170s 11 -0.5521 -4.407 170s 12 -2.5920 -1.482 170s 13 -1.7095 0.895 170s 14 -0.3902 -3.220 170s 15 1.9290 -6.617 170s 16 -3.3627 -3.607 170s 17 -0.6125 -12.896 170s 18 -1.9758 -0.562 170s 19 1.8877 -1.126 170s 20 0.0085 3.051 170s > print( residuals( fitsuri4$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 170s 5.775 7.198 6.280 6.531 1.465 2.021 2.261 5.275 -0.890 -5.945 170s 11 12 13 14 15 16 17 18 19 20 170s -4.407 -1.482 0.895 -3.220 -6.617 -3.607 -12.896 -0.562 -1.126 3.051 170s > 170s > print( residuals( fitsuri4w ) ) 170s demand supply 170s 1 0.71463 5.775 170s 2 -0.60754 7.198 170s 3 2.41972 6.280 170s 4 1.59308 6.531 170s 5 2.12679 1.465 170s 6 1.30430 2.021 170s 7 1.66846 2.262 170s 8 -2.82945 5.275 170s 9 -1.21248 -0.890 170s 10 2.19209 -5.946 170s 11 -0.55215 -4.407 170s 12 -2.59194 -1.482 170s 13 -1.70948 0.895 170s 14 -0.39018 -3.220 170s 15 1.92897 -6.617 170s 16 -3.36276 -3.607 170s 17 -0.61256 -12.896 170s 18 -1.97579 -0.562 170s 19 1.88776 -1.126 170s 20 0.00854 3.051 170s > print( residuals( fitsuri4w$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 170s 5.775 7.198 6.280 6.531 1.465 2.021 2.262 5.275 -0.890 -5.946 170s 11 12 13 14 15 16 17 18 19 20 170s -4.407 -1.482 0.895 -3.220 -6.617 -3.607 -12.896 -0.562 -1.126 3.051 170s > 170s > print( residuals( fitsurio5r2 ) ) 170s demand supply 170s 1 0.655 0.0269 170s 2 -1.456 -1.5152 170s 3 1.737 1.5210 170s 4 0.696 0.3020 170s 5 2.530 2.9397 170s 6 1.417 1.5469 170s 7 1.459 1.8336 170s 8 -3.779 -5.0391 170s 9 -0.498 -1.0416 170s 10 3.950 5.0761 170s 11 0.836 0.6398 170s 12 -2.347 -2.5930 170s 13 -2.286 -3.0468 170s 14 -0.137 0.5081 170s 15 2.908 4.5036 170s 16 -3.050 -3.3786 170s 17 2.091 3.6824 170s 18 -2.775 -4.1107 170s 19 0.737 0.7819 170s 20 -2.686 -2.6370 170s > print( residuals( fitsurio5r2$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 170s 0.655 -1.456 1.737 0.696 2.530 1.417 1.459 -3.779 -0.498 3.950 0.836 170s 12 13 14 15 16 17 18 19 20 170s -2.347 -2.286 -0.137 2.908 -3.050 2.091 -2.775 0.737 -2.686 170s > print( residuals( fitsuri5r2 ) ) 170s demand supply 170s 1 0.7199 5.756 170s 2 -0.5979 7.202 170s 3 2.4279 6.281 170s 4 1.6030 6.535 170s 5 2.1212 1.472 170s 6 1.3017 2.029 170s 7 1.6683 2.275 170s 8 -2.8233 5.299 170s 9 -1.2202 -0.892 170s 10 2.1760 -5.965 170s 11 -0.5578 -4.458 170s 12 -2.5854 -1.528 170s 13 -1.6970 0.866 170s 14 -0.3899 -3.237 170s 15 1.9153 -6.607 170s 16 -3.3698 -3.593 170s 17 -0.6429 -12.902 170s 18 -1.9698 -0.549 170s 19 1.8949 -1.099 170s 20 0.0259 3.114 170s > print( residuals( fitsuri5r2$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 170s 0.7199 -0.5979 2.4279 1.6030 2.1212 1.3017 1.6683 -2.8233 -1.2202 2.1760 170s 11 12 13 14 15 16 17 18 19 20 170s -0.5578 -2.5854 -1.6970 -0.3899 1.9153 -3.3698 -0.6429 -1.9698 1.8949 0.0259 170s > 170s > 170s > ## *************** coefficients ********************* 170s > print( round( coef( fitsur1r3 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income supply_(Intercept) 170s 99.225 -0.268 0.292 62.958 170s supply_price supply_farmPrice supply_trend 170s 0.144 0.207 0.333 170s > print( round( coef( fitsur1r3$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) price farmPrice trend 170s 62.958 0.144 0.207 0.333 170s > 170s > print( round( coef( fitsuri2 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income supply_(Intercept) 170s 107.368 -0.394 0.338 85.045 170s supply_income supply_farmPrice supply_trend 170s 0.312 -0.197 0.338 170s > print( round( coef( fitsuri2$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s 107.368 -0.394 0.338 170s > 170s > print( round( coef( fitsur2we ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income supply_(Intercept) 170s 98.754 -0.234 0.261 67.888 170s supply_price supply_farmPrice supply_trend 170s 0.132 0.177 0.261 170s > print( round( coef( fitsur2we$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s 98.754 -0.234 0.261 170s > 170s > print( round( coef( fitsur3 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income supply_(Intercept) 170s 98.841 -0.240 0.267 67.428 170s supply_price supply_farmPrice supply_trend 170s 0.133 0.179 0.267 170s > print( round( coef( fitsur3, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s 98.841 -0.240 0.267 67.428 0.133 0.179 170s > print( round( coef( fitsur3$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) price farmPrice trend 170s 67.428 0.133 0.179 0.267 170s > 170s > print( round( coef( fitsur4r2 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income supply_(Intercept) 170s 92.527 -0.230 0.322 48.701 170s supply_price supply_farmPrice supply_trend 170s 0.270 0.226 0.322 170s > print( round( coef( fitsur4r2$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s 92.527 -0.230 0.322 170s > 170s > print( round( coef( fitsuri5e ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income supply_(Intercept) 170s 97.630 -0.258 0.298 89.544 170s supply_income supply_farmPrice supply_trend 170s 0.242 -0.169 0.298 170s > print( round( coef( fitsuri5e, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s 97.630 -0.258 0.298 89.544 0.242 -0.169 170s > print( round( coef( fitsuri5e$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) income farmPrice trend 170s 89.544 0.242 -0.169 0.298 170s > 170s > print( round( coef( fitsur5w ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income supply_(Intercept) 170s 96.442 -0.275 0.328 52.576 170s supply_price supply_farmPrice supply_trend 170s 0.225 0.232 0.328 170s > print( round( coef( fitsur5w, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s 96.442 -0.275 0.328 52.576 0.225 0.232 170s > print( round( coef( fitsur5w$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s 96.442 -0.275 0.328 170s > 170s > 170s > ## *************** coefficients with stats ********************* 170s > print( round( coef( summary( fitsur1r3 ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 99.225 7.5129 13.21 0.000000 170s demand_price -0.268 0.0878 -3.05 0.007262 170s demand_income 0.292 0.0408 7.15 0.000002 170s supply_(Intercept) 62.958 10.9850 5.73 0.000031 170s supply_price 0.144 0.0944 1.53 0.145991 170s supply_farmPrice 0.207 0.0386 5.37 0.000062 170s supply_trend 0.333 0.0644 5.18 0.000092 170s > print( round( coef( summary( fitsur1r3$eq[[ 2 ]] ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 62.958 10.9850 5.73 0.000031 170s price 0.144 0.0944 1.53 0.145991 170s farmPrice 0.207 0.0386 5.37 0.000062 170s trend 0.333 0.0644 5.18 0.000092 170s > 170s > print( round( coef( summary( fitsuri2, useDfSys = FALSE ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 107.368 7.4986 14.32 0.000000 170s demand_price -0.394 0.0912 -4.33 0.000459 170s demand_income 0.338 0.0466 7.25 0.000001 170s supply_(Intercept) 85.045 12.1069 7.02 0.000003 170s supply_income 0.312 0.1233 2.53 0.022132 170s supply_farmPrice -0.197 0.1157 -1.70 0.107654 170s supply_trend 0.338 0.0466 7.25 0.000002 170s > print( round( coef( summary( fitsuri2$eq[[ 1 ]], useDfSys = FALSE ) ), 170s + digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 107.368 7.4986 14.32 0.000000 170s price -0.394 0.0912 -4.33 0.000459 170s income 0.338 0.0466 7.25 0.000001 170s > 170s > print( round( coef( summary( fitsur3 ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 98.841 7.5581 13.08 0.000000 170s demand_price -0.240 0.0860 -2.79 0.008613 170s demand_income 0.267 0.0368 7.25 0.000000 170s supply_(Intercept) 67.428 10.6647 6.32 0.000000 170s supply_price 0.133 0.0953 1.40 0.171250 170s supply_farmPrice 0.179 0.0337 5.33 0.000006 170s supply_trend 0.267 0.0368 7.25 0.000000 170s > print( round( coef( summary( fitsur3 ), modified.regMat = TRUE ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s C1 98.841 7.5581 13.08 0.000000 170s C2 -0.240 0.0860 -2.79 0.008613 170s C3 0.267 0.0368 7.25 0.000000 170s C4 67.428 10.6647 6.32 0.000000 170s C5 0.133 0.0953 1.40 0.171250 170s C6 0.179 0.0337 5.33 0.000006 170s > print( round( coef( summary( fitsur3$eq[[ 2 ]] ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 67.428 10.6647 6.32 0.000000 170s price 0.133 0.0953 1.40 0.171250 170s farmPrice 0.179 0.0337 5.33 0.000006 170s trend 0.267 0.0368 7.25 0.000000 170s > 170s > print( round( coef( summary( fitsuri3we ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 107.806 6.9270 15.56 0.000000 170s demand_price -0.399 0.0843 -4.73 0.000038 170s demand_income 0.338 0.0431 7.84 0.000000 170s supply_(Intercept) 85.107 10.8288 7.86 0.000000 170s supply_income 0.311 0.1101 2.82 0.007950 170s supply_farmPrice -0.196 0.1034 -1.89 0.066671 170s supply_trend 0.338 0.0431 7.84 0.000000 170s > print( round( coef( summary( fitsuri3we ), modified.regMat = TRUE ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s C1 107.806 6.9270 15.56 0.000000 170s C2 -0.399 0.0843 -4.73 0.000038 170s C3 0.338 0.0431 7.84 0.000000 170s C4 85.107 10.8288 7.86 0.000000 170s C5 0.311 0.1101 2.82 0.007950 170s C6 -0.196 0.1034 -1.89 0.066671 170s > print( round( coef( summary( fitsuri3we$eq[[ 1 ]] ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 107.806 6.9270 15.56 0.0e+00 170s price -0.399 0.0843 -4.73 3.8e-05 170s income 0.338 0.0431 7.84 0.0e+00 170s > 170s > print( round( coef( summary( fitsur4r2 ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 92.527 7.2896 12.69 0.00000 170s demand_price -0.230 0.0827 -2.79 0.00855 170s demand_income 0.322 0.0166 19.37 0.00000 170s supply_(Intercept) 48.701 7.4034 6.58 0.00000 170s supply_price 0.270 0.0827 3.26 0.00248 170s supply_farmPrice 0.226 0.0166 13.62 0.00000 170s supply_trend 0.322 0.0166 19.37 0.00000 170s > print( round( coef( summary( fitsur4r2$eq[[ 1 ]] ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 92.527 7.2896 12.69 0.00000 170s price -0.230 0.0827 -2.79 0.00855 170s income 0.322 0.0166 19.37 0.00000 170s > 170s > print( round( coef( summary( fitsur4we ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 96.941 6.8894 14.07 0.000000 170s demand_price -0.281 0.0766 -3.67 0.000796 170s demand_income 0.329 0.0181 18.18 0.000000 170s supply_(Intercept) 52.996 7.0652 7.50 0.000000 170s supply_price 0.219 0.0766 2.85 0.007215 170s supply_farmPrice 0.234 0.0183 12.76 0.000000 170s supply_trend 0.329 0.0181 18.18 0.000000 170s > print( round( coef( summary( fitsur4we$eq[[ 2 ]] ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 52.996 7.0652 7.50 0.00000 170s price 0.219 0.0766 2.85 0.00722 170s farmPrice 0.234 0.0183 12.76 0.00000 170s trend 0.329 0.0181 18.18 0.00000 170s > 170s > print( round( coef( summary( fitsuri5e, useDfSys = FALSE ) ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s demand_(Intercept) 97.630 6.1560 15.86 0.000000 170s demand_price -0.258 0.0709 -3.63 0.002060 170s demand_income 0.298 0.0403 7.38 0.000001 170s supply_(Intercept) 89.544 9.3372 9.59 0.000000 170s supply_income 0.242 0.0709 3.42 0.003516 170s supply_farmPrice -0.169 0.0988 -1.71 0.107123 170s supply_trend 0.298 0.0403 7.38 0.000002 170s > print( round( coef( summary( fitsuri5e, useDfSys = FALSE ), 170s + modified.regMat = TRUE ), digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s C1 97.630 6.1560 15.86 NA 170s C2 -0.258 0.0709 -3.63 NA 170s C3 0.298 0.0403 7.38 NA 170s C4 89.544 9.3372 9.59 NA 170s C5 0.242 0.0709 3.42 NA 170s C6 -0.169 0.0988 -1.71 NA 170s > print( round( coef( summary( fitsuri5e$eq[[ 2 ]], useDfSys = FALSE ) ), 170s + digits = 6 ) ) 170s Estimate Std. Error t value Pr(>|t|) 170s (Intercept) 89.544 9.3372 9.59 0.000000 170s income 0.242 0.0709 3.42 0.003516 170s farmPrice -0.169 0.0988 -1.71 0.107123 170s trend 0.298 0.0403 7.38 0.000002 170s > 170s > 170s > ## *********** variance covariance matrix of the coefficients ******* 170s > print( round( vcov( fitsur1e2 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 56.4403 -0.58751 0.025716 170s demand_price -0.5875 0.00769 -0.001866 170s demand_income 0.0257 -0.00187 0.001650 170s supply_(Intercept) 61.0550 -0.40370 -0.209805 170s supply_price -0.6325 0.00579 0.000546 170s supply_farmPrice 0.0215 -0.00156 0.001379 170s supply_trend 0.0327 -0.00237 0.002095 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 61.055 -0.632489 0.021495 170s demand_price -0.404 0.005792 -0.001559 170s demand_income -0.210 0.000546 0.001379 170s supply_(Intercept) 120.418 -0.954714 -0.221454 170s supply_price -0.955 0.008900 0.000584 170s supply_farmPrice -0.221 0.000584 0.001476 170s supply_trend -0.309 0.000772 0.001950 170s supply_trend 170s demand_(Intercept) 0.032652 170s demand_price -0.002369 170s demand_income 0.002095 170s supply_(Intercept) -0.308674 170s supply_price 0.000772 170s supply_farmPrice 0.001950 170s supply_trend 0.004100 170s > print( round( vcov( fitsur1e2$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s (Intercept) 56.4403 -0.58751 0.02572 170s price -0.5875 0.00769 -0.00187 170s income 0.0257 -0.00187 0.00165 170s > 170s > print( round( vcov( fitsur1r3 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 56.4432 -0.58772 0.025901 170s demand_price -0.5877 0.00771 -0.001879 170s demand_income 0.0259 -0.00188 0.001662 170s supply_(Intercept) 60.8607 -0.40086 -0.210729 170s supply_price -0.6307 0.00577 0.000548 170s supply_farmPrice 0.0216 -0.00157 0.001385 170s supply_trend 0.0328 -0.00238 0.002104 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 60.861 -0.630659 0.021589 170s demand_price -0.401 0.005771 -0.001566 170s demand_income -0.211 0.000548 0.001385 170s supply_(Intercept) 120.671 -0.955395 -0.223176 170s supply_price -0.955 0.008902 0.000589 170s supply_farmPrice -0.223 0.000589 0.001487 170s supply_trend -0.310 0.000776 0.001959 170s supply_trend 170s demand_(Intercept) 0.032796 170s demand_price -0.002379 170s demand_income 0.002104 170s supply_(Intercept) -0.310422 170s supply_price 0.000776 170s supply_farmPrice 0.001959 170s supply_trend 0.004149 170s > print( round( vcov( fitsur1r3$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) price farmPrice trend 170s (Intercept) 120.671 -0.955395 -0.223176 -0.310422 170s price -0.955 0.008902 0.000589 0.000776 170s farmPrice -0.223 0.000589 0.001487 0.001959 170s trend -0.310 0.000776 0.001959 0.004149 170s > 170s > print( round( vcov( fitsur2e ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 48.5631 -0.50188 0.018400 170s demand_price -0.5019 0.00632 -0.001335 170s demand_income 0.0184 -0.00134 0.001180 170s supply_(Intercept) 53.2014 -0.39283 -0.140738 170s supply_price -0.5462 0.00510 0.000373 170s supply_farmPrice 0.0147 -0.00107 0.000942 170s supply_trend 0.0184 -0.00134 0.001180 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 53.201 -0.546194 0.014689 170s demand_price -0.393 0.005097 -0.001066 170s demand_income -0.141 0.000373 0.000942 170s supply_(Intercept) 91.607 -0.766739 -0.136644 170s supply_price -0.767 0.007271 0.000368 170s supply_farmPrice -0.137 0.000368 0.000931 170s supply_trend -0.141 0.000373 0.000942 170s supply_trend 170s demand_(Intercept) 0.018400 170s demand_price -0.001335 170s demand_income 0.001180 170s supply_(Intercept) -0.140738 170s supply_price 0.000373 170s supply_farmPrice 0.000942 170s supply_trend 0.001180 170s > print( round( vcov( fitsur2e$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s (Intercept) 48.5631 -0.50188 0.01840 170s price -0.5019 0.00632 -0.00134 170s income 0.0184 -0.00134 0.00118 170s > 170s > print( round( vcov( fitsur3 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 57.1254 -0.58989 0.02116 170s demand_price -0.5899 0.00739 -0.00153 170s demand_income 0.0212 -0.00153 0.00136 170s supply_(Intercept) 64.5952 -0.48211 -0.16560 170s supply_price -0.6626 0.00619 0.00044 170s supply_farmPrice 0.0173 -0.00126 0.00111 170s supply_trend 0.0212 -0.00153 0.00136 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 64.595 -0.662552 0.017322 170s demand_price -0.482 0.006195 -0.001257 170s demand_income -0.166 0.000440 0.001111 170s supply_(Intercept) 113.736 -0.956493 -0.165927 170s supply_price -0.956 0.009084 0.000448 170s supply_farmPrice -0.166 0.000448 0.001133 170s supply_trend -0.166 0.000440 0.001111 170s supply_trend 170s demand_(Intercept) 0.02116 170s demand_price -0.00153 170s demand_income 0.00136 170s supply_(Intercept) -0.16560 170s supply_price 0.00044 170s supply_farmPrice 0.00111 170s supply_trend 0.00136 170s > print( round( vcov( fitsur3, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s C1 57.1254 -0.58989 0.02116 64.595 -0.662552 0.017322 170s C2 -0.5899 0.00739 -0.00153 -0.482 0.006195 -0.001257 170s C3 0.0212 -0.00153 0.00136 -0.166 0.000440 0.001111 170s C4 64.5952 -0.48211 -0.16560 113.736 -0.956493 -0.165927 170s C5 -0.6626 0.00619 0.00044 -0.956 0.009084 0.000448 170s C6 0.0173 -0.00126 0.00111 -0.166 0.000448 0.001133 170s > print( round( vcov( fitsur3$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) price farmPrice trend 170s (Intercept) 113.736 -0.956493 -0.165927 -0.16560 170s price -0.956 0.009084 0.000448 0.00044 170s farmPrice -0.166 0.000448 0.001133 0.00111 170s trend -0.166 0.000440 0.001111 0.00136 170s > 170s > print( round( vcov( fitsur3w ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 56.7267 -0.58513 0.020348 170s demand_price -0.5851 0.00729 -0.001476 170s demand_income 0.0203 -0.00148 0.001305 170s supply_(Intercept) 64.8820 -0.48999 -0.160451 170s supply_price -0.6648 0.00623 0.000426 170s supply_farmPrice 0.0168 -0.00122 0.001077 170s supply_trend 0.0203 -0.00148 0.001305 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 64.882 -0.664819 0.016795 170s demand_price -0.490 0.006231 -0.001219 170s demand_income -0.160 0.000426 0.001077 170s supply_(Intercept) 113.543 -0.959668 -0.161181 170s supply_price -0.960 0.009129 0.000435 170s supply_farmPrice -0.161 0.000435 0.001100 170s supply_trend -0.160 0.000426 0.001077 170s supply_trend 170s demand_(Intercept) 0.020348 170s demand_price -0.001476 170s demand_income 0.001305 170s supply_(Intercept) -0.160451 170s supply_price 0.000426 170s supply_farmPrice 0.001077 170s supply_trend 0.001305 170s > print( round( vcov( fitsur3w, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s C1 56.7267 -0.58513 0.020348 64.882 -0.664819 0.016795 170s C2 -0.5851 0.00729 -0.001476 -0.490 0.006231 -0.001219 170s C3 0.0203 -0.00148 0.001305 -0.160 0.000426 0.001077 170s C4 64.8820 -0.48999 -0.160451 113.543 -0.959668 -0.161181 170s C5 -0.6648 0.00623 0.000426 -0.960 0.009129 0.000435 170s C6 0.0168 -0.00122 0.001077 -0.161 0.000435 0.001100 170s > print( round( vcov( fitsur3w$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s (Intercept) 56.7267 -0.58513 0.02035 170s price -0.5851 0.00729 -0.00148 170s income 0.0203 -0.00148 0.00130 170s > 170s > print( round( vcov( fitsur4r2 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 53.1384 -0.593514 0.065746 170s demand_price -0.5935 0.006838 -0.000927 170s demand_income 0.0657 -0.000927 0.000276 170s supply_(Intercept) 53.3903 -0.599312 0.069540 170s supply_price -0.5935 0.006838 -0.000927 170s supply_farmPrice 0.0570 -0.000775 0.000210 170s supply_trend 0.0657 -0.000927 0.000276 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 53.3903 -0.593514 0.057048 170s demand_price -0.5993 0.006838 -0.000775 170s demand_income 0.0695 -0.000927 0.000210 170s supply_(Intercept) 54.8108 -0.599312 0.048653 170s supply_price -0.5993 0.006838 -0.000775 170s supply_farmPrice 0.0487 -0.000775 0.000276 170s supply_trend 0.0695 -0.000927 0.000210 170s supply_trend 170s demand_(Intercept) 0.065746 170s demand_price -0.000927 170s demand_income 0.000276 170s supply_(Intercept) 0.069540 170s supply_price -0.000927 170s supply_farmPrice 0.000210 170s supply_trend 0.000276 170s > print( round( vcov( fitsur4r2$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s (Intercept) 53.1384 -0.593514 0.065746 170s price -0.5935 0.006838 -0.000927 170s income 0.0657 -0.000927 0.000276 170s > 170s > print( round( vcov( fitsur5e ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 47.8867 -0.516747 0.040579 170s demand_price -0.5167 0.005886 -0.000738 170s demand_income 0.0406 -0.000738 0.000340 170s supply_(Intercept) 48.2187 -0.526670 0.047594 170s supply_price -0.5167 0.005886 -0.000738 170s supply_farmPrice 0.0334 -0.000562 0.000234 170s supply_trend 0.0406 -0.000738 0.000340 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 48.2187 -0.516747 0.033361 170s demand_price -0.5267 0.005886 -0.000562 170s demand_income 0.0476 -0.000738 0.000234 170s supply_(Intercept) 50.4739 -0.526670 0.020109 170s supply_price -0.5267 0.005886 -0.000562 170s supply_farmPrice 0.0201 -0.000562 0.000348 170s supply_trend 0.0476 -0.000738 0.000234 170s supply_trend 170s demand_(Intercept) 0.040579 170s demand_price -0.000738 170s demand_income 0.000340 170s supply_(Intercept) 0.047594 170s supply_price -0.000738 170s supply_farmPrice 0.000234 170s supply_trend 0.000340 170s > print( round( vcov( fitsur5e, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s C1 47.8867 -0.516747 0.040579 48.2187 -0.516747 0.033361 170s C2 -0.5167 0.005886 -0.000738 -0.5267 0.005886 -0.000562 170s C3 0.0406 -0.000738 0.000340 0.0476 -0.000738 0.000234 170s C4 48.2187 -0.526670 0.047594 50.4739 -0.526670 0.020109 170s C5 -0.5167 0.005886 -0.000738 -0.5267 0.005886 -0.000562 170s C6 0.0334 -0.000562 0.000234 0.0201 -0.000562 0.000348 170s > print( round( vcov( fitsur5e$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) price farmPrice trend 170s (Intercept) 50.4739 -0.526670 0.020109 0.047594 170s price -0.5267 0.005886 -0.000562 -0.000738 170s farmPrice 0.0201 -0.000562 0.000348 0.000234 170s trend 0.0476 -0.000738 0.000234 0.000340 170s > 170s > print( round( vcov( fitsuri1r3 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 54.5505 -0.55698 0.013891 170s demand_price -0.5570 0.00770 -0.002185 170s demand_income 0.0139 -0.00218 0.002098 170s supply_(Intercept) -2.7032 -0.08733 0.115993 170s supply_income 0.2249 -0.00185 -0.000411 170s supply_farmPrice -0.1721 0.00238 -0.000675 170s supply_trend -0.2597 0.00359 -0.001019 170s supply_(Intercept) supply_income supply_farmPrice 170s demand_(Intercept) -2.7032 0.224902 -0.172110 170s demand_price -0.0873 -0.001848 0.002379 170s demand_income 0.1160 -0.000411 -0.000675 170s supply_(Intercept) 11.4659 -0.058750 -0.051728 170s supply_income -0.0587 0.001787 -0.001018 170s supply_farmPrice -0.0517 -0.001018 0.001368 170s supply_trend -0.0578 -0.001631 0.001794 170s supply_trend 170s demand_(Intercept) -0.25970 170s demand_price 0.00359 170s demand_income -0.00102 170s supply_(Intercept) -0.05784 170s supply_income -0.00163 170s supply_farmPrice 0.00179 170s supply_trend 0.00416 170s > print( round( vcov( fitsuri1r3$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s (Intercept) 54.5505 -0.55698 0.01389 170s price -0.5570 0.00770 -0.00218 170s income 0.0139 -0.00218 0.00210 170s > 170s > print( round( vcov( fitsuri2 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 56.2287 -0.59260 0.033216 170s demand_price -0.5926 0.00831 -0.002451 170s demand_income 0.0332 -0.00245 0.002173 170s supply_(Intercept) 5.9548 0.14141 -0.203885 170s supply_income -0.2516 0.00201 0.000518 170s supply_farmPrice 0.1910 -0.00323 0.001351 170s supply_trend 0.0332 -0.00245 0.002173 170s supply_(Intercept) supply_income supply_farmPrice 170s demand_(Intercept) 5.955 -0.251647 0.19097 170s demand_price 0.141 0.002011 -0.00323 170s demand_income -0.204 0.000518 0.00135 170s supply_(Intercept) 146.577 -0.828954 -0.64122 170s supply_income -0.829 0.015214 -0.00683 170s supply_farmPrice -0.641 -0.006835 0.01339 170s supply_trend -0.204 0.000518 0.00135 170s supply_trend 170s demand_(Intercept) 0.033216 170s demand_price -0.002451 170s demand_income 0.002173 170s supply_(Intercept) -0.203885 170s supply_income 0.000518 170s supply_farmPrice 0.001351 170s supply_trend 0.002173 170s > print( round( vcov( fitsuri2$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) income farmPrice trend 170s (Intercept) 146.577 -0.828954 -0.64122 -0.203885 170s income -0.829 0.015214 -0.00683 0.000518 170s farmPrice -0.641 -0.006835 0.01339 0.001351 170s trend -0.204 0.000518 0.00135 0.002173 170s > 170s > print( round( vcov( fitsuri3e ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 47.9834 -0.50592 0.028570 170s demand_price -0.5059 0.00710 -0.002098 170s demand_income 0.0286 -0.00210 0.001859 170s supply_(Intercept) 4.9860 0.11975 -0.172089 170s supply_income -0.2118 0.00170 0.000428 170s supply_farmPrice 0.1609 -0.00273 0.001147 170s supply_trend 0.0286 -0.00210 0.001859 170s supply_(Intercept) supply_income supply_farmPrice 170s demand_(Intercept) 4.986 -0.211763 0.16090 170s demand_price 0.120 0.001700 -0.00273 170s demand_income -0.172 0.000428 0.00115 170s supply_(Intercept) 117.261 -0.661134 -0.51405 170s supply_income -0.661 0.012132 -0.00545 170s supply_farmPrice -0.514 -0.005450 0.01070 170s supply_trend -0.172 0.000428 0.00115 170s supply_trend 170s demand_(Intercept) 0.028570 170s demand_price -0.002098 170s demand_income 0.001859 170s supply_(Intercept) -0.172089 170s supply_income 0.000428 170s supply_farmPrice 0.001147 170s supply_trend 0.001859 170s > print( round( vcov( fitsuri3e, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s C1 47.9834 -0.50592 0.028570 4.986 -0.211763 0.16090 170s C2 -0.5059 0.00710 -0.002098 0.120 0.001700 -0.00273 170s C3 0.0286 -0.00210 0.001859 -0.172 0.000428 0.00115 170s C4 4.9860 0.11975 -0.172089 117.261 -0.661134 -0.51405 170s C5 -0.2118 0.00170 0.000428 -0.661 0.012132 -0.00545 170s C6 0.1609 -0.00273 0.001147 -0.514 -0.005450 0.01070 170s > print( round( vcov( fitsuri3e$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s (Intercept) 47.9834 -0.5059 0.02857 170s price -0.5059 0.0071 -0.00210 170s income 0.0286 -0.0021 0.00186 170s > 170s > print( round( vcov( fitsurio4e ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 47.0268 -0.525375 0.058300 170s demand_price -0.5254 0.006074 -0.000842 170s demand_income 0.0583 -0.000842 0.000266 170s supply_(Intercept) 47.2346 -0.530682 0.061997 170s supply_price -0.5254 0.006074 -0.000842 170s supply_farmPrice 0.0508 -0.000704 0.000201 170s supply_trend 0.0583 -0.000842 0.000266 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 47.2346 -0.525375 0.050751 170s demand_price -0.5307 0.006074 -0.000704 170s demand_income 0.0620 -0.000842 0.000201 170s supply_(Intercept) 48.6183 -0.530682 0.042182 170s supply_price -0.5307 0.006074 -0.000704 170s supply_farmPrice 0.0422 -0.000704 0.000270 170s supply_trend 0.0620 -0.000842 0.000201 170s supply_trend 170s demand_(Intercept) 0.058300 170s demand_price -0.000842 170s demand_income 0.000266 170s supply_(Intercept) 0.061997 170s supply_price -0.000842 170s supply_farmPrice 0.000201 170s supply_trend 0.000266 170s > print( round( vcov( fitsurio4e$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) price farmPrice trend 170s (Intercept) 48.6183 -0.530682 0.042182 0.061997 170s price -0.5307 0.006074 -0.000704 -0.000842 170s farmPrice 0.0422 -0.000704 0.000270 0.000201 170s trend 0.0620 -0.000842 0.000201 0.000266 170s > print( round( vcov( fitsuri4e ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 37.8960 -0.36274 -0.01487 170s demand_price -0.3627 0.00503 -0.00144 170s demand_income -0.0149 -0.00144 0.00163 170s supply_(Intercept) 19.0822 -0.20611 0.01617 170s supply_income -0.3627 0.00503 -0.00144 170s supply_farmPrice 0.1707 -0.00279 0.00111 170s supply_trend -0.0149 -0.00144 0.00163 170s supply_(Intercept) supply_income supply_farmPrice 170s demand_(Intercept) 19.0822 -0.36274 0.17073 170s demand_price -0.2061 0.00503 -0.00279 170s demand_income 0.0162 -0.00144 0.00111 170s supply_(Intercept) 87.1827 -0.20611 -0.68294 170s supply_income -0.2061 0.00503 -0.00279 170s supply_farmPrice -0.6829 -0.00279 0.00976 170s supply_trend 0.0162 -0.00144 0.00111 170s supply_trend 170s demand_(Intercept) -0.01487 170s demand_price -0.00144 170s demand_income 0.00163 170s supply_(Intercept) 0.01617 170s supply_income -0.00144 170s supply_farmPrice 0.00111 170s supply_trend 0.00163 170s > print( round( vcov( fitsuri4e$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) income farmPrice trend 170s (Intercept) 87.1827 -0.20611 -0.68294 0.01617 170s income -0.2061 0.00503 -0.00279 -0.00144 170s farmPrice -0.6829 -0.00279 0.00976 0.00111 170s trend 0.0162 -0.00144 0.00111 0.00163 170s > 170s > print( round( vcov( fitsurio5r2 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 51.3196 -0.579747 0.070528 170s demand_price -0.5797 0.006646 -0.000872 170s demand_income 0.0705 -0.000872 0.000171 170s supply_(Intercept) 51.5518 -0.583025 0.072036 170s supply_price -0.5797 0.006646 -0.000872 170s supply_farmPrice 0.0617 -0.000751 0.000138 170s supply_trend 0.0705 -0.000872 0.000171 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 51.5518 -0.579747 0.061658 170s demand_price -0.5830 0.006646 -0.000751 170s demand_income 0.0720 -0.000872 0.000138 170s supply_(Intercept) 52.2109 -0.583025 0.058794 170s supply_price -0.5830 0.006646 -0.000751 170s supply_farmPrice 0.0588 -0.000751 0.000154 170s supply_trend 0.0720 -0.000872 0.000138 170s supply_trend 170s demand_(Intercept) 0.070528 170s demand_price -0.000872 170s demand_income 0.000171 170s supply_(Intercept) 0.072036 170s supply_price -0.000872 170s supply_farmPrice 0.000138 170s supply_trend 0.000171 170s > print( round( vcov( fitsurio5r2, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s C1 51.3196 -0.579747 0.070528 51.5518 -0.579747 0.061658 170s C2 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 170s C3 0.0705 -0.000872 0.000171 0.0720 -0.000872 0.000138 170s C4 51.5518 -0.583025 0.072036 52.2109 -0.583025 0.058794 170s C5 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 170s C6 0.0617 -0.000751 0.000138 0.0588 -0.000751 0.000154 170s > print( round( vcov( fitsurio5r2$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s (Intercept) 51.3196 -0.579747 0.070528 170s price -0.5797 0.006646 -0.000872 170s income 0.0705 -0.000872 0.000171 170s > print( round( vcov( fitsuri5r2 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 45.6881 -0.44008 -0.01517 170s demand_price -0.4401 0.00605 -0.00170 170s demand_income -0.0152 -0.00170 0.00190 170s supply_(Intercept) 22.8172 -0.23903 0.01186 170s supply_income -0.4401 0.00605 -0.00170 170s supply_farmPrice 0.2104 -0.00345 0.00138 170s supply_trend -0.0152 -0.00170 0.00190 170s supply_(Intercept) supply_income supply_farmPrice 170s demand_(Intercept) 22.8172 -0.44008 0.21042 170s demand_price -0.2390 0.00605 -0.00345 170s demand_income 0.0119 -0.00170 0.00138 170s supply_(Intercept) 108.8722 -0.23903 -0.87024 170s supply_income -0.2390 0.00605 -0.00345 170s supply_farmPrice -0.8702 -0.00345 0.01234 170s supply_trend 0.0119 -0.00170 0.00138 170s supply_trend 170s demand_(Intercept) -0.01517 170s demand_price -0.00170 170s demand_income 0.00190 170s supply_(Intercept) 0.01186 170s supply_income -0.00170 170s supply_farmPrice 0.00138 170s supply_trend 0.00190 170s > print( round( vcov( fitsuri5r2, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s C1 45.6881 -0.44008 -0.01517 22.8172 -0.44008 0.21042 170s C2 -0.4401 0.00605 -0.00170 -0.2390 0.00605 -0.00345 170s C3 -0.0152 -0.00170 0.00190 0.0119 -0.00170 0.00138 170s C4 22.8172 -0.23903 0.01186 108.8722 -0.23903 -0.87024 170s C5 -0.4401 0.00605 -0.00170 -0.2390 0.00605 -0.00345 170s C6 0.2104 -0.00345 0.00138 -0.8702 -0.00345 0.01234 170s > print( round( vcov( fitsuri5r2$eq[[ 1 ]] ), digits = 6 ) ) 170s (Intercept) price income 170s (Intercept) 45.6881 -0.44008 -0.0152 170s price -0.4401 0.00605 -0.0017 170s income -0.0152 -0.00170 0.0019 170s > 170s > print( round( vcov( fitsurio5wr2 ), digits = 6 ) ) 170s demand_(Intercept) demand_price demand_income 170s demand_(Intercept) 51.3196 -0.579747 0.070528 170s demand_price -0.5797 0.006646 -0.000872 170s demand_income 0.0705 -0.000872 0.000171 170s supply_(Intercept) 51.5518 -0.583025 0.072036 170s supply_price -0.5797 0.006646 -0.000872 170s supply_farmPrice 0.0617 -0.000751 0.000138 170s supply_trend 0.0705 -0.000872 0.000171 170s supply_(Intercept) supply_price supply_farmPrice 170s demand_(Intercept) 51.5518 -0.579747 0.061658 170s demand_price -0.5830 0.006646 -0.000751 170s demand_income 0.0720 -0.000872 0.000138 170s supply_(Intercept) 52.2109 -0.583025 0.058794 170s supply_price -0.5830 0.006646 -0.000751 170s supply_farmPrice 0.0588 -0.000751 0.000154 170s supply_trend 0.0720 -0.000872 0.000138 170s supply_trend 170s demand_(Intercept) 0.070528 170s demand_price -0.000872 170s demand_income 0.000171 170s supply_(Intercept) 0.072036 170s supply_price -0.000872 170s supply_farmPrice 0.000138 170s supply_trend 0.000171 170s > print( round( vcov( fitsurio5wr2, modified.regMat = TRUE ), digits = 6 ) ) 170s C1 C2 C3 C4 C5 C6 170s C1 51.3196 -0.579747 0.070528 51.5518 -0.579747 0.061658 170s C2 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 170s C3 0.0705 -0.000872 0.000171 0.0720 -0.000872 0.000138 170s C4 51.5518 -0.583025 0.072036 52.2109 -0.583025 0.058794 170s C5 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 170s C6 0.0617 -0.000751 0.000138 0.0588 -0.000751 0.000154 170s > print( round( vcov( fitsurio5wr2$eq[[ 2 ]] ), digits = 6 ) ) 170s (Intercept) price farmPrice trend 170s (Intercept) 52.2109 -0.583025 0.058794 0.072036 170s price -0.5830 0.006646 -0.000751 -0.000872 170s farmPrice 0.0588 -0.000751 0.000154 0.000138 170s trend 0.0720 -0.000872 0.000138 0.000171 170s > 170s > 170s > ## *********** confidence intervals of coefficients ************* 170s > print( confint( fitsur1e2, useDfSys = TRUE ) ) 170s 2.5 % 97.5 % 170s demand_(Intercept) 83.927 114.497 170s demand_price -0.445 -0.088 170s demand_income 0.208 0.373 170s supply_(Intercept) 40.751 85.403 170s supply_price -0.048 0.336 170s supply_farmPrice 0.128 0.285 170s supply_trend 0.202 0.463 170s > print( confint( fitsur1e2$eq[[ 2 ]], level = 0.9, useDfSys = TRUE ) ) 170s 5 % 95 % 170s (Intercept) 44.506 81.648 170s price -0.016 0.304 170s farmPrice 0.141 0.271 170s trend 0.224 0.441 170s > 170s > print( confint( fitsur1we2, useDfSys = TRUE ) ) 170s 2.5 % 97.5 % 170s demand_(Intercept) 83.927 114.497 170s demand_price -0.445 -0.088 170s demand_income 0.208 0.373 170s supply_(Intercept) 40.751 85.403 170s supply_price -0.048 0.336 170s supply_farmPrice 0.128 0.285 170s supply_trend 0.202 0.463 170s > print( confint( fitsur1we2$eq[[ 1 ]], level = 0.9, useDfSys = TRUE ) ) 170s 5 % 95 % 170s (Intercept) 86.498 111.926 170s price -0.415 -0.118 170s income 0.222 0.360 170s > 170s > print( confint( fitsur2e, level = 0.9 ) ) 170s 5 % 95 % 170s demand_(Intercept) 84.618 112.942 170s demand_price -0.397 -0.074 170s demand_income 0.193 0.333 170s supply_(Intercept) 48.153 87.055 170s supply_price -0.040 0.306 170s supply_farmPrice 0.116 0.240 170s supply_trend 0.193 0.333 170s > print( confint( fitsur2e$eq[[ 1 ]], level = 0.99 ) ) 170s 0.5 % 99.5 % 170s (Intercept) 79.767 117.793 170s price -0.452 -0.018 170s income 0.169 0.357 170s > 170s > print( confint( fitsur3, level = 0.99 ) ) 170s 0.5 % 99.5 % 170s demand_(Intercept) 83.481 114.201 170s demand_price -0.415 -0.065 170s demand_income 0.192 0.342 170s supply_(Intercept) 45.755 89.102 170s supply_price -0.060 0.327 170s supply_farmPrice 0.111 0.248 170s supply_trend 0.192 0.342 170s > print( confint( fitsur3$eq[[ 2 ]], level = 0.5 ) ) 170s 25 % 75 % 170s (Intercept) 60.157 74.699 170s price 0.068 0.198 170s farmPrice 0.157 0.202 170s trend 0.242 0.292 170s > 170s > print( confint( fitsur4r3, level = 0.5 ) ) 170s 25 % 75 % 170s demand_(Intercept) 78.344 108.052 170s demand_price -0.406 -0.070 170s demand_income 0.289 0.358 170s supply_(Intercept) 34.267 64.468 170s supply_price 0.094 0.430 170s supply_farmPrice 0.192 0.262 170s supply_trend 0.289 0.358 170s > print( confint( fitsur4r3$eq[[ 1 ]], level = 0.25 ) ) 170s 37.5 % 62.5 % 170s (Intercept) 90.848 95.548 170s price -0.265 -0.211 170s income 0.318 0.329 170s > 170s > print( confint( fitsur5, level = 0.25 ) ) 170s 37.5 % 62.5 % 170s demand_(Intercept) 81.670 111.985 170s demand_price -0.450 -0.109 170s demand_income 0.287 0.371 170s supply_(Intercept) 37.377 68.500 170s supply_price 0.050 0.391 170s supply_farmPrice 0.190 0.276 170s supply_trend 0.287 0.371 170s > print( confint( fitsur5$eq[[ 2 ]], level = 0.975 ) ) 170s 1.3 % 98.8 % 170s (Intercept) 34.986 70.891 170s price 0.024 0.417 170s farmPrice 0.183 0.282 170s trend 0.280 0.377 170s > 170s > print( confint( fitsuri1r3, level = 0.975 ) ) 170s 1.3 % 98.8 % 170s demand_(Intercept) 77.960 109.125 170s demand_price -0.414 -0.043 170s demand_income 0.213 0.406 170s supply_(Intercept) 82.005 96.361 170s supply_income 0.574 0.753 170s supply_farmPrice -0.550 -0.393 170s supply_trend -0.932 -0.659 170s > print( confint( fitsuri1r3$eq[[ 1 ]], level = 0.999 ) ) 170s 0.1 % 100 % 170s (Intercept) 64.257 122.828 170s price -0.576 0.119 170s income 0.128 0.491 170s > 170s > print( confint( fitsuri2, level = 0.999 ) ) 170s 0.1 % 100 % 170s demand_(Intercept) 92.129 122.607 170s demand_price -0.580 -0.209 170s demand_income 0.243 0.433 170s supply_(Intercept) 60.441 109.649 170s supply_income 0.062 0.563 170s supply_farmPrice -0.432 0.038 170s supply_trend 0.243 0.433 170s > print( confint( fitsuri2$eq[[ 2 ]], level = 0.1 ) ) 170s 45 % 55 % 170s (Intercept) 83.512 86.578 170s income 0.297 0.328 170s farmPrice -0.212 -0.183 170s trend 0.332 0.344 170s > 170s > print( confint( fitsuri3e, level = 0.1 ) ) 170s 45 % 55 % 170s demand_(Intercept) 93.728 121.882 170s demand_price -0.570 -0.227 170s demand_income 0.250 0.426 170s supply_(Intercept) 63.100 107.114 170s supply_income 0.087 0.534 170s supply_farmPrice -0.406 0.014 170s supply_trend 0.250 0.426 170s > print( confint( fitsuri3e$eq[[ 1 ]], level = 0.01 ) ) 170s 49.5 % 50.5 % 170s (Intercept) 107.718 107.893 170s price -0.400 -0.398 170s income 0.337 0.338 170s > 170s > print( confint( fitsurio4, level = 0.01 ) ) 170s 49.5 % 50.5 % 170s demand_(Intercept) 77.496 107.356 170s demand_price -0.400 -0.055 170s demand_income 0.283 0.358 170s supply_(Intercept) 33.588 63.871 170s supply_price 0.100 0.445 170s supply_farmPrice 0.185 0.262 170s supply_trend 0.283 0.358 170s > print( confint( fitsurio4$eq[[ 2 ]], level = 0.33 ) ) 170s 33.5 % 66.5 % 170s (Intercept) 45.524 51.935 170s price 0.236 0.309 170s farmPrice 0.215 0.231 170s trend 0.312 0.328 170s > print( confint( fitsuri4, level = 0.01 ) ) 170s 49.5 % 50.5 % 170s demand_(Intercept) 84.345 111.726 170s demand_price -0.422 -0.107 170s demand_income 0.212 0.389 170s supply_(Intercept) 68.817 111.192 170s supply_income 0.078 0.393 170s supply_farmPrice -0.392 0.058 170s supply_trend 0.212 0.389 170s > print( confint( fitsuri4$eq[[ 2 ]], level = 0.33 ) ) 170s 33.5 % 66.5 % 170s (Intercept) 85.519 94.490 170s income 0.202 0.269 170s farmPrice -0.214 -0.119 170s trend 0.282 0.319 170s > 170s > print( confint( fitsurio4w, level = 0.01 ) ) 170s 49.5 % 50.5 % 170s demand_(Intercept) 77.496 107.356 170s demand_price -0.400 -0.055 170s demand_income 0.283 0.358 170s supply_(Intercept) 33.587 63.871 170s supply_price 0.100 0.445 170s supply_farmPrice 0.185 0.262 170s supply_trend 0.283 0.358 170s > print( confint( fitsurio4w$eq[[ 1 ]], level = 0.33 ) ) 170s 33.5 % 66.5 % 170s (Intercept) 89.266 95.587 170s price -0.264 -0.191 170s income 0.312 0.328 170s > 170s > print( confint( fitsurio5r2, level = 0.33 ) ) 170s 33.5 % 66.5 % 170s demand_(Intercept) 63.491 92.577 170s demand_price -0.230 0.101 170s demand_income 0.274 0.327 170s supply_(Intercept) 19.527 48.865 170s supply_price 0.270 0.601 170s supply_farmPrice 0.182 0.232 170s supply_trend 0.274 0.327 170s > print( confint( fitsurio5r2$eq[[ 1 ]] ) ) 170s 2.5 % 97.5 % 170s (Intercept) 63.491 92.577 170s price -0.230 0.101 170s income 0.274 0.327 170s > print( confint( fitsuri5r2, level = 0.33 ) ) 170s 33.5 % 66.5 % 170s demand_(Intercept) 84.498 111.942 170s demand_price -0.425 -0.109 170s demand_income 0.213 0.390 170s supply_(Intercept) 69.034 111.399 170s supply_income 0.075 0.391 170s supply_farmPrice -0.392 0.059 170s supply_trend 0.213 0.390 170s > print( confint( fitsuri5r2$eq[[ 1 ]] ) ) 170s 2.5 % 97.5 % 170s (Intercept) 84.498 111.942 170s price -0.425 -0.109 170s income 0.213 0.390 170s > 170s > 170s > ## *********** fitted values ************* 170s > print( fitted( fitsur1e2 ) ) 170s demand supply 170s 1 97.9 98.1 170s 2 99.8 99.2 170s 3 99.7 99.4 170s 4 99.9 99.7 170s 5 102.1 101.7 170s 6 101.9 101.7 170s 7 102.3 101.7 170s 8 102.6 103.5 170s 9 101.6 102.4 170s 10 100.7 100.3 170s 11 96.2 96.8 170s 12 95.2 95.4 170s 13 96.4 96.8 170s 14 99.2 98.7 170s 15 103.8 102.9 170s 16 103.5 104.2 170s 17 104.2 104.0 170s 18 101.8 103.1 170s 19 103.2 103.0 170s 20 105.9 105.2 170s > print( fitted( fitsur1e2$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 98.1 99.2 99.4 99.7 101.7 101.7 101.7 103.5 102.4 100.3 96.8 95.4 96.8 170s 14 15 16 17 18 19 20 170s 98.7 102.9 104.2 104.0 103.1 103.0 105.2 170s > 170s > print( fitted( fitsur2e ) ) 170s demand supply 170s 1 98.2 98.7 170s 2 99.9 99.7 170s 3 99.9 99.8 170s 4 100.0 100.0 170s 5 102.0 101.7 170s 6 101.8 101.7 170s 7 102.1 101.7 170s 8 102.5 103.2 170s 9 101.5 102.2 170s 10 100.7 100.3 170s 11 96.6 97.3 170s 12 95.8 96.1 170s 13 96.8 97.3 170s 14 99.4 98.9 170s 15 103.5 102.4 170s 16 103.3 103.6 170s 17 103.8 103.3 170s 18 101.8 102.7 170s 19 103.0 102.6 170s 20 105.5 104.5 170s > print( fitted( fitsur2e$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 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 170s 14 15 16 17 18 19 20 170s 99.4 103.5 103.3 103.8 101.8 103.0 105.5 170s > 170s > print( fitted( fitsur2we ) ) 170s demand supply 170s 1 98.2 98.7 170s 2 99.9 99.7 170s 3 99.9 99.8 170s 4 100.0 100.1 170s 5 102.0 101.7 170s 6 101.8 101.7 170s 7 102.1 101.7 170s 8 102.5 103.2 170s 9 101.5 102.2 170s 10 100.7 100.3 170s 11 96.7 97.4 170s 12 95.8 96.2 170s 13 96.8 97.4 170s 14 99.4 99.0 170s 15 103.5 102.4 170s 16 103.2 103.6 170s 17 103.8 103.3 170s 18 101.8 102.7 170s 19 103.0 102.6 170s 20 105.5 104.5 170s > print( fitted( fitsur2we$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 98.7 99.7 99.8 100.1 101.7 101.7 101.7 103.2 102.2 100.3 97.4 96.2 97.4 170s 14 15 16 17 18 19 20 170s 99.0 102.4 103.6 103.3 102.7 102.6 104.5 170s > 170s > print( fitted( fitsur3 ) ) 170s demand supply 170s 1 98.1 98.6 170s 2 99.9 99.6 170s 3 99.9 99.8 170s 4 100.0 100.0 170s 5 102.0 101.7 170s 6 101.8 101.7 170s 7 102.2 101.7 170s 8 102.5 103.2 170s 9 101.5 102.2 170s 10 100.7 100.3 170s 11 96.6 97.3 170s 12 95.7 96.1 170s 13 96.8 97.3 170s 14 99.3 98.9 170s 15 103.6 102.5 170s 16 103.3 103.7 170s 17 103.8 103.3 170s 18 101.8 102.7 170s 19 103.0 102.6 170s 20 105.6 104.6 170s > print( fitted( fitsur3$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 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 170s 14 15 16 17 18 19 20 170s 98.9 102.5 103.7 103.3 102.7 102.6 104.6 170s > 170s > print( fitted( fitsur4r3 ) ) 170s demand supply 170s 1 97.6 98.2 170s 2 99.9 99.8 170s 3 99.8 99.9 170s 4 100.0 100.3 170s 5 102.1 101.8 170s 6 102.0 101.9 170s 7 102.5 102.1 170s 8 103.1 104.3 170s 9 101.4 102.2 170s 10 100.2 99.3 170s 11 95.3 95.7 170s 12 94.5 94.7 170s 13 96.0 96.6 170s 14 99.0 98.2 170s 15 103.9 102.4 170s 16 103.7 104.2 170s 17 103.8 102.6 170s 18 102.2 103.4 170s 19 103.8 103.5 170s 20 107.2 106.7 170s > print( fitted( fitsur4r3$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 97.6 99.9 99.8 100.0 102.1 102.0 102.5 103.1 101.4 100.2 95.3 94.5 96.0 170s 14 15 16 17 18 19 20 170s 99.0 103.9 103.7 103.8 102.2 103.8 107.2 170s > 170s > print( fitted( fitsur5 ) ) 170s demand supply 170s 1 97.5 98.2 170s 2 99.7 99.6 170s 3 99.7 99.8 170s 4 99.9 100.1 170s 5 102.2 101.9 170s 6 102.0 102.0 170s 7 102.5 102.1 170s 8 102.9 104.2 170s 9 101.6 102.4 170s 10 100.5 99.7 170s 11 95.5 95.9 170s 12 94.5 94.6 170s 13 95.8 96.4 170s 14 99.0 98.2 170s 15 104.1 102.6 170s 16 103.8 104.3 170s 17 104.3 103.3 170s 18 102.0 103.3 170s 19 103.6 103.3 170s 20 106.8 106.1 170s > print( fitted( fitsur5$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 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 170s 14 15 16 17 18 19 20 170s 98.2 102.6 104.3 103.3 103.3 103.3 106.1 170s > 170s > print( fitted( fitsuri1r3 ) ) 170s demand supply 170s 1 97.7 100.2 170s 2 99.9 105.7 170s 3 99.9 104.3 170s 4 100.1 104.9 170s 5 102.1 99.2 170s 6 101.9 100.1 170s 7 102.4 102.3 170s 8 103.0 102.6 170s 9 101.4 94.9 170s 10 100.2 92.8 170s 11 95.5 92.1 170s 12 94.8 98.3 170s 13 96.2 101.6 170s 14 99.0 99.8 170s 15 103.7 97.5 170s 16 103.6 96.7 170s 17 103.6 87.6 170s 18 102.1 100.6 170s 19 103.7 105.5 170s 20 107.0 113.8 170s > print( fitted( fitsuri1r3$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 97.7 99.9 99.9 100.1 102.1 101.9 102.4 103.0 101.4 100.2 95.5 94.8 96.2 170s 14 15 16 17 18 19 20 170s 99.0 103.7 103.6 103.6 102.1 103.7 107.0 170s > 170s > print( fitted( fitsuri1wr3 ) ) 170s demand supply 170s 1 97.7 100.2 170s 2 99.9 105.7 170s 3 99.9 104.3 170s 4 100.1 104.9 170s 5 102.1 99.2 170s 6 101.9 100.1 170s 7 102.4 102.3 170s 8 103.0 102.6 170s 9 101.4 94.9 170s 10 100.2 92.8 170s 11 95.5 92.1 170s 12 94.8 98.3 170s 13 96.2 101.6 170s 14 99.0 99.8 170s 15 103.7 97.5 170s 16 103.6 96.7 170s 17 103.6 87.6 170s 18 102.1 100.6 170s 19 103.7 105.5 170s 20 107.0 113.8 170s > print( fitted( fitsuri1wr3$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 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 170s 14 15 16 17 18 19 20 170s 99.8 97.5 96.7 87.6 100.6 105.5 113.8 170s > 170s > print( fitted( fitsuri2 ) ) 170s demand supply 170s 1 97.4 93.4 170s 2 99.2 96.7 170s 3 99.3 96.7 170s 4 99.4 97.7 170s 5 102.5 96.1 170s 6 102.1 97.1 170s 7 102.4 98.8 170s 8 102.5 99.8 170s 9 102.0 96.8 170s 10 101.4 96.4 170s 11 96.0 96.3 170s 12 94.4 99.6 170s 13 95.4 101.9 170s 14 99.1 102.0 170s 15 104.7 102.2 170s 16 104.1 102.6 170s 17 105.8 99.1 170s 18 101.6 105.5 170s 19 103.1 108.5 170s 20 105.6 113.2 170s > print( fitted( fitsuri2$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 93.4 96.7 96.7 97.7 96.1 97.1 98.8 99.8 96.8 96.4 96.3 99.6 101.9 170s 14 15 16 17 18 19 20 170s 102.0 102.2 102.6 99.1 105.5 108.5 113.2 170s > 170s > print( fitted( fitsuri3e ) ) 170s demand supply 170s 1 97.4 93.4 170s 2 99.2 96.7 170s 3 99.3 96.7 170s 4 99.3 97.7 170s 5 102.5 96.1 170s 6 102.1 97.2 170s 7 102.4 98.8 170s 8 102.5 99.8 170s 9 102.0 96.9 170s 10 101.5 96.4 170s 11 96.1 96.3 170s 12 94.4 99.6 170s 13 95.4 101.9 170s 14 99.1 102.0 170s 15 104.7 102.2 170s 16 104.1 102.6 170s 17 105.9 99.1 170s 18 101.6 105.5 170s 19 103.1 108.4 170s 20 105.5 113.1 170s > print( fitted( fitsuri3e$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 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 170s 14 15 16 17 18 19 20 170s 99.1 104.7 104.1 105.9 101.6 103.1 105.5 170s > 170s > print( fitted( fitsurio4 ) ) 170s demand supply 170s 1 97.6 98.2 170s 2 100.0 99.9 170s 3 99.9 100.0 170s 4 100.1 100.4 170s 5 102.1 101.8 170s 6 102.0 101.9 170s 7 102.5 102.1 170s 8 103.1 104.3 170s 9 101.4 102.1 170s 10 100.1 99.2 170s 11 95.3 95.7 170s 12 94.6 94.8 170s 13 96.1 96.7 170s 14 99.0 98.3 170s 15 103.8 102.3 170s 16 103.7 104.1 170s 17 103.6 102.4 170s 18 102.2 103.5 170s 19 103.8 103.6 170s 20 107.3 106.8 170s > print( fitted( fitsurio4$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 98.2 99.9 100.0 100.4 101.8 101.9 102.1 104.3 102.1 99.2 95.7 94.8 96.7 170s 14 15 16 17 18 19 20 170s 98.3 102.3 104.1 102.4 103.5 103.6 106.8 170s > print( fitted( fitsuri4 ) ) 170s demand supply 170s 1 97.8 94.5 170s 2 99.8 97.1 170s 3 99.7 97.2 170s 4 99.9 98.0 170s 5 102.1 96.5 170s 6 101.9 97.4 170s 7 102.3 98.8 170s 8 102.7 99.5 170s 9 101.6 97.3 170s 10 100.6 97.2 170s 11 96.0 97.5 170s 12 95.0 100.3 170s 13 96.2 102.0 170s 14 99.1 102.0 170s 15 103.9 101.7 170s 16 103.6 102.1 170s 17 104.1 99.4 170s 18 101.9 104.6 170s 19 103.3 106.9 170s 20 106.2 110.4 170s > print( fitted( fitsuri4$eq[[ 2 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 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 170s 14 15 16 17 18 19 20 170s 102.0 101.7 102.1 99.4 104.6 106.9 110.4 170s > 170s > print( fitted( fitsurio5r2 ) ) 170s demand supply 170s 1 97.8 98.5 170s 2 100.6 100.7 170s 3 100.4 100.6 170s 4 100.8 101.2 170s 5 101.7 101.3 170s 6 101.8 101.7 170s 7 102.5 102.2 170s 8 103.7 104.9 170s 9 100.8 101.4 170s 10 98.9 97.7 170s 11 94.6 94.8 170s 12 94.8 95.0 170s 13 96.8 97.6 170s 14 98.9 98.2 170s 15 102.9 101.3 170s 16 103.3 103.6 170s 17 101.4 99.8 170s 18 102.7 104.0 170s 19 104.5 104.4 170s 20 108.9 108.9 170s > print( fitted( fitsurio5r2$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 97.8 100.6 100.4 100.8 101.7 101.8 102.5 103.7 100.8 98.9 94.6 94.8 96.8 170s 14 15 16 17 18 19 20 170s 98.9 102.9 103.3 101.4 102.7 104.5 108.9 170s > print( fitted( fitsuri5r2 ) ) 170s demand supply 170s 1 97.8 94.6 170s 2 99.8 97.1 170s 3 99.7 97.2 170s 4 99.9 98.0 170s 5 102.1 96.5 170s 6 101.9 97.4 170s 7 102.3 98.8 170s 8 102.7 99.5 170s 9 101.6 97.3 170s 10 100.6 97.2 170s 11 96.0 97.5 170s 12 95.0 100.3 170s 13 96.2 102.0 170s 14 99.1 102.0 170s 15 103.9 101.7 170s 16 103.6 102.0 170s 17 104.2 99.4 170s 18 101.9 104.6 170s 19 103.3 106.9 170s 20 106.2 110.4 170s > print( fitted( fitsuri5r2$eq[[ 1 ]] ) ) 170s 1 2 3 4 5 6 7 8 9 10 11 12 13 170s 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 170s 14 15 16 17 18 19 20 170s 99.1 103.9 103.6 104.2 101.9 103.3 106.2 170s > 170s > 170s > ## *********** predicted values ************* 170s > predictData <- Kmenta 170s > predictData$consump <- NULL 170s > predictData$price <- Kmenta$price * 0.9 170s > predictData$income <- Kmenta$income * 1.1 170s > 170s > print( predict( fitsur1e2, se.fit = TRUE, interval = "prediction", 170s + useDfSys = TRUE ) ) 170s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 170s 1 97.9 0.607 93.7 102.1 98.1 0.780 170s 2 99.8 0.569 95.6 104.0 99.2 0.793 170s 3 99.7 0.537 95.6 103.9 99.4 0.728 170s 4 99.9 0.575 95.7 104.1 99.7 0.755 170s 5 102.1 0.493 97.9 106.3 101.7 0.652 170s 6 101.9 0.458 97.8 106.0 101.7 0.605 170s 7 102.3 0.475 98.1 106.4 101.7 0.592 170s 8 102.6 0.593 98.4 106.8 103.5 0.835 170s 9 101.6 0.523 97.4 105.8 102.4 0.717 170s 10 100.7 0.788 96.4 105.1 100.3 0.980 170s 11 96.2 0.898 91.8 100.7 96.8 1.081 170s 12 95.2 0.898 90.8 99.7 95.4 1.159 170s 13 96.4 0.816 92.0 100.7 96.8 1.019 170s 14 99.2 0.495 95.1 103.4 98.7 0.710 170s 15 103.8 0.724 99.5 108.1 102.9 0.816 170s 16 103.5 0.586 99.3 107.7 104.2 0.830 170s 17 104.2 1.240 99.4 108.9 104.0 1.540 170s 18 101.8 0.533 97.7 106.0 103.1 0.770 170s 19 103.2 0.666 98.9 107.4 103.0 0.862 170s 20 105.9 1.240 101.1 110.7 105.2 1.517 170s supply.lwr supply.upr 170s 1 92.6 104 170s 2 93.7 105 170s 3 94.0 105 170s 4 94.2 105 170s 5 96.3 107 170s 6 96.3 107 170s 7 96.4 107 170s 8 98.0 109 170s 9 97.0 108 170s 10 94.7 106 170s 11 91.2 103 170s 12 89.7 101 170s 13 91.2 102 170s 14 93.3 104 170s 15 97.4 108 170s 16 98.7 110 170s 17 97.9 110 170s 18 97.7 109 170s 19 97.5 109 170s 20 99.2 111 170s > print( predict( fitsur1e2$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 170s + useDfSys = TRUE ) ) 170s fit se.fit lwr upr 170s 1 98.1 0.780 92.6 104 170s 2 99.2 0.793 93.7 105 170s 3 99.4 0.728 94.0 105 170s 4 99.7 0.755 94.2 105 170s 5 101.7 0.652 96.3 107 170s 6 101.7 0.605 96.3 107 170s 7 101.7 0.592 96.4 107 170s 8 103.5 0.835 98.0 109 170s 9 102.4 0.717 97.0 108 170s 10 100.3 0.980 94.7 106 170s 11 96.8 1.081 91.2 103 170s 12 95.4 1.159 89.7 101 170s 13 96.8 1.019 91.2 102 170s 14 98.7 0.710 93.3 104 170s 15 102.9 0.816 97.4 108 170s 16 104.2 0.830 98.7 110 170s 17 104.0 1.540 97.9 110 170s 18 103.1 0.770 97.7 109 170s 19 103.0 0.862 97.5 109 170s 20 105.2 1.517 99.2 111 170s > 170s > print( predict( fitsur2e, se.pred = TRUE, interval = "confidence", 170s + level = 0.999, newdata = predictData ) ) 170s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 170s 1 103 2.23 99.8 106 97.4 2.80 170s 2 105 2.22 102.0 108 98.3 2.71 170s 3 105 2.23 101.8 108 98.4 2.72 170s 4 105 2.23 102.1 108 98.7 2.70 170s 5 107 2.42 102.3 111 100.4 2.83 170s 6 107 2.39 102.5 111 100.4 2.79 170s 7 107 2.37 103.0 111 100.4 2.75 170s 8 108 2.34 103.8 112 101.8 2.70 170s 9 106 2.44 101.7 111 100.9 2.87 170s 10 105 2.54 99.8 111 99.1 3.05 170s 11 101 2.39 96.5 105 96.1 3.05 170s 12 100 2.24 97.0 103 94.8 2.96 170s 13 101 2.17 99.1 104 96.0 2.83 170s 14 104 2.30 100.5 108 97.6 2.85 170s 15 108 2.58 102.9 114 101.2 2.91 170s 16 108 2.49 103.4 113 102.3 2.83 170s 17 108 2.85 101.3 115 102.1 3.26 170s 18 107 2.31 103.2 111 101.3 2.70 170s 19 108 2.36 104.3 113 101.2 2.68 170s 20 112 2.52 106.4 117 103.0 2.66 170s supply.lwr supply.upr 170s 1 93.6 101.1 170s 2 95.5 101.1 170s 3 95.5 101.3 170s 4 96.0 101.3 170s 5 96.4 104.4 170s 6 96.7 104.1 170s 7 97.1 103.7 170s 8 99.2 104.5 170s 9 96.5 105.3 170s 10 93.4 104.8 170s 11 90.3 101.8 170s 12 89.7 99.9 170s 13 91.9 100.0 170s 14 93.4 101.8 170s 15 96.4 105.9 170s 16 98.3 106.4 170s 17 95.1 109.2 170s 18 98.6 103.9 170s 19 98.9 103.5 170s 20 101.0 105.1 170s > print( predict( fitsur2e$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 170s + level = 0.999, newdata = predictData ) ) 170s fit se.pred lwr upr 170s 1 103 2.23 99.8 106 170s 2 105 2.22 102.0 108 170s 3 105 2.23 101.8 108 170s 4 105 2.23 102.1 108 170s 5 107 2.42 102.3 111 170s 6 107 2.39 102.5 111 170s 7 107 2.37 103.0 111 170s 8 108 2.34 103.8 112 170s 9 106 2.44 101.7 111 170s 10 105 2.54 99.8 111 170s 11 101 2.39 96.5 105 170s 12 100 2.24 97.0 103 170s 13 101 2.17 99.1 104 170s 14 104 2.30 100.5 108 170s 15 108 2.58 102.9 114 170s 16 108 2.49 103.4 113 170s 17 108 2.85 101.3 115 170s 18 107 2.31 103.2 111 170s 19 108 2.36 104.3 113 170s 20 112 2.52 106.4 117 170s > 170s > print( predict( fitsur3, se.pred = TRUE, interval = "prediction", 170s + level = 0.975 ) ) 170s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 170s 1 98.1 2.13 93.1 103 98.6 2.67 170s 2 99.9 2.13 94.9 105 99.6 2.69 170s 3 99.9 2.12 94.9 105 99.8 2.68 170s 4 100.0 2.13 95.0 105 100.0 2.69 170s 5 102.0 2.11 97.0 107 101.7 2.67 170s 6 101.8 2.10 96.9 107 101.7 2.66 170s 7 102.2 2.11 97.2 107 101.7 2.66 170s 8 102.5 2.14 97.5 108 103.2 2.72 170s 9 101.5 2.12 96.5 106 102.2 2.69 170s 10 100.7 2.20 95.5 106 100.3 2.78 170s 11 96.6 2.23 91.3 102 97.3 2.80 170s 12 95.7 2.22 90.5 101 96.1 2.81 170s 13 96.8 2.19 91.6 102 97.3 2.77 170s 14 99.3 2.11 94.4 104 98.9 2.69 170s 15 103.6 2.17 98.5 109 102.5 2.71 170s 16 103.3 2.13 98.3 108 103.7 2.69 170s 17 103.8 2.39 98.2 109 103.3 2.99 170s 18 101.8 2.12 96.8 107 102.7 2.69 170s 19 103.0 2.16 98.0 108 102.6 2.71 170s 20 105.6 2.39 100.0 111 104.6 2.97 170s supply.lwr supply.upr 170s 1 92.4 105 170s 2 93.3 106 170s 3 93.5 106 170s 4 93.7 106 170s 5 95.4 108 170s 6 95.5 108 170s 7 95.5 108 170s 8 96.8 110 170s 9 95.9 109 170s 10 93.8 107 170s 11 90.7 104 170s 12 89.5 103 170s 13 90.8 104 170s 14 92.6 105 170s 15 96.1 109 170s 16 97.3 110 170s 17 96.3 110 170s 18 96.4 109 170s 19 96.3 109 170s 20 97.6 112 170s > print( predict( fitsur3$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 170s + level = 0.975 ) ) 170s fit se.pred lwr upr 170s 1 98.6 2.67 92.4 105 170s 2 99.6 2.69 93.3 106 170s 3 99.8 2.68 93.5 106 170s 4 100.0 2.69 93.7 106 170s 5 101.7 2.67 95.4 108 170s 6 101.7 2.66 95.5 108 170s 7 101.7 2.66 95.5 108 170s 8 103.2 2.72 96.8 110 170s 9 102.2 2.69 95.9 109 170s 10 100.3 2.78 93.8 107 170s 11 97.3 2.80 90.7 104 170s 12 96.1 2.81 89.5 103 170s 13 97.3 2.77 90.8 104 170s 14 98.9 2.69 92.6 105 170s 15 102.5 2.71 96.1 109 170s 16 103.7 2.69 97.3 110 170s 17 103.3 2.99 96.3 110 170s 18 102.7 2.69 96.4 109 170s 19 102.6 2.71 96.3 109 170s 20 104.6 2.97 97.6 112 170s > 170s > print( predict( fitsur4r3, se.fit = TRUE, interval = "confidence", 170s + level = 0.25 ) ) 170s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 170s 1 97.6 0.474 97.4 97.7 98.2 0.571 170s 2 99.9 0.558 99.7 100.1 99.8 0.699 170s 3 99.8 0.523 99.6 100.0 99.9 0.651 170s 4 100.0 0.567 99.9 100.2 100.3 0.701 170s 5 102.1 0.476 102.0 102.3 101.8 0.620 170s 6 102.0 0.443 101.8 102.1 101.9 0.574 170s 7 102.5 0.440 102.3 102.6 102.1 0.559 170s 8 103.1 0.532 102.9 103.3 104.3 0.646 170s 9 101.4 0.520 101.3 101.6 102.2 0.692 170s 10 100.2 0.774 100.0 100.4 99.3 0.939 170s 11 95.3 0.612 95.1 95.5 95.7 0.732 170s 12 94.5 0.525 94.4 94.7 94.7 0.687 170s 13 96.0 0.603 95.8 96.2 96.6 0.791 170s 14 99.0 0.444 98.8 99.1 98.2 0.580 170s 15 103.9 0.643 103.7 104.1 102.4 0.759 170s 16 103.7 0.494 103.6 103.9 104.2 0.634 170s 17 103.8 1.191 103.4 104.1 102.6 1.456 170s 18 102.2 0.510 102.0 102.3 103.4 0.622 170s 19 103.8 0.570 103.6 104.0 103.5 0.714 170s 20 107.2 0.973 106.9 107.6 106.7 1.183 170s supply.lwr supply.upr 170s 1 98.0 98.4 170s 2 99.6 100.0 170s 3 99.7 100.1 170s 4 100.1 100.5 170s 5 101.6 102.0 170s 6 101.7 102.1 170s 7 101.9 102.3 170s 8 104.1 104.5 170s 9 102.0 102.4 170s 10 99.0 99.6 170s 11 95.5 95.9 170s 12 94.5 94.9 170s 13 96.4 96.9 170s 14 98.1 98.4 170s 15 102.1 102.6 170s 16 104.0 104.4 170s 17 102.1 103.1 170s 18 103.2 103.6 170s 19 103.3 103.7 170s 20 106.3 107.1 170s > print( predict( fitsur4r3$eq[[ 1 ]], se.fit = TRUE, interval = "confidence", 170s + level = 0.25 ) ) 170s fit se.fit lwr upr 170s 1 97.6 0.474 97.4 97.7 170s 2 99.9 0.558 99.7 100.1 170s 3 99.8 0.523 99.6 100.0 170s 4 100.0 0.567 99.9 100.2 170s 5 102.1 0.476 102.0 102.3 170s 6 102.0 0.443 101.8 102.1 170s 7 102.5 0.440 102.3 102.6 170s 8 103.1 0.532 102.9 103.3 170s 9 101.4 0.520 101.3 101.6 170s 10 100.2 0.774 100.0 100.4 170s 11 95.3 0.612 95.1 95.5 170s 12 94.5 0.525 94.4 94.7 170s 13 96.0 0.603 95.8 96.2 170s 14 99.0 0.444 98.8 99.1 170s 15 103.9 0.643 103.7 104.1 170s 16 103.7 0.494 103.6 103.9 170s 17 103.8 1.191 103.4 104.1 170s 18 102.2 0.510 102.0 102.3 170s 19 103.8 0.570 103.6 104.0 170s 20 107.2 0.973 106.9 107.6 170s > 170s > print( predict( fitsur4we, se.fit = TRUE, interval = "confidence", 170s + level = 0.25 ) ) 170s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 170s 1 97.5 0.445 97.3 97.6 98.2 0.519 170s 2 99.7 0.514 99.6 99.9 99.6 0.636 170s 3 99.7 0.482 99.5 99.8 99.8 0.591 170s 4 99.9 0.523 99.7 100.0 100.1 0.636 170s 5 102.2 0.438 102.1 102.4 102.0 0.568 170s 6 102.0 0.408 101.9 102.2 102.0 0.523 170s 7 102.5 0.409 102.3 102.6 102.1 0.508 170s 8 102.9 0.503 102.8 103.1 104.2 0.603 170s 9 101.6 0.479 101.4 101.7 102.4 0.631 170s 10 100.5 0.724 100.3 100.8 99.7 0.856 170s 11 95.5 0.612 95.3 95.7 95.9 0.694 170s 12 94.4 0.520 94.3 94.6 94.6 0.677 170s 13 95.8 0.565 95.6 96.0 96.3 0.748 170s 14 99.0 0.414 98.8 99.1 98.2 0.540 170s 15 104.1 0.592 103.9 104.3 102.6 0.690 170s 16 103.8 0.458 103.7 104.0 104.3 0.581 170s 17 104.3 1.100 104.0 104.7 103.3 1.334 170s 18 102.0 0.477 101.9 102.2 103.3 0.564 170s 19 103.6 0.545 103.4 103.8 103.2 0.651 170s 20 106.8 0.958 106.5 107.1 106.1 1.091 170s supply.lwr supply.upr 170s 1 98.0 98.3 170s 2 99.4 99.8 170s 3 99.6 99.9 170s 4 99.9 100.3 170s 5 101.8 102.1 170s 6 101.8 102.2 170s 7 101.9 102.2 170s 8 104.0 104.4 170s 9 102.2 102.6 170s 10 99.5 100.0 170s 11 95.7 96.1 170s 12 94.4 94.8 170s 13 96.1 96.6 170s 14 98.0 98.4 170s 15 102.4 102.9 170s 16 104.1 104.5 170s 17 102.9 103.8 170s 18 103.1 103.5 170s 19 103.0 103.5 170s 20 105.8 106.5 170s > print( predict( fitsur4we$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 170s + level = 0.25 ) ) 170s fit se.fit lwr upr 170s 1 98.2 0.519 98.0 98.3 170s 2 99.6 0.636 99.4 99.8 170s 3 99.8 0.591 99.6 99.9 170s 4 100.1 0.636 99.9 100.3 170s 5 102.0 0.568 101.8 102.1 170s 6 102.0 0.523 101.8 102.2 170s 7 102.1 0.508 101.9 102.2 170s 8 104.2 0.603 104.0 104.4 170s 9 102.4 0.631 102.2 102.6 170s 10 99.7 0.856 99.5 100.0 170s 11 95.9 0.694 95.7 96.1 170s 12 94.6 0.677 94.4 94.8 170s 13 96.3 0.748 96.1 96.6 170s 14 98.2 0.540 98.0 98.4 170s 15 102.6 0.690 102.4 102.9 170s 16 104.3 0.581 104.1 104.5 170s 17 103.3 1.334 102.9 103.8 170s 18 103.3 0.564 103.1 103.5 170s 19 103.2 0.651 103.0 103.5 170s 20 106.1 1.091 105.8 106.5 170s > 170s > print( predict( fitsur5, se.fit = TRUE, se.pred = TRUE, 170s + interval = "prediction", level = 0.5, newdata = predictData ) ) 170s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 170s 1 103.2 0.911 2.14 101.7 105 96.0 170s 2 105.9 0.786 2.09 104.4 107 97.3 170s 3 105.7 0.824 2.11 104.3 107 97.5 170s 4 106.0 0.780 2.09 104.6 107 97.8 170s 5 108.2 1.233 2.30 106.7 110 99.8 170s 6 108.1 1.143 2.25 106.6 110 99.8 170s 7 108.7 1.076 2.22 107.2 110 99.8 170s 8 109.4 0.919 2.15 108.0 111 101.9 170s 9 107.5 1.295 2.33 105.9 109 100.3 170s 10 106.0 1.568 2.49 104.3 108 97.7 170s 11 100.5 1.292 2.33 98.9 102 93.8 170s 12 99.7 0.921 2.15 98.3 101 92.4 170s 13 101.5 0.720 2.07 100.1 103 94.1 170s 14 104.7 1.054 2.21 103.2 106 96.1 170s 15 110.1 1.485 2.44 108.5 112 100.5 170s 16 110.0 1.284 2.33 108.4 112 102.1 170s 17 109.9 2.013 2.80 108.0 112 101.4 170s 18 108.4 0.906 2.14 106.9 110 101.0 170s 19 110.2 0.911 2.14 108.8 112 100.9 170s 20 114.2 0.898 2.14 112.7 116 103.6 170s supply.se.fit supply.se.pred supply.lwr supply.upr 170s 1 0.916 2.68 94.1 97.8 170s 2 0.715 2.62 95.5 99.1 170s 3 0.760 2.63 95.7 99.3 170s 4 0.708 2.62 96.0 99.6 170s 5 1.213 2.80 97.9 101.7 170s 6 1.100 2.75 97.9 101.7 170s 7 0.982 2.70 98.0 101.7 170s 8 0.825 2.65 100.1 103.7 170s 9 1.339 2.85 98.4 102.2 170s 10 1.631 3.00 95.7 99.8 170s 11 1.375 2.87 91.9 95.8 170s 12 1.025 2.72 90.6 94.3 170s 13 0.831 2.65 92.3 95.9 170s 14 1.033 2.72 94.2 97.9 170s 15 1.434 2.90 98.5 102.5 170s 16 1.249 2.81 100.2 104.1 170s 17 2.163 3.32 99.1 103.6 170s 18 0.809 2.65 99.2 102.8 170s 19 0.712 2.62 99.1 102.7 170s 20 0.572 2.58 101.9 105.4 170s > print( predict( fitsur5$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 170s + interval = "prediction", level = 0.5, newdata = predictData ) ) 170s fit se.fit se.pred lwr upr 170s 1 96.0 0.916 2.68 94.1 97.8 170s 2 97.3 0.715 2.62 95.5 99.1 170s 3 97.5 0.760 2.63 95.7 99.3 170s 4 97.8 0.708 2.62 96.0 99.6 170s 5 99.8 1.213 2.80 97.9 101.7 170s 6 99.8 1.100 2.75 97.9 101.7 170s 7 99.8 0.982 2.70 98.0 101.7 170s 8 101.9 0.825 2.65 100.1 103.7 170s 9 100.3 1.339 2.85 98.4 102.2 170s 10 97.7 1.631 3.00 95.7 99.8 170s 11 93.8 1.375 2.87 91.9 95.8 170s 12 92.4 1.025 2.72 90.6 94.3 170s 13 94.1 0.831 2.65 92.3 95.9 170s 14 96.1 1.033 2.72 94.2 97.9 170s 15 100.5 1.434 2.90 98.5 102.5 170s 16 102.1 1.249 2.81 100.2 104.1 170s 17 101.4 2.163 3.32 99.1 103.6 170s 18 101.0 0.809 2.65 99.2 102.8 170s 19 100.9 0.712 2.62 99.1 102.7 170s 20 103.6 0.572 2.58 101.9 105.4 170s > 170s > print( predict( fitsuri1r3, se.fit = TRUE, se.pred = TRUE, 170s + interval = "confidence", level = 0.99 ) ) 170s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 170s 1 97.7 0.653 2.09 95.8 99.6 100.2 170s 2 99.9 0.578 2.07 98.3 101.6 105.7 170s 3 99.9 0.548 2.06 98.3 101.4 104.3 170s 4 100.1 0.583 2.07 98.4 101.8 104.9 170s 5 102.1 0.509 2.05 100.6 103.5 99.2 170s 6 101.9 0.474 2.04 100.6 103.3 100.1 170s 7 102.4 0.496 2.04 101.0 103.9 102.3 170s 8 103.0 0.615 2.08 101.2 104.8 102.6 170s 9 101.4 0.531 2.05 99.9 103.0 94.9 170s 10 100.2 0.785 2.13 98.0 102.5 92.8 170s 11 95.5 0.971 2.21 92.7 98.3 92.1 170s 12 94.8 0.996 2.22 91.9 97.7 98.3 170s 13 96.2 0.880 2.17 93.7 98.8 101.6 170s 14 99.0 0.521 2.05 97.5 100.5 99.8 170s 15 103.7 0.752 2.12 101.6 105.9 97.5 170s 16 103.6 0.622 2.08 101.8 105.4 96.7 170s 17 103.6 1.241 2.34 100.0 107.2 87.6 170s 18 102.1 0.546 2.06 100.5 103.7 100.6 170s 19 103.7 0.696 2.10 101.6 105.7 105.5 170s 20 107.0 1.299 2.37 103.2 110.7 113.8 170s supply.se.fit supply.se.pred supply.lwr supply.upr 170s 1 0.599 1.72 98.4 101.9 170s 2 0.604 1.72 103.9 107.4 170s 3 0.539 1.70 102.7 105.8 170s 4 0.536 1.70 103.4 106.5 170s 5 0.486 1.69 97.8 100.6 170s 6 0.448 1.68 98.8 101.4 170s 7 0.444 1.67 101.0 103.6 170s 8 0.522 1.70 101.1 104.1 170s 9 0.542 1.70 93.3 96.5 170s 10 0.579 1.72 91.1 94.5 170s 11 0.812 1.81 89.7 94.5 170s 12 0.865 1.83 95.8 100.9 170s 13 0.747 1.78 99.4 103.8 170s 14 0.507 1.69 98.3 101.3 170s 15 0.509 1.69 96.0 98.9 170s 16 0.596 1.72 95.0 98.5 170s 17 0.975 1.89 84.7 90.4 170s 18 0.500 1.69 99.1 102.0 170s 19 0.649 1.74 103.6 107.3 170s 20 1.124 1.97 110.5 117.1 170s > print( predict( fitsuri1r3$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 170s + interval = "confidence", level = 0.99 ) ) 170s fit se.fit se.pred lwr upr 170s 1 97.7 0.653 2.09 95.8 99.6 170s 2 99.9 0.578 2.07 98.3 101.6 170s 3 99.9 0.548 2.06 98.3 101.4 170s 4 100.1 0.583 2.07 98.4 101.8 170s 5 102.1 0.509 2.05 100.6 103.5 170s 6 101.9 0.474 2.04 100.6 103.3 170s 7 102.4 0.496 2.04 101.0 103.9 170s 8 103.0 0.615 2.08 101.2 104.8 170s 9 101.4 0.531 2.05 99.9 103.0 170s 10 100.2 0.785 2.13 98.0 102.5 170s 11 95.5 0.971 2.21 92.7 98.3 170s 12 94.8 0.996 2.22 91.9 97.7 170s 13 96.2 0.880 2.17 93.7 98.8 170s 14 99.0 0.521 2.05 97.5 100.5 170s 15 103.7 0.752 2.12 101.6 105.9 170s 16 103.6 0.622 2.08 101.8 105.4 170s 17 103.6 1.241 2.34 100.0 107.2 170s 18 102.1 0.546 2.06 100.5 103.7 170s 19 103.7 0.696 2.10 101.6 105.7 170s 20 107.0 1.299 2.37 103.2 110.7 170s > 170s > print( predict( fitsuri2, se.fit = TRUE, interval = "prediction", 170s + level = 0.9, newdata = predictData ) ) 170s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 170s 1 104 0.960 100.5 108 96.1 1.37 170s 2 107 1.011 102.9 110 99.7 1.69 170s 3 107 1.032 102.8 110 99.8 1.61 170s 4 107 1.019 103.0 111 100.8 1.76 170s 5 110 1.547 105.4 114 99.2 2.00 170s 6 109 1.468 105.3 114 100.3 1.94 170s 7 110 1.465 105.7 114 102.1 2.12 170s 8 110 1.423 106.1 114 103.2 2.60 170s 9 109 1.543 104.8 113 99.9 1.80 170s 10 108 1.699 103.6 112 99.1 1.35 170s 11 102 1.299 98.2 106 98.6 2.25 170s 12 101 0.939 97.2 105 102.0 3.10 170s 13 102 0.731 98.7 106 104.5 3.01 170s 14 106 1.164 102.1 110 104.9 2.27 170s 15 112 1.896 107.3 117 105.4 2.20 170s 16 112 1.733 107.1 116 105.9 2.40 170s 17 113 2.316 107.4 118 102.1 2.02 170s 18 109 1.316 105.2 113 108.8 2.75 170s 19 111 1.497 106.8 115 111.9 3.73 170s 20 114 1.918 109.7 119 117.2 5.62 170s supply.lwr supply.upr 170s 1 86.2 106 170s 2 89.7 110 170s 3 89.7 110 170s 4 90.7 111 170s 5 89.0 109 170s 6 90.1 110 170s 7 91.8 112 170s 8 92.6 114 170s 9 89.7 110 170s 10 89.2 109 170s 11 88.2 109 170s 12 91.0 113 170s 13 93.6 115 170s 14 94.5 115 170s 15 95.0 116 170s 16 95.4 116 170s 17 91.9 112 170s 18 98.1 119 170s 19 100.4 123 170s 20 103.6 131 170s > print( predict( fitsuri2$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 170s + level = 0.9, newdata = predictData ) ) 170s fit se.fit lwr upr 170s 1 96.1 1.37 86.2 106 170s 2 99.7 1.69 89.7 110 170s 3 99.8 1.61 89.7 110 170s 4 100.8 1.76 90.7 111 170s 5 99.2 2.00 89.0 109 170s 6 100.3 1.94 90.1 110 170s 7 102.1 2.12 91.8 112 170s 8 103.2 2.60 92.6 114 170s 9 99.9 1.80 89.7 110 170s 10 99.1 1.35 89.2 109 170s 11 98.6 2.25 88.2 109 170s 12 102.0 3.10 91.0 113 170s 13 104.5 3.01 93.6 115 170s 14 104.9 2.27 94.5 115 170s 15 105.4 2.20 95.0 116 170s 16 105.9 2.40 95.4 116 170s 17 102.1 2.02 91.9 112 170s 18 108.8 2.75 98.1 119 170s 19 111.9 3.73 100.4 123 170s 20 117.2 5.62 103.6 131 170s > 170s > print( predict( fitsuri2w, se.fit = TRUE, interval = "prediction", 170s + level = 0.9, newdata = predictData ) ) 170s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 170s 1 104 0.960 100.5 108 96.1 1.37 170s 2 107 1.011 102.9 110 99.7 1.69 170s 3 107 1.032 102.8 110 99.8 1.61 170s 4 107 1.019 103.0 111 100.8 1.76 170s 5 110 1.547 105.4 114 99.2 2.00 170s 6 109 1.468 105.3 114 100.3 1.94 170s 7 110 1.465 105.7 114 102.1 2.12 170s 8 110 1.423 106.1 114 103.2 2.60 170s 9 109 1.543 104.8 113 99.9 1.80 170s 10 108 1.699 103.6 112 99.1 1.35 170s 11 102 1.299 98.2 106 98.6 2.25 170s 12 101 0.939 97.2 105 102.0 3.10 170s 13 102 0.731 98.7 106 104.5 3.01 170s 14 106 1.164 102.1 110 104.9 2.27 170s 15 112 1.896 107.3 117 105.4 2.20 170s 16 112 1.733 107.1 116 105.9 2.40 170s 17 113 2.316 107.4 118 102.1 2.02 170s 18 109 1.316 105.2 113 108.8 2.75 170s 19 111 1.497 106.8 115 111.9 3.73 170s 20 114 1.918 109.7 119 117.2 5.62 170s supply.lwr supply.upr 170s 1 86.2 106 170s 2 89.7 110 170s 3 89.7 110 170s 4 90.7 111 170s 5 89.0 109 170s 6 90.1 110 170s 7 91.8 112 170s 8 92.6 114 170s 9 89.7 110 170s 10 89.2 109 170s 11 88.2 109 170s 12 91.0 113 170s 13 93.6 115 170s 14 94.5 115 170s 15 95.0 116 170s 16 95.4 116 170s 17 91.9 112 170s 18 98.1 119 170s 19 100.4 123 170s 20 103.6 131 170s > print( predict( fitsuri2w$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 170s + level = 0.9, newdata = predictData ) ) 170s fit se.fit lwr upr 170s 1 96.1 1.37 86.2 106 170s 2 99.7 1.69 89.7 110 170s 3 99.8 1.61 89.7 110 170s 4 100.8 1.76 90.7 111 170s 5 99.2 2.00 89.0 109 170s 6 100.3 1.94 90.1 110 170s 7 102.1 2.12 91.8 112 170s 8 103.2 2.60 92.6 114 170s 9 99.9 1.80 89.7 110 170s 10 99.1 1.35 89.2 109 170s 11 98.6 2.25 88.2 109 170s 12 102.0 3.10 91.0 113 170s 13 104.5 3.01 93.6 115 170s 14 104.9 2.27 94.5 115 170s 15 105.4 2.20 95.0 116 170s 16 105.9 2.40 95.4 116 170s 17 102.1 2.02 91.9 112 170s 18 108.8 2.75 98.1 119 170s 19 111.9 3.73 100.4 123 170s 20 117.2 5.62 103.6 131 170s > 170s > print( predict( fitsuri3e, interval = "prediction", level = 0.925 ) ) 170s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 170s 1 97.4 93.5 101.2 93.4 82.5 104 170s 2 99.2 95.4 103.0 96.7 86.0 107 170s 3 99.3 95.5 103.0 96.7 86.0 107 170s 4 99.3 95.5 103.1 97.7 87.0 108 170s 5 102.5 98.7 106.2 96.1 85.1 107 170s 6 102.1 98.4 105.9 97.2 86.3 108 170s 7 102.4 98.6 106.2 98.8 88.1 110 170s 8 102.5 98.7 106.3 99.8 88.9 111 170s 9 102.0 98.2 105.8 96.9 85.9 108 170s 10 101.5 97.6 105.4 96.4 85.5 107 170s 11 96.1 92.1 100.1 96.3 84.9 108 170s 12 94.4 90.4 98.4 99.6 87.9 111 170s 13 95.4 91.4 99.3 101.9 90.4 113 170s 14 99.1 95.3 102.8 102.0 91.1 113 170s 15 104.7 100.8 108.6 102.2 91.4 113 170s 16 104.1 100.3 107.9 102.6 91.8 113 170s 17 105.9 101.6 110.2 99.1 88.1 110 170s 18 101.6 97.9 105.4 105.5 94.6 116 170s 19 103.1 99.2 106.9 108.4 97.1 120 170s 20 105.5 101.3 109.8 113.1 100.7 126 170s > print( predict( fitsuri3e$eq[[ 1 ]], interval = "prediction", level = 0.925 ) ) 170s fit lwr upr 170s 1 97.4 93.5 101.2 170s 2 99.2 95.4 103.0 170s 3 99.3 95.5 103.0 170s 4 99.3 95.5 103.1 170s 5 102.5 98.7 106.2 170s 6 102.1 98.4 105.9 170s 7 102.4 98.6 106.2 170s 8 102.5 98.7 106.3 170s 9 102.0 98.2 105.8 170s 10 101.5 97.6 105.4 170s 11 96.1 92.1 100.1 170s 12 94.4 90.4 98.4 170s 13 95.4 91.4 99.3 170s 14 99.1 95.3 102.8 170s 15 104.7 100.8 108.6 170s 16 104.1 100.3 107.9 170s 17 105.9 101.6 110.2 170s 18 101.6 97.9 105.4 170s 19 103.1 99.2 106.9 170s 20 105.5 101.3 109.8 170s > 170s > print( predict( fitsurio4, interval = "confidence", newdata = predictData ) ) 170s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 170s 1 102.7 100.8 105 95.5 93.6 97.4 170s 2 105.5 103.8 107 97.0 95.5 98.5 170s 3 105.3 103.6 107 97.2 95.6 98.8 170s 4 105.6 104.0 107 97.5 96.0 99.0 170s 5 107.5 105.0 110 99.1 96.5 101.6 170s 6 107.5 105.1 110 99.2 96.9 101.5 170s 7 108.1 105.9 110 99.3 97.2 101.4 170s 8 108.9 107.1 111 101.5 99.7 103.2 170s 9 106.7 104.0 109 99.5 96.7 102.3 170s 10 105.1 101.8 108 96.7 93.4 100.1 170s 11 99.8 97.2 102 93.1 90.4 95.9 170s 12 99.3 97.4 101 92.1 90.1 94.1 170s 13 101.1 99.7 103 93.9 92.3 95.5 170s 14 104.1 101.9 106 95.6 93.5 97.7 170s 15 109.3 106.2 112 99.7 96.7 102.7 170s 16 109.3 106.6 112 101.4 98.8 104.0 170s 17 108.7 104.5 113 100.0 95.5 104.5 170s 18 107.9 106.0 110 100.6 98.9 102.3 170s 19 109.8 107.9 112 100.7 99.2 102.2 170s 20 114.0 112.3 116 103.7 102.5 104.9 170s > print( predict( fitsurio4$eq[[ 2 ]], interval = "confidence", 170s + newdata = predictData ) ) 170s fit lwr upr 170s 1 95.5 93.6 97.4 170s 2 97.0 95.5 98.5 170s 3 97.2 95.6 98.8 170s 4 97.5 96.0 99.0 170s 5 99.1 96.5 101.6 170s 6 99.2 96.9 101.5 170s 7 99.3 97.2 101.4 170s 8 101.5 99.7 103.2 170s 9 99.5 96.7 102.3 170s 10 96.7 93.4 100.1 170s 11 93.1 90.4 95.9 170s 12 92.1 90.1 94.1 170s 13 93.9 92.3 95.5 170s 14 95.6 93.5 97.7 170s 15 99.7 96.7 102.7 170s 16 101.4 98.8 104.0 170s 17 100.0 95.5 104.5 170s 18 100.6 98.9 102.3 170s 19 100.7 99.2 102.2 170s 20 103.7 102.5 104.9 170s > print( predict( fitsuri4, interval = "confidence", newdata = predictData ) ) 170s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 170s 1 103.1 101.3 105 96.6 93.9 99.3 170s 2 105.5 103.7 107 99.4 96.2 102.5 170s 3 105.4 103.5 107 99.4 96.4 102.5 170s 4 105.6 103.8 107 100.3 97.1 103.5 170s 5 107.7 105.0 110 98.9 94.9 102.9 170s 6 107.6 105.0 110 99.8 96.1 103.5 170s 7 108.1 105.5 111 101.2 97.6 104.9 170s 8 108.7 106.1 111 102.0 97.7 106.4 170s 9 107.0 104.3 110 99.6 96.0 103.2 170s 10 105.7 102.7 109 99.3 96.6 102.0 170s 11 100.7 98.3 103 99.3 95.0 103.5 170s 12 99.9 98.2 102 102.1 95.8 108.4 170s 13 101.5 100.2 103 104.0 97.9 110.1 170s 14 104.5 102.4 107 104.1 99.8 108.4 170s 15 109.5 106.1 113 104.2 100.8 107.5 170s 16 109.4 106.3 112 104.5 100.9 108.2 170s 17 109.3 105.3 113 101.7 97.7 105.6 170s 18 107.8 105.4 110 107.0 103.1 110.9 170s 19 109.5 106.7 112 109.5 104.4 114.6 170s 20 113.0 109.4 117 113.4 106.3 120.6 170s > print( predict( fitsuri4$eq[[ 2 ]], interval = "confidence", 170s + newdata = predictData ) ) 170s fit lwr upr 170s 1 96.6 93.9 99.3 170s 2 99.4 96.2 102.5 170s 3 99.4 96.4 102.5 170s 4 100.3 97.1 103.5 170s 5 98.9 94.9 102.9 170s 6 99.8 96.1 103.5 170s 7 101.2 97.6 104.9 170s 8 102.0 97.7 106.4 170s 9 99.6 96.0 103.2 170s 10 99.3 96.6 102.0 170s 11 99.3 95.0 103.5 170s 12 102.1 95.8 108.4 170s 13 104.0 97.9 110.1 170s 14 104.1 99.8 108.4 170s 15 104.2 100.8 107.5 170s 16 104.5 100.9 108.2 170s 17 101.7 97.7 105.6 170s 18 107.0 103.1 110.9 170s 19 109.5 104.4 114.6 170s 20 113.4 106.3 120.6 170s > 170s > print( predict( fitsurio5r2 ) ) 170s demand.pred supply.pred 170s 1 97.8 98.5 170s 2 100.6 100.7 170s 3 100.4 100.6 170s 4 100.8 101.2 170s 5 101.7 101.3 170s 6 101.8 101.7 170s 7 102.5 102.2 170s 8 103.7 104.9 170s 9 100.8 101.4 170s 10 98.9 97.7 170s 11 94.6 94.8 170s 12 94.8 95.0 170s 13 96.8 97.6 170s 14 98.9 98.2 170s 15 102.9 101.3 170s 16 103.3 103.6 170s 17 101.4 99.8 170s 18 102.7 104.0 170s 19 104.5 104.4 170s 20 108.9 108.9 170s > print( predict( fitsurio5r2$eq[[ 1 ]] ) ) 170s fit 170s 1 97.8 170s 2 100.6 170s 3 100.4 170s 4 100.8 170s 5 101.7 170s 6 101.8 170s 7 102.5 170s 8 103.7 170s 9 100.8 170s 10 98.9 170s 11 94.6 170s 12 94.8 170s 13 96.8 170s 14 98.9 170s 15 102.9 170s 16 103.3 170s 17 101.4 170s 18 102.7 170s 19 104.5 170s 20 108.9 170s > print( predict( fitsuri5r2 ) ) 170s demand.pred supply.pred 170s 1 97.8 94.6 170s 2 99.8 97.1 170s 3 99.7 97.2 170s 4 99.9 98.0 170s 5 102.1 96.5 170s 6 101.9 97.4 170s 7 102.3 98.8 170s 8 102.7 99.5 170s 9 101.6 97.3 170s 10 100.6 97.2 170s 11 96.0 97.5 170s 12 95.0 100.3 170s 13 96.2 102.0 170s 14 99.1 102.0 170s 15 103.9 101.7 170s 16 103.6 102.0 170s 17 104.2 99.4 170s 18 101.9 104.6 170s 19 103.3 106.9 170s 20 106.2 110.4 170s > print( predict( fitsuri5r2$eq[[ 1 ]] ) ) 170s fit 170s 1 97.8 170s 2 99.8 170s 3 99.7 170s 4 99.9 170s 5 102.1 170s 6 101.9 170s 7 102.3 170s 8 102.7 170s 9 101.6 170s 10 100.6 170s 11 96.0 170s 12 95.0 170s 13 96.2 170s 14 99.1 170s 15 103.9 170s 16 103.6 170s 17 104.2 170s 18 101.9 170s 19 103.3 170s 20 106.2 170s > 170s > # predict just one observation 170s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 170s + trend = 25 ) 170s > 170s > print( predict( fitsur1e2, newdata = smallData ) ) 170s demand.pred supply.pred 170s 1 108 115 170s > print( predict( fitsur1e2$eq[[ 1 ]], newdata = smallData ) ) 170s fit 170s 1 108 170s > 170s > print( predict( fitsur2e, se.fit = TRUE, level = 0.9, 170s + newdata = smallData ) ) 170s demand.pred demand.se.fit supply.pred supply.se.fit 170s 1 108 2.21 113 3 170s > print( predict( fitsur2e$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 170s + newdata = smallData ) ) 170s fit se.pred 170s 1 108 3.03 170s > 170s > print( predict( fitsur3, interval = "prediction", level = 0.975, 170s + newdata = smallData ) ) 170s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 170s 1 108 100 115 113 103 123 170s > print( predict( fitsur3$eq[[ 1 ]], interval = "confidence", level = 0.8, 170s + newdata = smallData ) ) 170s fit lwr upr 170s 1 108 105 111 170s > 170s > print( predict( fitsur4r3, se.fit = TRUE, interval = "confidence", 170s + level = 0.999, newdata = smallData ) ) 170s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 170s 1 111 2.06 103 118 119 2.22 170s supply.lwr supply.upr 170s 1 111 127 170s > print( predict( fitsur4r3$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 170s + level = 0.75, newdata = smallData ) ) 170s fit se.pred lwr upr 170s 1 119 3.41 115 123 170s > 170s > print( predict( fitsur5, se.fit = TRUE, interval = "prediction", 170s + newdata = smallData ) ) 170s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 170s 1 110 2.15 104 116 118 2.29 170s supply.lwr supply.upr 170s 1 111 125 170s > print( predict( fitsur5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 170s + newdata = smallData ) ) 170s fit se.pred lwr upr 170s 1 110 2.9 105 114 170s > 170s > print( predict( fitsurio5r2, se.fit = TRUE, se.pred = TRUE, 170s + interval = "prediction", level = 0.5, newdata = smallData ) ) 170s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 170s 1 115 1.98 3.09 113 117 123 170s supply.se.fit supply.se.pred supply.lwr supply.upr 170s 1 2.17 3.82 121 126 170s > print( predict( fitsurio5r2$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 170s + interval = "confidence", level = 0.25, newdata = smallData ) ) 170s fit se.fit se.pred lwr upr 170s 1 115 1.98 3.09 114 115 170s > print( predict( fitsuri5r2, se.fit = TRUE, se.pred = TRUE, 170s + interval = "prediction", level = 0.5, newdata = smallData ) ) 170s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 170s 1 109 2.35 3.06 107 111 113 170s supply.se.fit supply.se.pred supply.lwr supply.upr 170s 1 3.91 6.87 108 117 170s > print( predict( fitsuri5r2$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 170s + interval = "confidence", level = 0.25, newdata = smallData ) ) 170s fit se.fit se.pred lwr upr 170s 1 109 2.35 3.06 108 109 170s > 170s > print( predict( fitsuri5wr2, se.fit = TRUE, se.pred = TRUE, 170s + interval = "prediction", level = 0.5, newdata = smallData ) ) 170s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 170s 1 109 2.35 3.06 107 111 113 170s supply.se.fit supply.se.pred supply.lwr supply.upr 170s 1 3.91 6.87 108 117 170s > print( predict( fitsuri5wr2$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 170s + interval = "confidence", level = 0.25, newdata = smallData ) ) 170s fit se.fit se.pred lwr upr 170s 1 109 2.35 3.06 108 109 170s > 170s > 170s > ## ************ correlation of predicted values *************** 170s > print( correlation.systemfit( fitsur1e2, 2, 1 ) ) 170s [,1] 170s [1,] 0.849 170s [2,] 0.856 170s [3,] 0.864 170s [4,] 0.882 170s [5,] 0.844 170s [6,] 0.861 170s [7,] 0.875 170s [8,] 0.877 170s [9,] 0.884 170s [10,] 0.918 170s [11,] 0.903 170s [12,] 0.884 170s [13,] 0.880 170s [14,] 0.863 170s [15,] 0.896 170s [16,] 0.897 170s [17,] 0.914 170s [18,] 0.839 170s [19,] 0.867 170s [20,] 0.902 170s > 170s > print( correlation.systemfit( fitsur2e, 1, 2 ) ) 170s [,1] 170s [1,] 0.942 170s [2,] 0.944 170s [3,] 0.942 170s [4,] 0.941 170s [5,] 0.902 170s [6,] 0.909 170s [7,] 0.917 170s [8,] 0.903 170s [9,] 0.910 170s [10,] 0.941 170s [11,] 0.923 170s [12,] 0.902 170s [13,] 0.901 170s [14,] 0.893 170s [15,] 0.925 170s [16,] 0.952 170s [17,] 0.944 170s [18,] 0.935 170s [19,] 0.930 170s [20,] 0.938 170s > 170s > print( correlation.systemfit( fitsur3, 2, 1 ) ) 170s [,1] 170s [1,] 0.939 170s [2,] 0.943 170s [3,] 0.941 170s [4,] 0.940 170s [5,] 0.902 170s [6,] 0.909 170s [7,] 0.918 170s [8,] 0.903 170s [9,] 0.910 170s [10,] 0.941 170s [11,] 0.922 170s [12,] 0.900 170s [13,] 0.899 170s [14,] 0.892 170s [15,] 0.923 170s [16,] 0.952 170s [17,] 0.943 170s [18,] 0.936 170s [19,] 0.929 170s [20,] 0.937 170s > 170s > print( correlation.systemfit( fitsur3w, 2, 1 ) ) 170s [,1] 170s [1,] 0.940 170s [2,] 0.946 170s [3,] 0.944 170s [4,] 0.944 170s [5,] 0.908 170s [6,] 0.914 170s [7,] 0.922 170s [8,] 0.907 170s [9,] 0.914 170s [10,] 0.944 170s [11,] 0.926 170s [12,] 0.904 170s [13,] 0.903 170s [14,] 0.897 170s [15,] 0.926 170s [16,] 0.954 170s [17,] 0.946 170s [18,] 0.940 170s [19,] 0.932 170s [20,] 0.940 170s > 170s > print( correlation.systemfit( fitsur4r3, 1, 2 ) ) 170s [,1] 170s [1,] 0.963 170s [2,] 0.971 170s [3,] 0.971 170s [4,] 0.973 170s [5,] 0.940 170s [6,] 0.944 170s [7,] 0.947 170s [8,] 0.942 170s [9,] 0.947 170s [10,] 0.973 170s [11,] 0.910 170s [12,] 0.858 170s [13,] 0.914 170s [14,] 0.923 170s [15,] 0.977 170s [16,] 0.964 170s [17,] 0.978 170s [18,] 0.969 170s [19,] 0.946 170s [20,] 0.941 170s > 170s > print( correlation.systemfit( fitsur5, 2, 1 ) ) 170s [,1] 170s [1,] 0.938 170s [2,] 0.948 170s [3,] 0.948 170s [4,] 0.951 170s [5,] 0.892 170s [6,] 0.897 170s [7,] 0.903 170s [8,] 0.900 170s [9,] 0.907 170s [10,] 0.952 170s [11,] 0.853 170s [12,] 0.784 170s [13,] 0.858 170s [14,] 0.867 170s [15,] 0.961 170s [16,] 0.935 170s [17,] 0.961 170s [18,] 0.944 170s [19,] 0.907 170s [20,] 0.904 170s > 170s > print( correlation.systemfit( fitsuri1r3, 1, 2 ) ) 170s [,1] 170s [1,] -0.662 170s [2,] -0.656 170s [3,] -0.664 170s [4,] -0.689 170s [5,] -0.629 170s [6,] -0.664 170s [7,] -0.696 170s [8,] -0.675 170s [9,] -0.722 170s [10,] -0.757 170s [11,] -0.759 170s [12,] -0.732 170s [13,] -0.710 170s [14,] -0.669 170s [15,] -0.728 170s [16,] -0.737 170s [17,] -0.741 170s [18,] -0.583 170s [19,] -0.684 170s [20,] -0.746 170s > 170s > print( correlation.systemfit( fitsuri2, 2, 1 ) ) 170s [,1] 170s [1,] 0.360 170s [2,] 0.337 170s [3,] 0.337 170s [4,] 0.336 170s [5,] 0.286 170s [6,] 0.299 170s [7,] 0.317 170s [8,] 0.275 170s [9,] 0.322 170s [10,] 0.318 170s [11,] 0.334 170s [12,] 0.334 170s [13,] 0.318 170s [14,] 0.286 170s [15,] 0.358 170s [16,] 0.432 170s [17,] 0.367 170s [18,] 0.362 170s [19,] 0.333 170s [20,] 0.335 170s > 170s > print( correlation.systemfit( fitsuri2w, 1, 2 ) ) 170s [,1] 170s [1,] 0.360 170s [2,] 0.337 170s [3,] 0.337 170s [4,] 0.336 170s [5,] 0.286 170s [6,] 0.299 170s [7,] 0.317 170s [8,] 0.275 170s [9,] 0.322 170s [10,] 0.318 170s [11,] 0.334 170s [12,] 0.334 170s [13,] 0.318 170s [14,] 0.286 170s [15,] 0.358 170s [16,] 0.432 170s [17,] 0.367 170s [18,] 0.362 170s [19,] 0.333 170s [20,] 0.335 170s > 170s > print( correlation.systemfit( fitsuri3e, 1, 2 ) ) 170s [,1] 170s [1,] 0.368 170s [2,] 0.345 170s [3,] 0.344 170s [4,] 0.344 170s [5,] 0.292 170s [6,] 0.305 170s [7,] 0.323 170s [8,] 0.280 170s [9,] 0.329 170s [10,] 0.325 170s [11,] 0.340 170s [12,] 0.340 170s [13,] 0.324 170s [14,] 0.291 170s [15,] 0.366 170s [16,] 0.441 170s [17,] 0.375 170s [18,] 0.369 170s [19,] 0.340 170s [20,] 0.342 170s > 170s > print( correlation.systemfit( fitsurio4, 2, 1 ) ) 170s [,1] 170s [1,] 0.961 170s [2,] 0.971 170s [3,] 0.971 170s [4,] 0.973 170s [5,] 0.940 170s [6,] 0.944 170s [7,] 0.947 170s [8,] 0.939 170s [9,] 0.947 170s [10,] 0.972 170s [11,] 0.904 170s [12,] 0.861 170s [13,] 0.917 170s [14,] 0.922 170s [15,] 0.976 170s [16,] 0.964 170s [17,] 0.978 170s [18,] 0.967 170s [19,] 0.942 170s [20,] 0.934 170s > print( correlation.systemfit( fitsuri4, 2, 1 ) ) 170s [,1] 170s [1,] 0.0384 170s [2,] 0.1213 170s [3,] 0.0975 170s [4,] 0.1381 170s [5,] 0.1295 170s [6,] 0.0937 170s [7,] 0.0630 170s [8,] 0.1056 170s [9,] 0.2180 170s [10,] 0.4042 170s [11,] 0.1074 170s [12,] 0.0337 170s [13,] 0.0760 170s [14,] 0.0701 170s [15,] 0.0680 170s [16,] 0.1263 170s [17,] 0.3859 170s [18,] 0.2715 170s [19,] 0.2850 170s [20,] 0.3967 170s > 170s > print( correlation.systemfit( fitsurio5r2, 1, 2 ) ) 170s [,1] 170s [1,] 0.986 170s [2,] 0.991 170s [3,] 0.991 170s [4,] 0.991 170s [5,] 0.981 170s [6,] 0.983 170s [7,] 0.984 170s [8,] 0.980 170s [9,] 0.982 170s [10,] 0.991 170s [11,] 0.968 170s [12,] 0.947 170s [13,] 0.970 170s [14,] 0.975 170s [15,] 0.991 170s [16,] 0.989 170s [17,] 0.992 170s [18,] 0.990 170s [19,] 0.982 170s [20,] 0.978 170s > print( correlation.systemfit( fitsuri5r2, 1, 2 ) ) 170s [,1] 170s [1,] 0.0440 170s [2,] 0.1279 170s [3,] 0.1045 170s [4,] 0.1451 170s [5,] 0.1375 170s [6,] 0.1021 170s [7,] 0.0719 170s [8,] 0.1124 170s [9,] 0.2252 170s [10,] 0.4097 170s [11,] 0.1145 170s [12,] 0.0410 170s [13,] 0.0834 170s [14,] 0.0778 170s [15,] 0.0750 170s [16,] 0.1344 170s [17,] 0.3900 170s [18,] 0.2789 170s [19,] 0.2897 170s [20,] 0.4005 170s > 170s > 170s > ## ************ Log-Likelihood values *************** 170s > print( logLik( fitsur1e2 ) ) 170s 'log Lik.' -50.9 (df=10) 170s > print( logLik( fitsur1e2, residCovDiag = TRUE ) ) 170s 'log Lik.' -85.4 (df=10) 170s > 170s > print( logLik( fitsur2e ) ) 170s 'log Lik.' -52 (df=9) 170s > print( logLik( fitsur2e, residCovDiag = TRUE ) ) 170s 'log Lik.' -86.5 (df=9) 170s > 170s > print( logLik( fitsur3 ) ) 170s 'log Lik.' -52.2 (df=9) 170s > print( logLik( fitsur3, residCovDiag = TRUE ) ) 170s 'log Lik.' -86.4 (df=9) 170s > 170s > print( logLik( fitsur4r3 ) ) 170s 'log Lik.' -58.4 (df=8) 170s > print( logLik( fitsur4r3, residCovDiag = TRUE ) ) 170s 'log Lik.' -85.5 (df=8) 170s > 170s > print( logLik( fitsur5 ) ) 170s 'log Lik.' -58.5 (df=8) 170s > print( logLik( fitsur5, residCovDiag = TRUE ) ) 170s 'log Lik.' -84.6 (df=8) 170s > 170s > print( logLik( fitsur5w ) ) 170s 'log Lik.' -58.5 (df=8) 170s > print( logLik( fitsur5w, residCovDiag = TRUE ) ) 170s 'log Lik.' -84.7 (df=8) 170s > 170s > print( logLik( fitsuri1r3 ) ) 170s 'log Lik.' -67.8 (df=10) 170s > print( logLik( fitsuri1r3, residCovDiag = TRUE ) ) 170s 'log Lik.' -76.2 (df=10) 170s > 170s > print( logLik( fitsuri2 ) ) 170s 'log Lik.' -99.9 (df=9) 170s > print( logLik( fitsuri2, residCovDiag = TRUE ) ) 170s 'log Lik.' -101 (df=9) 170s > 170s > print( logLik( fitsuri3e ) ) 170s 'log Lik.' -99.9 (df=9) 170s > print( logLik( fitsuri3e, residCovDiag = TRUE ) ) 170s 'log Lik.' -102 (df=9) 170s > 170s > print( logLik( fitsurio4 ) ) 170s 'log Lik.' -58.5 (df=8) 170s > print( logLik( fitsurio4, residCovDiag = TRUE ) ) 170s 'log Lik.' -85.9 (df=8) 170s > 170s > print( logLik( fitsuri4 ) ) 170s 'log Lik.' -101 (df=8) 170s > print( logLik( fitsuri4, residCovDiag = TRUE ) ) 170s 'log Lik.' -101 (df=8) 170s > 170s > print( logLik( fitsuri4w ) ) 170s 'log Lik.' -101 (df=8) 170s > print( logLik( fitsuri4w, residCovDiag = TRUE ) ) 170s 'log Lik.' -101 (df=8) 170s > 170s > print( logLik( fitsurio5r2 ) ) 170s 'log Lik.' -59.8 (df=8) 170s > print( logLik( fitsurio5r2, residCovDiag = TRUE ) ) 170s 'log Lik.' -93.1 (df=8) 170s > 170s > print( logLik( fitsuri5r2 ) ) 170s 'log Lik.' -101 (df=8) 170s > print( logLik( fitsuri5r2, residCovDiag = TRUE ) ) 170s 'log Lik.' -101 (df=8) 170s > 170s > 170s > ## *********** likelihood ratio tests ************* 170s > # testing first restriction 170s > # non-iterating, methodResidCov = 1 170s > print( lrtest( fitsur2, fitsur1 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur2 170s Model 2: fitsur1 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -52.2 170s 2 10 -51.6 1 1.19 0.28 170s > print( lrtest( fitsur3, fitsur1 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur3 170s Model 2: fitsur1 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -52.2 170s 2 10 -51.6 1 1.19 0.28 170s > # non-iterating, methodResidCov = 0 170s > print( lrtest( fitsur2e, fitsur1e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur2e 170s Model 2: fitsur1e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -52.0 170s 2 10 -51.6 1 0.7 0.4 170s > print( lrtest( fitsur3e, fitsur1e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur3e 170s Model 2: fitsur1e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -52.0 170s 2 10 -51.6 1 0.7 0.4 170s > # iterating, methodResidCov = 1 170s > print( lrtest( fitsuri2, fitsuri1 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri2 170s Model 2: fitsuri1 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 10 -67.8 1 64.3 1.1e-15 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsuri3, fitsuri1 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri3 170s Model 2: fitsuri1 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 10 -67.8 1 64.3 1.1e-15 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > # iterating, methodResidCov = 0 170s > print( lrtest( fitsuri2e, fitsuri1e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri2e 170s Model 2: fitsuri1e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 10 -67.8 1 64.3 1.1e-15 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsuri3e, fitsuri1e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri3e 170s Model 2: fitsuri1e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 10 -67.8 1 64.3 1.1e-15 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > # non-iterating, methodResidCov = 1, WSUR 170s > print( lrtest( fitsur3w, fitsur1w ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur3w 170s Model 2: fitsur1w 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -52.1 170s 2 10 -51.6 1 0.87 0.35 170s > 170s > # testing second restriction 170s > # non-iterating, methodResidCov = 1 170s > print( lrtest( fitsur4, fitsur2 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur4 170s Model 2: fitsur2 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 9 -52.2 1 12.7 0.00037 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsur4, fitsur3 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur4 170s Model 2: fitsur3 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 9 -52.2 1 12.7 0.00037 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsur5, fitsur2 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur5 170s Model 2: fitsur2 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 9 -52.2 1 12.7 0.00037 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsur5, fitsur3 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur5 170s Model 2: fitsur3 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 9 -52.2 1 12.7 0.00037 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > # non-iterating, methodResidCov = 0 170s > print( lrtest( fitsur4e, fitsur2e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur4e 170s Model 2: fitsur2e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.6 170s 2 9 -52.0 1 13.2 0.00028 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsur4e, fitsur3e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur4e 170s Model 2: fitsur3e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.6 170s 2 9 -52.0 1 13.2 0.00028 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsur5e, fitsur2e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur5e 170s Model 2: fitsur2e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.6 170s 2 9 -52.0 1 13.2 0.00028 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsur5e, fitsur3e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur5e 170s Model 2: fitsur3e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.6 170s 2 9 -52.0 1 13.2 0.00028 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > # iterating, methodResidCov = 1 170s > print( lrtest( fitsurio4, fitsuri2 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsurio4 170s Model 2: fitsuri2 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 9 -99.9 1 82.9 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s Warning message: 170s In lrtest.systemfit(fitsurio4, fitsuri2) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s > print( lrtest( fitsurio4, fitsuri3 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsurio4 170s Model 2: fitsuri3 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 9 -99.9 1 82.9 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s Warning message: 170s In lrtest.systemfit(fitsurio4, fitsuri3) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s > print( lrtest( fitsurio5, fitsuri2 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsurio5 170s Model 2: fitsuri2 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 9 -99.9 1 82.9 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsurio5, fitsuri3 ) ) 170s Warning message: 170s In lrtest.systemfit(fitsurio5, fitsuri2) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s Likelihood ratio test 170s 170s Model 1: fitsurio5 170s Model 2: fitsuri3 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 9 -99.9 1 82.9 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s Warning message: 170s In lrtest.systemfit(fitsurio5, fitsuri3) :> # corrected 170s > print( lrtest( fitsuri2, fitsuri4 ) ) 170s 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s Likelihood ratio test 170s 170s Model 1: fitsuri2 170s Model 2: fitsuri4 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 8 -100.9 -1 1.9 0.17 170s > print( lrtest( fitsuri3, fitsuri4 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri3 170s Model 2: fitsuri4 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 8 -100.9 -1 1.9 0.17 170s > print( lrtest( fitsuri2, fitsuri5 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri2 170s Model 2: fitsuri5 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 8 -100.9 -1 1.9 0.17 170s > print( lrtest( fitsuri3, fitsuri5 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri3 170s Model 2: fitsuri5 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 8 -100.9 -1 1.9 0.17 170s > 170s > # iterating, methodResidCov = 0 170s > print( lrtest( fitsurio4e, fitsuri2e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsurio4e 170s Model 2: fitsuri2e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.4 170s 2 9 -99.9 1 83 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s Warning message: 170s > print( lrtest( fitsurio4e, fitsuri3e ) ) 170s In lrtest.systemfit(fitsurio4e, fitsuri2e) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s Likelihood ratio test 170s 170s Model 1: fitsurio4e 170s Model 2: fitsuri3e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.4 170s 2 9 -99.9 1 83 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsurio5e, fitsuri2e ) ) 170s Warning message: 170s In lrtest.systemfit(fitsurio4e, fitsuri3e) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s Likelihood ratio test 170s 170s Model 1: fitsurio5e 170s Model 2: fitsuri2e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.4 170s 2 9 -99.9 1 83 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsurio5e, fitsuri3e ) ) 170s Warning message: 170s In lrtest.systemfit(fitsurio5e, fitsuri2e) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s Likelihood ratio test 170s 170s Model 1: fitsurio5e 170s Model 2: fitsuri3e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.4 170s 2 9 -99.9 1 83 <2e-16 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > # corrected 170s Warning message: 170s In lrtest.systemfit(fitsurio5e, fitsuri3e) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s > print( lrtest( fitsuri2e, fitsuri4e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri2e 170s Model 2: fitsuri4e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 8 -100.9 -1 1.9 0.17 170s > print( lrtest( fitsuri3e, fitsuri4e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri3e 170s Model 2: fitsuri4e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 8 -100.9 -1 1.9 0.17 170s > print( lrtest( fitsuri2e, fitsuri5e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri2e 170s Model 2: fitsuri5e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 8 -100.9 -1 1.9 0.17 170s > print( lrtest( fitsuri3e, fitsuri5e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri3e 170s Model 2: fitsuri5e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 8 -100.9 -1 1.9 0.17 170s > 170s > # non-iterating, methodResidCov = 0, WSUR 170s > print( lrtest( fitsur4we, fitsur2we ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur4we 170s Model 2: fitsur2we 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.6 170s 2 9 -51.8 1 13.5 0.00024 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > 170s > # iterating, methodResidCov = 1, WSUR 170s > print( lrtest( fitsuri2w, fitsuri4w ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri2w 170s Model 2: fitsuri4w 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 9 -99.9 170s 2 8 -100.9 -1 1.9 0.17 170s > 170s > # testing both of the restrictions 170s > # non-iterating, methodResidCov = 1 170s > print( lrtest( fitsur4, fitsur1 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur4 170s Model 2: fitsur1 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 10 -51.6 2 13.8 0.00098 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsur5, fitsur1 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur5 170s Model 2: fitsur1 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 10 -51.6 2 13.8 0.00098 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > # non-iterating, methodResidCov = 0 170s > print( lrtest( fitsur4e, fitsur1e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur4e 170s Model 2: fitsur1e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.6 170s 2 10 -51.6 2 13.9 0.00095 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsur5e, fitsur1e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur5e 170s Model 2: fitsur1e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.6 170s 2 10 -51.6 2 13.9 0.00095 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > # iterating, methodResidCov = 1 170s > print( lrtest( fitsurio4, fitsuri1 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsurio4 170s Model 2: fitsuri1 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 10 -67.8 2 18.6 9e-05 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsurio5, fitsuri1 ) ) 170s Warning message: 170s In lrtest.systemfit(fitsurio4, fitsuri1) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s Likelihood ratio test 170s 170s Model 1: fitsurio5 170s Model 2: fitsuri1 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 10 -67.8 2 18.6 9e-05 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s Warning message: 170s In lrtest.systemfit(fitsurio5, fitsuri1) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s > # corrected 170s > print( lrtest( fitsuri1, fitsuri4 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri1 170s Model 2: fitsuri4 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 10 -67.8 170s 2 8 -100.9 -2 66.2 4.2e-15 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsuri1, fitsuri5 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri1 170s Model 2: fitsuri5 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 10 -67.8 170s 2 8 -100.9 -2 66.2 4.2e-15 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > # iterating, methodResidCov = 0 170s > print( lrtest( fitsurio4e, fitsuri1e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsurio4e 170s Model 2: fitsuri1e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.4 170s 2 10 -67.8 2 18.7 8.9e-05 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsurio5e, fitsuri1e ) ) 170s Warning message: 170s In lrtest.systemfit(fitsurio4e, fitsuri1e) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s Likelihood ratio test 170s 170s Model 1: fitsurio5e 170s Model 2: fitsuri1e 170s Warning message: 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.4 170s 2 10 -67.8 2 18.7 8.9e-05 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s In lrtest.systemfit(fitsurio5e, fitsuri1e) : 170s model '2' has a smaller log-likelihood value than the more restricted model '1' 170s > # corrected 170s > print( lrtest( fitsuri1e, fitsuri4e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri1e 170s Model 2: fitsuri4e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 10 -67.8 170s 2 8 -100.9 -2 66.2 4.2e-15 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsuri1e, fitsuri5e ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsuri1e 170s Model 2: fitsuri5e 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 10 -67.8 170s 2 8 -100.9 -2 66.2 4.2e-15 *** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > # non-iterating, methodResidCov = 1, WSUR 170s > print( lrtest( fitsur5w, fitsur1w ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur5w 170s Model 2: fitsur1w 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 10 -51.6 2 13.8 0.001 ** 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > 170s > # testing the two restrictions with one call 170s > # non-iterating, methodResidCov = 1 170s > print( lrtest( fitsur4, fitsur2, fitsur1 ) ) 170s Likelihood ratio test 170s 170s Model 1: fitsur4 170s Model 2: fitsur2 170s Model 3: fitsur1 170s #Df LogLik Df Chisq Pr(>Chisq) 170s 1 8 -58.5 170s 2 9 -52.2 1 12.66 0.00037 *** 170s 3 10 -51.6 1 1.19 0.27520 170s --- 170s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 170s > print( lrtest( fitsur5, fitsur3, fitsur1 ) ) 171s Likelihood ratio test 171s 171s Model 1: fitsur5 171s Model 2: fitsur3 171s Model 3: fitsur1 171s #Df LogLik Df Chisq Pr(>Chisq) 171s 1 8 -58.5 171s 2 9 -52.2 1 12.66 0.00037 *** 171s 3 10 -51.6 1 1.19 0.27520 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > print( lrtest( fitsur1, fitsur3, fitsur5 ) ) 171s Likelihood ratio test 171s 171s Model 1: fitsur1 171s Model 2: fitsur3 171s Model 3: fitsur5 171s #Df LogLik Df Chisq Pr(>Chisq) 171s 1 10 -51.6 171s 2 9 -52.2 -1 1.19 0.27520 171s 3 8 -58.5 -1 12.66 0.00037 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > print( lrtest( object = fitsur5, fitsur3, fitsur1 ) ) 171s Likelihood ratio test 171s 171s Model 1: fitsur5 171s Model 2: fitsur3 171s Model 3: fitsur1 171s #Df LogLik Df Chisq Pr(>Chisq) 171s 1 8 -58.5 171s 2 9 -52.2 1 12.66 0.00037 *** 171s 3 10 -51.6 1 1.19 0.27520 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > print( lrtest( fitsur3, object = fitsur5, fitsur1 ) ) 171s Likelihood ratio test 171s 171s Model 1: fitsur5 171s Model 2: fitsur3 171s Model 3: fitsur1 171s #Df LogLik Df Chisq Pr(>Chisq) 171s 1 8 -58.5 171s 2 9 -52.2 1 12.66 0.00037 *** 171s 3 10 -51.6 1 1.19 0.27520 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > print( lrtest( fitsur3, fitsur1, object = fitsur5 ) ) 171s Likelihood ratio test 171s 171s Model 1: fitsur5 171s Model 2: fitsur3 171s Model 3: fitsur1 171s #Df LogLik Df Chisq Pr(>Chisq) 171s 1 8 -58.5 171s 2 9 -52.2 1 12.66 0.00037 *** 171s 3 10 -51.6 1 1.19 0.27520 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > # iterating, methodResidCov = 0 171s > print( lrtest( fitsuri4e, fitsuri2e, fitsuri1e ) ) 171s Likelihood ratio test 171s 171s Model 1: fitsuri4e 171s Model 2: fitsuri2e 171s Model 3: fitsuri1e 171s #Df LogLik Df Chisq Pr(>Chisq) 171s 1 8 -100.9 171s 2 9 -99.9 1 1.9 0.17 171s 3 10 -67.8 1 64.3 1.1e-15 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > print( lrtest( fitsuri5e, fitsuri3e, fitsuri1e ) ) 171s Likelihood ratio test 171s 171s Model 1: fitsuri5e 171s Model 2: fitsuri3e 171s Model 3: fitsuri1e 171s #Df LogLik Df Chisq Pr(>Chisq) 171s 1 8 -100.9 171s 2 9 -99.9 1 1.9 0.17 171s 3 10 -67.8 1 64.3 1.1e-15 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > ## ************** F tests **************** 171s > # testing first restriction 171s > print( linearHypothesis( fitsur1, restrm ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 1.24 0.27 171s > linearHypothesis( fitsur1, restrict ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 1.24 0.27 171s > 171s > print( linearHypothesis( fitsur1r2, restrm ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1r2 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 1.65 0.21 171s > linearHypothesis( fitsur1r2, restrict ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1r2 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 1.65 0.21 171s > 171s > print( linearHypothesis( fitsuri1e2, restrm ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1e2 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 140 2.1e-13 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1e2, restrict ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1e2 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 140 2.1e-13 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsuri1r3, restrm ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1r3 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 141 1.9e-13 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1r3, restrict ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1r3 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 141 1.9e-13 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsur1we2, restrm ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1we2 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 1.65 0.21 171s > linearHypothesis( fitsur1we2, restrict ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1we2 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 1.65 0.21 171s > 171s > print( linearHypothesis( fitsuri1wr3, restrm ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1wr3 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 141 1.9e-13 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1wr3, restrict ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1wr3 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 141 1.9e-13 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > # testing second restriction 171s > restrOnly2m <- matrix(0,1,7) 171s > restrOnly2q <- 0.5 171s > restrOnly2m[1,2] <- -1 171s > restrOnly2m[1,5] <- 1 171s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 171s > restrictOnly2i <- "- demand_price + supply_income = 0.5" 171s > # first restriction not imposed 171s > print( linearHypothesis( fitsur1e2, restrOnly2m, restrOnly2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1e2 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 2.36 0.13 171s > linearHypothesis( fitsur1e2, restrictOnly2 ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1e2 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 2.36 0.13 171s > 171s > print( linearHypothesis( fitsuri1, restrOnly2m, restrOnly2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 12.2 0.0014 ** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1, restrictOnly2i ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1 171s 171s Res.Df Df F Pr(>F) 171s 1 34 171s 2 33 1 12.2 0.0014 ** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > # first restriction imposed 171s > print( linearHypothesis( fitsur2, restrOnly2m, restrOnly2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur2 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 5.5 0.025 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsur2, restrictOnly2 ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur2 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 5.5 0.025 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsur3, restrOnly2m, restrOnly2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur3 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 5.5 0.025 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsur3, restrictOnly2 ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur3 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 5.5 0.025 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsuri2e, restrOnly2m, restrOnly2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri2e 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 2.35 0.13 171s > linearHypothesis( fitsuri2e, restrictOnly2i ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri2e 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 2.35 0.13 171s > 171s > print( linearHypothesis( fitsuri3e, restrOnly2m, restrOnly2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri3e 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 2.35 0.13 171s > linearHypothesis( fitsuri3e, restrictOnly2i ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri3e 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 2.35 0.13 171s > 171s > print( linearHypothesis( fitsur2we, restrOnly2m, restrOnly2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur2we 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 6.26 0.017 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsur2we, restrictOnly2 ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur2we 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 6.26 0.017 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsuri3we, restrOnly2m, restrOnly2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri3we 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 2.35 0.13 171s > linearHypothesis( fitsuri3we, restrictOnly2i ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri3we 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 34 1 2.35 0.13 171s > 171s > # testing both of the restrictions 171s > print( linearHypothesis( fitsur1r3, restr2m, restr2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1r3 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 33 2 2.6 0.089 . 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsur1r3, restrict2 ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1r3 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 33 2 2.6 0.089 . 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsuri1e2, restr2m, restr2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1e2 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 33 2 89.1 5e-14 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1e2, restrict2i ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1e2 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 33 2 89.1 5e-14 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsur1w, restr2m, restr2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1w 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 33 2 1.8 0.18 171s > linearHypothesis( fitsur1w, restrict2 ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1w 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 33 2 1.8 0.18 171s > 171s > print( linearHypothesis( fitsuri1wr3, restr2m, restr2q ) ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1wr3 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 33 2 89.6 4.6e-14 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1wr3, restrict2i ) 171s Linear hypothesis test (Theil's F test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1wr3 171s 171s Res.Df Df F Pr(>F) 171s 1 35 171s 2 33 2 89.6 4.6e-14 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > 171s > ## ************** Wald tests **************** 171s > # testing first restriction 171s > print( linearHypothesis( fitsur1, restrm, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 0.81 0.37 171s > linearHypothesis( fitsur1, restrict, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 0.81 0.37 171s > 171s > print( linearHypothesis( fitsur1r2, restrm, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1r2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 1.12 0.29 171s > linearHypothesis( fitsur1r2, restrict, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1r2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 1.12 0.29 171s > 171s > print( linearHypothesis( fitsuri1e2, restrm, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1e2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 147 <2e-16 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1e2, restrict, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1e2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 147 <2e-16 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsuri1r3, restrm, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1r3 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 147 <2e-16 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1r3, restrict, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsuri1r3 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 147 <2e-16 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsur1w, restrm, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1w 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 0.81 0.37 171s > linearHypothesis( fitsur1w, restrict, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s 171s Model 1: restricted model 171s Model 2: fitsur1w 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 0.81 0.37 171s > 171s > # testing second restriction 171s > # first restriction not imposed 171s > print( linearHypothesis( fitsur1e2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1e2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 1.6 0.21 171s > linearHypothesis( fitsur1e2, restrictOnly2, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1e2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 1.6 0.21 171s > 171s > print( linearHypothesis( fitsuri1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 12.2 0.00047 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1, restrictOnly2i, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 34 171s 2 33 1 12.2 0.00047 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > # first restriction imposed 171s > print( linearHypothesis( fitsur2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 3.95 0.047 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsur2, restrictOnly2, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 3.95 0.047 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsur3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur3 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 3.95 0.047 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsur3, restrictOnly2, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur3 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 3.95 0.047 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsuri2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri2e 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 2.76 0.096 . 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri2e, restrictOnly2i, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri2e 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 2.76 0.096 . 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsuri3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri3e 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 2.76 0.096 . 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri3e, restrictOnly2i, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri3e 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 2.76 0.096 . 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsuri2w, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri2w 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 2.2 0.14 171s > linearHypothesis( fitsuri2w, restrictOnly2i, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri2w 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 2.2 0.14 171s > 171s > print( linearHypothesis( fitsur3w, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur3w 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 4.26 0.039 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsur3w, restrictOnly2, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur3w 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 34 1 4.26 0.039 * 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > 171s > # testing both of the restrictions 171s > print( linearHypothesis( fitsur1r3, restr2m, restr2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1r3 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 33 2 3.51 0.17 171s > linearHypothesis( fitsur1r3, restrict2, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1r3 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 33 2 3.51 0.17 171s > 171s > print( linearHypothesis( fitsuri1e2, restr2m, restr2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1e2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 33 2 188 <2e-16 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1e2, restrict2i, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1e2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 33 2 188 <2e-16 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > print( linearHypothesis( fitsur1we2, restr2m, restr2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1we2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 33 2 3.66 0.16 171s > linearHypothesis( fitsur1we2, restrict2, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_price = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsur1we2 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 33 2 3.66 0.16 171s > 171s > print( linearHypothesis( fitsuri1wr3, restr2m, restr2q, test = "Chisq" ) ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1wr3 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 33 2 187 <2e-16 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > linearHypothesis( fitsuri1wr3, restrict2i, test = "Chisq" ) 171s Linear hypothesis test (Chi^2 statistic of a Wald test) 171s 171s Hypothesis: 171s demand_income - supply_trend = 0 171s - demand_price + supply_income = 0.5 171s 171s Model 1: restricted model 171s Model 2: fitsuri1wr3 171s 171s Res.Df Df Chisq Pr(>Chisq) 171s 1 35 171s 2 33 2 187 <2e-16 *** 171s --- 171s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 171s > 171s > 171s > ## ****************** model frame ************************** 171s > print( mf <- model.frame( fitsur1e2 ) ) 171s consump price income farmPrice trend 171s 1 98.5 100.3 87.4 98.0 1 171s 2 99.2 104.3 97.6 99.1 2 171s 3 102.2 103.4 96.7 99.1 3 171s 4 101.5 104.5 98.2 98.1 4 171s 5 104.2 98.0 99.8 110.8 5 171s 6 103.2 99.5 100.5 108.2 6 171s 7 104.0 101.1 103.2 105.6 7 171s 8 99.9 104.8 107.8 109.8 8 171s 9 100.3 96.4 96.6 108.7 9 171s 10 102.8 91.2 88.9 100.6 10 171s 11 95.4 93.1 75.1 81.0 11 171s 12 92.4 98.8 76.9 68.6 12 171s 13 94.5 102.9 84.6 70.9 13 171s 14 98.8 98.8 90.6 81.4 14 171s 15 105.8 95.1 103.1 102.3 15 171s 16 100.2 98.5 105.1 105.0 16 171s 17 103.5 86.5 96.4 110.5 17 171s 18 99.9 104.0 104.4 92.5 18 171s 19 105.2 105.8 110.7 89.3 19 171s 20 106.2 113.5 127.1 93.0 20 171s > print( mf1 <- model.frame( fitsur1e2$eq[[ 1 ]] ) ) 171s consump price income 171s 1 98.5 100.3 87.4 171s 2 99.2 104.3 97.6 171s 3 102.2 103.4 96.7 171s 4 101.5 104.5 98.2 171s 5 104.2 98.0 99.8 171s 6 103.2 99.5 100.5 171s 7 104.0 101.1 103.2 171s 8 99.9 104.8 107.8 171s 9 100.3 96.4 96.6 171s 10 102.8 91.2 88.9 171s 11 95.4 93.1 75.1 171s 12 92.4 98.8 76.9 171s 13 94.5 102.9 84.6 171s 14 98.8 98.8 90.6 171s 15 105.8 95.1 103.1 171s 16 100.2 98.5 105.1 171s 17 103.5 86.5 96.4 171s 18 99.9 104.0 104.4 171s 19 105.2 105.8 110.7 171s 20 106.2 113.5 127.1 171s > print( attributes( mf1 )$terms ) 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s > print( mf2 <- model.frame( fitsur1e2$eq[[ 2 ]] ) ) 171s consump price farmPrice trend 171s 1 98.5 100.3 98.0 1 171s 2 99.2 104.3 99.1 2 171s 3 102.2 103.4 99.1 3 171s 4 101.5 104.5 98.1 4 171s 5 104.2 98.0 110.8 5 171s 6 103.2 99.5 108.2 6 171s 7 104.0 101.1 105.6 7 171s 8 99.9 104.8 109.8 8 171s 9 100.3 96.4 108.7 9 171s 10 102.8 91.2 100.6 10 171s 11 95.4 93.1 81.0 11 171s 12 92.4 98.8 68.6 12 171s 13 94.5 102.9 70.9 13 171s 14 98.8 98.8 81.4 14 171s 15 105.8 95.1 102.3 15 171s 16 100.2 98.5 105.0 16 171s 17 103.5 86.5 110.5 17 171s 18 99.9 104.0 92.5 18 171s 19 105.2 105.8 89.3 19 171s 20 106.2 113.5 93.0 20 171s > print( attributes( mf2 )$terms ) 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s > 171s > print( all.equal( mf, model.frame( fitsur1w ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsur1w$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsur2e ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsur2e$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsur3 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf2, model.frame( fitsur3$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsur4r3 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsur4r3$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsur4we ) ) ) 171s [1] TRUE 171s > print( all.equal( mf2, model.frame( fitsur4we$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsur5 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf2, model.frame( fitsur5$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsuri1r3 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsuri1r3$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsuri2 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsuri2$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsuri3e ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsuri3e$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsurio4 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf2, model.frame( fitsurio4$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mf, model.frame( fitsuri4 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsuri4$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsurio5r2 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsurio5r2$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mf, model.frame( fitsuri5r2 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsuri5r2$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > print( all.equal( mf, model.frame( fitsuri5wr2 ) ) ) 171s [1] TRUE 171s > print( all.equal( mf1, model.frame( fitsuri5wr2$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > 171s > ## **************** model matrix ************************ 171s > # with x (returnModelMatrix) = TRUE 171s > print( !is.null( fitsur1e2$eq[[ 1 ]]$x ) ) 171s [1] TRUE 171s > print( mm <- model.matrix( fitsur1e2 ) ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s demand_1 1 100.3 87.4 0 171s demand_2 1 104.3 97.6 0 171s demand_3 1 103.4 96.7 0 171s demand_4 1 104.5 98.2 0 171s demand_5 1 98.0 99.8 0 171s demand_6 1 99.5 100.5 0 171s demand_7 1 101.1 103.2 0 171s demand_8 1 104.8 107.8 0 171s demand_9 1 96.4 96.6 0 171s demand_10 1 91.2 88.9 0 171s demand_11 1 93.1 75.1 0 171s demand_12 1 98.8 76.9 0 171s demand_13 1 102.9 84.6 0 171s demand_14 1 98.8 90.6 0 171s demand_15 1 95.1 103.1 0 171s demand_16 1 98.5 105.1 0 171s demand_17 1 86.5 96.4 0 171s demand_18 1 104.0 104.4 0 171s demand_19 1 105.8 110.7 0 171s demand_20 1 113.5 127.1 0 171s supply_1 0 0.0 0.0 1 171s supply_2 0 0.0 0.0 1 171s supply_3 0 0.0 0.0 1 171s supply_4 0 0.0 0.0 1 171s supply_5 0 0.0 0.0 1 171s supply_6 0 0.0 0.0 1 171s supply_7 0 0.0 0.0 1 171s supply_8 0 0.0 0.0 1 171s supply_9 0 0.0 0.0 1 171s supply_10 0 0.0 0.0 1 171s supply_11 0 0.0 0.0 1 171s supply_12 0 0.0 0.0 1 171s supply_13 0 0.0 0.0 1 171s supply_14 0 0.0 0.0 1 171s supply_15 0 0.0 0.0 1 171s supply_16 0 0.0 0.0 1 171s supply_17 0 0.0 0.0 1 171s supply_18 0 0.0 0.0 1 171s supply_19 0 0.0 0.0 1 171s supply_20 0 0.0 0.0 1 171s supply_price supply_farmPrice supply_trend 171s demand_1 0.0 0.0 0 171s demand_2 0.0 0.0 0 171s demand_3 0.0 0.0 0 171s demand_4 0.0 0.0 0 171s demand_5 0.0 0.0 0 171s demand_6 0.0 0.0 0 171s demand_7 0.0 0.0 0 171s demand_8 0.0 0.0 0 171s demand_9 0.0 0.0 0 171s demand_10 0.0 0.0 0 171s demand_11 0.0 0.0 0 171s demand_12 0.0 0.0 0 171s demand_13 0.0 0.0 0 171s demand_14 0.0 0.0 0 171s demand_15 0.0 0.0 0 171s demand_16 0.0 0.0 0 171s demand_17 0.0 0.0 0 171s demand_18 0.0 0.0 0 171s demand_19 0.0 0.0 0 171s demand_20 0.0 0.0 0 171s supply_1 100.3 98.0 1 171s supply_2 104.3 99.1 2 171s supply_3 103.4 99.1 3 171s supply_4 104.5 98.1 4 171s supply_5 98.0 110.8 5 171s supply_6 99.5 108.2 6 171s supply_7 101.1 105.6 7 171s supply_8 104.8 109.8 8 171s supply_9 96.4 108.7 9 171s supply_10 91.2 100.6 10 171s supply_11 93.1 81.0 11 171s supply_12 98.8 68.6 12 171s supply_13 102.9 70.9 13 171s supply_14 98.8 81.4 14 171s supply_15 95.1 102.3 15 171s supply_16 98.5 105.0 16 171s supply_17 86.5 110.5 17 171s supply_18 104.0 92.5 18 171s supply_19 105.8 89.3 19 171s supply_20 113.5 93.0 20 171s > print( mm1 <- model.matrix( fitsur1e2$eq[[ 1 ]] ) ) 171s (Intercept) price income 171s 1 1 100.3 87.4 171s 2 1 104.3 97.6 171s 3 1 103.4 96.7 171s 4 1 104.5 98.2 171s 5 1 98.0 99.8 171s 6 1 99.5 100.5 171s 7 1 101.1 103.2 171s 8 1 104.8 107.8 171s 9 1 96.4 96.6 171s 10 1 91.2 88.9 171s 11 1 93.1 75.1 171s 12 1 98.8 76.9 171s 13 1 102.9 84.6 171s 14 1 98.8 90.6 171s 15 1 95.1 103.1 171s 16 1 98.5 105.1 171s 17 1 86.5 96.4 171s 18 1 104.0 104.4 171s 19 1 105.8 110.7 171s 20 1 113.5 127.1 171s attr(,"assign") 171s [1] 0 1 2 171s > print( mm2 <- model.matrix( fitsur1e2$eq[[ 2 ]] ) ) 171s (Intercept) price farmPrice trend 171s 1 1 100.3 98.0 1 171s 2 1 104.3 99.1 2 171s 3 1 103.4 99.1 3 171s 4 1 104.5 98.1 4 171s 5 1 98.0 110.8 5 171s 6 1 99.5 108.2 6 171s 7 1 101.1 105.6 7 171s 8 1 104.8 109.8 8 171s 9 1 96.4 108.7 9 171s 10 1 91.2 100.6 10 171s 11 1 93.1 81.0 11 171s 12 1 98.8 68.6 12 171s 13 1 102.9 70.9 13 171s 14 1 98.8 81.4 14 171s 15 1 95.1 102.3 15 171s 16 1 98.5 105.0 16 171s 17 1 86.5 110.5 17 171s 18 1 104.0 92.5 18 171s 19 1 105.8 89.3 19 171s 20 1 113.5 93.0 20 171s attr(,"assign") 171s [1] 0 1 2 3 171s > 171s > # with x (returnModelMatrix) = FALSE 171s > print( all.equal( mm, model.matrix( fitsur1r2 ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur1r2$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur1r2$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > print( !is.null( fitsur1r2$eq[[ 1 ]]$x ) ) 171s [1] FALSE 171s > 171s > # with x (returnModelMatrix) = TRUE 171s > print( !is.null( fitsur2e$eq[[ 1 ]]$x ) ) 171s [1] TRUE 171s > print( all.equal( mm, model.matrix( fitsur2e ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur2e$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur2e$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > 171s > # with x (returnModelMatrix) = FALSE 171s > print( all.equal( mm, model.matrix( fitsur2 ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur2$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur2$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > print( !is.null( fitsur2$eq[[ 1 ]]$x ) ) 171s [1] FALSE 171s > 171s > # with x (returnModelMatrix) = TRUE 171s > print( !is.null( fitsur2we$eq[[ 1 ]]$x ) ) 171s [1] TRUE 171s > print( all.equal( mm, model.matrix( fitsur2we ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur2we$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur2we$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > 171s > # with x (returnModelMatrix) = FALSE 171s > print( all.equal( mm, model.matrix( fitsur2 ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur2$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur2$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > print( !is.null( fitsuri2$eq[[ 1 ]]$x ) ) 171s [1] FALSE 171s > 171s > # with x (returnModelMatrix) = TRUE 171s > print( !is.null( fitsur3e$eq[[ 1 ]]$x ) ) 171s [1] TRUE 171s > print( all.equal( mm, model.matrix( fitsur3e ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur3e$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur3e$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > 171s > # with x (returnModelMatrix) = FALSE 171s > print( all.equal( mm, model.matrix( fitsur3 ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur3$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur3$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > print( !is.null( fitsur3$eq[[ 1 ]]$x ) ) 171s [1] FALSE 171s > 171s > # with x (returnModelMatrix) = TRUE 171s > print( !is.null( fitsur3w$eq[[ 1 ]]$x ) ) 171s [1] TRUE 171s > print( all.equal( mm, model.matrix( fitsur3w ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur3w$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur3w$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > 171s > # with x (returnModelMatrix) = FALSE 171s > print( all.equal( mm, model.matrix( fitsur3 ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur3$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur3$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > print( !is.null( fitsuri3$eq[[ 1 ]]$x ) ) 171s [1] FALSE 171s > 171s > # with x (returnModelMatrix) = TRUE 171s > print( !is.null( fitsur4r3$eq[[ 1 ]]$x ) ) 171s [1] TRUE 171s > print( all.equal( mm, model.matrix( fitsur4r3 ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur4r3$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur4r3$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > 171s > # with x (returnModelMatrix) = FALSE 171s > print( all.equal( mm, model.matrix( fitsur4we ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur4we$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm2, model.matrix( fitsur4we$eq[[ 2 ]] ) ) ) 171s [1] TRUE 171s > print( !is.null( fitsur4we$eq[[ 1 ]]$x ) ) 171s [1] FALSE 171s > 171s > # with x (returnModelMatrix) = TRUE 171s > print( !is.null( fitsurio5r2$eq[[ 1 ]]$x ) ) 171s [1] TRUE 171s > print( !is.null( fitsur5$eq[[ 1 ]]$x ) ) 171s [1] TRUE 171s > print( all.equal( mm, model.matrix( fitsurio5r2 ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsurio5r2$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > print( all.equal( mm, model.matrix( fitsur5 ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur5$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > #print( all.equal( mm2, model.matrix( fitsuri5r2$eq[[ 2 ]] ) ) ) 171s > 171s > # with x (returnModelMatrix) = FALSE 171s > print( all.equal( mm, model.matrix( fitsurio5 ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsurio5$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > 171s > # with x (returnModelMatrix) = FALSE 171s > print( all.equal( mm, model.matrix( fitsur5w ) ) ) 171s [1] TRUE 171s > print( all.equal( mm1, model.matrix( fitsur5w$eq[[ 1 ]] ) ) ) 171s [1] TRUE 171s > #print( all.equal( mm2, model.matrix( fitsuri5r2$eq[[ 1 ]] ) ) ) 171s > print( !is.null( fitsurio5$eq[[ 1 ]]$x ) ) 171s [1] FALSE 171s > print( !is.null( fitsur5w$eq[[ 1 ]]$x ) ) 171s [1] FALSE 171s > 171s > 171s > ## **************** formulas ************************ 171s > formula( fitsur1e2 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s 171s > formula( fitsur1e2$eq[[ 2 ]] ) 171s consump ~ price + farmPrice + trend 171s > 171s > formula( fitsur2e ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s 171s > formula( fitsur2e$eq[[ 1 ]] ) 171s consump ~ price + income 171s > 171s > formula( fitsur2we ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s 171s > formula( fitsur2we$eq[[ 1 ]] ) 171s consump ~ price + income 171s > 171s > formula( fitsur3 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s 171s > formula( fitsur3$eq[[ 2 ]] ) 171s consump ~ price + farmPrice + trend 171s > 171s > formula( fitsur4r3 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s 171s > formula( fitsur4r3$eq[[ 1 ]] ) 171s consump ~ price + income 171s > 171s > formula( fitsur5 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s 171s > formula( fitsur5$eq[[ 2 ]] ) 171s consump ~ price + farmPrice + trend 171s > 171s > formula( fitsuri1r3 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s price ~ income + farmPrice + trend 171s 171s > formula( fitsuri1r3$eq[[ 1 ]] ) 171s consump ~ price + income 171s > 171s > formula( fitsuri2 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s price ~ income + farmPrice + trend 171s 171s > formula( fitsuri2$eq[[ 2 ]] ) 171s price ~ income + farmPrice + trend 171s > 171s > formula( fitsuri3e ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s price ~ income + farmPrice + trend 171s 171s > formula( fitsuri3e$eq[[ 1 ]] ) 171s consump ~ price + income 171s > 171s > formula( fitsurio4 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s 171s > formula( fitsurio4$eq[[ 2 ]] ) 171s consump ~ price + farmPrice + trend 171s > formula( fitsuri4 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s price ~ income + farmPrice + trend 171s 171s > formula( fitsuri4$eq[[ 2 ]] ) 171s price ~ income + farmPrice + trend 171s > 171s > formula( fitsurio5r2 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s 171s > formula( fitsurio5r2$eq[[ 1 ]] ) 171s consump ~ price + income 171s > formula( fitsuri5r2 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s price ~ income + farmPrice + trend 171s 171s > formula( fitsuri5r2$eq[[ 1 ]] ) 171s consump ~ price + income 171s > 171s > formula( fitsuri5wr2 ) 171s $demand 171s consump ~ price + income 171s 171s $supply 171s price ~ income + farmPrice + trend 171s 171s > formula( fitsuri5wr2$eq[[ 1 ]] ) 171s consump ~ price + income 171s > 171s > 171s > ## **************** model terms ******************* 171s > terms( fitsur1e2 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsur1e2$eq[[ 2 ]] ) 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s > 171s > terms( fitsur2e ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsur2e$eq[[ 1 ]] ) 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s > 171s > terms( fitsur3 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsur3$eq[[ 2 ]] ) 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s > 171s > terms( fitsur3w ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsur3w$eq[[ 2 ]] ) 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s > 171s > terms( fitsur4r3 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsur4r3$eq[[ 1 ]] ) 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s > 171s > terms( fitsur4we ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsur4we$eq[[ 1 ]] ) 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s > 171s > terms( fitsur5 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsur5$eq[[ 2 ]] ) 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s > 171s > terms( fitsuri1r3 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s price ~ income + farmPrice + trend 171s attr(,"variables") 171s list(price, income, farmPrice, trend) 171s attr(,"factors") 171s income farmPrice trend 171s price 0 0 0 171s income 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "income" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(price, income, farmPrice, trend) 171s attr(,"dataClasses") 171s price income farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsuri1r3$eq[[ 1 ]] ) 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s > 171s > terms( fitsuri2 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s price ~ income + farmPrice + trend 171s attr(,"variables") 171s list(price, income, farmPrice, trend) 171s attr(,"factors") 171s income farmPrice trend 171s price 0 0 0 171s income 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "income" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(price, income, farmPrice, trend) 171s attr(,"dataClasses") 171s price income farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsuri2$eq[[ 2 ]] ) 171s price ~ income + farmPrice + trend 171s attr(,"variables") 171s list(price, income, farmPrice, trend) 171s attr(,"factors") 171s income farmPrice trend 171s price 0 0 0 171s income 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "income" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(price, income, farmPrice, trend) 171s attr(,"dataClasses") 171s price income farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s > 171s > terms( fitsuri3e ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s price ~ income + farmPrice + trend 171s attr(,"variables") 171s list(price, income, farmPrice, trend) 171s attr(,"factors") 171s income farmPrice trend 171s price 0 0 0 171s income 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "income" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(price, income, farmPrice, trend) 171s attr(,"dataClasses") 171s price income farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsuri3e$eq[[ 1 ]] ) 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s > 171s > terms( fitsurio4 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsurio4$eq[[ 2 ]] ) 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s > terms( fitsuri4 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s price ~ income + farmPrice + trend 171s attr(,"variables") 171s list(price, income, farmPrice, trend) 171s attr(,"factors") 171s income farmPrice trend 171s price 0 0 0 171s income 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "income" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(price, income, farmPrice, trend) 171s attr(,"dataClasses") 171s price income farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsuri4$eq[[ 2 ]] ) 171s price ~ income + farmPrice + trend 171s attr(,"variables") 171s list(price, income, farmPrice, trend) 171s attr(,"factors") 171s income farmPrice trend 171s price 0 0 0 171s income 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "income" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(price, income, farmPrice, trend) 171s attr(,"dataClasses") 171s price income farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s > 171s > terms( fitsurio5r2 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s consump ~ price + farmPrice + trend 171s attr(,"variables") 171s list(consump, price, farmPrice, trend) 171s attr(,"factors") 171s price farmPrice trend 171s consump 0 0 0 171s price 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "price" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, farmPrice, trend) 171s attr(,"dataClasses") 171s consump price farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsurio5r2$eq[[ 1 ]] ) 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s > terms( fitsuri5r2 ) 171s $demand 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s 171s $supply 171s price ~ income + farmPrice + trend 171s attr(,"variables") 171s list(price, income, farmPrice, trend) 171s attr(,"factors") 171s income farmPrice trend 171s price 0 0 0 171s income 1 0 0 171s farmPrice 0 1 0 171s trend 0 0 1 171s attr(,"term.labels") 171s [1] "income" "farmPrice" "trend" 171s attr(,"order") 171s [1] 1 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(price, income, farmPrice, trend) 171s attr(,"dataClasses") 171s price income farmPrice trend 171s "numeric" "numeric" "numeric" "numeric" 171s 171s > terms( fitsuri5r2$eq[[ 1 ]] ) 171s consump ~ price + income 171s attr(,"variables") 171s list(consump, price, income) 171s attr(,"factors") 171s price income 171s consump 0 0 171s price 1 0 171s income 0 1 171s attr(,"term.labels") 171s [1] "price" "income" 171s attr(,"order") 171s [1] 1 1 171s attr(,"intercept") 171s [1] 1 171s attr(,"response") 171s [1] 1 171s attr(,".Environment") 171s 171s attr(,"predvars") 171s list(consump, price, income) 171s attr(,"dataClasses") 171s consump price income 171s "numeric" "numeric" "numeric" 171s > 171s > 171s > ## **************** estfun ************************ 171s > library( "sandwich" ) 171s > 171s > estfun( fitsur1 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s demand_1 0.9083 91.12 79.38 -0.6496 171s demand_2 -0.7320 -76.32 -71.44 0.5235 171s demand_3 3.2023 331.23 309.66 -2.2902 171s demand_4 2.1435 224.00 210.49 -1.5330 171s demand_5 2.7516 269.66 274.61 -1.9679 171s demand_6 1.7015 169.22 171.00 -1.2169 171s demand_7 2.2068 223.03 227.74 -1.5783 171s demand_8 -3.5946 -376.58 -387.50 2.5708 171s demand_9 -1.6348 -157.67 -157.92 1.1692 171s demand_10 2.7103 247.26 240.95 -1.9384 171s demand_11 -0.8810 -82.01 -66.16 0.6301 171s demand_12 -3.4554 -341.39 -265.72 2.4712 171s demand_13 -2.2246 -228.93 -188.20 1.5910 171s demand_14 -0.5461 -53.93 -49.48 0.3906 171s demand_15 2.4619 234.17 253.82 -1.7607 171s demand_16 -4.3873 -431.94 -461.11 3.1378 171s demand_17 -0.9942 -85.99 -95.84 0.7110 171s demand_18 -2.5012 -260.17 -261.13 1.7888 171s demand_19 2.5805 272.93 285.66 -1.8455 171s demand_20 0.2846 32.30 36.17 -0.2036 171s supply_1 -0.4396 -44.11 -38.42 0.3959 171s supply_2 -0.0184 -1.92 -1.79 0.0166 171s supply_3 -2.5916 -268.06 -250.60 2.3337 171s supply_4 -1.7132 -179.04 -168.24 1.5428 171s supply_5 -2.3049 -225.88 -230.03 2.0756 171s supply_6 -1.3780 -137.06 -138.49 1.2410 171s supply_7 -2.0596 -208.16 -212.55 1.8547 171s supply_8 3.4200 358.29 368.68 -3.0798 171s supply_9 1.9576 188.80 189.10 -1.7628 171s supply_10 -2.3620 -215.48 -209.98 2.1270 171s supply_11 1.1852 110.32 89.01 -1.0673 171s supply_12 2.6183 258.69 201.34 -2.3578 171s supply_13 1.9874 204.52 168.14 -1.7897 171s supply_14 -0.1072 -10.59 -9.72 0.0966 171s supply_15 -2.6839 -255.29 -276.71 2.4169 171s supply_16 3.8259 376.66 402.10 -3.4452 171s supply_17 0.5270 45.59 50.80 -0.4746 171s supply_18 3.0021 312.27 313.42 -2.7035 171s supply_19 -2.0184 -213.48 -223.44 1.8176 171s supply_20 -0.8466 -96.08 -107.60 0.7623 171s supply_price supply_farmPrice supply_trend 171s demand_1 -65.17 -63.66 -0.6496 171s demand_2 54.58 51.88 1.0470 171s demand_3 -236.89 -226.96 -6.8707 171s demand_4 -160.20 -150.38 -6.1319 171s demand_5 -192.86 -218.05 -9.8397 171s demand_6 -121.02 -131.66 -7.3012 171s demand_7 -159.51 -166.67 -11.0480 171s demand_8 269.33 282.28 20.5665 171s demand_9 112.76 127.09 10.5227 171s demand_10 -176.84 -195.00 -19.3840 171s demand_11 58.65 51.04 6.9309 171s demand_12 244.16 169.53 29.6547 171s demand_13 163.73 112.80 20.6833 171s demand_14 38.57 31.79 5.4681 171s demand_15 -167.48 -180.12 -26.4104 171s demand_16 308.92 329.47 50.2044 171s demand_17 61.50 78.57 12.0871 171s demand_18 186.07 165.47 32.1991 171s demand_19 -195.20 -164.81 -35.0650 171s demand_20 -23.10 -18.93 -4.0710 171s supply_1 39.72 38.80 0.3959 171s supply_2 1.73 1.64 0.0331 171s supply_3 241.39 231.27 7.0012 171s supply_4 161.23 151.34 6.1710 171s supply_5 203.41 229.98 10.3781 171s supply_6 123.42 134.27 7.4457 171s supply_7 187.45 195.86 12.9829 171s supply_8 -322.64 -338.16 -24.6380 171s supply_9 -170.02 -191.62 -15.8653 171s supply_10 194.04 213.98 21.2699 171s supply_11 -99.35 -86.45 -11.7402 171s supply_12 -232.95 -161.74 -28.2933 171s supply_13 -184.18 -126.89 -23.2663 171s supply_14 9.54 7.86 1.3521 171s supply_15 229.90 247.25 36.2539 171s supply_16 -339.19 -361.75 -55.1237 171s supply_17 -41.05 -52.44 -8.0678 171s supply_18 -281.20 -250.07 -48.6623 171s supply_19 192.24 162.31 34.5341 171s supply_20 86.52 70.90 15.2466 171s > round( colSums( estfun( fitsur1 ) ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s 0 0 0 0 171s supply_price supply_farmPrice supply_trend 171s 0 0 0 171s > 171s > estfun( fitsur1e2 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s demand_1 1.09034 109.386 95.295 -0.80605 171s demand_2 -1.05992 -110.511 -103.448 0.78356 171s demand_3 4.28760 443.488 414.611 -3.16968 171s demand_4 2.85253 298.107 280.119 -2.10878 171s demand_5 3.80226 372.625 379.466 -2.81088 171s demand_6 2.36197 234.912 237.378 -1.74612 171s demand_7 3.06088 309.351 315.883 -2.26280 171s demand_8 -4.81806 -504.754 -519.386 3.56182 171s demand_9 -2.17915 -210.170 -210.506 1.61097 171s demand_10 3.70159 337.689 329.071 -2.73646 171s demand_11 -1.39799 -130.132 -104.989 1.03349 171s demand_12 -4.96091 -490.143 -381.494 3.66743 171s demand_13 -3.24623 -334.063 -274.631 2.39983 171s demand_14 -0.81794 -80.776 -74.105 0.60467 171s demand_15 3.49861 332.784 360.707 -2.58640 171s demand_16 -5.83443 -574.406 -613.199 4.31320 171s demand_17 -1.15650 -100.035 -111.487 0.85496 171s demand_18 -3.36717 -350.239 -351.532 2.48923 171s demand_19 3.59870 380.631 398.376 -2.66040 171s demand_20 0.58382 66.257 74.203 -0.43160 171s supply_1 -0.54811 -54.988 -47.905 0.47751 171s supply_2 0.00819 0.854 0.799 -0.00713 171s supply_3 -3.61236 -373.644 -349.315 3.14703 171s supply_4 -2.38151 -248.882 -233.865 2.07474 171s supply_5 -3.32295 -325.653 -331.631 2.89490 171s supply_6 -2.00948 -199.855 -201.953 1.75063 171s supply_7 -2.95622 -298.773 -305.081 2.57541 171s supply_8 4.67628 489.901 504.103 -4.07390 171s supply_9 2.65680 256.238 256.647 -2.31456 171s supply_10 -3.31875 -302.763 -295.037 2.89124 171s supply_11 1.84429 171.676 138.506 -1.60672 171s supply_12 3.95003 390.267 303.757 -3.44120 171s supply_13 3.01568 310.338 255.127 -2.62722 171s supply_14 -0.02452 -2.421 -2.221 0.02136 171s supply_15 -3.84791 -366.010 -396.720 3.35224 171s supply_16 5.24831 516.701 551.597 -4.57224 171s supply_17 0.59732 51.667 57.582 -0.52037 171s supply_18 4.17631 434.404 436.007 -3.63834 171s supply_19 -2.86060 -302.562 -316.668 2.49211 171s supply_20 -1.29079 -146.492 -164.060 1.12452 171s supply_price supply_farmPrice supply_trend 171s demand_1 -80.865 -78.993 -0.8060 171s demand_2 81.697 77.651 1.5671 171s demand_3 -327.856 -314.115 -9.5090 171s demand_4 -220.380 -206.871 -8.4351 171s demand_5 -275.469 -311.446 -14.0544 171s demand_6 -173.662 -188.931 -10.4767 171s demand_7 -228.692 -238.952 -15.8396 171s demand_8 373.147 391.088 28.4946 171s demand_9 155.372 175.113 14.4987 171s demand_10 -249.642 -275.288 -27.3646 171s demand_11 96.202 83.712 11.3683 171s demand_12 362.346 251.586 44.0092 171s demand_13 246.962 170.148 31.1978 171s demand_14 59.715 49.220 8.4654 171s demand_15 -246.016 -264.589 -38.7961 171s demand_16 424.638 452.886 69.0111 171s demand_17 73.953 94.473 14.5344 171s demand_18 258.920 230.254 44.8061 171s demand_19 -281.388 -237.573 -50.5475 171s demand_20 -48.982 -40.138 -8.6319 171s supply_1 47.905 46.796 0.4775 171s supply_2 -0.744 -0.707 -0.0143 171s supply_3 325.513 311.871 9.4411 171s supply_4 216.822 203.532 8.2989 171s supply_5 283.704 320.755 14.4745 171s supply_6 174.111 189.418 10.5038 171s supply_7 260.286 271.963 18.0279 171s supply_8 -426.794 -447.314 -32.5912 171s supply_9 -223.230 -251.593 -20.8310 171s supply_10 263.762 290.859 28.9124 171s supply_11 -149.561 -130.144 -17.6739 171s supply_12 -339.994 -236.066 -41.2944 171s supply_13 -270.361 -186.270 -34.1538 171s supply_14 2.109 1.739 0.2990 171s supply_15 318.862 342.934 50.2836 171s supply_16 -450.142 -480.085 -73.1559 171s supply_17 -45.011 -57.501 -8.8464 171s supply_18 -378.445 -336.546 -65.4901 171s supply_19 263.588 222.545 47.3500 171s supply_20 127.621 104.580 22.4903 171s > round( colSums( estfun( fitsur1e2 ) ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s 0 0 0 0 171s supply_price supply_farmPrice supply_trend 171s 0 0 0 171s > 171s > estfun( fitsur1r3 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s demand_1 1.07229 107.575 93.718 -0.79049 171s demand_2 -1.02096 -106.450 -99.646 0.75265 171s demand_3 4.16424 430.729 402.682 -3.06988 171s demand_4 2.77231 289.723 272.240 -2.04374 171s demand_5 3.68037 360.680 367.301 -2.71316 171s demand_6 2.28513 227.270 229.656 -1.68460 171s demand_7 2.96157 299.314 305.634 -2.18327 171s demand_8 -4.67889 -490.175 -504.385 3.44927 171s demand_9 -2.11749 -204.223 -204.549 1.56101 171s demand_10 3.58740 327.271 318.920 -2.64463 171s demand_11 -1.33464 -124.235 -100.231 0.98389 171s demand_12 -4.78276 -472.541 -367.794 3.52584 171s demand_13 -3.12449 -321.535 -264.332 2.30337 171s demand_14 -0.78522 -77.545 -71.141 0.57886 171s demand_15 3.37652 321.171 348.119 -2.48917 171s demand_16 -5.67080 -558.296 -596.001 4.18051 171s demand_17 -1.14172 -98.757 -110.062 0.84168 171s demand_18 -3.26836 -339.962 -341.217 2.40943 171s demand_19 3.47995 368.071 385.231 -2.56542 171s demand_20 0.54555 61.914 69.339 -0.40218 171s supply_1 -0.53834 -54.008 -47.051 0.47031 171s supply_2 0.00335 0.349 0.327 -0.00293 171s supply_3 -3.49682 -361.694 -338.143 3.05492 171s supply_4 -2.30621 -241.013 -226.470 2.01477 171s supply_5 -3.20507 -314.100 -319.866 2.80004 171s supply_6 -1.93606 -192.553 -194.574 1.69139 171s supply_7 -2.85248 -288.289 -294.376 2.49200 171s supply_8 4.53460 475.059 488.830 -3.96155 171s supply_9 2.57840 248.676 249.073 -2.25256 171s supply_10 -3.20906 -292.756 -285.286 2.80352 171s supply_11 1.76494 164.289 132.547 -1.54190 171s supply_12 3.79168 374.622 291.580 -3.31251 171s supply_13 2.89330 297.744 244.773 -2.52766 171s supply_14 -0.03625 -3.580 -3.284 0.03167 171s supply_15 -3.71220 -353.101 -382.728 3.24307 171s supply_16 5.08854 500.972 534.805 -4.44548 171s supply_17 0.59312 51.303 57.176 -0.51816 171s supply_18 4.04346 420.584 422.137 -3.53247 171s supply_19 -2.76240 -292.176 -305.797 2.41330 171s supply_20 -1.23648 -140.329 -157.157 1.08023 171s supply_price supply_farmPrice supply_trend 171s demand_1 -79.304 -77.47 -0.79049 171s demand_2 78.475 74.59 1.50531 171s demand_3 -317.533 -304.22 -9.20963 171s demand_4 -213.583 -200.49 -8.17496 171s demand_5 -265.893 -300.62 -13.56581 171s demand_6 -167.543 -182.27 -10.10759 171s demand_7 -220.654 -230.55 -15.28289 171s demand_8 361.356 378.73 27.59420 171s demand_9 150.553 169.68 14.04907 171s demand_10 -241.264 -266.05 -26.44627 171s demand_11 91.586 79.70 10.82281 171s demand_12 348.357 241.87 42.31014 171s demand_13 237.035 163.31 29.94383 171s demand_14 57.166 47.12 8.10410 171s demand_15 -236.767 -254.64 -37.33751 171s demand_16 411.575 438.95 66.88809 171s demand_17 72.803 93.01 14.30850 171s demand_18 250.619 222.87 43.36977 171s demand_19 -271.341 -229.09 -48.74290 171s demand_20 -45.643 -37.40 -8.04353 171s supply_1 47.183 46.09 0.47031 171s supply_2 -0.305 -0.29 -0.00585 171s supply_3 315.985 302.74 9.16476 171s supply_4 210.555 197.65 8.05908 171s supply_5 274.406 310.24 14.00018 171s supply_6 168.219 183.01 10.14835 171s supply_7 251.857 263.16 17.44401 171s supply_8 -415.024 -434.98 -31.69241 171s supply_9 -217.250 -244.85 -20.27300 171s supply_10 255.760 282.03 28.03523 171s supply_11 -143.528 -124.89 -16.96088 171s supply_12 -327.279 -227.24 -39.75013 171s supply_13 -260.117 -179.21 -32.85963 171s supply_14 3.128 2.58 0.44339 171s supply_15 308.478 331.77 48.64611 171s supply_16 -437.662 -466.78 -71.12773 171s supply_17 -44.820 -57.26 -8.80876 171s supply_18 -367.434 -326.75 -63.58452 171s supply_19 255.253 215.51 45.85274 171s supply_20 122.595 100.46 21.60450 171s > round( colSums( estfun( fitsur1r3 ) ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s 0 0 0 0 171s supply_price supply_farmPrice supply_trend 171s 0 0 0 171s > 171s > estfun( fitsur1w ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s demand_1 0.9083 91.12 79.38 -0.6496 171s demand_2 -0.7320 -76.32 -71.44 0.5235 171s demand_3 3.2023 331.23 309.66 -2.2902 171s demand_4 2.1435 224.00 210.49 -1.5330 171s demand_5 2.7516 269.66 274.61 -1.9679 171s demand_6 1.7015 169.22 171.00 -1.2169 171s demand_7 2.2068 223.03 227.74 -1.5783 171s demand_8 -3.5946 -376.58 -387.50 2.5708 171s demand_9 -1.6348 -157.67 -157.92 1.1692 171s demand_10 2.7103 247.26 240.95 -1.9384 171s demand_11 -0.8810 -82.01 -66.16 0.6301 171s demand_12 -3.4554 -341.39 -265.72 2.4712 171s demand_13 -2.2246 -228.93 -188.20 1.5910 171s demand_14 -0.5461 -53.93 -49.48 0.3906 171s demand_15 2.4619 234.17 253.82 -1.7607 171s demand_16 -4.3873 -431.94 -461.11 3.1378 171s demand_17 -0.9942 -85.99 -95.84 0.7110 171s demand_18 -2.5012 -260.17 -261.13 1.7888 171s demand_19 2.5805 272.93 285.66 -1.8455 171s demand_20 0.2846 32.30 36.17 -0.2036 171s supply_1 -0.4396 -44.11 -38.42 0.3959 171s supply_2 -0.0184 -1.92 -1.79 0.0166 171s supply_3 -2.5916 -268.06 -250.60 2.3337 171s supply_4 -1.7132 -179.04 -168.24 1.5428 171s supply_5 -2.3049 -225.88 -230.03 2.0756 171s supply_6 -1.3780 -137.06 -138.49 1.2410 171s supply_7 -2.0596 -208.16 -212.55 1.8547 171s supply_8 3.4200 358.29 368.68 -3.0798 171s supply_9 1.9576 188.80 189.10 -1.7628 171s supply_10 -2.3620 -215.48 -209.98 2.1270 171s supply_11 1.1852 110.32 89.01 -1.0673 171s supply_12 2.6183 258.69 201.34 -2.3578 171s supply_13 1.9874 204.52 168.14 -1.7897 171s supply_14 -0.1072 -10.59 -9.72 0.0966 171s supply_15 -2.6839 -255.29 -276.71 2.4169 171s supply_16 3.8259 376.66 402.10 -3.4452 171s supply_17 0.5270 45.59 50.80 -0.4746 171s supply_18 3.0021 312.27 313.42 -2.7035 171s supply_19 -2.0184 -213.48 -223.44 1.8176 171s supply_20 -0.8466 -96.08 -107.60 0.7623 171s supply_price supply_farmPrice supply_trend 171s demand_1 -65.17 -63.66 -0.6496 171s demand_2 54.58 51.88 1.0470 171s demand_3 -236.89 -226.96 -6.8707 171s demand_4 -160.20 -150.38 -6.1319 171s demand_5 -192.86 -218.05 -9.8397 171s demand_6 -121.02 -131.66 -7.3012 171s demand_7 -159.51 -166.67 -11.0480 171s demand_8 269.33 282.28 20.5665 171s demand_9 112.76 127.09 10.5227 171s demand_10 -176.84 -195.00 -19.3840 171s demand_11 58.65 51.04 6.9309 171s demand_12 244.16 169.53 29.6547 171s demand_13 163.73 112.80 20.6833 171s demand_14 38.57 31.79 5.4681 171s demand_15 -167.48 -180.12 -26.4104 171s demand_16 308.92 329.47 50.2044 171s demand_17 61.50 78.57 12.0871 171s demand_18 186.07 165.47 32.1991 171s demand_19 -195.20 -164.81 -35.0650 171s demand_20 -23.10 -18.93 -4.0710 171s supply_1 39.72 38.80 0.3959 171s supply_2 1.73 1.64 0.0331 171s supply_3 241.39 231.27 7.0012 171s supply_4 161.23 151.34 6.1710 171s supply_5 203.41 229.98 10.3781 171s supply_6 123.42 134.27 7.4457 171s supply_7 187.45 195.86 12.9829 171s supply_8 -322.64 -338.16 -24.6380 171s supply_9 -170.02 -191.62 -15.8653 171s supply_10 194.04 213.98 21.2699 171s supply_11 -99.35 -86.45 -11.7402 171s supply_12 -232.95 -161.74 -28.2933 171s supply_13 -184.18 -126.89 -23.2663 171s supply_14 9.54 7.86 1.3521 171s supply_15 229.90 247.25 36.2539 171s supply_16 -339.19 -361.75 -55.1237 171s supply_17 -41.05 -52.44 -8.0678 171s supply_18 -281.20 -250.07 -48.6623 171s supply_19 192.24 162.31 34.5341 171s supply_20 86.52 70.90 15.2466 171s > round( colSums( estfun( fitsur1w ) ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s 0 0 0 0 171s supply_price supply_farmPrice supply_trend 171s 0 0 0 171s > 171s > estfun( fitsuri1e ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s demand_1 0.5467 54.84 47.78 0.5219 171s demand_2 -0.5182 -54.03 -50.58 -0.4947 171s demand_3 1.5799 163.41 152.77 1.5082 171s demand_4 0.9787 102.28 96.11 0.9343 171s demand_5 1.4899 146.02 148.70 1.4224 171s demand_6 0.8875 88.27 89.19 0.8472 171s demand_7 1.0809 109.24 111.55 1.0319 171s demand_8 -2.1165 -221.73 -228.15 -2.0205 171s demand_9 -0.7383 -71.21 -71.32 -0.7049 171s demand_10 1.7668 161.19 157.07 1.6867 171s demand_11 -0.0682 -6.35 -5.12 -0.0651 171s demand_12 -1.6133 -159.40 -124.07 -1.5402 171s demand_13 -1.1570 -119.06 -97.88 -1.1045 171s demand_14 -0.1925 -19.01 -17.44 -0.1838 171s demand_15 1.4026 133.41 144.61 1.3390 171s demand_16 -2.3128 -227.70 -243.08 -2.2080 171s demand_17 -0.0876 -7.58 -8.44 -0.0836 171s demand_18 -1.4924 -155.23 -155.81 -1.4247 171s demand_19 1.0702 113.20 118.47 1.0217 171s demand_20 -0.5064 -57.47 -64.36 -0.4834 171s supply_1 0.1054 10.57 9.21 0.1789 171s supply_2 -0.8882 -92.60 -86.68 -1.5080 171s supply_3 -0.5218 -53.97 -50.46 -0.8859 171s supply_4 -0.2644 -27.63 -25.96 -0.4489 171s supply_5 -0.7666 -75.13 -76.51 -1.3016 171s supply_6 -0.4056 -40.34 -40.77 -0.6887 171s supply_7 -0.8114 -82.00 -83.74 -1.3777 171s supply_8 1.4243 149.22 153.54 2.4183 171s supply_9 1.0270 99.05 99.21 1.7438 171s supply_10 -1.0278 -93.77 -91.37 -1.7451 171s supply_11 0.6336 58.98 47.58 1.0758 171s supply_12 0.2724 26.92 20.95 0.4626 171s supply_13 0.8434 86.79 71.35 1.4319 171s supply_14 -0.7107 -70.19 -64.39 -1.2067 171s supply_15 -1.5343 -145.94 -158.18 -2.6050 171s supply_16 1.1276 111.01 118.51 1.9145 171s supply_17 -0.6907 -59.75 -66.58 -1.1727 171s supply_18 2.2394 232.94 233.79 3.8022 171s supply_19 0.1792 18.96 19.84 0.3043 171s supply_20 -0.2309 -26.21 -29.35 -0.3921 171s supply_income supply_farmPrice supply_trend 171s demand_1 45.61 51.15 0.522 171s demand_2 -48.28 -49.03 -0.989 171s demand_3 145.85 149.47 4.525 171s demand_4 91.75 91.66 3.737 171s demand_5 141.95 157.60 7.112 171s demand_6 85.15 91.67 5.083 171s demand_7 106.49 108.97 7.223 171s demand_8 -217.81 -221.85 -16.164 171s demand_9 -68.09 -76.62 -6.344 171s demand_10 149.95 169.69 16.867 171s demand_11 -4.89 -5.28 -0.717 171s demand_12 -118.44 -105.66 -18.482 171s demand_13 -93.44 -78.31 -14.359 171s demand_14 -16.65 -14.96 -2.573 171s demand_15 138.05 136.98 20.085 171s demand_16 -232.06 -231.84 -35.327 171s demand_17 -8.06 -9.24 -1.421 171s demand_18 -148.74 -131.79 -25.645 171s demand_19 113.10 91.24 19.412 171s demand_20 -61.44 -44.96 -9.668 171s supply_1 15.64 17.53 0.179 171s supply_2 -147.18 -149.44 -3.016 171s supply_3 -85.67 -87.79 -2.658 171s supply_4 -44.08 -44.04 -1.796 171s supply_5 -129.90 -144.21 -6.508 171s supply_6 -69.22 -74.52 -4.132 171s supply_7 -142.17 -145.48 -9.644 171s supply_8 260.69 265.53 19.346 171s supply_9 168.45 189.55 15.694 171s supply_10 -155.14 -175.56 -17.451 171s supply_11 80.79 87.14 11.833 171s supply_12 35.57 31.73 5.551 171s supply_13 121.14 101.52 18.615 171s supply_14 -109.33 -98.23 -16.894 171s supply_15 -268.57 -266.49 -39.075 171s supply_16 201.22 201.03 30.633 171s supply_17 -113.05 -129.59 -19.937 171s supply_18 396.95 351.71 68.440 171s supply_19 33.69 27.18 5.782 171s supply_20 -49.83 -36.46 -7.841 171s > round( colSums( estfun( fitsuri1e ) ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s 0 0 0 0 171s supply_income supply_farmPrice supply_trend 171s 0 0 0 171s > 171s > estfun( fitsuri1wr3 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s demand_1 0.5102 51.19 44.59 0.4867 171s demand_2 -0.4886 -50.94 -47.68 -0.4661 171s demand_3 1.4782 152.90 142.94 1.4102 171s demand_4 0.9143 95.55 89.79 0.8722 171s demand_5 1.3982 137.03 139.54 1.3339 171s demand_6 0.8327 82.82 83.69 0.7944 171s demand_7 1.0134 102.42 104.59 0.9668 171s demand_8 -1.9849 -207.94 -213.97 -1.8935 171s demand_9 -0.6897 -66.52 -66.63 -0.6580 171s demand_10 1.6602 151.46 147.60 1.5838 171s demand_11 -0.0636 -5.92 -4.77 -0.0606 171s demand_12 -1.5152 -149.71 -116.52 -1.4455 171s demand_13 -1.0888 -112.05 -92.11 -1.0387 171s demand_14 -0.1809 -17.86 -16.39 -0.1726 171s demand_15 1.3190 125.46 135.99 1.2583 171s demand_16 -2.1651 -213.16 -227.55 -2.0655 171s demand_17 -0.0731 -6.33 -7.05 -0.0698 171s demand_18 -1.4001 -145.63 -146.17 -1.3357 171s demand_19 1.0017 105.95 110.89 0.9556 171s demand_20 -0.4780 -54.25 -60.76 -0.4560 171s supply_1 0.0755 7.57 6.60 0.1193 171s supply_2 -0.8526 -88.90 -83.22 -1.3478 171s supply_3 -0.5074 -52.48 -49.07 -0.8021 171s supply_4 -0.2631 -27.49 -25.83 -0.4159 171s supply_5 -0.7425 -72.77 -74.10 -1.1737 171s supply_6 -0.3998 -39.77 -40.18 -0.6320 171s supply_7 -0.7750 -78.33 -79.98 -1.2251 171s supply_8 1.3178 138.06 142.06 2.0831 171s supply_9 0.9476 91.39 91.54 1.4979 171s supply_10 -0.9683 -88.34 -86.08 -1.5306 171s supply_11 0.6060 56.40 45.51 0.9578 171s supply_12 0.2813 27.79 21.63 0.4446 171s supply_13 0.8170 84.07 69.12 1.2914 171s supply_14 -0.6451 -63.71 -58.44 -1.0197 171s supply_15 -1.4315 -136.17 -147.59 -2.2629 171s supply_16 1.0615 104.50 111.56 1.6779 171s supply_17 -0.6453 -55.82 -62.21 -1.0200 171s supply_18 2.1183 220.33 221.15 3.3484 171s supply_19 0.1946 20.58 21.54 0.3076 171s supply_20 -0.1888 -21.42 -23.99 -0.2984 171s supply_income supply_farmPrice supply_trend 171s demand_1 42.54 47.70 0.487 171s demand_2 -45.49 -46.19 -0.932 171s demand_3 136.37 139.75 4.231 171s demand_4 85.65 85.57 3.489 171s demand_5 133.12 147.79 6.669 171s demand_6 79.84 85.95 4.766 171s demand_7 99.77 102.09 6.768 171s demand_8 -204.12 -207.91 -15.148 171s demand_9 -63.56 -71.52 -5.922 171s demand_10 140.80 159.34 15.838 171s demand_11 -4.55 -4.91 -0.667 171s demand_12 -111.16 -99.16 -17.346 171s demand_13 -87.88 -73.64 -13.503 171s demand_14 -15.63 -14.05 -2.416 171s demand_15 129.73 128.72 18.874 171s demand_16 -217.08 -216.88 -33.048 171s demand_17 -6.73 -7.71 -1.186 171s demand_18 -139.45 -123.55 -24.042 171s demand_19 105.78 85.33 18.156 171s demand_20 -57.96 -42.41 -9.120 171s supply_1 10.43 11.69 0.119 171s supply_2 -131.54 -133.56 -2.696 171s supply_3 -77.56 -79.49 -2.406 171s supply_4 -40.84 -40.80 -1.663 171s supply_5 -117.13 -130.04 -5.868 171s supply_6 -63.52 -68.39 -3.792 171s supply_7 -126.43 -129.37 -8.575 171s supply_8 224.56 228.72 16.665 171s supply_9 144.70 162.82 13.481 171s supply_10 -136.07 -153.98 -15.306 171s supply_11 71.93 77.58 10.536 171s supply_12 34.19 30.50 5.335 171s supply_13 109.25 91.56 16.788 171s supply_14 -92.38 -83.00 -14.276 171s supply_15 -233.30 -231.49 -33.943 171s supply_16 176.34 176.17 26.846 171s supply_17 -98.33 -112.71 -17.341 171s supply_18 349.57 309.73 60.271 171s supply_19 34.05 27.47 5.845 171s supply_20 -37.92 -27.75 -5.967 171s > round( colSums( estfun( fitsuri1wr3 ) ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s 0 0 0 0 171s supply_income supply_farmPrice supply_trend 171s 0 0 0 171s > 171s > estfun( fitsurS1 ) 171s eq1_consump eq2_(Intercept) eq2_consump eq2_trend 171s eq1_1 7.162 0.02160 2.127 0.0216 171s eq1_2 15.562 0.04659 4.621 0.0932 171s eq1_3 6.026 0.01752 1.789 0.0525 171s eq1_4 10.524 0.03079 3.125 0.1232 171s eq1_5 -14.099 -0.04017 -4.187 -0.2008 171s eq1_6 -7.426 -0.02136 -2.205 -0.1282 171s eq1_7 -5.141 -0.01468 -1.527 -0.1028 171s eq1_8 15.138 0.04500 4.495 0.3600 171s eq1_9 -7.596 -0.02248 -2.256 -0.2023 171s eq1_10 -28.217 -0.08150 -8.379 -0.8150 171s eq1_11 -3.498 -0.01088 -1.039 -0.1197 171s eq1_12 17.457 0.05609 5.184 0.6731 171s eq1_13 22.800 0.07162 6.771 0.9311 171s eq1_14 2.479 0.00746 0.736 0.1044 171s eq1_15 -26.446 -0.07423 -7.853 -1.1135 171s eq1_16 -2.054 -0.00609 -0.610 -0.0974 171s eq1_17 -42.973 -0.12327 -12.761 -2.0956 171s eq1_18 13.132 0.03902 3.900 0.7024 171s eq1_19 4.307 0.01216 1.279 0.2310 171s eq1_20 22.866 0.06392 6.790 1.2784 171s eq2_1 -1.322 -0.02928 -2.884 -0.0293 171s eq2_2 -0.971 -0.02136 -2.118 -0.0427 171s eq2_3 -5.293 -0.11298 -11.542 -0.3389 171s eq2_4 -4.273 -0.09180 -9.318 -0.3672 171s eq2_5 1.836 0.03840 4.003 0.1920 171s eq2_6 2.119 0.04477 4.622 0.2686 171s eq2_7 -0.532 -0.01115 -1.160 -0.0781 171s eq2_8 10.068 0.21978 21.956 1.7582 171s eq2_9 9.192 0.19974 20.044 1.7977 171s eq2_10 -0.465 -0.00986 -1.014 -0.0986 171s eq2_11 -2.679 -0.06122 -5.843 -0.6735 171s eq2_12 -6.257 -0.14762 -13.644 -1.7715 171s eq2_13 -7.360 -0.16978 -16.050 -2.2072 171s eq2_14 -5.865 -0.12951 -12.790 -1.8131 171s eq2_15 -0.730 -0.01505 -1.593 -0.2258 171s eq2_16 11.188 0.24342 24.396 3.8947 171s eq2_17 11.047 0.23271 24.091 3.9561 171s eq2_18 3.346 0.07302 7.297 1.3144 171s eq2_19 -7.478 -0.15498 -16.307 -2.9445 171s eq2_20 -5.570 -0.11434 -12.146 -2.2868 171s > round( colSums( estfun( fitsurS1 ) ), digits = 7 ) 171s eq1_consump eq2_(Intercept) eq2_consump eq2_trend 171s 0 Error in estfun.systemfit(fitsurS4) : 171s returning the estimation function for models with restrictions has not yet been implemented. 171s Error in bread.systemfit(fitsurS4) : 171s returning the 'bread' for models with restrictions has not yet been implemented. 171s Loading required package: Matrix 171s 0 0 0 171s > 171s > estfun( fitsurS2 ) 171s eq1_price eq2_trend 171s eq1_1 -5.42871 -0.000114 171s eq1_2 -13.14782 -0.000531 171s eq1_3 -4.34907 -0.000266 171s eq1_4 -8.39779 -0.000677 171s eq1_5 12.19030 0.001310 171s eq1_6 6.97176 0.000886 171s eq1_7 5.14513 0.000750 171s eq1_8 -12.72321 -0.002046 171s eq1_9 7.04895 0.001385 171s eq1_10 22.20478 0.005126 171s eq1_11 3.65437 0.000909 171s eq1_12 -15.21951 -0.003893 171s eq1_13 -20.44077 -0.005438 171s eq1_14 -1.31641 -0.000393 171s eq1_15 21.18383 0.007035 171s eq1_16 2.54257 0.000870 171s eq1_17 31.47441 0.013026 171s eq1_18 -10.84129 -0.003951 171s eq1_19 -2.78655 -0.001054 171s eq1_20 -19.91341 -0.007390 171s eq2_1 0.42448 0.037215 171s eq2_2 0.40866 0.068949 171s eq2_3 0.38411 0.097989 171s eq2_4 0.34891 0.117463 171s eq2_5 0.30591 0.137281 171s eq2_6 0.27161 0.144126 171s eq2_7 0.24474 0.149098 171s eq2_8 0.19771 0.132796 171s eq2_9 0.15083 0.123801 171s eq2_10 0.12174 0.117373 171s eq2_11 0.06024 0.062610 171s eq2_12 0.01611 0.017205 171s eq2_13 -0.00856 -0.009507 171s eq2_14 -0.02284 -0.028474 171s eq2_15 -0.02363 -0.032773 171s eq2_16 -0.08383 -0.119831 171s eq2_17 -0.09018 -0.155889 171s eq2_18 -0.16161 -0.245985 171s eq2_19 -0.17473 -0.276076 171s eq2_20 -0.22123 -0.342915 171s > round( colSums( estfun( fitsurS2 ) ), digits = 7 ) 171s eq1_price eq2_trend 171s 0 0 171s > 171s > estfun( fitsurS3 ) 171s eq1_trend eq2_trend 171s eq1_1 2.069 -2.039 171s eq1_2 3.833 -3.777 171s eq1_3 5.448 -5.369 171s eq1_4 6.531 -6.436 171s eq1_5 7.634 -7.523 171s eq1_6 8.015 -7.899 171s eq1_7 8.293 -8.173 171s eq1_8 7.389 -7.281 171s eq1_9 6.890 -6.790 171s eq1_10 6.535 -6.440 171s eq1_11 3.493 -3.443 171s eq1_12 0.972 -0.958 171s eq1_13 -0.510 0.503 171s eq1_14 -1.562 1.539 171s eq1_15 -1.798 1.772 171s eq1_16 -6.634 6.537 171s eq1_17 -8.634 8.509 171s eq1_18 -13.639 13.441 171s eq1_19 -15.308 15.085 171s eq1_20 -19.019 18.743 171s eq2_1 -2.082 2.089 171s eq2_2 -4.012 4.027 171s eq2_3 -5.472 5.491 171s eq2_4 -6.736 6.760 171s eq2_5 -6.873 6.897 171s eq2_6 -7.460 7.486 171s eq2_7 -7.809 7.837 171s eq2_8 -8.276 8.305 171s eq2_9 -6.161 6.182 171s eq2_10 -4.039 4.053 171s eq2_11 -3.098 3.109 171s eq2_12 -2.949 2.960 171s eq2_13 -2.261 2.269 171s eq2_14 1.160 -1.164 171s eq2_15 4.921 -4.939 171s eq2_16 6.677 -6.701 171s eq2_17 14.428 -14.479 171s eq2_18 11.167 -11.207 171s eq2_19 14.155 -14.205 171s eq2_20 14.719 -14.771 171s > round( colSums( estfun( fitsurS3 ) ), digits = 7 ) 171s eq1_trend eq2_trend 171s 0 0 171s > 171s > try( estfun( fitsurS4 ) ) 171s > 171s > estfun( fitsurS5 ) 171s eq1_(Intercept) eq2_(Intercept) 171s eq1_1 -0.17267 0.01074 171s eq1_2 -0.12244 0.00761 171s eq1_3 0.09050 -0.00563 171s eq1_4 0.04335 -0.00270 171s eq1_5 0.23912 -0.01487 171s eq1_6 0.16778 -0.01043 171s eq1_7 0.22144 -0.01377 171s eq1_8 -0.07143 0.00444 171s eq1_9 -0.03923 0.00244 171s eq1_10 0.13751 -0.00855 171s eq1_11 -0.39091 0.02431 171s eq1_12 -0.60636 0.03770 171s eq1_13 -0.45531 0.02831 171s eq1_14 -0.15321 0.00953 171s eq1_15 0.35053 -0.02180 171s eq1_16 -0.04817 0.00300 171s eq1_17 0.18774 -0.01167 171s eq1_18 -0.06935 0.00431 171s eq1_19 0.30946 -0.01924 171s eq1_20 0.38165 -0.02373 171s eq2_1 -0.00135 0.00874 171s eq2_2 -0.01889 0.12205 171s eq2_3 -0.01520 0.09821 171s eq2_4 -0.01996 0.12901 171s eq2_5 0.00898 -0.05802 171s eq2_6 0.00251 -0.01619 171s eq2_7 -0.00466 0.03010 171s eq2_8 -0.02111 0.13640 171s eq2_9 0.01590 -0.10273 171s eq2_10 0.03911 -0.25276 171s eq2_11 0.03085 -0.19937 171s eq2_12 0.00542 -0.03502 171s eq2_13 -0.01285 0.08306 171s eq2_14 0.00562 -0.03631 171s eq2_15 0.02180 -0.14088 171s eq2_16 0.00698 -0.04508 171s eq2_17 0.06016 -0.38875 171s eq2_18 -0.01778 0.11492 171s eq2_19 -0.02558 0.16532 171s eq2_20 -0.05994 0.38731 171s > round( colSums( estfun( fitsurS5 ) ), digits = 7 ) 171s eq1_(Intercept) eq2_(Intercept) 171s 0 0 171s > 171s > 171s > ## **************** bread ************************ 171s > round( bread( fitsur1 ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s [1,] 2258.680 -23.5779 1.0971 2354.23 171s [2,] -23.578 0.3134 -0.0796 -15.01 171s [3,] 1.097 -0.0796 0.0704 -8.66 171s [4,] 2354.232 -15.0109 -8.6593 4911.36 171s [5,] -24.454 0.2225 0.0225 -38.45 171s [6,] 0.887 -0.0644 0.0569 -9.51 171s [7,] 1.348 -0.0978 0.0864 -12.94 171s supply_price supply_farmPrice supply_trend 171s [1,] -24.4536 0.8871 1.3477 171s [2,] 0.2225 -0.0644 -0.0978 171s [3,] 0.0225 0.0569 0.0864 171s [4,] -38.4456 -9.5077 -12.9352 171s [5,] 0.3567 0.0252 0.0320 171s [6,] 0.0252 0.0636 0.0807 171s [7,] 0.0320 0.0807 0.1845 171s > 171s > round( bread( fitsur1e2 ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s [1,] 2257.61 -23.5004 1.0286 2442.20 171s [2,] -23.50 0.3077 -0.0746 -16.15 171s [3,] 1.03 -0.0746 0.0660 -8.39 171s [4,] 2442.20 -16.1480 -8.3922 4816.72 171s [5,] -25.30 0.2317 0.0218 -38.19 171s [6,] 0.86 -0.0624 0.0552 -8.86 171s [7,] 1.31 -0.0948 0.0838 -12.35 171s supply_price supply_farmPrice supply_trend 171s [1,] -25.2995 0.8598 1.3061 171s [2,] 0.2317 -0.0624 -0.0948 171s [3,] 0.0218 0.0552 0.0838 171s [4,] -38.1886 -8.8582 -12.3470 171s [5,] 0.3560 0.0234 0.0309 171s [6,] 0.0234 0.0590 0.0780 171s [7,] 0.0309 0.0780 0.1640 171s > 171s > round( bread( fitsur1r3 ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s [1,] 2257.728 -23.5088 1.0361 2434.43 171s [2,] -23.509 0.3083 -0.0752 -16.03 171s [3,] 1.036 -0.0752 0.0665 -8.43 171s [4,] 2434.429 -16.0346 -8.4292 4826.83 171s [5,] -25.226 0.2308 0.0219 -38.22 171s [6,] 0.864 -0.0627 0.0554 -8.93 171s [7,] 1.312 -0.0952 0.0842 -12.42 171s supply_price supply_farmPrice supply_trend 171s [1,] -25.2264 0.8636 1.3118 171s [2,] 0.2308 -0.0627 -0.0952 171s [3,] 0.0219 0.0554 0.0842 171s [4,] -38.2158 -8.9270 -12.4169 171s [5,] 0.3561 0.0235 0.0310 171s [6,] 0.0235 0.0595 0.0784 171s [7,] 0.0310 0.0784 0.1660 171s > 171s > round( bread( fitsur1w ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s [1,] 2258.680 -23.5779 1.0971 2354.23 171s [2,] -23.578 0.3134 -0.0796 -15.01 171s [3,] 1.097 -0.0796 0.0704 -8.66 171s [4,] 2354.232 -15.0109 -8.6593 4911.36 171s [5,] -24.454 0.2225 0.0225 -38.45 171s [6,] 0.887 -0.0644 0.0569 -9.51 171s [7,] 1.348 -0.0978 0.0864 -12.94 171s supply_price supply_farmPrice supply_trend 171s [1,] -24.4536 0.8871 1.3477 171s [2,] 0.2225 -0.0644 -0.0978 171s [3,] 0.0225 0.0569 0.0864 171s [4,] -38.4456 -9.5077 -12.9352 171s [5,] 0.3567 0.0252 0.0320 171s [6,] 0.0252 0.0636 0.0807 171s [7,] 0.0320 0.0807 0.1845 171s > 171s > round( bread( fitsuri1e ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s [1,] 1876.862 -19.2519 0.5677 -81.89 171s [2,] -19.252 0.2661 -0.0755 -2.81 171s [3,] 0.568 -0.0755 0.0716 3.68 171s [4,] -81.887 -2.8102 3.6811 363.96 171s [5,] 7.186 -0.0595 -0.0127 -1.84 171s [6,] -5.538 0.0766 -0.0217 -1.67 171s [7,] -8.357 0.1155 -0.0328 -1.82 171s supply_income supply_farmPrice supply_trend 171s [1,] 7.1857 -5.5385 -8.3572 171s [2,] -0.0595 0.0766 0.1155 171s [3,] -0.0127 -0.0217 -0.0328 171s [4,] -1.8380 -1.6714 -1.8169 171s [5,] 0.0569 -0.0327 -0.0527 171s [6,] -0.0327 0.0441 0.0571 171s [7,] -0.0527 0.0571 0.1367 171s > 171s > round( bread( fitsuri1wr3 ), digits = 7 ) 171s demand_(Intercept) demand_price demand_income supply_(Intercept) 171s [1,] 2182.020 -22.2793 0.5557 -108.13 171s [2,] -22.279 0.3080 -0.0874 -3.49 171s [3,] 0.556 -0.0874 0.0839 4.64 171s [4,] -108.127 -3.4932 4.6397 458.64 171s [5,] 8.996 -0.0739 -0.0164 -2.35 171s [6,] -6.884 0.0952 -0.0270 -2.07 171s [7,] -10.388 0.1436 -0.0408 -2.31 171s supply_income supply_farmPrice supply_trend 171s [1,] 8.9961 -6.8844 -10.3882 171s [2,] -0.0739 0.0952 0.1436 171s [3,] -0.0164 -0.0270 -0.0408 171s [4,] -2.3500 -2.0691 -2.3134 171s [5,] 0.0715 -0.0407 -0.0653 171s [6,] -0.0407 0.0547 0.0717 171s [7,] -0.0653 0.0717 0.1662 171s > 171s > round( bread( fitsurS1 ), digits = 7 ) 171s eq1_consump eq2_(Intercept) eq2_consump eq2_trend 171s [1,] 0.00876 0.0 -4.02e-03 0.000 171s [2,] 0.00000 91218.4 -9.08e+02 48.892 171s [3,] -0.00402 -908.0 9.09e+00 -0.866 171s [4,] 0.00000 48.9 -8.66e-01 3.664 171s > 171s > round( bread( fitsurS2 ), digits = 7 ) 171s eq1_price eq2_trend 171s [1,] 0.00903 -0.00752 171s [2,] -0.00752 34.11430 171s > 171s > round( bread( fitsurS3 ), digits = 7 ) 171s eq1_trend eq2_trend 171s [1,] 34.1 34.0 171s [2,] 34.0 34.5 171s > 171s > try( bread( fitsurS4 ) ) 171s > 171s BEGIN TEST test_w2sls.R 171s 171s R version 4.3.2 (2023-10-31) -- "Eye Holes" 171s Copyright (C) 2023 The R Foundation for Statistical Computing 171s Platform: x86_64-pc-linux-gnu (64-bit) 171s 171s R is free software and comes with ABSOLUTELY NO WARRANTY. 171s You are welcome to redistribute it under certain conditions. 171s Type 'license()' or 'licence()' for distribution details. 171s 171s R is a collaborative project with many contributors. 171s Type 'contributors()' for more information and 171s 'citation()' on how to cite R or R packages in publications. 171s 171s Type 'demo()' for some demos, 'help()' for on-line help, or 171s 'help.start()' for an HTML browser interface to help. 171s Type 'q()' to quit R. 171s 171s > library( systemfit ) 172s Loading required package: car 172s Loading required package: carData 172s Loading required package: lmtest 172s Loading required package: zoo 172s 172s Attaching package: ‘zoo’ 172s 172s The following objects are masked from ‘package:base’: 172s 172s as.Date, as.Date.numeric 172s 172s 172s Please cite the 'systemfit' package as: 172s 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/. 172s 172s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 172s https://r-forge.r-project.org/projects/systemfit/ 172s > options( digits = 3 ) 172s > 172s > data( "Kmenta" ) 172s > useMatrix <- FALSE 172s > 172s > demand <- consump ~ price + income 172s > supply <- consump ~ price + farmPrice + trend 172s > inst <- ~ income + farmPrice + trend 172s > inst1 <- ~ income + farmPrice 172s > instlist <- list( inst1, inst ) 172s > system <- list( demand = demand, supply = supply ) 172s > restrm <- matrix(0,1,7) # restriction matrix "R" 172s > restrm[1,3] <- 1 172s > restrm[1,7] <- -1 172s > restrict <- "demand_income - supply_trend = 0" 172s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 172s > restr2m[1,3] <- 1 172s > restr2m[1,7] <- -1 172s > restr2m[2,2] <- -1 172s > restr2m[2,5] <- 1 172s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 172s > restrict2 <- c( "demand_income - supply_trend = 0", 172s + "- demand_price + supply_price = 0.5" ) 172s > tc <- matrix(0,7,6) 172s > tc[1,1] <- 1 172s > tc[2,2] <- 1 172s > tc[3,3] <- 1 172s > tc[4,4] <- 1 172s > tc[5,5] <- 1 172s > tc[6,6] <- 1 172s > tc[7,3] <- 1 172s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 172s > restr3m[1,2] <- -1 172s > restr3m[1,5] <- 1 172s > restr3q <- c( 0.5 ) # restriction vector "q" 2 172s > restrict3 <- "- C2 + C5 = 0.5" 172s > 172s > 172s > ## ********************* W2SLS ***************** 172s > fitw2sls1 <- systemfit( system, "W2SLS", data = Kmenta, inst = inst, 172s + useMatrix = useMatrix ) 172s > print( summary( fitw2sls1 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 33 162 4.36 0.697 0.548 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 65.7 3.87 1.97 0.755 0.726 172s supply 20 16 96.6 6.04 2.46 0.640 0.572 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.87 0.00 172s supply 0.00 6.04 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.87 4.36 172s supply 4.36 6.04 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.902 172s supply 0.902 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 172s price -0.2436 0.0965 -2.52 0.022 * 172s income 0.3140 0.0469 6.69 3.8e-06 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.966 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 172s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 172s price 0.2401 0.0999 2.40 0.0288 * 172s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 172s trend 0.2529 0.0997 2.54 0.0219 * 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.458 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 172s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 172s 172s > 172s > ## ********************* W2SLS (EViews-like) ***************** 172s > fitw2sls1e <- systemfit( system, "W2SLS", data = Kmenta, inst = inst, 172s + methodResidCov = "noDfCor", x = TRUE, 172s + useMatrix = useMatrix ) 172s > print( summary( fitw2sls1e, useDfSys = TRUE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 33 162 2.97 0.697 0.525 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 65.7 3.87 1.97 0.755 0.726 172s supply 20 16 96.6 6.04 2.46 0.640 0.572 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.29 0.00 172s supply 0.00 4.83 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.29 3.59 172s supply 3.59 4.83 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.902 172s supply 0.902 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 172s price -0.2436 0.0890 -2.74 0.0099 ** 172s income 0.3140 0.0433 7.25 2.5e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.966 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 172s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 172s price 0.2401 0.0894 2.69 0.0112 * 172s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 172s trend 0.2529 0.0891 2.84 0.0077 ** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.458 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 172s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 172s 172s > 172s > ## ********************* W2SLS with restriction ******************* 172s > fitw2sls2 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 172s + inst = inst, useMatrix = useMatrix ) 172s > print( summary( fitw2sls2 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 165 3.41 0.692 0.565 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 66.8 3.93 1.98 0.751 0.721 172s supply 20 16 98.4 6.15 2.48 0.633 0.564 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.97 0.00 172s supply 0.00 6.13 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.93 4.56 172s supply 4.56 6.15 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.927 172s supply 0.927 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 94.3832 8.0090 11.78 1.5e-13 *** 172s price -0.2302 0.0946 -2.43 0.02 * 172s income 0.3028 0.0430 7.05 3.9e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.983 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 66.838 MSE: 3.932 Root MSE: 1.983 172s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 48.0494 11.8001 4.07 0.00026 *** 172s price 0.2430 0.1006 2.42 0.02122 * 172s farmPrice 0.2625 0.0459 5.72 2.0e-06 *** 172s trend 0.3028 0.0430 7.05 3.9e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.48 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 98.445 MSE: 6.153 Root MSE: 2.48 172s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 172s 172s > # the same with symbolically specified restrictions 172s > fitw2sls2Sym <- systemfit( system, "W2SLS", data = Kmenta, 172s + restrict.matrix = restrict, inst = inst, useMatrix = useMatrix ) 172s > all.equal( fitw2sls2, fitw2sls2Sym ) 172s [1] "Component “call”: target, current do not match when deparsed" 172s > 172s > ## ********************* W2SLS with restriction (EViews-like) ************** 172s > fitw2sls2e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 172s + inst = inst, methodResidCov = "noDfCor", x = TRUE, 172s + useMatrix = useMatrix ) 172s > print( summary( fitw2sls2e, useDfSys = TRUE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 165 2.33 0.692 0.535 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 66.9 3.94 1.98 0.750 0.721 172s supply 20 16 98.4 6.15 2.48 0.633 0.564 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.37 0.00 172s supply 0.00 4.91 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.35 3.76 172s supply 3.76 4.92 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.926 172s supply 0.926 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 94.3706 7.3834 12.78 1.6e-14 *** 172s price -0.2295 0.0871 -2.63 0.013 * 172s income 0.3022 0.0394 7.67 6.4e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.984 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 66.906 MSE: 3.936 Root MSE: 1.984 172s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 48.0661 10.5574 4.55 6.5e-05 *** 172s price 0.2430 0.0900 2.70 0.011 * 172s farmPrice 0.2624 0.0411 6.39 2.7e-07 *** 172s trend 0.3022 0.0394 7.67 6.4e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.48 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 98.408 MSE: 6.15 Root MSE: 2.48 172s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 172s 172s > nobs( fitw2sls2e ) 172s [1] 40 172s > 172s > ## ********************* W2SLS with restriction via restrict.regMat ******************* 172s > fitw2sls3 <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 172s + inst = inst, x = TRUE, useMatrix = useMatrix ) 172s > print( summary( fitw2sls3 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 165 3.41 0.692 0.565 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 66.8 3.93 1.98 0.751 0.721 172s supply 20 16 98.4 6.15 2.48 0.633 0.564 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.97 0.00 172s supply 0.00 6.13 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.93 4.56 172s supply 4.56 6.15 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.927 172s supply 0.927 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 94.3832 8.0090 11.78 1.5e-13 *** 172s price -0.2302 0.0946 -2.43 0.02 * 172s income 0.3028 0.0430 7.05 3.9e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.983 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 66.838 MSE: 3.932 Root MSE: 1.983 172s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 48.0494 11.8001 4.07 0.00026 *** 172s price 0.2430 0.1006 2.42 0.02122 * 172s farmPrice 0.2625 0.0459 5.72 2.0e-06 *** 172s trend 0.3028 0.0430 7.05 3.9e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.48 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 98.445 MSE: 6.153 Root MSE: 2.48 172s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 172s 172s > 172s > ## ********************* W2SLS with restriction via restrict.regMat (EViews-like) ************** 172s > fitw2sls3e <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 172s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 172s > print( summary( fitw2sls3e, useDfSys = TRUE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 165 2.33 0.692 0.535 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 66.9 3.94 1.98 0.750 0.721 172s supply 20 16 98.4 6.15 2.48 0.633 0.564 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.37 0.00 172s supply 0.00 4.91 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.35 3.76 172s supply 3.76 4.92 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.926 172s supply 0.926 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 94.3706 7.3834 12.78 1.6e-14 *** 172s price -0.2295 0.0871 -2.63 0.013 * 172s income 0.3022 0.0394 7.67 6.4e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.984 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 66.906 MSE: 3.936 Root MSE: 1.984 172s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 48.0661 10.5574 4.55 6.5e-05 *** 172s price 0.2430 0.0900 2.70 0.011 * 172s farmPrice 0.2624 0.0411 6.39 2.7e-07 *** 172s trend 0.3022 0.0394 7.67 6.4e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.48 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 98.408 MSE: 6.15 Root MSE: 2.48 172s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 172s 172s > 172s > ## ***************** W2SLS with 2 restrictions ******************** 172s > fitw2sls4 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr2m, 172s + restrict.rhs = restr2q, inst = inst, x = TRUE, 172s + useMatrix = useMatrix ) 172s > print( summary( fitw2sls4 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 35 166 3.57 0.69 0.575 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 65.9 3.88 1.97 0.754 0.725 172s supply 20 16 100.3 6.27 2.50 0.626 0.556 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.89 0.00 172s supply 0.00 6.25 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.88 4.55 172s supply 4.55 6.27 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.924 172s supply 0.924 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 95.3043 6.3056 15.11 < 2e-16 *** 172s price -0.2428 0.0684 -3.55 0.0011 ** 172s income 0.3063 0.0394 7.78 3.9e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.969 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 65.931 MSE: 3.878 Root MSE: 1.969 172s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 46.4229 8.3296 5.57 2.8e-06 *** 172s price 0.2572 0.0684 3.76 0.00062 *** 172s farmPrice 0.2642 0.0455 5.80 1.4e-06 *** 172s trend 0.3063 0.0394 7.78 3.9e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.503 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 100.255 MSE: 6.266 Root MSE: 2.503 172s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 172s 172s > # the same with symbolically specified restrictions 172s > fitw2sls4Sym <- systemfit( system, "W2SLS", data = Kmenta, 172s + restrict.matrix = restrict2, inst = inst, x = TRUE, 172s + useMatrix = useMatrix ) 172s > all.equal( fitw2sls4, fitw2sls4Sym ) 172s [1] "Component “call”: target, current do not match when deparsed" 172s > 172s > ## ***************** W2SLS with 2 restrictions (EViews-like) ************** 172s > fitw2sls4e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr2m, 172s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 172s + useMatrix = useMatrix ) 172s > print( summary( fitw2sls4e, useDfSys = TRUE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 35 166 2.44 0.69 0.546 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 65.9 3.88 1.97 0.754 0.725 172s supply 20 16 100.2 6.26 2.50 0.626 0.556 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.3 0 172s supply 0.0 5 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.30 3.75 172s supply 3.75 5.01 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.923 172s supply 0.923 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 95.3470 5.7579 16.56 < 2e-16 *** 172s price -0.2428 0.0621 -3.91 0.00041 *** 172s income 0.3059 0.0360 8.49 5.1e-10 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.97 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 65.945 MSE: 3.879 Root MSE: 1.97 172s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 46.4366 7.5360 6.16 4.7e-07 *** 172s price 0.2572 0.0621 4.14 0.00021 *** 172s farmPrice 0.2642 0.0407 6.48 1.8e-07 *** 172s trend 0.3059 0.0360 8.49 5.1e-10 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.503 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 100.225 MSE: 6.264 Root MSE: 2.503 172s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 172s 172s > 172s > ## ***************** W2SLS with 2 restrictions via R and restrict.regMat ****************** 172s > fitw2sls5 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr3m, 172s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 172s + x = TRUE, useMatrix = useMatrix ) 172s > print( summary( fitw2sls5 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 35 166 3.57 0.69 0.575 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 65.9 3.88 1.97 0.754 0.725 172s supply 20 16 100.3 6.27 2.50 0.626 0.556 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.89 0.00 172s supply 0.00 6.25 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.88 4.55 172s supply 4.55 6.27 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.924 172s supply 0.924 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 95.3043 6.3056 15.11 < 2e-16 *** 172s price -0.2428 0.0684 -3.55 0.0011 ** 172s income 0.3063 0.0394 7.78 3.9e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.969 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 65.931 MSE: 3.878 Root MSE: 1.969 172s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 46.4229 8.3296 5.57 2.8e-06 *** 172s price 0.2572 0.0684 3.76 0.00062 *** 172s farmPrice 0.2642 0.0455 5.80 1.4e-06 *** 172s trend 0.3063 0.0394 7.78 3.9e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.503 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 100.255 MSE: 6.266 Root MSE: 2.503 172s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 172s 172s > # the same with symbolically specified restrictions 172s > fitw2sls5Sym <- systemfit( system, "W2SLS", data = Kmenta, 172s + restrict.matrix = restrict3, restrict.regMat = tc, inst = inst, 172s + x = TRUE, useMatrix = useMatrix ) 172s > all.equal( fitw2sls5, fitw2sls5Sym ) 172s [1] "Component “call”: target, current do not match when deparsed" 172s > 172s > ## ***************** W2SLS with 2 restrictions via R and restrict.regMat (EViews-like) ************** 172s > fitw2sls5e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr3m, 172s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 172s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 172s > print( summary( fitw2sls5e, useDfSys = TRUE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 35 166 2.44 0.69 0.546 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 65.9 3.88 1.97 0.754 0.725 172s supply 20 16 100.2 6.26 2.50 0.626 0.556 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.3 0 172s supply 0.0 5 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.30 3.75 172s supply 3.75 5.01 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.923 172s supply 0.923 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 95.3470 5.7579 16.56 < 2e-16 *** 172s price -0.2428 0.0621 -3.91 0.00041 *** 172s income 0.3059 0.0360 8.49 5.1e-10 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.97 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 65.945 MSE: 3.879 Root MSE: 1.97 172s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 46.4366 7.5360 6.16 4.7e-07 *** 172s price 0.2572 0.0621 4.14 0.00021 *** 172s farmPrice 0.2642 0.0407 6.48 1.8e-07 *** 172s trend 0.3059 0.0360 8.49 5.1e-10 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.503 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 100.225 MSE: 6.264 Root MSE: 2.503 172s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 172s 172s > 172s > ## ****** 2SLS estimation with different instruments ********************** 172s > fitw2slsd1 <- systemfit( system, "W2SLS", data = Kmenta, inst = instlist, 172s + useMatrix = useMatrix ) 172s > print( summary( fitw2slsd1 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 33 164 9.25 0.694 0.512 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 67.4 3.97 1.99 0.748 0.719 172s supply 20 16 96.6 6.04 2.46 0.640 0.572 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.97 0.00 172s supply 0.00 6.04 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.97 3.84 172s supply 3.84 6.04 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.784 172s supply 0.784 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 172s price -0.4116 0.1448 -2.84 0.011 * 172s income 0.3617 0.0564 6.41 6.4e-06 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.992 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 172s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 172s price 0.2401 0.0999 2.40 0.0288 * 172s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 172s trend 0.2529 0.0997 2.54 0.0219 * 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.458 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 172s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 172s 172s > 172s > ## ****** 2SLS estimation with different instruments (EViews-like)****************** 172s > fitw2slsd1e <- systemfit( system, "W2SLS", data = Kmenta, inst = instlist, 172s + methodResidCov = "noDfCor", x = TRUE, 172s + useMatrix = useMatrix ) 172s > print( summary( fitw2slsd1e, useDfSys = TRUE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 33 164 6.29 0.694 0.5 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 67.4 3.97 1.99 0.748 0.719 172s supply 20 16 96.6 6.04 2.46 0.640 0.572 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.37 0.00 172s supply 0.00 4.83 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.37 3.16 172s supply 3.16 4.83 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.784 172s supply 0.784 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 172s price -0.412 0.134 -3.08 0.0041 ** 172s income 0.362 0.052 6.95 6.0e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.992 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 172s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 172s price 0.2401 0.0894 2.69 0.0112 * 172s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 172s trend 0.2529 0.0891 2.84 0.0077 ** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.458 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 172s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 172s 172s > 172s > ## **** W2SLS estimation with different instruments and restriction ******** 172s > fitw2slsd2 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 172s + inst = instlist, useMatrix = useMatrix ) 172s > print( summary( fitw2slsd2 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 166 5.11 0.69 0.557 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 64.8 3.81 1.95 0.758 0.730 172s supply 20 16 101.4 6.34 2.52 0.622 0.551 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.79 0.00 172s supply 0.00 6.27 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.81 4.36 172s supply 4.36 6.34 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.888 172s supply 0.888 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 104.5695 10.6344 9.83 1.8e-11 *** 172s price -0.3653 0.1327 -2.75 0.0094 ** 172s income 0.3369 0.0485 6.95 5.1e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.952 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 64.776 MSE: 3.81 Root MSE: 1.952 172s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.73 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 47.0356 11.9466 3.94 0.00039 *** 172s price 0.2450 0.1017 2.41 0.02156 * 172s farmPrice 0.2672 0.0465 5.74 1.9e-06 *** 172s trend 0.3369 0.0485 6.95 5.1e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.518 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 101.426 MSE: 6.339 Root MSE: 2.518 172s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 172s 172s > 172s > ## **** W2SLS estimation with different instruments and restriction (EViews-like)* 172s > fitw2slsd2e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 172s + inst = instlist, methodResidCov = "noDfCor", x = TRUE, 172s + useMatrix = useMatrix ) 172s > print( summary( fitw2slsd2e, useDfSys = TRUE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 166 3.45 0.69 0.535 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 64.7 3.81 1.95 0.759 0.730 172s supply 20 16 101.3 6.33 2.52 0.622 0.551 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.22 0.00 172s supply 0.00 5.02 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.24 3.60 172s supply 3.60 5.06 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.888 172s supply 0.888 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 172s price -0.3630 0.1220 -2.98 0.0053 ** 172s income 0.3357 0.0444 7.57 8.6e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.951 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 64.715 MSE: 3.807 Root MSE: 1.951 172s Multiple R-Squared: 0.759 Adjusted R-Squared: 0.73 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 47.0706 10.6890 4.40 0.0001 *** 172s price 0.2449 0.0910 2.69 0.0109 * 172s farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 172s trend 0.3357 0.0444 7.57 8.6e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.516 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 101.299 MSE: 6.331 Root MSE: 2.516 172s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 172s 172s > 172s > ## ** W2SLS estimation with different instruments and restriction via restrict.regMat **** 172s > fitw2slsd3 <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 172s + inst = instlist, x = TRUE, useMatrix = useMatrix ) 172s > print( summary( fitw2slsd3 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 166 5.11 0.69 0.557 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 64.8 3.81 1.95 0.758 0.730 172s supply 20 16 101.4 6.34 2.52 0.622 0.551 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.79 0.00 172s supply 0.00 6.27 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.81 4.36 172s supply 4.36 6.34 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.888 172s supply 0.888 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 104.5695 10.6344 9.83 1.8e-11 *** 172s price -0.3653 0.1327 -2.75 0.0094 ** 172s income 0.3369 0.0485 6.95 5.1e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.952 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 64.776 MSE: 3.81 Root MSE: 1.952 172s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.73 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 47.0356 11.9466 3.94 0.00039 *** 172s price 0.2450 0.1017 2.41 0.02156 * 172s farmPrice 0.2672 0.0465 5.74 1.9e-06 *** 172s trend 0.3369 0.0485 6.95 5.1e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.518 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 101.426 MSE: 6.339 Root MSE: 2.518 172s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 172s 172s > 172s > ## W2SLS estimation with different instruments and restriction via restrict.regMat (EViews-like) 172s > fitw2slsd3e <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 172s + inst = instlist, methodResidCov = "noDfCor", useMatrix = useMatrix ) 172s > print( summary( fitw2slsd3e, useDfSys = TRUE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 166 3.45 0.69 0.535 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 64.7 3.81 1.95 0.759 0.730 172s supply 20 16 101.3 6.33 2.52 0.622 0.551 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.22 0.00 172s supply 0.00 5.02 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.24 3.60 172s supply 3.60 5.06 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.888 172s supply 0.888 1.000 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 172s price -0.3630 0.1220 -2.98 0.0053 ** 172s income 0.3357 0.0444 7.57 8.6e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.951 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 64.715 MSE: 3.807 Root MSE: 1.951 172s Multiple R-Squared: 0.759 Adjusted R-Squared: 0.73 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 47.0706 10.6890 4.40 0.0001 *** 172s price 0.2449 0.0910 2.69 0.0109 * 172s farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 172s trend 0.3357 0.0444 7.57 8.6e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.516 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 101.299 MSE: 6.331 Root MSE: 2.516 172s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 172s 172s > 172s > 172s > ## *********** estimations with a single regressor ************ 172s > fitw2slsS1 <- systemfit( 172s + list( consump ~ price - 1, price ~ consump + trend ), "W2SLS", 172s + data = Kmenta, inst = ~ farmPrice + trend + income, useMatrix = useMatrix ) 172s > print( summary( fitw2slsS1 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 36 1544 179 -0.65 0.852 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s eq1 20 19 861 45.3 6.73 -2.213 -2.213 172s eq2 20 17 682 40.1 6.33 -0.022 -0.143 172s 172s The covariance matrix of the residuals used for estimation 172s eq1 eq2 172s eq1 45.3 0.0 172s eq2 0.0 40.1 172s 172s The covariance matrix of the residuals 172s eq1 eq2 172s eq1 45.3 -40.5 172s eq2 -40.5 40.1 172s 172s The correlations of the residuals 172s eq1 eq2 172s eq1 1.00 -0.95 172s eq2 -0.95 1.00 172s 172s 172s W2SLS estimates for 'eq1' (equation 1) 172s Model Formula: consump ~ price - 1 172s Instruments: ~farmPrice + trend + income 172s 172s Estimate Std. Error t value Pr(>|t|) 172s price 1.006 0.015 66.9 <2e-16 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 6.734 on 19 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 19 172s SSR: 861.48 MSE: 45.341 Root MSE: 6.734 172s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 172s 172s 172s W2SLS estimates for 'eq2' (equation 2) 172s Model Formula: price ~ consump + trend 172s Instruments: ~farmPrice + trend + income 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 55.5365 46.2668 1.20 0.25 172s consump 0.4453 0.4622 0.96 0.35 172s trend -0.0426 0.2496 -0.17 0.87 172s 172s Residual standard error: 6.335 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 682.257 MSE: 40.133 Root MSE: 6.335 172s Multiple R-Squared: -0.022 Adjusted R-Squared: -0.143 172s 172s > fitw2slsS2 <- systemfit( 172s + list( consump ~ price - 1, consump ~ trend - 1 ), "W2SLS", 172s + data = Kmenta, inst = ~ farmPrice + price + income, useMatrix = useMatrix ) 172s > print( summary( fitw2slsS2 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 38 47456 111148 -87.5 -5.28 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s eq1 20 19 861 45.3 6.73 -2.21 -2.21 172s eq2 20 19 46595 2452.3 49.52 -172.79 -172.79 172s 172s The covariance matrix of the residuals used for estimation 172s eq1 eq2 172s eq1 45.3 0 172s eq2 0.0 2452 172s 172s The covariance matrix of the residuals 172s eq1 eq2 172s eq1 45.34 -6.33 172s eq2 -6.33 2452.34 172s 172s The correlations of the residuals 172s eq1 eq2 172s eq1 1.0000 -0.0448 172s eq2 -0.0448 1.0000 172s 172s 172s W2SLS estimates for 'eq1' (equation 1) 172s Model Formula: consump ~ price - 1 172s Instruments: ~farmPrice + price + income 172s 172s Estimate Std. Error t value Pr(>|t|) 172s price 1.006 0.015 66.9 <2e-16 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 6.733 on 19 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 19 172s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 172s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 172s 172s 172s W2SLS estimates for 'eq2' (equation 2) 172s Model Formula: consump ~ trend - 1 172s Instruments: ~farmPrice + price + income 172s 172s Estimate Std. Error t value Pr(>|t|) 172s trend 7.578 0.934 8.11 1.4e-07 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 49.521 on 19 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 19 172s SSR: 46594.549 MSE: 2452.345 Root MSE: 49.521 172s Multiple R-Squared: -172.786 Adjusted R-Squared: -172.786 172s 172s > fitw2slsS3 <- systemfit( 172s + list( consump ~ trend - 1, price ~ trend - 1 ), "W2SLS", 172s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 172s > print( summary( fitw2slsS3 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 38 97978 687515 -104 -10.6 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s eq1 20 19 50950 2682 51.8 -189.0 -189.0 172s eq2 20 19 47028 2475 49.8 -69.5 -69.5 172s 172s The covariance matrix of the residuals used for estimation 172s eq1 eq2 172s eq1 2682 0 172s eq2 0 2475 172s 172s The covariance matrix of the residuals 172s eq1 eq2 172s eq1 2682 2439 172s eq2 2439 2475 172s 172s The correlations of the residuals 172s eq1 eq2 172s eq1 1.000 0.989 172s eq2 0.989 1.000 172s 172s 172s W2SLS estimates for 'eq1' (equation 1) 172s Model Formula: consump ~ trend - 1 172s Instruments: ~income + farmPrice 172s 172s Estimate Std. Error t value Pr(>|t|) 172s trend 8.65 1.05 8.27 1e-07 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 51.784 on 19 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 19 172s SSR: 50949.985 MSE: 2681.578 Root MSE: 51.784 172s Multiple R-Squared: -189.031 Adjusted R-Squared: -189.031 172s 172s 172s W2SLS estimates for 'eq2' (equation 2) 172s Model Formula: price ~ trend - 1 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s trend 7.318 0.929 7.88 2.1e-07 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 49.751 on 19 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 19 172s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 172s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 172s 172s > fitw2slsS4 <- systemfit( 172s + list( consump ~ trend - 1, price ~ trend - 1 ), "W2SLS", 172s + data = Kmenta, inst = ~ farmPrice + trend + income, 172s + restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), useMatrix = useMatrix ) 172s > print( summary( fitw2slsS4 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 39 93548 111736 -99 -1.03 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s eq1 20 19 46514 2448 49.5 -172.5 -172.5 172s eq2 20 19 47034 2475 49.8 -69.5 -69.5 172s 172s The covariance matrix of the residuals used for estimation 172s eq1 eq2 172s eq1 2448 0 172s eq2 0 2475 172s 172s The covariance matrix of the residuals 172s eq1 eq2 172s eq1 2448 2439 172s eq2 2439 2475 172s 172s The correlations of the residuals 172s eq1 eq2 172s eq1 1.000 0.988 172s eq2 0.988 1.000 172s 172s 172s W2SLS estimates for 'eq1' (equation 1) 172s Model Formula: consump ~ trend - 1 172s Instruments: ~farmPrice + trend + income 172s 172s Estimate Std. Error t value Pr(>|t|) 172s trend 7.362 0.655 11.2 8.4e-14 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 49.478 on 19 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 19 172s SSR: 46514.224 MSE: 2448.117 Root MSE: 49.478 172s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 172s 172s 172s W2SLS estimates for 'eq2' (equation 2) 172s Model Formula: price ~ trend - 1 172s Instruments: ~farmPrice + trend + income 172s 172s Estimate Std. Error t value Pr(>|t|) 172s trend 7.362 0.655 11.2 8.4e-14 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 49.754 on 19 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 19 172s SSR: 47033.528 MSE: 2475.449 Root MSE: 49.754 172s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 172s 172s > fitw2slsS5 <- systemfit( 172s + list( consump ~ 1, price ~ 1 ), "W2SLS", 172s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 172s > print( summary( fitw2slsS5 ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 38 935 491 0 0 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s eq1 20 19 268 14.1 3.76 0 0 172s eq2 20 19 667 35.1 5.93 0 0 172s 172s The covariance matrix of the residuals used for estimation 172s eq1 eq2 172s eq1 14.1 0.0 172s eq2 0.0 35.1 172s 172s The covariance matrix of the residuals 172s eq1 eq2 172s eq1 14.11 2.18 172s eq2 2.18 35.12 172s 172s The correlations of the residuals 172s eq1 eq2 172s eq1 1.0000 0.0981 172s eq2 0.0981 1.0000 172s 172s 172s W2SLS estimates for 'eq1' (equation 1) 172s Model Formula: consump ~ 1 172s Instruments: ~income + farmPrice 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 100.90 0.84 120 <2e-16 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 3.756 on 19 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 19 172s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 172s Multiple R-Squared: 0 Adjusted R-Squared: 0 172s 172s 172s W2SLS estimates for 'eq2' (equation 2) 172s Model Formula: price ~ 1 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 100.02 1.33 75.5 <2e-16 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 5.926 on 19 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 19 172s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 172s Multiple R-Squared: 0 Adjusted R-Squared: 0 172s 172s > 172s > 172s > ## **************** shorter summaries ********************** 172s > print( summary( fitw2sls1e, residCov = FALSE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 33 162 2.97 0.697 0.525 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 65.7 3.87 1.97 0.755 0.726 172s supply 20 16 96.6 6.04 2.46 0.640 0.572 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 94.6333 7.3027 12.96 3.1e-10 *** 172s price -0.2436 0.0890 -2.74 0.014 * 172s income 0.3140 0.0433 7.25 1.3e-06 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.966 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 172s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 49.5324 10.7425 4.61 0.00029 *** 172s price 0.2401 0.0894 2.69 0.01623 * 172s farmPrice 0.2556 0.0423 6.05 1.7e-05 *** 172s trend 0.2529 0.0891 2.84 0.01188 * 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.458 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 172s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 172s 172s > 172s > print( summary( fitw2sls2, residCov = FALSE, equations = FALSE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 165 3.41 0.692 0.565 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 66.8 3.93 1.98 0.751 0.721 172s supply 20 16 98.4 6.15 2.48 0.633 0.564 172s 172s 172s Coefficients: 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 94.3832 8.0090 11.78 1.5e-13 *** 172s demand_price -0.2302 0.0946 -2.43 0.02042 * 172s demand_income 0.3028 0.0430 7.05 3.9e-08 *** 172s supply_(Intercept) 48.0494 11.8001 4.07 0.00026 *** 172s supply_price 0.2430 0.1006 2.42 0.02122 * 172s supply_farmPrice 0.2625 0.0459 5.72 2.0e-06 *** 172s supply_trend 0.3028 0.0430 7.05 3.9e-08 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s > 172s > print( summary( fitw2sls3, useDfSys = FALSE ), equations = FALSE ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 165 3.41 0.692 0.565 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 66.8 3.93 1.98 0.751 0.721 172s supply 20 16 98.4 6.15 2.48 0.633 0.564 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.97 0.00 172s supply 0.00 6.13 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.93 4.56 172s supply 4.56 6.15 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.927 172s supply 0.927 1.000 172s 172s 172s Coefficients: 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 94.3832 8.0090 11.78 1.3e-09 *** 172s demand_price -0.2302 0.0946 -2.43 0.02634 * 172s demand_income 0.3028 0.0430 7.05 2.0e-06 *** 172s supply_(Intercept) 48.0494 11.8001 4.07 0.00089 *** 172s supply_price 0.2430 0.1006 2.42 0.02802 * 172s supply_farmPrice 0.2625 0.0459 5.72 3.2e-05 *** 172s supply_trend 0.3028 0.0430 7.05 2.8e-06 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s > 172s > print( summary( fitw2sls4e ), residCov = FALSE ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 35 166 2.44 0.69 0.546 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 65.9 3.88 1.97 0.754 0.725 172s supply 20 16 100.2 6.26 2.50 0.626 0.556 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 95.3470 5.7579 16.56 < 2e-16 *** 172s price -0.2428 0.0621 -3.91 0.00041 *** 172s income 0.3059 0.0360 8.49 5.1e-10 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.97 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 65.945 MSE: 3.879 Root MSE: 1.97 172s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 46.4366 7.5360 6.16 4.7e-07 *** 172s price 0.2572 0.0621 4.14 0.00021 *** 172s farmPrice 0.2642 0.0407 6.48 1.8e-07 *** 172s trend 0.3059 0.0360 8.49 5.1e-10 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.503 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 100.225 MSE: 6.264 Root MSE: 2.503 172s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 172s 172s > 172s > print( summary( fitw2sls5, useDfSys = FALSE, residCov = FALSE ) ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 35 166 3.57 0.69 0.575 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 65.9 3.88 1.97 0.754 0.725 172s supply 20 16 100.3 6.27 2.50 0.626 0.556 172s 172s 172s W2SLS estimates for 'demand' (equation 1) 172s Model Formula: consump ~ price + income 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 95.3043 6.3056 15.11 2.7e-11 *** 172s price -0.2428 0.0684 -3.55 0.0025 ** 172s income 0.3063 0.0394 7.78 5.4e-07 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 1.969 on 17 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 17 172s SSR: 65.931 MSE: 3.878 Root MSE: 1.969 172s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 172s 172s 172s W2SLS estimates for 'supply' (equation 2) 172s Model Formula: consump ~ price + farmPrice + trend 172s Instruments: ~income + farmPrice + trend 172s 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 46.4229 8.3296 5.57 4.2e-05 *** 172s price 0.2572 0.0684 3.76 0.0017 ** 172s farmPrice 0.2642 0.0455 5.80 2.7e-05 *** 172s trend 0.3063 0.0394 7.78 8.0e-07 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s 172s Residual standard error: 2.503 on 16 degrees of freedom 172s Number of observations: 20 Degrees of Freedom: 16 172s SSR: 100.255 MSE: 6.266 Root MSE: 2.503 172s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 172s 172s > 172s > print( summary( fitw2slsd1, useDfSys = TRUE ), residCov = FALSE, 172s + equations = FALSE ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 33 164 9.25 0.694 0.512 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 67.4 3.97 1.99 0.748 0.719 172s supply 20 16 96.6 6.04 2.46 0.640 0.572 172s 172s 172s Coefficients: 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 172s demand_price -0.4116 0.1448 -2.84 0.00764 ** 172s demand_income 0.3617 0.0564 6.41 2.9e-07 *** 172s supply_(Intercept) 49.5324 12.0105 4.12 0.00024 *** 172s supply_price 0.2401 0.0999 2.40 0.02208 * 172s supply_farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 172s supply_trend 0.2529 0.0997 2.54 0.01605 * 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s > 172s > print( summary( fitw2slsd2e, equations = TRUE ), equations = FALSE ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 166 3.45 0.69 0.535 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 64.7 3.81 1.95 0.759 0.730 172s supply 20 16 101.3 6.33 2.52 0.622 0.551 172s 172s The covariance matrix of the residuals used for estimation 172s demand supply 172s demand 3.22 0.00 172s supply 0.00 5.02 172s 172s The covariance matrix of the residuals 172s demand supply 172s demand 3.24 3.60 172s supply 3.60 5.06 172s 172s The correlations of the residuals 172s demand supply 172s demand 1.000 0.888 172s supply 0.888 1.000 172s 172s 172s Coefficients: 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 172s demand_price -0.3630 0.1220 -2.98 0.0053 ** 172s demand_income 0.3357 0.0444 7.57 8.6e-09 *** 172s supply_(Intercept) 47.0706 10.6890 4.40 0.0001 *** 172s supply_price 0.2449 0.0910 2.69 0.0109 * 172s supply_farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 172s supply_trend 0.3357 0.0444 7.57 8.6e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s > 172s > print( summary( fitw2slsd3e, equations = FALSE ), residCov = FALSE ) 172s 172s systemfit results 172s method: W2SLS 172s 172s N DF SSR detRCov OLS-R2 McElroy-R2 172s system 40 34 166 3.45 0.69 0.535 172s 172s N DF SSR MSE RMSE R2 Adj R2 172s demand 20 17 64.7 3.81 1.95 0.759 0.730 172s supply 20 16 101.3 6.33 2.52 0.622 0.551 172s 172s 172s Coefficients: 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 172s demand_price -0.3630 0.1220 -2.98 0.0053 ** 172s demand_income 0.3357 0.0444 7.57 8.6e-09 *** 172s supply_(Intercept) 47.0706 10.6890 4.40 0.0001 *** 172s supply_price 0.2449 0.0910 2.69 0.0109 * 172s supply_farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 172s supply_trend 0.3357 0.0444 7.57 8.6e-09 *** 172s --- 172s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 172s > 172s > 172s > ## ****************** residuals ************************** 172s > print( residuals( fitw2sls1e ) ) 172s demand supply 172s 1 0.843 -0.4348 172s 2 -0.698 -1.2131 172s 3 2.359 1.7090 172s 4 1.490 0.7956 172s 5 2.139 1.5942 172s 6 1.277 0.6595 172s 7 1.571 1.4346 172s 8 -3.066 -4.8724 172s 9 -1.125 -2.3975 172s 10 2.492 3.1427 172s 11 -0.108 0.0689 172s 12 -2.292 -1.3978 172s 13 -1.598 -1.1136 172s 14 -0.271 1.1684 172s 15 1.958 3.4865 172s 16 -3.430 -3.8285 172s 17 -0.313 0.6793 172s 18 -2.151 -2.7713 172s 19 1.592 2.6668 172s 20 -0.668 0.6235 172s > print( residuals( fitw2sls1e$eq[[ 1 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 172s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 172s 12 13 14 15 16 17 18 19 20 172s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 172s > 172s > print( residuals( fitw2sls2 ) ) 172s demand supply 172s 1 0.726 0.0287 172s 2 -0.754 -0.8185 172s 3 2.304 2.0561 172s 4 1.437 1.0966 172s 5 2.191 1.7764 172s 6 1.317 0.8056 172s 7 1.620 1.5441 172s 8 -3.015 -4.8526 172s 9 -1.087 -2.3957 172s 10 2.513 3.1658 172s 11 -0.265 0.1722 172s 12 -2.506 -1.2753 172s 13 -1.781 -1.0688 172s 14 -0.332 1.1028 172s 15 2.086 3.2370 172s 16 -3.325 -4.1563 172s 17 -0.144 0.2984 172s 18 -2.128 -3.1286 172s 19 1.662 2.2767 172s 20 -0.518 0.1355 172s > print( residuals( fitw2sls2$eq[[ 2 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 172s 0.0287 -0.8185 2.0561 1.0966 1.7764 0.8056 1.5441 -4.8526 -2.3957 3.1658 172s 11 12 13 14 15 16 17 18 19 20 172s 0.1722 -1.2753 -1.0688 1.1028 3.2370 -4.1563 0.2984 -3.1286 2.2767 0.1355 172s > 172s > print( residuals( fitw2sls3 ) ) 172s demand supply 172s 1 0.726 0.0287 172s 2 -0.754 -0.8185 172s 3 2.304 2.0561 172s 4 1.437 1.0966 172s 5 2.191 1.7764 172s 6 1.317 0.8056 172s 7 1.620 1.5441 172s 8 -3.015 -4.8526 172s 9 -1.087 -2.3957 172s 10 2.513 3.1658 172s 11 -0.265 0.1722 172s 12 -2.506 -1.2753 172s 13 -1.781 -1.0688 172s 14 -0.332 1.1028 172s 15 2.086 3.2370 172s 16 -3.325 -4.1563 172s 17 -0.144 0.2984 172s 18 -2.128 -3.1286 172s 19 1.662 2.2767 172s 20 -0.518 0.1355 172s > print( residuals( fitw2sls3$eq[[ 1 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 172s 0.726 -0.754 2.304 1.437 2.191 1.317 1.620 -3.015 -1.087 2.513 -0.265 172s 12 13 14 15 16 17 18 19 20 172s -2.506 -1.781 -0.332 2.086 -3.325 -0.144 -2.128 1.662 -0.518 172s > 172s > print( residuals( fitw2sls4e ) ) 172s demand supply 172s 1 0.761 0.0514 172s 2 -0.700 -0.8567 172s 3 2.350 2.0266 172s 4 1.492 1.0504 172s 5 2.159 1.7988 172s 6 1.301 0.8085 172s 7 1.616 1.5253 172s 8 -2.986 -4.9339 172s 9 -1.130 -2.3600 172s 10 2.429 3.2858 172s 11 -0.284 0.2948 172s 12 -2.458 -1.2168 172s 13 -1.705 -1.0756 172s 14 -0.327 1.1348 172s 15 2.007 3.2835 172s 16 -3.368 -4.1646 172s 17 -0.312 0.4480 172s 18 -2.099 -3.2018 172s 19 1.694 2.1807 172s 20 -0.439 -0.0794 172s > print( residuals( fitw2sls4e$eq[[ 2 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 172s 0.0514 -0.8567 2.0266 1.0504 1.7988 0.8085 1.5253 -4.9339 -2.3600 3.2858 172s 11 12 13 14 15 16 17 18 19 20 172s 0.2948 -1.2168 -1.0756 1.1348 3.2835 -4.1646 0.4480 -3.2018 2.1807 -0.0794 172s > 172s > print( residuals( fitw2sls5 ) ) 172s demand supply 172s 1 0.765 0.0551 172s 2 -0.701 -0.8537 172s 3 2.350 2.0293 172s 4 1.491 1.0527 172s 5 2.158 1.8003 172s 6 1.300 0.8097 172s 7 1.614 1.5262 172s 8 -2.991 -4.9339 172s 9 -1.129 -2.3600 172s 10 2.433 3.2862 172s 11 -0.275 0.2958 172s 12 -2.450 -1.2157 172s 13 -1.700 -1.0752 172s 14 -0.324 1.1344 172s 15 2.005 3.2816 172s 16 -3.371 -4.1672 172s 17 -0.311 0.4452 172s 18 -2.102 -3.2047 172s 19 1.688 2.1776 172s 20 -0.451 -0.0835 172s > print( residuals( fitw2sls5$eq[[ 1 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 172s 0.765 -0.701 2.350 1.491 2.158 1.300 1.614 -2.991 -1.129 2.433 -0.275 172s 12 13 14 15 16 17 18 19 20 172s -2.450 -1.700 -0.324 2.005 -3.371 -0.311 -2.102 1.688 -0.451 172s > 172s > print( residuals( fitw2slsd1 ) ) 172s demand supply 172s 1 1.3775 -0.4348 172s 2 0.0125 -1.2131 172s 3 2.9728 1.7090 172s 4 2.2121 0.7956 172s 5 1.6920 1.5942 172s 6 1.0407 0.6595 172s 7 1.4768 1.4346 172s 8 -2.7583 -4.8724 172s 9 -1.6807 -2.3975 172s 10 1.4265 3.1427 172s 11 -0.2029 0.0689 172s 12 -1.5123 -1.3978 172s 13 -0.4958 -1.1136 172s 14 -0.1528 1.1684 172s 15 0.8692 3.4865 172s 16 -4.0547 -3.8285 172s 17 -2.5309 0.6793 172s 18 -1.8070 -2.7713 172s 19 1.9299 2.6668 172s 20 0.1853 0.6235 172s > print( residuals( fitw2slsd1$eq[[ 2 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 172s -0.4348 -1.2131 1.7090 0.7956 1.5942 0.6595 1.4346 -4.8724 -2.3975 3.1427 172s 11 12 13 14 15 16 17 18 19 20 172s 0.0689 -1.3978 -1.1136 1.1684 3.4865 -3.8285 0.6793 -2.7713 2.6668 0.6235 172s > 172s > print( residuals( fitw2slsd2e ) ) 172s demand supply 172s 1 1.100 0.3346 172s 2 -0.192 -0.5581 172s 3 2.785 2.2852 172s 4 2.012 1.2953 172s 5 1.849 1.8966 172s 6 1.145 0.9020 172s 7 1.573 1.6164 172s 8 -2.722 -4.8395 172s 9 -1.531 -2.3946 172s 10 1.629 3.1810 172s 11 -0.448 0.2403 172s 12 -1.988 -1.1944 172s 13 -0.972 -1.0393 172s 14 -0.271 1.0594 172s 15 1.251 3.0723 172s 16 -3.782 -4.3726 172s 17 -1.904 0.0471 172s 18 -1.823 -3.3644 172s 19 1.992 2.0193 172s 20 0.298 -0.1866 172s > print( residuals( fitw2slsd2e$eq[[ 1 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 172s 1.100 -0.192 2.785 2.012 1.849 1.145 1.573 -2.722 -1.531 1.629 -0.448 172s 12 13 14 15 16 17 18 19 20 172s -1.988 -0.972 -0.271 1.251 -3.782 -1.904 -1.823 1.992 0.298 172s > 172s > print( residuals( fitw2slsd3e ) ) 172s demand supply 172s 1 1.100 0.3346 172s 2 -0.192 -0.5581 172s 3 2.785 2.2852 172s 4 2.012 1.2953 172s 5 1.849 1.8966 172s 6 1.145 0.9020 172s 7 1.573 1.6164 172s 8 -2.722 -4.8395 172s 9 -1.531 -2.3946 172s 10 1.629 3.1810 172s 11 -0.448 0.2403 172s 12 -1.988 -1.1944 172s 13 -0.972 -1.0393 172s 14 -0.271 1.0594 172s 15 1.251 3.0723 172s 16 -3.782 -4.3726 172s 17 -1.904 0.0471 172s 18 -1.823 -3.3644 172s 19 1.992 2.0193 172s 20 0.298 -0.1866 172s > print( residuals( fitw2slsd3e$eq[[ 2 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 172s 0.3346 -0.5581 2.2852 1.2953 1.8966 0.9020 1.6164 -4.8395 -2.3946 3.1810 172s 11 12 13 14 15 16 17 18 19 20 172s 0.2403 -1.1944 -1.0393 1.0594 3.0723 -4.3726 0.0471 -3.3644 2.0193 -0.1866 172s > 172s > 172s > ## *************** coefficients ********************* 172s > print( round( coef( fitw2sls1e ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income supply_(Intercept) 172s 94.633 -0.244 0.314 49.532 172s supply_price supply_farmPrice supply_trend 172s 0.240 0.256 0.253 172s > print( round( coef( fitw2sls1e$eq[[ 2 ]] ), digits = 6 ) ) 172s (Intercept) price farmPrice trend 172s 49.532 0.240 0.256 0.253 172s > 172s > print( round( coef( fitw2slsd2e ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income supply_(Intercept) 172s 104.464 -0.363 0.336 47.071 172s supply_price supply_farmPrice supply_trend 172s 0.245 0.267 0.336 172s > print( round( coef( fitw2slsd2e$eq[[ 1 ]] ), digits = 6 ) ) 172s (Intercept) price income 172s 104.464 -0.363 0.336 172s > 172s > print( round( coef( fitw2slsd3e ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income supply_(Intercept) 172s 104.464 -0.363 0.336 47.071 172s supply_price supply_farmPrice supply_trend 172s 0.245 0.267 0.336 172s > print( round( coef( fitw2slsd3e, modified.regMat = TRUE ), digits = 6 ) ) 172s C1 C2 C3 C4 C5 C6 172s 104.464 -0.363 0.336 47.071 0.245 0.267 172s > print( round( coef( fitw2slsd3e$eq[[ 2 ]] ), digits = 6 ) ) 172s (Intercept) price farmPrice trend 172s 47.071 0.245 0.267 0.336 172s > 172s > print( round( coef( fitw2sls4 ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income supply_(Intercept) 172s 95.304 -0.243 0.306 46.423 172s supply_price supply_farmPrice supply_trend 172s 0.257 0.264 0.306 172s > print( round( coef( fitw2sls4$eq[[ 1 ]] ), digits = 6 ) ) 172s (Intercept) price income 172s 95.304 -0.243 0.306 172s > 172s > print( round( coef( fitw2sls5 ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income supply_(Intercept) 172s 95.304 -0.243 0.306 46.423 172s supply_price supply_farmPrice supply_trend 172s 0.257 0.264 0.306 172s > print( round( coef( fitw2sls5, modified.regMat = TRUE ), digits = 6 ) ) 172s C1 C2 C3 C4 C5 C6 172s 95.304 -0.243 0.306 46.423 0.257 0.264 172s > print( round( coef( fitw2sls5$eq[[ 2 ]] ), digits = 6 ) ) 172s (Intercept) price farmPrice trend 172s 46.423 0.257 0.264 0.306 172s > 172s > 172s > ## *************** coefficients with stats ********************* 172s > print( round( coef( summary( fitw2sls1e, useDfSys = FALSE ) ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 94.633 7.3027 12.96 0.000000 172s demand_price -0.244 0.0890 -2.74 0.014016 172s demand_income 0.314 0.0433 7.25 0.000001 172s supply_(Intercept) 49.532 10.7425 4.61 0.000289 172s supply_price 0.240 0.0894 2.69 0.016234 172s supply_farmPrice 0.256 0.0423 6.05 0.000017 172s supply_trend 0.253 0.0891 2.84 0.011883 172s > print( round( coef( summary( fitw2sls1e$eq[[ 2 ]], useDfSys = FALSE ) ), 172s + digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 49.532 10.7425 4.61 0.000289 172s price 0.240 0.0894 2.69 0.016234 172s farmPrice 0.256 0.0423 6.05 0.000017 172s trend 0.253 0.0891 2.84 0.011883 172s > 172s > print( round( coef( summary( fitw2slsd2e ) ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 104.464 9.7929 10.67 0.00000 172s demand_price -0.363 0.1220 -2.98 0.00534 172s demand_income 0.336 0.0444 7.57 0.00000 172s supply_(Intercept) 47.071 10.6890 4.40 0.00010 172s supply_price 0.245 0.0910 2.69 0.01093 172s supply_farmPrice 0.267 0.0416 6.41 0.00000 172s supply_trend 0.336 0.0444 7.57 0.00000 172s > print( round( coef( summary( fitw2slsd2e$eq[[ 1 ]] ) ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 104.464 9.7929 10.67 0.00000 172s price -0.363 0.1220 -2.98 0.00534 172s income 0.336 0.0444 7.57 0.00000 172s > 172s > print( round( coef( summary( fitw2slsd3e, useDfSys = FALSE ) ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 104.464 9.7929 10.67 0.000000 172s demand_price -0.363 0.1220 -2.98 0.008475 172s demand_income 0.336 0.0444 7.57 0.000001 172s supply_(Intercept) 47.071 10.6890 4.40 0.000444 172s supply_price 0.245 0.0910 2.69 0.016014 172s supply_farmPrice 0.267 0.0416 6.41 0.000009 172s supply_trend 0.336 0.0444 7.57 0.000001 172s > print( round( coef( summary( fitw2slsd3e, useDfSys = FALSE ), 172s + modified.regMat = TRUE ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s C1 104.464 9.7929 10.67 NA 172s C2 -0.363 0.1220 -2.98 NA 172s C3 0.336 0.0444 7.57 NA 172s C4 47.071 10.6890 4.40 NA 172s C5 0.245 0.0910 2.69 NA 172s C6 0.267 0.0416 6.41 NA 172s > print( round( coef( summary( fitw2slsd3e$eq[[ 2 ]], useDfSys = FALSE ) ), 172s + digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 47.071 10.6890 4.40 0.000444 172s price 0.245 0.0910 2.69 0.016014 172s farmPrice 0.267 0.0416 6.41 0.000009 172s trend 0.336 0.0444 7.57 0.000001 172s > 172s > print( round( coef( summary( fitw2sls4 ) ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 95.304 6.3056 15.11 0.000000 172s demand_price -0.243 0.0684 -3.55 0.001128 172s demand_income 0.306 0.0394 7.78 0.000000 172s supply_(Intercept) 46.423 8.3296 5.57 0.000003 172s supply_price 0.257 0.0684 3.76 0.000622 172s supply_farmPrice 0.264 0.0455 5.80 0.000001 172s supply_trend 0.306 0.0394 7.78 0.000000 172s > print( round( coef( summary( fitw2sls4$eq[[ 1 ]] ) ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 95.304 6.3056 15.11 0.00000 172s price -0.243 0.0684 -3.55 0.00113 172s income 0.306 0.0394 7.78 0.00000 172s > 172s > print( round( coef( summary( fitw2sls5 ) ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s demand_(Intercept) 95.304 6.3056 15.11 0.000000 172s demand_price -0.243 0.0684 -3.55 0.001128 172s demand_income 0.306 0.0394 7.78 0.000000 172s supply_(Intercept) 46.423 8.3296 5.57 0.000003 172s supply_price 0.257 0.0684 3.76 0.000622 172s supply_farmPrice 0.264 0.0455 5.80 0.000001 172s supply_trend 0.306 0.0394 7.78 0.000000 172s > print( round( coef( summary( fitw2sls5 ), modified.regMat = TRUE ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s C1 95.304 6.3056 15.11 0.000000 172s C2 -0.243 0.0684 -3.55 0.001128 172s C3 0.306 0.0394 7.78 0.000000 172s C4 46.423 8.3296 5.57 0.000003 172s C5 0.257 0.0684 3.76 0.000622 172s C6 0.264 0.0455 5.80 0.000001 172s > print( round( coef( summary( fitw2sls5$eq[[ 2 ]] ) ), digits = 6 ) ) 172s Estimate Std. Error t value Pr(>|t|) 172s (Intercept) 46.423 8.3296 5.57 0.000003 172s price 0.257 0.0684 3.76 0.000622 172s farmPrice 0.264 0.0455 5.80 0.000001 172s trend 0.306 0.0394 7.78 0.000000 172s > 172s > 172s > ## *********** variance covariance matrix of the coefficients ******* 172s > print( round( vcov( fitw2sls1e ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income 172s demand_(Intercept) 53.3287 -0.57241 0.04191 172s demand_price -0.5724 0.00791 -0.00225 172s demand_income 0.0419 -0.00225 0.00187 172s supply_(Intercept) 0.0000 0.00000 0.00000 172s supply_price 0.0000 0.00000 0.00000 172s supply_farmPrice 0.0000 0.00000 0.00000 172s supply_trend 0.0000 0.00000 0.00000 172s supply_(Intercept) supply_price supply_farmPrice 172s demand_(Intercept) 0.000 0.000000 0.000000 172s demand_price 0.000 0.000000 0.000000 172s demand_income 0.000 0.000000 0.000000 172s supply_(Intercept) 115.402 -0.876328 -0.259055 172s supply_price -0.876 0.007989 0.000749 172s supply_farmPrice -0.259 0.000749 0.001786 172s supply_trend -0.236 0.000463 0.001101 172s supply_trend 172s demand_(Intercept) 0.000000 172s demand_price 0.000000 172s demand_income 0.000000 172s supply_(Intercept) -0.236183 172s supply_price 0.000463 172s supply_farmPrice 0.001101 172s supply_trend 0.007945 172s > print( round( vcov( fitw2sls1e$eq[[ 2 ]] ), digits = 6 ) ) 172s (Intercept) price farmPrice trend 172s (Intercept) 115.402 -0.876328 -0.259055 -0.236183 172s price -0.876 0.007989 0.000749 0.000463 172s farmPrice -0.259 0.000749 0.001786 0.001101 172s trend -0.236 0.000463 0.001101 0.007945 172s > 172s > print( round( vcov( fitw2sls2 ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income 172s demand_(Intercept) 64.14482 -0.679629 0.041312 172s demand_price -0.67963 0.008954 -0.002214 172s demand_income 0.04131 -0.002214 0.001847 172s supply_(Intercept) -1.22810 0.065809 -0.054894 172s supply_price 0.00241 -0.000129 0.000108 172s supply_farmPrice 0.00573 -0.000307 0.000256 172s supply_trend 0.04131 -0.002214 0.001847 172s supply_(Intercept) supply_price supply_farmPrice 172s demand_(Intercept) -1.2281 0.002409 0.005727 172s demand_price 0.0658 -0.000129 -0.000307 172s demand_income -0.0549 0.000108 0.000256 172s supply_(Intercept) 139.2416 -1.098376 -0.294954 172s supply_price -1.0984 0.010116 0.000884 172s supply_farmPrice -0.2950 0.000884 0.002109 172s supply_trend -0.0549 0.000108 0.000256 172s supply_trend 172s demand_(Intercept) 0.041312 172s demand_price -0.002214 172s demand_income 0.001847 172s supply_(Intercept) -0.054894 172s supply_price 0.000108 172s supply_farmPrice 0.000256 172s supply_trend 0.001847 172s > print( round( vcov( fitw2sls2$eq[[ 1 ]] ), digits = 6 ) ) 172s (Intercept) price income 172s (Intercept) 64.1448 -0.67963 0.04131 172s price -0.6796 0.00895 -0.00221 172s income 0.0413 -0.00221 0.00185 172s > 172s > print( round( vcov( fitw2sls3e ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income 172s demand_(Intercept) 54.51421 -0.577209 0.034718 172s demand_price -0.57721 0.007585 -0.001860 172s demand_income 0.03472 -0.001860 0.001552 172s supply_(Intercept) -1.03208 0.055305 -0.046132 172s supply_price 0.00202 -0.000108 0.000090 172s supply_farmPrice 0.00481 -0.000258 0.000215 172s supply_trend 0.03472 -0.001860 0.001552 172s supply_(Intercept) supply_price supply_farmPrice 172s demand_(Intercept) -1.0321 0.002024 0.004813 172s demand_price 0.0553 -0.000108 -0.000258 172s demand_income -0.0461 0.000090 0.000215 172s supply_(Intercept) 111.4592 -0.878830 -0.236271 172s supply_price -0.8788 0.008093 0.000708 172s supply_farmPrice -0.2363 0.000708 0.001689 172s supply_trend -0.0461 0.000090 0.000215 172s supply_trend 172s demand_(Intercept) 0.034718 172s demand_price -0.001860 172s demand_income 0.001552 172s supply_(Intercept) -0.046132 172s supply_price 0.000090 172s supply_farmPrice 0.000215 172s supply_trend 0.001552 172s > print( round( vcov( fitw2sls3e, modified.regMat = TRUE ), digits = 6 ) ) 172s C1 C2 C3 C4 C5 C6 172s C1 54.51421 -0.577209 0.034718 -1.0321 0.002024 0.004813 172s C2 -0.57721 0.007585 -0.001860 0.0553 -0.000108 -0.000258 172s C3 0.03472 -0.001860 0.001552 -0.0461 0.000090 0.000215 172s C4 -1.03208 0.055305 -0.046132 111.4592 -0.878830 -0.236271 172s C5 0.00202 -0.000108 0.000090 -0.8788 0.008093 0.000708 172s C6 0.00481 -0.000258 0.000215 -0.2363 0.000708 0.001689 172s > print( round( vcov( fitw2sls3e$eq[[ 2 ]] ), digits = 6 ) ) 172s (Intercept) price farmPrice trend 172s (Intercept) 111.4592 -0.878830 -0.236271 -0.046132 172s price -0.8788 0.008093 0.000708 0.000090 172s farmPrice -0.2363 0.000708 0.001689 0.000215 172s trend -0.0461 0.000090 0.000215 0.001552 172s > 172s > print( round( vcov( fitw2sls4 ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income 172s demand_(Intercept) 39.7610 -0.358128 -0.03842 172s demand_price -0.3581 0.004681 -0.00113 172s demand_income -0.0384 -0.001129 0.00155 172s supply_(Intercept) 39.6949 -0.480685 0.08595 172s supply_price -0.3581 0.004681 -0.00113 172s supply_farmPrice -0.0359 0.000252 0.00011 172s supply_trend -0.0384 -0.001129 0.00155 172s supply_(Intercept) supply_price supply_farmPrice 172s demand_(Intercept) 39.6949 -0.358128 -0.035932 172s demand_price -0.4807 0.004681 0.000252 172s demand_income 0.0859 -0.001129 0.000110 172s supply_(Intercept) 69.3817 -0.480685 -0.226588 172s supply_price -0.4807 0.004681 0.000252 172s supply_farmPrice -0.2266 0.000252 0.002072 172s supply_trend 0.0859 -0.001129 0.000110 172s supply_trend 172s demand_(Intercept) -0.03842 172s demand_price -0.00113 172s demand_income 0.00155 172s supply_(Intercept) 0.08595 172s supply_price -0.00113 172s supply_farmPrice 0.00011 172s supply_trend 0.00155 172s > print( round( vcov( fitw2sls4$eq[[ 1 ]] ), digits = 6 ) ) 172s (Intercept) price income 172s (Intercept) 39.7610 -0.35813 -0.03842 172s price -0.3581 0.00468 -0.00113 172s income -0.0384 -0.00113 0.00155 172s > 172s > print( round( vcov( fitw2sls5 ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income 172s demand_(Intercept) 39.7610 -0.358128 -0.03842 172s demand_price -0.3581 0.004681 -0.00113 172s demand_income -0.0384 -0.001129 0.00155 172s supply_(Intercept) 39.6949 -0.480685 0.08595 172s supply_price -0.3581 0.004681 -0.00113 172s supply_farmPrice -0.0359 0.000252 0.00011 172s supply_trend -0.0384 -0.001129 0.00155 172s supply_(Intercept) supply_price supply_farmPrice 172s demand_(Intercept) 39.6949 -0.358128 -0.035932 172s demand_price -0.4807 0.004681 0.000252 172s demand_income 0.0859 -0.001129 0.000110 172s supply_(Intercept) 69.3817 -0.480685 -0.226588 172s supply_price -0.4807 0.004681 0.000252 172s supply_farmPrice -0.2266 0.000252 0.002072 172s supply_trend 0.0859 -0.001129 0.000110 172s supply_trend 172s demand_(Intercept) -0.03842 172s demand_price -0.00113 172s demand_income 0.00155 172s supply_(Intercept) 0.08595 172s supply_price -0.00113 172s supply_farmPrice 0.00011 172s supply_trend 0.00155 172s > print( round( vcov( fitw2sls5, modified.regMat = TRUE ), digits = 6 ) ) 172s C1 C2 C3 C4 C5 C6 172s C1 39.7610 -0.358128 -0.03842 39.6949 -0.358128 -0.035932 172s C2 -0.3581 0.004681 -0.00113 -0.4807 0.004681 0.000252 172s C3 -0.0384 -0.001129 0.00155 0.0859 -0.001129 0.000110 172s C4 39.6949 -0.480685 0.08595 69.3817 -0.480685 -0.226588 172s C5 -0.3581 0.004681 -0.00113 -0.4807 0.004681 0.000252 172s C6 -0.0359 0.000252 0.00011 -0.2266 0.000252 0.002072 172s > print( round( vcov( fitw2sls5$eq[[ 2 ]] ), digits = 6 ) ) 172s (Intercept) price farmPrice trend 172s (Intercept) 69.3817 -0.480685 -0.226588 0.08595 172s price -0.4807 0.004681 0.000252 -0.00113 172s farmPrice -0.2266 0.000252 0.002072 0.00011 172s trend 0.0859 -0.001129 0.000110 0.00155 172s > 172s > print( round( vcov( fitw2slsd1 ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income 172s demand_(Intercept) 124.179 -1.51767 0.28519 172s demand_price -1.518 0.02098 -0.00595 172s demand_income 0.285 -0.00595 0.00318 172s supply_(Intercept) 0.000 0.00000 0.00000 172s supply_price 0.000 0.00000 0.00000 172s supply_farmPrice 0.000 0.00000 0.00000 172s supply_trend 0.000 0.00000 0.00000 172s supply_(Intercept) supply_price supply_farmPrice 172s demand_(Intercept) 0.000 0.000000 0.000000 172s demand_price 0.000 0.000000 0.000000 172s demand_income 0.000 0.000000 0.000000 172s supply_(Intercept) 144.253 -1.095410 -0.323818 172s supply_price -1.095 0.009987 0.000936 172s supply_farmPrice -0.324 0.000936 0.002233 172s supply_trend -0.295 0.000579 0.001377 172s supply_trend 172s demand_(Intercept) 0.000000 172s demand_price 0.000000 172s demand_income 0.000000 172s supply_(Intercept) -0.295229 172s supply_price 0.000579 172s supply_farmPrice 0.001377 172s supply_trend 0.009931 172s > print( round( vcov( fitw2slsd1$eq[[ 1 ]] ), digits = 6 ) ) 172s (Intercept) price income 172s (Intercept) 124.179 -1.51767 0.28519 172s price -1.518 0.02098 -0.00595 172s income 0.285 -0.00595 0.00318 172s > 172s > print( round( vcov( fitw2slsd2e ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income 172s demand_(Intercept) 95.9017 -1.129212 0.176368 172s demand_price -1.1292 0.014881 -0.003682 172s demand_income 0.1764 -0.003682 0.001968 172s supply_(Intercept) -5.2430 0.109460 -0.058492 172s supply_price 0.0103 -0.000215 0.000115 172s supply_farmPrice 0.0245 -0.000510 0.000273 172s supply_trend 0.1764 -0.003682 0.001968 172s supply_(Intercept) supply_price supply_farmPrice 172s demand_(Intercept) -5.2430 0.010284 0.024451 172s demand_price 0.1095 -0.000215 -0.000510 172s demand_income -0.0585 0.000115 0.000273 172s supply_(Intercept) 114.2555 -0.898881 -0.243056 172s supply_price -0.8989 0.008273 0.000727 172s supply_farmPrice -0.2431 0.000727 0.001733 172s supply_trend -0.0585 0.000115 0.000273 172s supply_trend 172s demand_(Intercept) 0.176368 172s demand_price -0.003682 172s demand_income 0.001968 172s supply_(Intercept) -0.058492 172s supply_price 0.000115 172s supply_farmPrice 0.000273 172s supply_trend 0.001968 172s > print( round( vcov( fitw2slsd2e$eq[[ 2 ]] ), digits = 6 ) ) 172s (Intercept) price farmPrice trend 172s (Intercept) 114.2555 -0.898881 -0.243056 -0.058492 172s price -0.8989 0.008273 0.000727 0.000115 172s farmPrice -0.2431 0.000727 0.001733 0.000273 172s trend -0.0585 0.000115 0.000273 0.001968 172s > 172s > print( round( vcov( fitw2slsd3 ), digits = 6 ) ) 172s demand_(Intercept) demand_price demand_income 172s demand_(Intercept) 113.0903 -1.334011 0.210445 172s demand_price -1.3340 0.017622 -0.004394 172s demand_income 0.2104 -0.004394 0.002348 172s supply_(Intercept) -6.2560 0.130609 -0.069794 172s supply_price 0.0123 -0.000256 0.000137 172s supply_farmPrice 0.0292 -0.000609 0.000325 172s supply_trend 0.2104 -0.004394 0.002348 172s supply_(Intercept) supply_price supply_farmPrice 172s demand_(Intercept) -6.2560 0.012271 0.029175 172s demand_price 0.1306 -0.000256 -0.000609 172s demand_income -0.0698 0.000137 0.000325 172s supply_(Intercept) 142.7207 -1.123408 -0.303360 172s supply_price -1.1234 0.010341 0.000908 172s supply_farmPrice -0.3034 0.000908 0.002165 172s supply_trend -0.0698 0.000137 0.000325 172s supply_trend 172s demand_(Intercept) 0.210445 172s demand_price -0.004394 172s demand_income 0.002348 172s supply_(Intercept) -0.069794 172s supply_price 0.000137 172s supply_farmPrice 0.000325 172s supply_trend 0.002348 172s > print( round( vcov( fitw2slsd3, modified.regMat = TRUE ), digits = 6 ) ) 172s C1 C2 C3 C4 C5 C6 172s C1 113.0903 -1.334011 0.210445 -6.2560 0.012271 0.029175 172s C2 -1.3340 0.017622 -0.004394 0.1306 -0.000256 -0.000609 172s C3 0.2104 -0.004394 0.002348 -0.0698 0.000137 0.000325 172s C4 -6.2560 0.130609 -0.069794 142.7207 -1.123408 -0.303360 172s C5 0.0123 -0.000256 0.000137 -1.1234 0.010341 0.000908 172s C6 0.0292 -0.000609 0.000325 -0.3034 0.000908 0.002165 172s > print( round( vcov( fitw2slsd3$eq[[ 1 ]] ), digits = 6 ) ) 172s (Intercept) price income 172s (Intercept) 113.09 -1.33401 0.21044 172s price -1.33 0.01762 -0.00439 172s income 0.21 -0.00439 0.00235 172s > 172s > 172s > ## *********** confidence intervals of coefficients ************* 172s > print( confint( fitw2sls1e, useDfSys = TRUE ) ) 172s 2.5 % 97.5 % 172s demand_(Intercept) 79.776 109.491 172s demand_price -0.425 -0.063 172s demand_income 0.226 0.402 172s supply_(Intercept) 27.677 71.388 172s supply_price 0.058 0.422 172s supply_farmPrice 0.170 0.342 172s supply_trend 0.072 0.434 172s > print( confint( fitw2sls1e$eq[[ 1 ]], level = 0.9, useDfSys = TRUE ) ) 172s 5 % 95 % 172s (Intercept) 82.275 106.992 172s price -0.394 -0.093 172s income 0.241 0.387 172s > 172s > print( confint( fitw2sls2, level = 0.9 ) ) 172s 5 % 95 % 172s demand_(Intercept) 78.107 110.660 172s demand_price -0.422 -0.038 172s demand_income 0.215 0.390 172s supply_(Intercept) 24.069 72.030 172s supply_price 0.039 0.447 172s supply_farmPrice 0.169 0.356 172s supply_trend 0.215 0.390 172s > print( confint( fitw2sls2$eq[[ 2 ]], level = 0.99 ) ) 172s 0.5 % 99.5 % 172s (Intercept) 15.854 80.245 172s price -0.031 0.517 172s farmPrice 0.137 0.388 172s trend 0.186 0.420 172s > 172s > print( confint( fitw2sls3, level = 0.99 ) ) 172s 0.5 % 99.5 % 172s demand_(Intercept) 78.107 110.660 172s demand_price -0.422 -0.038 172s demand_income 0.215 0.390 172s supply_(Intercept) 24.069 72.030 172s supply_price 0.039 0.447 172s supply_farmPrice 0.169 0.356 172s supply_trend 0.215 0.390 172s > print( confint( fitw2sls3$eq[[ 1 ]], level = 0.5 ) ) 172s 25 % 75 % 172s (Intercept) 88.923 99.844 172s price -0.295 -0.166 172s income 0.274 0.332 172s > 172s > print( confint( fitw2sls4e, level = 0.5, useDfSys = TRUE ) ) 172s 25 % 75 % 172s demand_(Intercept) 83.658 107.036 172s demand_price -0.369 -0.117 172s demand_income 0.233 0.379 172s supply_(Intercept) 31.138 61.736 172s supply_price 0.131 0.383 172s supply_farmPrice 0.181 0.347 172s supply_trend 0.233 0.379 172s > print( confint( fitw2sls4e$eq[[ 2 ]], level = 0.25, useDfSys = TRUE ) ) 172s 37.5 % 62.5 % 172s (Intercept) 44.016 48.857 172s price 0.237 0.277 172s farmPrice 0.251 0.277 172s trend 0.294 0.317 172s > 172s > print( confint( fitw2sls5, level = 0.25 ) ) 172s 37.5 % 62.5 % 172s demand_(Intercept) 82.503 108.105 172s demand_price -0.382 -0.104 172s demand_income 0.226 0.386 172s supply_(Intercept) 29.513 63.333 172s supply_price 0.118 0.396 172s supply_farmPrice 0.172 0.357 172s supply_trend 0.226 0.386 172s > print( confint( fitw2sls5$eq[[ 1 ]], level = 0.975 ) ) 172s 1.3 % 98.8 % 172s (Intercept) 80.537 110.072 172s price -0.403 -0.083 172s income 0.214 0.399 172s > 172s > print( confint( fitw2slsd1, level = 0.975 ) ) 172s 1.3 % 98.8 % 172s demand_(Intercept) 83.279 130.300 172s demand_price -0.717 -0.106 172s demand_income 0.243 0.481 172s supply_(Intercept) 24.071 74.994 172s supply_price 0.028 0.452 172s supply_farmPrice 0.155 0.356 172s supply_trend 0.042 0.464 172s > print( confint( fitw2slsd1$eq[[ 2 ]], level = 0.999 ) ) 172s 0.1 % 100 % 172s (Intercept) 1.310 97.755 172s price -0.161 0.641 172s farmPrice 0.066 0.445 172s trend -0.147 0.653 172s > 172s > print( confint( fitw2slsd2e, level = 0.999, useDfSys = TRUE ) ) 172s 0.1 % 100 % 172s demand_(Intercept) 84.562 124.365 172s demand_price -0.611 -0.115 172s demand_income 0.246 0.426 172s supply_(Intercept) 25.348 68.793 172s supply_price 0.060 0.430 172s supply_farmPrice 0.182 0.352 172s supply_trend 0.246 0.426 172s > print( confint( fitw2slsd2e$eq[[ 1 ]], level = 0.01, useDfSys = TRUE ) ) 172s 49.5 % 50.5 % 172s (Intercept) 104.340 104.587 172s price -0.365 -0.362 172s income 0.335 0.336 172s > 172s > print( confint( fitw2slsd3e, level = 0.01, useDfSys = TRUE ) ) 172s 49.5 % 50.5 % 172s demand_(Intercept) 84.562 124.365 172s demand_price -0.611 -0.115 172s demand_income 0.246 0.426 172s supply_(Intercept) 25.348 68.793 172s supply_price 0.060 0.430 172s supply_farmPrice 0.182 0.352 172s supply_trend 0.246 0.426 172s > print( confint( fitw2slsd3e$eq[[ 2 ]], useDfSys = TRUE ) ) 172s 2.5 % 97.5 % 172s (Intercept) 25.348 68.793 172s price 0.060 0.430 172s farmPrice 0.182 0.352 172s trend 0.246 0.426 172s > 172s > 172s > ## *********** fitted values ************* 172s > print( fitted( fitw2sls1e ) ) 172s demand supply 172s 1 97.6 98.9 172s 2 99.9 100.4 172s 3 99.8 100.5 172s 4 100.0 100.7 172s 5 102.1 102.6 172s 6 102.0 102.6 172s 7 102.4 102.6 172s 8 103.0 104.8 172s 9 101.5 102.7 172s 10 100.3 99.7 172s 11 95.5 95.4 172s 12 94.7 93.8 172s 13 96.1 95.6 172s 14 99.0 97.6 172s 15 103.8 102.3 172s 16 103.7 104.1 172s 17 103.8 102.8 172s 18 102.1 102.7 172s 19 103.6 102.6 172s 20 106.9 105.6 172s > print( fitted( fitw2sls1e$eq[[ 1 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 12 13 172s 97.6 99.9 99.8 100.0 102.1 102.0 102.4 103.0 101.5 100.3 95.5 94.7 96.1 172s 14 15 16 17 18 19 20 172s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 172s > 172s > print( fitted( fitw2sls2 ) ) 172s demand supply 172s 1 97.8 98.5 172s 2 99.9 100.0 172s 3 99.9 100.1 172s 4 100.1 100.4 172s 5 102.0 102.5 172s 6 101.9 102.4 172s 7 102.4 102.4 172s 8 102.9 104.8 172s 9 101.4 102.7 172s 10 100.3 99.7 172s 11 95.7 95.3 172s 12 94.9 93.7 172s 13 96.3 95.6 172s 14 99.1 97.7 172s 15 103.7 102.6 172s 16 103.5 104.4 172s 17 103.7 103.2 172s 18 102.1 103.1 172s 19 103.6 102.9 172s 20 106.8 106.1 172s > print( fitted( fitw2sls2$eq[[ 2 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 12 13 172s 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 172s 14 15 16 17 18 19 20 172s 97.7 102.6 104.4 103.2 103.1 102.9 106.1 172s > 172s > print( fitted( fitw2sls3 ) ) 172s demand supply 172s 1 97.8 98.5 172s 2 99.9 100.0 172s 3 99.9 100.1 172s 4 100.1 100.4 172s 5 102.0 102.5 172s 6 101.9 102.4 172s 7 102.4 102.4 172s 8 102.9 104.8 172s 9 101.4 102.7 172s 10 100.3 99.7 172s 11 95.7 95.3 172s 12 94.9 93.7 172s 13 96.3 95.6 172s 14 99.1 97.7 172s 15 103.7 102.6 172s 16 103.5 104.4 172s 17 103.7 103.2 172s 18 102.1 103.1 172s 19 103.6 102.9 172s 20 106.8 106.1 172s > print( fitted( fitw2sls3$eq[[ 1 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 12 13 172s 97.8 99.9 99.9 100.1 102.0 101.9 102.4 102.9 101.4 100.3 95.7 94.9 96.3 172s 14 15 16 17 18 19 20 172s 99.1 103.7 103.5 103.7 102.1 103.6 106.8 172s > 172s > print( fitted( fitw2sls4e ) ) 172s demand supply 172s 1 97.7 98.4 172s 2 99.9 100.0 172s 3 99.8 100.1 172s 4 100.0 100.5 172s 5 102.1 102.4 172s 6 101.9 102.4 172s 7 102.4 102.5 172s 8 102.9 104.8 172s 9 101.5 102.7 172s 10 100.4 99.5 172s 11 95.7 95.1 172s 12 94.9 93.6 172s 13 96.2 95.6 172s 14 99.1 97.6 172s 15 103.8 102.5 172s 16 103.6 104.4 172s 17 103.8 103.1 172s 18 102.0 103.1 172s 19 103.5 103.0 172s 20 106.7 106.3 172s > print( fitted( fitw2sls4e$eq[[ 2 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 12 13 172s 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 172s 14 15 16 17 18 19 20 172s 97.6 102.5 104.4 103.1 103.1 103.0 106.3 172s > 172s > print( fitted( fitw2sls5 ) ) 172s demand supply 172s 1 97.7 98.4 172s 2 99.9 100.0 172s 3 99.8 100.1 172s 4 100.0 100.5 172s 5 102.1 102.4 172s 6 101.9 102.4 172s 7 102.4 102.5 172s 8 102.9 104.8 172s 9 101.5 102.7 172s 10 100.4 99.5 172s 11 95.7 95.1 172s 12 94.9 93.6 172s 13 96.2 95.6 172s 14 99.1 97.6 172s 15 103.8 102.5 172s 16 103.6 104.4 172s 17 103.8 103.1 172s 18 102.0 103.1 172s 19 103.5 103.0 172s 20 106.7 106.3 172s > print( fitted( fitw2sls5$eq[[ 1 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 12 13 172s 97.7 99.9 99.8 100.0 102.1 101.9 102.4 102.9 101.5 100.4 95.7 94.9 96.2 172s 14 15 16 17 18 19 20 172s 99.1 103.8 103.6 103.8 102.0 103.5 106.7 172s > 172s > print( fitted( fitw2slsd1 ) ) 172s demand supply 172s 1 97.1 98.9 172s 2 99.2 100.4 172s 3 99.2 100.5 172s 4 99.3 100.7 172s 5 102.5 102.6 172s 6 102.2 102.6 172s 7 102.5 102.6 172s 8 102.7 104.8 172s 9 102.0 102.7 172s 10 101.4 99.7 172s 11 95.6 95.4 172s 12 93.9 93.8 172s 13 95.0 95.6 172s 14 98.9 97.6 172s 15 104.9 102.3 172s 16 104.3 104.1 172s 17 106.1 102.8 172s 18 101.7 102.7 172s 19 103.3 102.6 172s 20 106.0 105.6 172s > print( fitted( fitw2slsd1$eq[[ 2 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 12 13 172s 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 172s 14 15 16 17 18 19 20 172s 97.6 102.3 104.1 102.8 102.7 102.6 105.6 172s > 172s > print( fitted( fitw2slsd2e ) ) 172s demand supply 172s 1 97.4 98.2 172s 2 99.4 99.7 172s 3 99.4 99.9 172s 4 99.5 100.2 172s 5 102.4 102.3 172s 6 102.1 102.3 172s 7 102.4 102.4 172s 8 102.6 104.7 172s 9 101.9 102.7 172s 10 101.2 99.6 172s 11 95.9 95.2 172s 12 94.4 93.6 172s 13 95.5 95.6 172s 14 99.0 97.7 172s 15 104.5 102.7 172s 16 104.0 104.6 172s 17 105.4 103.5 172s 18 101.8 103.3 172s 19 103.2 103.2 172s 20 105.9 106.4 172s > print( fitted( fitw2slsd2e$eq[[ 1 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 12 13 172s 97.4 99.4 99.4 99.5 102.4 102.1 102.4 102.6 101.9 101.2 95.9 94.4 95.5 172s 14 15 16 17 18 19 20 172s 99.0 104.5 104.0 105.4 101.8 103.2 105.9 172s > 172s > print( fitted( fitw2slsd3e ) ) 172s demand supply 172s 1 97.4 98.2 172s 2 99.4 99.7 172s 3 99.4 99.9 172s 4 99.5 100.2 172s 5 102.4 102.3 172s 6 102.1 102.3 172s 7 102.4 102.4 172s 8 102.6 104.7 172s 9 101.9 102.7 172s 10 101.2 99.6 172s 11 95.9 95.2 172s 12 94.4 93.6 172s 13 95.5 95.6 172s 14 99.0 97.7 172s 15 104.5 102.7 172s 16 104.0 104.6 172s 17 105.4 103.5 172s 18 101.8 103.3 172s 19 103.2 103.2 172s 20 105.9 106.4 172s > print( fitted( fitw2slsd3e$eq[[ 2 ]] ) ) 172s 1 2 3 4 5 6 7 8 9 10 11 12 13 172s 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 172s 14 15 16 17 18 19 20 172s 97.7 102.7 104.6 103.5 103.3 103.2 106.4 172s > 172s > 172s > ## *********** predicted values ************* 172s > predictData <- Kmenta 172s > predictData$consump <- NULL 172s > predictData$price <- Kmenta$price * 0.9 172s > predictData$income <- Kmenta$income * 1.1 172s > 172s > print( predict( fitw2sls1e, se.fit = TRUE, interval = "prediction", 172s + useDfSys = TRUE ) ) 172s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 172s 1 97.6 0.609 93.5 101.8 98.9 0.965 172s 2 99.9 0.553 95.7 104.0 100.4 0.952 172s 3 99.8 0.520 95.7 103.9 100.5 0.861 172s 4 100.0 0.558 95.9 104.2 100.7 0.839 172s 5 102.1 0.476 98.0 106.2 102.6 0.818 172s 6 102.0 0.437 97.9 106.1 102.6 0.723 172s 7 102.4 0.454 98.3 106.5 102.6 0.658 172s 8 103.0 0.567 98.8 107.1 104.8 0.889 172s 9 101.5 0.502 97.3 105.6 102.7 0.723 172s 10 100.3 0.758 96.0 104.6 99.7 0.915 172s 11 95.5 0.888 91.2 99.9 95.4 1.098 172s 12 94.7 0.928 90.3 99.1 93.8 1.277 172s 13 96.1 0.844 91.8 100.5 95.6 1.137 172s 14 99.0 0.477 94.9 103.1 97.6 0.820 172s 15 103.8 0.731 99.6 108.1 102.3 0.804 172s 16 103.7 0.587 99.5 107.8 104.1 0.837 172s 17 103.8 1.243 99.1 108.6 102.8 1.489 172s 18 102.1 0.506 97.9 106.2 102.7 0.884 172s 19 103.6 0.641 99.4 107.8 102.6 1.010 172s 20 106.9 1.204 102.2 111.6 105.6 1.550 172s supply.lwr supply.upr 172s 1 93.5 104.3 172s 2 95.0 105.8 172s 3 95.2 105.8 172s 4 95.4 106.0 172s 5 97.4 107.9 172s 6 97.4 107.8 172s 7 97.4 107.7 172s 8 99.5 110.1 172s 9 97.5 108.0 172s 10 94.3 105.0 172s 11 89.9 100.8 172s 12 88.2 99.5 172s 13 90.1 101.2 172s 14 92.3 102.9 172s 15 97.1 107.6 172s 16 98.8 109.3 172s 17 97.0 108.7 172s 18 97.4 108.0 172s 19 97.2 108.0 172s 20 99.7 111.5 172s > print( predict( fitw2sls1e$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 172s + useDfSys = TRUE ) ) 172s fit se.fit lwr upr 172s 1 97.6 0.609 93.5 101.8 172s 2 99.9 0.553 95.7 104.0 172s 3 99.8 0.520 95.7 103.9 172s 4 100.0 0.558 95.9 104.2 172s 5 102.1 0.476 98.0 106.2 172s 6 102.0 0.437 97.9 106.1 172s 7 102.4 0.454 98.3 106.5 172s 8 103.0 0.567 98.8 107.1 172s 9 101.5 0.502 97.3 105.6 172s 10 100.3 0.758 96.0 104.6 172s 11 95.5 0.888 91.2 99.9 172s 12 94.7 0.928 90.3 99.1 172s 13 96.1 0.844 91.8 100.5 172s 14 99.0 0.477 94.9 103.1 172s 15 103.8 0.731 99.6 108.1 172s 16 103.7 0.587 99.5 107.8 172s 17 103.8 1.243 99.1 108.6 172s 18 102.1 0.506 97.9 106.2 172s 19 103.6 0.641 99.4 107.8 172s 20 106.9 1.204 102.2 111.6 172s > 172s > print( predict( fitw2sls2, se.pred = TRUE, interval = "confidence", 172s + level = 0.999, newdata = predictData ) ) 172s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 172s 1 102.7 2.22 99.1 106 96.0 2.75 172s 2 105.3 2.22 101.7 109 97.5 2.64 172s 3 105.2 2.23 101.5 109 97.6 2.65 172s 4 105.4 2.22 101.9 109 97.9 2.62 172s 5 107.3 2.51 101.8 113 100.1 2.83 172s 6 107.3 2.46 102.0 112 100.0 2.77 172s 7 107.8 2.44 102.7 113 100.0 2.71 172s 8 108.6 2.40 103.7 113 102.2 2.65 172s 9 106.6 2.52 101.0 112 100.4 2.87 172s 10 105.1 2.65 98.8 111 97.4 3.10 172s 11 100.1 2.41 95.2 105 93.0 3.18 172s 12 99.5 2.21 96.0 103 91.3 3.15 172s 13 101.2 2.12 98.5 104 93.1 2.95 172s 14 104.1 2.31 99.8 108 95.3 2.91 172s 15 109.0 2.73 102.3 116 100.2 2.92 172s 16 109.0 2.61 102.9 115 102.0 2.80 172s 17 108.6 3.08 100.1 117 101.1 3.37 172s 18 107.6 2.35 103.0 112 100.5 2.65 172s 19 109.3 2.44 104.2 114 100.4 2.64 172s 20 113.2 2.66 106.8 120 103.3 2.58 172s supply.lwr supply.upr 172s 1 91.7 100.3 172s 2 94.2 100.7 172s 3 94.2 101.0 172s 4 94.8 101.0 172s 5 95.1 105.0 172s 6 95.6 104.4 172s 7 96.1 103.9 172s 8 98.8 105.6 172s 9 95.2 105.6 172s 10 90.7 104.1 172s 11 85.9 100.1 172s 12 84.3 98.3 172s 13 87.3 98.9 172s 14 89.7 100.8 172s 15 94.7 105.8 172s 16 97.3 106.6 172s 17 92.9 109.4 172s 18 97.1 103.9 172s 19 97.1 103.6 172s 20 100.7 105.9 172s > print( predict( fitw2sls2$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 172s + level = 0.999, newdata = predictData ) ) 172s fit se.pred lwr upr 172s 1 96.0 2.75 91.7 100.3 172s 2 97.5 2.64 94.2 100.7 172s 3 97.6 2.65 94.2 101.0 172s 4 97.9 2.62 94.8 101.0 172s 5 100.1 2.83 95.1 105.0 172s 6 100.0 2.77 95.6 104.4 172s 7 100.0 2.71 96.1 103.9 172s 8 102.2 2.65 98.8 105.6 172s 9 100.4 2.87 95.2 105.6 172s 10 97.4 3.10 90.7 104.1 172s 11 93.0 3.18 85.9 100.1 172s 12 91.3 3.15 84.3 98.3 172s 13 93.1 2.95 87.3 98.9 172s 14 95.3 2.91 89.7 100.8 172s 15 100.2 2.92 94.7 105.8 172s 16 102.0 2.80 97.3 106.6 172s 17 101.1 3.37 92.9 109.4 172s 18 100.5 2.65 97.1 103.9 172s 19 100.4 2.64 97.1 103.6 172s 20 103.3 2.58 100.7 105.9 172s > 172s > print( predict( fitw2sls3, se.pred = TRUE, interval = "prediction", 172s + level = 0.975 ) ) 172s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 172s 1 97.8 2.08 92.9 103 98.5 2.57 172s 2 99.9 2.07 95.1 105 100.0 2.61 172s 3 99.9 2.06 95.0 105 100.1 2.59 172s 4 100.1 2.07 95.2 105 100.4 2.60 172s 5 102.0 2.05 97.2 107 102.5 2.63 172s 6 101.9 2.04 97.1 107 102.4 2.60 172s 7 102.4 2.04 97.6 107 102.4 2.58 172s 8 102.9 2.08 98.0 108 104.8 2.68 172s 9 101.4 2.06 96.6 106 102.7 2.61 172s 10 100.3 2.15 95.3 105 99.7 2.69 172s 11 95.7 2.19 90.6 101 95.3 2.77 172s 12 94.9 2.20 89.8 100 93.7 2.86 172s 13 96.3 2.16 91.2 101 95.6 2.79 172s 14 99.1 2.05 94.3 104 97.7 2.64 172s 15 103.7 2.13 98.7 109 102.6 2.60 172s 16 103.5 2.08 98.7 108 104.4 2.59 172s 17 103.7 2.39 98.1 109 103.2 2.91 172s 18 102.1 2.06 97.2 107 103.1 2.59 172s 19 103.6 2.10 98.6 108 102.9 2.64 172s 20 106.8 2.37 101.2 112 106.1 2.90 172s supply.lwr supply.upr 172s 1 92.4 104 172s 2 93.9 106 172s 3 94.0 106 172s 4 94.3 106 172s 5 96.3 109 172s 6 96.3 109 172s 7 96.4 109 172s 8 98.5 111 172s 9 96.6 109 172s 10 93.4 106 172s 11 88.8 102 172s 12 87.0 100 172s 13 89.1 102 172s 14 91.5 104 172s 15 96.5 109 172s 16 98.3 110 172s 17 96.4 110 172s 18 97.0 109 172s 19 96.8 109 172s 20 99.3 113 172s > print( predict( fitw2sls3$eq[[ 1 ]], se.pred = TRUE, interval = "prediction", 172s + level = 0.975 ) ) 172s fit se.pred lwr upr 172s 1 97.8 2.08 92.9 103 172s 2 99.9 2.07 95.1 105 172s 3 99.9 2.06 95.0 105 172s 4 100.1 2.07 95.2 105 172s 5 102.0 2.05 97.2 107 172s 6 101.9 2.04 97.1 107 172s 7 102.4 2.04 97.6 107 172s 8 102.9 2.08 98.0 108 172s 9 101.4 2.06 96.6 106 172s 10 100.3 2.15 95.3 105 172s 11 95.7 2.19 90.6 101 172s 12 94.9 2.20 89.8 100 172s 13 96.3 2.16 91.2 101 172s 14 99.1 2.05 94.3 104 172s 15 103.7 2.13 98.7 109 172s 16 103.5 2.08 98.7 108 172s 17 103.7 2.39 98.1 109 172s 18 102.1 2.06 97.2 107 172s 19 103.6 2.10 98.6 108 172s 20 106.8 2.37 101.2 112 172s > 172s > print( predict( fitw2sls4e, se.fit = TRUE, interval = "confidence", 172s + level = 0.25, useDfSys = TRUE ) ) 172s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 172s 1 97.7 0.552 97.5 97.9 98.4 0.611 172s 2 99.9 0.484 99.7 100.0 100.0 0.700 172s 3 99.8 0.465 99.7 100.0 100.1 0.652 172s 4 100.0 0.488 99.9 100.2 100.5 0.664 172s 5 102.1 0.443 101.9 102.2 102.4 0.769 172s 6 101.9 0.425 101.8 102.1 102.4 0.695 172s 7 102.4 0.447 102.2 102.5 102.5 0.639 172s 8 102.9 0.547 102.7 103.1 104.8 0.821 172s 9 101.5 0.458 101.3 101.6 102.7 0.716 172s 10 100.4 0.648 100.2 100.6 99.5 0.743 172s 11 95.7 0.847 95.4 96.0 95.1 0.944 172s 12 94.9 0.823 94.6 95.1 93.6 1.254 172s 13 96.2 0.695 96.0 96.5 95.6 1.154 172s 14 99.1 0.467 98.9 99.2 97.6 0.814 172s 15 103.8 0.590 103.6 104.0 102.5 0.675 172s 16 103.6 0.520 103.4 103.8 104.4 0.659 172s 17 103.8 0.919 103.5 104.1 103.1 1.196 172s 18 102.0 0.487 101.9 102.2 103.1 0.587 172s 19 103.5 0.615 103.3 103.7 103.0 0.664 172s 20 106.7 1.126 106.3 107.0 106.3 0.909 172s supply.lwr supply.upr 172s 1 98.2 98.6 172s 2 99.8 100.3 172s 3 99.9 100.3 172s 4 100.2 100.7 172s 5 102.2 102.7 172s 6 102.2 102.7 172s 7 102.3 102.7 172s 8 104.6 105.1 172s 9 102.5 102.9 172s 10 99.3 99.8 172s 11 94.8 95.4 172s 12 93.2 94.0 172s 13 95.2 96.0 172s 14 97.4 97.9 172s 15 102.3 102.7 172s 16 104.2 104.6 172s 17 102.7 103.5 172s 18 102.9 103.3 172s 19 102.8 103.3 172s 20 106.0 106.6 172s > print( predict( fitw2sls4e$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 172s + level = 0.25, useDfSys = TRUE ) ) 172s fit se.fit lwr upr 172s 1 98.4 0.611 98.2 98.6 172s 2 100.0 0.700 99.8 100.3 172s 3 100.1 0.652 99.9 100.3 172s 4 100.5 0.664 100.2 100.7 172s 5 102.4 0.769 102.2 102.7 172s 6 102.4 0.695 102.2 102.7 172s 7 102.5 0.639 102.3 102.7 172s 8 104.8 0.821 104.6 105.1 172s 9 102.7 0.716 102.5 102.9 172s 10 99.5 0.743 99.3 99.8 172s 11 95.1 0.944 94.8 95.4 172s 12 93.6 1.254 93.2 94.0 172s 13 95.6 1.154 95.2 96.0 172s 14 97.6 0.814 97.4 97.9 172s 15 102.5 0.675 102.3 102.7 172s 16 104.4 0.659 104.2 104.6 172s 17 103.1 1.196 102.7 103.5 172s 18 103.1 0.587 102.9 103.3 172s 19 103.0 0.664 102.8 103.3 172s 20 106.3 0.909 106.0 106.6 172s > 172s > print( predict( fitw2sls5, se.fit = TRUE, se.pred = TRUE, 172s + interval = "prediction", level = 0.5, newdata = predictData ) ) 172s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 172s 1 102.8 0.781 2.12 101.4 104 95.8 172s 2 105.4 0.812 2.13 104.0 107 97.4 172s 3 105.3 0.824 2.13 103.8 107 97.5 172s 4 105.6 0.820 2.13 104.1 107 97.8 172s 5 107.5 1.186 2.30 106.0 109 99.9 172s 6 107.4 1.133 2.27 105.9 109 99.9 172s 7 108.0 1.141 2.28 106.4 110 99.9 172s 8 108.7 1.143 2.28 107.2 110 102.1 172s 9 106.8 1.179 2.30 105.2 108 100.2 172s 10 105.3 1.307 2.36 103.7 107 97.2 172s 11 100.3 1.108 2.26 98.7 102 92.7 172s 12 99.6 0.841 2.14 98.2 101 91.1 172s 13 101.3 0.638 2.07 99.9 103 93.0 172s 14 104.3 0.914 2.17 102.8 106 95.1 172s 15 109.3 1.440 2.44 107.6 111 100.1 172s 16 109.2 1.333 2.38 107.6 111 101.9 172s 17 108.9 1.742 2.63 107.1 111 100.9 172s 18 107.8 1.049 2.23 106.2 109 100.5 172s 19 109.5 1.216 2.31 107.9 111 100.3 172s 20 113.3 1.669 2.58 111.6 115 103.4 172s supply.se.fit supply.se.pred supply.lwr supply.upr 172s 1 0.825 2.64 94.1 97.6 172s 2 0.696 2.60 95.6 99.1 172s 3 0.712 2.60 95.7 99.2 172s 4 0.674 2.59 96.0 99.5 172s 5 1.087 2.73 98.1 101.8 172s 6 0.979 2.69 98.0 101.7 172s 7 0.874 2.65 98.1 101.7 172s 8 0.871 2.65 100.3 103.9 172s 9 1.143 2.75 98.4 102.1 172s 10 1.338 2.84 95.3 99.1 172s 11 1.483 2.91 90.8 94.7 172s 12 1.645 3.00 89.1 93.1 172s 13 1.440 2.89 91.0 94.9 172s 14 1.247 2.80 93.2 97.0 172s 15 1.222 2.79 98.2 102.0 172s 16 1.104 2.74 100.0 103.7 172s 17 1.808 3.09 98.7 103.0 172s 18 0.861 2.65 98.7 102.3 172s 19 0.861 2.65 98.5 102.1 172s 20 0.666 2.59 101.6 105.2 172s > print( predict( fitw2sls5$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 172s + interval = "prediction", level = 0.5, newdata = predictData ) ) 172s fit se.fit se.pred lwr upr 172s 1 102.8 0.781 2.12 101.4 104 172s 2 105.4 0.812 2.13 104.0 107 172s 3 105.3 0.824 2.13 103.8 107 172s 4 105.6 0.820 2.13 104.1 107 172s 5 107.5 1.186 2.30 106.0 109 172s 6 107.4 1.133 2.27 105.9 109 172s 7 108.0 1.141 2.28 106.4 110 172s 8 108.7 1.143 2.28 107.2 110 172s 9 106.8 1.179 2.30 105.2 108 172s 10 105.3 1.307 2.36 103.7 107 172s 11 100.3 1.108 2.26 98.7 102 172s 12 99.6 0.841 2.14 98.2 101 172s 13 101.3 0.638 2.07 99.9 103 172s 14 104.3 0.914 2.17 102.8 106 172s 15 109.3 1.440 2.44 107.6 111 172s 16 109.2 1.333 2.38 107.6 111 172s 17 108.9 1.742 2.63 107.1 111 172s 18 107.8 1.049 2.23 106.2 109 172s 19 109.5 1.216 2.31 107.9 111 172s 20 113.3 1.669 2.58 111.6 115 172s > 172s > print( predict( fitw2slsd1, se.fit = TRUE, se.pred = TRUE, 172s + interval = "confidence", level = 0.99 ) ) 172s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 172s 1 97.1 0.751 2.13 94.9 99.3 98.9 172s 2 99.2 0.757 2.13 97.0 101.4 100.4 172s 3 99.2 0.692 2.11 97.2 101.2 100.5 172s 4 99.3 0.766 2.13 97.1 101.5 100.7 172s 5 102.5 0.595 2.08 100.8 104.3 102.6 172s 6 102.2 0.503 2.05 100.7 103.7 102.6 172s 7 102.5 0.503 2.05 101.1 104.0 102.6 172s 8 102.7 0.653 2.10 100.8 104.5 104.8 172s 9 102.0 0.655 2.10 100.1 103.9 102.7 172s 10 101.4 1.074 2.26 98.3 104.5 99.7 172s 11 95.6 0.978 2.22 92.8 98.5 95.4 172s 12 93.9 1.134 2.29 90.7 97.2 93.8 172s 13 95.0 1.162 2.31 91.7 98.4 95.6 172s 14 98.9 0.530 2.06 97.4 100.4 97.6 172s 15 104.9 1.061 2.26 101.9 108.0 102.3 172s 16 104.3 0.757 2.13 102.1 106.5 104.1 172s 17 106.1 1.963 2.80 100.4 111.7 102.8 172s 18 101.7 0.597 2.08 100.0 103.5 102.7 172s 19 103.3 0.736 2.12 101.2 105.4 102.6 172s 20 106.0 1.430 2.45 101.9 110.2 105.6 172s supply.se.fit supply.se.pred supply.lwr supply.upr 172s 1 1.079 2.68 95.8 102.1 172s 2 1.064 2.68 97.3 103.5 172s 3 0.962 2.64 97.6 103.3 172s 4 0.938 2.63 98.0 103.4 172s 5 0.914 2.62 100.0 105.3 172s 6 0.808 2.59 100.2 104.9 172s 7 0.736 2.57 100.4 104.7 172s 8 0.994 2.65 101.9 107.7 172s 9 0.808 2.59 100.4 105.1 172s 10 1.023 2.66 96.7 102.7 172s 11 1.228 2.75 91.8 99.0 172s 12 1.428 2.84 89.7 98.0 172s 13 1.272 2.77 91.9 99.4 172s 14 0.917 2.62 94.9 100.3 172s 15 0.899 2.62 99.7 104.9 172s 16 0.936 2.63 101.3 106.8 172s 17 1.665 2.97 98.0 107.7 172s 18 0.988 2.65 99.8 105.6 172s 19 1.129 2.70 99.3 105.9 172s 20 1.733 3.01 100.5 110.7 172s > print( predict( fitw2slsd1$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 172s + interval = "confidence", level = 0.99 ) ) 172s fit se.fit se.pred lwr upr 172s 1 98.9 1.079 2.68 95.8 102.1 172s 2 100.4 1.064 2.68 97.3 103.5 172s 3 100.5 0.962 2.64 97.6 103.3 172s 4 100.7 0.938 2.63 98.0 103.4 172s 5 102.6 0.914 2.62 100.0 105.3 172s 6 102.6 0.808 2.59 100.2 104.9 172s 7 102.6 0.736 2.57 100.4 104.7 172s 8 104.8 0.994 2.65 101.9 107.7 172s 9 102.7 0.808 2.59 100.4 105.1 172s 10 99.7 1.023 2.66 96.7 102.7 172s 11 95.4 1.228 2.75 91.8 99.0 172s 12 93.8 1.428 2.84 89.7 98.0 172s 13 95.6 1.272 2.77 91.9 99.4 172s 14 97.6 0.917 2.62 94.9 100.3 172s 15 102.3 0.899 2.62 99.7 104.9 172s 16 104.1 0.936 2.63 101.3 106.8 172s 17 102.8 1.665 2.97 98.0 107.7 172s 18 102.7 0.988 2.65 99.8 105.6 172s 19 102.6 1.129 2.70 99.3 105.9 172s 20 105.6 1.733 3.01 100.5 110.7 172s > 172s > print( predict( fitw2slsd2e, se.fit = TRUE, interval = "prediction", 172s + level = 0.9, newdata = predictData, useDfSys = TRUE ) ) 172s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 172s 1 104 1.214 100.1 108 95.7 1.100 172s 2 106 1.169 102.6 110 97.2 0.835 172s 3 106 1.216 102.5 110 97.3 0.864 172s 4 107 1.169 102.7 110 97.6 0.789 172s 5 109 1.897 104.7 114 99.9 1.242 172s 6 109 1.773 104.6 114 99.9 1.115 172s 7 110 1.718 105.2 114 99.9 0.983 172s 8 110 1.552 105.8 114 102.2 0.843 172s 9 109 1.939 104.0 113 100.4 1.310 172s 10 107 2.229 102.5 112 97.4 1.683 172s 11 102 1.655 97.5 106 92.9 1.794 172s 12 101 1.125 96.8 104 91.2 1.750 172s 13 102 0.879 98.5 106 93.1 1.449 172s 14 106 1.480 101.5 110 95.3 1.383 172s 15 111 2.331 106.3 117 100.4 1.395 172s 16 111 2.064 106.3 116 102.2 1.175 172s 17 112 3.001 105.7 118 101.4 2.074 172s 18 109 1.475 104.9 113 100.7 0.861 172s 19 111 1.589 106.5 115 100.6 0.829 172s 20 114 1.756 109.9 119 103.6 0.680 172s supply.lwr supply.upr 172s 1 91.1 100.3 172s 2 92.7 101.7 172s 3 92.8 101.8 172s 4 93.2 102.1 172s 5 95.2 104.7 172s 6 95.3 104.6 172s 7 95.3 104.5 172s 8 97.7 106.7 172s 9 95.6 105.2 172s 10 92.3 102.5 172s 11 87.7 98.1 172s 12 86.0 96.4 172s 13 88.1 98.0 172s 14 90.4 100.1 172s 15 95.5 105.3 172s 16 97.5 106.9 172s 17 95.8 106.9 172s 18 96.2 105.2 172s 19 96.1 105.1 172s 20 99.2 108.0 172s > print( predict( fitw2slsd2e$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 172s + level = 0.9, newdata = predictData, useDfSys = TRUE ) ) 172s fit se.fit lwr upr 172s 1 104 1.214 100.1 108 172s 2 106 1.169 102.6 110 172s 3 106 1.216 102.5 110 172s 4 107 1.169 102.7 110 172s 5 109 1.897 104.7 114 172s 6 109 1.773 104.6 114 172s 7 110 1.718 105.2 114 172s 8 110 1.552 105.8 114 172s 9 109 1.939 104.0 113 172s 10 107 2.229 102.5 112 172s 11 102 1.655 97.5 106 172s 12 101 1.125 96.8 104 172s 13 102 0.879 98.5 106 172s 14 106 1.480 101.5 110 172s 15 111 2.331 106.3 117 172s 16 111 2.064 106.3 116 172s 17 112 3.001 105.7 118 172s 18 109 1.475 104.9 113 172s 19 111 1.589 106.5 115 172s 20 114 1.756 109.9 119 172s > 172s > print( predict( fitw2slsd3e, se.fit = TRUE, se.pred = TRUE, 172s + interval = "prediction", level = 0.01, useDfSys = TRUE ) ) 172s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 172s 1 97.4 0.622 2.05 97.4 97.4 98.2 172s 2 99.4 0.654 2.06 99.4 99.4 99.7 172s 3 99.4 0.598 2.04 99.4 99.4 99.9 172s 4 99.5 0.663 2.06 99.5 99.5 100.2 172s 5 102.4 0.515 2.02 102.4 102.4 102.3 172s 6 102.1 0.442 2.00 102.1 102.1 102.3 172s 7 102.4 0.444 2.00 102.4 102.4 102.4 172s 8 102.6 0.587 2.04 102.6 102.6 104.7 172s 9 101.9 0.573 2.03 101.9 101.9 102.7 172s 10 101.2 0.948 2.17 101.2 101.2 99.6 172s 11 95.9 0.849 2.13 95.9 95.9 95.2 172s 12 94.4 0.914 2.15 94.4 94.4 93.6 172s 13 95.5 0.943 2.17 95.5 95.5 95.6 172s 14 99.0 0.464 2.01 99.0 99.1 97.7 172s 15 104.5 0.883 2.14 104.5 104.6 102.7 172s 16 104.0 0.631 2.05 104.0 104.0 104.6 172s 17 105.4 1.665 2.56 105.4 105.5 103.5 172s 18 101.8 0.538 2.02 101.7 101.8 103.3 172s 19 103.2 0.661 2.06 103.2 103.3 103.2 172s 20 105.9 1.284 2.34 105.9 106.0 106.4 172s supply.se.fit supply.se.pred supply.lwr supply.upr 172s 1 0.652 2.60 98.1 98.2 172s 2 0.740 2.62 99.7 99.8 172s 3 0.682 2.61 99.8 99.9 172s 4 0.708 2.61 100.2 100.2 172s 5 0.782 2.63 102.3 102.4 172s 6 0.699 2.61 102.3 102.4 172s 7 0.648 2.60 102.3 102.4 172s 8 0.906 2.67 104.7 104.8 172s 9 0.736 2.62 102.7 102.8 172s 10 0.931 2.68 99.6 99.7 172s 11 1.107 2.75 95.2 95.2 172s 12 1.287 2.83 93.6 93.7 172s 13 1.157 2.77 95.5 95.6 172s 14 0.829 2.65 97.7 97.7 172s 15 0.717 2.62 102.7 102.8 172s 16 0.676 2.61 104.6 104.6 172s 17 1.392 2.88 103.4 103.5 172s 18 0.699 2.61 103.3 103.3 172s 19 0.822 2.65 103.2 103.2 172s 20 1.376 2.87 106.4 106.5 172s > print( predict( fitw2slsd3e$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 172s + interval = "prediction", level = 0.01, useDfSys = TRUE ) ) 172s fit se.fit se.pred lwr upr 172s 1 98.2 0.652 2.60 98.1 98.2 172s 2 99.7 0.740 2.62 99.7 99.8 172s 3 99.9 0.682 2.61 99.8 99.9 172s 4 100.2 0.708 2.61 100.2 100.2 172s 5 102.3 0.782 2.63 102.3 102.4 172s 6 102.3 0.699 2.61 102.3 102.4 172s 7 102.4 0.648 2.60 102.3 102.4 172s 8 104.7 0.906 2.67 104.7 104.8 172s 9 102.7 0.736 2.62 102.7 102.8 172s 10 99.6 0.931 2.68 99.6 99.7 172s 11 95.2 1.107 2.75 95.2 95.2 172s 12 93.6 1.287 2.83 93.6 93.7 172s 13 95.6 1.157 2.77 95.5 95.6 172s 14 97.7 0.829 2.65 97.7 97.7 172s 15 102.7 0.717 2.62 102.7 102.8 172s 16 104.6 0.676 2.61 104.6 104.6 172s 17 103.5 1.392 2.88 103.4 103.5 172s 18 103.3 0.699 2.61 103.3 103.3 172s 19 103.2 0.822 2.65 103.2 103.2 172s 20 106.4 1.376 2.87 106.4 106.5 172s > 172s > # predict just one observation 172s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 172s + trend = 25 ) 172s > 172s > print( predict( fitw2sls1e, newdata = smallData ) ) 172s demand.pred supply.pred 172s 1 110 118 172s > print( predict( fitw2sls1e$eq[[ 1 ]], newdata = smallData ) ) 172s fit 172s 1 110 172s > 172s > print( predict( fitw2sls2, se.fit = TRUE, level = 0.9, 172s + newdata = smallData ) ) 172s demand.pred demand.se.fit supply.pred supply.se.fit 172s 1 110 2.52 119 3.53 172s > print( predict( fitw2sls2$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 172s + newdata = smallData ) ) 172s fit se.pred 172s 1 110 3.21 172s > 172s > print( predict( fitw2sls3, interval = "prediction", level = 0.975, 172s + newdata = smallData ) ) 172s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 172s 1 110 102 117 119 109 129 172s > print( predict( fitw2sls3$eq[[ 1 ]], interval = "confidence", level = 0.8, 172s + newdata = smallData ) ) 172s fit lwr upr 172s 1 110 107 113 172s > 172s > print( predict( fitw2sls4e, se.fit = TRUE, interval = "confidence", 172s + level = 0.999, newdata = smallData ) ) 172s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 172s 1 110 2.08 102 117 119 2.11 172s supply.lwr supply.upr 172s 1 112 127 172s > print( predict( fitw2sls4e$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 172s + level = 0.75, newdata = smallData ) ) 172s fit se.pred lwr upr 172s 1 119 3.27 115 123 172s > 172s > print( predict( fitw2sls5, se.fit = TRUE, interval = "prediction", 172s + newdata = smallData ) ) 172s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 172s 1 110 2.26 104 116 119 2.33 172s supply.lwr supply.upr 172s 1 112 126 172s > print( predict( fitw2sls5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 172s + newdata = smallData ) ) 172s fit se.pred lwr upr 172s 1 110 3 105 114 172s > 172s > print( predict( fitw2slsd2e, se.fit = TRUE, se.pred = TRUE, 172s + interval = "prediction", level = 0.5, newdata = smallData ) ) 172s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 172s 1 108 2.71 3.34 105 110 119 172s supply.se.fit supply.se.pred supply.lwr supply.upr 172s 1 3.22 4.08 117 122 172s > print( predict( fitw2slsd2e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 172s + interval = "confidence", level = 0.25, newdata = smallData ) ) 172s fit se.fit se.pred lwr upr 172s 1 108 2.71 3.34 107 109 172s > 172s > 172s > ## ************ correlation of predicted values *************** 172s > print( correlation.systemfit( fitw2sls1e, 1, 2 ) ) 172s [,1] 172s [1,] 0 172s [2,] 0 172s [3,] 0 172s [4,] 0 172s [5,] 0 172s [6,] 0 172s [7,] 0 172s [8,] 0 172s [9,] 0 172s [10,] 0 172s [11,] 0 172s [12,] 0 172s [13,] 0 172s [14,] 0 172s [15,] 0 172s [16,] 0 172s [17,] 0 172s [18,] 0 172s [19,] 0 172s [20,] 0 172s > 172s > print( correlation.systemfit( fitw2sls2, 2, 1 ) ) 172s [,1] 172s [1,] 0.413453 172s [2,] 0.153759 172s [3,] 0.152962 172s [4,] 0.112671 172s [5,] -0.071442 172s [6,] -0.053943 172s [7,] -0.050961 172s [8,] -0.005442 172s [9,] -0.000476 172s [10,] -0.001894 172s [11,] 0.047351 172s [12,] 0.064973 172s [13,] 0.024591 172s [14,] -0.028036 172s [15,] 0.175326 172s [16,] 0.254878 172s [17,] 0.104540 172s [18,] 0.065579 172s [19,] 0.147008 172s [20,] 0.124593 172s > 172s > print( correlation.systemfit( fitw2sls3, 1, 2 ) ) 172s [,1] 172s [1,] 0.413453 172s [2,] 0.153759 172s [3,] 0.152962 172s [4,] 0.112671 172s [5,] -0.071442 172s [6,] -0.053943 172s [7,] -0.050961 172s [8,] -0.005442 172s [9,] -0.000476 172s [10,] -0.001894 172s [11,] 0.047351 172s [12,] 0.064973 172s [13,] 0.024591 172s [14,] -0.028036 172s [15,] 0.175326 172s [16,] 0.254878 172s [17,] 0.104540 172s [18,] 0.065579 172s [19,] 0.147008 172s [20,] 0.124593 172s > 172s > print( correlation.systemfit( fitw2sls4e, 2, 1 ) ) 172s [,1] 172s [1,] 0.38438 172s [2,] 0.30697 172s [3,] 0.26690 172s [4,] 0.30163 172s [5,] -0.02768 172s [6,] -0.05086 172s [7,] -0.05895 172s [8,] 0.10102 172s [9,] 0.10072 172s [10,] 0.45547 172s [11,] 0.10817 172s [12,] 0.00552 172s [13,] 0.04219 172s [14,] -0.04054 172s [15,] 0.42100 172s [16,] 0.24974 172s [17,] 0.65722 172s [18,] 0.24286 172s [19,] 0.34336 172s [20,] 0.54717 172s > 172s > print( correlation.systemfit( fitw2sls5, 1, 2 ) ) 172s [,1] 172s [1,] 0.38030 172s [2,] 0.30892 172s [3,] 0.26808 172s [4,] 0.30325 172s [5,] -0.02730 172s [6,] -0.05035 172s [7,] -0.05831 172s [8,] 0.10036 172s [9,] 0.10045 172s [10,] 0.45492 172s [11,] 0.10525 172s [12,] 0.00394 172s [13,] 0.04171 172s [14,] -0.04037 172s [15,] 0.41958 172s [16,] 0.24706 172s [17,] 0.65619 172s [18,] 0.23872 172s [19,] 0.33729 172s [20,] 0.54239 172s > 172s > print( correlation.systemfit( fitw2slsd1, 2, 1 ) ) 172s [,1] 172s [1,] 0 172s [2,] 0 172s [3,] 0 172s [4,] 0 172s [5,] 0 172s [6,] 0 172s [7,] 0 172s [8,] 0 172s [9,] 0 172s [10,] 0 172s [11,] 0 172s [12,] 0 172s [13,] 0 172s [14,] 0 172s [15,] 0 172s [16,] 0 172s [17,] 0 172s [18,] 0 172s [19,] 0 172s [20,] 0 172s > 172s > print( correlation.systemfit( fitw2slsd2e, 1, 2 ) ) 172s [,1] 172s [1,] 0.482214 172s [2,] 0.253368 172s [3,] 0.242824 172s [4,] 0.195411 172s [5,] -0.107828 172s [6,] -0.074958 172s [7,] -0.055696 172s [8,] -0.002037 172s [9,] -0.000921 172s [10,] -0.008040 172s [11,] 0.040999 172s [12,] 0.075418 172s [13,] 0.029702 172s [14,] -0.030775 172s [15,] 0.229063 172s [16,] 0.318607 172s [17,] 0.156734 172s [18,] -0.023016 172s [19,] 0.068128 172s [20,] 0.047481 172s > 172s > print( correlation.systemfit( fitw2slsd3e, 2, 1 ) ) 172s [,1] 172s [1,] 0.482214 172s [2,] 0.253368 172s [3,] 0.242824 172s [4,] 0.195411 172s [5,] -0.107828 172s [6,] -0.074958 172s [7,] -0.055696 172s [8,] -0.002037 172s [9,] -0.000921 172s [10,] -0.008040 172s [11,] 0.040999 172s [12,] 0.075418 172s [13,] 0.029702 172s [14,] -0.030775 172s [15,] 0.229063 172s [16,] 0.318607 172s [17,] 0.156734 172s [18,] -0.023016 172s [19,] 0.068128 172s [20,] 0.047481 172s > 172s > 172s > ## ************ LOG-Likelihood values *************** 172s > print( logLik( fitw2sls1e ) ) 172s 'log Lik.' -67.6 (df=9) 172s > print( logLik( fitw2sls1e, residCovDiag = TRUE ) ) 172s 'log Lik.' -84.4 (df=9) 172s > 172s > print( logLik( fitw2sls2 ) ) 172s 'log Lik.' -65.2 (df=8) 172s > print( logLik( fitw2sls2, residCovDiag = TRUE ) ) 172s 'log Lik.' -84.8 (df=8) 172s > 172s > print( logLik( fitw2sls3 ) ) 172s 'log Lik.' -65.2 (df=8) 172s > print( logLik( fitw2sls3, residCovDiag = TRUE ) ) 172s 'log Lik.' -84.8 (df=8) 172s > 172s > print( logLik( fitw2sls4e ) ) 173s 'log Lik.' -65.7 (df=7) 173s > print( logLik( fitw2sls4e, residCovDiag = TRUE ) ) 173s 'log Lik.' -84.8 (df=7) 173s > 173s > print( logLik( fitw2sls5 ) ) 173s 'log Lik.' -65.6 (df=7) 173s > print( logLik( fitw2sls5, residCovDiag = TRUE ) ) 173s 'log Lik.' -84.8 (df=7) 173s > 173s > print( logLik( fitw2slsd1 ) ) 173s 'log Lik.' -75.1 (df=9) 173s > print( logLik( fitw2slsd1, residCovDiag = TRUE ) ) 173s 'log Lik.' -84.7 (df=9) 173s > 173s > print( logLik( fitw2slsd2e ) ) 173s 'log Lik.' -69.1 (df=8) 173s > print( logLik( fitw2slsd2e, residCovDiag = TRUE ) ) 173s 'log Lik.' -84.7 (df=8) 173s > 173s > print( logLik( fitw2slsd3e ) ) 173s 'log Lik.' -69.1 (df=8) 173s > print( logLik( fitw2slsd3e, residCovDiag = TRUE ) ) 173s 'log Lik.' -84.7 (df=8) 173s > 173s > 173s > ## ************** F tests **************** 173s > # testing first restriction 173s > print( linearHypothesis( fitw2sls1, restrm ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1 173s 173s Res.Df Df F Pr(>F) 173s 1 34 173s 2 33 1 0.31 0.58 173s > linearHypothesis( fitw2sls1, restrict ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1 173s 173s Res.Df Df F Pr(>F) 173s 1 34 173s 2 33 1 0.31 0.58 173s > 173s > print( linearHypothesis( fitw2slsd1e, restrm ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1e 173s 173s Res.Df Df F Pr(>F) 173s 1 34 173s 2 33 1 0.92 0.35 173s > linearHypothesis( fitw2slsd1e, restrict ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1e 173s 173s Res.Df Df F Pr(>F) 173s 1 34 173s 2 33 1 0.92 0.35 173s > 173s > # testing second restriction 173s > restrOnly2m <- matrix(0,1,7) 173s > restrOnly2q <- 0.5 173s > restrOnly2m[1,2] <- -1 173s > restrOnly2m[1,5] <- 1 173s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 173s > # first restriction not imposed 173s > print( linearHypothesis( fitw2sls1e, restrOnly2m, restrOnly2q ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1e 173s 173s Res.Df Df F Pr(>F) 173s 1 34 173s 2 33 1 0.01 0.91 173s > linearHypothesis( fitw2sls1e, restrictOnly2 ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1e 173s 173s Res.Df Df F Pr(>F) 173s 1 34 173s 2 33 1 0.01 0.91 173s > 173s > print( linearHypothesis( fitw2slsd1, restrOnly2m, restrOnly2q ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1 173s 173s Res.Df Df F Pr(>F) 173s 1 34 173s 2 33 1 0.74 0.39 173s > linearHypothesis( fitw2slsd1, restrictOnly2 ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1 173s 173s Res.Df Df F Pr(>F) 173s 1 34 173s 2 33 1 0.74 0.39 173s > 173s > # first restriction imposed 173s > print( linearHypothesis( fitw2sls2, restrOnly2m, restrOnly2q ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls2 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 34 1 0.04 0.85 173s > linearHypothesis( fitw2sls2, restrictOnly2 ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls2 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 34 1 0.04 0.85 173s > 173s > print( linearHypothesis( fitw2sls3, restrOnly2m, restrOnly2q ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls3 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 34 1 0.04 0.85 173s > linearHypothesis( fitw2sls3, restrictOnly2 ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls3 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 34 1 0.04 0.85 173s > 173s > print( linearHypothesis( fitw2slsd2e, restrOnly2m, restrOnly2q ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd2e 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 34 1 0.42 0.52 173s > linearHypothesis( fitw2slsd2e, restrictOnly2 ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd2e 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 34 1 0.42 0.52 173s > 173s > print( linearHypothesis( fitw2slsd3e, restrOnly2m, restrOnly2q ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd3e 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 34 1 0.42 0.52 173s > linearHypothesis( fitw2slsd3e, restrictOnly2 ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd3e 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 34 1 0.42 0.52 173s > 173s > # testing both of the restrictions 173s > print( linearHypothesis( fitw2sls1e, restr2m, restr2q ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1e 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 33 2 0.18 0.84 173s > linearHypothesis( fitw2sls1e, restrict2 ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1e 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 33 2 0.18 0.84 173s > 173s > print( linearHypothesis( fitw2slsd1, restr2m, restr2q ) ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 33 2 0.65 0.53 173s > linearHypothesis( fitw2slsd1, restrict2 ) 173s Linear hypothesis test (Theil's F test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1 173s 173s Res.Df Df F Pr(>F) 173s 1 35 173s 2 33 2 0.65 0.53 173s > 173s > 173s > ## ************** Wald tests **************** 173s > # testing first restriction 173s > print( linearHypothesis( fitw2sls1, restrm, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 34 173s 2 33 1 0.31 0.58 173s > linearHypothesis( fitw2sls1, restrict, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 34 173s 2 33 1 0.31 0.58 173s > 173s > print( linearHypothesis( fitw2slsd1e, restrm, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 34 173s 2 33 1 1.11 0.29 173s > linearHypothesis( fitw2slsd1e, restrict, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 34 173s 2 33 1 1.11 0.29 173s > 173s > # testing second restriction 173s > # first restriction not imposed 173s > print( linearHypothesis( fitw2sls1e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 34 173s 2 33 1 0.02 0.9 173s > linearHypothesis( fitw2sls1e, restrictOnly2, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 34 173s 2 33 1 0.02 0.9 173s > 173s > print( linearHypothesis( fitw2slsd1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 34 173s 2 33 1 0.74 0.39 173s > linearHypothesis( fitw2slsd1, restrictOnly2, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 34 173s 2 33 1 0.74 0.39 173s > # first restriction imposed 173s > print( linearHypothesis( fitw2sls2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls2 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 34 1 0.04 0.85 173s > linearHypothesis( fitw2sls2, restrictOnly2, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls2 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 34 1 0.04 0.85 173s > 173s > print( linearHypothesis( fitw2sls3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls3 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 34 1 0.04 0.85 173s > linearHypothesis( fitw2sls3, restrictOnly2, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls3 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 34 1 0.04 0.85 173s > 173s > print( linearHypothesis( fitw2slsd2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd2e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 34 1 0.49 0.48 173s > linearHypothesis( fitw2slsd2e, restrictOnly2, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd2e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 34 1 0.49 0.48 173s > 173s > print( linearHypothesis( fitw2slsd3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd3e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 34 1 0.49 0.48 173s > linearHypothesis( fitw2slsd3e, restrictOnly2, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd3e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 34 1 0.49 0.48 173s > 173s > # testing both of the restrictions 173s > print( linearHypothesis( fitw2sls1e, restr2m, restr2q, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 33 2 0.43 0.81 173s > linearHypothesis( fitw2sls1e, restrict2, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2sls1e 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 33 2 0.43 0.81 173s > 173s > print( linearHypothesis( fitw2slsd1, restr2m, restr2q, test = "Chisq" ) ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 33 2 1.3 0.52 173s > linearHypothesis( fitw2slsd1, restrict2, test = "Chisq" ) 173s Linear hypothesis test (Chi^2 statistic of a Wald test) 173s 173s Hypothesis: 173s demand_income - supply_trend = 0 173s - demand_price + supply_price = 0.5 173s 173s Model 1: restricted model 173s Model 2: fitw2slsd1 173s 173s Res.Df Df Chisq Pr(>Chisq) 173s 1 35 173s 2 33 2 1.3 0.52 173s > 173s > 173s > ## ****************** model frame ************************** 173s > print( mf <- model.frame( fitw2sls1e ) ) 173s consump price income farmPrice trend 173s 1 98.5 100.3 87.4 98.0 1 173s 2 99.2 104.3 97.6 99.1 2 173s 3 102.2 103.4 96.7 99.1 3 173s 4 101.5 104.5 98.2 98.1 4 173s 5 104.2 98.0 99.8 110.8 5 173s 6 103.2 99.5 100.5 108.2 6 173s 7 104.0 101.1 103.2 105.6 7 173s 8 99.9 104.8 107.8 109.8 8 173s 9 100.3 96.4 96.6 108.7 9 173s 10 102.8 91.2 88.9 100.6 10 173s 11 95.4 93.1 75.1 81.0 11 173s 12 92.4 98.8 76.9 68.6 12 173s 13 94.5 102.9 84.6 70.9 13 173s 14 98.8 98.8 90.6 81.4 14 173s 15 105.8 95.1 103.1 102.3 15 173s 16 100.2 98.5 105.1 105.0 16 173s 17 103.5 86.5 96.4 110.5 17 173s 18 99.9 104.0 104.4 92.5 18 173s 19 105.2 105.8 110.7 89.3 19 173s 20 106.2 113.5 127.1 93.0 20 173s > print( mf1 <- model.frame( fitw2sls1e$eq[[ 1 ]] ) ) 173s consump price income 173s 1 98.5 100.3 87.4 173s 2 99.2 104.3 97.6 173s 3 102.2 103.4 96.7 173s 4 101.5 104.5 98.2 173s 5 104.2 98.0 99.8 173s 6 103.2 99.5 100.5 173s 7 104.0 101.1 103.2 173s 8 99.9 104.8 107.8 173s 9 100.3 96.4 96.6 173s 10 102.8 91.2 88.9 173s 11 95.4 93.1 75.1 173s 12 92.4 98.8 76.9 173s 13 94.5 102.9 84.6 173s 14 98.8 98.8 90.6 173s 15 105.8 95.1 103.1 173s 16 100.2 98.5 105.1 173s 17 103.5 86.5 96.4 173s 18 99.9 104.0 104.4 173s 19 105.2 105.8 110.7 173s 20 106.2 113.5 127.1 173s > print( attributes( mf1 )$terms ) 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s > print( mf2 <- model.frame( fitw2sls1e$eq[[ 2 ]] ) ) 173s consump price farmPrice trend 173s 1 98.5 100.3 98.0 1 173s 2 99.2 104.3 99.1 2 173s 3 102.2 103.4 99.1 3 173s 4 101.5 104.5 98.1 4 173s 5 104.2 98.0 110.8 5 173s 6 103.2 99.5 108.2 6 173s 7 104.0 101.1 105.6 7 173s 8 99.9 104.8 109.8 8 173s 9 100.3 96.4 108.7 9 173s 10 102.8 91.2 100.6 10 173s 11 95.4 93.1 81.0 11 173s 12 92.4 98.8 68.6 12 173s 13 94.5 102.9 70.9 13 173s 14 98.8 98.8 81.4 14 173s 15 105.8 95.1 102.3 15 173s 16 100.2 98.5 105.0 16 173s 17 103.5 86.5 110.5 17 173s 18 99.9 104.0 92.5 18 173s 19 105.2 105.8 89.3 19 173s 20 106.2 113.5 93.0 20 173s > print( attributes( mf2 )$terms ) 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s > 173s > print( all.equal( mf, model.frame( fitw2sls2 ) ) ) 173s [1] TRUE 173s > print( all.equal( mf2, model.frame( fitw2sls2$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > 173s > print( all.equal( mf, model.frame( fitw2sls3 ) ) ) 173s [1] TRUE 173s > print( all.equal( mf1, model.frame( fitw2sls3$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > 173s > print( all.equal( mf, model.frame( fitw2sls4e ) ) ) 173s [1] TRUE 173s > print( all.equal( mf2, model.frame( fitw2sls4e$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > 173s > print( all.equal( mf, model.frame( fitw2sls5 ) ) ) 173s [1] TRUE 173s > print( all.equal( mf1, model.frame( fitw2sls5$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > 173s > print( all.equal( mf, model.frame( fitw2slsd1 ) ) ) 173s [1] TRUE 173s > print( all.equal( mf2, model.frame( fitw2slsd1$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > 173s > print( all.equal( mf, model.frame( fitw2slsd2e ) ) ) 173s [1] TRUE 173s > print( all.equal( mf1, model.frame( fitw2slsd2e$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > 173s > print( all.equal( mf, model.frame( fitw2slsd3e ) ) ) 173s [1] TRUE 173s > print( all.equal( mf2, model.frame( fitw2slsd3e$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > 173s > fitw2sls1e$eq[[ 1 ]]$modelInst 173s income farmPrice trend 173s 1 87.4 98.0 1 173s 2 97.6 99.1 2 173s 3 96.7 99.1 3 173s 4 98.2 98.1 4 173s 5 99.8 110.8 5 173s 6 100.5 108.2 6 173s 7 103.2 105.6 7 173s 8 107.8 109.8 8 173s 9 96.6 108.7 9 173s 10 88.9 100.6 10 173s 11 75.1 81.0 11 173s 12 76.9 68.6 12 173s 13 84.6 70.9 13 173s 14 90.6 81.4 14 173s 15 103.1 102.3 15 173s 16 105.1 105.0 16 173s 17 96.4 110.5 17 173s 18 104.4 92.5 18 173s 19 110.7 89.3 19 173s 20 127.1 93.0 20 173s > fitw2sls1e$eq[[ 2 ]]$modelInst 173s income farmPrice trend 173s 1 87.4 98.0 1 173s 2 97.6 99.1 2 173s 3 96.7 99.1 3 173s 4 98.2 98.1 4 173s 5 99.8 110.8 5 173s 6 100.5 108.2 6 173s 7 103.2 105.6 7 173s 8 107.8 109.8 8 173s 9 96.6 108.7 9 173s 10 88.9 100.6 10 173s 11 75.1 81.0 11 173s 12 76.9 68.6 12 173s 13 84.6 70.9 13 173s 14 90.6 81.4 14 173s 15 103.1 102.3 15 173s 16 105.1 105.0 16 173s 17 96.4 110.5 17 173s 18 104.4 92.5 18 173s 19 110.7 89.3 19 173s 20 127.1 93.0 20 173s > 173s > fitw2sls4Sym$eq[[ 1 ]]$modelInst 173s income farmPrice trend 173s 1 87.4 98.0 1 173s 2 97.6 99.1 2 173s 3 96.7 99.1 3 173s 4 98.2 98.1 4 173s 5 99.8 110.8 5 173s 6 100.5 108.2 6 173s 7 103.2 105.6 7 173s 8 107.8 109.8 8 173s 9 96.6 108.7 9 173s 10 88.9 100.6 10 173s 11 75.1 81.0 11 173s 12 76.9 68.6 12 173s 13 84.6 70.9 13 173s 14 90.6 81.4 14 173s 15 103.1 102.3 15 173s 16 105.1 105.0 16 173s 17 96.4 110.5 17 173s 18 104.4 92.5 18 173s 19 110.7 89.3 19 173s 20 127.1 93.0 20 173s > fitw2sls4Sym$eq[[ 2 ]]$modelInst 173s income farmPrice trend 173s 1 87.4 98.0 1 173s 2 97.6 99.1 2 173s 3 96.7 99.1 3 173s 4 98.2 98.1 4 173s 5 99.8 110.8 5 173s 6 100.5 108.2 6 173s 7 103.2 105.6 7 173s 8 107.8 109.8 8 173s 9 96.6 108.7 9 173s 10 88.9 100.6 10 173s 11 75.1 81.0 11 173s 12 76.9 68.6 12 173s 13 84.6 70.9 13 173s 14 90.6 81.4 14 173s 15 103.1 102.3 15 173s 16 105.1 105.0 16 173s 17 96.4 110.5 17 173s 18 104.4 92.5 18 173s 19 110.7 89.3 19 173s 20 127.1 93.0 20 173s > 173s > fitw2sls5$eq[[ 1 ]]$modelInst 173s income farmPrice trend 173s 1 87.4 98.0 1 173s 2 97.6 99.1 2 173s 3 96.7 99.1 3 173s 4 98.2 98.1 4 173s 5 99.8 110.8 5 173s 6 100.5 108.2 6 173s 7 103.2 105.6 7 173s 8 107.8 109.8 8 173s 9 96.6 108.7 9 173s 10 88.9 100.6 10 173s 11 75.1 81.0 11 173s 12 76.9 68.6 12 173s 13 84.6 70.9 13 173s 14 90.6 81.4 14 173s 15 103.1 102.3 15 173s 16 105.1 105.0 16 173s 17 96.4 110.5 17 173s 18 104.4 92.5 18 173s 19 110.7 89.3 19 173s 20 127.1 93.0 20 173s > fitw2sls5$eq[[ 2 ]]$modelInst 173s income farmPrice trend 173s 1 87.4 98.0 1 173s 2 97.6 99.1 2 173s 3 96.7 99.1 3 173s 4 98.2 98.1 4 173s 5 99.8 110.8 5 173s 6 100.5 108.2 6 173s 7 103.2 105.6 7 173s 8 107.8 109.8 8 173s 9 96.6 108.7 9 173s 10 88.9 100.6 10 173s 11 75.1 81.0 11 173s 12 76.9 68.6 12 173s 13 84.6 70.9 13 173s 14 90.6 81.4 14 173s 15 103.1 102.3 15 173s 16 105.1 105.0 16 173s 17 96.4 110.5 17 173s 18 104.4 92.5 18 173s 19 110.7 89.3 19 173s 20 127.1 93.0 20 173s > 173s > 173s > ## **************** model matrix ************************ 173s > # with x (returnModelMatrix) = TRUE 173s > print( !is.null( fitw2sls1e$eq[[ 1 ]]$x ) ) 173s [1] TRUE 173s > print( mm <- model.matrix( fitw2sls1e ) ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s demand_1 1 100.3 87.4 0 173s demand_2 1 104.3 97.6 0 173s demand_3 1 103.4 96.7 0 173s demand_4 1 104.5 98.2 0 173s demand_5 1 98.0 99.8 0 173s demand_6 1 99.5 100.5 0 173s demand_7 1 101.1 103.2 0 173s demand_8 1 104.8 107.8 0 173s demand_9 1 96.4 96.6 0 173s demand_10 1 91.2 88.9 0 173s demand_11 1 93.1 75.1 0 173s demand_12 1 98.8 76.9 0 173s demand_13 1 102.9 84.6 0 173s demand_14 1 98.8 90.6 0 173s demand_15 1 95.1 103.1 0 173s demand_16 1 98.5 105.1 0 173s demand_17 1 86.5 96.4 0 173s demand_18 1 104.0 104.4 0 173s demand_19 1 105.8 110.7 0 173s demand_20 1 113.5 127.1 0 173s supply_1 0 0.0 0.0 1 173s supply_2 0 0.0 0.0 1 173s supply_3 0 0.0 0.0 1 173s supply_4 0 0.0 0.0 1 173s supply_5 0 0.0 0.0 1 173s supply_6 0 0.0 0.0 1 173s supply_7 0 0.0 0.0 1 173s supply_8 0 0.0 0.0 1 173s supply_9 0 0.0 0.0 1 173s supply_10 0 0.0 0.0 1 173s supply_11 0 0.0 0.0 1 173s supply_12 0 0.0 0.0 1 173s supply_13 0 0.0 0.0 1 173s supply_14 0 0.0 0.0 1 173s supply_15 0 0.0 0.0 1 173s supply_16 0 0.0 0.0 1 173s supply_17 0 0.0 0.0 1 173s supply_18 0 0.0 0.0 1 173s supply_19 0 0.0 0.0 1 173s supply_20 0 0.0 0.0 1 173s supply_price supply_farmPrice supply_trend 173s demand_1 0.0 0.0 0 173s demand_2 0.0 0.0 0 173s demand_3 0.0 0.0 0 173s demand_4 0.0 0.0 0 173s demand_5 0.0 0.0 0 173s demand_6 0.0 0.0 0 173s demand_7 0.0 0.0 0 173s demand_8 0.0 0.0 0 173s demand_9 0.0 0.0 0 173s demand_10 0.0 0.0 0 173s demand_11 0.0 0.0 0 173s demand_12 0.0 0.0 0 173s demand_13 0.0 0.0 0 173s demand_14 0.0 0.0 0 173s demand_15 0.0 0.0 0 173s demand_16 0.0 0.0 0 173s demand_17 0.0 0.0 0 173s demand_18 0.0 0.0 0 173s demand_19 0.0 0.0 0 173s demand_20 0.0 0.0 0 173s supply_1 100.3 98.0 1 173s supply_2 104.3 99.1 2 173s supply_3 103.4 99.1 3 173s supply_4 104.5 98.1 4 173s supply_5 98.0 110.8 5 173s supply_6 99.5 108.2 6 173s supply_7 101.1 105.6 7 173s supply_8 104.8 109.8 8 173s supply_9 96.4 108.7 9 173s supply_10 91.2 100.6 10 173s supply_11 93.1 81.0 11 173s supply_12 98.8 68.6 12 173s supply_13 102.9 70.9 13 173s supply_14 98.8 81.4 14 173s supply_15 95.1 102.3 15 173s supply_16 98.5 105.0 16 173s supply_17 86.5 110.5 17 173s supply_18 104.0 92.5 18 173s supply_19 105.8 89.3 19 173s supply_20 113.5 93.0 20 173s > print( mm1 <- model.matrix( fitw2sls1e$eq[[ 1 ]] ) ) 173s (Intercept) price income 173s 1 1 100.3 87.4 173s 2 1 104.3 97.6 173s 3 1 103.4 96.7 173s 4 1 104.5 98.2 173s 5 1 98.0 99.8 173s 6 1 99.5 100.5 173s 7 1 101.1 103.2 173s 8 1 104.8 107.8 173s 9 1 96.4 96.6 173s 10 1 91.2 88.9 173s 11 1 93.1 75.1 173s 12 1 98.8 76.9 173s 13 1 102.9 84.6 173s 14 1 98.8 90.6 173s 15 1 95.1 103.1 173s 16 1 98.5 105.1 173s 17 1 86.5 96.4 173s 18 1 104.0 104.4 173s 19 1 105.8 110.7 173s 20 1 113.5 127.1 173s attr(,"assign") 173s [1] 0 1 2 173s > print( mm2 <- model.matrix( fitw2sls1e$eq[[ 2 ]] ) ) 173s (Intercept) price farmPrice trend 173s 1 1 100.3 98.0 1 173s 2 1 104.3 99.1 2 173s 3 1 103.4 99.1 3 173s 4 1 104.5 98.1 4 173s 5 1 98.0 110.8 5 173s 6 1 99.5 108.2 6 173s 7 1 101.1 105.6 7 173s 8 1 104.8 109.8 8 173s 9 1 96.4 108.7 9 173s 10 1 91.2 100.6 10 173s 11 1 93.1 81.0 11 173s 12 1 98.8 68.6 12 173s 13 1 102.9 70.9 13 173s 14 1 98.8 81.4 14 173s 15 1 95.1 102.3 15 173s 16 1 98.5 105.0 16 173s 17 1 86.5 110.5 17 173s 18 1 104.0 92.5 18 173s 19 1 105.8 89.3 19 173s 20 1 113.5 93.0 20 173s attr(,"assign") 173s [1] 0 1 2 3 173s > 173s > # with x (returnModelMatrix) = FALSE 173s > print( all.equal( mm, model.matrix( fitw2sls1 ) ) ) 173s [1] TRUE 173s > print( all.equal( mm1, model.matrix( fitw2sls1$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > print( all.equal( mm2, model.matrix( fitw2sls1$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > print( !is.null( fitw2sls1$eq[[ 1 ]]$x ) ) 173s [1] FALSE 173s > 173s > # with x (returnModelMatrix) = TRUE 173s > print( !is.null( fitw2sls2e$eq[[ 1 ]]$x ) ) 173s [1] TRUE 173s > print( all.equal( mm, model.matrix( fitw2sls2e ) ) ) 173s [1] TRUE 173s > print( all.equal( mm1, model.matrix( fitw2sls2e$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > print( all.equal( mm2, model.matrix( fitw2sls2e$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > 173s > # with x (returnModelMatrix) = FALSE 173s > print( all.equal( mm, model.matrix( fitw2sls2Sym ) ) ) 173s [1] TRUE 173s > print( all.equal( mm1, model.matrix( fitw2sls2Sym$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > print( all.equal( mm2, model.matrix( fitw2sls2Sym$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > print( !is.null( fitw2sls2Sym$eq[[ 1 ]]$x ) ) 173s [1] FALSE 173s > 173s > # with x (returnModelMatrix) = TRUE 173s > print( !is.null( fitw2slsd3$eq[[ 1 ]]$x ) ) 173s [1] TRUE 173s > print( all.equal( mm, model.matrix( fitw2slsd3 ) ) ) 173s [1] TRUE 173s > print( all.equal( mm1, model.matrix( fitw2slsd3$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > print( all.equal( mm2, model.matrix( fitw2slsd3$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > 173s > # with x (returnModelMatrix) = FALSE 173s > print( all.equal( mm, model.matrix( fitw2slsd3e ) ) ) 173s [1] TRUE 173s > print( all.equal( mm1, model.matrix( fitw2slsd3e$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > print( all.equal( mm2, model.matrix( fitw2slsd3e$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > print( !is.null( fitw2slsd3e$eq[[ 1 ]]$x ) ) 173s [1] FALSE 173s > 173s > # with x (returnModelMatrix) = TRUE 173s > print( !is.null( fitw2sls4$eq[[ 1 ]]$x ) ) 173s [1] TRUE 173s > print( all.equal( mm, model.matrix( fitw2sls4 ) ) ) 173s [1] TRUE 173s > print( all.equal( mm1, model.matrix( fitw2sls4$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > print( all.equal( mm2, model.matrix( fitw2sls4$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > 173s > # with x (returnModelMatrix) = FALSE 173s > print( all.equal( mm, model.matrix( fitw2sls4e ) ) ) 173s [1] TRUE 173s > print( all.equal( mm1, model.matrix( fitw2sls4e$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > print( all.equal( mm2, model.matrix( fitw2sls4e$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > print( !is.null( fitw2sls4e$eq[[ 1 ]]$x ) ) 173s [1] FALSE 173s > 173s > # with x (returnModelMatrix) = TRUE 173s > print( !is.null( fitw2sls5$eq[[ 1 ]]$x ) ) 173s [1] TRUE 173s > print( all.equal( mm, model.matrix( fitw2sls5 ) ) ) 173s [1] TRUE 173s > print( all.equal( mm1, model.matrix( fitw2sls5$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > print( all.equal( mm2, model.matrix( fitw2sls5$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > 173s > # with x (returnModelMatrix) = FALSE 173s > print( all.equal( mm, model.matrix( fitw2sls5e ) ) ) 173s [1] TRUE 173s > print( all.equal( mm1, model.matrix( fitw2sls5e$eq[[ 1 ]] ) ) ) 173s [1] TRUE 173s > print( all.equal( mm2, model.matrix( fitw2sls5e$eq[[ 2 ]] ) ) ) 173s [1] TRUE 173s > print( !is.null( fitw2sls5e$eq[[ 1 ]]$x ) ) 173s [1] FALSE 173s > 173s > # matrices of instrumental variables 173s > model.matrix( fitw2sls1, which = "z" ) 173s demand_(Intercept) demand_income demand_farmPrice demand_trend 173s demand_1 1 87.4 98.0 1 173s demand_2 1 97.6 99.1 2 173s demand_3 1 96.7 99.1 3 173s demand_4 1 98.2 98.1 4 173s demand_5 1 99.8 110.8 5 173s demand_6 1 100.5 108.2 6 173s demand_7 1 103.2 105.6 7 173s demand_8 1 107.8 109.8 8 173s demand_9 1 96.6 108.7 9 173s demand_10 1 88.9 100.6 10 173s demand_11 1 75.1 81.0 11 173s demand_12 1 76.9 68.6 12 173s demand_13 1 84.6 70.9 13 173s demand_14 1 90.6 81.4 14 173s demand_15 1 103.1 102.3 15 173s demand_16 1 105.1 105.0 16 173s demand_17 1 96.4 110.5 17 173s demand_18 1 104.4 92.5 18 173s demand_19 1 110.7 89.3 19 173s demand_20 1 127.1 93.0 20 173s supply_1 0 0.0 0.0 0 173s supply_2 0 0.0 0.0 0 173s supply_3 0 0.0 0.0 0 173s supply_4 0 0.0 0.0 0 173s supply_5 0 0.0 0.0 0 173s supply_6 0 0.0 0.0 0 173s supply_7 0 0.0 0.0 0 173s supply_8 0 0.0 0.0 0 173s supply_9 0 0.0 0.0 0 173s supply_10 0 0.0 0.0 0 173s supply_11 0 0.0 0.0 0 173s supply_12 0 0.0 0.0 0 173s supply_13 0 0.0 0.0 0 173s supply_14 0 0.0 0.0 0 173s supply_15 0 0.0 0.0 0 173s supply_16 0 0.0 0.0 0 173s supply_17 0 0.0 0.0 0 173s supply_18 0 0.0 0.0 0 173s supply_19 0 0.0 0.0 0 173s supply_20 0 0.0 0.0 0 173s supply_(Intercept) supply_income supply_farmPrice supply_trend 173s demand_1 0 0.0 0.0 0 173s demand_2 0 0.0 0.0 0 173s demand_3 0 0.0 0.0 0 173s demand_4 0 0.0 0.0 0 173s demand_5 0 0.0 0.0 0 173s demand_6 0 0.0 0.0 0 173s demand_7 0 0.0 0.0 0 173s demand_8 0 0.0 0.0 0 173s demand_9 0 0.0 0.0 0 173s demand_10 0 0.0 0.0 0 173s demand_11 0 0.0 0.0 0 173s demand_12 0 0.0 0.0 0 173s demand_13 0 0.0 0.0 0 173s demand_14 0 0.0 0.0 0 173s demand_15 0 0.0 0.0 0 173s demand_16 0 0.0 0.0 0 173s demand_17 0 0.0 0.0 0 173s demand_18 0 0.0 0.0 0 173s demand_19 0 0.0 0.0 0 173s demand_20 0 0.0 0.0 0 173s supply_1 1 87.4 98.0 1 173s supply_2 1 97.6 99.1 2 173s supply_3 1 96.7 99.1 3 173s supply_4 1 98.2 98.1 4 173s supply_5 1 99.8 110.8 5 173s supply_6 1 100.5 108.2 6 173s supply_7 1 103.2 105.6 7 173s supply_8 1 107.8 109.8 8 173s supply_9 1 96.6 108.7 9 173s supply_10 1 88.9 100.6 10 173s supply_11 1 75.1 81.0 11 173s supply_12 1 76.9 68.6 12 173s supply_13 1 84.6 70.9 13 173s supply_14 1 90.6 81.4 14 173s supply_15 1 103.1 102.3 15 173s supply_16 1 105.1 105.0 16 173s supply_17 1 96.4 110.5 17 173s supply_18 1 104.4 92.5 18 173s supply_19 1 110.7 89.3 19 173s supply_20 1 127.1 93.0 20 173s > model.matrix( fitw2sls1$eq[[ 1 ]], which = "z" ) 173s (Intercept) income farmPrice trend 173s 1 1 87.4 98.0 1 173s 2 1 97.6 99.1 2 173s 3 1 96.7 99.1 3 173s 4 1 98.2 98.1 4 173s 5 1 99.8 110.8 5 173s 6 1 100.5 108.2 6 173s 7 1 103.2 105.6 7 173s 8 1 107.8 109.8 8 173s 9 1 96.6 108.7 9 173s 10 1 88.9 100.6 10 173s 11 1 75.1 81.0 11 173s 12 1 76.9 68.6 12 173s 13 1 84.6 70.9 13 173s 14 1 90.6 81.4 14 173s 15 1 103.1 102.3 15 173s 16 1 105.1 105.0 16 173s 17 1 96.4 110.5 17 173s 18 1 104.4 92.5 18 173s 19 1 110.7 89.3 19 173s 20 1 127.1 93.0 20 173s attr(,"assign") 173s [1] 0 1 2 3 173s > model.matrix( fitw2sls1$eq[[ 2 ]], which = "z" ) 173s (Intercept) income farmPrice trend 173s 1 1 87.4 98.0 1 173s 2 1 97.6 99.1 2 173s 3 1 96.7 99.1 3 173s 4 1 98.2 98.1 4 173s 5 1 99.8 110.8 5 173s 6 1 100.5 108.2 6 173s 7 1 103.2 105.6 7 173s 8 1 107.8 109.8 8 173s 9 1 96.6 108.7 9 173s 10 1 88.9 100.6 10 173s 11 1 75.1 81.0 11 173s 12 1 76.9 68.6 12 173s 13 1 84.6 70.9 13 173s 14 1 90.6 81.4 14 173s 15 1 103.1 102.3 15 173s 16 1 105.1 105.0 16 173s 17 1 96.4 110.5 17 173s 18 1 104.4 92.5 18 173s 19 1 110.7 89.3 19 173s 20 1 127.1 93.0 20 173s attr(,"assign") 173s [1] 0 1 2 3 173s > 173s > # matrices of fitted regressors 173s > model.matrix( fitw2sls5e, which = "xHat" ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s demand_1 1 99.6 87.4 0 173s demand_2 1 105.1 97.6 0 173s demand_3 1 103.8 96.7 0 173s demand_4 1 104.5 98.2 0 173s demand_5 1 98.7 99.8 0 173s demand_6 1 99.6 100.5 0 173s demand_7 1 102.0 103.2 0 173s demand_8 1 102.2 107.8 0 173s demand_9 1 94.6 96.6 0 173s demand_10 1 92.7 88.9 0 173s demand_11 1 92.4 75.1 0 173s demand_12 1 98.9 76.9 0 173s demand_13 1 102.2 84.6 0 173s demand_14 1 100.3 90.6 0 173s demand_15 1 97.6 103.1 0 173s demand_16 1 96.9 105.1 0 173s demand_17 1 87.7 96.4 0 173s demand_18 1 101.1 104.4 0 173s demand_19 1 106.1 110.7 0 173s demand_20 1 114.4 127.1 0 173s supply_1 0 0.0 0.0 1 173s supply_2 0 0.0 0.0 1 173s supply_3 0 0.0 0.0 1 173s supply_4 0 0.0 0.0 1 173s supply_5 0 0.0 0.0 1 173s supply_6 0 0.0 0.0 1 173s supply_7 0 0.0 0.0 1 173s supply_8 0 0.0 0.0 1 173s supply_9 0 0.0 0.0 1 173s supply_10 0 0.0 0.0 1 173s supply_11 0 0.0 0.0 1 173s supply_12 0 0.0 0.0 1 173s supply_13 0 0.0 0.0 1 173s supply_14 0 0.0 0.0 1 173s supply_15 0 0.0 0.0 1 173s supply_16 0 0.0 0.0 1 173s supply_17 0 0.0 0.0 1 173s supply_18 0 0.0 0.0 1 173s supply_19 0 0.0 0.0 1 173s supply_20 0 0.0 0.0 1 173s supply_price supply_farmPrice supply_trend 173s demand_1 0.0 0.0 0 173s demand_2 0.0 0.0 0 173s demand_3 0.0 0.0 0 173s demand_4 0.0 0.0 0 173s demand_5 0.0 0.0 0 173s demand_6 0.0 0.0 0 173s demand_7 0.0 0.0 0 173s demand_8 0.0 0.0 0 173s demand_9 0.0 0.0 0 173s demand_10 0.0 0.0 0 173s demand_11 0.0 0.0 0 173s demand_12 0.0 0.0 0 173s demand_13 0.0 0.0 0 173s demand_14 0.0 0.0 0 173s demand_15 0.0 0.0 0 173s demand_16 0.0 0.0 0 173s demand_17 0.0 0.0 0 173s demand_18 0.0 0.0 0 173s demand_19 0.0 0.0 0 173s demand_20 0.0 0.0 0 173s supply_1 99.6 98.0 1 173s supply_2 105.1 99.1 2 173s supply_3 103.8 99.1 3 173s supply_4 104.5 98.1 4 173s supply_5 98.7 110.8 5 173s supply_6 99.6 108.2 6 173s supply_7 102.0 105.6 7 173s supply_8 102.2 109.8 8 173s supply_9 94.6 108.7 9 173s supply_10 92.7 100.6 10 173s supply_11 92.4 81.0 11 173s supply_12 98.9 68.6 12 173s supply_13 102.2 70.9 13 173s supply_14 100.3 81.4 14 173s supply_15 97.6 102.3 15 173s supply_16 96.9 105.0 16 173s supply_17 87.7 110.5 17 173s supply_18 101.1 92.5 18 173s supply_19 106.1 89.3 19 173s supply_20 114.4 93.0 20 173s > model.matrix( fitw2sls5e$eq[[ 1 ]], which = "xHat" ) 173s (Intercept) price income 173s 1 1 99.6 87.4 173s 2 1 105.1 97.6 173s 3 1 103.8 96.7 173s 4 1 104.5 98.2 173s 5 1 98.7 99.8 173s 6 1 99.6 100.5 173s 7 1 102.0 103.2 173s 8 1 102.2 107.8 173s 9 1 94.6 96.6 173s 10 1 92.7 88.9 173s 11 1 92.4 75.1 173s 12 1 98.9 76.9 173s 13 1 102.2 84.6 173s 14 1 100.3 90.6 173s 15 1 97.6 103.1 173s 16 1 96.9 105.1 173s 17 1 87.7 96.4 173s 18 1 101.1 104.4 173s 19 1 106.1 110.7 173s 20 1 114.4 127.1 173s > model.matrix( fitw2sls5e$eq[[ 2 ]], which = "xHat" ) 173s (Intercept) price farmPrice trend 173s 1 1 99.6 98.0 1 173s 2 1 105.1 99.1 2 173s 3 1 103.8 99.1 3 173s 4 1 104.5 98.1 4 173s 5 1 98.7 110.8 5 173s 6 1 99.6 108.2 6 173s 7 1 102.0 105.6 7 173s 8 1 102.2 109.8 8 173s 9 1 94.6 108.7 9 173s 10 1 92.7 100.6 10 173s 11 1 92.4 81.0 11 173s 12 1 98.9 68.6 12 173s 13 1 102.2 70.9 13 173s 14 1 100.3 81.4 14 173s 15 1 97.6 102.3 15 173s 16 1 96.9 105.0 16 173s 17 1 87.7 110.5 17 173s 18 1 101.1 92.5 18 173s 19 1 106.1 89.3 19 173s 20 1 114.4 93.0 20 173s > 173s > 173s > ## **************** formulas ************************ 173s > formula( fitw2sls1e ) 173s $demand 173s consump ~ price + income 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s 173s > formula( fitw2sls1e$eq[[ 1 ]] ) 173s consump ~ price + income 173s > 173s > formula( fitw2sls2 ) 173s $demand 173s consump ~ price + income 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s 173s > formula( fitw2sls2$eq[[ 2 ]] ) 173s consump ~ price + farmPrice + trend 173s > 173s > formula( fitw2sls3 ) 173s $demand 173s consump ~ price + income 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s 173s > formula( fitw2sls3$eq[[ 1 ]] ) 173s consump ~ price + income 173s > 173s > formula( fitw2sls4e ) 173s $demand 173s consump ~ price + income 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s 173s > formula( fitw2sls4e$eq[[ 2 ]] ) 173s consump ~ price + farmPrice + trend 173s > 173s > formula( fitw2sls5 ) 173s $demand 173s consump ~ price + income 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s 173s > formula( fitw2sls5$eq[[ 1 ]] ) 173s consump ~ price + income 173s > 173s > formula( fitw2slsd1 ) 173s $demand 173s consump ~ price + income 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s 173s > formula( fitw2slsd1$eq[[ 2 ]] ) 173s consump ~ price + farmPrice + trend 173s > 173s > formula( fitw2slsd2e ) 173s $demand 173s consump ~ price + income 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s 173s > formula( fitw2slsd2e$eq[[ 1 ]] ) 173s consump ~ price + income 173s > 173s > formula( fitw2slsd3e ) 173s $demand 173s consump ~ price + income 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s 173s > formula( fitw2slsd3e$eq[[ 2 ]] ) 173s consump ~ price + farmPrice + trend 173s > 173s > 173s > ## **************** model terms ******************* 173s > terms( fitw2sls1e ) 173s $demand 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s 173s > terms( fitw2sls1e$eq[[ 1 ]] ) 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s > 173s > terms( fitw2sls2 ) 173s $demand 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s 173s > terms( fitw2sls2$eq[[ 2 ]] ) 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s > 173s > terms( fitw2sls3 ) 173s $demand 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s 173s > terms( fitw2sls3$eq[[ 1 ]] ) 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s > 173s > terms( fitw2sls4e ) 173s $demand 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s 173s > terms( fitw2sls4e$eq[[ 2 ]] ) 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s > 173s > terms( fitw2sls5 ) 173s $demand 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s 173s > terms( fitw2sls5$eq[[ 1 ]] ) 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s > 173s > terms( fitw2slsd1 ) 173s $demand 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s 173s > terms( fitw2slsd1$eq[[ 2 ]] ) 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s > 173s > terms( fitw2slsd2e ) 173s $demand 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s 173s > terms( fitw2slsd2e$eq[[ 1 ]] ) 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s > 173s > terms( fitw2slsd3e ) 173s $demand 173s consump ~ price + income 173s attr(,"variables") 173s list(consump, price, income) 173s attr(,"factors") 173s price income 173s consump 0 0 173s price 1 0 173s income 0 1 173s attr(,"term.labels") 173s [1] "price" "income" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, income) 173s attr(,"dataClasses") 173s consump price income 173s "numeric" "numeric" "numeric" 173s 173s $supply 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s 173s > terms( fitw2slsd3e$eq[[ 2 ]] ) 173s consump ~ price + farmPrice + trend 173s attr(,"variables") 173s list(consump, price, farmPrice, trend) 173s attr(,"factors") 173s price farmPrice trend 173s consump 0 0 0 173s price 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "price" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 1 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(consump, price, farmPrice, trend) 173s attr(,"dataClasses") 173s consump price farmPrice trend 173s "numeric" "numeric" "numeric" "numeric" 173s > 173s > 173s > ## **************** terms of instruments ******************* 173s > fitw2sls1e$eq[[ 1 ]]$termsInst 173s ~income + farmPrice + trend 173s attr(,"variables") 173s list(income, farmPrice, trend) 173s attr(,"factors") 173s income farmPrice trend 173s income 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "income" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 0 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(income, farmPrice, trend) 173s attr(,"dataClasses") 173s income farmPrice trend 173s "numeric" "numeric" "numeric" 173s > 173s > fitw2sls2$eq[[ 2 ]]$termsInst 173s ~income + farmPrice + trend 173s attr(,"variables") 173s list(income, farmPrice, trend) 173s attr(,"factors") 173s income farmPrice trend 173s income 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "income" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 0 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(income, farmPrice, trend) 173s attr(,"dataClasses") 173s income farmPrice trend 173s "numeric" "numeric" "numeric" 173s > 173s > fitw2sls3$eq[[ 1 ]]$termsInst 173s ~income + farmPrice + trend 173s attr(,"variables") 173s list(income, farmPrice, trend) 173s attr(,"factors") 173s income farmPrice trend 173s income 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "income" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 0 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(income, farmPrice, trend) 173s attr(,"dataClasses") 173s income farmPrice trend 173s "numeric" "numeric" "numeric" 173s > 173s > fitw2sls4e$eq[[ 2 ]]$termsInst 173s ~income + farmPrice + trend 173s attr(,"variables") 173s list(income, farmPrice, trend) 173s attr(,"factors") 173s income farmPrice trend 173s income 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "income" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 0 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(income, farmPrice, trend) 173s attr(,"dataClasses") 173s income farmPrice trend 173s "numeric" "numeric" "numeric" 173s > 173s > fitw2sls5$eq[[ 1 ]]$termsInst 173s ~income + farmPrice + trend 173s attr(,"variables") 173s list(income, farmPrice, trend) 173s attr(,"factors") 173s income farmPrice trend 173s income 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "income" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 0 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(income, farmPrice, trend) 173s attr(,"dataClasses") 173s income farmPrice trend 173s "numeric" "numeric" "numeric" 173s > 173s > fitw2slsd1$eq[[ 2 ]]$termsInst 173s ~income + farmPrice + trend 173s attr(,"variables") 173s list(income, farmPrice, trend) 173s attr(,"factors") 173s income farmPrice trend 173s income 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "income" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 0 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(income, farmPrice, trend) 173s attr(,"dataClasses") 173s income farmPrice trend 173s "numeric" "numeric" "numeric" 173s > 173s > fitw2slsd2e$eq[[ 1 ]]$termsInst 173s ~income + farmPrice 173s attr(,"variables") 173s list(income, farmPrice) 173s attr(,"factors") 173s income farmPrice 173s income 1 0 173s farmPrice 0 1 173s attr(,"term.labels") 173s [1] "income" "farmPrice" 173s attr(,"order") 173s [1] 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 0 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(income, farmPrice) 173s attr(,"dataClasses") 173s income farmPrice 173s "numeric" "numeric" 173s > 173s > fitw2slsd3e$eq[[ 2 ]]$termsInst 173s ~income + farmPrice + trend 173s attr(,"variables") 173s list(income, farmPrice, trend) 173s attr(,"factors") 173s income farmPrice trend 173s income 1 0 0 173s farmPrice 0 1 0 173s trend 0 0 1 173s attr(,"term.labels") 173s [1] "income" "farmPrice" "trend" 173s attr(,"order") 173s [1] 1 1 1 173s attr(,"intercept") 173s [1] 1 173s attr(,"response") 173s [1] 0 173s attr(,".Environment") 173s 173s attr(,"predvars") 173s list(income, farmPrice, trend) 173s attr(,"dataClasses") 173s income farmPrice trend 173s "numeric" "numeric" "numeric" 173s > 173s > 173s > ## **************** estfun ************************ 173s > library( "sandwich" ) 173s > 173s > estfun( fitw2sls1 ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s demand_1 0.17426 17.362 15.231 0.0000 173s demand_2 -0.12666 -13.314 -12.362 0.0000 173s demand_3 0.63211 65.603 61.125 0.0000 173s demand_4 0.38686 40.439 37.990 0.0000 173s demand_5 0.59421 58.619 59.302 0.0000 173s demand_6 0.34231 34.111 34.403 0.0000 173s demand_7 0.46340 47.253 47.822 0.0000 173s demand_8 -0.95225 -97.353 -102.653 0.0000 173s demand_9 -0.40681 -38.486 -39.297 0.0000 173s demand_10 0.73846 68.469 65.649 0.0000 173s demand_11 -0.07078 -6.540 -5.315 0.0000 173s demand_12 -0.58541 -57.907 -45.018 0.0000 173s demand_13 -0.46025 -47.020 -38.937 0.0000 173s demand_14 0.02562 2.569 2.322 0.0000 173s demand_15 0.66403 64.824 68.462 0.0000 173s demand_16 -0.98546 -95.483 -103.572 0.0000 173s demand_17 -0.00533 -0.468 -0.514 0.0000 173s demand_18 -0.74266 -75.053 -77.534 0.0000 173s demand_19 0.43017 45.625 47.620 0.0000 173s demand_20 -0.11583 -13.250 -14.722 0.0000 173s supply_1 0.00000 0.000 0.000 -0.0444 173s supply_2 0.00000 0.000 0.000 -0.2348 173s supply_3 0.00000 0.000 0.000 0.2691 173s supply_4 0.00000 0.000 0.000 0.1308 173s supply_5 0.00000 0.000 0.000 0.2381 173s supply_6 0.00000 0.000 0.000 0.1015 173s supply_7 0.00000 0.000 0.000 0.2015 173s supply_8 0.00000 0.000 0.000 -0.7062 173s supply_9 0.00000 0.000 0.000 -0.3238 173s supply_10 0.00000 0.000 0.000 0.4611 173s supply_11 0.00000 0.000 0.000 0.0385 173s supply_12 0.00000 0.000 0.000 -0.2360 173s supply_13 0.00000 0.000 0.000 -0.1548 173s supply_14 0.00000 0.000 0.000 0.1330 173s supply_15 0.00000 0.000 0.000 0.4778 173s supply_16 0.00000 0.000 0.000 -0.5719 173s supply_17 0.00000 0.000 0.000 0.0648 173s supply_18 0.00000 0.000 0.000 -0.3413 173s supply_19 0.00000 0.000 0.000 0.4299 173s supply_20 0.00000 0.000 0.000 0.0672 173s supply_price supply_farmPrice supply_trend 173s demand_1 0.00 0.00 0.0000 173s demand_2 0.00 0.00 0.0000 173s demand_3 0.00 0.00 0.0000 173s demand_4 0.00 0.00 0.0000 173s demand_5 0.00 0.00 0.0000 173s demand_6 0.00 0.00 0.0000 173s demand_7 0.00 0.00 0.0000 173s demand_8 0.00 0.00 0.0000 173s demand_9 0.00 0.00 0.0000 173s demand_10 0.00 0.00 0.0000 173s demand_11 0.00 0.00 0.0000 173s demand_12 0.00 0.00 0.0000 173s demand_13 0.00 0.00 0.0000 173s demand_14 0.00 0.00 0.0000 173s demand_15 0.00 0.00 0.0000 173s demand_16 0.00 0.00 0.0000 173s demand_17 0.00 0.00 0.0000 173s demand_18 0.00 0.00 0.0000 173s demand_19 0.00 0.00 0.0000 173s demand_20 0.00 0.00 0.0000 173s supply_1 -4.42 -4.35 -0.0444 173s supply_2 -24.68 -23.27 -0.4696 173s supply_3 27.93 26.67 0.8073 173s supply_4 13.67 12.83 0.5230 173s supply_5 23.49 26.38 1.1905 173s supply_6 10.12 10.99 0.6093 173s supply_7 20.55 21.28 1.4107 173s supply_8 -72.20 -77.54 -5.6498 173s supply_9 -30.64 -35.20 -2.9145 173s supply_10 42.75 46.39 4.6109 173s supply_11 3.56 3.12 0.4235 173s supply_12 -23.35 -16.19 -2.8326 173s supply_13 -15.81 -10.97 -2.0121 173s supply_14 13.34 10.83 1.8621 173s supply_15 46.64 48.88 7.1671 173s supply_16 -55.42 -60.05 -9.1508 173s supply_17 5.68 7.16 1.1011 173s supply_18 -34.49 -31.57 -6.1438 173s supply_19 45.59 38.39 8.1674 173s supply_20 7.69 6.25 1.3448 173s > round( colSums( estfun( fitw2sls1 ) ), digits = 7 ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s 0 0 0 0 173s supply_price supply_farmPrice supply_trend 173s 0 0 0 173s > 173s > estfun( fitw2sls1e ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s demand_1 0.20502 20.43 17.918 0.0000 173s demand_2 -0.14901 -15.66 -14.543 0.0000 173s demand_3 0.74366 77.18 71.912 0.0000 173s demand_4 0.45513 47.57 44.694 0.0000 173s demand_5 0.69907 68.96 69.767 0.0000 173s demand_6 0.40272 40.13 40.474 0.0000 173s demand_7 0.54517 55.59 56.262 0.0000 173s demand_8 -1.12030 -114.53 -120.768 0.0000 173s demand_9 -0.47860 -45.28 -46.232 0.0000 173s demand_10 0.86877 80.55 77.234 0.0000 173s demand_11 -0.08327 -7.69 -6.253 0.0000 173s demand_12 -0.68871 -68.13 -52.962 0.0000 173s demand_13 -0.54147 -55.32 -45.808 0.0000 173s demand_14 0.03015 3.02 2.731 0.0000 173s demand_15 0.78121 76.26 80.543 0.0000 173s demand_16 -1.15937 -112.33 -121.850 0.0000 173s demand_17 -0.00627 -0.55 -0.605 0.0000 173s demand_18 -0.87372 -88.30 -91.217 0.0000 173s demand_19 0.50608 53.68 56.023 0.0000 173s demand_20 -0.13627 -15.59 -17.320 0.0000 173s supply_1 0.00000 0.00 0.000 -0.0554 173s supply_2 0.00000 0.00 0.000 -0.2935 173s supply_3 0.00000 0.00 0.000 0.3364 173s supply_4 0.00000 0.00 0.000 0.1634 173s supply_5 0.00000 0.00 0.000 0.2976 173s supply_6 0.00000 0.00 0.000 0.1269 173s supply_7 0.00000 0.00 0.000 0.2519 173s supply_8 0.00000 0.00 0.000 -0.8828 173s supply_9 0.00000 0.00 0.000 -0.4048 173s supply_10 0.00000 0.00 0.000 0.5764 173s supply_11 0.00000 0.00 0.000 0.0481 173s supply_12 0.00000 0.00 0.000 -0.2951 173s supply_13 0.00000 0.00 0.000 -0.1935 173s supply_14 0.00000 0.00 0.000 0.1663 173s supply_15 0.00000 0.00 0.000 0.5973 173s supply_16 0.00000 0.00 0.000 -0.7149 173s supply_17 0.00000 0.00 0.000 0.0810 173s supply_18 0.00000 0.00 0.000 -0.4267 173s supply_19 0.00000 0.00 0.000 0.5373 173s supply_20 0.00000 0.00 0.000 0.0841 173s supply_price supply_farmPrice supply_trend 173s demand_1 0.00 0.00 0.0000 173s demand_2 0.00 0.00 0.0000 173s demand_3 0.00 0.00 0.0000 173s demand_4 0.00 0.00 0.0000 173s demand_5 0.00 0.00 0.0000 173s demand_6 0.00 0.00 0.0000 173s demand_7 0.00 0.00 0.0000 173s demand_8 0.00 0.00 0.0000 173s demand_9 0.00 0.00 0.0000 173s demand_10 0.00 0.00 0.0000 173s demand_11 0.00 0.00 0.0000 173s demand_12 0.00 0.00 0.0000 173s demand_13 0.00 0.00 0.0000 173s demand_14 0.00 0.00 0.0000 173s demand_15 0.00 0.00 0.0000 173s demand_16 0.00 0.00 0.0000 173s demand_17 0.00 0.00 0.0000 173s demand_18 0.00 0.00 0.0000 173s demand_19 0.00 0.00 0.0000 173s demand_20 0.00 0.00 0.0000 173s supply_1 -5.52 -5.43 -0.0554 173s supply_2 -30.85 -29.09 -0.5870 173s supply_3 34.91 33.33 1.0091 173s supply_4 17.09 16.03 0.6538 173s supply_5 29.36 32.98 1.4882 173s supply_6 12.65 13.73 0.7616 173s supply_7 25.69 26.60 1.7633 173s supply_8 -90.25 -96.93 -7.0623 173s supply_9 -38.30 -44.00 -3.6431 173s supply_10 53.44 57.98 5.7636 173s supply_11 4.45 3.90 0.5294 173s supply_12 -29.19 -20.24 -3.5407 173s supply_13 -19.77 -13.72 -2.5151 173s supply_14 16.67 13.53 2.3277 173s supply_15 58.30 61.10 8.9588 173s supply_16 -69.27 -75.07 -11.4386 173s supply_17 7.10 8.95 1.3763 173s supply_18 -43.12 -39.47 -7.6797 173s supply_19 56.99 47.98 10.2092 173s supply_20 9.62 7.82 1.6810 173s > round( colSums( estfun( fitw2sls1e ) ), digits = 7 ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s 0 0 0 0 173s supply_price supply_farmPrice supply_trend 173s 0 0 0 173s > 173s > estfun( fitw2slsd1e ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s demand_1 -0.2141 -20.39 -18.71 0.0000 173s demand_2 -0.5971 -59.32 -58.28 0.0000 173s demand_3 0.3342 33.06 32.31 0.0000 173s demand_4 0.0923 9.21 9.06 0.0000 173s demand_5 0.3748 36.34 37.40 0.0000 173s demand_6 0.1317 12.91 13.23 0.0000 173s demand_7 0.2982 29.80 30.78 0.0000 173s demand_8 -1.3110 -132.05 -141.32 0.0000 173s demand_9 -0.5322 -51.18 -51.41 0.0000 173s demand_10 0.8995 85.57 79.97 0.0000 173s demand_11 0.1399 13.25 10.51 0.0000 173s demand_12 -0.4189 -41.49 -32.21 0.0000 173s demand_13 -0.2903 -29.54 -24.56 0.0000 173s demand_14 0.2709 27.46 24.55 0.0000 173s demand_15 0.9535 96.13 98.30 0.0000 173s demand_16 -0.9012 -90.95 -94.71 0.0000 173s demand_17 0.3566 34.08 34.37 0.0000 173s demand_18 -0.5159 -53.75 -53.86 0.0000 173s demand_19 0.8239 88.84 91.20 0.0000 173s demand_20 0.1054 12.00 13.39 0.0000 173s supply_1 0.0000 0.00 0.00 -0.0554 173s supply_2 0.0000 0.00 0.00 -0.2935 173s supply_3 0.0000 0.00 0.00 0.3364 173s supply_4 0.0000 0.00 0.00 0.1634 173s supply_5 0.0000 0.00 0.00 0.2976 173s supply_6 0.0000 0.00 0.00 0.1269 173s supply_7 0.0000 0.00 0.00 0.2519 173s supply_8 0.0000 0.00 0.00 -0.8828 173s supply_9 0.0000 0.00 0.00 -0.4048 173s supply_10 0.0000 0.00 0.00 0.5764 173s supply_11 0.0000 0.00 0.00 0.0481 173s supply_12 0.0000 0.00 0.00 -0.2951 173s supply_13 0.0000 0.00 0.00 -0.1935 173s supply_14 0.0000 0.00 0.00 0.1663 173s supply_15 0.0000 0.00 0.00 0.5973 173s supply_16 0.0000 0.00 0.00 -0.7149 173s supply_17 0.0000 0.00 0.00 0.0810 173s supply_18 0.0000 0.00 0.00 -0.4267 173s supply_19 0.0000 0.00 0.00 0.5373 173s supply_20 0.0000 0.00 0.00 0.0841 173s supply_price supply_farmPrice supply_trend 173s demand_1 0.00 0.00 0.0000 173s demand_2 0.00 0.00 0.0000 173s demand_3 0.00 0.00 0.0000 173s demand_4 0.00 0.00 0.0000 173s demand_5 0.00 0.00 0.0000 173s demand_6 0.00 0.00 0.0000 173s demand_7 0.00 0.00 0.0000 173s demand_8 0.00 0.00 0.0000 173s demand_9 0.00 0.00 0.0000 173s demand_10 0.00 0.00 0.0000 173s demand_11 0.00 0.00 0.0000 173s demand_12 0.00 0.00 0.0000 173s demand_13 0.00 0.00 0.0000 173s demand_14 0.00 0.00 0.0000 173s demand_15 0.00 0.00 0.0000 173s demand_16 0.00 0.00 0.0000 173s demand_17 0.00 0.00 0.0000 173s demand_18 0.00 0.00 0.0000 173s demand_19 0.00 0.00 0.0000 173s demand_20 0.00 0.00 0.0000 173s supply_1 -5.52 -5.43 -0.0554 173s supply_2 -30.85 -29.09 -0.5870 173s supply_3 34.91 33.33 1.0091 173s supply_4 17.09 16.03 0.6538 173s supply_5 29.36 32.98 1.4882 173s supply_6 12.65 13.73 0.7616 173s supply_7 25.69 26.60 1.7633 173s supply_8 -90.25 -96.93 -7.0623 173s supply_9 -38.30 -44.00 -3.6431 173s supply_10 53.44 57.98 5.7636 173s supply_11 4.45 3.90 0.5294 173s supply_12 -29.19 -20.24 -3.5407 173s supply_13 -19.77 -13.72 -2.5151 173s supply_14 16.67 13.53 2.3277 173s supply_15 58.30 61.10 8.9588 173s supply_16 -69.27 -75.07 -11.4386 173s supply_17 7.10 8.95 1.3763 173s supply_18 -43.12 -39.47 -7.6797 173s supply_19 56.99 47.98 10.2092 173s supply_20 9.62 7.82 1.6810 173s > round( colSums( estfun( fitw2slsd1e ) ), digits = 7 ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s 0 0 0 0 173s supply_price supply_farmPrice supply_trend 173s 0 0 0 173s > 173s > 173s > ## **************** bread ************************ 173s > bread( fitw2sls1 ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s [1,] 2509.59 -26.937 1.9721 0.0 173s [2,] -26.94 0.372 -0.1057 0.0 173s [3,] 1.97 -0.106 0.0881 0.0 173s [4,] 0.00 0.000 0.0000 5770.1 173s [5,] 0.00 0.000 0.0000 -43.8 173s [6,] 0.00 0.000 0.0000 -13.0 173s [7,] 0.00 0.000 0.0000 -11.8 173s supply_price supply_farmPrice supply_trend 173s [1,] 0.0000 0.0000 0.0000 173s [2,] 0.0000 0.0000 0.0000 173s [3,] 0.0000 0.0000 0.0000 173s [4,] -43.8164 -12.9527 -11.8092 173s [5,] 0.3995 0.0374 0.0232 173s [6,] 0.0374 0.0893 0.0551 173s [7,] 0.0232 0.0551 0.3972 173s > 173s > bread( fitw2sls1e ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s [1,] 2133.15 -22.8963 1.6763 0.00 173s [2,] -22.90 0.3165 -0.0898 0.00 173s [3,] 1.68 -0.0898 0.0749 0.00 173s [4,] 0.00 0.0000 0.0000 4616.09 173s [5,] 0.00 0.0000 0.0000 -35.05 173s [6,] 0.00 0.0000 0.0000 -10.36 173s [7,] 0.00 0.0000 0.0000 -9.45 173s supply_price supply_farmPrice supply_trend 173s [1,] 0.0000 0.0000 0.0000 173s [2,] 0.0000 0.0000 0.0000 173s [3,] 0.0000 0.0000 0.0000 173s [4,] -35.0531 -10.3622 -9.4473 173s [5,] 0.3196 0.0300 0.0185 173s [6,] 0.0300 0.0714 0.0441 173s [7,] 0.0185 0.0441 0.3178 173s > 173s > bread( fitw2slsd1e ) 173s demand_(Intercept) demand_price demand_income supply_(Intercept) 173s [1,] 4222.1 -51.601 9.696 0.00 173s [2,] -51.6 0.713 -0.202 0.00 173s [3,] 9.7 -0.202 0.108 0.00 173s [4,] 0.0 0.000 0.000 4616.09 173s [5,] 0.0 0.000 0.000 -35.05 173s [6,] 0.0 0.000 0.000 -10.36 173s [7,] 0.0 0.000 0.000 -9.45 173s supply_price supply_farmPrice supply_trend 173s [1,] 0.0000 0.0000 0.0000 173s [2,] 0.0000 0.0000 0.0000 173s [3,] 0.0000 0.0000 0.0000 173s [4,] -35.0531 -10.3622 -9.4473 173s [5,] 0.3196 0.0300 0.0185 173s [6,] 0.0300 0.0714 0.0441 173s [7,] 0.0185 0.0441 0.3178 173s > 173s BEGIN TEST test_wls.R 173s 173s R version 4.3.2 (2023-10-31) -- "Eye Holes" 173s Copyright (C) 2023 The R Foundation for Statistical Computing 173s Platform: x86_64-pc-linux-gnu (64-bit) 173s 173s R is free software and comes with ABSOLUTELY NO WARRANTY. 173s You are welcome to redistribute it under certain conditions. 173s Type 'license()' or 'licence()' for distribution details. 173s 173s R is a collaborative project with many contributors. 173s Type 'contributors()' for more information and 173s 'citation()' on how to cite R or R packages in publications. 173s 173s Type 'demo()' for some demos, 'help()' for on-line help, or 173s 'help.start()' for an HTML browser interface to help. 173s Type 'q()' to quit R. 173s 173s > library( systemfit ) 173s Loading required package: Matrix 174s Loading required package: car 174s Loading required package: carData 174s Loading required package: lmtest 174s Loading required package: zoo 174s 174s Attaching package: ‘zoo’ 174s 174s The following objects are masked from ‘package:base’: 174s 174s as.Date, as.Date.numeric 174s 174s > options( digits = 3 ) 174s > 174s > data( "Kmenta" ) 174s 174s Please cite the 'systemfit' package as: 174s 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/. 174s 174s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 174s https://r-forge.r-project.org/projects/systemfit/ 174s > useMatrix <- FALSE 174s > 174s > demand <- consump ~ price + income 174s > supply <- consump ~ price + farmPrice + trend 174s > system <- list( demand = demand, supply = supply ) 174s > restrm <- matrix(0,1,7) # restriction matrix "R" 174s > restrm[1,3] <- 1 174s > restrm[1,7] <- -1 174s > restrict <- "demand_income - supply_trend = 0" 174s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 174s > restr2m[1,3] <- 1 174s > restr2m[1,7] <- -1 174s > restr2m[2,2] <- -1 174s > restr2m[2,5] <- 1 174s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 174s > restrict2 <- c( "demand_income - supply_trend = 0", 174s + "- demand_price + supply_price = 0.5" ) 174s > tc <- matrix(0,7,6) 174s > tc[1,1] <- 1 174s > tc[2,2] <- 1 174s > tc[3,3] <- 1 174s > tc[4,4] <- 1 174s > tc[5,5] <- 1 174s > tc[6,6] <- 1 174s > tc[7,3] <- 1 174s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 174s > restr3m[1,2] <- -1 174s > restr3m[1,5] <- 1 174s > restr3q <- c( 0.5 ) # restriction vector "q" 2 174s > restrict3 <- "- C2 + C5 = 0.5" 174s > 174s > 174s > ## ******* single-equation OLS estimations ********************* 174s > lmDemand <- lm( demand, data = Kmenta ) 174s > lmSupply <- lm( supply, data = Kmenta ) 174s > 174s > ## *************** WLS estimation ************************ 174s > fitwls1 <- systemfit( system, "WLS", data = Kmenta, useMatrix = useMatrix ) 174s > print( summary( fitwls1 ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 33 156 4.43 0.709 0.558 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.3 3.73 1.93 0.764 0.736 174s supply 20 16 92.6 5.78 2.40 0.655 0.590 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.73 0.00 174s supply 0.00 5.78 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.73 4.14 174s supply 4.14 5.78 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.891 174s supply 0.891 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 174s price -0.3163 0.0907 -3.49 0.0028 ** 174s income 0.3346 0.0454 7.37 1.1e-06 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.93 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 174s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 174s price 0.1604 0.0949 1.69 0.11039 174s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 174s trend 0.2483 0.0975 2.55 0.02157 * 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.405 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 174s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 174s 174s > all.equal( coef( fitwls1 ), c( coef( lmDemand ), coef( lmSupply ) ), 174s + check.attributes = FALSE ) 174s [1] TRUE 174s > all.equal( coef( summary( fitwls1 ) ), 174s + rbind( coef( summary( lmDemand ) ), coef( summary( lmSupply ) ) ), 174s + check.attributes = FALSE ) 174s [1] TRUE 174s > all.equal( vcov( fitwls1 ), 174s + as.matrix( bdiag( vcov( lmDemand ), vcov( lmSupply ) ) ), 174s + check.attributes = FALSE ) 174s [1] TRUE 174s > 174s > ## *************** WLS estimation (EViews-like) ************************ 174s > fitwls1e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 174s + x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwls1e, useDfSys = TRUE ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 33 156 3.02 0.709 0.537 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.3 3.73 1.93 0.764 0.736 174s supply 20 16 92.6 5.78 2.40 0.655 0.590 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.17 0.00 174s supply 0.00 4.63 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.17 3.41 174s supply 3.41 4.63 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.891 174s supply 0.891 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.8954 6.9325 14.41 8.9e-16 *** 174s price -0.3163 0.0836 -3.78 0.00062 *** 174s income 0.3346 0.0419 7.99 3.2e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.93 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 174s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 58.2754 10.2527 5.68 2.4e-06 *** 174s price 0.1604 0.0849 1.89 0.0676 . 174s farmPrice 0.2481 0.0413 6.01 9.5e-07 *** 174s trend 0.2483 0.0872 2.85 0.0075 ** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.405 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 174s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 174s 174s > all.equal( coef( fitwls1e ), c( coef( lmDemand ), coef( lmSupply ) ), 174s + check.attributes = FALSE ) 174s [1] TRUE 174s > 174s > ## ************** WLS with cross-equation restriction *************** 174s > fitwls2 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 174s + x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwls2 ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 2.35 0.703 0.622 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.8 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.98 2.44 0.643 0.576 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.78 0.00 174s supply 0.00 5.94 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.75 4.48 174s supply 4.48 5.98 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.946 174s supply 0.946 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.6582 7.5640 13.18 6.4e-15 *** 174s price -0.2991 0.0887 -3.37 0.0019 ** 174s income 0.3194 0.0415 7.70 6.0e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.936 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.75 MSE: 3.75 Root MSE: 1.936 174s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.1877 11.3165 4.97 1.9e-05 *** 174s price 0.1643 0.0960 1.71 0.096 . 174s farmPrice 0.2580 0.0451 5.71 2.0e-06 *** 174s trend 0.3194 0.0415 7.70 6.0e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.445 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 95.627 MSE: 5.977 Root MSE: 2.445 174s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 174s 174s > # the same with symbolically specified restrictions 174s > fitwls2Sym <- systemfit( system, "WLS", data = Kmenta, 174s + restrict.matrix = restrict, x = TRUE, 174s + useMatrix = useMatrix ) 174s > all.equal( fitwls2, fitwls2Sym ) 174s [1] "Component “call”: target, current do not match when deparsed" 174s > 174s > ## ************** WLS with cross-equation restriction (EViews-like) ******* 174s > fitwls2e <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 174s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 174s > print( summary( fitwls2e ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 1.61 0.703 0.589 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.8 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.97 2.44 0.644 0.577 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.21 0.00 174s supply 0.00 4.75 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.19 3.69 174s supply 3.69 4.78 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.946 174s supply 0.946 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.6461 6.9734 14.29 6.7e-16 *** 174s price -0.2982 0.0816 -3.65 0.00086 *** 174s income 0.3186 0.0381 8.37 8.9e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.937 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.794 MSE: 3.753 Root MSE: 1.937 174s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.2104 10.1248 5.55 3.3e-06 *** 174s price 0.1642 0.0859 1.91 0.064 . 174s farmPrice 0.2579 0.0404 6.38 2.7e-07 *** 174s trend 0.3186 0.0381 8.37 8.9e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.444 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 95.561 MSE: 5.973 Root MSE: 2.444 174s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 174s 174s > 174s > ## ******* WLS with cross-equation restriction via restrict.regMat ********** 174s > fitwls3 <- systemfit( system,"WLS", data = Kmenta, restrict.regMat = tc, 174s + x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwls3 ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 2.35 0.703 0.622 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.8 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.98 2.44 0.643 0.576 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.78 0.00 174s supply 0.00 5.94 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.75 4.48 174s supply 4.48 5.98 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.946 174s supply 0.946 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.6582 7.5640 13.18 6.4e-15 *** 174s price -0.2991 0.0887 -3.37 0.0019 ** 174s income 0.3194 0.0415 7.70 6.0e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.936 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.75 MSE: 3.75 Root MSE: 1.936 174s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.1877 11.3165 4.97 1.9e-05 *** 174s price 0.1643 0.0960 1.71 0.096 . 174s farmPrice 0.2580 0.0451 5.71 2.0e-06 *** 174s trend 0.3194 0.0415 7.70 6.0e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.445 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 95.627 MSE: 5.977 Root MSE: 2.445 174s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 174s 174s > 174s > ## ******* WLS with cross-equation restriction via restrict.regMat (EViews-like) ***** 174s > fitwls3e <- systemfit( system,"WLS", data = Kmenta, restrict.regMat = tc, 174s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 174s > print( summary( fitwls3e ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 1.61 0.703 0.589 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.8 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.97 2.44 0.644 0.577 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.21 0.00 174s supply 0.00 4.75 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.19 3.69 174s supply 3.69 4.78 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.946 174s supply 0.946 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.6461 6.9734 14.29 6.7e-16 *** 174s price -0.2982 0.0816 -3.65 0.00086 *** 174s income 0.3186 0.0381 8.37 8.9e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.937 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.794 MSE: 3.753 Root MSE: 1.937 174s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.2104 10.1248 5.55 3.3e-06 *** 174s price 0.1642 0.0859 1.91 0.064 . 174s farmPrice 0.2579 0.0404 6.38 2.7e-07 *** 174s trend 0.3186 0.0381 8.37 8.9e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.444 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 95.561 MSE: 5.973 Root MSE: 2.444 174s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 174s 174s > 174s > ## ***** WLS with 2 cross-equation restrictions *************** 174s > fitwls4 <- systemfit( system,"WLS", data = Kmenta, restrict.matrix = restr2m, 174s + restrict.rhs = restr2q, useMatrix = useMatrix ) 174s > print( summary( fitwls4 ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 2.51 0.702 0.619 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.6 3.74 1.94 0.763 0.735 174s supply 20 16 96.3 6.02 2.45 0.641 0.574 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.76 0.00 174s supply 0.00 5.99 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.74 4.47 174s supply 4.47 6.02 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.943 174s supply 0.943 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9138 6.0474 16.69 < 2e-16 *** 174s price -0.3160 0.0648 -4.87 2.3e-05 *** 174s income 0.3238 0.0385 8.42 6.3e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.636 MSE: 3.743 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9416 7.9687 6.77 7.6e-08 *** 174s price 0.1840 0.0648 2.84 0.0075 ** 174s farmPrice 0.2603 0.0446 5.84 1.3e-06 *** 174s trend 0.3238 0.0385 8.42 6.3e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.453 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.268 MSE: 6.017 Root MSE: 2.453 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > # the same with symbolically specified restrictions 174s > fitwls4Sym <- systemfit( system, "WLS", data = Kmenta, 174s + restrict.matrix = restrict2, useMatrix = useMatrix ) 174s > all.equal( fitwls4, fitwls4Sym ) 174s [1] "Component “call”: target, current do not match when deparsed" 174s > 174s > ## ***** WLS with 2 cross-equation restrictions (EViews-like) ********** 174s > fitwls4e <- systemfit( system,"WLS", data = Kmenta, methodResidCov = "noDfCor", 174s + restrict.matrix = restr2m, restrict.rhs = restr2q, 174s + x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwls4e ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 1.72 0.702 0.586 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.7 3.75 1.94 0.763 0.735 174s supply 20 16 96.2 6.01 2.45 0.641 0.574 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.2 0.00 174s supply 0.0 4.79 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.18 3.69 174s supply 3.69 4.81 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.942 174s supply 0.942 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9762 5.5234 18.28 < 2e-16 *** 174s price -0.3160 0.0589 -5.37 5.3e-06 *** 174s income 0.3233 0.0352 9.18 7.6e-11 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.67 MSE: 3.745 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9630 7.2089 7.49 9.1e-09 *** 174s price 0.1840 0.0589 3.13 0.0036 ** 174s farmPrice 0.2602 0.0399 6.53 1.6e-07 *** 174s trend 0.3233 0.0352 9.18 7.6e-11 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.452 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.215 MSE: 6.013 Root MSE: 2.452 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > 174s > ## *********** WLS with 2 cross-equation restrictions via R and restrict.regMat ****** 174s > fitwls5 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restr3m, 174s + restrict.rhs = restr3q, restrict.regMat = tc, 174s + x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwls5 ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 2.51 0.702 0.619 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.6 3.74 1.94 0.763 0.735 174s supply 20 16 96.3 6.02 2.45 0.641 0.574 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.76 0.00 174s supply 0.00 5.99 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.74 4.47 174s supply 4.47 6.02 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.943 174s supply 0.943 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9138 6.0474 16.69 < 2e-16 *** 174s price -0.3160 0.0648 -4.87 2.3e-05 *** 174s income 0.3238 0.0385 8.42 6.3e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.636 MSE: 3.743 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9416 7.9687 6.77 7.6e-08 *** 174s price 0.1840 0.0648 2.84 0.0075 ** 174s farmPrice 0.2603 0.0446 5.84 1.3e-06 *** 174s trend 0.3238 0.0385 8.42 6.3e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.453 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.268 MSE: 6.017 Root MSE: 2.453 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > # the same with symbolically specified restrictions 174s > fitwls5Sym <- systemfit( system, "WLS", data = Kmenta, 174s + restrict.matrix = restrict3, restrict.regMat = tc, 174s + x = TRUE, useMatrix = useMatrix ) 174s > all.equal( fitwls5, fitwls5Sym ) 174s [1] "Component “call”: target, current do not match when deparsed" 174s > 174s > ## *********** WLS with 2 cross-equation restrictions via R and restrict.regMat (EViews-like) 174s > fitwls5e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 174s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 174s + useMatrix = useMatrix ) 174s > print( summary( fitwls5e ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 1.72 0.702 0.586 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.7 3.75 1.94 0.763 0.735 174s supply 20 16 96.2 6.01 2.45 0.641 0.574 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.2 0.00 174s supply 0.0 4.79 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.18 3.69 174s supply 3.69 4.81 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.942 174s supply 0.942 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9762 5.5234 18.28 < 2e-16 *** 174s price -0.3160 0.0589 -5.37 5.3e-06 *** 174s income 0.3233 0.0352 9.18 7.6e-11 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.67 MSE: 3.745 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9630 7.2089 7.49 9.1e-09 *** 174s price 0.1840 0.0589 3.13 0.0036 ** 174s farmPrice 0.2602 0.0399 6.53 1.6e-07 *** 174s trend 0.3233 0.0352 9.18 7.6e-11 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.452 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.215 MSE: 6.013 Root MSE: 2.452 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > 174s > ## *************** iterated WLS estimation ********************* 174s > fitwlsi1 <- systemfit( system, "WLS", data = Kmenta, 174s + maxit = 100, useMatrix = useMatrix ) 174s > print( summary( fitwlsi1, useDfSys = TRUE ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 33 156 4.43 0.709 0.558 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.3 3.73 1.93 0.764 0.736 174s supply 20 16 92.6 5.78 2.40 0.655 0.590 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.73 0.00 174s supply 0.00 5.78 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.73 4.14 174s supply 4.14 5.78 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.891 174s supply 0.891 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.8954 7.5194 13.29 8.4e-15 *** 174s price -0.3163 0.0907 -3.49 0.0014 ** 174s income 0.3346 0.0454 7.37 1.8e-08 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.93 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 174s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 58.2754 11.4629 5.08 1.4e-05 *** 174s price 0.1604 0.0949 1.69 0.100 174s farmPrice 0.2481 0.0462 5.37 6.1e-06 *** 174s trend 0.2483 0.0975 2.55 0.016 * 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.405 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 174s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 174s 174s > 174s > ## *************** iterated WLS estimation (EViews-like) ************ 174s > fitwlsi1e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 174s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwlsi1e, useDfSys = TRUE ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 33 156 3.02 0.709 0.537 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.3 3.73 1.93 0.764 0.736 174s supply 20 16 92.6 5.78 2.40 0.655 0.590 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.17 0.00 174s supply 0.00 4.63 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.17 3.41 174s supply 3.41 4.63 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.891 174s supply 0.891 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.8954 6.9325 14.41 8.9e-16 *** 174s price -0.3163 0.0836 -3.78 0.00062 *** 174s income 0.3346 0.0419 7.99 3.2e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.93 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 174s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 58.2754 10.2527 5.68 2.4e-06 *** 174s price 0.1604 0.0849 1.89 0.0676 . 174s farmPrice 0.2481 0.0413 6.01 9.5e-07 *** 174s trend 0.2483 0.0872 2.85 0.0075 ** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.405 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 174s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 174s 174s > 174s > ## ****** iterated WLS with cross-equation restriction *************** 174s > fitwlsi2 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 174s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwlsi2 ) ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 2.34 0.703 0.623 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.7 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.98 2.44 0.643 0.576 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.75 0.00 174s supply 0.00 5.98 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.75 4.48 174s supply 4.48 5.98 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.946 174s supply 0.946 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.6607 7.5378 13.22 5.8e-15 *** 174s price -0.2993 0.0884 -3.39 0.0018 ** 174s income 0.3196 0.0414 7.72 5.6e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.936 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.741 MSE: 3.749 Root MSE: 1.936 174s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.1830 11.3487 4.95 2.0e-05 *** 174s price 0.1643 0.0963 1.71 0.097 . 174s farmPrice 0.2580 0.0453 5.70 2.1e-06 *** 174s trend 0.3196 0.0414 7.72 5.6e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.445 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 95.641 MSE: 5.978 Root MSE: 2.445 174s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 174s 174s > 174s > ## ****** iterated WLS with cross-equation restriction (EViews-like) ******** 174s > fitwlsi2e <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 174s + methodResidCov = "noDfCor", maxit = 100, useMatrix = useMatrix ) 174s > print( summary( fitwlsi2e ) ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 1.6 0.703 0.589 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.8 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.97 2.44 0.644 0.577 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.19 0.00 174s supply 0.00 4.78 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.19 3.69 174s supply 3.69 4.78 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.946 174s supply 0.946 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.6484 6.9516 14.33 4.4e-16 *** 174s price -0.2984 0.0814 -3.67 0.00083 *** 174s income 0.3188 0.0380 8.39 8.4e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.937 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.785 MSE: 3.752 Root MSE: 1.937 174s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.2061 10.1500 5.54 3.4e-06 *** 174s price 0.1642 0.0861 1.91 0.065 . 174s farmPrice 0.2579 0.0405 6.37 2.9e-07 *** 174s trend 0.3188 0.0380 8.39 8.4e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.444 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 95.573 MSE: 5.973 Root MSE: 2.444 174s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 174s 174s > 174s > ## ******* iterated WLS with cross-equation restriction via restrict.regMat ********** 174s > fitwlsi3 <- systemfit( system, "WLS", data = Kmenta, restrict.regMat = tc, 174s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwlsi3 ) ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 2.34 0.703 0.623 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.7 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.98 2.44 0.643 0.576 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.75 0.00 174s supply 0.00 5.98 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.75 4.48 174s supply 4.48 5.98 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.946 174s supply 0.946 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.6607 7.5378 13.22 5.8e-15 *** 174s price -0.2993 0.0884 -3.39 0.0018 ** 174s income 0.3196 0.0414 7.72 5.6e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.936 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.741 MSE: 3.749 Root MSE: 1.936 174s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.1830 11.3487 4.95 2.0e-05 *** 174s price 0.1643 0.0963 1.71 0.097 . 174s farmPrice 0.2580 0.0453 5.70 2.1e-06 *** 174s trend 0.3196 0.0414 7.72 5.6e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.445 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 95.641 MSE: 5.978 Root MSE: 2.445 174s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 174s 174s > 174s > ## ******* iterated WLS with cross-equation restriction via restrict.regMat (EViews-like) *** 174s > fitwlsi3e <- systemfit( system, "WLS", data = Kmenta, restrict.regMat = tc, 174s + methodResidCov = "noDfCor", maxit = 100, useMatrix = useMatrix ) 174s > print( summary( fitwlsi3e ) ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 1.6 0.703 0.589 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.8 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.97 2.44 0.644 0.577 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.19 0.00 174s supply 0.00 4.78 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.19 3.69 174s supply 3.69 4.78 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.946 174s supply 0.946 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.6484 6.9516 14.33 4.4e-16 *** 174s price -0.2984 0.0814 -3.67 0.00083 *** 174s income 0.3188 0.0380 8.39 8.4e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.937 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.785 MSE: 3.752 Root MSE: 1.937 174s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.2061 10.1500 5.54 3.4e-06 *** 174s price 0.1642 0.0861 1.91 0.065 . 174s farmPrice 0.2579 0.0405 6.37 2.9e-07 *** 174s trend 0.3188 0.0380 8.39 8.4e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.444 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 95.573 MSE: 5.973 Root MSE: 2.444 174s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 174s 174s > nobs( fitwlsi3e ) 174s [1] 40 174s > 174s > ## ******* iterated WLS with 2 cross-equation restrictions *********** 174s > fitwlsi4 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restr2m, 174s + restrict.rhs = restr2q, maxit = 100, useMatrix = useMatrix ) 174s > print( summary( fitwlsi4 ) ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 2.51 0.702 0.619 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.6 3.74 1.94 0.763 0.735 174s supply 20 16 96.3 6.02 2.45 0.641 0.574 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.74 0.00 174s supply 0.00 6.02 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.74 4.47 174s supply 4.47 6.02 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.943 174s supply 0.943 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9031 6.0396 16.71 < 2e-16 *** 174s price -0.3159 0.0648 -4.88 2.3e-05 *** 174s income 0.3239 0.0384 8.43 6.0e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.63 MSE: 3.743 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9379 7.9718 6.77 7.7e-08 *** 174s price 0.1841 0.0648 2.84 0.0075 ** 174s farmPrice 0.2603 0.0447 5.83 1.3e-06 *** 174s trend 0.3239 0.0384 8.43 6.0e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.453 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.277 MSE: 6.017 Root MSE: 2.453 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > 174s > ## ******* iterated WLS with 2 cross-equation restrictions (EViews-like) ***** 174s > fitwlsi4e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 174s + restrict.matrix = restr2m, restrict.rhs = restr2q, maxit = 100, 174s + x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwlsi4e ) ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 1.72 0.702 0.586 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.7 3.75 1.94 0.763 0.735 174s supply 20 16 96.2 6.01 2.45 0.641 0.574 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.18 0.00 174s supply 0.00 4.81 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.18 3.69 174s supply 3.69 4.81 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.942 174s supply 0.942 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9662 5.5170 18.30 < 2e-16 *** 174s price -0.3160 0.0589 -5.37 5.2e-06 *** 174s income 0.3234 0.0352 9.20 7.3e-11 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.665 MSE: 3.745 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9595 7.2114 7.48 9.2e-09 *** 174s price 0.1840 0.0589 3.13 0.0036 ** 174s farmPrice 0.2602 0.0400 6.51 1.6e-07 *** 174s trend 0.3234 0.0352 9.20 7.3e-11 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.452 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.223 MSE: 6.014 Root MSE: 2.452 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > 174s > ## ***** iterated WLS with 2 cross-equation restrictions via R and restrict.regMat ****** 174s > fitwlsi5 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restr3m, 174s + restrict.rhs = restr3q, restrict.regMat = tc, maxit = 100, 174s + x = TRUE, useMatrix = useMatrix ) 174s > print( summary( fitwlsi5 ) ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 2.51 0.702 0.619 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.6 3.74 1.94 0.763 0.735 174s supply 20 16 96.3 6.02 2.45 0.641 0.574 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.74 0.00 174s supply 0.00 6.02 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.74 4.47 174s supply 4.47 6.02 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.943 174s supply 0.943 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9031 6.0396 16.71 < 2e-16 *** 174s price -0.3159 0.0648 -4.88 2.3e-05 *** 174s income 0.3239 0.0384 8.43 6.0e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.63 MSE: 3.743 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9379 7.9718 6.77 7.7e-08 *** 174s price 0.1841 0.0648 2.84 0.0075 ** 174s farmPrice 0.2603 0.0447 5.83 1.3e-06 *** 174s trend 0.3239 0.0384 8.43 6.0e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.453 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.277 MSE: 6.017 Root MSE: 2.453 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > 174s > ## *** iterated WLS with 2 cross-equation restrictions via R and restrict.regMat (EViews-like) 174s > fitwlsi5e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 174s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 174s + maxit = 100, useMatrix = useMatrix ) 174s > print( summary( fitwlsi5e ) ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 1.72 0.702 0.586 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.7 3.75 1.94 0.763 0.735 174s supply 20 16 96.2 6.01 2.45 0.641 0.574 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.18 0.00 174s supply 0.00 4.81 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.18 3.69 174s supply 3.69 4.81 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.942 174s supply 0.942 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9662 5.5170 18.30 < 2e-16 *** 174s price -0.3160 0.0589 -5.37 5.2e-06 *** 174s income 0.3234 0.0352 9.20 7.3e-11 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.665 MSE: 3.745 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9595 7.2114 7.48 9.2e-09 *** 174s price 0.1840 0.0589 3.13 0.0036 ** 174s farmPrice 0.2602 0.0400 6.51 1.6e-07 *** 174s trend 0.3234 0.0352 9.20 7.3e-11 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.452 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.223 MSE: 6.014 Root MSE: 2.452 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > 174s > 174s > ## *********** estimations with a single regressor ************ 174s > fitwlsS1 <- systemfit( 174s + list( consump ~ price - 1, consump ~ price + trend ), "WLS", 174s + data = Kmenta, useMatrix = useMatrix ) 174s > print( summary( fitwlsS1 ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 36 1121 484 -1.09 -1.05 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s eq1 20 19 861 45.3 6.73 -2.213 -2.213 174s eq2 20 17 259 15.3 3.91 0.032 -0.082 174s 174s The covariance matrix of the residuals used for estimation 174s eq1 eq2 174s eq1 45.3 0.0 174s eq2 0.0 15.3 174s 174s The covariance matrix of the residuals 174s eq1 eq2 174s eq1 45.3 14.4 174s eq2 14.4 15.3 174s 174s The correlations of the residuals 174s eq1 eq2 174s eq1 1.000 0.549 174s eq2 0.549 1.000 174s 174s 174s WLS estimates for 'eq1' (equation 1) 174s Model Formula: consump ~ price - 1 174s 174s Estimate Std. Error t value Pr(>|t|) 174s price 1.006 0.015 66.9 <2e-16 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 6.733 on 19 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 19 174s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 174s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 174s 174s 174s WLS estimates for 'eq2' (equation 2) 174s Model Formula: consump ~ price + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 93.6767 15.2367 6.15 1.1e-05 *** 174s price 0.0622 0.1513 0.41 0.69 174s trend 0.0953 0.1515 0.63 0.54 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 3.907 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 259.497 MSE: 15.265 Root MSE: 3.907 174s Multiple R-Squared: 0.032 Adjusted R-Squared: -0.082 174s 174s > fitwlsS2 <- systemfit( 174s + list( consump ~ price - 1, consump ~ trend - 1 ), "WLS", 174s + data = Kmenta, useMatrix = useMatrix ) 174s > print( summary( fitwlsS2 ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 38 47370 110957 -87.3 -5.28 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s eq1 20 19 861 45.3 6.73 -2.21 -2.21 174s eq2 20 19 46509 2447.8 49.48 -172.47 -172.47 174s 174s The covariance matrix of the residuals used for estimation 174s eq1 eq2 174s eq1 45.3 0 174s eq2 0.0 2448 174s 174s The covariance matrix of the residuals 174s eq1 eq2 174s eq1 45.34 -5.15 174s eq2 -5.15 2447.84 174s 174s The correlations of the residuals 174s eq1 eq2 174s eq1 1.0000 -0.0439 174s eq2 -0.0439 1.0000 174s 174s 174s WLS estimates for 'eq1' (equation 1) 174s Model Formula: consump ~ price - 1 174s 174s Estimate Std. Error t value Pr(>|t|) 174s price 1.006 0.015 66.9 <2e-16 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 6.733 on 19 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 19 174s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 174s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 174s 174s 174s WLS estimates for 'eq2' (equation 2) 174s Model Formula: consump ~ trend - 1 174s 174s Estimate Std. Error t value Pr(>|t|) 174s trend 7.405 0.924 8.02 1.6e-07 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 49.476 on 19 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 19 174s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 174s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 174s 174s > fitwlsS3 <- systemfit( 174s + list( consump ~ trend - 1, price ~ trend - 1 ), "WLS", 174s + data = Kmenta, useMatrix = useMatrix ) 174s > print( summary( fitwlsS3 ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 38 93537 108970 -99 -0.977 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s eq1 20 19 46509 2448 49.5 -172.5 -172.5 174s eq2 20 19 47028 2475 49.8 -69.5 -69.5 174s 174s The covariance matrix of the residuals used for estimation 174s eq1 eq2 174s eq1 2448 0 174s eq2 0 2475 174s 174s The covariance matrix of the residuals 174s eq1 eq2 174s eq1 2448 2439 174s eq2 2439 2475 174s 174s The correlations of the residuals 174s eq1 eq2 174s eq1 1.000 0.988 174s eq2 0.988 1.000 174s 174s 174s WLS estimates for 'eq1' (equation 1) 174s Model Formula: consump ~ trend - 1 174s 174s Estimate Std. Error t value Pr(>|t|) 174s trend 7.405 0.924 8.02 1.6e-07 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 49.476 on 19 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 19 174s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 174s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 174s 174s 174s WLS estimates for 'eq2' (equation 2) 174s Model Formula: price ~ trend - 1 174s 174s Estimate Std. Error t value Pr(>|t|) 174s trend 7.318 0.929 7.88 2.1e-07 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 49.751 on 19 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 19 174s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 174s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 174s 174s > fitwlsS4 <- systemfit( 174s + list( consump ~ trend - 1, price ~ trend - 1 ), "WLS", 174s + data = Kmenta, restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), 174s + useMatrix = useMatrix ) 174s > print( summary( fitwlsS4 ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 39 93548 111736 -99 -1.03 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s eq1 20 19 46514 2448 49.5 -172.5 -172.5 174s eq2 20 19 47034 2475 49.8 -69.5 -69.5 174s 174s The covariance matrix of the residuals used for estimation 174s eq1 eq2 174s eq1 2448 0 174s eq2 0 2475 174s 174s The covariance matrix of the residuals 174s eq1 eq2 174s eq1 2448 2439 174s eq2 2439 2475 174s 174s The correlations of the residuals 174s eq1 eq2 174s eq1 1.000 0.988 174s eq2 0.988 1.000 174s 174s 174s WLS estimates for 'eq1' (equation 1) 174s Model Formula: consump ~ trend - 1 174s 174s Estimate Std. Error t value Pr(>|t|) 174s trend 7.362 0.655 11.2 8.4e-14 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 49.478 on 19 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 19 174s SSR: 46514.224 MSE: 2448.117 Root MSE: 49.478 174s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 174s 174s 174s WLS estimates for 'eq2' (equation 2) 174s Model Formula: price ~ trend - 1 174s 174s Estimate Std. Error t value Pr(>|t|) 174s trend 7.362 0.655 11.2 8.4e-14 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 49.754 on 19 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 19 174s SSR: 47033.528 MSE: 2475.449 Root MSE: 49.754 174s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 174s 174s > fitwlsS5 <- systemfit( 174s + list( consump ~ 1, price ~ 1 ), "WLS", 174s + data = Kmenta, useMatrix = useMatrix ) 174s > print( summary( fitwlsS5) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 38 935 491 0 0 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s eq1 20 19 268 14.1 3.76 0 0 174s eq2 20 19 667 35.1 5.93 0 0 174s 174s The covariance matrix of the residuals used for estimation 174s eq1 eq2 174s eq1 14.1 0.0 174s eq2 0.0 35.1 174s 174s The covariance matrix of the residuals 174s eq1 eq2 174s eq1 14.11 2.18 174s eq2 2.18 35.12 174s 174s The correlations of the residuals 174s eq1 eq2 174s eq1 1.0000 0.0981 174s eq2 0.0981 1.0000 174s 174s 174s WLS estimates for 'eq1' (equation 1) 174s Model Formula: consump ~ 1 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.90 0.84 120 <2e-16 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 3.756 on 19 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 19 174s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 174s Multiple R-Squared: 0 Adjusted R-Squared: 0 174s 174s 174s WLS estimates for 'eq2' (equation 2) 174s Model Formula: price ~ 1 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.02 1.33 75.5 <2e-16 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 5.926 on 19 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 19 174s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 174s Multiple R-Squared: 0 Adjusted R-Squared: 0 174s 174s > 174s > 174s > ## **************** shorter summaries ********************** 174s > print( summary( fitwls1 ), residCov = FALSE, equations = FALSE ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 33 156 4.43 0.709 0.558 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.3 3.73 1.93 0.764 0.736 174s supply 20 16 92.6 5.78 2.40 0.655 0.590 174s 174s 174s Coefficients: 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 174s demand_price -0.3163 0.0907 -3.49 0.00282 ** 174s demand_income 0.3346 0.0454 7.37 1.1e-06 *** 174s supply_(Intercept) 58.2754 11.4629 5.08 0.00011 *** 174s supply_price 0.1604 0.0949 1.69 0.11039 174s supply_farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 174s supply_trend 0.2483 0.0975 2.55 0.02157 * 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s > 174s > print( summary( fitwls2e, useDfSys = FALSE, residCov = FALSE ), 174s + equations = FALSE ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 1.61 0.703 0.589 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.8 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.97 2.44 0.644 0.577 174s 174s 174s Coefficients: 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 99.6461 6.9734 14.29 6.7e-11 *** 174s demand_price -0.2982 0.0816 -3.65 0.002 ** 174s demand_income 0.3186 0.0381 8.37 2.0e-07 *** 174s supply_(Intercept) 56.2104 10.1248 5.55 4.4e-05 *** 174s supply_price 0.1642 0.0859 1.91 0.074 . 174s supply_farmPrice 0.2579 0.0404 6.38 9.1e-06 *** 174s supply_trend 0.3186 0.0381 8.37 3.1e-07 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s > 174s > print( summary( fitwls3 ), residCov = FALSE ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 2.35 0.703 0.622 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.8 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.98 2.44 0.643 0.576 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.6582 7.5640 13.18 6.4e-15 *** 174s price -0.2991 0.0887 -3.37 0.0019 ** 174s income 0.3194 0.0415 7.70 6.0e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.936 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.75 MSE: 3.75 Root MSE: 1.936 174s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.1877 11.3165 4.97 1.9e-05 *** 174s price 0.1643 0.0960 1.71 0.096 . 174s farmPrice 0.2580 0.0451 5.71 2.0e-06 *** 174s trend 0.3194 0.0415 7.70 6.0e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.445 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 95.627 MSE: 5.977 Root MSE: 2.445 174s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 174s 174s > 174s > print( summary( fitwls4e, residCov = FALSE, equations = FALSE ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 1.72 0.702 0.586 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.7 3.75 1.94 0.763 0.735 174s supply 20 16 96.2 6.01 2.45 0.641 0.574 174s 174s 174s Coefficients: 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 100.9762 5.5234 18.28 < 2e-16 *** 174s demand_price -0.3160 0.0589 -5.37 5.3e-06 *** 174s demand_income 0.3233 0.0352 9.18 7.6e-11 *** 174s supply_(Intercept) 53.9630 7.2089 7.49 9.1e-09 *** 174s supply_price 0.1840 0.0589 3.13 0.0036 ** 174s supply_farmPrice 0.2602 0.0399 6.53 1.6e-07 *** 174s supply_trend 0.3233 0.0352 9.18 7.6e-11 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s > 174s > print( summary( fitwls5, useDfSys = FALSE ), residCov = FALSE ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 2.51 0.702 0.619 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.6 3.74 1.94 0.763 0.735 174s supply 20 16 96.3 6.02 2.45 0.641 0.574 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9138 6.0474 16.69 5.6e-12 *** 174s price -0.3160 0.0648 -4.87 0.00014 *** 174s income 0.3238 0.0385 8.42 1.8e-07 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.636 MSE: 3.743 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9416 7.9687 6.77 4.5e-06 *** 174s price 0.1840 0.0648 2.84 0.012 * 174s farmPrice 0.2603 0.0446 5.84 2.5e-05 *** 174s trend 0.3238 0.0385 8.42 2.9e-07 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.453 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.268 MSE: 6.017 Root MSE: 2.453 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > 174s > print( summary( fitwlsi1e, useDfSys = TRUE, equations = FALSE ) ) 174s 174s systemfit results 174s method: WLS 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 33 156 3.02 0.709 0.537 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.3 3.73 1.93 0.764 0.736 174s supply 20 16 92.6 5.78 2.40 0.655 0.590 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.17 0.00 174s supply 0.00 4.63 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.17 3.41 174s supply 3.41 4.63 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.891 174s supply 0.891 1.000 174s 174s 174s Coefficients: 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 99.8954 6.9325 14.41 8.9e-16 *** 174s demand_price -0.3163 0.0836 -3.78 0.00062 *** 174s demand_income 0.3346 0.0419 7.99 3.2e-09 *** 174s supply_(Intercept) 58.2754 10.2527 5.68 2.4e-06 *** 174s supply_price 0.1604 0.0849 1.89 0.06762 . 174s supply_farmPrice 0.2481 0.0413 6.01 9.5e-07 *** 174s supply_trend 0.2483 0.0872 2.85 0.00754 ** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s > 174s > print( summary( fitwlsi2, equations = FALSE, residCov = FALSE ), 174s + residCov = TRUE ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 2.34 0.703 0.623 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.7 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.98 2.44 0.643 0.576 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.75 0.00 174s supply 0.00 5.98 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.75 4.48 174s supply 4.48 5.98 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.946 174s supply 0.946 1.000 174s 174s 174s Coefficients: 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 99.6607 7.5378 13.22 5.8e-15 *** 174s demand_price -0.2993 0.0884 -3.39 0.0018 ** 174s demand_income 0.3196 0.0414 7.72 5.6e-09 *** 174s supply_(Intercept) 56.1830 11.3487 4.95 2.0e-05 *** 174s supply_price 0.1643 0.0963 1.71 0.0972 . 174s supply_farmPrice 0.2580 0.0453 5.70 2.1e-06 *** 174s supply_trend 0.3196 0.0414 7.72 5.6e-09 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s > 174s > print( summary( fitwlsi3e ), equations = FALSE, residCov = FALSE ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 34 159 1.6 0.703 0.589 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.8 3.75 1.94 0.762 0.734 174s supply 20 16 95.6 5.97 2.44 0.644 0.577 174s 174s 174s Coefficients: 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 99.6484 6.9516 14.33 4.4e-16 *** 174s demand_price -0.2984 0.0814 -3.67 0.00083 *** 174s demand_income 0.3188 0.0380 8.39 8.4e-10 *** 174s supply_(Intercept) 56.2061 10.1500 5.54 3.4e-06 *** 174s supply_price 0.1642 0.0861 1.91 0.06502 . 174s supply_farmPrice 0.2579 0.0405 6.37 2.9e-07 *** 174s supply_trend 0.3188 0.0380 8.39 8.4e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s > 174s > print( summary( fitwlsi4, equations = FALSE ), equations = TRUE ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 2.51 0.702 0.619 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.6 3.74 1.94 0.763 0.735 174s supply 20 16 96.3 6.02 2.45 0.641 0.574 174s 174s The covariance matrix of the residuals used for estimation 174s demand supply 174s demand 3.74 0.00 174s supply 0.00 6.02 174s 174s The covariance matrix of the residuals 174s demand supply 174s demand 3.74 4.47 174s supply 4.47 6.02 174s 174s The correlations of the residuals 174s demand supply 174s demand 1.000 0.943 174s supply 0.943 1.000 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9031 6.0396 16.71 < 2e-16 *** 174s price -0.3159 0.0648 -4.88 2.3e-05 *** 174s income 0.3239 0.0384 8.43 6.0e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.63 MSE: 3.743 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9379 7.9718 6.77 7.7e-08 *** 174s price 0.1841 0.0648 2.84 0.0075 ** 174s farmPrice 0.2603 0.0447 5.83 1.3e-06 *** 174s trend 0.3239 0.0384 8.43 6.0e-10 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.453 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.277 MSE: 6.017 Root MSE: 2.453 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > 174s > print( summary( fitwlsi5e, useDfSys = FALSE, residCov = FALSE ) ) 174s 174s systemfit results 174s method: iterated WLS 174s 174s convergence achieved after 3 iterations 174s 174s N DF SSR detRCov OLS-R2 McElroy-R2 174s system 40 35 160 1.72 0.702 0.586 174s 174s N DF SSR MSE RMSE R2 Adj R2 174s demand 20 17 63.7 3.75 1.94 0.763 0.735 174s supply 20 16 96.2 6.01 2.45 0.641 0.574 174s 174s 174s WLS estimates for 'demand' (equation 1) 174s Model Formula: consump ~ price + income 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.9662 5.5170 18.30 1.3e-12 *** 174s price -0.3160 0.0589 -5.37 5.1e-05 *** 174s income 0.3234 0.0352 9.20 5.2e-08 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 1.935 on 17 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 17 174s SSR: 63.665 MSE: 3.745 Root MSE: 1.935 174s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 174s 174s 174s WLS estimates for 'supply' (equation 2) 174s Model Formula: consump ~ price + farmPrice + trend 174s 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.9595 7.2114 7.48 1.3e-06 *** 174s price 0.1840 0.0589 3.13 0.0065 ** 174s farmPrice 0.2602 0.0400 6.51 7.2e-06 *** 174s trend 0.3234 0.0352 9.20 8.7e-08 *** 174s --- 174s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 174s 174s Residual standard error: 2.452 on 16 degrees of freedom 174s Number of observations: 20 Degrees of Freedom: 16 174s SSR: 96.223 MSE: 6.014 Root MSE: 2.452 174s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 174s 174s > 174s > 174s > ## ****************** residuals ************************** 174s > print( residuals( fitwls1 ) ) 174s demand supply 174s 1 1.074 -0.444 174s 2 -0.390 -0.896 174s 3 2.625 1.965 174s 4 1.802 1.134 174s 5 1.946 1.514 174s 6 1.175 0.680 174s 7 1.530 1.569 174s 8 -2.933 -4.407 174s 9 -1.365 -2.599 174s 10 2.031 2.469 174s 11 -0.149 -0.598 174s 12 -1.954 -1.697 174s 13 -1.121 -1.064 174s 14 -0.220 0.970 174s 15 1.487 3.159 174s 16 -3.701 -3.866 174s 17 -1.273 -0.265 174s 18 -2.002 -2.449 174s 19 1.738 3.110 174s 20 -0.299 1.714 174s > print( residuals( fitwls1$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 174s -0.444 -0.896 1.965 1.134 1.514 0.680 1.569 -4.407 -2.599 2.469 -0.598 174s 12 13 14 15 16 17 18 19 20 174s -1.697 -1.064 0.970 3.159 -3.866 -0.265 -2.449 3.110 1.714 174s > 174s > print( residuals( fitwls2e ) ) 174s demand supply 174s 1 0.9069 0.209 174s 2 -0.4660 -0.338 174s 3 2.5495 2.455 174s 4 1.7320 1.560 174s 5 2.0183 1.771 174s 6 1.2321 0.886 174s 7 1.6019 1.724 174s 8 -2.8544 -4.378 174s 9 -1.3158 -2.597 174s 10 2.0517 2.500 174s 11 -0.3823 -0.455 174s 12 -2.2623 -1.525 174s 13 -1.3801 -1.001 174s 14 -0.3081 0.877 174s 15 1.6643 2.806 174s 16 -3.5513 -4.328 174s 17 -1.0466 -0.805 174s 18 -1.9647 -2.952 174s 19 1.8446 2.561 174s 20 -0.0697 1.029 174s > print( residuals( fitwls2e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 174s 0.9069 -0.4660 2.5495 1.7320 2.0183 1.2321 1.6019 -2.8544 -1.3158 2.0517 174s 11 12 13 14 15 16 17 18 19 20 174s -0.3823 -2.2623 -1.3801 -0.3081 1.6643 -3.5513 -1.0466 -1.9647 1.8446 -0.0697 174s > 174s > print( residuals( fitwls3 ) ) 174s demand supply 174s 1 0.9150 0.217 174s 2 -0.4624 -0.332 174s 3 2.5532 2.461 174s 4 1.7354 1.564 174s 5 2.0148 1.773 174s 6 1.2293 0.889 174s 7 1.5984 1.725 174s 8 -2.8582 -4.378 174s 9 -1.3182 -2.597 174s 10 2.0507 2.500 174s 11 -0.3710 -0.453 174s 12 -2.2473 -1.524 174s 13 -1.3675 -1.000 174s 14 -0.3038 0.876 174s 15 1.6557 2.802 174s 16 -3.5586 -4.333 174s 17 -1.0576 -0.811 174s 18 -1.9666 -2.957 174s 19 1.8394 2.555 174s 20 -0.0808 1.022 174s > print( residuals( fitwls3$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 174s 0.217 -0.332 2.461 1.564 1.773 0.889 1.725 -4.378 -2.597 2.500 -0.453 174s 12 13 14 15 16 17 18 19 20 174s -1.524 -1.000 0.876 2.802 -4.333 -0.811 -2.957 2.555 1.022 174s > 174s > print( residuals( fitwls4e ) ) 174s demand supply 174s 1 0.9593 0.244 174s 2 -0.3907 -0.388 174s 3 2.6143 2.417 174s 4 1.8088 1.498 174s 5 1.9718 1.803 174s 6 1.2083 0.892 174s 7 1.5943 1.699 174s 8 -2.8174 -4.491 174s 9 -1.3751 -2.548 174s 10 1.9351 2.667 174s 11 -0.4019 -0.284 174s 12 -2.1883 -1.443 174s 13 -1.2686 -1.010 174s 14 -0.2984 0.921 174s 15 1.5512 2.869 174s 16 -3.6143 -4.342 174s 17 -1.2823 -0.600 174s 18 -1.9253 -3.056 174s 19 1.8860 2.425 174s 20 0.0333 0.728 174s > print( residuals( fitwls4e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 174s 0.9593 -0.3907 2.6143 1.8088 1.9718 1.2083 1.5943 -2.8174 -1.3751 1.9351 174s 11 12 13 14 15 16 17 18 19 20 174s -0.4019 -2.1883 -1.2686 -0.2984 1.5512 -3.6143 -1.2823 -1.9253 1.8860 0.0333 174s > 174s > print( residuals( fitwls5 ) ) 174s demand supply 174s 1 0.9649 0.249 174s 2 -0.3911 -0.384 174s 3 2.6145 2.421 174s 4 1.8081 1.501 174s 5 1.9707 1.805 174s 6 1.2067 0.893 174s 7 1.5910 1.700 174s 8 -2.8235 -4.491 174s 9 -1.3743 -2.548 174s 10 1.9406 2.667 174s 11 -0.3887 -0.282 174s 12 -2.1767 -1.442 174s 13 -1.2616 -1.009 174s 14 -0.2944 0.920 174s 15 1.5485 2.866 174s 16 -3.6185 -4.345 174s 17 -1.2806 -0.604 174s 18 -1.9295 -3.060 174s 19 1.8782 2.420 174s 20 0.0157 0.721 174s > print( residuals( fitwls5$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 174s 0.249 -0.384 2.421 1.501 1.805 0.893 1.700 -4.491 -2.548 2.667 -0.282 174s 12 13 14 15 16 17 18 19 20 174s -1.442 -1.009 0.920 2.866 -4.345 -0.604 -3.060 2.420 0.721 174s > 174s > print( residuals( fitwlsi1e ) ) 174s demand supply 174s 1 1.074 -0.444 174s 2 -0.390 -0.896 174s 3 2.625 1.965 174s 4 1.802 1.134 174s 5 1.946 1.514 174s 6 1.175 0.680 174s 7 1.530 1.569 174s 8 -2.933 -4.407 174s 9 -1.365 -2.599 174s 10 2.031 2.469 174s 11 -0.149 -0.598 174s 12 -1.954 -1.697 174s 13 -1.121 -1.064 174s 14 -0.220 0.970 174s 15 1.487 3.159 174s 16 -3.701 -3.866 174s 17 -1.273 -0.265 174s 18 -2.002 -2.449 174s 19 1.738 3.110 174s 20 -0.299 1.714 174s > print( residuals( fitwlsi1e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 174s 1.074 -0.390 2.625 1.802 1.946 1.175 1.530 -2.933 -1.365 2.031 -0.149 174s 12 13 14 15 16 17 18 19 20 174s -1.954 -1.121 -0.220 1.487 -3.701 -1.273 -2.002 1.738 -0.299 174s > 174s > print( residuals( fitwlsi2 ) ) 174s demand supply 174s 1 0.9167 0.218 174s 2 -0.4616 -0.331 174s 3 2.5539 2.462 174s 4 1.7361 1.565 174s 5 2.0140 1.774 174s 6 1.2288 0.889 174s 7 1.5977 1.726 174s 8 -2.8589 -4.378 174s 9 -1.3187 -2.597 174s 10 2.0505 2.500 174s 11 -0.3686 -0.453 174s 12 -2.2443 -1.523 174s 13 -1.3649 -1.000 174s 14 -0.3029 0.876 174s 15 1.6539 2.802 174s 16 -3.5601 -4.334 174s 17 -1.0599 -0.812 174s 18 -1.9669 -2.958 174s 19 1.8383 2.554 174s 20 -0.0831 1.020 174s > print( residuals( fitwlsi2$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 174s 0.218 -0.331 2.462 1.565 1.774 0.889 1.726 -4.378 -2.597 2.500 -0.453 174s 12 13 14 15 16 17 18 19 20 174s -1.523 -1.000 0.876 2.802 -4.334 -0.812 -2.958 2.554 1.020 174s > 174s > print( residuals( fitwlsi3e ) ) 174s demand supply 174s 1 0.9084 0.211 174s 2 -0.4653 -0.337 174s 3 2.5502 2.456 174s 4 1.7326 1.561 174s 5 2.0176 1.771 174s 6 1.2316 0.887 174s 7 1.6012 1.724 174s 8 -2.8551 -4.378 174s 9 -1.3162 -2.597 174s 10 2.0515 2.500 174s 11 -0.3801 -0.454 174s 12 -2.2594 -1.525 174s 13 -1.3777 -1.001 174s 14 -0.3073 0.877 174s 15 1.6627 2.806 174s 16 -3.5527 -4.329 174s 17 -1.0487 -0.806 174s 18 -1.9651 -2.953 174s 19 1.8436 2.560 174s 20 -0.0718 1.028 174s > print( residuals( fitwlsi3e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 174s 0.9084 -0.4653 2.5502 1.7326 2.0176 1.2316 1.6012 -2.8551 -1.3162 2.0515 174s 11 12 13 14 15 16 17 18 19 20 174s -0.3801 -2.2594 -1.3777 -0.3073 1.6627 -3.5527 -1.0487 -1.9651 1.8436 -0.0718 174s > 174s > print( residuals( fitwlsi4 ) ) 174s demand supply 174s 1 0.9659 0.250 174s 2 -0.3911 -0.383 174s 3 2.6145 2.421 174s 4 1.8080 1.502 174s 5 1.9705 1.805 174s 6 1.2064 0.893 174s 7 1.5905 1.700 174s 8 -2.8246 -4.491 174s 9 -1.3742 -2.547 174s 10 1.9415 2.667 174s 11 -0.3865 -0.282 174s 12 -2.1747 -1.442 174s 13 -1.2604 -1.009 174s 14 -0.2938 0.920 174s 15 1.5480 2.866 174s 16 -3.6192 -4.346 174s 17 -1.2804 -0.604 174s 18 -1.9302 -3.061 174s 19 1.8768 2.420 174s 20 0.0127 0.720 174s > print( residuals( fitwlsi4$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 174s 0.250 -0.383 2.421 1.502 1.805 0.893 1.700 -4.491 -2.547 2.667 -0.282 174s 12 13 14 15 16 17 18 19 20 174s -1.442 -1.009 0.920 2.866 -4.346 -0.604 -3.061 2.420 0.720 174s > 174s > print( residuals( fitwlsi5e ) ) 174s demand supply 174s 1 0.9602 0.245 174s 2 -0.3908 -0.388 174s 3 2.6143 2.418 174s 4 1.8087 1.498 174s 5 1.9716 1.803 174s 6 1.2081 0.892 174s 7 1.5938 1.699 174s 8 -2.8184 -4.491 174s 9 -1.3750 -2.548 174s 10 1.9360 2.667 174s 11 -0.3997 -0.284 174s 12 -2.1865 -1.443 174s 13 -1.2675 -1.010 174s 14 -0.2978 0.921 174s 15 1.5508 2.869 174s 16 -3.6150 -4.342 174s 17 -1.2820 -0.601 174s 18 -1.9260 -3.057 174s 19 1.8848 2.424 174s 20 0.0305 0.727 174s > print( residuals( fitwlsi5e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 174s 0.9602 -0.3908 2.6143 1.8087 1.9716 1.2081 1.5938 -2.8184 -1.3750 1.9360 174s 11 12 13 14 15 16 17 18 19 20 174s -0.3997 -2.1865 -1.2675 -0.2978 1.5508 -3.6150 -1.2820 -1.9260 1.8848 0.0305 174s > 174s > 174s > ## *************** coefficients ********************* 174s > print( round( coef( fitwls1e ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income supply_(Intercept) 174s 99.895 -0.316 0.335 58.275 174s supply_price supply_farmPrice supply_trend 174s 0.160 0.248 0.248 174s > print( round( coef( fitwls1e$eq[[ 1 ]] ), digits = 6 ) ) 174s (Intercept) price income 174s 99.895 -0.316 0.335 174s > 174s > print( round( coef( fitwlsi2 ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income supply_(Intercept) 174s 99.661 -0.299 0.320 56.183 174s supply_price supply_farmPrice supply_trend 174s 0.164 0.258 0.320 174s > print( round( coef( fitwlsi2$eq[[ 2 ]] ), digits = 6 ) ) 174s (Intercept) price farmPrice trend 174s 56.183 0.164 0.258 0.320 174s > 174s > print( round( coef( fitwls3e ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income supply_(Intercept) 174s 99.646 -0.298 0.319 56.210 174s supply_price supply_farmPrice supply_trend 174s 0.164 0.258 0.319 174s > print( round( coef( fitwls3e, modified.regMat = TRUE ), digits = 6 ) ) 174s C1 C2 C3 C4 C5 C6 174s 99.646 -0.298 0.319 56.210 0.164 0.258 174s > print( round( coef( fitwls3e$eq[[ 1 ]] ), digits = 6 ) ) 174s (Intercept) price income 174s 99.646 -0.298 0.319 174s > 174s > print( round( coef( fitwls4 ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income supply_(Intercept) 174s 100.914 -0.316 0.324 53.942 174s supply_price supply_farmPrice supply_trend 174s 0.184 0.260 0.324 174s > print( round( coef( fitwls4$eq[[ 2 ]] ), digits = 6 ) ) 174s (Intercept) price farmPrice trend 174s 53.942 0.184 0.260 0.324 174s > 174s > print( round( coef( fitwlsi5 ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income supply_(Intercept) 174s 100.903 -0.316 0.324 53.938 174s supply_price supply_farmPrice supply_trend 174s 0.184 0.260 0.324 174s > print( round( coef( fitwlsi5, modified.regMat = TRUE ), digits = 6 ) ) 174s C1 C2 C3 C4 C5 C6 174s 100.903 -0.316 0.324 53.938 0.184 0.260 174s > print( round( coef( fitwlsi5$eq[[ 1 ]] ), digits = 6 ) ) 174s (Intercept) price income 174s 100.903 -0.316 0.324 174s > 174s > 174s > ## *************** coefficients with stats ********************* 174s > print( round( coef( summary( fitwls1e ) ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 99.895 6.9325 14.41 0.000000 174s demand_price -0.316 0.0836 -3.78 0.001483 174s demand_income 0.335 0.0419 7.99 0.000000 174s supply_(Intercept) 58.275 10.2527 5.68 0.000034 174s supply_price 0.160 0.0849 1.89 0.077067 174s supply_farmPrice 0.248 0.0413 6.01 0.000018 174s supply_trend 0.248 0.0872 2.85 0.011659 174s > print( round( coef( summary( fitwls1e$eq[[ 1 ]] ) ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.895 6.9325 14.41 0.00000 174s price -0.316 0.0836 -3.78 0.00148 174s income 0.335 0.0419 7.99 0.00000 174s > 174s > print( round( coef( summary( fitwlsi2 ) ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 99.661 7.5378 13.22 0.000000 174s demand_price -0.299 0.0884 -3.39 0.001805 174s demand_income 0.320 0.0414 7.72 0.000000 174s supply_(Intercept) 56.183 11.3487 4.95 0.000020 174s supply_price 0.164 0.0963 1.71 0.097239 174s supply_farmPrice 0.258 0.0453 5.70 0.000002 174s supply_trend 0.320 0.0414 7.72 0.000000 174s > print( round( coef( summary( fitwlsi2$eq[[ 2 ]] ) ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 56.183 11.3487 4.95 0.000020 174s price 0.164 0.0963 1.71 0.097239 174s farmPrice 0.258 0.0453 5.70 0.000002 174s trend 0.320 0.0414 7.72 0.000000 174s > 174s > print( round( coef( summary( fitwls3e ) ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 99.646 6.9734 14.29 0.000000 174s demand_price -0.298 0.0816 -3.65 0.000863 174s demand_income 0.319 0.0381 8.37 0.000000 174s supply_(Intercept) 56.210 10.1248 5.55 0.000003 174s supply_price 0.164 0.0859 1.91 0.064384 174s supply_farmPrice 0.258 0.0404 6.38 0.000000 174s supply_trend 0.319 0.0381 8.37 0.000000 174s > print( round( coef( summary( fitwls3e ), modified.regMat = TRUE ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s C1 99.646 6.9734 14.29 0.000000 174s C2 -0.298 0.0816 -3.65 0.000863 174s C3 0.319 0.0381 8.37 0.000000 174s C4 56.210 10.1248 5.55 0.000003 174s C5 0.164 0.0859 1.91 0.064384 174s C6 0.258 0.0404 6.38 0.000000 174s > print( round( coef( summary( fitwls3e$eq[[ 1 ]] ) ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 99.646 6.9734 14.29 0.000000 174s price -0.298 0.0816 -3.65 0.000863 174s income 0.319 0.0381 8.37 0.000000 174s > 174s > print( round( coef( summary( fitwls4, useDfSys = FALSE ) ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 100.914 6.0474 16.69 0.000000 174s demand_price -0.316 0.0648 -4.87 0.000143 174s demand_income 0.324 0.0385 8.42 0.000000 174s supply_(Intercept) 53.942 7.9687 6.77 0.000005 174s supply_price 0.184 0.0648 2.84 0.011833 174s supply_farmPrice 0.260 0.0446 5.84 0.000025 174s supply_trend 0.324 0.0385 8.42 0.000000 174s > print( round( coef( summary( fitwls4$eq[[ 2 ]], useDfSys = FALSE ) ), 174s + digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 53.942 7.9687 6.77 0.000005 174s price 0.184 0.0648 2.84 0.011833 174s farmPrice 0.260 0.0446 5.84 0.000025 174s trend 0.324 0.0385 8.42 0.000000 174s > 174s > print( round( coef( summary( fitwlsi5, useDfSys = FALSE ) ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s demand_(Intercept) 100.903 6.0396 16.71 0.000000 174s demand_price -0.316 0.0648 -4.88 0.000142 174s demand_income 0.324 0.0384 8.43 0.000000 174s supply_(Intercept) 53.938 7.9718 6.77 0.000005 174s supply_price 0.184 0.0648 2.84 0.011806 174s supply_farmPrice 0.260 0.0447 5.83 0.000026 174s supply_trend 0.324 0.0384 8.43 0.000000 174s > print( round( coef( summary( fitwlsi5, useDfSys = FALSE ), 174s + modified.regMat = TRUE ), digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s C1 100.903 6.0396 16.71 NA 174s C2 -0.316 0.0648 -4.88 NA 174s C3 0.324 0.0384 8.43 NA 174s C4 53.938 7.9718 6.77 NA 174s C5 0.184 0.0648 2.84 NA 174s C6 0.260 0.0447 5.83 NA 174s > print( round( coef( summary( fitwlsi5$eq[[ 1 ]], useDfSys = FALSE ) ), 174s + digits = 6 ) ) 174s Estimate Std. Error t value Pr(>|t|) 174s (Intercept) 100.903 6.0396 16.71 0.000000 174s price -0.316 0.0648 -4.88 0.000142 174s income 0.324 0.0384 8.43 0.000000 174s > 174s > 174s > ## *********** variance covariance matrix of the coefficients ******* 174s > print( round( vcov( fitwls1e ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 48.0597 -0.50558 0.02734 174s demand_price -0.5056 0.00699 -0.00198 174s demand_income 0.0273 -0.00198 0.00175 174s supply_(Intercept) 0.0000 0.00000 0.00000 174s supply_price 0.0000 0.00000 0.00000 174s supply_farmPrice 0.0000 0.00000 0.00000 174s supply_trend 0.0000 0.00000 0.00000 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) 0.000 0.000000 0.000000 174s demand_price 0.000 0.000000 0.000000 174s demand_income 0.000 0.000000 0.000000 174s supply_(Intercept) 105.119 -0.790000 -0.243489 174s supply_price -0.790 0.007202 0.000675 174s supply_farmPrice -0.243 0.000675 0.001707 174s supply_trend -0.223 0.000418 0.001052 174s supply_trend 174s demand_(Intercept) 0.000000 174s demand_price 0.000000 174s demand_income 0.000000 174s supply_(Intercept) -0.223347 174s supply_price 0.000418 174s supply_farmPrice 0.001052 174s supply_trend 0.007608 174s > print( round( vcov( fitwls1e$eq[[ 1 ]] ), digits = 6 ) ) 174s (Intercept) price income 174s (Intercept) 48.0597 -0.50558 0.02734 174s price -0.5056 0.00699 -0.00198 174s income 0.0273 -0.00198 0.00175 174s > 174s > print( round( vcov( fitwls2 ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 57.21413 -0.596328 0.026850 174s demand_price -0.59633 0.007862 -0.001948 174s demand_income 0.02685 -0.001948 0.001722 174s supply_(Intercept) -0.78825 0.057190 -0.050565 174s supply_price 0.00147 -0.000107 0.000095 174s supply_farmPrice 0.00371 -0.000269 0.000238 174s supply_trend 0.02685 -0.001948 0.001722 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) -0.7883 0.001474 0.003714 174s demand_price 0.0572 -0.000107 -0.000269 174s demand_income -0.0506 0.000095 0.000238 174s supply_(Intercept) 128.0635 -1.001596 -0.280017 174s supply_price -1.0016 0.009225 0.000806 174s supply_farmPrice -0.2800 0.000806 0.002038 174s supply_trend -0.0506 0.000095 0.000238 174s supply_trend 174s demand_(Intercept) 0.026850 174s demand_price -0.001948 174s demand_income 0.001722 174s supply_(Intercept) -0.050565 174s supply_price 0.000095 174s supply_farmPrice 0.000238 174s supply_trend 0.001722 174s > print( round( vcov( fitwls2$eq[[ 2 ]] ), digits = 6 ) ) 174s (Intercept) price farmPrice trend 174s (Intercept) 128.0635 -1.001596 -0.280017 -0.050565 174s price -1.0016 0.009225 0.000806 0.000095 174s farmPrice -0.2800 0.000806 0.002038 0.000238 174s trend -0.0506 0.000095 0.000238 0.001722 174s > 174s > print( round( vcov( fitwls3e ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 48.62814 -0.506597 0.022574 174s demand_price -0.50660 0.006662 -0.001638 174s demand_income 0.02257 -0.001638 0.001448 174s supply_(Intercept) -0.66271 0.048082 -0.042512 174s supply_price 0.00124 -0.000090 0.000079 174s supply_farmPrice 0.00312 -0.000227 0.000200 174s supply_trend 0.02257 -0.001638 0.001448 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) -0.6627 0.001239 0.003123 174s demand_price 0.0481 -0.000090 -0.000227 174s demand_income -0.0425 0.000079 0.000200 174s supply_(Intercept) 102.5112 -0.801390 -0.224299 174s supply_price -0.8014 0.007381 0.000645 174s supply_farmPrice -0.2243 0.000645 0.001632 174s supply_trend -0.0425 0.000079 0.000200 174s supply_trend 174s demand_(Intercept) 0.022574 174s demand_price -0.001638 174s demand_income 0.001448 174s supply_(Intercept) -0.042512 174s supply_price 0.000079 174s supply_farmPrice 0.000200 174s supply_trend 0.001448 174s > print( round( vcov( fitwls3e, modified.regMat = TRUE ), digits = 6 ) ) 174s C1 C2 C3 C4 C5 C6 174s C1 48.62814 -0.506597 0.022574 -0.6627 0.001239 0.003123 174s C2 -0.50660 0.006662 -0.001638 0.0481 -0.000090 -0.000227 174s C3 0.02257 -0.001638 0.001448 -0.0425 0.000079 0.000200 174s C4 -0.66271 0.048082 -0.042512 102.5112 -0.801390 -0.224299 174s C5 0.00124 -0.000090 0.000079 -0.8014 0.007381 0.000645 174s C6 0.00312 -0.000227 0.000200 -0.2243 0.000645 0.001632 174s > print( round( vcov( fitwls3e$eq[[ 1 ]] ), digits = 6 ) ) 174s (Intercept) price income 174s (Intercept) 48.6281 -0.50660 0.02257 174s price -0.5066 0.00666 -0.00164 174s income 0.0226 -0.00164 0.00145 174s > 174s > print( round( vcov( fitwls4 ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 36.5710 -0.321554 -0.043279 174s demand_price -0.3216 0.004201 -0.001011 174s demand_income -0.0433 -0.001011 0.001481 174s supply_(Intercept) 35.8467 -0.431417 0.074877 174s supply_price -0.3216 0.004201 -0.001011 174s supply_farmPrice -0.0334 0.000226 0.000111 174s supply_trend -0.0433 -0.001011 0.001481 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) 35.8467 -0.321554 -0.033436 174s demand_price -0.4314 0.004201 0.000226 174s demand_income 0.0749 -0.001011 0.000111 174s supply_(Intercept) 63.5001 -0.431417 -0.215648 174s supply_price -0.4314 0.004201 0.000226 174s supply_farmPrice -0.2156 0.000226 0.001986 174s supply_trend 0.0749 -0.001011 0.000111 174s supply_trend 174s demand_(Intercept) -0.043279 174s demand_price -0.001011 174s demand_income 0.001481 174s supply_(Intercept) 0.074877 174s supply_price -0.001011 174s supply_farmPrice 0.000111 174s supply_trend 0.001481 174s > print( round( vcov( fitwls4$eq[[ 2 ]] ), digits = 6 ) ) 174s (Intercept) price farmPrice trend 174s (Intercept) 63.5001 -0.431417 -0.215648 0.074877 174s price -0.4314 0.004201 0.000226 -0.001011 174s farmPrice -0.2156 0.000226 0.001986 0.000111 174s trend 0.0749 -0.001011 0.000111 0.001481 174s > 174s > print( round( vcov( fitwls5 ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 36.5710 -0.321554 -0.043279 174s demand_price -0.3216 0.004201 -0.001011 174s demand_income -0.0433 -0.001011 0.001481 174s supply_(Intercept) 35.8467 -0.431417 0.074877 174s supply_price -0.3216 0.004201 -0.001011 174s supply_farmPrice -0.0334 0.000226 0.000111 174s supply_trend -0.0433 -0.001011 0.001481 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) 35.8467 -0.321554 -0.033436 174s demand_price -0.4314 0.004201 0.000226 174s demand_income 0.0749 -0.001011 0.000111 174s supply_(Intercept) 63.5001 -0.431417 -0.215648 174s supply_price -0.4314 0.004201 0.000226 174s supply_farmPrice -0.2156 0.000226 0.001986 174s supply_trend 0.0749 -0.001011 0.000111 174s supply_trend 174s demand_(Intercept) -0.043279 174s demand_price -0.001011 174s demand_income 0.001481 174s supply_(Intercept) 0.074877 174s supply_price -0.001011 174s supply_farmPrice 0.000111 174s supply_trend 0.001481 174s > print( round( vcov( fitwls5, modified.regMat = TRUE ), digits = 6 ) ) 174s C1 C2 C3 C4 C5 C6 174s C1 36.5710 -0.321554 -0.043279 35.8467 -0.321554 -0.033436 174s C2 -0.3216 0.004201 -0.001011 -0.4314 0.004201 0.000226 174s C3 -0.0433 -0.001011 0.001481 0.0749 -0.001011 0.000111 174s C4 35.8467 -0.431417 0.074877 63.5001 -0.431417 -0.215648 174s C5 -0.3216 0.004201 -0.001011 -0.4314 0.004201 0.000226 174s C6 -0.0334 0.000226 0.000111 -0.2156 0.000226 0.001986 174s > print( round( vcov( fitwls5$eq[[ 1 ]] ), digits = 6 ) ) 174s (Intercept) price income 174s (Intercept) 36.5710 -0.32155 -0.04328 174s price -0.3216 0.00420 -0.00101 174s income -0.0433 -0.00101 0.00148 174s > 174s > print( round( vcov( fitwlsi1 ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 56.5408 -0.59480 0.03216 174s demand_price -0.5948 0.00822 -0.00233 174s demand_income 0.0322 -0.00233 0.00206 174s supply_(Intercept) 0.0000 0.00000 0.00000 174s supply_price 0.0000 0.00000 0.00000 174s supply_farmPrice 0.0000 0.00000 0.00000 174s supply_trend 0.0000 0.00000 0.00000 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) 0.000 0.000000 0.000000 174s demand_price 0.000 0.000000 0.000000 174s demand_income 0.000 0.000000 0.000000 174s supply_(Intercept) 131.398 -0.987500 -0.304361 174s supply_price -0.988 0.009003 0.000844 174s supply_farmPrice -0.304 0.000844 0.002133 174s supply_trend -0.279 0.000522 0.001316 174s supply_trend 174s demand_(Intercept) 0.000000 174s demand_price 0.000000 174s demand_income 0.000000 174s supply_(Intercept) -0.279183 174s supply_price 0.000522 174s supply_farmPrice 0.001316 174s supply_trend 0.009510 174s > print( round( vcov( fitwlsi1$eq[[ 2 ]] ), digits = 6 ) ) 174s (Intercept) price farmPrice trend 174s (Intercept) 131.398 -0.987500 -0.304361 -0.279183 174s price -0.988 0.009003 0.000844 0.000522 174s farmPrice -0.304 0.000844 0.002133 0.001316 174s trend -0.279 0.000522 0.001316 0.009510 174s > 174s > print( round( vcov( fitwlsi2e ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 48.32515 -0.503487 0.022480 174s demand_price -0.50349 0.006624 -0.001631 174s demand_income 0.02248 -0.001631 0.001442 174s supply_(Intercept) -0.65995 0.047882 -0.042335 174s supply_price 0.00123 -0.000090 0.000079 174s supply_farmPrice 0.00311 -0.000226 0.000199 174s supply_trend 0.02248 -0.001631 0.001442 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) -0.6600 0.001234 0.003110 174s demand_price 0.0479 -0.000090 -0.000226 174s demand_income -0.0423 0.000079 0.000199 174s supply_(Intercept) 103.0226 -0.805456 -0.225388 174s supply_price -0.8055 0.007418 0.000649 174s supply_farmPrice -0.2254 0.000649 0.001640 174s supply_trend -0.0423 0.000079 0.000199 174s supply_trend 174s demand_(Intercept) 0.022480 174s demand_price -0.001631 174s demand_income 0.001442 174s supply_(Intercept) -0.042335 174s supply_price 0.000079 174s supply_farmPrice 0.000199 174s supply_trend 0.001442 174s > print( round( vcov( fitwlsi2e$eq[[ 1 ]] ), digits = 6 ) ) 174s (Intercept) price income 174s (Intercept) 48.3251 -0.50349 0.02248 174s price -0.5035 0.00662 -0.00163 174s income 0.0225 -0.00163 0.00144 174s > 174s > print( round( vcov( fitwlsi3 ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 56.81857 -0.592263 0.026724 174s demand_price -0.59226 0.007812 -0.001939 174s demand_income 0.02672 -0.001939 0.001714 174s supply_(Intercept) -0.78454 0.056921 -0.050327 174s supply_price 0.00147 -0.000106 0.000094 174s supply_farmPrice 0.00370 -0.000268 0.000237 174s supply_trend 0.02672 -0.001939 0.001714 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) -0.7845 0.001467 0.003697 174s demand_price 0.0569 -0.000106 -0.000268 174s demand_income -0.0503 0.000094 0.000237 174s supply_(Intercept) 128.7924 -1.007391 -0.281572 174s supply_price -1.0074 0.009279 0.000811 174s supply_farmPrice -0.2816 0.000811 0.002049 174s supply_trend -0.0503 0.000094 0.000237 174s supply_trend 174s demand_(Intercept) 0.026724 174s demand_price -0.001939 174s demand_income 0.001714 174s supply_(Intercept) -0.050327 174s supply_price 0.000094 174s supply_farmPrice 0.000237 174s supply_trend 0.001714 174s > print( round( vcov( fitwlsi3, modified.regMat = TRUE ), digits = 6 ) ) 174s C1 C2 C3 C4 C5 C6 174s C1 56.81857 -0.592263 0.026724 -0.7845 0.001467 0.003697 174s C2 -0.59226 0.007812 -0.001939 0.0569 -0.000106 -0.000268 174s C3 0.02672 -0.001939 0.001714 -0.0503 0.000094 0.000237 174s C4 -0.78454 0.056921 -0.050327 128.7924 -1.007391 -0.281572 174s C5 0.00147 -0.000106 0.000094 -1.0074 0.009279 0.000811 174s C6 0.00370 -0.000268 0.000237 -0.2816 0.000811 0.002049 174s > print( round( vcov( fitwlsi3$eq[[ 2 ]] ), digits = 6 ) ) 174s (Intercept) price farmPrice trend 174s (Intercept) 128.7924 -1.007391 -0.281572 -0.050327 174s price -1.0074 0.009279 0.000811 0.000094 174s farmPrice -0.2816 0.000811 0.002049 0.000237 174s trend -0.0503 0.000094 0.000237 0.001714 174s > 174s > print( round( vcov( fitwlsi4e ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 30.4377 -0.265752 -0.037918 174s demand_price -0.2658 0.003463 -0.000827 174s demand_income -0.0379 -0.000827 0.001237 174s supply_(Intercept) 29.6762 -0.355820 0.060620 174s supply_price -0.2658 0.003463 -0.000827 174s supply_farmPrice -0.0279 0.000187 0.000094 174s supply_trend -0.0379 -0.000827 0.001237 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) 29.6762 -0.265752 -0.027921 174s demand_price -0.3558 0.003463 0.000187 174s demand_income 0.0606 -0.000827 0.000094 174s supply_(Intercept) 52.0044 -0.355820 -0.173988 174s supply_price -0.3558 0.003463 0.000187 174s supply_farmPrice -0.1740 0.000187 0.001596 174s supply_trend 0.0606 -0.000827 0.000094 174s supply_trend 174s demand_(Intercept) -0.037918 174s demand_price -0.000827 174s demand_income 0.001237 174s supply_(Intercept) 0.060620 174s supply_price -0.000827 174s supply_farmPrice 0.000094 174s supply_trend 0.001237 174s > print( round( vcov( fitwlsi4e$eq[[ 1 ]] ), digits = 6 ) ) 174s (Intercept) price income 174s (Intercept) 30.4377 -0.265752 -0.037918 174s price -0.2658 0.003463 -0.000827 174s income -0.0379 -0.000827 0.001237 174s > 174s > print( round( vcov( fitwlsi5e ), digits = 6 ) ) 174s demand_(Intercept) demand_price demand_income 174s demand_(Intercept) 30.4377 -0.265752 -0.037918 174s demand_price -0.2658 0.003463 -0.000827 174s demand_income -0.0379 -0.000827 0.001237 174s supply_(Intercept) 29.6762 -0.355820 0.060620 174s supply_price -0.2658 0.003463 -0.000827 174s supply_farmPrice -0.0279 0.000187 0.000094 174s supply_trend -0.0379 -0.000827 0.001237 174s supply_(Intercept) supply_price supply_farmPrice 174s demand_(Intercept) 29.6762 -0.265752 -0.027921 174s demand_price -0.3558 0.003463 0.000187 174s demand_income 0.0606 -0.000827 0.000094 174s supply_(Intercept) 52.0044 -0.355820 -0.173988 174s supply_price -0.3558 0.003463 0.000187 174s supply_farmPrice -0.1740 0.000187 0.001596 174s supply_trend 0.0606 -0.000827 0.000094 174s supply_trend 174s demand_(Intercept) -0.037918 174s demand_price -0.000827 174s demand_income 0.001237 174s supply_(Intercept) 0.060620 174s supply_price -0.000827 174s supply_farmPrice 0.000094 174s supply_trend 0.001237 174s > print( round( vcov( fitwlsi5e, modified.regMat = TRUE ), digits = 6 ) ) 174s C1 C2 C3 C4 C5 C6 174s C1 30.4377 -0.265752 -0.037918 29.6762 -0.265752 -0.027921 174s C2 -0.2658 0.003463 -0.000827 -0.3558 0.003463 0.000187 174s C3 -0.0379 -0.000827 0.001237 0.0606 -0.000827 0.000094 174s C4 29.6762 -0.355820 0.060620 52.0044 -0.355820 -0.173988 174s C5 -0.2658 0.003463 -0.000827 -0.3558 0.003463 0.000187 174s C6 -0.0279 0.000187 0.000094 -0.1740 0.000187 0.001596 174s > print( round( vcov( fitwlsi5e$eq[[ 2 ]] ), digits = 6 ) ) 174s (Intercept) price farmPrice trend 174s (Intercept) 52.0044 -0.355820 -0.173988 0.060620 174s price -0.3558 0.003463 0.000187 -0.000827 174s farmPrice -0.1740 0.000187 0.001596 0.000094 174s trend 0.0606 -0.000827 0.000094 0.001237 174s > 174s > 174s > ## *********** confidence intervals of coefficients ************* 174s > print( confint( fitwls1 ) ) 174s 2.5 % 97.5 % 174s demand_(Intercept) 84.031 115.760 174s demand_price -0.508 -0.125 174s demand_income 0.239 0.430 174s supply_(Intercept) 33.975 82.576 174s supply_price -0.041 0.362 174s supply_farmPrice 0.150 0.346 174s supply_trend 0.042 0.455 174s > print( confint( fitwls1$eq[[ 2 ]], level = 0.9 ) ) 174s 5 % 95 % 174s (Intercept) 38.263 78.288 174s price -0.005 0.326 174s farmPrice 0.167 0.329 174s trend 0.078 0.419 174s > 174s > print( confint( fitwls2e, level = 0.9 ) ) 174s 5 % 95 % 174s demand_(Intercept) 85.474 113.818 174s demand_price -0.464 -0.132 174s demand_income 0.241 0.396 174s supply_(Intercept) 35.634 76.786 174s supply_price -0.010 0.339 174s supply_farmPrice 0.176 0.340 174s supply_trend 0.241 0.396 174s > print( confint( fitwls2e$eq[[ 1 ]], level = 0.99 ) ) 174s 0.5 % 99.5 % 174s (Intercept) 80.620 118.672 174s price -0.521 -0.076 174s income 0.215 0.422 174s > 174s > print( confint( fitwls3, level = 0.99 ) ) 174s 0.5 % 99.5 % 174s demand_(Intercept) 84.286 115.030 174s demand_price -0.479 -0.119 174s demand_income 0.235 0.404 174s supply_(Intercept) 33.190 79.186 174s supply_price -0.031 0.359 174s supply_farmPrice 0.166 0.350 174s supply_trend 0.235 0.404 174s > print( confint( fitwls3$eq[[ 2 ]], level = 0.5 ) ) 174s 25 % 75 % 174s (Intercept) 48.472 63.903 174s price 0.099 0.230 174s farmPrice 0.227 0.289 174s trend 0.291 0.348 174s > 174s > print( confint( fitwls4e, level = 0.5 ) ) 174s 25 % 75 % 174s demand_(Intercept) 89.763 112.189 174s demand_price -0.436 -0.197 174s demand_income 0.252 0.395 174s supply_(Intercept) 39.328 68.598 174s supply_price 0.064 0.303 174s supply_farmPrice 0.179 0.341 174s supply_trend 0.252 0.395 174s > print( confint( fitwls4e$eq[[ 1 ]], level = 0.25 ) ) 174s 37.5 % 62.5 % 174s (Intercept) 99.202 102.750 174s price -0.335 -0.297 174s income 0.312 0.335 174s > 174s > print( confint( fitwls5, level = 0.25 ) ) 174s 37.5 % 62.5 % 174s demand_(Intercept) 88.637 113.191 174s demand_price -0.448 -0.184 174s demand_income 0.246 0.402 174s supply_(Intercept) 37.764 70.119 174s supply_price 0.052 0.316 174s supply_farmPrice 0.170 0.351 174s supply_trend 0.246 0.402 174s > print( confint( fitwls5$eq[[ 2 ]], level = 0.975 ) ) 174s 1.3 % 98.8 % 174s (Intercept) 35.279 72.604 174s price 0.032 0.336 174s farmPrice 0.156 0.365 174s trend 0.234 0.414 174s > 174s > print( confint( fitwlsi1e, level = 0.975, useDfSys = TRUE ) ) 174s 1.3 % 98.8 % 174s demand_(Intercept) 85.791 114.000 174s demand_price -0.486 -0.146 174s demand_income 0.249 0.420 174s supply_(Intercept) 37.416 79.135 174s supply_price -0.012 0.333 174s supply_farmPrice 0.164 0.332 174s supply_trend 0.071 0.426 174s > print( confint( fitwlsi1e$eq[[ 1 ]], level = 0.999, useDfSys = TRUE ) ) 174s 0.1 % 100 % 174s (Intercept) 74.863 124.928 174s price -0.618 -0.014 174s income 0.183 0.486 174s > 174s > print( confint( fitwlsi2, level = 0.999 ) ) 174s 0.1 % 100 % 174s demand_(Intercept) 84.342 114.979 174s demand_price -0.479 -0.120 174s demand_income 0.235 0.404 174s supply_(Intercept) 33.120 79.246 174s supply_price -0.031 0.360 174s supply_farmPrice 0.166 0.350 174s supply_trend 0.235 0.404 174s > print( confint( fitwlsi2$eq[[ 2 ]], level = 0.1 ) ) 174s 45 % 55 % 174s (Intercept) 54.746 57.620 174s price 0.152 0.176 174s farmPrice 0.252 0.264 174s trend 0.314 0.325 174s > 174s > print( confint( fitwlsi3e, level = 0.1 ) ) 174s 45 % 55 % 174s demand_(Intercept) 85.521 113.776 174s demand_price -0.464 -0.133 174s demand_income 0.242 0.396 174s supply_(Intercept) 35.579 76.833 174s supply_price -0.011 0.339 174s supply_farmPrice 0.176 0.340 174s supply_trend 0.242 0.396 174s > print( confint( fitwlsi3e$eq[[ 1 ]], level = 0.01 ) ) 174s 49.5 % 50.5 % 174s (Intercept) 99.561 99.736 174s price -0.299 -0.297 174s income 0.318 0.319 174s > 174s > print( confint( fitwlsi4, level = 0.01 ) ) 174s 49.5 % 50.5 % 174s demand_(Intercept) 88.642 113.164 174s demand_price -0.447 -0.184 174s demand_income 0.246 0.402 174s supply_(Intercept) 37.754 70.122 174s supply_price 0.053 0.316 174s supply_farmPrice 0.170 0.351 174s supply_trend 0.246 0.402 174s > print( confint( fitwlsi4$eq[[ 2 ]], level = 0.33 ) ) 174s 33.5 % 66.5 % 174s (Intercept) 50.512 57.364 174s price 0.156 0.212 174s farmPrice 0.241 0.279 174s trend 0.307 0.340 174s > 174s > print( confint( fitwlsi5e, level = 0.33 ) ) 174s 33.5 % 66.5 % 174s demand_(Intercept) 89.766 112.166 174s demand_price -0.435 -0.197 174s demand_income 0.252 0.395 174s supply_(Intercept) 39.320 68.599 174s supply_price 0.065 0.303 174s supply_farmPrice 0.179 0.341 174s supply_trend 0.252 0.395 174s > print( confint( fitwlsi5e$eq[[ 1 ]] ) ) 174s 2.5 % 97.5 % 174s (Intercept) 89.766 112.166 174s price -0.435 -0.197 174s income 0.252 0.395 174s > 174s > 174s > ## *********** fitted values ************* 174s > print( fitted( fitwls1 ) ) 174s demand supply 174s 1 97.4 98.9 174s 2 99.6 100.1 174s 3 99.5 100.2 174s 4 99.7 100.4 174s 5 102.3 102.7 174s 6 102.1 102.6 174s 7 102.5 102.4 174s 8 102.8 104.3 174s 9 101.7 102.9 174s 10 100.8 100.4 174s 11 95.6 96.0 174s 12 94.4 94.1 174s 13 95.7 95.6 174s 14 99.0 97.8 174s 15 104.3 102.6 174s 16 103.9 104.1 174s 17 104.8 103.8 174s 18 101.9 102.4 174s 19 103.5 102.1 174s 20 106.5 104.5 174s > print( fitted( fitwls1$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 98.9 100.1 100.2 100.4 102.7 102.6 102.4 104.3 102.9 100.4 96.0 94.1 95.6 174s 14 15 16 17 18 19 20 174s 97.8 102.6 104.1 103.8 102.4 102.1 104.5 174s > 174s > print( fitted( fitwls2e ) ) 174s demand supply 174s 1 97.6 98.3 174s 2 99.7 99.5 174s 3 99.6 99.7 174s 4 99.8 99.9 174s 5 102.2 102.5 174s 6 102.0 102.4 174s 7 102.4 102.3 174s 8 102.8 104.3 174s 9 101.7 102.9 174s 10 100.8 100.3 174s 11 95.8 95.9 174s 12 94.7 93.9 174s 13 95.9 95.5 174s 14 99.1 97.9 174s 15 104.1 103.0 174s 16 103.8 104.6 174s 17 104.6 104.3 174s 18 101.9 102.9 174s 19 103.4 102.7 174s 20 106.3 105.2 174s > print( fitted( fitwls2e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 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 174s 14 15 16 17 18 19 20 174s 99.1 104.1 103.8 104.6 101.9 103.4 106.3 174s > 174s > print( fitted( fitwls3 ) ) 174s demand supply 174s 1 97.6 98.3 174s 2 99.6 99.5 174s 3 99.6 99.7 174s 4 99.8 99.9 174s 5 102.2 102.5 174s 6 102.0 102.4 174s 7 102.4 102.3 174s 8 102.8 104.3 174s 9 101.7 102.9 174s 10 100.8 100.3 174s 11 95.8 95.9 174s 12 94.7 93.9 174s 13 95.9 95.5 174s 14 99.1 97.9 174s 15 104.1 103.0 174s 16 103.8 104.6 174s 17 104.6 104.3 174s 18 101.9 102.9 174s 19 103.4 102.7 174s 20 106.3 105.2 174s > print( fitted( fitwls3$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 98.3 99.5 99.7 99.9 102.5 102.4 102.3 104.3 102.9 100.3 95.9 93.9 95.5 174s 14 15 16 17 18 19 20 174s 97.9 103.0 104.6 104.3 102.9 102.7 105.2 174s > 174s > print( fitted( fitwls4e ) ) 174s demand supply 174s 1 97.5 98.2 174s 2 99.6 99.6 174s 3 99.5 99.7 174s 4 99.7 100.0 174s 5 102.3 102.4 174s 6 102.0 102.4 174s 7 102.4 102.3 174s 8 102.7 104.4 174s 9 101.7 102.9 174s 10 100.9 100.2 174s 11 95.8 95.7 174s 12 94.6 93.9 174s 13 95.8 95.5 174s 14 99.1 97.8 174s 15 104.2 102.9 174s 16 103.8 104.6 174s 17 104.8 104.1 174s 18 101.9 103.0 174s 19 103.3 102.8 174s 20 106.2 105.5 174s > print( fitted( fitwls4e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 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 174s 14 15 16 17 18 19 20 174s 99.1 104.2 103.8 104.8 101.9 103.3 106.2 174s > 174s > print( fitted( fitwls5 ) ) 174s demand supply 174s 1 97.5 98.2 174s 2 99.6 99.6 174s 3 99.5 99.7 174s 4 99.7 100.0 174s 5 102.3 102.4 174s 6 102.0 102.3 174s 7 102.4 102.3 174s 8 102.7 104.4 174s 9 101.7 102.9 174s 10 100.9 100.2 174s 11 95.8 95.7 174s 12 94.6 93.9 174s 13 95.8 95.5 174s 14 99.1 97.8 174s 15 104.2 102.9 174s 16 103.8 104.6 174s 17 104.8 104.1 174s 18 101.9 103.0 174s 19 103.3 102.8 174s 20 106.2 105.5 174s > print( fitted( fitwls5$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 98.2 99.6 99.7 100.0 102.4 102.3 102.3 104.4 102.9 100.2 95.7 93.9 95.5 174s 14 15 16 17 18 19 20 174s 97.8 102.9 104.6 104.1 103.0 102.8 105.5 174s > 174s > print( fitted( fitwlsi1e ) ) 174s demand supply 174s 1 97.4 98.9 174s 2 99.6 100.1 174s 3 99.5 100.2 174s 4 99.7 100.4 174s 5 102.3 102.7 174s 6 102.1 102.6 174s 7 102.5 102.4 174s 8 102.8 104.3 174s 9 101.7 102.9 174s 10 100.8 100.4 174s 11 95.6 96.0 174s 12 94.4 94.1 174s 13 95.7 95.6 174s 14 99.0 97.8 174s 15 104.3 102.6 174s 16 103.9 104.1 174s 17 104.8 103.8 174s 18 101.9 102.4 174s 19 103.5 102.1 174s 20 106.5 104.5 174s > print( fitted( fitwlsi1e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 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 174s 14 15 16 17 18 19 20 174s 99.0 104.3 103.9 104.8 101.9 103.5 106.5 174s > 174s > print( fitted( fitwlsi2 ) ) 174s demand supply 174s 1 97.6 98.3 174s 2 99.6 99.5 174s 3 99.6 99.7 174s 4 99.8 99.9 174s 5 102.2 102.5 174s 6 102.0 102.4 174s 7 102.4 102.3 174s 8 102.8 104.3 174s 9 101.7 102.9 174s 10 100.8 100.3 174s 11 95.8 95.9 174s 12 94.7 93.9 174s 13 95.9 95.5 174s 14 99.1 97.9 174s 15 104.1 103.0 174s 16 103.8 104.6 174s 17 104.6 104.3 174s 18 101.9 102.9 174s 19 103.4 102.7 174s 20 106.3 105.2 174s > print( fitted( fitwlsi2$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 98.3 99.5 99.7 99.9 102.5 102.4 102.3 104.3 102.9 100.3 95.9 93.9 95.5 174s 14 15 16 17 18 19 20 174s 97.9 103.0 104.6 104.3 102.9 102.7 105.2 174s > 174s > print( fitted( fitwlsi3e ) ) 174s demand supply 174s 1 97.6 98.3 174s 2 99.7 99.5 174s 3 99.6 99.7 174s 4 99.8 99.9 174s 5 102.2 102.5 174s 6 102.0 102.4 174s 7 102.4 102.3 174s 8 102.8 104.3 174s 9 101.7 102.9 174s 10 100.8 100.3 174s 11 95.8 95.9 174s 12 94.7 93.9 174s 13 95.9 95.5 174s 14 99.1 97.9 174s 15 104.1 103.0 174s 16 103.8 104.6 174s 17 104.6 104.3 174s 18 101.9 102.9 174s 19 103.4 102.7 174s 20 106.3 105.2 174s > print( fitted( fitwlsi3e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 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 174s 14 15 16 17 18 19 20 174s 99.1 104.1 103.8 104.6 101.9 103.4 106.3 174s > 174s > print( fitted( fitwlsi4 ) ) 174s demand supply 174s 1 97.5 98.2 174s 2 99.6 99.6 174s 3 99.5 99.7 174s 4 99.7 100.0 174s 5 102.3 102.4 174s 6 102.0 102.3 174s 7 102.4 102.3 174s 8 102.7 104.4 174s 9 101.7 102.9 174s 10 100.9 100.2 174s 11 95.8 95.7 174s 12 94.6 93.9 174s 13 95.8 95.5 174s 14 99.1 97.8 174s 15 104.2 102.9 174s 16 103.8 104.6 174s 17 104.8 104.1 174s 18 101.9 103.0 174s 19 103.3 102.8 174s 20 106.2 105.5 174s > print( fitted( fitwlsi4$eq[[ 2 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 98.2 99.6 99.7 100.0 102.4 102.3 102.3 104.4 102.9 100.2 95.7 93.9 95.5 174s 14 15 16 17 18 19 20 174s 97.8 102.9 104.6 104.1 103.0 102.8 105.5 174s > 174s > print( fitted( fitwlsi5e ) ) 174s demand supply 174s 1 97.5 98.2 174s 2 99.6 99.6 174s 3 99.5 99.7 174s 4 99.7 100.0 174s 5 102.3 102.4 174s 6 102.0 102.4 174s 7 102.4 102.3 174s 8 102.7 104.4 174s 9 101.7 102.9 174s 10 100.9 100.2 174s 11 95.8 95.7 174s 12 94.6 93.9 174s 13 95.8 95.5 174s 14 99.1 97.8 174s 15 104.2 102.9 174s 16 103.8 104.6 174s 17 104.8 104.1 174s 18 101.9 103.0 174s 19 103.3 102.8 174s 20 106.2 105.5 174s > print( fitted( fitwlsi5e$eq[[ 1 ]] ) ) 174s 1 2 3 4 5 6 7 8 9 10 11 12 13 174s 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 174s 14 15 16 17 18 19 20 174s 99.1 104.2 103.8 104.8 101.9 103.3 106.2 174s > 174s > 174s > ## *********** predicted values ************* 174s > predictData <- Kmenta 174s > predictData$consump <- NULL 174s > predictData$price <- Kmenta$price * 0.9 174s > predictData$income <- Kmenta$income * 1.1 174s > 174s > print( predict( fitwls1, se.fit = TRUE, interval = "prediction" ) ) 174s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 174s 1 97.4 0.643 93.1 101.7 98.9 1.056 174s 2 99.6 0.577 95.3 103.8 100.1 1.037 174s 3 99.5 0.545 95.3 103.8 100.2 0.939 174s 4 99.7 0.582 95.4 104.0 100.4 0.912 174s 5 102.3 0.502 98.1 106.5 102.7 0.895 174s 6 102.1 0.463 97.9 106.3 102.6 0.791 174s 7 102.5 0.484 98.3 106.7 102.4 0.719 174s 8 102.8 0.601 98.6 107.1 104.3 0.963 174s 9 101.7 0.527 97.5 105.9 102.9 0.788 174s 10 100.8 0.788 96.4 105.2 100.4 0.981 174s 11 95.6 0.946 91.0 100.1 96.0 1.185 174s 12 94.4 0.980 89.8 98.9 94.1 1.394 174s 13 95.7 0.880 91.2 100.1 95.6 1.244 174s 14 99.0 0.508 94.8 103.2 97.8 0.896 174s 15 104.3 0.758 99.9 108.7 102.6 0.874 174s 16 103.9 0.616 99.7 108.2 104.1 0.916 174s 17 104.8 1.273 99.9 109.7 103.8 1.605 174s 18 101.9 0.536 97.7 106.2 102.4 0.962 174s 19 103.5 0.680 99.2 107.8 102.1 1.098 174s 20 106.5 1.274 101.7 111.4 104.5 1.664 174s supply.lwr supply.upr 174s 1 93.4 104 174s 2 94.5 106 174s 3 94.7 106 174s 4 94.9 106 174s 5 97.3 108 174s 6 97.2 108 174s 7 97.1 108 174s 8 98.8 110 174s 9 97.6 108 174s 10 94.8 106 174s 11 90.3 102 174s 12 88.2 100 174s 13 89.9 101 174s 14 92.3 103 174s 15 97.2 108 174s 16 98.6 110 174s 17 97.7 110 174s 18 96.9 108 174s 19 96.5 108 174s 20 98.3 111 174s > print( predict( fitwls1$eq[[ 2 ]], se.fit = TRUE, interval = "prediction" ) ) 174s fit se.fit lwr upr 174s 1 98.9 1.056 93.4 104 174s 2 100.1 1.037 94.5 106 174s 3 100.2 0.939 94.7 106 174s 4 100.4 0.912 94.9 106 174s 5 102.7 0.895 97.3 108 174s 6 102.6 0.791 97.2 108 174s 7 102.4 0.719 97.1 108 174s 8 104.3 0.963 98.8 110 174s 9 102.9 0.788 97.6 108 174s 10 100.4 0.981 94.8 106 174s 11 96.0 1.185 90.3 102 174s 12 94.1 1.394 88.2 100 174s 13 95.6 1.244 89.9 101 174s 14 97.8 0.896 92.3 103 174s 15 102.6 0.874 97.2 108 174s 16 104.1 0.916 98.6 110 174s 17 103.8 1.605 97.7 110 174s 18 102.4 0.962 96.9 108 174s 19 102.1 1.098 96.5 108 174s 20 104.5 1.664 98.3 111 174s > 174s > print( predict( fitwls2e, se.pred = TRUE, interval = "confidence", 174s + level = 0.999, newdata = predictData ) ) 174s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 174s 1 103 2.12 100.2 106 96.6 2.65 174s 2 106 2.12 102.7 109 97.8 2.57 174s 3 106 2.13 102.6 109 98.0 2.58 174s 4 106 2.12 102.9 109 98.2 2.56 174s 5 108 2.35 103.5 113 100.9 2.72 174s 6 108 2.31 103.6 113 100.7 2.67 174s 7 109 2.30 104.2 113 100.6 2.62 174s 8 109 2.27 105.0 114 102.6 2.58 174s 9 108 2.36 102.8 112 101.4 2.74 174s 10 106 2.46 100.8 112 98.8 2.92 174s 11 101 2.28 96.7 105 94.4 2.98 174s 12 100 2.12 97.0 103 92.3 2.96 174s 13 102 2.05 99.3 104 93.8 2.81 174s 14 105 2.20 101.2 109 96.3 2.78 174s 15 110 2.53 104.4 116 101.4 2.78 174s 16 110 2.44 104.7 115 102.9 2.69 174s 17 110 2.81 102.9 118 102.9 3.14 174s 18 108 2.23 104.3 112 101.2 2.58 174s 19 110 2.30 105.6 115 100.9 2.57 174s 20 114 2.50 108.1 119 103.3 2.52 174s supply.lwr supply.upr 174s 1 92.9 100.3 174s 2 95.0 100.6 174s 3 95.1 100.9 174s 4 95.5 100.9 174s 5 96.6 105.1 174s 6 96.9 104.6 174s 7 97.2 104.0 174s 8 99.6 105.5 174s 9 96.9 105.9 174s 10 93.1 104.6 174s 11 88.2 100.5 174s 12 86.3 98.4 174s 13 88.8 98.9 174s 14 91.5 101.0 174s 15 96.7 106.2 174s 16 98.9 106.9 174s 17 95.8 110.0 174s 18 98.2 104.1 174s 19 98.1 103.8 174s 20 101.1 105.6 174s > print( predict( fitwls2e$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 174s + level = 0.999, newdata = predictData ) ) 174s fit se.pred lwr upr 174s 1 103 2.12 100.2 106 174s 2 106 2.12 102.7 109 174s 3 106 2.13 102.6 109 174s 4 106 2.12 102.9 109 174s 5 108 2.35 103.5 113 174s 6 108 2.31 103.6 113 174s 7 109 2.30 104.2 113 174s 8 109 2.27 105.0 114 174s 9 108 2.36 102.8 112 174s 10 106 2.46 100.8 112 174s 11 101 2.28 96.7 105 174s 12 100 2.12 97.0 103 174s 13 102 2.05 99.3 104 174s 14 105 2.20 101.2 109 174s 15 110 2.53 104.4 116 174s 16 110 2.44 104.7 115 174s 17 110 2.81 102.9 118 174s 18 108 2.23 104.3 112 174s 19 110 2.30 105.6 115 174s 20 114 2.50 108.1 119 174s > 174s > print( predict( fitwls3, se.pred = TRUE, interval = "prediction", 174s + level = 0.975 ) ) 174s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 174s 1 97.6 2.03 92.8 102.3 98.3 2.54 174s 2 99.6 2.02 94.9 104.4 99.5 2.56 174s 3 99.6 2.01 94.9 104.3 99.7 2.55 174s 4 99.8 2.02 95.0 104.5 99.9 2.56 174s 5 102.2 2.00 97.5 106.9 102.5 2.59 174s 6 102.0 1.99 97.3 106.7 102.4 2.56 174s 7 102.4 1.99 97.7 107.1 102.3 2.54 174s 8 102.8 2.03 98.0 107.5 104.3 2.63 174s 9 101.7 2.01 97.0 106.4 102.9 2.57 174s 10 100.8 2.09 95.9 105.7 100.3 2.64 174s 11 95.8 2.14 90.8 100.8 95.9 2.72 174s 12 94.7 2.14 89.6 99.7 93.9 2.82 174s 13 95.9 2.11 91.0 100.8 95.5 2.75 174s 14 99.1 2.00 94.4 103.8 97.9 2.61 174s 15 104.1 2.07 99.3 109.0 103.0 2.56 174s 16 103.8 2.03 99.0 108.5 104.6 2.55 174s 17 104.6 2.31 99.2 110.0 104.3 2.85 174s 18 101.9 2.01 97.2 106.6 102.9 2.55 174s 19 103.4 2.05 98.6 108.2 102.7 2.59 174s 20 106.3 2.31 100.9 111.7 105.2 2.84 174s supply.lwr supply.upr 174s 1 92.3 104 174s 2 93.5 106 174s 3 93.7 106 174s 4 93.9 106 174s 5 96.4 109 174s 6 96.4 108 174s 7 96.3 108 174s 8 98.1 110 174s 9 96.9 109 174s 10 94.1 107 174s 11 89.5 102 174s 12 87.3 101 174s 13 89.1 102 174s 14 91.8 104 174s 15 97.0 109 174s 16 98.6 111 174s 17 97.6 111 174s 18 96.9 109 174s 19 96.6 109 174s 20 98.6 112 174s > print( predict( fitwls3$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 174s + level = 0.975 ) ) 174s fit se.pred lwr upr 174s 1 98.3 2.54 92.3 104 174s 2 99.5 2.56 93.5 106 174s 3 99.7 2.55 93.7 106 174s 4 99.9 2.56 93.9 106 174s 5 102.5 2.59 96.4 109 174s 6 102.4 2.56 96.4 108 174s 7 102.3 2.54 96.3 108 174s 8 104.3 2.63 98.1 110 174s 9 102.9 2.57 96.9 109 174s 10 100.3 2.64 94.1 107 174s 11 95.9 2.72 89.5 102 174s 12 93.9 2.82 87.3 101 174s 13 95.5 2.75 89.1 102 174s 14 97.9 2.61 91.8 104 174s 15 103.0 2.56 97.0 109 174s 16 104.6 2.55 98.6 111 174s 17 104.3 2.85 97.6 111 174s 18 102.9 2.55 96.9 109 174s 19 102.7 2.59 96.6 109 174s 20 105.2 2.84 98.6 112 174s > 174s > print( predict( fitwls4e, se.fit = TRUE, interval = "confidence", 174s + level = 0.25 ) ) 174s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 174s 1 97.5 0.541 97.4 97.7 98.2 0.598 174s 2 99.6 0.471 99.4 99.7 99.6 0.679 174s 3 99.5 0.454 99.4 99.7 99.7 0.634 174s 4 99.7 0.475 99.5 99.8 100.0 0.643 174s 5 102.3 0.434 102.1 102.4 102.4 0.753 174s 6 102.0 0.418 101.9 102.2 102.4 0.680 174s 7 102.4 0.440 102.3 102.5 102.3 0.625 174s 8 102.7 0.537 102.5 102.9 104.4 0.799 174s 9 101.7 0.447 101.6 101.9 102.9 0.700 174s 10 100.9 0.628 100.7 101.1 100.2 0.716 174s 11 95.8 0.833 95.6 96.1 95.7 0.916 174s 12 94.6 0.807 94.4 94.9 93.9 1.226 174s 13 95.8 0.677 95.6 96.0 95.5 1.130 174s 14 99.1 0.459 98.9 99.2 97.8 0.796 174s 15 104.2 0.572 104.1 104.4 102.9 0.656 174s 16 103.8 0.509 103.7 104.0 104.6 0.644 174s 17 104.8 0.877 104.5 105.1 104.1 1.150 174s 18 101.9 0.478 101.7 102.0 103.0 0.575 174s 19 103.3 0.604 103.1 103.5 102.8 0.649 174s 20 106.2 1.102 105.8 106.6 105.5 0.875 174s supply.lwr supply.upr 174s 1 98.0 98.4 174s 2 99.4 99.8 174s 3 99.5 99.9 174s 4 99.8 100.2 174s 5 102.2 102.7 174s 6 102.1 102.6 174s 7 102.1 102.5 174s 8 104.1 104.6 174s 9 102.7 103.1 174s 10 99.9 100.4 174s 11 95.4 96.0 174s 12 93.5 94.3 174s 13 95.2 95.9 174s 14 97.6 98.1 174s 15 102.7 103.1 174s 16 104.4 104.8 174s 17 103.8 104.5 174s 18 102.8 103.2 174s 19 102.6 103.0 174s 20 105.2 105.8 174s > print( predict( fitwls4e$eq[[ 1 ]], se.fit = TRUE, interval = "confidence", 174s + level = 0.25 ) ) 174s fit se.fit lwr upr 174s 1 97.5 0.541 97.4 97.7 174s 2 99.6 0.471 99.4 99.7 174s 3 99.5 0.454 99.4 99.7 174s 4 99.7 0.475 99.5 99.8 174s 5 102.3 0.434 102.1 102.4 174s 6 102.0 0.418 101.9 102.2 174s 7 102.4 0.440 102.3 102.5 174s 8 102.7 0.537 102.5 102.9 174s 9 101.7 0.447 101.6 101.9 174s 10 100.9 0.628 100.7 101.1 174s 11 95.8 0.833 95.6 96.1 174s 12 94.6 0.807 94.4 94.9 174s 13 95.8 0.677 95.6 96.0 174s 14 99.1 0.459 98.9 99.2 174s 15 104.2 0.572 104.1 104.4 174s 16 103.8 0.509 103.7 104.0 174s 17 104.8 0.877 104.5 105.1 174s 18 101.9 0.478 101.7 102.0 174s 19 103.3 0.604 103.1 103.5 174s 20 106.2 1.102 105.8 106.6 174s > 174s > print( predict( fitwls5, se.fit = TRUE, se.pred = TRUE, 174s + interval = "prediction", level = 0.5, newdata = predictData ) ) 174s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 174s 1 104 0.749 2.07 102.1 105 96.4 174s 2 106 0.784 2.09 104.6 107 97.7 174s 3 106 0.793 2.09 104.5 107 97.8 174s 4 106 0.792 2.09 104.8 108 98.1 174s 5 109 1.136 2.24 107.1 110 100.6 174s 6 108 1.086 2.22 106.9 110 100.5 174s 7 109 1.097 2.22 107.4 110 100.4 174s 8 110 1.107 2.23 108.0 111 102.5 174s 9 108 1.126 2.24 106.4 109 101.1 174s 10 107 1.243 2.30 105.1 108 98.5 174s 11 101 1.066 2.21 99.7 103 94.0 174s 12 100 0.814 2.10 98.8 102 92.0 174s 13 102 0.617 2.03 100.4 103 93.7 174s 14 105 0.874 2.12 103.7 107 96.0 174s 15 111 1.377 2.37 109.0 112 101.2 174s 16 110 1.279 2.32 108.8 112 102.8 174s 17 111 1.656 2.55 108.9 112 102.5 174s 18 109 1.014 2.18 107.0 110 101.1 174s 19 110 1.180 2.27 108.7 112 100.9 174s 20 114 1.635 2.53 112.2 116 103.4 174s supply.se.fit supply.se.pred supply.lwr supply.upr 174s 1 0.799 2.58 94.6 98.1 174s 2 0.679 2.55 95.9 99.4 174s 3 0.692 2.55 96.1 99.6 174s 4 0.657 2.54 96.3 99.8 174s 5 1.051 2.67 98.8 102.5 174s 6 0.947 2.63 98.7 102.3 174s 7 0.845 2.59 98.7 102.2 174s 8 0.849 2.60 100.7 104.2 174s 9 1.100 2.69 99.3 103.0 174s 10 1.276 2.77 96.6 100.4 174s 11 1.422 2.84 92.1 95.9 174s 12 1.595 2.93 90.1 94.0 174s 13 1.401 2.82 91.7 95.6 174s 14 1.201 2.73 94.2 97.9 174s 15 1.169 2.72 99.3 103.0 174s 16 1.060 2.67 100.9 104.6 174s 17 1.727 3.00 100.5 104.6 174s 18 0.831 2.59 99.3 102.8 174s 19 0.834 2.59 99.1 102.6 174s 20 0.653 2.54 101.7 105.2 174s > print( predict( fitwls5$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 174s + interval = "prediction", level = 0.5, newdata = predictData ) ) 174s fit se.fit se.pred lwr upr 174s 1 96.4 0.799 2.58 94.6 98.1 174s 2 97.7 0.679 2.55 95.9 99.4 174s 3 97.8 0.692 2.55 96.1 99.6 174s 4 98.1 0.657 2.54 96.3 99.8 174s 5 100.6 1.051 2.67 98.8 102.5 174s 6 100.5 0.947 2.63 98.7 102.3 174s 7 100.4 0.845 2.59 98.7 102.2 174s 8 102.5 0.849 2.60 100.7 104.2 174s 9 101.1 1.100 2.69 99.3 103.0 174s 10 98.5 1.276 2.77 96.6 100.4 174s 11 94.0 1.422 2.84 92.1 95.9 174s 12 92.0 1.595 2.93 90.1 94.0 174s 13 93.7 1.401 2.82 91.7 95.6 174s 14 96.0 1.201 2.73 94.2 97.9 174s 15 101.2 1.169 2.72 99.3 103.0 174s 16 102.8 1.060 2.67 100.9 104.6 174s 17 102.5 1.727 3.00 100.5 104.6 174s 18 101.1 0.831 2.59 99.3 102.8 174s 19 100.9 0.834 2.59 99.1 102.6 174s 20 103.4 0.653 2.54 101.7 105.2 174s > 174s > print( predict( fitwlsi1e, se.fit = TRUE, se.pred = TRUE, 174s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 174s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 174s 1 97.4 0.593 2.02 95.8 99.0 98.9 174s 2 99.6 0.532 2.00 98.1 101.0 100.1 174s 3 99.5 0.502 1.99 98.2 100.9 100.2 174s 4 99.7 0.537 2.00 98.2 101.2 100.4 174s 5 102.3 0.463 1.98 101.0 103.6 102.7 174s 6 102.1 0.427 1.98 100.9 103.2 102.6 174s 7 102.5 0.446 1.98 101.2 103.7 102.4 174s 8 102.8 0.554 2.01 101.3 104.3 104.3 174s 9 101.7 0.486 1.99 100.4 103.0 102.9 174s 10 100.8 0.727 2.06 98.8 102.8 100.4 174s 11 95.6 0.872 2.12 93.2 98.0 96.0 174s 12 94.4 0.903 2.13 91.9 96.8 94.1 174s 13 95.7 0.811 2.09 93.4 97.9 95.6 174s 14 99.0 0.468 1.99 97.7 100.3 97.8 174s 15 104.3 0.699 2.05 102.4 106.2 102.6 174s 16 103.9 0.568 2.01 102.4 105.5 104.1 174s 17 104.8 1.174 2.26 101.6 108.0 103.8 174s 18 101.9 0.494 1.99 100.6 103.3 102.4 174s 19 103.5 0.627 2.03 101.8 105.2 102.1 174s 20 106.5 1.175 2.26 103.3 109.7 104.5 174s supply.se.fit supply.se.pred supply.lwr supply.upr 174s 1 0.945 2.58 96.3 101.5 174s 2 0.928 2.58 97.5 102.6 174s 3 0.839 2.55 97.9 102.5 174s 4 0.816 2.54 98.1 102.6 174s 5 0.800 2.53 100.5 104.9 174s 6 0.707 2.51 100.6 104.5 174s 7 0.643 2.49 100.7 104.2 174s 8 0.862 2.55 102.0 106.7 174s 9 0.705 2.51 101.0 104.9 174s 10 0.877 2.56 98.0 102.7 174s 11 1.060 2.63 93.1 98.9 174s 12 1.247 2.71 90.7 97.5 174s 13 1.113 2.65 92.6 98.6 174s 14 0.801 2.53 95.6 100.0 174s 15 0.782 2.53 100.5 104.8 174s 16 0.819 2.54 101.9 106.3 174s 17 1.436 2.80 99.9 107.7 174s 18 0.861 2.55 100.0 104.7 174s 19 0.982 2.60 99.4 104.8 174s 20 1.489 2.83 100.4 108.6 174s > print( predict( fitwlsi1e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 174s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 174s fit se.fit se.pred lwr upr 174s 1 97.4 0.593 2.02 95.8 99.0 174s 2 99.6 0.532 2.00 98.1 101.0 174s 3 99.5 0.502 1.99 98.2 100.9 174s 4 99.7 0.537 2.00 98.2 101.2 174s 5 102.3 0.463 1.98 101.0 103.6 174s 6 102.1 0.427 1.98 100.9 103.2 174s 7 102.5 0.446 1.98 101.2 103.7 174s 8 102.8 0.554 2.01 101.3 104.3 174s 9 101.7 0.486 1.99 100.4 103.0 174s 10 100.8 0.727 2.06 98.8 102.8 174s 11 95.6 0.872 2.12 93.2 98.0 174s 12 94.4 0.903 2.13 91.9 96.8 174s 13 95.7 0.811 2.09 93.4 97.9 174s 14 99.0 0.468 1.99 97.7 100.3 174s 15 104.3 0.699 2.05 102.4 106.2 174s 16 103.9 0.568 2.01 102.4 105.5 174s 17 104.8 1.174 2.26 101.6 108.0 174s 18 101.9 0.494 1.99 100.6 103.3 174s 19 103.5 0.627 2.03 101.8 105.2 174s 20 106.5 1.175 2.26 103.3 109.7 174s > 174s > print( predict( fitwlsi2, se.fit = TRUE, interval = "prediction", 174s + level = 0.9, newdata = predictData ) ) 174s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 174s 1 103 0.937 99.7 107 96.6 1.151 174s 2 106 0.942 102.2 110 97.8 0.875 174s 3 106 0.966 102.1 109 98.0 0.909 174s 4 106 0.947 102.4 110 98.2 0.833 174s 5 108 1.448 104.3 112 100.9 1.327 174s 6 108 1.368 104.2 112 100.7 1.192 174s 7 109 1.352 104.7 113 100.6 1.052 174s 8 109 1.293 105.4 113 102.6 0.914 174s 9 108 1.459 103.5 112 101.4 1.400 174s 10 106 1.647 102.0 111 98.8 1.787 174s 11 101 1.300 97.0 105 94.4 1.911 174s 12 100 0.938 96.4 104 92.3 1.880 174s 13 102 0.722 98.2 105 93.8 1.565 174s 14 105 1.121 101.1 109 96.3 1.479 174s 15 110 1.769 105.8 115 101.4 1.481 174s 16 110 1.602 105.8 114 102.9 1.248 174s 17 110 2.210 105.3 115 102.9 2.201 174s 18 108 1.205 104.5 112 101.2 0.911 174s 19 110 1.353 106.1 114 100.9 0.877 174s 20 114 1.714 109.4 118 103.3 0.705 174s supply.lwr supply.upr 174s 1 92.0 101.2 174s 2 93.4 102.2 174s 3 93.6 102.4 174s 4 93.9 102.6 174s 5 96.2 105.6 174s 6 96.1 105.3 174s 7 96.1 105.1 174s 8 98.1 107.0 174s 9 96.6 106.1 174s 10 93.7 103.9 174s 11 89.1 99.6 174s 12 87.1 97.5 174s 13 88.9 98.8 174s 14 91.4 101.1 174s 15 96.6 106.3 174s 16 98.3 107.6 174s 17 97.4 108.5 174s 18 96.8 105.6 174s 19 96.5 105.3 174s 20 99.0 107.7 174s > print( predict( fitwlsi2$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 174s + level = 0.9, newdata = predictData ) ) 174s fit se.fit lwr upr 174s 1 96.6 1.151 92.0 101.2 174s 2 97.8 0.875 93.4 102.2 174s 3 98.0 0.909 93.6 102.4 174s 4 98.2 0.833 93.9 102.6 174s 5 100.9 1.327 96.2 105.6 174s 6 100.7 1.192 96.1 105.3 174s 7 100.6 1.052 96.1 105.1 174s 8 102.6 0.914 98.1 107.0 174s 9 101.4 1.400 96.6 106.1 174s 10 98.8 1.787 93.7 103.9 174s 11 94.4 1.911 89.1 99.6 174s 12 92.3 1.880 87.1 97.5 174s 13 93.8 1.565 88.9 98.8 174s 14 96.3 1.479 91.4 101.1 174s 15 101.4 1.481 96.6 106.3 174s 16 102.9 1.248 98.3 107.6 174s 17 102.9 2.201 97.4 108.5 174s 18 101.2 0.911 96.8 105.6 174s 19 100.9 0.877 96.5 105.3 174s 20 103.3 0.705 99.0 107.7 174s > 174s > print( predict( fitwlsi3e, interval = "prediction", level = 0.925 ) ) 174s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 174s 1 97.6 93.9 101.3 98.3 93.6 103 174s 2 99.7 96.0 103.3 99.5 94.9 104 174s 3 99.6 95.9 103.3 99.7 95.1 104 174s 4 99.8 96.1 103.5 99.9 95.3 105 174s 5 102.2 98.6 105.9 102.5 97.8 107 174s 6 102.0 98.4 105.7 102.4 97.7 107 174s 7 102.4 98.7 106.0 102.3 97.6 107 174s 8 102.8 99.1 106.5 104.3 99.5 109 174s 9 101.7 98.0 105.3 102.9 98.3 108 174s 10 100.8 97.0 104.6 100.3 95.5 105 174s 11 95.8 91.9 99.7 95.9 91.0 101 174s 12 94.7 90.8 98.6 93.9 88.9 99 174s 13 95.9 92.1 99.7 95.5 90.6 100 174s 14 99.1 95.4 102.7 97.9 93.2 103 174s 15 104.1 100.4 107.9 103.0 98.3 108 174s 16 103.8 100.1 107.5 104.6 99.9 109 174s 17 104.6 100.4 108.7 104.3 99.2 109 174s 18 101.9 98.2 105.6 102.9 98.2 108 174s 19 103.4 99.6 107.1 102.7 98.0 107 174s 20 106.3 102.2 110.4 105.2 100.1 110 174s > print( predict( fitwlsi3e$eq[[ 1 ]], interval = "prediction", level = 0.925 ) ) 174s fit lwr upr 174s 1 97.6 93.9 101.3 174s 2 99.7 96.0 103.3 174s 3 99.6 95.9 103.3 174s 4 99.8 96.1 103.5 174s 5 102.2 98.6 105.9 174s 6 102.0 98.4 105.7 174s 7 102.4 98.7 106.0 174s 8 102.8 99.1 106.5 174s 9 101.7 98.0 105.3 174s 10 100.8 97.0 104.6 174s 11 95.8 91.9 99.7 174s 12 94.7 90.8 98.6 174s 13 95.9 92.1 99.7 174s 14 99.1 95.4 102.7 174s 15 104.1 100.4 107.9 174s 16 103.8 100.1 107.5 174s 17 104.6 100.4 108.7 174s 18 101.9 98.2 105.6 174s 19 103.4 99.6 107.1 174s 20 106.3 102.2 110.4 174s > 174s > print( predict( fitwlsi4, interval = "confidence", newdata = predictData ) ) 174s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 174s 1 104 102.0 105 96.4 94.8 98.0 174s 2 106 104.4 108 97.7 96.3 99.0 174s 3 106 104.3 108 97.8 96.4 99.2 174s 4 106 104.6 108 98.1 96.7 99.4 174s 5 109 106.3 111 100.6 98.5 102.8 174s 6 108 106.2 111 100.5 98.6 102.4 174s 7 109 106.7 111 100.4 98.7 102.2 174s 8 110 107.3 112 102.5 100.7 104.2 174s 9 108 105.6 110 101.1 98.9 103.4 174s 10 107 104.1 109 98.5 95.9 101.1 174s 11 101 99.0 103 94.0 91.1 96.9 174s 12 100 98.6 102 92.0 88.8 95.3 174s 13 102 100.5 103 93.7 90.8 96.5 174s 14 105 103.3 107 96.0 93.6 98.5 174s 15 111 107.8 113 101.2 98.8 103.6 174s 16 110 107.8 113 102.8 100.6 104.9 174s 17 111 107.3 114 102.5 99.0 106.0 174s 18 109 106.5 111 101.1 99.4 102.8 174s 19 110 107.9 113 100.9 99.2 102.6 174s 20 114 110.6 117 103.4 102.1 104.7 174s > print( predict( fitwlsi4$eq[[ 2 ]], interval = "confidence", 174s + newdata = predictData ) ) 174s fit lwr upr 174s 1 96.4 94.8 98.0 174s 2 97.7 96.3 99.0 174s 3 97.8 96.4 99.2 174s 4 98.1 96.7 99.4 174s 5 100.6 98.5 102.8 174s 6 100.5 98.6 102.4 174s 7 100.4 98.7 102.2 174s 8 102.5 100.7 104.2 174s 9 101.1 98.9 103.4 174s 10 98.5 95.9 101.1 174s 11 94.0 91.1 96.9 174s 12 92.0 88.8 95.3 174s 13 93.7 90.8 96.5 174s 14 96.0 93.6 98.5 174s 15 101.2 98.8 103.6 174s 16 102.8 100.6 104.9 174s 17 102.5 99.0 106.0 174s 18 101.1 99.4 102.8 174s 19 100.9 99.2 102.6 174s 20 103.4 102.1 104.7 174s > 174s > print( predict( fitwlsi5e, se.fit = TRUE, se.pred = TRUE, 174s + interval = "prediction", level = 0.01 ) ) 174s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 174s 1 97.5 0.540 2.01 97.5 97.6 98.2 174s 2 99.6 0.470 1.99 99.6 99.6 99.6 174s 3 99.5 0.453 1.99 99.5 99.6 99.7 174s 4 99.7 0.474 1.99 99.7 99.7 100.0 174s 5 102.3 0.433 1.98 102.2 102.3 102.4 174s 6 102.0 0.417 1.98 102.0 102.1 102.4 174s 7 102.4 0.439 1.98 102.4 102.4 102.3 174s 8 102.7 0.536 2.01 102.7 102.7 104.4 174s 9 101.7 0.446 1.99 101.7 101.8 102.9 174s 10 100.9 0.627 2.03 100.9 100.9 100.2 174s 11 95.8 0.831 2.11 95.8 95.9 95.7 174s 12 94.6 0.806 2.10 94.6 94.6 93.9 174s 13 95.8 0.676 2.05 95.8 95.8 95.5 174s 14 99.1 0.458 1.99 99.0 99.1 97.8 174s 15 104.2 0.571 2.02 104.2 104.3 102.9 174s 16 103.8 0.508 2.00 103.8 103.9 104.6 174s 17 104.8 0.877 2.12 104.8 104.8 104.1 174s 18 101.9 0.477 1.99 101.8 101.9 103.0 174s 19 103.3 0.602 2.03 103.3 103.4 102.8 174s 20 106.2 1.100 2.23 106.2 106.2 105.5 174s supply.se.fit supply.se.pred supply.lwr supply.upr 174s 1 0.598 2.52 98.2 98.3 174s 2 0.680 2.54 99.5 99.6 174s 3 0.634 2.53 99.7 99.8 174s 4 0.644 2.54 100.0 100.0 174s 5 0.754 2.57 102.4 102.5 174s 6 0.681 2.55 102.3 102.4 174s 7 0.626 2.53 102.3 102.3 174s 8 0.800 2.58 104.4 104.4 174s 9 0.701 2.55 102.9 102.9 174s 10 0.716 2.55 100.1 100.2 174s 11 0.918 2.62 95.7 95.8 174s 12 1.229 2.74 93.8 93.9 174s 13 1.132 2.70 95.5 95.6 174s 14 0.797 2.58 97.8 97.9 174s 15 0.657 2.54 102.9 103.0 174s 16 0.645 2.54 104.5 104.6 174s 17 1.151 2.71 104.1 104.2 174s 18 0.575 2.52 103.0 103.0 174s 19 0.649 2.54 102.8 102.8 174s 20 0.875 2.60 105.5 105.5 174s > print( predict( fitwlsi5e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 174s + interval = "prediction", level = 0.01 ) ) 174s fit se.fit se.pred lwr upr 174s 1 97.5 0.540 2.01 97.5 97.6 174s 2 99.6 0.470 1.99 99.6 99.6 174s 3 99.5 0.453 1.99 99.5 99.6 174s 4 99.7 0.474 1.99 99.7 99.7 174s 5 102.3 0.433 1.98 102.2 102.3 174s 6 102.0 0.417 1.98 102.0 102.1 174s 7 102.4 0.439 1.98 102.4 102.4 174s 8 102.7 0.536 2.01 102.7 102.7 174s 9 101.7 0.446 1.99 101.7 101.8 174s 10 100.9 0.627 2.03 100.9 100.9 174s 11 95.8 0.831 2.11 95.8 95.9 174s 12 94.6 0.806 2.10 94.6 94.6 174s 13 95.8 0.676 2.05 95.8 95.8 174s 14 99.1 0.458 1.99 99.0 99.1 174s 15 104.2 0.571 2.02 104.2 104.3 174s 16 103.8 0.508 2.00 103.8 103.9 174s 17 104.8 0.877 2.12 104.8 104.8 174s 18 101.9 0.477 1.99 101.8 101.9 174s 19 103.3 0.602 2.03 103.3 103.4 174s 20 106.2 1.100 2.23 106.2 106.2 174s > 174s > # predict just one observation 174s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 174s + trend = 25 ) 174s > 174s > print( predict( fitwls1, newdata = smallData ) ) 174s demand.pred supply.pred 174s 1 109 115 174s > print( predict( fitwls1$eq[[ 1 ]], newdata = smallData ) ) 174s fit 174s 1 109 174s > 174s > print( predict( fitwls2e, se.fit = TRUE, level = 0.9, 174s + newdata = smallData ) ) 174s demand.pred demand.se.fit supply.pred supply.se.fit 174s 1 109 2.23 116 3.03 174s > print( predict( fitwls2e$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 174s + newdata = smallData ) ) 174s fit se.pred 174s 1 109 2.96 174s > 174s > print( predict( fitwls3, interval = "prediction", level = 0.975, 174s + newdata = smallData ) ) 174s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 174s 1 109 101 116 116 107 126 174s > print( predict( fitwls3$eq[[ 1 ]], interval = "confidence", level = 0.8, 174s + newdata = smallData ) ) 174s fit lwr upr 174s 1 109 106 112 174s > 174s > print( predict( fitwls4e, se.fit = TRUE, interval = "confidence", 174s + level = 0.999, newdata = smallData ) ) 174s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 174s 1 108 2.02 101 116 117 2.02 174s supply.lwr supply.upr 174s 1 110 124 174s > print( predict( fitwls4e$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 174s + level = 0.75, newdata = smallData ) ) 174s fit se.pred lwr upr 174s 1 117 3.18 113 121 174s > 174s > print( predict( fitwls5, se.fit = TRUE, interval = "prediction", 174s + newdata = smallData ) ) 174s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 174s 1 108 2.2 102 114 117 2.23 174s supply.lwr supply.upr 174s 1 110 124 174s > print( predict( fitwls5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 174s + newdata = smallData ) ) 174s fit se.pred lwr upr 174s 1 108 2.93 104 113 174s > 174s > print( predict( fitwlsi3e, se.fit = TRUE, se.pred = TRUE, 174s + interval = "prediction", level = 0.5, newdata = smallData ) ) 174s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 174s 1 109 2.23 2.95 107 111 116 174s supply.se.fit supply.se.pred supply.lwr supply.upr 174s 1 3.04 3.9 114 119 174s > print( predict( fitwlsi3e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 174s + interval = "confidence", level = 0.25, newdata = smallData ) ) 174s fit se.fit se.pred lwr upr 174s 1 109 2.23 2.95 108 109 174s > 174s > 174s > ## ************ correlation of predicted values *************** 174s > print( correlation.systemfit( fitwls1, 2, 1 ) ) 174s [,1] 174s [1,] 0 174s [2,] 0 174s [3,] 0 174s [4,] 0 174s [5,] 0 174s [6,] 0 174s [7,] 0 174s [8,] 0 174s [9,] 0 174s [10,] 0 174s [11,] 0 174s [12,] 0 174s [13,] 0 174s [14,] 0 174s [15,] 0 174s [16,] 0 174s [17,] 0 174s [18,] 0 174s [19,] 0 174s [20,] 0 174s > 174s > print( correlation.systemfit( fitwls2e, 1, 2 ) ) 175s [,1] 175s [1,] 0.411525 175s [2,] 0.147624 175s [3,] 0.147711 175s [4,] 0.107654 175s [5,] -0.069284 175s [6,] -0.053039 175s [7,] -0.051551 175s [8,] -0.006153 175s [9,] -0.000333 175s [10,] -0.001262 175s [11,] 0.048574 175s [12,] 0.064996 175s [13,] 0.024618 175s [14,] -0.028485 175s [15,] 0.174980 175s [16,] 0.252722 175s [17,] 0.103392 175s [18,] 0.074219 175s [19,] 0.156545 175s [20,] 0.135438 175s > 175s > print( correlation.systemfit( fitwls3, 2, 1 ) ) 175s [,1] 175s [1,] 0.405901 175s [2,] 0.145364 175s [3,] 0.145375 175s [4,] 0.105835 175s [5,] -0.067958 175s [6,] -0.052026 175s [7,] -0.050543 175s [8,] -0.006031 175s [9,] -0.000326 175s [10,] -0.001237 175s [11,] 0.047534 175s [12,] 0.063493 175s [13,] 0.024060 175s [14,] -0.027910 175s [15,] 0.171580 175s [16,] 0.248212 175s [17,] 0.101409 175s [18,] 0.073084 175s [19,] 0.153950 175s [20,] 0.132944 175s > 175s > print( correlation.systemfit( fitwls4e, 1, 2 ) ) 175s [,1] 175s [1,] 0.38162 175s [2,] 0.29173 175s [3,] 0.25421 175s [4,] 0.28598 175s [5,] -0.02775 175s [6,] -0.04974 175s [7,] -0.05850 175s [8,] 0.09388 175s [9,] 0.09469 175s [10,] 0.43814 175s [11,] 0.10559 175s [12,] 0.00876 175s [13,] 0.04090 175s [14,] -0.03984 175s [15,] 0.40767 175s [16,] 0.24571 175s [17,] 0.64160 175s [18,] 0.24037 175s [19,] 0.34075 175s [20,] 0.54270 175s > 175s > print( correlation.systemfit( fitwls5, 2, 1 ) ) 175s [,1] 175s [1,] 0.3775 175s [2,] 0.2936 175s [3,] 0.2553 175s [4,] 0.2875 175s [5,] -0.0274 175s [6,] -0.0492 175s [7,] -0.0578 175s [8,] 0.0932 175s [9,] 0.0944 175s [10,] 0.4375 175s [11,] 0.1027 175s [12,] 0.0072 175s [13,] 0.0404 175s [14,] -0.0396 175s [15,] 0.4062 175s [16,] 0.2430 175s [17,] 0.6406 175s [18,] 0.2362 175s [19,] 0.3347 175s [20,] 0.5378 175s > 175s > print( correlation.systemfit( fitwlsi1e, 1, 2 ) ) 175s [,1] 175s [1,] 0 175s [2,] 0 175s [3,] 0 175s [4,] 0 175s [5,] 0 175s [6,] 0 175s [7,] 0 175s [8,] 0 175s [9,] 0 175s [10,] 0 175s [11,] 0 175s [12,] 0 175s [13,] 0 175s [14,] 0 175s [15,] 0 175s [16,] 0 175s [17,] 0 175s [18,] 0 175s [19,] 0 175s [20,] 0 175s > 175s > print( correlation.systemfit( fitwlsi2, 2, 1 ) ) 175s [,1] 175s [1,] 0.404696 175s [2,] 0.144881 175s [3,] 0.144877 175s [4,] 0.105448 175s [5,] -0.067678 175s [6,] -0.051812 175s [7,] -0.050330 175s [8,] -0.006005 175s [9,] -0.000325 175s [10,] -0.001232 175s [11,] 0.047315 175s [12,] 0.063179 175s [13,] 0.023943 175s [14,] -0.027789 175s [15,] 0.170862 175s [16,] 0.247256 175s [17,] 0.100990 175s [18,] 0.072842 175s [19,] 0.153398 175s [20,] 0.132415 175s > 175s > print( correlation.systemfit( fitwlsi3e, 1, 2 ) ) 175s [,1] 175s [1,] 0.410485 175s [2,] 0.147206 175s [3,] 0.147278 175s [4,] 0.107316 175s [5,] -0.069036 175s [6,] -0.052850 175s [7,] -0.051363 175s [8,] -0.006130 175s [9,] -0.000331 175s [10,] -0.001257 175s [11,] 0.048379 175s [12,] 0.064714 175s [13,] 0.024513 175s [14,] -0.028377 175s [15,] 0.174345 175s [16,] 0.251882 175s [17,] 0.103022 175s [18,] 0.074009 175s [19,] 0.156063 175s [20,] 0.134974 175s > 175s > print( correlation.systemfit( fitwlsi4, 2, 1 ) ) 175s [,1] 175s [1,] 0.37672 175s [2,] 0.29387 175s [3,] 0.25544 175s [4,] 0.28775 175s [5,] -0.02729 175s [6,] -0.04911 175s [7,] -0.05771 175s [8,] 0.09311 175s [9,] 0.09437 175s [10,] 0.43736 175s [11,] 0.10223 175s [12,] 0.00693 175s [13,] 0.04035 175s [14,] -0.03961 175s [15,] 0.40591 175s [16,] 0.24248 175s [17,] 0.64034 175s [18,] 0.23551 175s [19,] 0.33360 175s [20,] 0.53687 175s > 175s > print( correlation.systemfit( fitwlsi5e, 1, 2 ) ) 175s [,1] 175s [1,] 0.38098 175s [2,] 0.29204 175s [3,] 0.25439 175s [4,] 0.28624 175s [5,] -0.02769 175s [6,] -0.04966 175s [7,] -0.05840 175s [8,] 0.09378 175s [9,] 0.09465 175s [10,] 0.43805 175s [11,] 0.10513 175s [12,] 0.00851 175s [13,] 0.04083 175s [14,] -0.03981 175s [15,] 0.40746 175s [16,] 0.24528 175s [17,] 0.64146 175s [18,] 0.23972 175s [19,] 0.33979 175s [20,] 0.54192 175s > 175s > 175s > ## ************ Log-Likelihood values *************** 175s > print( logLik( fitwls1 ) ) 175s 'log Lik.' -67.8 (df=9) 175s > print( logLik( fitwls1, residCovDiag = TRUE ) ) 175s 'log Lik.' -83.6 (df=9) 175s > all.equal( logLik( fitwls1, residCovDiag = TRUE ), 175s + logLik( lmDemand ) + logLik( lmSupply ), 175s + check.attributes = FALSE ) 175s [1] TRUE 175s > 175s > print( logLik( fitwls2e ) ) 175s 'log Lik.' -61.5 (df=8) 175s > print( logLik( fitwls2e, residCovDiag = TRUE ) ) 175s 'log Lik.' -84 (df=8) 175s > 175s > print( logLik( fitwls3 ) ) 175s 'log Lik.' -61.4 (df=8) 175s > print( logLik( fitwls3, residCovDiag = TRUE ) ) 175s 'log Lik.' -84 (df=8) 175s > 175s > print( logLik( fitwls4e ) ) 175s 'log Lik.' -62.2 (df=7) 175s > print( logLik( fitwls4e, residCovDiag = TRUE ) ) 175s 'log Lik.' -84 (df=7) 175s > 175s > print( logLik( fitwls5 ) ) 175s 'log Lik.' -62.1 (df=7) 175s > print( logLik( fitwls5, residCovDiag = TRUE ) ) 175s 'log Lik.' -84 (df=7) 175s > 175s > print( logLik( fitwlsi1e ) ) 175s 'log Lik.' -67.8 (df=9) 175s > print( logLik( fitwlsi1e, residCovDiag = TRUE ) ) 175s 'log Lik.' -83.6 (df=9) 175s > 175s > print( logLik( fitwlsi2 ) ) 175s 'log Lik.' -61.4 (df=8) 175s > print( logLik( fitwlsi2, residCovDiag = TRUE ) ) 175s 'log Lik.' -84 (df=8) 175s > 175s > print( logLik( fitwlsi3e ) ) 175s 'log Lik.' -61.5 (df=8) 175s > print( logLik( fitwlsi3e, residCovDiag = TRUE ) ) 175s 'log Lik.' -84 (df=8) 175s > 175s > print( logLik( fitwlsi4 ) ) 175s 'log Lik.' -62.1 (df=7) 175s > print( logLik( fitwlsi4, residCovDiag = TRUE ) ) 175s 'log Lik.' -84 (df=7) 175s > 175s > print( logLik( fitwlsi5e ) ) 175s 'log Lik.' -62.2 (df=7) 175s > print( logLik( fitwlsi5e, residCovDiag = TRUE ) ) 175s 'log Lik.' -84 (df=7) 175s > 175s > 175s > ## ************** F tests **************** 175s > # testing first restriction 175s > print( linearHypothesis( fitwls1, restrm ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s 175s Model 1: restricted model 175s Model 2: fitwls1 175s 175s Res.Df Df F Pr(>F) 175s 1 34 175s 2 33 1 0.64 0.43 175s > linearHypothesis( fitwls1, restrict ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s 175s Model 1: restricted model 175s Model 2: fitwls1 175s 175s Res.Df Df F Pr(>F) 175s 1 34 175s 2 33 1 0.64 0.43 175s > 175s > print( linearHypothesis( fitwlsi1e, restrm ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1e 175s 175s Res.Df Df F Pr(>F) 175s 1 34 175s 2 33 1 0.66 0.42 175s > linearHypothesis( fitwlsi1e, restrict ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1e 175s 175s Res.Df Df F Pr(>F) 175s 1 34 175s 2 33 1 0.66 0.42 175s > 175s > # testing second restriction 175s > restrOnly2m <- matrix(0,1,7) 175s > restrOnly2q <- 0.5 175s > restrOnly2m[1,2] <- -1 175s > restrOnly2m[1,5] <- 1 175s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 175s > # first restriction not imposed 175s > print( linearHypothesis( fitwls1e, restrOnly2m, restrOnly2q ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls1e 175s 175s Res.Df Df F Pr(>F) 175s 1 34 175s 2 33 1 0.03 0.86 175s > linearHypothesis( fitwls1e, restrictOnly2 ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls1e 175s 175s Res.Df Df F Pr(>F) 175s 1 34 175s 2 33 1 0.03 0.86 175s > 175s > print( linearHypothesis( fitwlsi1, restrOnly2m, restrOnly2q ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1 175s 175s Res.Df Df F Pr(>F) 175s 1 34 175s 2 33 1 0.03 0.86 175s > linearHypothesis( fitwlsi1, restrictOnly2 ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1 175s 175s Res.Df Df F Pr(>F) 175s 1 34 175s 2 33 1 0.03 0.86 175s > 175s > # first restriction imposed 175s > print( linearHypothesis( fitwls2, restrOnly2m, restrOnly2q ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls2 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 34 1 0.08 0.78 175s > linearHypothesis( fitwls2, restrictOnly2 ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls2 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 34 1 0.08 0.78 175s > 175s > print( linearHypothesis( fitwls3, restrOnly2m, restrOnly2q ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls3 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 34 1 0.08 0.78 175s > linearHypothesis( fitwls3, restrictOnly2 ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls3 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 34 1 0.08 0.78 175s > 175s > print( linearHypothesis( fitwlsi2e, restrOnly2m, restrOnly2q ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi2e 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 34 1 0.08 0.77 175s > linearHypothesis( fitwlsi2e, restrictOnly2 ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi2e 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 34 1 0.08 0.77 175s > 175s > print( linearHypothesis( fitwlsi3e, restrOnly2m, restrOnly2q ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi3e 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 34 1 0.08 0.77 175s > linearHypothesis( fitwlsi3e, restrictOnly2 ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi3e 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 34 1 0.08 0.77 175s > 175s > # testing both of the restrictions 175s > print( linearHypothesis( fitwls1e, restr2m, restr2q ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls1e 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 33 2 0.37 0.69 175s > linearHypothesis( fitwls1e, restrict2 ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls1e 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 33 2 0.37 0.69 175s > 175s > print( linearHypothesis( fitwlsi1, restr2m, restr2q ) ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 33 2 0.36 0.7 175s > linearHypothesis( fitwlsi1, restrict2 ) 175s Linear hypothesis test (Theil's F test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1 175s 175s Res.Df Df F Pr(>F) 175s 1 35 175s 2 33 2 0.36 0.7 175s > 175s > 175s > ## ************** Wald tests **************** 175s > # testing first restriction 175s > print( linearHypothesis( fitwls1, restrm, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s 175s Model 1: restricted model 175s Model 2: fitwls1 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 34 175s 2 33 1 0.64 0.42 175s > linearHypothesis( fitwls1, restrict, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s 175s Model 1: restricted model 175s Model 2: fitwls1 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 34 175s 2 33 1 0.64 0.42 175s > 175s > print( linearHypothesis( fitwlsi1e, restrm, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 34 175s 2 33 1 0.8 0.37 175s > linearHypothesis( fitwlsi1e, restrict, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 34 175s 2 33 1 0.8 0.37 175s > 175s > # testing second restriction 175s > # first restriction not imposed 175s > print( linearHypothesis( fitwls1e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls1e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 34 175s 2 33 1 0.04 0.84 175s > linearHypothesis( fitwls1e, restrictOnly2, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls1e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 34 175s 2 33 1 0.04 0.84 175s > 175s > print( linearHypothesis( fitwlsi1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 34 175s 2 33 1 0.03 0.86 175s > linearHypothesis( fitwlsi1, restrictOnly2, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 34 175s 2 33 1 0.03 0.86 175s > 175s > # first restriction imposed 175s > print( linearHypothesis( fitwls2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls2 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 34 1 0.08 0.78 175s > linearHypothesis( fitwls2, restrictOnly2, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls2 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 34 1 0.08 0.78 175s > 175s > print( linearHypothesis( fitwls3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls3 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 34 1 0.08 0.78 175s > linearHypothesis( fitwls3, restrictOnly2, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls3 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 34 1 0.08 0.78 175s > 175s > print( linearHypothesis( fitwlsi2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi2e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 34 1 0.1 0.75 175s > linearHypothesis( fitwlsi2e, restrictOnly2, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi2e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 34 1 0.1 0.75 175s > 175s > print( linearHypothesis( fitwlsi3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi3e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 34 1 0.1 0.75 175s > linearHypothesis( fitwlsi3e, restrictOnly2, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi3e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 34 1 0.1 0.75 175s > 175s > # testing both of the restrictions 175s > print( linearHypothesis( fitwls1e, restr2m, restr2q, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls1e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 33 2 0.9 0.64 175s > linearHypothesis( fitwls1e, restrict2, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwls1e 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 33 2 0.9 0.64 175s > 175s > print( linearHypothesis( fitwlsi1, restr2m, restr2q, test = "Chisq" ) ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 33 2 0.72 0.7 175s > linearHypothesis( fitwlsi1, restrict2, test = "Chisq" ) 175s Linear hypothesis test (Chi^2 statistic of a Wald test) 175s 175s Hypothesis: 175s demand_income - supply_trend = 0 175s - demand_price + supply_price = 0.5 175s 175s Model 1: restricted model 175s Model 2: fitwlsi1 175s 175s Res.Df Df Chisq Pr(>Chisq) 175s 1 35 175s 2 33 2 0.72 0.7 175s > 175s > 175s > ## ****************** model frame ************************** 175s > print( mf <- model.frame( fitwls1 ) ) 175s consump price income farmPrice trend 175s 1 98.5 100.3 87.4 98.0 1 175s 2 99.2 104.3 97.6 99.1 2 175s 3 102.2 103.4 96.7 99.1 3 175s 4 101.5 104.5 98.2 98.1 4 175s 5 104.2 98.0 99.8 110.8 5 175s 6 103.2 99.5 100.5 108.2 6 175s 7 104.0 101.1 103.2 105.6 7 175s 8 99.9 104.8 107.8 109.8 8 175s 9 100.3 96.4 96.6 108.7 9 175s 10 102.8 91.2 88.9 100.6 10 175s 11 95.4 93.1 75.1 81.0 11 175s 12 92.4 98.8 76.9 68.6 12 175s 13 94.5 102.9 84.6 70.9 13 175s 14 98.8 98.8 90.6 81.4 14 175s 15 105.8 95.1 103.1 102.3 15 175s 16 100.2 98.5 105.1 105.0 16 175s 17 103.5 86.5 96.4 110.5 17 175s 18 99.9 104.0 104.4 92.5 18 175s 19 105.2 105.8 110.7 89.3 19 175s 20 106.2 113.5 127.1 93.0 20 175s > print( mf1 <- model.frame( fitwls1$eq[[ 1 ]] ) ) 175s consump price income 175s 1 98.5 100.3 87.4 175s 2 99.2 104.3 97.6 175s 3 102.2 103.4 96.7 175s 4 101.5 104.5 98.2 175s 5 104.2 98.0 99.8 175s 6 103.2 99.5 100.5 175s 7 104.0 101.1 103.2 175s 8 99.9 104.8 107.8 175s 9 100.3 96.4 96.6 175s 10 102.8 91.2 88.9 175s 11 95.4 93.1 75.1 175s 12 92.4 98.8 76.9 175s 13 94.5 102.9 84.6 175s 14 98.8 98.8 90.6 175s 15 105.8 95.1 103.1 175s 16 100.2 98.5 105.1 175s 17 103.5 86.5 96.4 175s 18 99.9 104.0 104.4 175s 19 105.2 105.8 110.7 175s 20 106.2 113.5 127.1 175s > print( attributes( mf1 )$terms ) 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s > print( mf2 <- model.frame( fitwls1$eq[[ 2 ]] ) ) 175s consump price farmPrice trend 175s 1 98.5 100.3 98.0 1 175s 2 99.2 104.3 99.1 2 175s 3 102.2 103.4 99.1 3 175s 4 101.5 104.5 98.1 4 175s 5 104.2 98.0 110.8 5 175s 6 103.2 99.5 108.2 6 175s 7 104.0 101.1 105.6 7 175s 8 99.9 104.8 109.8 8 175s 9 100.3 96.4 108.7 9 175s 10 102.8 91.2 100.6 10 175s 11 95.4 93.1 81.0 11 175s 12 92.4 98.8 68.6 12 175s 13 94.5 102.9 70.9 13 175s 14 98.8 98.8 81.4 14 175s 15 105.8 95.1 102.3 15 175s 16 100.2 98.5 105.0 16 175s 17 103.5 86.5 110.5 17 175s 18 99.9 104.0 92.5 18 175s 19 105.2 105.8 89.3 19 175s 20 106.2 113.5 93.0 20 175s > print( attributes( mf2 )$terms ) 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s > 175s > print( all.equal( mf, model.frame( fitwls2e ) ) ) 175s [1] TRUE 175s > print( all.equal( mf1, model.frame( fitwls2e$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > 175s > print( all.equal( mf, model.frame( fitwls3 ) ) ) 175s [1] TRUE 175s > print( all.equal( mf2, model.frame( fitwls3$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > 175s > print( all.equal( mf, model.frame( fitwls4e ) ) ) 175s [1] TRUE 175s > print( all.equal( mf1, model.frame( fitwls4e$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > 175s > print( all.equal( mf, model.frame( fitwls5 ) ) ) 175s [1] TRUE 175s > print( all.equal( mf2, model.frame( fitwls5$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > 175s > print( all.equal( mf, model.frame( fitwlsi1e ) ) ) 175s [1] TRUE 175s > print( all.equal( mf1, model.frame( fitwlsi1e$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > 175s > print( all.equal( mf, model.frame( fitwlsi2 ) ) ) 175s [1] TRUE 175s > print( all.equal( mf2, model.frame( fitwlsi2$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > 175s > print( all.equal( mf, model.frame( fitwlsi3e ) ) ) 175s [1] TRUE 175s > print( all.equal( mf1, model.frame( fitwlsi3e$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > 175s > print( all.equal( mf, model.frame( fitwlsi4 ) ) ) 175s [1] TRUE 175s > print( all.equal( mf2, model.frame( fitwlsi4$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > 175s > print( all.equal( mf, model.frame( fitwlsi5e ) ) ) 175s [1] TRUE 175s > print( all.equal( mf1, model.frame( fitwlsi5e$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > 175s > 175s > ## **************** model matrix ************************ 175s > # with x (returnModelMatrix) = TRUE 175s > print( !is.null( fitwls1e$eq[[ 1 ]]$x ) ) 175s [1] TRUE 175s > print( mm <- model.matrix( fitwlsi1e ) ) 175s demand_(Intercept) demand_price demand_income supply_(Intercept) 175s demand_1 1 100.3 87.4 0 175s demand_2 1 104.3 97.6 0 175s demand_3 1 103.4 96.7 0 175s demand_4 1 104.5 98.2 0 175s demand_5 1 98.0 99.8 0 175s demand_6 1 99.5 100.5 0 175s demand_7 1 101.1 103.2 0 175s demand_8 1 104.8 107.8 0 175s demand_9 1 96.4 96.6 0 175s demand_10 1 91.2 88.9 0 175s demand_11 1 93.1 75.1 0 175s demand_12 1 98.8 76.9 0 175s demand_13 1 102.9 84.6 0 175s demand_14 1 98.8 90.6 0 175s demand_15 1 95.1 103.1 0 175s demand_16 1 98.5 105.1 0 175s demand_17 1 86.5 96.4 0 175s demand_18 1 104.0 104.4 0 175s demand_19 1 105.8 110.7 0 175s demand_20 1 113.5 127.1 0 175s supply_1 0 0.0 0.0 1 175s supply_2 0 0.0 0.0 1 175s supply_3 0 0.0 0.0 1 175s supply_4 0 0.0 0.0 1 175s supply_5 0 0.0 0.0 1 175s supply_6 0 0.0 0.0 1 175s supply_7 0 0.0 0.0 1 175s supply_8 0 0.0 0.0 1 175s supply_9 0 0.0 0.0 1 175s supply_10 0 0.0 0.0 1 175s supply_11 0 0.0 0.0 1 175s supply_12 0 0.0 0.0 1 175s supply_13 0 0.0 0.0 1 175s supply_14 0 0.0 0.0 1 175s supply_15 0 0.0 0.0 1 175s supply_16 0 0.0 0.0 1 175s supply_17 0 0.0 0.0 1 175s supply_18 0 0.0 0.0 1 175s supply_19 0 0.0 0.0 1 175s supply_20 0 0.0 0.0 1 175s supply_price supply_farmPrice supply_trend 175s demand_1 0.0 0.0 0 175s demand_2 0.0 0.0 0 175s demand_3 0.0 0.0 0 175s demand_4 0.0 0.0 0 175s demand_5 0.0 0.0 0 175s demand_6 0.0 0.0 0 175s demand_7 0.0 0.0 0 175s demand_8 0.0 0.0 0 175s demand_9 0.0 0.0 0 175s demand_10 0.0 0.0 0 175s demand_11 0.0 0.0 0 175s demand_12 0.0 0.0 0 175s demand_13 0.0 0.0 0 175s demand_14 0.0 0.0 0 175s demand_15 0.0 0.0 0 175s demand_16 0.0 0.0 0 175s demand_17 0.0 0.0 0 175s demand_18 0.0 0.0 0 175s demand_19 0.0 0.0 0 175s demand_20 0.0 0.0 0 175s supply_1 100.3 98.0 1 175s supply_2 104.3 99.1 2 175s supply_3 103.4 99.1 3 175s supply_4 104.5 98.1 4 175s supply_5 98.0 110.8 5 175s supply_6 99.5 108.2 6 175s supply_7 101.1 105.6 7 175s supply_8 104.8 109.8 8 175s supply_9 96.4 108.7 9 175s supply_10 91.2 100.6 10 175s supply_11 93.1 81.0 11 175s supply_12 98.8 68.6 12 175s supply_13 102.9 70.9 13 175s supply_14 98.8 81.4 14 175s supply_15 95.1 102.3 15 175s supply_16 98.5 105.0 16 175s supply_17 86.5 110.5 17 175s supply_18 104.0 92.5 18 175s supply_19 105.8 89.3 19 175s supply_20 113.5 93.0 20 175s > print( mm1 <- model.matrix( fitwlsi1e$eq[[ 1 ]] ) ) 175s (Intercept) price income 175s 1 1 100.3 87.4 175s 2 1 104.3 97.6 175s 3 1 103.4 96.7 175s 4 1 104.5 98.2 175s 5 1 98.0 99.8 175s 6 1 99.5 100.5 175s 7 1 101.1 103.2 175s 8 1 104.8 107.8 175s 9 1 96.4 96.6 175s 10 1 91.2 88.9 175s 11 1 93.1 75.1 175s 12 1 98.8 76.9 175s 13 1 102.9 84.6 175s 14 1 98.8 90.6 175s 15 1 95.1 103.1 175s 16 1 98.5 105.1 175s 17 1 86.5 96.4 175s 18 1 104.0 104.4 175s 19 1 105.8 110.7 175s 20 1 113.5 127.1 175s attr(,"assign") 175s [1] 0 1 2 175s > print( mm2 <- model.matrix( fitwlsi1e$eq[[ 2 ]] ) ) 175s (Intercept) price farmPrice trend 175s 1 1 100.3 98.0 1 175s 2 1 104.3 99.1 2 175s 3 1 103.4 99.1 3 175s 4 1 104.5 98.1 4 175s 5 1 98.0 110.8 5 175s 6 1 99.5 108.2 6 175s 7 1 101.1 105.6 7 175s 8 1 104.8 109.8 8 175s 9 1 96.4 108.7 9 175s 10 1 91.2 100.6 10 175s 11 1 93.1 81.0 11 175s 12 1 98.8 68.6 12 175s 13 1 102.9 70.9 13 175s 14 1 98.8 81.4 14 175s 15 1 95.1 102.3 15 175s 16 1 98.5 105.0 16 175s 17 1 86.5 110.5 17 175s 18 1 104.0 92.5 18 175s 19 1 105.8 89.3 19 175s 20 1 113.5 93.0 20 175s attr(,"assign") 175s [1] 0 1 2 3 175s > 175s > # with x (returnModelMatrix) = FALSE 175s > print( all.equal( mm, model.matrix( fitwlsi1 ) ) ) 175s [1] TRUE 175s > print( all.equal( mm1, model.matrix( fitwlsi1$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > print( all.equal( mm2, model.matrix( fitwlsi1$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > print( !is.null( fitwls1$eq[[ 1 ]]$x ) ) 175s [1] FALSE 175s > 175s > # with x (returnModelMatrix) = TRUE 175s > print( !is.null( fitwls2$eq[[ 1 ]]$x ) ) 175s [1] TRUE 175s > print( all.equal( mm, model.matrix( fitwls2 ) ) ) 175s [1] TRUE 175s > print( all.equal( mm1, model.matrix( fitwls2$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > print( all.equal( mm2, model.matrix( fitwls2$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > 175s > # with x (returnModelMatrix) = FALSE 175s > print( all.equal( mm, model.matrix( fitwls2e ) ) ) 175s [1] TRUE 175s > print( all.equal( mm1, model.matrix( fitwls2e$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > print( all.equal( mm2, model.matrix( fitwls2e$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > print( !is.null( fitwls2e$eq[[ 1 ]]$x ) ) 175s [1] FALSE 175s > 175s > # with x (returnModelMatrix) = TRUE 175s > print( !is.null( fitwlsi3$eq[[ 1 ]]$x ) ) 175s [1] TRUE 175s > print( all.equal( mm, model.matrix( fitwlsi3 ) ) ) 175s [1] TRUE 175s > print( all.equal( mm1, model.matrix( fitwlsi3$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > print( all.equal( mm2, model.matrix( fitwlsi3$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > 175s > # with x (returnModelMatrix) = FALSE 175s > print( all.equal( mm, model.matrix( fitwlsi3e ) ) ) 175s [1] TRUE 175s > print( all.equal( mm1, model.matrix( fitwlsi3e$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > print( all.equal( mm2, model.matrix( fitwlsi3e$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > print( !is.null( fitwlsi3e$eq[[ 1 ]]$x ) ) 175s [1] FALSE 175s > 175s > # with x (returnModelMatrix) = TRUE 175s > print( !is.null( fitwls4e$eq[[ 1 ]]$x ) ) 175s [1] TRUE 175s > print( all.equal( mm, model.matrix( fitwls4e ) ) ) 175s [1] TRUE 175s > print( all.equal( mm1, model.matrix( fitwls4e$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > print( all.equal( mm2, model.matrix( fitwls4e$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > 175s > # with x (returnModelMatrix) = FALSE 175s > print( all.equal( mm, model.matrix( fitwls4Sym ) ) ) 175s [1] TRUE 175s > print( all.equal( mm1, model.matrix( fitwls4Sym$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > print( all.equal( mm2, model.matrix( fitwls4Sym$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > print( !is.null( fitwls4Sym$eq[[ 1 ]]$x ) ) 175s [1] FALSE 175s > 175s > # with x (returnModelMatrix) = TRUE 175s > print( !is.null( fitwls5$eq[[ 1 ]]$x ) ) 175s [1] TRUE 175s > print( all.equal( mm, model.matrix( fitwls5 ) ) ) 175s [1] TRUE 175s > print( all.equal( mm1, model.matrix( fitwls5$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > print( all.equal( mm2, model.matrix( fitwls5$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > 175s > # with x (returnModelMatrix) = FALSE 175s > print( all.equal( mm, model.matrix( fitwls5e ) ) ) 175s [1] TRUE 175s > print( all.equal( mm1, model.matrix( fitwls5e$eq[[ 1 ]] ) ) ) 175s [1] TRUE 175s > print( all.equal( mm2, model.matrix( fitwls5e$eq[[ 2 ]] ) ) ) 175s [1] TRUE 175s > print( !is.null( fitwls5e$eq[[ 1 ]]$x ) ) 175s [1] FALSE 175s > 175s > 175s > ## **************** formulas ************************ 175s > formula( fitwls1 ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwls1$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s > 175s > formula( fitwls2e ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwls2e$eq[[ 1 ]] ) 175s consump ~ price + income 175s > 175s > formula( fitwls3 ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwls3$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s > 175s > formula( fitwls4e ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwls4e$eq[[ 1 ]] ) 175s consump ~ price + income 175s > 175s > formula( fitwls5 ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwls5$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s > 175s > formula( fitwlsi1e ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwlsi1e$eq[[ 1 ]] ) 175s consump ~ price + income 175s > 175s > formula( fitwlsi2 ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwlsi2$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s > 175s > formula( fitwlsi3e ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwlsi3e$eq[[ 1 ]] ) 175s consump ~ price + income 175s > 175s > formula( fitwlsi4 ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwlsi4$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s > 175s > formula( fitwlsi5e ) 175s $demand 175s consump ~ price + income 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s 175s > formula( fitwlsi5e$eq[[ 1 ]] ) 175s consump ~ price + income 175s > 175s > 175s > ## **************** model terms ******************* 175s > terms( fitwls1 ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwls1$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s > 175s > terms( fitwls2e ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwls2e$eq[[ 1 ]] ) 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s > 175s > terms( fitwls3 ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwls3$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s > 175s > terms( fitwls4e ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwls4e$eq[[ 1 ]] ) 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s > 175s > terms( fitwls5 ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwls5$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s > 175s > terms( fitwlsi1e ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwlsi1e$eq[[ 1 ]] ) 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s > 175s > terms( fitwlsi2 ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwlsi2$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s > 175s > terms( fitwlsi3e ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwlsi3e$eq[[ 1 ]] ) 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s > 175s > terms( fitwlsi4 ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwlsi4$eq[[ 2 ]] ) 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s > 175s > terms( fitwlsi5e ) 175s $demand 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s 175s $supply 175s consump ~ price + farmPrice + trend 175s attr(,"variables") 175s list(consump, price, farmPrice, trend) 175s attr(,"factors") 175s price farmPrice trend 175s consump 0 0 0 175s price 1 0 0 175s farmPrice 0 1 0 175s trend 0 0 1 175s attr(,"term.labels") 175s [1] "price" "farmPrice" "trend" 175s attr(,"order") 175s [1] 1 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, farmPrice, trend) 175s attr(,"dataClasses") 175s consump price farmPrice trend 175s "numeric" "numeric" "numeric" "numeric" 175s 175s > terms( fitwlsi5e$eq[[ 1 ]] ) 175s consump ~ price + income 175s attr(,"variables") 175s list(consump, price, income) 175s attr(,"factors") 175s price income 175s consump 0 0 175s price 1 0 175s income 0 1 175s attr(,"term.labels") 175s [1] "price" "income" 175s attr(,"order") 175s [1] 1 1 175s attr(,"intercept") 175s [1] 1 175s attr(,"response") 175s [1] 1 175s attr(,".Environment") 175s 175s attr(,"predvars") 175s list(consump, price, income) 175s attr(,"dataClasses") 175s consump price income 175s "numeric" "numeric" "numeric" 175s > 175s > 175s > ## **************** estfun ************************ 175s > library( "sandwich" ) 175s > 175s > estfun( fitwls1 ) 175s demand_(Intercept) demand_price demand_income supply_(Intercept) 175s demand_1 0.2884 28.93 25.21 0.0000 175s demand_2 -0.1048 -10.92 -10.22 0.0000 175s demand_3 0.7045 72.87 68.13 0.0000 175s demand_4 0.4838 50.56 47.51 0.0000 175s demand_5 0.5222 51.18 52.12 0.0000 175s demand_6 0.3153 31.36 31.68 0.0000 175s demand_7 0.4108 41.51 42.39 0.0000 175s demand_8 -0.7872 -82.47 -84.86 0.0000 175s demand_9 -0.3665 -35.35 -35.41 0.0000 175s demand_10 0.5451 49.73 48.46 0.0000 175s demand_11 -0.0400 -3.72 -3.00 0.0000 175s demand_12 -0.5246 -51.83 -40.34 0.0000 175s demand_13 -0.3009 -30.96 -25.45 0.0000 175s demand_14 -0.0591 -5.83 -5.35 0.0000 175s demand_15 0.3991 37.96 41.14 0.0000 175s demand_16 -0.9934 -97.80 -104.40 0.0000 175s demand_17 -0.3417 -29.56 -32.94 0.0000 175s demand_18 -0.5375 -55.90 -56.11 0.0000 175s demand_19 0.4665 49.34 51.65 0.0000 175s demand_20 -0.0802 -9.10 -10.20 0.0000 175s supply_1 0.0000 0.00 0.00 -0.0768 175s supply_2 0.0000 0.00 0.00 -0.1548 175s supply_3 0.0000 0.00 0.00 0.3397 175s supply_4 0.0000 0.00 0.00 0.1961 175s supply_5 0.0000 0.00 0.00 0.2617 175s supply_6 0.0000 0.00 0.00 0.1176 175s supply_7 0.0000 0.00 0.00 0.2712 175s supply_8 0.0000 0.00 0.00 -0.7619 175s supply_9 0.0000 0.00 0.00 -0.4493 175s supply_10 0.0000 0.00 0.00 0.4269 175s supply_11 0.0000 0.00 0.00 -0.1034 175s supply_12 0.0000 0.00 0.00 -0.2934 175s supply_13 0.0000 0.00 0.00 -0.1839 175s supply_14 0.0000 0.00 0.00 0.1677 175s supply_15 0.0000 0.00 0.00 0.5461 175s supply_16 0.0000 0.00 0.00 -0.6683 175s supply_17 0.0000 0.00 0.00 -0.0458 175s supply_18 0.0000 0.00 0.00 -0.4234 175s supply_19 0.0000 0.00 0.00 0.5376 175s supply_20 0.0000 0.00 0.00 0.2963 175s supply_price supply_farmPrice supply_trend 175s demand_1 0.00 0.00 0.0000 175s demand_2 0.00 0.00 0.0000 175s demand_3 0.00 0.00 0.0000 175s demand_4 0.00 0.00 0.0000 175s demand_5 0.00 0.00 0.0000 175s demand_6 0.00 0.00 0.0000 175s demand_7 0.00 0.00 0.0000 175s demand_8 0.00 0.00 0.0000 175s demand_9 0.00 0.00 0.0000 175s demand_10 0.00 0.00 0.0000 175s demand_11 0.00 0.00 0.0000 175s demand_12 0.00 0.00 0.0000 175s demand_13 0.00 0.00 0.0000 175s demand_14 0.00 0.00 0.0000 175s demand_15 0.00 0.00 0.0000 175s demand_16 0.00 0.00 0.0000 175s demand_17 0.00 0.00 0.0000 175s demand_18 0.00 0.00 0.0000 175s demand_19 0.00 0.00 0.0000 175s demand_20 0.00 0.00 0.0000 175s supply_1 -7.70 -7.53 -0.0768 175s supply_2 -16.14 -15.34 -0.3096 175s supply_3 35.14 33.67 1.0192 175s supply_4 20.49 19.24 0.7843 175s supply_5 25.65 29.00 1.3085 175s supply_6 11.70 12.73 0.7057 175s supply_7 27.41 28.64 1.8987 175s supply_8 -79.82 -83.66 -6.0955 175s supply_9 -43.33 -48.84 -4.0437 175s supply_10 38.95 42.95 4.2691 175s supply_11 -9.63 -8.38 -1.1377 175s supply_12 -28.99 -20.13 -3.5213 175s supply_13 -18.93 -13.04 -2.3913 175s supply_14 16.56 13.65 2.3480 175s supply_15 51.95 55.87 8.1920 175s supply_16 -65.79 -70.17 -10.6922 175s supply_17 -3.96 -5.06 -0.7779 175s supply_18 -44.04 -39.16 -7.6205 175s supply_19 56.86 48.01 10.2144 175s supply_20 33.63 27.56 5.9267 175s > round( colSums( estfun( fitwls1 ) ), digits = 7 ) 175s demand_(Intercept) demand_price demand_income supply_(Intercept) 175s 0 0 0 0 175s supply_price supply_farmPrice supply_trend 175s 0 0 0 175s > 175s > estfun( fitwlsi1e ) 175s demand_(Intercept) demand_price demand_income supply_(Intercept) 175s demand_1 0.3393 34.04 29.66 0.0000 175s demand_2 -0.1232 -12.85 -12.03 0.0000 175s demand_3 0.8289 85.73 80.15 0.0000 175s demand_4 0.5692 59.49 55.90 0.0000 175s demand_5 0.6144 60.21 61.32 0.0000 175s demand_6 0.3709 36.89 37.28 0.0000 175s demand_7 0.4832 48.84 49.87 0.0000 175s demand_8 -0.9261 -97.03 -99.84 0.0000 175s demand_9 -0.4312 -41.59 -41.66 0.0000 175s demand_10 0.6413 58.51 57.01 0.0000 175s demand_11 -0.0470 -4.38 -3.53 0.0000 175s demand_12 -0.6172 -60.98 -47.46 0.0000 175s demand_13 -0.3540 -36.43 -29.95 0.0000 175s demand_14 -0.0695 -6.86 -6.29 0.0000 175s demand_15 0.4695 44.66 48.40 0.0000 175s demand_16 -1.1687 -115.06 -122.83 0.0000 175s demand_17 -0.4020 -34.78 -38.76 0.0000 175s demand_18 -0.6323 -65.77 -66.01 0.0000 175s demand_19 0.5489 58.05 60.76 0.0000 175s demand_20 -0.0944 -10.71 -12.00 0.0000 175s supply_1 0.0000 0.00 0.00 -0.0960 175s supply_2 0.0000 0.00 0.00 -0.1935 175s supply_3 0.0000 0.00 0.00 0.4247 175s supply_4 0.0000 0.00 0.00 0.2451 175s supply_5 0.0000 0.00 0.00 0.3271 175s supply_6 0.0000 0.00 0.00 0.1470 175s supply_7 0.0000 0.00 0.00 0.3390 175s supply_8 0.0000 0.00 0.00 -0.9524 175s supply_9 0.0000 0.00 0.00 -0.5616 175s supply_10 0.0000 0.00 0.00 0.5336 175s supply_11 0.0000 0.00 0.00 -0.1293 175s supply_12 0.0000 0.00 0.00 -0.3668 175s supply_13 0.0000 0.00 0.00 -0.2299 175s supply_14 0.0000 0.00 0.00 0.2096 175s supply_15 0.0000 0.00 0.00 0.6827 175s supply_16 0.0000 0.00 0.00 -0.8353 175s supply_17 0.0000 0.00 0.00 -0.0572 175s supply_18 0.0000 0.00 0.00 -0.5292 175s supply_19 0.0000 0.00 0.00 0.6720 175s supply_20 0.0000 0.00 0.00 0.3704 175s supply_price supply_farmPrice supply_trend 175s demand_1 0.00 0.00 0.000 175s demand_2 0.00 0.00 0.000 175s demand_3 0.00 0.00 0.000 175s demand_4 0.00 0.00 0.000 175s demand_5 0.00 0.00 0.000 175s demand_6 0.00 0.00 0.000 175s demand_7 0.00 0.00 0.000 175s demand_8 0.00 0.00 0.000 175s demand_9 0.00 0.00 0.000 175s demand_10 0.00 0.00 0.000 175s demand_11 0.00 0.00 0.000 175s demand_12 0.00 0.00 0.000 175s demand_13 0.00 0.00 0.000 175s demand_14 0.00 0.00 0.000 175s demand_15 0.00 0.00 0.000 175s demand_16 0.00 0.00 0.000 175s demand_17 0.00 0.00 0.000 175s demand_18 0.00 0.00 0.000 175s demand_19 0.00 0.00 0.000 175s demand_20 0.00 0.00 0.000 175s supply_1 -9.63 -9.41 -0.096 175s supply_2 -20.18 -19.18 -0.387 175s supply_3 43.92 42.08 1.274 175s supply_4 25.61 24.04 0.980 175s supply_5 32.06 36.25 1.636 175s supply_6 14.62 15.91 0.882 175s supply_7 34.27 35.80 2.373 175s supply_8 -99.78 -104.58 -7.619 175s supply_9 -54.17 -61.05 -5.055 175s supply_10 48.68 53.68 5.336 175s supply_11 -12.03 -10.47 -1.422 175s supply_12 -36.24 -25.16 -4.402 175s supply_13 -23.66 -16.30 -2.989 175s supply_14 20.70 17.06 2.935 175s supply_15 64.93 69.84 10.240 175s supply_16 -82.24 -87.71 -13.365 175s supply_17 -4.95 -6.32 -0.972 175s supply_18 -55.05 -48.95 -9.526 175s supply_19 71.08 60.01 12.768 175s supply_20 42.04 34.45 7.408 175s > round( colSums( estfun( fitwlsi1e ) ), digits = 7 ) 175s demand_(Intercept) demand_price demand_income supply_(Intercept) 175s 0 0 0 0 175s supply_price supply_farmPrice supply_trend 175s 0 0 0 175s > 175s > 175s > ## **************** bread ************************ 175s > bread( fitwls1 ) 175s demand_(Intercept) demand_price demand_income supply_(Intercept) 175s [1,] 2261.63 -23.7921 1.2865 0.0 175s [2,] -23.79 0.3289 -0.0933 0.0 175s [3,] 1.29 -0.0933 0.0825 0.0 175s [4,] 0.00 0.0000 0.0000 5255.9 175s [5,] 0.00 0.0000 0.0000 -39.5 175s [6,] 0.00 0.0000 0.0000 -12.2 175s [7,] 0.00 0.0000 0.0000 -11.2 175s supply_price supply_farmPrice supply_trend 175s [1,] 0.0000 0.0000 0.0000 175s [2,] 0.0000 0.0000 0.0000 175s [3,] 0.0000 0.0000 0.0000 175s [4,] -39.5000 -12.1744 -11.1673 175s [5,] 0.3601 0.0338 0.0209 175s [6,] 0.0338 0.0853 0.0526 175s [7,] 0.0209 0.0526 0.3804 175s > 175s > bread( fitwlsi1e ) 175s demand_(Intercept) demand_price demand_income supply_(Intercept) 175s [1,] 1922.39 -20.2232 1.0935 0.00 175s [2,] -20.22 0.2796 -0.0793 0.00 175s [3,] 1.09 -0.0793 0.0701 0.00 175s [4,] 0.00 0.0000 0.0000 4204.75 175s [5,] 0.00 0.0000 0.0000 -31.60 175s [6,] 0.00 0.0000 0.0000 -9.74 175s [7,] 0.00 0.0000 0.0000 -8.93 175s supply_price supply_farmPrice supply_trend 175s [1,] 0.0000 0.0000 0.0000 175s [2,] 0.0000 0.0000 0.0000 175s [3,] 0.0000 0.0000 0.0000 175s [4,] -31.6000 -9.7395 -8.9339 175s [5,] 0.2881 0.0270 0.0167 175s [6,] 0.0270 0.0683 0.0421 175s [7,] 0.0167 0.0421 0.3043 175s > 175s autopkgtest [03:15:43]: test run-unit-test: -----------------------] 175s autopkgtest [03:15:43]: test run-unit-test: - - - - - - - - - - results - - - - - - - - - - 175s run-unit-test PASS 175s autopkgtest [03:15:43]: test pkg-r-autopkgtest: preparing testbed 176s Reading package lists... 176s Building dependency tree... 176s Reading state information... 176s Starting pkgProblemResolver with broken count: 0 177s Starting 2 pkgProblemResolver with broken count: 0 177s Done 177s The following additional packages will be installed: 177s build-essential cpp cpp-13 cpp-13-x86-64-linux-gnu cpp-x86-64-linux-gnu 177s dctrl-tools g++ g++-13 g++-13-x86-64-linux-gnu g++-x86-64-linux-gnu gcc 177s gcc-13 gcc-13-x86-64-linux-gnu gcc-x86-64-linux-gnu gfortran gfortran-13 177s gfortran-13-x86-64-linux-gnu gfortran-x86-64-linux-gnu icu-devtools libasan8 177s libatomic1 libblas-dev libbz2-dev libc-dev-bin libc6-dev libcc1-0 177s libcrypt-dev libgcc-13-dev libgfortran-13-dev libhwasan0 libicu-dev libisl23 177s libitm1 libjpeg-dev libjpeg-turbo8-dev libjpeg8-dev liblapack-dev liblsan0 177s liblzma-dev libmpc3 libncurses-dev libnsl-dev libpcre2-16-0 libpcre2-32-0 177s libpcre2-dev libpcre2-posix3 libpkgconf3 libpng-dev libquadmath0 177s libreadline-dev libstdc++-13-dev libtirpc-dev libtsan2 libubsan1 177s linux-libc-dev pkg-config pkg-r-autopkgtest pkgconf pkgconf-bin r-base-dev 177s r-cran-arm r-cran-coda r-cran-mi r-cran-sem rpcsvc-proto zlib1g-dev 177s Suggested packages: 177s cpp-doc gcc-13-locales cpp-13-doc debtags g++-multilib g++-13-multilib 177s gcc-13-doc gcc-multilib manpages-dev autoconf automake libtool flex bison 177s gdb gcc-doc gcc-13-multilib gdb-x86-64-linux-gnu gfortran-multilib 177s gfortran-doc gfortran-13-multilib gfortran-13-doc libcoarrays-dev 177s liblapack-doc glibc-doc icu-doc liblzma-doc ncurses-doc readline-doc 177s libstdc++-13-doc texlive-base texlive-latex-base texlive-plain-generic 177s texlive-fonts-recommended texlive-fonts-extra texlive-extra-utils 177s texlive-latex-recommended texlive-latex-extra texinfo r-cran-sn 177s r-cran-polycor 177s Recommended packages: 177s bzip2-doc manpages manpages-dev libc-devtools libpng-tools r-cran-truncnorm 177s The following NEW packages will be installed: 177s autopkgtest-satdep build-essential cpp cpp-13 cpp-13-x86-64-linux-gnu 177s cpp-x86-64-linux-gnu dctrl-tools g++ g++-13 g++-13-x86-64-linux-gnu 177s g++-x86-64-linux-gnu gcc gcc-13 gcc-13-x86-64-linux-gnu gcc-x86-64-linux-gnu 177s gfortran gfortran-13 gfortran-13-x86-64-linux-gnu gfortran-x86-64-linux-gnu 177s icu-devtools libasan8 libatomic1 libblas-dev libbz2-dev libc-dev-bin 177s libc6-dev libcc1-0 libcrypt-dev libgcc-13-dev libgfortran-13-dev libhwasan0 177s libicu-dev libisl23 libitm1 libjpeg-dev libjpeg-turbo8-dev libjpeg8-dev 177s liblapack-dev liblsan0 liblzma-dev libmpc3 libncurses-dev libnsl-dev 177s libpcre2-16-0 libpcre2-32-0 libpcre2-dev libpcre2-posix3 libpkgconf3 177s libpng-dev libquadmath0 libreadline-dev libstdc++-13-dev libtirpc-dev 177s libtsan2 libubsan1 linux-libc-dev pkg-config pkg-r-autopkgtest pkgconf 177s pkgconf-bin r-base-dev r-cran-arm r-cran-coda r-cran-mi r-cran-sem 177s rpcsvc-proto zlib1g-dev 177s 0 upgraded, 67 newly installed, 0 to remove and 0 not upgraded. 177s Need to get 103 MB/103 MB of archives. 177s After this operation, 379 MB of additional disk space will be used. 177s Get:1 /tmp/autopkgtest.tI0y9z/2-autopkgtest-satdep.deb autopkgtest-satdep amd64 0 [732 B] 177s Get:2 http://ftpmaster.internal/ubuntu noble/main amd64 libc-dev-bin amd64 2.39-0ubuntu2 [20.4 kB] 177s Get:3 http://ftpmaster.internal/ubuntu noble/main amd64 linux-libc-dev amd64 6.8.0-11.11 [1595 kB] 177s Get:4 http://ftpmaster.internal/ubuntu noble/main amd64 libcrypt-dev amd64 1:4.4.36-4 [128 kB] 177s Get:5 http://ftpmaster.internal/ubuntu noble/main amd64 libtirpc-dev amd64 1.3.4+ds-1build1 [222 kB] 177s Get:6 http://ftpmaster.internal/ubuntu noble/main amd64 libnsl-dev amd64 1.3.0-3 [71.2 kB] 177s Get:7 http://ftpmaster.internal/ubuntu noble/main amd64 rpcsvc-proto amd64 1.4.2-0ubuntu6 [68.5 kB] 177s Get:8 http://ftpmaster.internal/ubuntu noble/main amd64 libc6-dev amd64 2.39-0ubuntu2 [2126 kB] 177s Get:9 http://ftpmaster.internal/ubuntu noble/main amd64 libisl23 amd64 0.26-3 [741 kB] 177s Get:10 http://ftpmaster.internal/ubuntu noble/main amd64 libmpc3 amd64 1.3.1-1 [54.1 kB] 177s Get:11 http://ftpmaster.internal/ubuntu noble/main amd64 cpp-13-x86-64-linux-gnu amd64 13.2.0-17ubuntu2 [11.2 MB] 177s Get:12 http://ftpmaster.internal/ubuntu noble/main amd64 cpp-13 amd64 13.2.0-17ubuntu2 [1030 B] 177s Get:13 http://ftpmaster.internal/ubuntu noble/main amd64 cpp-x86-64-linux-gnu amd64 4:13.2.0-7ubuntu1 [5326 B] 177s Get:14 http://ftpmaster.internal/ubuntu noble/main amd64 cpp amd64 4:13.2.0-7ubuntu1 [22.4 kB] 177s Get:15 http://ftpmaster.internal/ubuntu noble/main amd64 libcc1-0 amd64 14-20240303-1ubuntu1 [47.7 kB] 177s Get:16 http://ftpmaster.internal/ubuntu noble/main amd64 libitm1 amd64 14-20240303-1ubuntu1 [29.1 kB] 177s Get:17 http://ftpmaster.internal/ubuntu noble/main amd64 libatomic1 amd64 14-20240303-1ubuntu1 [10.4 kB] 177s Get:18 http://ftpmaster.internal/ubuntu noble/main amd64 libasan8 amd64 14-20240303-1ubuntu1 [3026 kB] 177s Get:19 http://ftpmaster.internal/ubuntu noble/main amd64 liblsan0 amd64 14-20240303-1ubuntu1 [1310 kB] 177s Get:20 http://ftpmaster.internal/ubuntu noble/main amd64 libtsan2 amd64 14-20240303-1ubuntu1 [2732 kB] 177s Get:21 http://ftpmaster.internal/ubuntu noble/main amd64 libubsan1 amd64 14-20240303-1ubuntu1 [1172 kB] 177s Get:22 http://ftpmaster.internal/ubuntu noble/main amd64 libhwasan0 amd64 14-20240303-1ubuntu1 [1629 kB] 177s Get:23 http://ftpmaster.internal/ubuntu noble/main amd64 libquadmath0 amd64 14-20240303-1ubuntu1 [155 kB] 177s Get:24 http://ftpmaster.internal/ubuntu noble/main amd64 libgcc-13-dev amd64 13.2.0-17ubuntu2 [2687 kB] 177s Get:25 http://ftpmaster.internal/ubuntu noble/main amd64 gcc-13-x86-64-linux-gnu amd64 13.2.0-17ubuntu2 [21.9 MB] 177s Get:26 http://ftpmaster.internal/ubuntu noble/main amd64 gcc-13 amd64 13.2.0-17ubuntu2 [477 kB] 177s Get:27 http://ftpmaster.internal/ubuntu noble/main amd64 gcc-x86-64-linux-gnu amd64 4:13.2.0-7ubuntu1 [1212 B] 177s Get:28 http://ftpmaster.internal/ubuntu noble/main amd64 gcc amd64 4:13.2.0-7ubuntu1 [5018 B] 177s Get:29 http://ftpmaster.internal/ubuntu noble/main amd64 libstdc++-13-dev amd64 13.2.0-17ubuntu2 [2340 kB] 177s Get:30 http://ftpmaster.internal/ubuntu noble/main amd64 g++-13-x86-64-linux-gnu amd64 13.2.0-17ubuntu2 [12.5 MB] 177s Get:31 http://ftpmaster.internal/ubuntu noble/main amd64 g++-13 amd64 13.2.0-17ubuntu2 [14.5 kB] 177s Get:32 http://ftpmaster.internal/ubuntu noble/main amd64 g++-x86-64-linux-gnu amd64 4:13.2.0-7ubuntu1 [964 B] 177s Get:33 http://ftpmaster.internal/ubuntu noble/main amd64 g++ amd64 4:13.2.0-7ubuntu1 [1100 B] 177s Get:34 http://ftpmaster.internal/ubuntu noble/main amd64 build-essential amd64 12.10ubuntu1 [4928 B] 177s Get:35 http://ftpmaster.internal/ubuntu noble/main amd64 dctrl-tools amd64 2.24-3build2 [66.9 kB] 177s Get:36 http://ftpmaster.internal/ubuntu noble/main amd64 libgfortran-13-dev amd64 13.2.0-17ubuntu2 [942 kB] 177s Get:37 http://ftpmaster.internal/ubuntu noble/main amd64 gfortran-13-x86-64-linux-gnu amd64 13.2.0-17ubuntu2 [11.6 MB] 178s Get:38 http://ftpmaster.internal/ubuntu noble/main amd64 gfortran-13 amd64 13.2.0-17ubuntu2 [10.3 kB] 178s Get:39 http://ftpmaster.internal/ubuntu noble/main amd64 gfortran-x86-64-linux-gnu amd64 4:13.2.0-7ubuntu1 [1024 B] 178s Get:40 http://ftpmaster.internal/ubuntu noble/main amd64 gfortran amd64 4:13.2.0-7ubuntu1 [1176 B] 178s Get:41 http://ftpmaster.internal/ubuntu noble/main amd64 icu-devtools amd64 74.2-1ubuntu1 [212 kB] 178s Get:42 http://ftpmaster.internal/ubuntu noble/main amd64 libblas-dev amd64 3.12.0-3 [170 kB] 178s Get:43 http://ftpmaster.internal/ubuntu noble/main amd64 libbz2-dev amd64 1.0.8-5ubuntu1 [33.6 kB] 178s Get:44 http://ftpmaster.internal/ubuntu noble/main amd64 libicu-dev amd64 74.2-1ubuntu1 [11.9 MB] 178s Get:45 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg-turbo8-dev amd64 2.1.5-2ubuntu1 [294 kB] 178s Get:46 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg8-dev amd64 8c-2ubuntu11 [1484 B] 178s Get:47 http://ftpmaster.internal/ubuntu noble/main amd64 libjpeg-dev amd64 8c-2ubuntu11 [1482 B] 178s Get:48 http://ftpmaster.internal/ubuntu noble/main amd64 liblapack-dev amd64 3.12.0-3 [5196 kB] 178s Get:49 http://ftpmaster.internal/ubuntu noble/main amd64 libncurses-dev amd64 6.4+20240113-1ubuntu1 [384 kB] 178s Get:50 http://ftpmaster.internal/ubuntu noble/main amd64 libpcre2-16-0 amd64 10.42-4ubuntu1 [211 kB] 178s Get:51 http://ftpmaster.internal/ubuntu noble/main amd64 libpcre2-32-0 amd64 10.42-4ubuntu1 [198 kB] 178s Get:52 http://ftpmaster.internal/ubuntu noble/main amd64 libpcre2-posix3 amd64 10.42-4ubuntu1 [6808 B] 178s Get:53 http://ftpmaster.internal/ubuntu noble/main amd64 libpcre2-dev amd64 10.42-4ubuntu1 [743 kB] 178s Get:54 http://ftpmaster.internal/ubuntu noble/main amd64 libpkgconf3 amd64 1.8.1-2 [31.1 kB] 178s Get:55 http://ftpmaster.internal/ubuntu noble/main amd64 zlib1g-dev amd64 1:1.3.dfsg-3ubuntu1 [896 kB] 178s Get:56 http://ftpmaster.internal/ubuntu noble/main amd64 libpng-dev amd64 1.6.43-1 [264 kB] 178s Get:57 http://ftpmaster.internal/ubuntu noble/main amd64 libreadline-dev amd64 8.2-3 [167 kB] 178s Get:58 http://ftpmaster.internal/ubuntu noble/main amd64 pkgconf-bin amd64 1.8.1-2 [20.7 kB] 178s Get:59 http://ftpmaster.internal/ubuntu noble/main amd64 pkgconf amd64 1.8.1-2 [16.8 kB] 178s Get:60 http://ftpmaster.internal/ubuntu noble/main amd64 pkg-config amd64 1.8.1-2 [7170 B] 178s Get:61 http://ftpmaster.internal/ubuntu noble/main amd64 liblzma-dev amd64 5.4.5-0.3 [205 kB] 178s Get:62 http://ftpmaster.internal/ubuntu noble/universe amd64 r-base-dev all 4.3.2-1build1 [4336 B] 178s Get:63 http://ftpmaster.internal/ubuntu noble/universe amd64 pkg-r-autopkgtest all 20231212ubuntu1 [6448 B] 178s Get:64 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-coda all 0.19-4.1-1 [321 kB] 178s Get:65 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-arm all 1.13-1-1 [407 kB] 178s Get:66 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-mi all 1.1-1 [1840 kB] 178s Get:67 http://ftpmaster.internal/ubuntu noble/universe amd64 r-cran-sem amd64 3.1.15-1 [631 kB] 178s Fetched 103 MB in 1s (132 MB/s) 178s Selecting previously unselected package libc-dev-bin. 178s (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 ... 92671 files and directories currently installed.) 178s Preparing to unpack .../00-libc-dev-bin_2.39-0ubuntu2_amd64.deb ... 178s Unpacking libc-dev-bin (2.39-0ubuntu2) ... 178s Selecting previously unselected package linux-libc-dev:amd64. 178s Preparing to unpack .../01-linux-libc-dev_6.8.0-11.11_amd64.deb ... 178s Unpacking linux-libc-dev:amd64 (6.8.0-11.11) ... 178s Selecting previously unselected package libcrypt-dev:amd64. 178s Preparing to unpack .../02-libcrypt-dev_1%3a4.4.36-4_amd64.deb ... 178s Unpacking libcrypt-dev:amd64 (1:4.4.36-4) ... 178s Selecting previously unselected package libtirpc-dev:amd64. 178s Preparing to unpack .../03-libtirpc-dev_1.3.4+ds-1build1_amd64.deb ... 178s Unpacking libtirpc-dev:amd64 (1.3.4+ds-1build1) ... 179s Selecting previously unselected package libnsl-dev:amd64. 179s Preparing to unpack .../04-libnsl-dev_1.3.0-3_amd64.deb ... 179s Unpacking libnsl-dev:amd64 (1.3.0-3) ... 179s Selecting previously unselected package rpcsvc-proto. 179s Preparing to unpack .../05-rpcsvc-proto_1.4.2-0ubuntu6_amd64.deb ... 179s Unpacking rpcsvc-proto (1.4.2-0ubuntu6) ... 179s Selecting previously unselected package libc6-dev:amd64. 179s Preparing to unpack .../06-libc6-dev_2.39-0ubuntu2_amd64.deb ... 179s Unpacking libc6-dev:amd64 (2.39-0ubuntu2) ... 179s Selecting previously unselected package libisl23:amd64. 179s Preparing to unpack .../07-libisl23_0.26-3_amd64.deb ... 179s Unpacking libisl23:amd64 (0.26-3) ... 179s Selecting previously unselected package libmpc3:amd64. 179s Preparing to unpack .../08-libmpc3_1.3.1-1_amd64.deb ... 179s Unpacking libmpc3:amd64 (1.3.1-1) ... 179s Selecting previously unselected package cpp-13-x86-64-linux-gnu. 179s Preparing to unpack .../09-cpp-13-x86-64-linux-gnu_13.2.0-17ubuntu2_amd64.deb ... 179s Unpacking cpp-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 179s Selecting previously unselected package cpp-13. 179s Preparing to unpack .../10-cpp-13_13.2.0-17ubuntu2_amd64.deb ... 179s Unpacking cpp-13 (13.2.0-17ubuntu2) ... 179s Selecting previously unselected package cpp-x86-64-linux-gnu. 179s Preparing to unpack .../11-cpp-x86-64-linux-gnu_4%3a13.2.0-7ubuntu1_amd64.deb ... 179s Unpacking cpp-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 179s Selecting previously unselected package cpp. 179s Preparing to unpack .../12-cpp_4%3a13.2.0-7ubuntu1_amd64.deb ... 179s Unpacking cpp (4:13.2.0-7ubuntu1) ... 179s Selecting previously unselected package libcc1-0:amd64. 179s Preparing to unpack .../13-libcc1-0_14-20240303-1ubuntu1_amd64.deb ... 179s Unpacking libcc1-0:amd64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libitm1:amd64. 179s Preparing to unpack .../14-libitm1_14-20240303-1ubuntu1_amd64.deb ... 179s Unpacking libitm1:amd64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libatomic1:amd64. 179s Preparing to unpack .../15-libatomic1_14-20240303-1ubuntu1_amd64.deb ... 179s Unpacking libatomic1:amd64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libasan8:amd64. 179s Preparing to unpack .../16-libasan8_14-20240303-1ubuntu1_amd64.deb ... 179s Unpacking libasan8:amd64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package liblsan0:amd64. 179s Preparing to unpack .../17-liblsan0_14-20240303-1ubuntu1_amd64.deb ... 179s Unpacking liblsan0:amd64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libtsan2:amd64. 179s Preparing to unpack .../18-libtsan2_14-20240303-1ubuntu1_amd64.deb ... 179s Unpacking libtsan2:amd64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libubsan1:amd64. 179s Preparing to unpack .../19-libubsan1_14-20240303-1ubuntu1_amd64.deb ... 179s Unpacking libubsan1:amd64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libhwasan0:amd64. 179s Preparing to unpack .../20-libhwasan0_14-20240303-1ubuntu1_amd64.deb ... 179s Unpacking libhwasan0:amd64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libquadmath0:amd64. 179s Preparing to unpack .../21-libquadmath0_14-20240303-1ubuntu1_amd64.deb ... 179s Unpacking libquadmath0:amd64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libgcc-13-dev:amd64. 179s Preparing to unpack .../22-libgcc-13-dev_13.2.0-17ubuntu2_amd64.deb ... 179s Unpacking libgcc-13-dev:amd64 (13.2.0-17ubuntu2) ... 180s Selecting previously unselected package gcc-13-x86-64-linux-gnu. 180s Preparing to unpack .../23-gcc-13-x86-64-linux-gnu_13.2.0-17ubuntu2_amd64.deb ... 180s Unpacking gcc-13-x86-64-linux-gnu (13.2.0-17ubuntu2) ... 180s Selecting previously unselected package gcc-13. 180s Preparing to unpack .../24-gcc-13_13.2.0-17ubuntu2_amd64.deb ... 180s Unpacking gcc-13 (13.2.0-17ubuntu2) ... 180s Selecting previously unselected package gcc-x86-64-linux-gnu. 180s Preparing to unpack .../25-gcc-x86-64-linux-gnu_4%3a13.2.0-7ubuntu1_amd64.deb ... 180s Unpacking gcc-x86-64-linux-gnu (4:13.2.0-7ubuntu1) ... 180s Selecting previously unselected package gcc. 180s Preparing to unpack .../26-gcc_4%3a13.2.0-7ubuntu1_amd64.deb ... 180s Unpacking gcc (4:13.2.0-7ubuntu1) ... 180s Selecting previously unselected package libstdc++-13-dev:amd64. 180s Preparing to unpack .../27-libstdc++-13-dev_13.2.0-17ubuntu2_amd64.deb ... 180s Unpacking libstdc++-13-dev:amd64 (13.2.0-17ubuntu2) ... 180s Selecting previously unselected package g++-13-x86-64-linux-gnu. 180s Preparing to unpack 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mode 182s 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 182s update-alternatives: using /usr/bin/gfortran to provide /usr/bin/f77 (f77) in auto mode 182s 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 182s Setting up g++ (4:13.2.0-7ubuntu1) ... 182s update-alternatives: using /usr/bin/g++ to provide /usr/bin/c++ (c++) in auto mode 182s Setting up build-essential (12.10ubuntu1) ... 182s Setting up r-base-dev (4.3.2-1build1) ... 182s Setting up pkg-r-autopkgtest (20231212ubuntu1) ... 182s Setting up autopkgtest-satdep (0) ... 182s Processing triggers for man-db (2.12.0-3) ... 183s Processing triggers for install-info (7.1-3) ... 183s Processing triggers for libc-bin (2.39-0ubuntu2) ... 185s (Reading database ... 96538 files and directories currently installed.) 185s Removing autopkgtest-satdep (0) ... 185s autopkgtest [03:15:53]: test pkg-r-autopkgtest: /usr/share/dh-r/pkg-r-autopkgtest 185s autopkgtest [03:15:53]: test pkg-r-autopkgtest: [----------------------- 185s Test: Try to load the R library systemfit 185s 185s R version 4.3.2 (2023-10-31) -- "Eye Holes" 185s Copyright (C) 2023 The R Foundation for Statistical Computing 185s Platform: x86_64-pc-linux-gnu (64-bit) 185s 185s R is free software and comes with ABSOLUTELY NO WARRANTY. 185s You are welcome to redistribute it under certain conditions. 185s Type 'license()' or 'licence()' for distribution details. 185s 185s R is a collaborative project with many contributors. 185s Type 'contributors()' for more information and 185s 'citation()' on how to cite R or R packages in publications. 185s 185s Type 'demo()' for some demos, 'help()' for on-line help, or 185s 'help.start()' for an HTML browser interface to help. 185s Type 'q()' to quit R. 185s 185s > library('systemfit') 185s Loading required package: Matrix 186s Loading required package: car 186s Loading required package: carData 186s Loading required package: lmtest 186s Loading required package: zoo 186s 186s Attaching package: ‘zoo’ 186s 186s The following objects are masked from ‘package:base’: 186s 186s as.Date, as.Date.numeric 186s 186s 186s Please cite the 'systemfit' package as: 186s 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/. 186s 186s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 186s https://r-forge.r-project.org/projects/systemfit/ 186s > 186s > 186s Other tests are currently unsupported! 186s They will be progressively added. 187s autopkgtest [03:15:55]: test pkg-r-autopkgtest: -----------------------] 187s autopkgtest [03:15:55]: test pkg-r-autopkgtest: - - - - - - - - - - results - - - - - - - - - - 187s pkg-r-autopkgtest PASS 187s autopkgtest [03:15:55]: @@@@@@@@@@@@@@@@@@@@ summary 187s run-unit-test PASS 187s pkg-r-autopkgtest PASS 197s Creating nova instance adt-noble-amd64-r-cran-systemfit-20240323-031248-juju-7f2275-prod-proposed-migration-environment-2 from image adt/ubuntu-noble-amd64-server-20240322.img (UUID 485815e0-0f91-4788-a5b5-e5301593a332)...